Finite Group Databasebeta

← #17197679

Subgroups — #17197679

Order 4352.

2874 conjugacy classes of subgroups.

The subgroup lattice has 1762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763374C211yesmaximal, characteristic
2#14531959C211yesmaximal, characteristic, complemented
3#14531953C211yesmaximal, characteristic, complemented
4#14531937C211yesmaximal, characteristic, complemented
5#14531935C211yesmaximal, characteristic, complemented
6#14531891C211yesmaximal, characteristic, complemented
7#14531845C211yesmaximal, characteristic, complemented
8#14531832C211yesmaximal, characteristic, complemented
9#14531828C211yesmaximal, characteristic, complemented
10#14531766C211yesmaximal, characteristic, complemented
11#14531764C211yesmaximal, characteristic, complemented
12#14531761C211yesmaximal, characteristic, complemented
13#14531760C211yesmaximal, characteristic, complemented
14#14531642C211yesmaximal, characteristic, complemented
15#14531638C211yesmaximal, characteristic, complemented
16#14531610C211yesmaximal, characteristic, complemented
17#14531609C211yesmaximal, characteristic, complemented
18#14531595C211yesmaximal, characteristic, complemented
19#14531591C211yesmaximal, characteristic, complemented
20#14531547C211yesmaximal, characteristic, complemented
21#14531543C211yesmaximal, characteristic, complemented
22#14531508C211yesmaximal, characteristic, complemented
23#14531505C211yesmaximal, characteristic, complemented
24#14531488C211yesmaximal, characteristic, complemented
25#14531485C211yesmaximal, characteristic, complemented
26#14531442C211yesmaximal, characteristic, complemented
27#14531360C211yesmaximal, characteristic, complemented
28#120×Dic17C211yesmaximal, characteristic, complemented
29#14531283C211yesmaximal, characteristic, complemented
30C2×#11762686C211yesmaximal, characteristic, complemented
31C17×#2321C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C23×C22⋊D17C2211yescharacteristic
34C24×Dic17C2211yescharacteristic
35#11763374C4116yescomplemented
36C2×#10587626C2211yescharacteristic
37C2×#10587626C2211yescharacteristic
38C2×#10587571C2211yescharacteristic
39C2×#10587571C2211yescharacteristic
40C2×#10587570C2211yescharacteristic
41C2×#10587570C2211yescharacteristic
42C2×#10587625C2211yescharacteristic
43C2×#10587625C2211yescharacteristic
44C2×#10587568C2211yescharacteristic
45C2×#10587639C2211yescharacteristic
46C2×#10587623C2211yescharacteristic
47C2×C4×D68C2211yescharacteristic, complemented
48C2×D4×Dic17C2211yescharacteristic
49C2×D4×Dic17C2211yescharacteristic, complemented
50C2×D4×Dic17C2211yescharacteristic, complemented
51C2×#10587579C2211yescharacteristic, complemented
52C2×C4×C22⋊D17C2211yescharacteristic
53C2×C4×C22⋊D17C2211yescharacteristic, complemented
54C2×#10587567C2211yescharacteristic
55C2×#10587567C2211yescharacteristic, complemented
56C2×#10587567C2211yescharacteristic, complemented
57C2×#10587567C2211yescharacteristic, complemented
58C2×#10587563C2211yescharacteristic
59C22×#63227C2211yescharacteristic
60C22×#63227C2211yescharacteristic
61C2×C22⋊C4×D17C2211yescharacteristic
62C2×C22⋊C4×D17C2211yescharacteristic
63#11762715C2211yescharacteristic, complemented
64#11762714C2211yescharacteristic, complemented
65#11762713C2211yescharacteristic, complemented
66#11762713C2211yescharacteristic, complemented
67#11762711C2211yescharacteristic, complemented
68#11762710C2211yescharacteristic, complemented
69#11762709C2211yescharacteristic, complemented
70#11762709C2211yescharacteristic, complemented
71#11762709C2211yescharacteristic, complemented
72#11762709C2211yescharacteristic, complemented
73#11762703C2211yescharacteristic, complemented
74#11762703C2211yescharacteristic, complemented
75#11762701C2211yescharacteristic, complemented
76#11762701C2211yescharacteristic, complemented
77#11762700C2211yescharacteristic, complemented
78#11762700C2211yescharacteristic, complemented
79#11762699C2211yescharacteristic, complemented
80#11762699C2211yescharacteristic, complemented
81#11762698C2211yescharacteristic, complemented
82#11762698C2211yescharacteristic, complemented
83#11762697C2211yescharacteristic, complemented
84#11762697C2211yescharacteristic, complemented
85#11762696C2211yescharacteristic, complemented
86#11762696C2211yescharacteristic, complemented
87#11762693C2211yescharacteristic, complemented
88#11762693C2211yescharacteristic, complemented
89#11762691C2211yescharacteristic, complemented
90#11762691C2211yescharacteristic, complemented
91#11762690C2211yescharacteristic, complemented
92#11762690C2211yescharacteristic, complemented
93#11762689C2211yescharacteristic
94#11762689C2211yescharacteristic, complemented
95#11762689C2211yescharacteristic, complemented
96#11762688C2211yescharacteristic
97#11762688C2211yescharacteristic, complemented
98#11762688C2211yescharacteristic, complemented
99#11762687C2211yescharacteristic, complemented
100#11762687C2211yescharacteristic, complemented
101#11762687C2211yescharacteristic, complemented
102#11762687C2211yescharacteristic, complemented
103#11762686C2211yescharacteristic
104#11762686C2211yescharacteristic
105#11762686C2211yescharacteristic
106#11762686C2211yescharacteristic
107#11762686C2211yescharacteristic
108#11762686C2211yescharacteristic
109#11762686C2211yescharacteristic
110#11762686C2211yescharacteristic
111#11762686C2211yescharacteristic
112#11762686C2211yescharacteristic, complemented
113#11762686C2211yescharacteristic, complemented
114#11762686C2211yescharacteristic, complemented
115#11762686C2211yescharacteristic, complemented
116#11762685C2211yescharacteristic
117#11762685C2211yescharacteristic
118#11762685C2211yescharacteristic
119#11762685C2211yescharacteristic
120#11762685C2211yescharacteristic
121#11762685C2211yescharacteristic
122#11762685C2211yescharacteristic
