Finite Group Databasebeta

← #17200261

Subgroups — #17200261

Order 4352.

2464 conjugacy classes of subgroups.

The subgroup lattice has 1654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763547C211yesmaximal, characteristic
2#14531937C211yesmaximal, characteristic, complemented
3#14531936C211yesmaximal, characteristic, complemented
4#14531931C211yesmaximal, characteristic, complemented
5#14531906C211yesmaximal, characteristic, complemented
6#14531903C211yesmaximal, characteristic, complemented
7#14531846C211yesmaximal, characteristic, complemented
8#14531832C211yesmaximal, characteristic, complemented
9#14531825C211yesmaximal, characteristic, complemented
10#14531820C211yesmaximal, characteristic, complemented
11#14531778C211yesmaximal, characteristic, complemented
12#14531772C211yesmaximal, characteristic, complemented
13#14531764C211yesmaximal, characteristic, complemented
14#14531762C211yesmaximal, characteristic, complemented
15#14531761C211yesmaximal, characteristic, complemented
16#14531579C211yesmaximal, characteristic, complemented
17#14531574C211yesmaximal, characteristic, complemented
18#14531565C211yesmaximal, characteristic, complemented
19#14531556C211yesmaximal, characteristic, complemented
20#14531505C211yesmaximal, characteristic, complemented
21#14531487C211yesmaximal, characteristic, complemented
22#14531482C211yesmaximal, characteristic, complemented
23#14531479C211yesmaximal, characteristic, complemented
24#14531474C211yesmaximal, characteristic, complemented
25#14531444C211yesmaximal, characteristic, complemented
26#14531440C211yesmaximal, characteristic, complemented
27#14531440C211yesmaximal, characteristic, complemented
28#14531305C211yesmaximal, characteristic, complemented
29C4×#10587570C211yesmaximal, characteristic, complemented
30C4×#10587624C211yesmaximal, characteristic, complemented
31C17×#2364C211yesmaximal, characteristic, complemented
32#11763547C4116yescomplemented
33C2×#10587626C2211yescharacteristic
34C2×#10587584C2211yescharacteristic
35C2×#10587565C2211yescharacteristic
36C2×#10587580C2211yescharacteristic
37C2×#10587572C2211yescharacteristic
38C2×#10587615C2211yescharacteristic
39C2×#10587616C2211yescharacteristic
40C2×#10587570C2211yescharacteristic
41C2×#10587625C2211yescharacteristic
42C2×#10587625C2211yescharacteristic
43C2×#10587624C2211yescharacteristic
44C2×#10587568C2211yescharacteristic
45C2×#10587623C2211yescharacteristic
46C2×#10587623C2211yescharacteristic
47C2×C4×D68C2211yescharacteristic
48C2×D4×Dic17C2211yescharacteristic
49C2×#10587579C2211yescharacteristic
50C2×C4×C22⋊D17C2211yescharacteristic
51C2×C4×C22⋊D17C2211yescharacteristic
52C2×C4×C22⋊D17C2211yescharacteristic
53C2×C4×C22⋊D17C2211yescharacteristic
54C2×C4×C22⋊D17C2211yescharacteristic, complemented
55C2×C4×C22⋊D17C2211yescharacteristic, complemented
56C2×#10587567C2211yescharacteristic
