Finite Group Databasebeta

← #17197844

Subgroups — #17197844

Order 4352.

2766 conjugacy classes of subgroups.

The subgroup lattice has 1752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763374C211yesmaximal, characteristic
2#14531957C211yesmaximal, characteristic, complemented
3#14531953C211yesmaximal, characteristic, complemented
4#14531924C211yesmaximal, characteristic, complemented
5#14531923C211yesmaximal, characteristic, complemented
6#14531892C211yesmaximal, characteristic, complemented
7#14531891C211yesmaximal, characteristic, complemented
8#14531823C211yesmaximal, characteristic, complemented
9#14531817C211yesmaximal, characteristic, complemented
10#14531803C211yesmaximal, characteristic, complemented
11#14531797C211yesmaximal, characteristic, complemented
12#14531763C211yesmaximal, characteristic, complemented
13#14531762C211yesmaximal, characteristic, complemented
14#14531666C211yesmaximal, characteristic, complemented
15#14531666C211yesmaximal, characteristic, complemented
16C22⋊C4×C22⋊D17C211yesmaximal, characteristic, complemented
17#14531600C211yesmaximal, characteristic, complemented
18#14531508C211yesmaximal, characteristic, complemented
19#14531506C211yesmaximal, characteristic, complemented
20#14531505C211yesmaximal, characteristic, complemented
21#14531505C211yesmaximal, characteristic, complemented
22#14531474C211yesmaximal, characteristic, complemented
23#14531470C211yesmaximal, characteristic, complemented
24#14531445C211yesmaximal, characteristic, complemented
25#14531443C211yesmaximal, characteristic, complemented
26#14531440C211yesmaximal, characteristic, complemented
27#14531374C211yesmaximal, characteristic, complemented
28#14531294C211yesmaximal, characteristic, complemented
29C4×#10587625C211yesmaximal, characteristic, complemented
30#14531269C211yesmaximal, characteristic, complemented
31C17×#2321C211yesmaximal, characteristic, complemented
32C22×#63254C2211yescharacteristic
33C23×C22⋊D17C2211yescharacteristic
34#11763374C4116yescomplemented
35C2×#10587626C2211yescharacteristic
36C2×#10587626C2211yescharacteristic
37C2×#10587571C2211yescharacteristic
38C2×#10587571C2211yescharacteristic
39C2×#10587570C2211yescharacteristic
40C2×#10587570C2211yescharacteristic
41C2×#10587625C2211yescharacteristic
42C2×#10587625C2211yescharacteristic
43C2×#10587568C2211yescharacteristic
44C2×#10587639C2211yescharacteristic
45C2×#10587623C2211yescharacteristic
46C2×C4×D68C2211yescharacteristic, complemented
47C2×D4×Dic17C2211yescharacteristic, complemented
48C2×#10587579C2211yescharacteristic, complemented
49C2×C4×C22⋊D17C2211yescharacteristic
50C2×C4×C22⋊D17C2211yescharacteristic
51C2×C4×C22⋊D17C2211yescharacteristic, complemented
52C2×C4×C22⋊D17C2211yescharacteristic, complemented
53C2×#10587567C2211yescharacteristic
54C2×#10587567C2211yescharacteristic
55C2×#10587567C2211yescharacteristic, complemented
56C2×#10587567C2211yescharacteristic, complemented
57C2×#10587558C2211yescharacteristic, complemented
58C2×#10587563C2211yescharacteristic
59C2×#10587563C2211yescharacteristic, complemented
60C2×C4⋊C4×D17C2211yescharacteristic, complemented
61C22×C22⋊Dic17C2211yescharacteristic
62C2×C22⋊C4×D17C2211yescharacteristic
63C2×C22⋊C4×D17C2211yescharacteristic
64C22×C4×Dic17C2211yescharacteristic, complemented
65#11762715C2211yescharacteristic, complemented
66#11762714C2211yescharacteristic, complemented
67#11762713C2211yescharacteristic, complemented
68#11762713C2211yescharacteristic, complemented
69#11762712C2211yescharacteristic
70#11762712C2211yescharacteristic, complemented
71#11762711C2211yescharacteristic, complemented
72#11762710C2211yescharacteristic, complemented
73#11762709C2211yescharacteristic
74#11762709C2211yescharacteristic
75#11762709C2211yescharacteristic
76#11762709C2211yescharacteristic
77#11762709C2211yescharacteristic
78#11762709C2211yescharacteristic
79#11762709C2211yescharacteristic, complemented
80#11762709C2211yescharacteristic, complemented
81#11762709C2211yescharacteristic, complemented
82#11762709C2211yescharacteristic, complemented
83#11762706C2211yescharacteristic, complemented
84#11762706C2211yescharacteristic, complemented
85#11762704C2211yescharacteristic, complemented
86#11762704C2211yescharacteristic, complemented
87#11762703C2211yescharacteristic
88#11762703C2211yescharacteristic
89#11762703C2211yescharacteristic, complemented
90#11762703C2211yescharacteristic, complemented
91#11762702C2211yescharacteristic
92#11762702C2211yescharacteristic
93#11762702C2211yescharacteristic, complemented
94#11762702C2211yescharacteristic, complemented