123#11762685C2211yescharacteristic
124#11762685C2211yescharacteristic, complemented
125#11762685C2211yescharacteristic, complemented
126#11762685C2211yescharacteristic, complemented
127#11762685C2211yescharacteristic, complemented
128#11762685C2211yescharacteristic, complemented
129#11762685C2211yescharacteristic, complemented
130#11762684C2211yescharacteristic
131#11762684C2211yescharacteristic, complemented
132#11762684C2211yescharacteristic, complemented
133#11762683C2211yescharacteristic, complemented
134#11762683C2211yescharacteristic, complemented
135#11762682C2211yescharacteristic
136#11762681C2211yescharacteristic
137#11762681C2211yescharacteristic, complemented
138#11762681C2211yescharacteristic, complemented
139#11762680C2211yescharacteristic, complemented
140#11762680C2211yescharacteristic, complemented
141#11762676C2211yescharacteristic, complemented
142#11762676C2211yescharacteristic, complemented
143#11762674C2211yescharacteristic, complemented
144#11762673C2211yescharacteristic, complemented
145#11762671C2211yescharacteristic, complemented
146#11762670C2211yescharacteristic
147#11762670C2211yescharacteristic
148#11762670C2211yescharacteristic, complemented
149#11762667C2211yescharacteristic, complemented
150#11762666C2211yescharacteristic, complemented
151#11762665C2211yescharacteristic
152C4⋊C4×Dic17C2211yescharacteristic, complemented
153C4×#63225C2211yescharacteristic, complemented
154C22⋊C4×Dic17C2211yescharacteristic
155C22⋊C4×Dic17C2211yescharacteristic
156C22⋊C4×Dic17C2211yescharacteristic, complemented
157C22⋊C4×Dic17C2211yescharacteristic, complemented
158C22⋊C4×Dic17C2211yescharacteristic, complemented
159C22⋊C4×Dic17C2211yescharacteristic, complemented
160C22⋊C4×Dic17C2211yescharacteristic, complemented
161C4×#63227C2211yescharacteristic, complemented
162C4×#63227C2211yescharacteristic, complemented
163C4×#63227C2211yescharacteristic, complemented
164C4×C22⋊Dic17C2211yescharacteristic
165#11762656C2211yescharacteristic, complemented
166#11762656C2211yescharacteristic, complemented
167#11762655C2211yescharacteristic, complemented
168#11762654C2211yescharacteristic, complemented
169C2×#10587502C2211yescharacteristic
170C2×#10587502C2211yescharacteristic
171C2×#10587502C2211yescharacteristic, complemented
172#95×D17C2211yescharacteristic, complemented
173C2×C17×#120C2211yescharacteristic
174C2×C4×D4×C17C2211yescharacteristic
175C22×C22⋊C4×C17C2211yescharacteristic
176C17×#390C2211yescharacteristic, complemented
177C17×#390C2211yescharacteristic, complemented
178C17×#388C2211yescharacteristic, complemented
179C17×#388C2211yescharacteristic, complemented
180C17×#388C2211yescharacteristic, complemented
181C17×#388C2211yescharacteristic, complemented
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic, complemented
184C17×#386C2211yescharacteristic, complemented
185C17×#385C2211yescharacteristic
186C17×#379C2211yescharacteristic
187C4×C22⋊C4×C17C2211yescharacteristic
188C25×C17C2311yescharacteristic
189C24×D17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C22×D4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C22×C22⋊D17—42no—
197C22×C22⋊D17—42no—
198C22×C22⋊D17C2×C418yescomplemented
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C22×C22⋊D17C2311yescharacteristic
205C22×C22⋊D17C2311yescharacteristic
206C22×C22⋊D17C2311yescharacteristic
207C22×C22⋊D17C2311yescharacteristic
208C22×C22⋊D17C2311yescharacteristic
209C23×Dic17—42no—
210C23×Dic17—42no—
211C23×Dic17—42no—
212C23×Dic17C2311yescharacteristic
213C23×Dic17C2311yescharacteristic
214C23×Dic17C2311yescharacteristic
215C23×Dic17C2311yescharacteristic
216C23×Dic17C2311yescharacteristic
217C23×Dic17C2311yescharacteristic
218C23×Dic17C2311yescharacteristic
219C23×Dic17C2311yescharacteristic
220C23×Dic17C2311yescharacteristic
221C2×#63254—42no—
222C2×#63254—42no—
223C2×#63254C2×C418yescomplemented
224C22×D68C2311yescharacteristic
225C22×D68C2311yescharacteristic
226C22×C4×D17C2311yescharacteristic
227C22×C4×D17C2311yescharacteristic
228C22×C4×D17C2311yescharacteristic
229C22×C4×D17C2311yescharacteristic
230C22×C4×D17C2311yescharacteristic
231C22×C4×D17C2311yescharacteristic
232C22×C4×D17C2311yescharacteristic
233C22×Dic34C2311yescharacteristic
234C17×#120C2×C418yescomplemented
235C4×D4×C17—42no—
236C2×C4⋊C4×C17C2311yescharacteristic
237C2×C4⋊C4×C17C2311yescharacteristic
238C2×C4⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17—42no—
240C2×C22⋊C4×C17C2311yescharacteristic
241C2×C22⋊C4×C17C2311yescharacteristic
242C2×C22⋊C4×C17C2311yescharacteristic
243C2×C22⋊C4×C17C2311yescharacteristic
244C2×C22⋊C4×C17C2311yescharacteristic
245C2×C22⋊C4×C17C2311yescharacteristic
246C2×C22⋊C4×C17C2311yescharacteristic
247C2×C22⋊C4×C17C2311yescharacteristic
248C2×C22⋊C4×C17C2311yescharacteristic
249C2×C22⋊C4×C17C2311yescharacteristic
250C2×C22⋊C4×C17C2311yescharacteristic
251C2×C22⋊C4×C17C2311yescharacteristic
252C2×C22⋊C4×C17C2311yescharacteristic
253C2×C22⋊C4×C17C2311yescharacteristic
254C2×C22⋊C4×C17C2311yescharacteristic
255C2×C22⋊C4×C17C2311yescharacteristic
256C2×C42×C17C2311yescharacteristic
257C2×C42×C17C2311yescharacteristic
258C2×C42×C17C2311yescharacteristic
259#10587639C2×C418yescomplemented
260C2×C22⋊Dic17C2311yescharacteristic
261C2×C22⋊Dic17C2311yescharacteristic
262C2×C22⋊Dic17C2311yescharacteristic
263C2×C22⋊Dic17C2311yescharacteristic
264C2×C22⋊Dic17C2311yescharacteristic
265C2×C22⋊Dic17C2311yescharacteristic
266C2×C22⋊Dic17C2311yescharacteristic
267C2×C22⋊Dic17C2311yescharacteristic
268C2×C22⋊Dic17C2311yescharacteristic
269C2×C22⋊Dic17C2311yescharacteristic
270C2×C22⋊Dic17C2311yescharacteristic
271C2×C22⋊Dic17C2311yescharacteristic
272#10587626C2×C418yescomplemented
273#10587626C2×C418yescomplemented
274#10587625C2×C418yescomplemented
275#10587625C2×C418yescomplemented