57C2×#10587612C2211yescharacteristic, complemented
58C2×#10587563C2211yescharacteristic, complemented
59C22×#63227C2211yescharacteristic
60C2×C22⋊C4×D17C2211yescharacteristic
61C2×C22⋊C4×D17C2211yescharacteristic
62C2×C42×D17C2211yescharacteristic, complemented
63#11762712C2211yescharacteristic
64#11762712C2211yescharacteristic
65#11762712C2211yescharacteristic, complemented
66#11762711C2211yescharacteristic
67#11762711C2211yescharacteristic
68#11762709C2211yescharacteristic
69#11762709C2211yescharacteristic
70#11762709C2211yescharacteristic
71#11762709C2211yescharacteristic
72#11762709C2211yescharacteristic
73#11762709C2211yescharacteristic, complemented
74#11762709C2211yescharacteristic, complemented
75#11762708C2211yescharacteristic, complemented
76#11762707C2211yescharacteristic, complemented
77#11762706C2211yescharacteristic, complemented
78#11762706C2211yescharacteristic, complemented
79#11762706C2211yescharacteristic, complemented
80#11762705C2211yescharacteristic, complemented
81#11762703C2211yescharacteristic, complemented
82#11762702C2211yescharacteristic
83#11762702C2211yescharacteristic, complemented
84#11762701C2211yescharacteristic
85#11762701C2211yescharacteristic
86#11762701C2211yescharacteristic
87#11762701C2211yescharacteristic
88#11762701C2211yescharacteristic
89#11762701C2211yescharacteristic, complemented
90#11762700C2211yescharacteristic
91#11762700C2211yescharacteristic
92#11762700C2211yescharacteristic
93#11762699C2211yescharacteristic
94#11762698C2211yescharacteristic
95#11762698C2211yescharacteristic
96#11762698C2211yescharacteristic
97#11762698C2211yescharacteristic, complemented
98#11762697C2211yescharacteristic
99#11762697C2211yescharacteristic
100#11762697C2211yescharacteristic
101#11762697C2211yescharacteristic
102#11762697C2211yescharacteristic, complemented
103#11762696C2211yescharacteristic, complemented
104#11762696C2211yescharacteristic, complemented
105#11762694C2211yescharacteristic, complemented
106#11762694C2211yescharacteristic, complemented
107#11762694C2211yescharacteristic, complemented
108#11762693C2211yescharacteristic, complemented
109#11762693C2211yescharacteristic, complemented
110#11762692C2211yescharacteristic, complemented
111#11762691C2211yescharacteristic, complemented
112#11762690C2211yescharacteristic, complemented
113#11762689C2211yescharacteristic
114#11762689C2211yescharacteristic, complemented
115#11762688C2211yescharacteristic
116#11762688C2211yescharacteristic
117#11762688C2211yescharacteristic
118#11762688C2211yescharacteristic, complemented
119#11762687C2211yescharacteristic
120#11762687C2211yescharacteristic
121#11762687C2211yescharacteristic
122#11762687C2211yescharacteristic
123#11762686C2211yescharacteristic
124#11762686C2211yescharacteristic
125#11762686C2211yescharacteristic, complemented
126#11762685C2211yescharacteristic
127#11762685C2211yescharacteristic
128#11762685C2211yescharacteristic