95#11762701C2211yescharacteristic, complemented
96#11762701C2211yescharacteristic, complemented
97#11762700C2211yescharacteristic, complemented
98#11762700C2211yescharacteristic, complemented
99#11762699C2211yescharacteristic, complemented
100#11762699C2211yescharacteristic, complemented
101#11762698C2211yescharacteristic, complemented
102#11762698C2211yescharacteristic, complemented
103#11762697C2211yescharacteristic
104#11762697C2211yescharacteristic
105#11762697C2211yescharacteristic, complemented
106#11762697C2211yescharacteristic, complemented
107#11762689C2211yescharacteristic
108#11762689C2211yescharacteristic, complemented
109#11762689C2211yescharacteristic, complemented
110#11762688C2211yescharacteristic
111#11762688C2211yescharacteristic
112#11762688C2211yescharacteristic, complemented
113#11762688C2211yescharacteristic, complemented
114#11762688C2211yescharacteristic, complemented
115#11762687C2211yescharacteristic, complemented
116#11762687C2211yescharacteristic, complemented
117#11762687C2211yescharacteristic, complemented
118#11762687C2211yescharacteristic, complemented
119#11762686C2211yescharacteristic
120#11762686C2211yescharacteristic
121#11762686C2211yescharacteristic, complemented
122#11762686C2211yescharacteristic, complemented
123#11762686C2211yescharacteristic, complemented
124#11762685C2211yescharacteristic
125#11762685C2211yescharacteristic
126#11762685C2211yescharacteristic
127#11762685C2211yescharacteristic
128#11762685C2211yescharacteristic
129#11762685C2211yescharacteristic
130#11762685C2211yescharacteristic, complemented
131#11762685C2211yescharacteristic, complemented
132#11762685C2211yescharacteristic, complemented
133#11762685C2211yescharacteristic, complemented
134#11762685C2211yescharacteristic, complemented
135#11762685C2211yescharacteristic, complemented
136#11762684C2211yescharacteristic, complemented
137#11762683C2211yescharacteristic, complemented
138#11762683C2211yescharacteristic, complemented
139#11762682C2211yescharacteristic, complemented
140#11762681C2211yescharacteristic, complemented
141#11762680C2211yescharacteristic, complemented
142#11762680C2211yescharacteristic, complemented
143#11762674C2211yescharacteristic, complemented
144#11762674C2211yescharacteristic, complemented
145#11762673C2211yescharacteristic, complemented
146#11762673C2211yescharacteristic, complemented
147#11762667C2211yescharacteristic
148#11762667C2211yescharacteristic
149#11762667C2211yescharacteristic, complemented
150#11762667C2211yescharacteristic, complemented
151#11762665C2211yescharacteristic
152#11762664C2211yescharacteristic
153#11762664C2211yescharacteristic
154C4×#63225C2211yescharacteristic, complemented
155C4×#63225C2211yescharacteristic, complemented
156#11762660C2211yescharacteristic, complemented
157#11762660C2211yescharacteristic, complemented
158C22⋊C4×Dic17C2211yescharacteristic
159C22⋊C4×Dic17C2211yescharacteristic
160C22⋊C4×Dic17C2211yescharacteristic, complemented
161C22⋊C4×Dic17C2211yescharacteristic, complemented
162C4×#63227C2211yescharacteristic, complemented
163C4×#63227C2211yescharacteristic, complemented
164C4×C22⋊Dic17C2211yescharacteristic, complemented
165#11762656C2211yescharacteristic, complemented
166#11762656C2211yescharacteristic, complemented
167#11762656C2211yescharacteristic, complemented
168#11762656C2211yescharacteristic, complemented
169#11762655C2211yescharacteristic, complemented
170#11762655C2211yescharacteristic, complemented
171#11762654C2211yescharacteristic, complemented
172#11762654C2211yescharacteristic, complemented
173C2×C17×#120C2211yescharacteristic
174C2×C4×D4×C17C2211yescharacteristic, complemented
175C22×C22⋊C4×C17C2211yescharacteristic
176C17×#390C2211yescharacteristic
177C17×#390C2211yescharacteristic, complemented
178C17×#388C2211yescharacteristic
179C17×#388C2211yescharacteristic
180C17×#388C2211yescharacteristic, complemented
181C17×#388C2211yescharacteristic, complemented
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic, complemented
184C17×#386C2211yescharacteristic, complemented
185C17×#385C2211yescharacteristic, complemented
186C17×#379C2211yescharacteristic
187C4×C22⋊C4×C17C2211yescharacteristic, complemented
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×Dic17C2311yescharacteristic
210C23×Dic17C2311yescharacteristic
211C23×Dic17C2311yescharacteristic
212C23×Dic17C2311yescharacteristic
213C23×Dic17C2311yescharacteristic
214C2×#63254—42no—
215C2×#63254—42no—
216C2×#63254C2×C418yescomplemented
217C22×D68C2311yescharacteristic