276#10587623C2×C418yescomplemented
277D4×Dic17—42no—
278D4×Dic17—42no—
279D4×Dic17—42no—
280C4×C22⋊D17—42no—
281C4×C22⋊D17—42no—
282C2×#63227—42no—
283C2×#63227—42no—
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290C2×#63227C2311yescharacteristic
291C2×#63227C2311yescharacteristic
292C2×#63227C2311yescharacteristic
293C2×#63227C2311yescharacteristic
294C2×#63227C2311yescharacteristic
295C2×#63227C2311yescharacteristic
296C2×#63227C2311yescharacteristic
297C2×#63227C2311yescharacteristic
298C2×#63227C2311yescharacteristic
299C2×#63227C2311yescharacteristic
300C2×#63227C2311yescharacteristic
301C2×#63227C2311yescharacteristic
302C2×#63227C2311yescharacteristic
303C2×#63227C2311yescharacteristic
304C2×#63227C2311yescharacteristic
305C2×#63227C2311yescharacteristic
306C2×C4⋊Dic17C2311yescharacteristic
307C2×C4⋊Dic17C2311yescharacteristic
308C2×C4⋊Dic17C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×C4×Dic17C2311yescharacteristic
318C2×C4×Dic17C2311yescharacteristic
319C2×C4×Dic17C2311yescharacteristic
320C2×C4×Dic17C2311yescharacteristic
321C2×C4×Dic17C2311yescharacteristic
322C2×C4×Dic17C2311yescharacteristic
323C2×C4×Dic17C2311yescharacteristic
324C2×C4×Dic17C2311yescharacteristic
325C2×C4×Dic17C2311yescharacteristic
326C2×C4×Dic17C2311yescharacteristic
327C2×C4×Dic17C2311yescharacteristic
328#10587579—42no—
329#10587571C2×C418yescomplemented
330#10587571C2×C418yescomplemented
331#10587570C2×C418yescomplemented
332#10587570C2×C418yescomplemented
333#10587568C2×C418yescomplemented
334#10587567—42no—
335#10587567—42no—
336#10587567—42no—
337#10587567—42no—
338C22⋊C4×D17—42no—
339C22⋊C4×D17—42no—
340#10587563C2×C418yescomplemented
341C4×D68—42no—
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
344C17×#95C2311yescharacteristic
345C17×#95C2311yescharacteristic
346C17×#95C2311yescharacteristic
347C17×#95C2311yescharacteristic
348#10587502C2311yescharacteristic
349#10587502C2311yescharacteristic
350#10587502C2311yescharacteristic
351#10587502C2311yescharacteristic
352#10587502C2311yescharacteristic
353#10587502C2311yescharacteristic
354#10587502C2311yescharacteristic
355#10587502C2311yescharacteristic
356#10587502C2311yescharacteristic
357#10587502C2311yescharacteristic
358#10587502C2311yescharacteristic
359#10587502C2311yescharacteristic
360#10587502C2311yescharacteristic
361#10587502C2311yescharacteristic
362#10587502C2311yescharacteristic
363#10587502C2311yescharacteristic
364#10587502C2311yescharacteristic
365#10587502C2311yescharacteristic
366#10587502C2311yescharacteristic
367#10587502C2311yescharacteristic
368#10587502C2311yescharacteristic
369#10587502C2311yescharacteristic
370#10587502C2311yescharacteristic
371#10587502C2311yescharacteristic
372#10587502C2311yescharacteristic
373#10587502C2311yescharacteristic
374#10587502C2311yescharacteristic
375#10587502C2311yescharacteristic
376#10587502C2311yescharacteristic
377#10587502C2311yescharacteristic
378#10587502C2311yescharacteristic
379#10587502C2311yescharacteristic
380#10587502C2311yescharacteristic
381#10587502C2311yescharacteristic
382C24×C17—22no—
383C24×C17—22no—
384C24×C17—41no—
385C24×C17—41no—
386C24×C17—41no—
387C24×C17—41no—
388C24×C17C22×C414yes—
389C24×C17C2411yescharacteristic
390C24×C17C2411yescharacteristic
391C24×C17C2411yescharacteristic
392C24×C17C2411yescharacteristic
393C23×D17—22no—
394C23×D17—22no—
395C23×D17—41no—
396C23×D17—41no—
397C23×D17—41no—
398C23×D17—41no—
399C23×D17C22×C414yes—
400C23×D17C2411yescharacteristic
401C23×D17C2411yescharacteristic
402C23×D17C2411yescharacteristic
403C2×D4×C17—22no—
404C2×D4×C17—22no—
405C2×D4×C17—41no—
406C2×D4×C17—41no—
407C2×D4×C17—41no—
408C2×D4×C17—41no—
409C2×D4×C17C22×C414yes—
410C2×D4×C17C22×C414yes—
411C2×D4×C17C22×C414yes—
412C22×C4×C17—22no—
413C22×C4×C17—22no—
414C22×C4×C17—41no—
415C22×C4×C17—41no—
416C22×C4×C17—41no—
417C22×C4×C17—41no—
418C22×C4×C17—41no—
419C22×C4×C17—41no—
420C22×C4×C17—41no—
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C22×C4×C17C2411yescharacteristic
426C22×C4×C17C2411yescharacteristic
427C22×C4×C17C2411yescharacteristic
428C22×C4×C17C2411yescharacteristic
429C22×C4×C17C2411yescharacteristic
430C22×C4×C17C2411yescharacteristic
431C22×C4×C17C2411yescharacteristic
432C2×C22⋊D17—22no—
433C2×C22⋊D17—22no—
434C2×C22⋊D17—41no—
435C2×C22⋊D17—41no—
436C2×C22⋊D17—416no—
437C2×C22⋊D17—41no—
438C2×C22⋊D17—41no—
439C2×C22⋊D17—41no—
440C2×C22⋊D17—41no—
441C2×C22⋊D17—41no—
442C2×C22⋊D17—41no—
443C2×C22⋊D17—41no—
444C2×C22⋊D17—41no—
445C2×C22⋊D17—41no—
446C2×C22⋊D17—41no—
447C2×C22⋊D17—41no—
448C2×C22⋊D17—41no—
449C2×C22⋊D17—41no—
450C2×C22⋊D17—41no—
451C2×C22⋊D17—41no—
452C2×C22⋊D17—41no—
453C2×C22⋊D17C22×C414yes—
454C2×C22⋊D17C22×C414yes—
455C2×C22⋊D17C22×C414yes—
456C2×C22⋊D17C22×C414yes—
457C2×C22⋊D17C22×C414yes—
458C2×C22⋊D17C22×C414yes—
459C2×C22⋊D17C22×C414yes—
460C2×C22⋊D17C22×C414yescomplemented
461C2×C22⋊D17C22×C414yescomplemented
462C2×C22⋊D17C22×C414yescomplemented
463C22×Dic17—22no—
464C22×Dic17—22no—
465C22×Dic17—22no—
466C22×Dic17—22no—
467C22×Dic17—22no—
468C22×Dic17—22no—
469C22×Dic17—22no—
470C22×Dic17—22no—
471C22×Dic17—22no—
472C22×Dic17—22no—
473C22×Dic17—22no—
474C22×Dic17—41no—
475C22×Dic17—41no—
476C22×Dic17—41no—
477C22×Dic17—41no—
478C22×Dic17—41no—
479C22×Dic17—41no—
480C22×Dic17—41no—
481C22×Dic17—41no—
482C22×Dic17—41no—
483C22×Dic17—41no—
484C22×Dic17—41no—
485C22×Dic17—41no—
486C22×Dic17—41no—
487C22×Dic17—41no—
488C22×Dic17—416no—
489C22×Dic17C22×C414yes—
490C22×Dic17C22×C414yescomplemented
491C22×Dic17C2411yescharacteristic
492C22×Dic17C2411yescharacteristic
493C22×Dic17C2411yescharacteristic
494C22×Dic17C2411yescharacteristic
495C22×Dic17C2411yescharacteristic
496C22×Dic17C2411yescharacteristic
497C22×Dic17C2411yescharacteristic
498C22×Dic17C2411yescharacteristic