129#11762685C2211yescharacteristic
130#11762685C2211yescharacteristic
131#11762685C2211yescharacteristic, complemented
132#11762685C2211yescharacteristic, complemented
133#11762684C2211yescharacteristic
134#11762684C2211yescharacteristic, complemented
135#11762683C2211yescharacteristic
136#11762683C2211yescharacteristic
137#11762683C2211yescharacteristic
138#11762683C2211yescharacteristic
139#11762683C2211yescharacteristic, complemented
140#11762682C2211yescharacteristic
141#11762682C2211yescharacteristic, complemented
142#11762681C2211yescharacteristic
143#11762680C2211yescharacteristic
144#11762680C2211yescharacteristic
145#11762673C2211yescharacteristic, complemented
146#11762671C2211yescharacteristic, complemented
147#11762669C2211yescharacteristic, complemented
148#11762668C2211yescharacteristic, complemented
149#11762667C2211yescharacteristic, complemented
150#11762666C2211yescharacteristic, complemented
151#11762664C2211yescharacteristic
152C4⋊C4×Dic17C2211yescharacteristic, complemented
153C4⋊C4×Dic17C2211yescharacteristic, complemented
154C4×#63225C2211yescharacteristic, complemented
155C4×#63225C2211yescharacteristic, complemented
156C4×C4⋊Dic17C2211yescharacteristic, complemented
157C4×C4⋊Dic17C2211yescharacteristic, complemented
158#11762660C2211yescharacteristic, complemented
159#11762660C2211yescharacteristic, complemented
160C22⋊C4×Dic17C2211yescharacteristic
161C22⋊C4×Dic17C2211yescharacteristic, complemented
162C4×#63227C2211yescharacteristic
163C4×#63227C2211yescharacteristic
164C4×C22⋊Dic17C2211yescharacteristic
165C4×C22⋊Dic17C2211yescharacteristic, complemented
166#11762656C2211yescharacteristic
167#11762656C2211yescharacteristic
168#11762656C2211yescharacteristic
169#11762656C2211yescharacteristic
170#11762656C2211yescharacteristic, complemented
171#11762654C2211yescharacteristic, complemented
172C2×#10587502C2211yescharacteristic, complemented
173C2×C17×#121C2211yescharacteristic
174C2×C4×D4×C17C2211yescharacteristic
175C2×C4×D4×C17C2211yescharacteristic, complemented
176C17×#388C2211yescharacteristic
177C17×#388C2211yescharacteristic, complemented
178C17×#387C2211yescharacteristic, complemented
179C17×#387C2211yescharacteristic, complemented
180C17×#386C2211yescharacteristic
181C17×#386C2211yescharacteristic
182C17×#386C2211yescharacteristic
183C17×#386C2211yescharacteristic, complemented
184C4×C22⋊C4×C17C2211yescharacteristic
185C4×C22⋊C4×C17C2211yescharacteristic, complemented
186C4×C22⋊C4×C17C2211yescharacteristic, complemented
187C2×C17×#95C2211yescharacteristic, complemented
188C24×D17C2311yescharacteristic
189C22×D4×C17C2311yescharacteristic
190C22×D4×C17C2311yescharacteristic
191C22×D4×C17C2311yescharacteristic
192C23×C4×C17C2311yescharacteristic
193C23×C4×C17C2311yescharacteristic
194C23×C4×C17C2311yescharacteristic
195C23×C4×C17C2311yescharacteristic
196C23×C4×C17C2311yescharacteristic