218C22×D68C2311yescharacteristic
219C22×C4×D17C2311yescharacteristic
220C22×C4×D17C2311yescharacteristic
221C22×C4×D17C2311yescharacteristic
222C22×C4×D17C2311yescharacteristic
223C22×C4×D17C2311yescharacteristic
224C22×C4×D17C2311yescharacteristic
225C22×C4×D17C2311yescharacteristic
226C22×Dic34C2311yescharacteristic
227C17×#120C2×C418yescomplemented
228C4×D4×C17—42no—
229C2×C4⋊C4×C17C2311yescharacteristic
230C2×C4⋊C4×C17C2311yescharacteristic
231C2×C4⋊C4×C17C2311yescharacteristic
232C2×C22⋊C4×C17—42no—
233C2×C22⋊C4×C17C2311yescharacteristic
234C2×C22⋊C4×C17C2311yescharacteristic
235C2×C22⋊C4×C17C2311yescharacteristic
236C2×C22⋊C4×C17C2311yescharacteristic
237C2×C22⋊C4×C17C2311yescharacteristic
238C2×C22⋊C4×C17C2311yescharacteristic
239C2×C22⋊C4×C17C2311yescharacteristic
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×C42×C17C2311yescharacteristic
250C2×C42×C17C2311yescharacteristic
251C2×C42×C17C2311yescharacteristic
252#10587639C2×C418yescomplemented
253C2×C22⋊Dic17—42no—
254C2×C22⋊Dic17C2311yescharacteristic
255C2×C22⋊Dic17C2311yescharacteristic
256C2×C22⋊Dic17C2311yescharacteristic
257C2×C22⋊Dic17C2311yescharacteristic
258C2×C22⋊Dic17C2311yescharacteristic
259C2×C22⋊Dic17C2311yescharacteristic
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
270#10587626C2×C418yescomplemented
271#10587626C2×C418yescomplemented
272#10587625C2×C418yescomplemented
273#10587625C2×C418yescomplemented
274#10587623C2×C418yescomplemented
275D4×Dic17—42no—
276C4×C22⋊D17—42no—
277C4×C22⋊D17—42no—
278C4×C22⋊D17—42no—
279C4×C22⋊D17—42no—
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
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×C4⋊Dic17C2311yescharacteristic
303C2×C4⋊Dic17C2311yescharacteristic
304C2×C4⋊Dic17C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×#63225C2311yescharacteristic
313C2×#63225C2311yescharacteristic
314C2×#63225C2311yescharacteristic
315C2×#63225C2311yescharacteristic
316C2×#63225C2311yescharacteristic
317C2×C4×Dic17—42no—
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
328C2×C4×Dic17C2311yescharacteristic
329C2×C4×Dic17C2311yescharacteristic
330C2×C4×Dic17C2311yescharacteristic
331C2×C4×Dic17C2311yescharacteristic
332C2×C4×Dic17C2311yescharacteristic
333#10587579—42no—
334C4⋊C4×D17—42no—
335#10587571C2×C418yescomplemented
336#10587571C2×C418yescomplemented
337#10587570C2×C418yescomplemented
338#10587570C2×C418yescomplemented
339#10587568C2×C418yescomplemented
340#10587567—42no—
341#10587567—42no—
342#10587567—42no—
343#10587567—42no—
344C22⋊C4×D17—42no—
345C22⋊C4×D17—42no—
346#10587563—42no—
347#10587563C2×C418yescomplemented
348C4×D68—42no—
349#10587558—42no—
350C17×#95C2311yescharacteristic
351C17×#95C2311yescharacteristic
352C17×#95C2311yescharacteristic
353C17×#95C2311yescharacteristic
354C17×#95C2311yescharacteristic
355C17×#95C2311yescharacteristic
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—41no—
383C24×C17—41no—
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—41no—
394C23×D17—41no—
395C23×D17—41no—
396C23×D17—41no—
397C23×D17—41no—
398C23×D17—41no—
399C23×D17C22×C414yes—
400C23×D17C2411yescharacteristic
401C23×D17C2411yescharacteristic
402C23×D17C2411yescharacteristic
403C2×D4×C17—41no—
404C2×D4×C17—41no—
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—22no—
435C2×C22⋊D17—22no—
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×C414yes—
461C2×C22⋊D17C22×C414yes—
462C2×C22⋊D17C22×C414yes—
463C22×Dic17—22no—
464C22×Dic17—22no—
465C22×Dic17—22no—
466C22×Dic17—22no—
467C22×Dic17—22no—
468C22×Dic17—22no—
469C22×Dic17—41no—
470C22×Dic17—41no—
471C22×Dic17—41no—
472C22×Dic17—41no—
473C22×Dic17—41no—
474C22×Dic17—41no—
475C22×Dic17—41no—
476C22×Dic17C22×C414yes—
477C22×Dic17C22×C414yes—
478C22×Dic17C2411yescharacteristic
479C22×Dic17C2411yescharacteristic
480C22×Dic17C2411yescharacteristic
481C22×Dic17C2411yescharacteristic
482C22×Dic17C2411yescharacteristic
483C22×Dic17C2411yescharacteristic
484C22×Dic17C2411yescharacteristic
485C22×Dic17C2411yescharacteristic
486C22×Dic17C2411yescharacteristic
487C22×Dic17C2411yescharacteristic
488C22×Dic17C2411yescharacteristic
489C22×Dic17C2411yescharacteristic
490C22×Dic17C2411yescharacteristic
491#63254—416no—
492C2×D68—41no—
493C2×D68—41no—
494C2×D68—41no—
495C2×D68—41no—
496C2×D68C22×C414yes—
497C2×D68C22×C414yes—
498C2×C4×D17—22no—
499C2×C4×D17—22no—
500C2×C4×D17—22no—
501C2×C4×D17—22no—
502C2×C4×D17—41no—
503C2×C4×D17—41no—
504C2×C4×D17—41no—
505C2×C4×D17—41no—
506C2×C4×D17—41no—
507C2×C4×D17—41no—
508C2×C4×D17—41no—
509C2×C4×D17—41no—
510C2×C4×D17—41no—
511C2×C4×D17—41no—