499C22×Dic17C2411yescharacteristic
500C22×Dic17C2411yescharacteristic
501C22×Dic17C2411yescharacteristic
502C22×Dic17C2411yescharacteristic
503C22×Dic17C2411yescharacteristic
504#63254—416no—
505C2×D68—41no—
506C2×D68—41no—
507C2×D68—41no—
508C2×D68—41no—
509C2×D68C22×C414yescomplemented
510C2×D68C22×C414yescomplemented
511C2×C4×D17—22no—
512C2×C4×D17—41no—
513C2×C4×D17—41no—
514C2×C4×D17—41no—
515C2×C4×D17—41no—
516C2×C4×D17—41no—
517C2×C4×D17—41no—
518C2×C4×D17—41no—
519C2×C4×D17—41no—
520C2×C4×D17—41no—
521C2×C4×D17—41no—
522C2×C4×D17—41no—
523C2×C4×D17—41no—
524C2×C4×D17—41no—
525C2×C4×D17—41no—
526C2×C4×D17—41no—
527C2×C4×D17—41no—
528C2×C4×D17—41no—
529C2×C4×D17—41no—
530C2×C4×D17—41no—
531C2×C4×D17C22×C414yescomplemented
532C2×Dic34—41no—
533C2×Dic34—41no—
534C2×Dic34C22×C414yescomplemented
535C4⋊C4×C17—41no—
536C4⋊C4×C17—41no—
537C4⋊C4×C17—41no—
538C22⋊C4×C17—22no—
539C22⋊C4×C17—22no—
540C22⋊C4×C17—41no—
541C22⋊C4×C17—41no—
542C22⋊C4×C17—41no—
543C22⋊C4×C17—41no—
544C22⋊C4×C17—41no—
545C22⋊C4×C17—41no—
546C22⋊C4×C17—41no—
547C22⋊C4×C17—41no—
548C22⋊C4×C17—41no—
549C22⋊C4×C17—41no—
550C22⋊C4×C17—41no—
551C22⋊C4×C17C22×C414yes—
552C22⋊C4×C17C22×C414yes—
553C22⋊C4×C17C22×C414yes—
554C42×C17—41no—
555C42×C17—41no—
556C42×C17—41no—
557C22⋊Dic17—22no—
558C22⋊Dic17—22no—
559C22⋊Dic17—22no—
560C22⋊Dic17—41no—
561C22⋊Dic17—41no—
562C22⋊Dic17—41no—
563C22⋊Dic17—41no—
564C22⋊Dic17—41no—
565C22⋊Dic17—41no—
566C22⋊Dic17C22×C414yes—
567C22⋊Dic17C22×C414yes—
568C22⋊Dic17C22×C414yes—
569#63227—22no—
570#63227—22no—
571#63227—22no—
572#63227—22no—
573#63227—22no—
574#63227—41no—
575#63227—41no—
576#63227—41no—
577#63227—41no—
578#63227—41no—
579#63227—41no—
580#63227—41no—
581#63227—41no—
582#63227—41no—
583#63227—41no—
584#63227—41no—
585#63227—41no—
586#63227—41no—
587#63227C22×C414yescomplemented
588#63227C22×C414yescomplemented
589#63227C22×C414yescomplemented
590#63227C22×C414yescomplemented
591C4⋊Dic17—22no—
592C4⋊Dic17—41no—
593C4⋊Dic17—41no—
594#63225—22no—
595#63225—41no—
596#63225—41no—
597#63225—41no—
598#63225—41no—
599#63225—41no—
600#63225C22×C414yescomplemented
601#63225C22×C414yescomplemented
602C4×Dic17—22no—
603C4×Dic17—22no—
604C4×Dic17—41no—
605C4×Dic17—41no—
606C4×Dic17—41no—
607C4×Dic17—41no—
608C4×Dic17—41no—
609C4×Dic17—41no—
610C4×Dic17—41no—
611C4×Dic17C22×C414yescomplemented
612C4×Dic17C22×C414yescomplemented
613#34406—171nomaximal, Sylow
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—21no—
617C23×C17—21no—
618C23×C17—28no—
619C23×C17—21no—
620C23×C17—21no—
621C23×C17—21no—
622C23×C17—21no—
623C23×C17—21no—
624C23×C17—21no—
625C23×C17—21no—
626C23×C17—21no—
627C23×C17—21no—
628C23×C17—21no—
629C23×C17—21no—
630C23×C17—21no—
631C23×C17—21no—
632C23×C17—21no—
633C23×C17—21no—
634C23×C17—21no—
635C23×C17—21no—
636C23×C17—21no—
637C23×C17—44no—
638C23×C17—44no—
639C23×C17—44no—
640C23×C17—44no—
641C23×C17—44no—
642C23×C17—44no—
643C23×C17C23×C412yes—
644C23×C17C23×C412yes—
645C23×C17C23×C412yes—
646C23×C17C23×C412yes—
647C23×C17H(5,𝔽2)12yes—
648C23×C17H(5,𝔽2)12yes—
649C23×C17C2511yescharacteristic
650C22×D17—21no—
651C22×D17—21no—
652C22×D17—21no—
653C22×D17—21no—
654C22×D17—21no—
655C22×D17—21no—
656C22×D17—21no—
657C22×D17—21no—
658C22×D17—21no—
659C22×D17—21no—
660C22×D17—21no—
661C22×D17—21no—
662C22×D17—21no—
663C22×D17—21no—
664C22×D17—21no—
665C22×D17—21no—
666C22×D17—21no—
667C22×D17—21no—
668C22×D17—28no—
669C22×D17—44no—
670C22×D17—44no—
671C22×D17—82no—
672C22×D17—82no—
673C22×D17—82no—
674C22×D17—82no—
675C22×D17C23×C412yes—
676C22×D17C23×C412yes—
677C22×D17C23×C412yes—
678D4×C17—28no—
679D4×C17—44no—
680D4×C17—44no—
681C2×C4×C17—21no—
682C2×C4×C17—21no—
683C2×C4×C17—21no—
684C2×C4×C17—21no—
685C2×C4×C17—21no—
686C2×C4×C17—21no—
687C2×C4×C17—21no—
688C2×C4×C17—21no—
689C2×C4×C17—21no—
690C2×C4×C17—21no—
691C2×C4×C17—21no—
692C2×C4×C17—21no—
693C2×C4×C17—21no—
694C2×C4×C17—21no—
695C2×C4×C17—21no—
696C2×C4×C17—21no—
697C2×C4×C17—21no—
698C2×C4×C17—21no—
699C2×C4×C17—21no—
700C2×C4×C17—21no—
701C2×C4×C17—21no—
702C2×C4×C17—21no—
703C2×C4×C17—21no—
704C2×C4×C17—21no—
705C2×C4×C17—21no—
706C2×C4×C17—21no—
707C2×C4×C17—21no—
708C2×C4×C17—21no—
709C2×C4×C17—21no—
710C2×C4×C17—21no—
711C2×C4×C17—82no—
712C2×C4×C17—82no—
713C2×C4×C17—82no—
714C2×C4×C17C23×C412yes—
715C2×C4×C17C23×C412yes—
716C2×C4×C17C23×C412yes—
717C22⋊D17—28no—
718C22⋊D17—44no—
719C22⋊D17—44no—
720C22⋊D17—44no—
721C22⋊D17—44no—
722C22⋊D17—44no—
723C22⋊D17—44no—
724C22⋊D17—44no—
725C22⋊D17—44no—
726C22⋊D17—44no—
727C2×Dic17—28no—
728C2×Dic17—21no—
729C2×Dic17—21no—
730C2×Dic17—21no—
731C2×Dic17—21no—
732C2×Dic17—21no—
733C2×Dic17—21no—
734C2×Dic17—21no—
735C2×Dic17—21no—
736C2×Dic17—21no—
737C2×Dic17—21no—
738C2×Dic17—21no—
739C2×Dic17—21no—
740C2×Dic17—21no—
741C2×Dic17—21no—
742C2×Dic17—21no—
743C2×Dic17—21no—
744C2×Dic17—21no—
745C2×Dic17—21no—
746C2×Dic17—21no—
747C2×Dic17—21no—
748C2×Dic17—21no—
749C2×Dic17—21no—
750C2×Dic17—21no—
751C2×Dic17—21no—
752C2×Dic17—21no—
753C2×Dic17—21no—
754C2×Dic17—21no—
755C2×Dic17—21no—
756C2×Dic17—21no—
757C2×Dic17—21no—
758C2×Dic17—21no—
759C2×Dic17—21no—
760C2×Dic17—44no—
761C2×Dic17—44no—
762C2×Dic17—44no—
763C2×Dic17—44no—
764C2×Dic17—44no—
765C2×Dic17—44no—
766C2×Dic17—44no—
767C2×Dic17—82no—
768C2×Dic17C23×C412yes—
769C2×Dic17C23×C412yes—
770C2×Dic17C23×C412yes—
771C2×Dic17C23×C412yes—
772C2×Dic17C23×C412yes—
773C2×Dic17H(5,𝔽2)12yes—
774C2×Dic17H(5,𝔽2)12yes—
775D68—44no—
776D68—44no—
777C4×D17—44no—
778C4×D17—82no—
779C4×D17—82no—
780C4×D17—82no—
781C4×D17—82no—
782C4×D17—82no—
783C4×D17—82no—
784Dic34—44no—
785C2×#535—171no—
786#2380—171no—
787#2379—171no—
788#2377—171no—
789#2377—171no—
790#2372—171no—
791#2366—171no—
792#2364—171no—
793#2364—171no—
794#2358—171no—
795#2358—171no—
796#2358—171no—
797#2358—171no—