197C22×C22⋊D17C2311yescharacteristic
198C22×C22⋊D17C2311yescharacteristic
199C22×C22⋊D17C2311yescharacteristic
200C22×C22⋊D17C2311yescharacteristic
201C22×C22⋊D17C2311yescharacteristic
202C22×C22⋊D17C2311yescharacteristic
203C22×C22⋊D17C2311yescharacteristic
204C23×Dic17C2311yescharacteristic
205C23×Dic17C2311yescharacteristic
206C23×Dic17C2311yescharacteristic
207C22×D68C2311yescharacteristic
208C22×D68C2311yescharacteristic
209C22×C4×D17C2311yescharacteristic
210C22×C4×D17C2311yescharacteristic
211C22×C4×D17C2311yescharacteristic
212C22×C4×D17C2311yescharacteristic
213C22×C4×D17C2311yescharacteristic
214C22×C4×D17C2311yescharacteristic
215C22×C4×D17C2311yescharacteristic
216C17×#121C2×C418yescomplemented
217C4×D4×C17—42no—
218C4×D4×C17—42no—
219C2×C4⋊C4×C17C2311yescharacteristic
220C2×C4⋊C4×C17C2311yescharacteristic
221C2×C4⋊C4×C17C2311yescharacteristic
222C2×C22⋊C4×C17C2311yescharacteristic
223C2×C22⋊C4×C17C2311yescharacteristic
224C2×C22⋊C4×C17C2311yescharacteristic
225C2×C22⋊C4×C17C2311yescharacteristic
226C2×C22⋊C4×C17C2311yescharacteristic
227C2×C22⋊C4×C17C2311yescharacteristic
228C2×C22⋊C4×C17C2311yescharacteristic
229C2×C22⋊C4×C17C2311yescharacteristic
230C2×C22⋊C4×C17C2311yescharacteristic
231C2×C22⋊C4×C17C2311yescharacteristic
232C2×C42×C17C2311yescharacteristic
233C2×C42×C17C2311yescharacteristic
234C2×C42×C17C2311yescharacteristic
235C2×C42×C17C2311yescharacteristic
236C2×C22⋊Dic17C2311yescharacteristic
237C2×C22⋊Dic17C2311yescharacteristic
238C2×C22⋊Dic17C2311yescharacteristic
239C2×C22⋊Dic17C2311yescharacteristic
240C2×C22⋊Dic17C2311yescharacteristic
241C2×C22⋊Dic17C2311yescharacteristic
242C2×C22⋊Dic17C2311yescharacteristic
243C2×C22⋊Dic17C2311yescharacteristic
244C2×C22⋊Dic17C2311yescharacteristic
245C2×C22⋊Dic17C2311yescharacteristic
246C2×C22⋊Dic17C2311yescharacteristic
247C2×C22⋊Dic17C2311yescharacteristic
248C2×C22⋊Dic17C2311yescharacteristic
249#10587626C2×C418yescomplemented
250#10587625C2×C418yescomplemented
251#10587625C2×C418yescomplemented
252#10587624C2×C418yescomplemented
253#10587623C2×C418yescomplemented
254#10587623C2×C418yescomplemented
255D4×Dic17—42no—
256#10587616C2×C418yescomplemented
257#10587615C2×C418yescomplemented
258C4×C22⋊D17—42no—
259C4×C22⋊D17—42no—
260C4×C22⋊D17—42no—
261C4×C22⋊D17—42no—
262C4×C22⋊D17—42no—
263C4×C22⋊D17—42no—
264C2×#63227—42no—
265C2×#63227C2311yescharacteristic
266C2×#63227C2311yescharacteristic
267C2×#63227C2311yescharacteristic
268C2×#63227C2311yescharacteristic
269C2×#63227C2311yescharacteristic
270C2×#63227C2311yescharacteristic
271C2×#63227C2311yescharacteristic
272C2×#63227C2311yescharacteristic
273C2×#63227C2311yescharacteristic
274C2×#63227C2311yescharacteristic
275C2×#63227C2311yescharacteristic
276C2×#63227C2311yescharacteristic
277C2×#63227C2311yescharacteristic
278C2×#63227C2311yescharacteristic
279C2×#63227C2311yescharacteristic
280C2×#63227C2311yescharacteristic