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×D17C22×C414yes—
519C2×Dic34—41no—
520C2×Dic34—41no—
521C2×Dic34C22×C414yes—
522C4⋊C4×C17—41no—
523C4⋊C4×C17—41no—
524C4⋊C4×C17—41no—
525C22⋊C4×C17—22no—
526C22⋊C4×C17—22no—
527C22⋊C4×C17—41no—
528C22⋊C4×C17—41no—
529C22⋊C4×C17—41no—
530C22⋊C4×C17—41no—
531C22⋊C4×C17—41no—
532C22⋊C4×C17—41no—
533C22⋊C4×C17—41no—
534C22⋊C4×C17—41no—
535C22⋊C4×C17—41no—
536C22⋊C4×C17—41no—
537C22⋊C4×C17—41no—
538C22⋊C4×C17C22×C414yes—
539C22⋊C4×C17C22×C414yes—
540C22⋊C4×C17C22×C414yes—
541C42×C17—22no—
542C42×C17—41no—
543C42×C17—41no—
544C22⋊Dic17—22no—
545C22⋊Dic17—22no—
546C22⋊Dic17—41no—
547C22⋊Dic17—41no—
548C22⋊Dic17—41no—
549C22⋊Dic17—41no—
550C22⋊Dic17—41no—
551C22⋊Dic17—41no—
552C22⋊Dic17—41no—
553C22⋊Dic17—41no—
554C22⋊Dic17—41no—
555C22⋊Dic17—41no—
556C22⋊Dic17—41no—
557C22⋊Dic17C22×C414yes—
558C22⋊Dic17C22×C414yes—
559C22⋊Dic17C22×C414yes—
560#63227—22no—
561#63227—22no—
562#63227—22no—
563#63227—22no—
564#63227—41no—
565#63227—41no—
566#63227—41no—
567#63227—41no—
568#63227—41no—
569#63227—41no—
570#63227—41no—
571#63227—41no—
572#63227—41no—
573#63227—41no—
574#63227—41no—
575#63227—41no—
576#63227—41no—
577#63227—41no—
578#63227C22×C414yes—
579#63227C22×C414yes—
580#63227C22×C414yes—
581#63227C22×C414yes—
582C4⋊Dic17—41no—
583C4⋊Dic17—41no—
584C4⋊Dic17—41no—
585#63225—22no—
586#63225—22no—
587#63225—22no—
588#63225—22no—
589#63225—41no—
590#63225—41no—
591#63225—41no—
592#63225—41no—
593#63225—41no—
594#63225—41no—
595#63225C22×C414yes—
596#63225C22×C414yes—
597C4×Dic17—22no—
598C4×Dic17—22no—
599C4×Dic17—22no—
600C4×Dic17—22no—
601C4×Dic17—22no—
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×Dic17C22×C414yes—
611C4×Dic17C22×C414yes—
612#34415—171nomaximal, Sylow
613C23×C17—21no—
614C23×C17—21no—
615C23×C17—21no—
616C23×C17—21no—
617C23×C17—21no—
618C23×C17—21no—
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—82no—
641C23×C17—82no—
642C23×C17—82no—
643C23×C17—82no—
644C23×C17C23×C412yes—
645C23×C17C23×C412yes—
646C23×C17C23×C412yes—
647C23×C17C23×C412yes—
648C23×C17C2511yescharacteristic
649C22×D17—21no—
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—44no—
668C22×D17—44no—
669C22×D17—44no—
670C22×D17—82no—
671C22×D17—82no—
672C22×D17—82no—
673C22×D17—82no—
674C22×D17C23×C412yes—
675C22×D17C23×C412yes—
676C22×D17C23×C412yes—
677D4×C17—44no—
678D4×C17—44no—
679D4×C17—44no—
680C2×C4×C17—21no—
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—44no—
710C2×C4×C17—82no—
711C2×C4×C17—82no—
712C2×C4×C17C23×C412yes—
713C2×C4×C17C23×C412yes—
714C2×C4×C17C23×C412yes—
715C2×C4×C17H(5,𝔽2)12yes—
716C22⋊D17—28no—
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—
726C2×Dic17—21no—
727C2×Dic17—21no—
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—28no—
737C2×Dic17—28no—
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—44no—
760C2×Dic17—82no—
761C2×Dic17—82no—
762C2×Dic17C23×C412yes—
763C2×Dic17C23×C412yes—
764C2×Dic17C23×C412yes—
765C2×Dic17C23×C412yes—
766C2×Dic17C23×C412yes—
767C2×Dic17H(5,𝔽2)12yes—
768C2×Dic17H(5,𝔽2)12yes—
769C2×Dic17H(5,𝔽2)12yes—
770D68—44no—
771D68—44no—
772C4×D17—28no—
773C4×D17—82no—
774C4×D17—82no—
775C4×D17—82no—
776C4×D17—82no—
777C4×D17—82no—
778C4×D17—82no—
779Dic34—44no—
780C2×#535—171no—
781#2379—171no—
782#2379—171no—
783#2375—171no—
784#2375—171no—
785#2372—171no—
786#2372—171no—
787#2363—171no—
788#2363—171no—
789#2361—171no—
790#2361—171no—
791#2358—171no—
792#2358—171no—
793#2346—171no—
794#2346—171no—
795D4×C22⋊C4—171no—
796D4×C22⋊C4—171no—
797#2328—171no—
798#2328—171no—
799#2328—171no—
800#2328—171no—
801#2324—171no—
802#2324—171no—
803#2321—171no—
804#2321—171no—
805#2321—171no—
806#2321D1711yescharacteristic, complemented
807#2311—171no—
808C4×#121—171no—
809C4×#121—171no—
810#2297—171no—
811C22×C17—22no—
812C22×C17—22no—
813C22×C17—22no—
814C22×C17—22no—
815C22×C17—22no—
816C22×C17—22no—
817C22×C17—22no—
818C22×C17—22no—
819C22×C17—22no—
820C22×C17—22no—
821C22×C17—22no—
822C22×C17—22no—
823C22×C17—41no—
824C22×C17—41no—
825C22×C17—41no—
826C22×C17—41no—
827C22×C17—41no—
828C22×C17—41no—
829C22×C17—41no—
830C22×C17—41no—
831C22×C17—41no—
832C22×C17—41no—
833C22×C17—41no—
834C22×C17—41no—
835C22×C17—41no—
836C22×C17—41no—
837C22×C17—41no—
838C22×C17—41no—
839C22×C17—88no—
840C22×C17C24×C411yescharacteristic
841C22×C17C2×H(5,𝔽2)11yescharacteristic
842C22×C17C2×H(5,𝔽2)11yescharacteristic
843C22×C17C2×H(5,𝔽2)11yescharacteristic
844C22×C17C2×H(5,𝔽2)11yescharacteristic
845C22×C17#58511yescharacteristic
846C22×C17#58511yescharacteristic
847C2×D17—22no—