798#2343—171no—
799#2343—171no—
800#2339—171no—
801#2339—171no—
802#2337—171no—
803#2337—171no—
804#2333—171no—
805#2333—171no—
806#2328—171no—
807#2328—171no—
808#2325—171no—
809#2325—171no—
810#2321—171no—
811#2321D1711yescharacteristic, complemented
812#2308—171no—
813C4×#120—171no—
814C4×#120—171no—
815C2×#386—171no—
816C22×C17—22no—
817C22×C17—22no—
818C22×C17—22no—
819C22×C17—22no—
820C22×C17—22no—
821C22×C17—22no—
822C22×C17—22no—
823C22×C17—22no—
824C22×C17—22no—
825C22×C17—22no—
826C22×C17—22no—
827C22×C17—22no—
828C22×C17—22no—
829C22×C17—22no—
830C22×C17—22no—
831C22×C17—416no—
832C22×C17—41no—
833C22×C17—41no—
834C22×C17—41no—
835C22×C17—41no—
836C22×C17—41no—
837C22×C17—41no—
838C22×C17—41no—
839C22×C17—41no—
840C22×C17—41no—
841C22×C17—41no—
842C22×C17—41no—
843C22×C17—41no—
844C22×C17#51814yes—
845C22×C17C24×C411yescharacteristic
846C22×C17C2×H(5,𝔽2)11yescharacteristic
847C22×C17C2×H(5,𝔽2)11yescharacteristic
848C22×C17C2×H(5,𝔽2)11yescharacteristic
849C22×C17C2×H(5,𝔽2)11yescharacteristic
850C22×C17#58511yescharacteristic
851C22×C17#58511yescharacteristic
852C2×D17—22no—
853C2×D17—22no—
854C2×D17—22no—
855C2×D17—22no—
856C2×D17—22no—
857C2×D17—22no—
858C2×D17—22no—
859C2×D17—22no—
860C2×D17—22no—
861C2×D17—41no—
862C2×D17—41no—
863C2×D17—41no—
864C2×D17—41no—
865C2×D17—41no—
866C2×D17—41no—
867C2×D17—41no—
868C2×D17—41no—
869C2×D17—41no—
870C2×D17—41no—
871C2×D17—41no—
872C2×D17—41no—
873C2×D17—88no—
874C4×C17—22no—
875C4×C17—22no—
876C4×C17—22no—
877C4×C17—41no—
878C4×C17—41no—
879C4×C17—41no—
880C4×C17—41no—
881C4×C17—41no—
882C4×C17—41no—
883C4×C17—41no—
884C4×C17—41no—
885Dic17—22no—
886Dic17—22no—
887Dic17—22no—
888Dic17—22no—
889Dic17—22no—
890Dic17—22no—
891Dic17—22no—
892Dic17—41no—
893Dic17—41no—
894Dic17—41no—
895Dic17—41no—
896Dic17—41no—
897Dic17—41no—
898C22×#41—171no—
899C23×D4—171no—
900C24×C4—171no—
901#535—1716no—
902C2×#127—171no—
903C2×#127—171no—
904C2×#124—171no—
905C2×#124—171no—
906C2×#121—171no—
907C2×#121—171no—
908C2×#121—171no—
909C2×#121—171no—
910C2×#120—171no—
911C2×#120—171no—
912C2×#120—171no—
913C2×#120C2×D1711yescharacteristic
914C2×C4×D4—171no—
915C2×C4×D4—171no—
916C2×C4×D4—171no—
917C2×C4×D4—171no—
918C2×C4×D4—171no—
919C2×C4×D4—171no—
920C2×C4×D4—171no—
921C2×C4×D4—171no—
922C2×C4×D4—171no—
923C2×C4×D4—171no—
924C2×C4×D4—171no—
925C2×C4×D4C2×D1711yescharacteristic
926C2×#117—171no—
927C22×C22⋊C4—171no—
928C22×C22⋊C4—171no—
929C22×C22⋊C4—171no—
930C22×C22⋊C4—171no—
931C22×C22⋊C4C2×D1711yescharacteristic
932#391—171no—
933#391—171no—
934#391—171no—
935#391—171no—
936#390—171no—
937#390—171no—
938#390—171no—
939#390—171no—
940#390—171no—
941#390—171no—
942#390C2×D1711yescharacteristic, complemented
943#390C2×D1711yescharacteristic, complemented
944#388—171no—
945#388—171no—
946#388—171no—
947#388—171no—
948#388—171no—
949#388—171no—
950#388—171no—
951#388—171no—
952#388—171no—
953#388—171no—
954#388—171no—
955#388—171no—
956#388C2×D1711yescharacteristic, complemented
957#388C2×D1711yescharacteristic, complemented
958#388C2×D1711yescharacteristic, complemented
959#388C2×D1711yescharacteristic, complemented
960#387—171no—
961#387—171no—
962#387—171no—
963#387—171no—
964#387—171no—
965#387—171no—
966#387—171no—
967#387—171no—
968#386—171no—
969#386—171no—
970#386—171no—
971#386—171no—
972#386—171no—
973#386—171no—
974#386—171no—
975#386—171no—
976#386—171no—
977#386—171no—
978#386—171no—
979#386—171no—
980#386—171no—
981#386—171no—
982#386—171no—
983#386—171no—
984#386—171no—
985#386—171no—
986#386—171no—
987#386—171no—
988#386—171no—
989#386—171no—
990#386—171no—
991#386—171no—
992#386—171no—
993#386—171no—
994#386—171no—
995#386—171no—
996#386—171no—
997#386—171no—
998#386—171no—
999#386—171no—
1000#386—171no—
1001#386—171no—
1002#386—171no—
1003#386—171no—
1004#386—171no—
1005#386C2×D1711yescharacteristic
1006#386C2×D1711yescharacteristic, complemented
1007#386C2×D1711yescharacteristic, complemented
1008#385—171no—
1009#385—171no—
1010#385—171no—
1011#385—171no—
1012#385—171no—
1013#385—171no—
1014#385—171no—
1015#385—171no—
1016#385—171no—
1017#385—171no—
1018#385—171no—
1019#385C2×D1711yescharacteristic
1020#383—171no—
1021#383—171no—
1022#382—171no—
1023#382—171no—
1024#381—171no—
1025#381—171no—
1026#381—171no—
1027#381—171no—
1028#380—171no—
1029#380—171no—
1030#379—171no—
1031#379C2×D1711yescharacteristic
1032C4×C4⋊C4—171no—
1033C4×C4⋊C4—171no—
1034C4×C22⋊C4—171no—
1035C4×C22⋊C4—171no—
1036C4×C22⋊C4—171no—
1037C4×C22⋊C4—171no—
1038C4×C22⋊C4—171no—
1039C4×C22⋊C4—171no—
1040C4×C22⋊C4—171no—
1041C4×C22⋊C4—171no—
1042C4×C22⋊C4—171no—
1043C4×C22⋊C4—171no—
1044C4×C22⋊C4—171no—
1045C4×C22⋊C4—171no—
1046C4×C22⋊C4—171no—
1047C4×C22⋊C4C2×D1711yescharacteristic
1048#376—171no—
1049#376—171no—
1050C2×#95—171no—
1051C2×#95—171no—
1052C2×#95—171no—
1053C2×#95—171no—
1054C2×C17—24no—
1055C2×C17—42no—
1056C2×C17—42no—
1057C2×C17—42no—
1058C2×C17C2×#51811yescharacteristic
1059C2×C17C4×H(5,𝔽2)11yescharacteristic
1060C2×C17C4×H(5,𝔽2)11yescharacteristic
1061C2×C17#353211yescharacteristic
1062C2×C17#353311yescharacteristic
1063C2×C17#354211yescharacteristic
1064C2×C17#354211yescharacteristic
1065D17—42no—
1066D17—42no—
1067D17—42no—
1068C25—171no—
1069C25C22×D1711yescharacteristic
1070C2×#41—178no—
1071C2×#41—682no—
1072C2×#41—682no—
1073C22×Q8—171no—
1074C22×D4—171no—
1075C22×D4—178no—
1076C22×D4—171no—
1077C22×D4—171no—
1078C22×D4—171no—
1079C22×D4—171no—
1080C22×D4—171no—
1081C22×D4—171no—
1082C22×D4—171no—
1083C22×D4—171no—
1084C22×D4—171no—
1085C22×D4—171no—
1086C22×D4—171no—
1087C22×D4—682no—
1088C22×D4—682no—
1089C22×D4C22×D1711yescharacteristic
1090C22×D4C22×D1711yescharacteristic
1091C22×D4C22×D1711yescharacteristic
1092C23×C4—171no—
1093C23×C4—171no—
1094C23×C4—171no—
1095C23×C4—171no—
1096C23×C4—171no—
1097C23×C4—171no—