281C2×#63227C2311yescharacteristic
282C2×#63227C2311yescharacteristic
283C2×#63227C2311yescharacteristic
284C2×#63227C2311yescharacteristic
285C2×#63227C2311yescharacteristic
286C2×#63227C2311yescharacteristic
287C2×#63227C2311yescharacteristic
288C2×#63227C2311yescharacteristic
289C2×#63227C2311yescharacteristic
290#10587612—42no—
291C2×C4⋊Dic17C2311yescharacteristic
292C2×C4⋊Dic17C2311yescharacteristic
293C2×C4⋊Dic17C2311yescharacteristic
294C2×C4⋊Dic17C2311yescharacteristic
295C2×C4⋊Dic17C2311yescharacteristic
296C2×C4⋊Dic17C2311yescharacteristic
297C2×C4⋊Dic17C2311yescharacteristic
298C2×C4⋊Dic17C2311yescharacteristic
299C2×#63225C2311yescharacteristic
300C2×#63225C2311yescharacteristic
301C2×#63225C2311yescharacteristic
302C2×#63225C2311yescharacteristic
303C2×#63225C2311yescharacteristic
304C2×#63225C2311yescharacteristic
305C2×#63225C2311yescharacteristic
306C2×#63225C2311yescharacteristic
307C2×#63225C2311yescharacteristic
308C2×#63225C2311yescharacteristic
309C2×#63225C2311yescharacteristic
310C2×#63225C2311yescharacteristic
311C2×#63225C2311yescharacteristic
312C2×C4×Dic17C2311yescharacteristic
313C2×C4×Dic17C2311yescharacteristic
314C2×C4×Dic17C2311yescharacteristic
315C2×C4×Dic17C2311yescharacteristic
316C2×C4×Dic17C2311yescharacteristic
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
327#10587584C2×C418yescomplemented
328#10587580C2×C418yescomplemented
329#10587579—42no—
330#10587572C2×C418yescomplemented
331#10587570C2×C418yescomplemented
332#10587568C2×C418yescomplemented
333#10587567—42no—
334C22⋊C4×D17—42no—
335C22⋊C4×D17—42no—
336#10587565C2×C418yescomplemented
337#10587563—42no—
338C4×D68—42no—
339C42×D17—42no—
340C17×#95C2311yescharacteristic
341C17×#95C2311yescharacteristic
342C17×#95C2311yescharacteristic
343C17×#95C2311yescharacteristic
344C17×#95C2311yescharacteristic
345C17×#95C2311yescharacteristic
346C17×#95C2311yescharacteristic
347C17×#95C2311yescharacteristic
348C17×#95C2311yescharacteristic
349C17×#95C2311yescharacteristic
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
376C24×C17C2411yescharacteristic
377C24×C17C2411yescharacteristic
378C24×C17C2411yescharacteristic
379C23×D17—41no—
380C23×D17—41no—
381C23×D17—41no—
382C23×D17—41no—
383C23×D17—41no—
384C23×D17—41no—
385C23×D17C22×C414yes—
386C23×D17C2411yescharacteristic
387C23×D17C2411yescharacteristic
388C23×D17C2411yescharacteristic
389C2×D4×C17—41no—
390C2×D4×C17—41no—
391C2×D4×C17—41no—
392C2×D4×C17—41no—
393C2×D4×C17—41no—
394C2×D4×C17—41no—
395C2×D4×C17C22×C414yes—
396C2×D4×C17C22×C414yes—
397C2×D4×C17C22×C414yes—
398C22×C4×C17—22no—
399C22×C4×C17—22no—
400C22×C4×C17—22no—
401C22×C4×C17—41no—
402C22×C4×C17—41no—
403C22×C4×C17—41no—
404C22×C4×C17—41no—
405C22×C4×C17—41no—
406C22×C4×C17—41no—
407C22×C4×C17—41no—
408C22×C4×C17—41no—
409C22×C4×C17—41no—
410C22×C4×C17—41no—
411C22×C4×C17—41no—
412C22×C4×C17C22×C414yes—