848C2×D17—22no—
849C2×D17—22no—
850C2×D17—22no—
851C2×D17—22no—
852C2×D17—22no—
853C2×D17—22no—
854C2×D17—22no—
855C2×D17—22no—
856C2×D17—41no—
857C2×D17—41no—
858C2×D17—41no—
859C2×D17—41no—
860C2×D17—41no—
861C2×D17—41no—
862C2×D17—41no—
863C2×D17—41no—
864C2×D17—41no—
865C2×D17—41no—
866C2×D17—41no—
867C2×D17—41no—
868C2×D17—88no—
869C4×C17—22no—
870C4×C17—22no—
871C4×C17—22no—
872C4×C17—22no—
873C4×C17—41no—
874C4×C17—41no—
875C4×C17—41no—
876C4×C17—41no—
877C4×C17—41no—
878C4×C17—41no—
879C4×C17—41no—
880Dic17—22no—
881Dic17—22no—
882Dic17—22no—
883Dic17—22no—
884Dic17—22no—
885Dic17—41no—
886Dic17—41no—
887Dic17—41no—
888Dic17—41no—
889Dic17—41no—
890Dic17—41no—
891Dic17—41no—
892Dic17#51814yes—
893C22×#41—171no—
894C23×D4—171no—
895#535—1716no—
896C2×#127—171no—
897C2×#127—171no—
898C2×#124—171no—
899C2×#124—171no—
900C2×#121—171no—
901C2×#121—171no—
902C2×#121—171no—
903C2×#121—171no—
904C2×#120—171no—
905C2×#120—171no—
906C2×#120—171no—
907C2×#120C2×D1711yescharacteristic
908C2×C4×D4—171no—
909C2×C4×D4—171no—
910C2×C4×D4—171no—
911C2×C4×D4—171no—
912C2×C4×D4—171no—
913C2×C4×D4—171no—
914C2×C4×D4—171no—
915C2×C4×D4—171no—
916C2×C4×D4—171no—
917C2×C4×D4—171no—
918C2×C4×D4—171no—
919C2×C4×D4C2×D1711yescharacteristic, complemented
920C2×#117—171no—
921C2×#117—171no—
922C2×#117—171no—
923C22×C4⋊C4—171no—
924C22×C22⋊C4—171no—
925C22×C22⋊C4—171no—
926C22×C22⋊C4—171no—
927C22×C22⋊C4C2×D1711yescharacteristic
928C22×C42—171no—
929#391—171no—
930#391—171no—
931#391—171no—
932#391—171no—
933#390—171no—
934#390—171no—
935#390—171no—
936#390—171no—
937#390—171no—
938#390—171no—
939#390—171no—
940#390—171no—
941#390—171no—
942#390—171no—
943#390—171no—
944#390—171no—
945#390—171no—
946#390—171no—
947#390C2×D1711yescharacteristic
948#390C2×D1711yescharacteristic, complemented
949#389—171no—
950#389—171no—
951#389—171no—
952#389—171no—
953#388—171no—
954#388—171no—
955#388—171no—
956#388—171no—
957#388—171no—
958#388—171no—
959#388—171no—
960#388—171no—
961#388—171no—
962#388—171no—
963#388—171no—
964#388—171no—
965#388—171no—
966#388—171no—
967#388—171no—
968#388—171no—
969#388—171no—
970#388—171no—
971#388—171no—
972#388—171no—
973#388C2×D1711yescharacteristic
974#388C2×D1711yescharacteristic
975#388C2×D1711yescharacteristic, complemented
976#388C2×D1711yescharacteristic, complemented
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#386—171no—
1006#386C2×D1711yescharacteristic
1007#386C2×D1711yescharacteristic, complemented
1008#386C2×D1711yescharacteristic, complemented
1009#385—171no—
1010#385—171no—
1011#385—171no—
1012#385—171no—
1013#385—171no—
1014#385—171no—
1015#385—171no—
1016#385C2×D1711yescharacteristic, complemented
1017#382—171no—
1018#382—171no—
1019#382—171no—
1020#382—171no—
1021#380—171no—
1022#380—171no—
1023#380—171no—
1024#380—171no—
1025#379—171no—
1026#379—171no—
1027#379—171no—
1028#379C2×D1711yescharacteristic
1029C4×C4⋊C4—171no—
1030C4×C4⋊C4—171no—
1031C4×C4⋊C4—171no—
1032C4×C4⋊C4—171no—
1033C4×C22⋊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⋊C4C2×D1711yescharacteristic, complemented
1045#376—171no—
1046#376—171no—
1047#376—171no—
1048#376—171no—
1049C2×C17—42no—
1050C2×C17—42no—
1051C2×C17—42no—
1052C2×C17—42no—
1053C2×C17C2×#51811yescharacteristic
1054C2×C17C4×H(5,𝔽2)11yescharacteristic
1055C2×C17C4×H(5,𝔽2)11yescharacteristic
1056C2×C17#354211yescharacteristic
1057C2×C17#354211yescharacteristic
1058C2×C17#354911yescharacteristic
1059C2×C17#355111yescharacteristic
1060D17—42no—
1061D17—42no—
1062D17—42no—
1063C25—171no—
1064C25C22×D1711yescharacteristic
1065C2×#41—178no—
1066C2×#41—682no—
1067C2×#41—682no—
1068C22×Q8—171no—
1069C22×D4—171no—
1070C22×D4—171no—
1071C22×D4—178no—
1072C22×D4—171no—
1073C22×D4—171no—
1074C22×D4—171no—
1075C22×D4—171no—
1076C22×D4—171no—
1077C22×D4—171no—
1078C22×D4—171no—
1079C22×D4—171no—
1080C22×D4—171no—
1081C22×D4—171no—
1082C22×D4—682no—
1083C22×D4—682no—
1084C22×D4C22×D1711yescharacteristic
1085C22×D4C22×D1711yescharacteristic
1086C22×D4C22×D1711yescharacteristic
1087C23×C4—171no—
1088C23×C4—171no—
1089C23×C4—171no—
1090C23×C4—171no—
1091C23×C4—171no—
1092C23×C4—171no—
1093C23×C4—171no—
1094C23×C4—171no—
1095C23×C4—171no—
1096C23×C4—171no—
1097C23×C4—171no—
1098C23×C4—171no—
1099C23×C4C22×D1711yescharacteristic
1100C23×C4C22×D1711yescharacteristic
1101C23×C4C22×D1711yescharacteristic
1102#127—178no—
1103#127—178no—
1104#124—178no—
1105#124—178no—
1106#121—178no—
1107#121—178no—
1108#121—178no—
1109#121—178no—
1110#120—178no—
1111#120—178no—
1112#120—178no—
1113#120C4×D1718yescomplemented
1114C4×D4—42no—