1098C23×C4—171no—
1099C23×C4—171no—
1100C23×C4—171no—
1101C23×C4—171no—
1102C23×C4—171no—
1103C23×C4—171no—
1104C23×C4—171no—
1105C23×C4—171no—
1106C23×C4—171no—
1107C23×C4—171no—
1108C23×C4—682no—
1109C23×C4—682no—
1110C23×C4—682no—
1111C23×C4C22×D1711yescharacteristic
1112C23×C4C22×D1711yescharacteristic
1113C23×C4C22×D1711yescharacteristic
1114#127—178no—
1115#127—178no—
1116#124—178no—
1117#124—178no—
1118#121—178no—
1119#121—178no—
1120#121—178no—
1121#121—178no—
1122#120—178no—
1123#120—178no—
1124#120—178no—
1125#120C4×D1718yescomplemented
1126C4×D4—42no—
1127C4×D4—682no—
1128C4×D4—682no—
1129C4×D4—682no—
1130C4×D4—682no—
1131C4×D4—682no—
1132C4×D4—682no—
1133C4×D4—682no—
1134C4×D4—682no—
1135C4×D4—682no—
1136C4×D4—682no—
1137C4×D4—682no—
1138#117—178no—
1139C2×C4⋊C4—171no—
1140C2×C4⋊C4—171no—
1141C2×C4⋊C4—171no—
1142C2×C4⋊C4—171no—
1143C2×C4⋊C4—171no—
1144C2×C4⋊C4—171no—
1145C2×C4⋊C4—171no—
1146C2×C4⋊C4—171no—
1147C2×C4⋊C4—171no—
1148C2×C4⋊C4—171no—
1149C2×C4⋊C4—171no—
1150C2×C4⋊C4C22×D1711yescharacteristic
1151C2×C4⋊C4C22×D1711yescharacteristic
1152C2×C4⋊C4C22×D1711yescharacteristic
1153C2×C22⋊C4—42no—
1154C2×C22⋊C4—171no—
1155C2×C22⋊C4—171no—
1156C2×C22⋊C4—171no—
1157C2×C22⋊C4—171no—
1158C2×C22⋊C4—171no—
1159C2×C22⋊C4—171no—
1160C2×C22⋊C4—171no—
1161C2×C22⋊C4—171no—
1162C2×C22⋊C4—171no—
1163C2×C22⋊C4—171no—
1164C2×C22⋊C4—171no—
1165C2×C22⋊C4—171no—
1166C2×C22⋊C4—171no—
1167C2×C22⋊C4—171no—
1168C2×C22⋊C4—171no—
1169C2×C22⋊C4—171no—
1170C2×C22⋊C4—171no—
1171C2×C22⋊C4—171no—
1172C2×C22⋊C4—171no—
1173C2×C22⋊C4—171no—
1174C2×C22⋊C4—171no—
1175C2×C22⋊C4—171no—
1176C2×C22⋊C4—171no—
1177C2×C22⋊C4—171no—
1178C2×C22⋊C4—171no—
1179C2×C22⋊C4—171no—
1180C2×C22⋊C4—171no—
1181C2×C22⋊C4—171no—
1182C2×C22⋊C4—171no—
1183C2×C22⋊C4—171no—
1184C2×C22⋊C4—171no—
1185C2×C22⋊C4—171no—
1186C2×C22⋊C4—171no—
1187C2×C22⋊C4—171no—
1188C2×C22⋊C4—682no—
1189C2×C22⋊C4—682no—
1190C2×C22⋊C4—682no—
1191C2×C22⋊C4—682no—
1192C2×C22⋊C4C22×D1711yescharacteristic
1193C2×C22⋊C4C22×D1711yescharacteristic
1194C2×C22⋊C4C22×D1711yescharacteristic
1195C2×C22⋊C4C22×D1711yescharacteristic
1196C2×C22⋊C4C22×D1711yescharacteristic
1197C2×C22⋊C4C22×D1711yescharacteristic
1198C2×C22⋊C4C22×D1711yescharacteristic
1199C2×C22⋊C4C22×D1711yescharacteristic
1200C2×C22⋊C4C22×D1711yescharacteristic
1201C2×C22⋊C4C22×D1711yescharacteristic
1202C2×C22⋊C4C22×D1711yescharacteristic
1203C2×C22⋊C4C22×D1711yescharacteristic
1204C2×C22⋊C4C22×D1711yescharacteristic
1205C2×C22⋊C4C22×D1711yescharacteristic
1206C2×C22⋊C4C22×D1711yescharacteristic
1207C2×C22⋊C4C22×D1711yescharacteristic
1208C2×C42—171no—
1209C2×C42—171no—
1210C2×C42—171no—
1211C2×C42—171no—
1212C2×C42—171no—
1213C2×C42—171no—
1214C2×C42—171no—
1215C2×C42—171no—
1216C2×C42—171no—
1217C2×C42—171no—
1218C2×C42—171no—
1219C2×C42C22×D1711yescharacteristic
1220C2×C42C22×D1711yescharacteristic
1221C2×C42C22×D1711yescharacteristic
1222#95—171no—
1223#95—171no—
1224#95—171no—
1225#95—171no—
1226#95—171no—
1227#95—171no—
1228#95—171no—
1229#95—171no—
1230#95—171no—
1231#95—171no—
1232#95—171no—
1233#95—171no—
1234#95—171no—
1235#95—171no—
1236#95—171no—
1237#95—171no—
1238#95—171no—
1239#95—171no—
1240#95—171no—
1241#95—171no—
1242#95—171no—
1243#95—171no—
1244#95—171no—
1245#95—171no—
1246#95—171no—
1247#95—171no—
1248#95—171no—
1249#95—171no—
1250#95—171no—
1251#95—171no—
1252#95—171no—
1253#95—171no—
1254#95—171no—
1255#95—171no—
1256#95C22×D1711yescharacteristic
1257#95C22×D1711yescharacteristic
1258#95C22×D1711yescharacteristic
1259#95C22×D1711yescharacteristic
1260#95C22×D1711yescharacteristic
1261#95C22×D1711yescharacteristic
1262C17#3440611yescharacteristic, complemented, Sylow
1263C24—22no—
1264C24—22no—
1265C24—41no—
1266C24—41no—
1267C24—41no—
1268C24—41no—
1269C24—171no—
1270C24—171no—
1271C24—171no—
1272C24—174no—
1273C24—342no—
1274C24—342no—
1275C24—681no—
1276C24—681no—
1277C24—681no—
1278C24—681no—
1279C24C2×C4×D1714yes—
1280C24C23×D1711yescharacteristic
1281C24C23×D1711yescharacteristic
1282C24C23×D1711yescharacteristic
1283C24C23×D1711yescharacteristic
1284#41—6816no—
1285C2×Q8—174no—
1286C2×Q8—681no—
1287C2×Q8—681no—
1288C2×D4—22no—
1289C2×D4—22no—
1290C2×D4—41no—
1291C2×D4—41no—
1292C2×D4—41no—
1293C2×D4—41no—
1294C2×D4—174no—
1295C2×D4—174no—
1296C2×D4—174no—
1297C2×D4—174no—
1298C2×D4—174no—
1299C2×D4—174no—
1300C2×D4—174no—
1301C2×D4—174no—
1302C2×D4—174no—
1303C2×D4—174no—
1304C2×D4—174no—
1305C2×D4—174no—
1306C2×D4—342no—
1307C2×D4—342no—
1308C2×D4—681no—
1309C2×D4—681no—
1310C2×D4—681no—
1311C2×D4—681no—
1312C2×D4—681no—
1313C2×D4—681no—
1314C2×D4—681no—
1315C2×D4—681no—
1316C2×D4—681no—
1317C2×D4—681no—
1318C2×D4—681no—
1319C2×D4—681no—
1320C2×D4—6816no—
1321C2×D4—681no—
1322C2×D4—681no—
1323C2×D4—681no—
1324C2×D4—681no—
1325C2×D4—681no—
1326C2×D4—681no—
1327C2×D4—681no—
1328C2×D4—681no—
1329C2×D4—681no—
1330C2×D4—681no—
1331C2×D4C2×C4×D1714yes—
1332C2×D4C2×C4×D1714yes—
1333C2×D4C2×C4×D1714yes—
1334C22×C4—22no—
1335C22×C4—22no—
1336C22×C4—41no—
1337C22×C4—41no—
1338C22×C4—41no—
1339C22×C4—41no—
1340C22×C4—41no—
1341C22×C4—41no—
1342C22×C4—41no—
1343C22×C4—174no—
1344C22×C4—171no—
1345C22×C4—171no—
1346C22×C4—171no—
1347C22×C4—171no—
1348C22×C4—171no—
1349C22×C4—171no—
1350C22×C4—171no—
1351C22×C4—174no—
1352C22×C4—174no—
1353C22×C4—171no—
1354C22×C4—171no—
1355C22×C4—171no—
1356C22×C4—171no—
1357C22×C4—171no—
1358C22×C4—171no—
1359C22×C4—342no—
1360C22×C4—342no—
1361C22×C4—342no—
1362C22×C4—342no—
1363C22×C4—342no—
1364C22×C4—342no—
1365C22×C4—342no—
1366C22×C4—342no—
1367C22×C4—342no—
1368C22×C4—342no—
1369C22×C4—342no—
1370C22×C4—342no—
1371C22×C4—681no—
1372C22×C4—681no—
1373C22×C4—681no—
1374C22×C4—681no—
1375C22×C4—681no—
1376C22×C4—681no—
1377C22×C4—681no—
1378C22×C4—681no—
1379C22×C4—681no—
1380C22×C4—681no—
1381C22×C4—681no—
1382C22×C4—681no—