1115C4×D4—682no—
1116C4×D4—682no—
1117C4×D4—682no—
1118C4×D4—682no—
1119C4×D4—682no—
1120C4×D4—682no—
1121C4×D4—682no—
1122C4×D4—682no—
1123C4×D4—682no—
1124C4×D4—682no—
1125C4×D4—682no—
1126#117—178no—
1127#117—682no—
1128#117—682no—
1129C2×C4⋊C4—171no—
1130C2×C4⋊C4—171no—
1131C2×C4⋊C4—171no—
1132C2×C4⋊C4—171no—
1133C2×C4⋊C4—171no—
1134C2×C4⋊C4—171no—
1135C2×C4⋊C4—171no—
1136C2×C4⋊C4—171no—
1137C2×C4⋊C4—171no—
1138C2×C4⋊C4—171no—
1139C2×C4⋊C4—171no—
1140C2×C4⋊C4—171no—
1141C2×C4⋊C4—171no—
1142C2×C4⋊C4—171no—
1143C2×C4⋊C4—171no—
1144C2×C4⋊C4—682no—
1145C2×C4⋊C4C22×D1711yescharacteristic
1146C2×C4⋊C4C22×D1711yescharacteristic
1147C2×C4⋊C4C22×D1711yescharacteristic
1148C2×C22⋊C4—42no—
1149C2×C22⋊C4—171no—
1150C2×C22⋊C4—171no—
1151C2×C22⋊C4—171no—
1152C2×C22⋊C4—171no—
1153C2×C22⋊C4—171no—
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—682no—
1188C2×C22⋊C4—682no—
1189C2×C22⋊C4—682no—
1190C2×C22⋊C4C22×D1711yescharacteristic
1191C2×C22⋊C4C22×D1711yescharacteristic
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×C42—171no—
1207C2×C42—171no—
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×C42—171no—
1220C2×C42—171no—
1221C2×C42—682no—
1222C2×C42C22×D1711yescharacteristic
1223C2×C42C22×D1711yescharacteristic
1224C2×C42C22×D1711yescharacteristic
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#95C22×D1711yescharacteristic
1252#95C22×D1711yescharacteristic
1253#95C22×D1711yescharacteristic
1254#95C22×D1711yescharacteristic
1255#95C22×D1711yescharacteristic
1256#95C22×D1711yescharacteristic
1257C17#3441511yescharacteristic, complemented, Sylow
1258C24—41no—
1259C24—41no—
1260C24—41no—
1261C24—41no—
1262C24—41no—
1263C24—41no—
1264C24—171no—
1265C24—171no—
1266C24—171no—
1267C24—174no—
1268C24—681no—
1269C24—681no—
1270C24—681no—
1271C24—681no—
1272C24—681no—
1273C24—681no—
1274C24C2×C4×D1714yes—
1275C24C23×D1711yescharacteristic
1276C24C23×D1711yescharacteristic
1277C24C23×D1711yescharacteristic
1278C24C23×D1711yescharacteristic
1279#41—6816no—
1280C2×Q8—174no—
1281C2×Q8—681no—
1282C2×Q8—681no—
1283C2×D4—41no—
1284C2×D4—41no—
1285C2×D4—41no—
1286C2×D4—41no—
1287C2×D4—41no—
1288C2×D4—41no—
1289C2×D4—174no—
1290C2×D4—174no—
1291C2×D4—174no—
1292C2×D4—174no—
1293C2×D4—174no—
1294C2×D4—174no—
1295C2×D4—174no—
1296C2×D4—174no—
1297C2×D4—174no—
1298C2×D4—174no—
1299C2×D4—174no—
1300C2×D4—174no—
1301C2×D4—342no—
1302C2×D4—342no—
1303C2×D4—342no—
1304C2×D4—342no—
1305C2×D4—681no—
1306C2×D4—681no—
1307C2×D4—681no—
1308C2×D4—681no—
1309C2×D4—6816no—
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—681no—
1321C2×D4—681no—
1322C2×D4—681no—
1323C2×D4—681no—
1324C2×D4—681no—
1325C2×D4—681no—
1326C2×D4C2×C4×D1714yes—
1327C2×D4C2×C4×D1714yes—
1328C2×D4C2×C4×D1714yes—
1329C22×C4—22no—
1330C22×C4—22no—
1331C22×C4—41no—
1332C22×C4—41no—
1333C22×C4—41no—
1334C22×C4—41no—
1335C22×C4—41no—
1336C22×C4—41no—
1337C22×C4—41no—
1338C22×C4—171no—
1339C22×C4—174no—
1340C22×C4—174no—
1341C22×C4—171no—
1342C22×C4—171no—
1343C22×C4—171no—
1344C22×C4—171no—
1345C22×C4—171no—
1346C22×C4—174no—
1347C22×C4—171no—
1348C22×C4—171no—
1349C22×C4—171no—
1350C22×C4—171no—
1351C22×C4—171no—
1352C22×C4—171no—
1353C22×C4—171no—
1354C22×C4—342no—
1355C22×C4—342no—
1356C22×C4—342no—
1357C22×C4—342no—
1358C22×C4—342no—
1359C22×C4—342no—
1360C22×C4—342no—
1361C22×C4—342no—
1362C22×C4—342no—
1363C22×C4—342no—
1364C22×C4—681no—
1365C22×C4—681no—
1366C22×C4—681no—
1367C22×C4—681no—
1368C22×C4—681no—
1369C22×C4—681no—
1370C22×C4—681no—
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×C4C23×D1711yescharacteristic
1388C22×C4C23×D1711yescharacteristic
1389C22×C4C23×D1711yescharacteristic
1390C22×C4C23×D1711yescharacteristic
1391C22×C4C23×D1711yescharacteristic
1392C22×C4C23×D1711yescharacteristic
1393C22×C4C23×D1711yescharacteristic
1394C22×C4C23×D1711yescharacteristic
1395C22×C4C23×D1711yescharacteristic
1396C22×C4C23×D1711yescharacteristic
1397C22×C4C23×D1711yescharacteristic
1398C4⋊C4—41no—
1399C4⋊C4—41no—
1400C4⋊C4—41no—
1401C4⋊C4—174no—
1402C4⋊C4—174no—
1403C4⋊C4—342no—
1404C4⋊C4—342no—
1405C4⋊C4—342no—
1406C4⋊C4—342no—
1407C4⋊C4—681no—
1408C4⋊C4—681no—
1409C4⋊C4—681no—
1410C4⋊C4—681no—
1411C4⋊C4—681no—
1412C4⋊C4—681no—
1413C4⋊C4—681no—
1414C4⋊C4—681no—
1415C4⋊C4—681no—
1416C22⋊C4—22no—
1417C22⋊C4—22no—
1418C22⋊C4—41no—
1419C22⋊C4—41no—
1420C22⋊C4—41no—
1421C22⋊C4—41no—
1422C22⋊C4—41no—
1423C22⋊C4—41no—
1424C22⋊C4—41no—
1425C22⋊C4—41no—
1426C22⋊C4—41no—
1427C22⋊C4—41no—
1428C22⋊C4—41no—
1429C22⋊C4—174no—
1430C22⋊C4—174no—
1431C22⋊C4—174no—
1432C22⋊C4—174no—
1433C22⋊C4—174no—
1434C22⋊C4—174no—
1435C22⋊C4—174no—
1436C22⋊C4—342no—
1437C22⋊C4—342no—
1438C22⋊C4—342no—
1439C22⋊C4—342no—
1440C22⋊C4—342no—
1441C22⋊C4—342no—
1442C22⋊C4—681no—
1443C22⋊C4—681no—
1444C22⋊C4—681no—
1445C22⋊C4—681no—
1446C22⋊C4—681no—
1447C22⋊C4—681no—
1448C22⋊C4—681no—
1449C22⋊C4—681no—
1450C22⋊C4—681no—
1451C22⋊C4—681no—
1452C22⋊C4—681no—
1453C22⋊C4—681no—
1454C22⋊C4—681no—
1455C22⋊C4—681no—
1456C22⋊C4—681no—
1457C22⋊C4—681no—
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⋊C4C2×C4×D1714yes—
1468C22⋊C4C2×C4×D1714yes—
1469C22⋊C4C2×C4×D1714yes—
1470C42—22no—
1471C42—41no—
1472C42—41no—
1473C42—174no—
1474C42—174no—
1475C42—342no—
1476C42—342no—
1477C42—342no—
1478C42—342no—
1479C42—342no—
1480C42—342no—
1481C42—342no—
1482C42—681no—
1483C42—681no—
1484C42—681no—
1485C42—681no—
1486C42—681no—
1487C42—681no—
1488C23—21no—
1489C23—21no—
1490C23—21no—
1491C23—21no—
1492C23—21no—
1493C23—21no—
1494C23—21no—
1495C23—21no—
1496C23—21no—
1497C23—21no—
1498C23—21no—
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—44no—
1513C23—44no—
1514C23—44no—
1515C23—82no—
1516C23—82no—
1517C23—82no—
1518C23—82no—
1519C23—172no—
1520C23—172no—
1521C23—172no—
1522C23—341no—
1523C23—341no—
1524C23—341no—
1525C23—341no—
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—684no—
1541C23—684no—
1542C23—684no—
1543C23—1362no—
1544C23—1362no—
1545C23—1362no—
1546C23—1362no—
1547C23C22×C4×D1712yes—
1548C23C22×C4×D1712yes—
1549C23C22×C4×D1712yes—
1550C23C22×C4×D1712yes—
1551C23C24×D1711yescharacteristic
1552Q8—684no—
1553D4—44no—
1554D4—44no—
1555D4—44no—
1556D4—348no—
1557D4—348no—
1558D4—684no—
1559D4—684no—
1560D4—684no—
1561D4—684no—
1562D4—684no—
1563D4—684no—
1564D4—684no—
1565D4—684no—
1566D4—684no—
1567D4—684no—
1568C2×C4—21no—
1569C2×C4—21no—
1570C2×C4—21no—
1571C2×C4—21no—
1572C2×C4—21no—
1573C2×C4—21no—
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—44no—
1598C2×C4—82no—
1599C2×C4—82no—
1600C2×C4—172no—
1601C2×C4—172no—
1602C2×C4—172no—
1603C2×C4—172no—
1604C2×C4—172no—
1605C2×C4—172no—
1606C2×C4—172no—
1607C2×C4—172no—
1608C2×C4—348no—
1609C2×C4—348no—
1610C2×C4—348no—
1611C2×C4—341no—
1612C2×C4—341no—
1613C2×C4—341no—
1614C2×C4—341no—
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—684no—
1643C2×C4—1362no—
1644C2×C4—1362no—
1645C2×C4—1362no—
1646C2×C4—1362no—
1647C2×C4—1362no—
1648C2×C4—1362no—
1649C2×C4—1362no—
1650C2×C4—1362no—
1651C2×C4C22×C4×D1712yes—
1652C2×C4C22×C4×D1712yes—
1653C2×C4C22×C4×D1712yes—
1654C2×C4#1058769112yes—
1655C22—22no—
1656C22—22no—
1657C22—22no—
1658C22—22no—
1659C22—22no—
1660C22—22no—
1661C22—22no—
1662C22—22no—
1663C22—22no—
1664C22—22no—
1665C22—22no—
1666C22—22no—
1667C22—41no—
1668C22—41no—
1669C22—41no—
1670C22—41no—
1671C22—41no—
1672C22—41no—
1673C22—41no—
1674C22—41no—
1675C22—41no—
1676C22—41no—
1677C22—41no—
1678C22—41no—
1679C22—41no—
1680C22—41no—
1681C22—41no—
1682C22—41no—
1683C22—88no—
1684C22—342no—
1685C22—342no—
1686C22—342no—
1687C22—342no—
1688C22—342no—
1689C22—342no—
1690C22—342no—
1691C22—342no—
1692C22—342no—
1693C22—681no—
1694C22—681no—
1695C22—681no—
1696C22—681no—
1697C22—681no—
1698C22—681no—
1699C22—681no—
1700C22—681no—
1701C22—681no—
1702C22—681no—
1703C22—681no—
1704C22—681no—
1705C22—1368no—
1706C22C23×C4×D1711yescharacteristic
1707C22H(5,𝔽2)×D1711yescharacteristic
1708C22H(5,𝔽2)×D1711yescharacteristic
1709C22H(5,𝔽2)×D1711yescharacteristic
1710C22C2×#1058769111yescharacteristic
1711C22#1176364411yescharacteristic
1712C22#1176364511yescharacteristic
1713C4—22no—
1714C4—22no—
1715C4—22no—
1716C4—22no—
1717C4—41no—
1718C4—41no—
1719C4—41no—
1720C4—41no—
1721C4—41no—
1722C4—41no—
1723C4—41no—
1724C4—174no—
1725C4—342no—
1726C4—342no—
1727C4—342no—
1728C4—342no—
1729C4—342no—
1730C4—681no—
1731C4—681no—
1732C4—681no—
1733C4—681no—
1734C4—681no—
1735C4—681no—
1736C4—681no—
1737C2—42no—
1738C2—42no—
1739C2—42no—
1740C2—42no—
1741C2—682no—
1742C2—682no—
1743C2—682no—
1744C2D17×#51811yescharacteristic
1745C2#1454198811yescharacteristic
1746C2C4×#1058769111yescharacteristic
1747C2#1454309511yescharacteristic
1748C2#1454309911yescharacteristic
1749C2#1454318711yescharacteristic
1750C2#1454320111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2321C2
socle, cosocleC23×C17C25
prime radicalC2×#11763374C2
hypercenter#2321D17
hypocenterC17#34415
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2321

Complements

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

NH ≅ G/Ntype
2. #14531957C2semidirect
3. #14531953C2semidirect
4. #14531924C2semidirect
5. #14531923C2semidirect
6. #14531892C2semidirect