1383C22×C4—681no—
1384C22×C4—681no—
1385C22×C4—681no—
1386C22×C4—681no—
1387C22×C4—681no—
1388C22×C4—681no—
1389C22×C4—681no—
1390C22×C4—681no—
1391C22×C4—681no—
1392C22×C4—681no—
1393C22×C4—681no—
1394C22×C4—681no—
1395C22×C4—681no—
1396C22×C4—681no—
1397C22×C4—681no—
1398C22×C4—681no—
1399C22×C4—681no—
1400C22×C4—681no—
1401C22×C4—681no—
1402C22×C4—681no—
1403C22×C4—681no—
1404C22×C4—6816no—
1405C22×C4C23×D1711yescharacteristic
1406C22×C4C23×D1711yescharacteristic
1407C22×C4C23×D1711yescharacteristic
1408C22×C4C23×D1711yescharacteristic
1409C22×C4C23×D1711yescharacteristic
1410C22×C4C23×D1711yescharacteristic
1411C22×C4C23×D1711yescharacteristic
1412C22×C4C23×D1711yescharacteristic
1413C22×C4C23×D1711yescharacteristic
1414C22×C4C23×D1711yescharacteristic
1415C22×C4C23×D1711yescharacteristic
1416C4⋊C4—41no—
1417C4⋊C4—41no—
1418C4⋊C4—41no—
1419C4⋊C4—174no—
1420C4⋊C4—174no—
1421C4⋊C4—342no—
1422C4⋊C4—342no—
1423C4⋊C4—681no—
1424C4⋊C4—681no—
1425C4⋊C4—681no—
1426C4⋊C4—681no—
1427C4⋊C4—681no—
1428C4⋊C4—681no—
1429C4⋊C4—681no—
1430C22⋊C4—22no—
1431C22⋊C4—22no—
1432C22⋊C4—41no—
1433C22⋊C4—41no—
1434C22⋊C4—41no—
1435C22⋊C4—41no—
1436C22⋊C4—41no—
1437C22⋊C4—41no—
1438C22⋊C4—41no—
1439C22⋊C4—41no—
1440C22⋊C4—41no—
1441C22⋊C4—41no—
1442C22⋊C4—41no—
1443C22⋊C4—174no—
1444C22⋊C4—174no—
1445C22⋊C4—174no—
1446C22⋊C4—174no—
1447C22⋊C4—174no—
1448C22⋊C4—174no—
1449C22⋊C4—174no—
1450C22⋊C4—342no—
1451C22⋊C4—342no—
1452C22⋊C4—342no—
1453C22⋊C4—342no—
1454C22⋊C4—342no—
1455C22⋊C4—342no—
1456C22⋊C4—342no—
1457C22⋊C4—342no—
1458C22⋊C4—681no—
1459C22⋊C4—681no—
1460C22⋊C4—681no—
1461C22⋊C4—681no—
1462C22⋊C4—681no—
1463C22⋊C4—681no—
1464C22⋊C4—681no—
1465C22⋊C4—681no—
1466C22⋊C4—681no—
1467C22⋊C4—681no—
1468C22⋊C4—681no—
1469C22⋊C4—681no—
1470C22⋊C4—681no—
1471C22⋊C4—681no—
1472C22⋊C4—681no—
1473C22⋊C4—681no—
1474C22⋊C4—681no—
1475C22⋊C4—681no—
1476C22⋊C4—681no—
1477C22⋊C4C2×C4×D1714yes—
1478C22⋊C4C2×C4×D1714yes—
1479C22⋊C4C2×C4×D1714yes—
1480C42—41no—
1481C42—41no—
1482C42—41no—
1483C42—174no—
1484C42—174no—
1485C42—342no—
1486C42—342no—
1487C42—681no—
1488C42—681no—
1489C42—681no—
1490C42—681no—
1491C42—681no—
1492C42—681no—
1493C42—681no—
1494C23—21no—
1495C23—21no—
1496C23—21no—
1497C23—21no—
1498C23—28no—
1499C23—21no—
1500C23—21no—
1501C23—21no—
1502C23—21no—
1503C23—21no—
1504C23—21no—
1505C23—21no—
1506C23—21no—
1507C23—21no—
1508C23—21no—
1509C23—21no—
1510C23—21no—
1511C23—21no—
1512C23—21no—
1513C23—21no—
1514C23—21no—
1515C23—21no—
1516C23—21no—
1517C23—44no—
1518C23—44no—
1519C23—44no—
1520C23—44no—
1521C23—44no—
1522C23—44no—
1523C23—172no—
1524C23—172no—
1525C23—172no—
1526C23—341no—
1527C23—341no—
1528C23—341no—
1529C23—341no—
1530C23—341no—
1531C23—341no—
1532C23—341no—
1533C23—341no—
1534C23—341no—
1535C23—341no—
1536C23—341no—
1537C23—341no—
1538C23—341no—
1539C23—341no—
1540C23—341no—
1541C23—341no—
1542C23—341no—
1543C23—341no—
1544C23—348no—
1545C23—684no—
1546C23—684no—
1547C23—1362no—
1548C23—1362no—
1549C23—1362no—
1550C23—1362no—
1551C23C22×C4×D1712yes—
1552C23C22×C4×D1712yes—
1553C23C22×C4×D1712yes—
1554C23C22×C4×D1712yes—
1555C23#1058769112yes—
1556C23#1058769612yes—
1557C23C24×D1711yescharacteristic
1558Q8—684no—
1559D4—28no—
1560D4—44no—
1561D4—44no—
1562D4—348no—
1563D4—684no—
1564D4—684no—
1565D4—684no—
1566D4—684no—
1567D4—684no—
1568D4—684no—
1569D4—684no—
1570D4—684no—
1571D4—684no—
1572D4—684no—
1573D4—684no—
1574C2×C4—21no—
1575C2×C4—21no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—82no—
1605C2×C4—82no—
1606C2×C4—82no—
1607C2×C4—172no—
1608C2×C4—172no—
1609C2×C4—172no—
1610C2×C4—172no—
1611C2×C4—172no—
1612C2×C4—172no—
1613C2×C4—172no—
1614C2×C4—348no—
1615C2×C4—341no—
1616C2×C4—341no—
1617C2×C4—341no—
1618C2×C4—341no—
1619C2×C4—341no—
1620C2×C4—341no—
1621C2×C4—341no—
1622C2×C4—341no—
1623C2×C4—341no—
1624C2×C4—341no—
1625C2×C4—341no—
1626C2×C4—341no—
1627C2×C4—341no—
1628C2×C4—341no—
1629C2×C4—341no—
1630C2×C4—341no—
1631C2×C4—341no—
1632C2×C4—341no—
1633C2×C4—341no—
1634C2×C4—341no—
1635C2×C4—341no—
1636C2×C4—341no—
1637C2×C4—341no—
1638C2×C4—341no—
1639C2×C4—341no—
1640C2×C4—341no—
1641C2×C4—341no—
1642C2×C4—341no—
1643C2×C4—341no—
1644C2×C4—341no—
1645C2×C4—341no—
1646C2×C4—341no—
1647C2×C4—684no—
1648C2×C4—684no—
1649C2×C4—684no—
1650C2×C4—684no—
1651C2×C4—684no—
1652C2×C4—684no—
1653C2×C4—684no—
1654C2×C4—684no—
1655C2×C4—1362no—
1656C2×C4—1362no—
1657C2×C4—1362no—
1658C2×C4—1362no—
1659C2×C4—1362no—
1660C2×C4—1362no—
1661C2×C4—1362no—
1662C2×C4C22×C4×D1712yes—
1663C2×C4C22×C4×D1712yes—
1664C2×C4C22×C4×D1712yes—
1665C22—22no—
1666C22—22no—
1667C22—22no—
1668C22—22no—
1669C22—22no—
1670C22—22no—
1671C22—22no—
1672C22—22no—
1673C22—22no—
1674C22—22no—
1675C22—22no—
1676C22—22no—
1677C22—22no—
1678C22—22no—
1679C22—22no—
1680C22—416no—
1681C22—41no—
1682C22—41no—
1683C22—41no—
1684C22—41no—
1685C22—41no—
1686C22—41no—
1687C22—41no—
1688C22—41no—
1689C22—41no—
1690C22—41no—
1691C22—41no—
1692C22—41no—
1693C22—342no—
1694C22—342no—
1695C22—342no—
1696C22—342no—
1697C22—342no—
1698C22—342no—
1699C22—342no—
1700C22—342no—
1701C22—342no—
1702C22—681no—
1703C22—681no—
1704C22—681no—
1705C22—681no—
1706C22—681no—
1707C22—681no—
1708C22—681no—
1709C22—681no—
1710C22—681no—
1711C22—681no—
1712C22—681no—
1713C22—681no—
1714C22—1368no—
1715C22#1176328114yes—
1716C22C23×C4×D1711yescharacteristic
1717C22H(5,𝔽2)×D1711yescharacteristic
1718C22H(5,𝔽2)×D1711yescharacteristic
1719C22C2×#1058769111yescharacteristic
1720C22C2×#1058769611yescharacteristic
1721C22#1176364411yescharacteristic
1722C22#1176364411yescharacteristic
1723C4—22no—
1724C4—22no—
1725C4—22no—
1726C4—41no—
1727C4—41no—
1728C4—41no—
1729C4—41no—
1730C4—41no—
1731C4—41no—
1732C4—41no—
1733C4—41no—
1734C4—342no—
1735C4—342no—
1736C4—342no—
1737C4—342no—
1738C4—342no—
1739C4—342no—