7. #14531891C2semidirect
8. #14531823C2semidirect
9. #14531817C2semidirect
10. #14531803C2semidirect
11. #14531797C2semidirect
12. #14531763C2semidirect
13. #14531762C2semidirect
14. #14531666C2semidirect
15. #14531666C2semidirect
16. C22⋊C4×C22⋊D17C2semidirect
17. #14531600C2semidirect
18. #14531508C2semidirect
19. #14531506C2semidirect
20. #14531505C2semidirect
21. #14531505C2semidirect
22. #14531474C2semidirect
23. #14531470C2semidirect
24. #14531445C2semidirect
25. #14531443C2semidirect
26. #14531440C2semidirect
27. #14531374C2semidirect
28. #14531294C2semidirect
29. C4×#10587625C2semidirect
30. #14531269C2semidirect
31. C17×#2321C2semidirect
34. #11763374C4semidirect
46. C2×C4×D68C22semidirect
47. C2×D4×Dic17C22semidirect
48. C2×#10587579C22semidirect
51. C2×C4×C22⋊D17C22semidirect
52. C2×C4×C22⋊D17C22semidirect
55. C2×#10587567C22semidirect
56. C2×#10587567C22semidirect
57. C2×#10587558C22semidirect
59. C2×#10587563C22semidirect
60. C2×C4⋊C4×D17C22semidirect
64. C22×C4×Dic17C22semidirect
65. #11762715C22semidirect
66. #11762714C22semidirect
67. #11762713C22semidirect
68. #11762713C22semidirect
70. #11762712C22semidirect
71. #11762711C22semidirect
72. #11762710C22semidirect
79. #11762709C22semidirect
80. #11762709C22semidirect
81. #11762709C22semidirect
82. #11762709C22semidirect
83. #11762706C22semidirect
84. #11762706C22semidirect
85. #11762704C22semidirect
86. #11762704C22semidirect
89. #11762703C22semidirect
90. #11762703C22semidirect
93. #11762702C22semidirect
94. #11762702C22semidirect
95. #11762701C22semidirect
96. #11762701C22semidirect
97. #11762700C22semidirect
98. #11762700C22semidirect
99. #11762699C22semidirect
100. #11762699C22semidirect
101. #11762698C22semidirect
102. #11762698C22semidirect
105. #11762697C22semidirect
106. #11762697C22semidirect
108. #11762689C22semidirect
109. #11762689C22semidirect
112. #11762688C22semidirect
113. #11762688C22semidirect
114. #11762688C22semidirect
115. #11762687C22semidirect
116. #11762687C22semidirect
117. #11762687C22semidirect
118. #11762687C22semidirect
121. #11762686C22semidirect
122. #11762686C22semidirect
123. #11762686C22semidirect
130. #11762685C22semidirect
131. #11762685C22semidirect
132. #11762685C22semidirect
133. #11762685C22semidirect
134. #11762685C22semidirect
135. #11762685C22semidirect
136. #11762684C22semidirect
137. #11762683C22semidirect
138. #11762683C22semidirect
139. #11762682C22semidirect
140. #11762681C22semidirect
141. #11762680C22semidirect
142. #11762680C22semidirect
143. #11762674C22semidirect
144. #11762674C22semidirect
145. #11762673C22semidirect
146. #11762673C22semidirect
149. #11762667C22semidirect
150. #11762667C22semidirect
154. C4×#63225C22semidirect
155. C4×#63225C22semidirect
156. #11762660C22semidirect
157. #11762660C22semidirect
160. C22⋊C4×Dic17C22semidirect
161. C22⋊C4×Dic17C22semidirect
162. C4×#63227C22semidirect
163. C4×#63227C22semidirect
164. C4×C22⋊Dic17C22semidirect
165. #11762656C22semidirect
166. #11762656C22semidirect
167. #11762656C22semidirect
168. #11762656C22semidirect
169. #11762655C22semidirect
170. #11762655C22semidirect
171. #11762654C22semidirect
172. #11762654C22semidirect
174. C2×C4×D4×C17C22semidirect
177. C17×#390C22semidirect
180. C17×#388C22semidirect
181. C17×#388C22semidirect
183. C17×#386C22semidirect
184. C17×#386C22semidirect
185. C17×#385C22semidirect
187. C4×C22⋊C4×C17C22semidirect
198. C22×C22⋊D17C2×C4semidirect
216. C2×#63254C2×C4semidirect
227. C17×#120C2×C4semidirect
252. #10587639C2×C4semidirect
270. #10587626C2×C4semidirect
271. #10587626C2×C4semidirect
272. #10587625C2×C4semidirect
273. #10587625C2×C4semidirect
274. #10587623C2×C4semidirect
335. #10587571C2×C4semidirect
336. #10587571C2×C4semidirect
337. #10587570C2×C4semidirect
338. #10587570C2×C4semidirect
339. #10587568C2×C4semidirect
347. #10587563C2×C4semidirect
806. #2321D17semidirect
919. C2×C4×D4C2×D17semidirect
948. #390C2×D17semidirect
975. #388C2×D17semidirect
976. #388C2×D17semidirect
1007. #386C2×D17semidirect
1008. #386C2×D17semidirect
1016. #385C2×D17semidirect
1044. C4×C22⋊C4C2×D17semidirect
1113. #120C4×D17semidirect
1257. C17#34415semidirect

Maximal subgroups

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

subgroupindex
C2×#117633742
#145319572
#145319532
#145319242
#145319232
#145318922
#145318912
#145318232
#145318172
#145318032
#145317972
#145317632
#145317622
#145316662
C22⋊C4×C22⋊D172
#145316002
#145315082
#145315062
#145315052
#145314742
#145314702
#145314452
#145314432
#145314402
#145313742
#145312942
C4×#105876252
#145312692
C17×#23212
#3441517