1740C4—342no—
1741C4—681no—
1742C4—681no—
1743C4—681no—
1744C4—681no—
1745C4—681no—
1746C4—681no—
1747C2—24no—
1748C2—42no—
1749C2—42no—
1750C2—42no—
1751C2—682no—
1752C2—682no—
1753C2—682no—
1754C2C2×#1176328111yescharacteristic
1755C2#1454198811yescharacteristic
1756C2#1454198811yescharacteristic
1757C2#1454293511yescharacteristic
1758C2#1454295211yescharacteristic
1759C2#1454308711yescharacteristic
1760C2#1454309511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2321C2
socle, cosocleC23×C17C25
prime radicalC2×#11763374C2
hypercenter#2321D17
hypocenterC17#34406
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2321

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14531959C2semidirect
3. #14531953C2semidirect
4. #14531937C2semidirect
5. #14531935C2semidirect
6. #14531891C2semidirect
7. #14531845C2semidirect
8. #14531832C2semidirect
9. #14531828C2semidirect
10. #14531766C2semidirect
11. #14531764C2semidirect
12. #14531761C2semidirect
13. #14531760C2semidirect
14. #14531642C2semidirect
15. #14531638C2semidirect
16. #14531610C2semidirect
17. #14531609C2semidirect
18. #14531595C2semidirect
19. #14531591C2semidirect
20. #14531547C2semidirect
21. #14531543C2semidirect
22. #14531508C2semidirect
23. #14531505C2semidirect
24. #14531488C2semidirect
25. #14531485C2semidirect
26. #14531442C2semidirect
27. #14531360C2semidirect
28. #120×Dic17C2semidirect
29. #14531283C2semidirect
30. C2×#11762686C2semidirect
31. C17×#2321C2semidirect
35. #11763374C4semidirect
47. C2×C4×D68C22semidirect
49. C2×D4×Dic17C22semidirect
50. C2×D4×Dic17C22semidirect
51. C2×#10587579C22semidirect
53. C2×C4×C22⋊D17C22semidirect
55. C2×#10587567C22semidirect
56. C2×#10587567C22semidirect
57. C2×#10587567C22semidirect
63. #11762715C22semidirect
64. #11762714C22semidirect
65. #11762713C22semidirect
66. #11762713C22semidirect
67. #11762711C22semidirect
68. #11762710C22semidirect
69. #11762709C22semidirect
70. #11762709C22semidirect
71. #11762709C22semidirect
72. #11762709C22semidirect
73. #11762703C22semidirect
74. #11762703C22semidirect
75. #11762701C22semidirect
76. #11762701C22semidirect
77. #11762700C22semidirect
78. #11762700C22semidirect
79. #11762699C22semidirect
80. #11762699C22semidirect
81. #11762698C22semidirect
82. #11762698C22semidirect
83. #11762697C22semidirect
84. #11762697C22semidirect
85. #11762696C22semidirect
86. #11762696C22semidirect
87. #11762693C22semidirect
88. #11762693C22semidirect
89. #11762691C22semidirect
90. #11762691C22semidirect
91. #11762690C22semidirect
92. #11762690C22semidirect
94. #11762689C22semidirect
95. #11762689C22semidirect
97. #11762688C22semidirect
98. #11762688C22semidirect
99. #11762687C22semidirect
100. #11762687C22semidirect
101. #11762687C22semidirect
102. #11762687C22semidirect
112. #11762686C22semidirect
113. #11762686C22semidirect
114. #11762686C22semidirect
115. #11762686C22semidirect
124. #11762685C22semidirect
125. #11762685C22semidirect
126. #11762685C22semidirect
127. #11762685C22semidirect
128. #11762685C22semidirect
129. #11762685C22semidirect
131. #11762684C22semidirect
132. #11762684C22semidirect
133. #11762683C22semidirect
134. #11762683C22semidirect
137. #11762681C22semidirect
138. #11762681C22semidirect
139. #11762680C22semidirect
140. #11762680C22semidirect
141. #11762676C22semidirect
142. #11762676C22semidirect
143. #11762674C22semidirect
144. #11762673C22semidirect
145. #11762671C22semidirect
148. #11762670C22semidirect
149. #11762667C22semidirect
150. #11762666C22semidirect
152. C4⋊C4×Dic17C22semidirect
153. C4×#63225C22semidirect
156. C22⋊C4×Dic17C22semidirect
157. C22⋊C4×Dic17C22semidirect
158. C22⋊C4×Dic17C22semidirect
159. C22⋊C4×Dic17C22semidirect
160. C22⋊C4×Dic17C22semidirect
161. C4×#63227C22semidirect
162. C4×#63227C22semidirect
163. C4×#63227C22semidirect
165. #11762656C22semidirect
166. #11762656C22semidirect
167. #11762655C22semidirect
168. #11762654C22semidirect
171. C2×#10587502C22semidirect
172. #95×D17C22semidirect
176. C17×#390C22semidirect
177. C17×#390C22semidirect
178. C17×#388C22semidirect
179. C17×#388C22semidirect
180. C17×#388C22semidirect
181. C17×#388C22semidirect
183. C17×#386C22semidirect
184. C17×#386C22semidirect
198. C22×C22⋊D17C2×C4semidirect
223. C2×#63254C2×C4semidirect
234. C17×#120C2×C4semidirect
259. #10587639C2×C4semidirect
272. #10587626C2×C4semidirect
273. #10587626C2×C4semidirect
274. #10587625C2×C4semidirect
275. #10587625C2×C4semidirect
276. #10587623C2×C4semidirect
329. #10587571C2×C4semidirect
330. #10587571C2×C4semidirect
331. #10587570C2×C4semidirect
332. #10587570C2×C4semidirect
333. #10587568C2×C4semidirect
340. #10587563C2×C4semidirect
460. C2×C22⋊D17C22×C4semidirect
461. C2×C22⋊D17C22×C4semidirect
462. C2×C22⋊D17C22×C4semidirect
490. C22×Dic17C22×C4semidirect
509. C2×D68C22×C4semidirect
510. C2×D68C22×C4semidirect
531. C2×C4×D17C22×C4semidirect
534. C2×Dic34C22×C4semidirect
587. #63227C22×C4semidirect
588. #63227C22×C4semidirect
589. #63227C22×C4semidirect
590. #63227C22×C4semidirect
600. #63225C22×C4semidirect
601. #63225C22×C4semidirect
611. C4×Dic17C22×C4semidirect
612. C4×Dic17C22×C4semidirect
811. #2321D17semidirect
942. #390C2×D17semidirect
943. #390C2×D17semidirect
956. #388C2×D17semidirect
957. #388C2×D17semidirect
958. #388C2×D17semidirect
959. #388C2×D17semidirect
1006. #386C2×D17semidirect
1007. #386C2×D17semidirect
1125. #120C4×D17semidirect
1262. C17#34406semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#117633742
#145319592
#145319532
#145319372
#145319352
#145318912
#145318452
#145318322
#145318282
#145317662
#145317642
#145317612
#145317602
#145316422
#145316382
#145316102
#145316092
#145315952
#145315912
#145315472
#145315432
#145315082
#145315052
#145314882
#145314852
#145314422
#145313602
#120×Dic172
#145312832
C2×#117626862
C17×#23212
#3440617