413C22×C4×C17C2411yescharacteristic
414C22×C4×C17C2411yescharacteristic
415C22×C4×C17C2411yescharacteristic
416C22×C4×C17C2411yescharacteristic
417C22×C4×C17C2411yescharacteristic
418C22×C4×C17C2411yescharacteristic
419C22×C4×C17C2411yescharacteristic
420C22×C4×C17C2411yescharacteristic
421C22×C4×C17C2411yescharacteristic
422C22×C4×C17C2411yescharacteristic
423C22×C4×C17C2411yescharacteristic
424C22×C4×C17C2411yescharacteristic
425C2×C22⋊D17—41no—
426C2×C22⋊D17—41no—
427C2×C22⋊D17—41no—
428C2×C22⋊D17—41no—
429C2×C22⋊D17—41no—
430C2×C22⋊D17—41no—
431C2×C22⋊D17—41no—
432C2×C22⋊D17—41no—
433C2×C22⋊D17—41no—
434C2×C22⋊D17—41no—
435C2×C22⋊D17—41no—
436C2×C22⋊D17—41no—
437C2×C22⋊D17—41no—
438C2×C22⋊D17—41no—
439C2×C22⋊D17C22×C414yes—
440C2×C22⋊D17C22×C414yes—
441C2×C22⋊D17C22×C414yes—
442C2×C22⋊D17C22×C414yes—
443C2×C22⋊D17C22×C414yes—
444C2×C22⋊D17C22×C414yes—
445C2×C22⋊D17C22×C414yes—
446C22×Dic17—41no—
447C22×Dic17—41no—
448C22×Dic17—41no—
449C22×Dic17—41no—
450C22×Dic17—41no—
451C22×Dic17—41no—
452C22×Dic17—41no—
453C22×Dic17—41no—
454C22×Dic17C22×C414yes—
455C22×Dic17C2411yescharacteristic
456C22×Dic17C2411yescharacteristic
457C22×Dic17C2411yescharacteristic
458C22×Dic17C2411yescharacteristic
459C22×Dic17C2411yescharacteristic
460C22×Dic17C2411yescharacteristic
461C22×Dic17C2411yescharacteristic
462C22×Dic17C2411yescharacteristic
463C22×Dic17C2411yescharacteristic
464C22×Dic17C2411yescharacteristic
465C22×Dic17C2411yescharacteristic
466C22×Dic17C2411yescharacteristic
467C22×Dic17C2411yescharacteristic
468C2×D68—41no—
469C2×D68—41no—
470C2×D68—41no—
471C2×D68—41no—
472C2×D68C22×C414yes—
473C2×D68C22×C414yes—
474C2×C4×D17—22no—
475C2×C4×D17—22no—
476C2×C4×D17—22no—
477C2×C4×D17—22no—
478C2×C4×D17—22no—
479C2×C4×D17—41no—
480C2×C4×D17—41no—
481C2×C4×D17—41no—
482C2×C4×D17—41no—
483C2×C4×D17—41no—
484C2×C4×D17—41no—
485C2×C4×D17—41no—
486C2×C4×D17—41no—
487C2×C4×D17—41no—
488C2×C4×D17—41no—
489C2×C4×D17—41no—
490C2×C4×D17—41no—
491C2×C4×D17—41no—
492C2×C4×D17—41no—
493C2×C4×D17—41no—
494C2×C4×D17C22×C414yes—
495C4⋊C4×C17—22no—
496C4⋊C4×C17—41no—
497C4⋊C4×C17C22×C414yes—
498C22⋊C4×C17—22no—
499C22⋊C4×C17—22no—
500C22⋊C4×C17—22no—
501C22⋊C4×C17—41no—
502C22⋊C4×C17—41no—
503C22⋊C4×C17—41no—
504C22⋊C4×C17—41no—
505C22⋊C4×C17—41no—
506C22⋊C4×C17C22×C414yes—
507C22⋊C4×C17C22×C414yes—
508C42×C17—22no—
509C42×C17—41no—
510C42×C17—41no—
511C42×C17—41no—
512C22⋊Dic17—22no—
513C22⋊Dic17—22no—
514C22⋊Dic17—22no—
515C22⋊Dic17—41no—
516C22⋊Dic17—41no—
517C22⋊Dic17—41no—
518C22⋊Dic17—41no—
519C22⋊Dic17—41no—
520C22⋊Dic17—41no—
521C22⋊Dic17—41no—
522C22⋊Dic17C22×C414yes—
523C22⋊Dic17C22×C414yes—
524C22⋊Dic17C22×C414yes—
525#63227—22no—
526#63227—22no—
527#63227—22no—
528#63227—22no—
529#63227—41no—
530#63227—41no—
531#63227—41no—
532#63227—41no—
533#63227—41no—
534#63227—41no—
535#63227—41no—
536#63227—41no—
537#63227—41no—
538#63227—41no—
539#63227—41no—
540#63227—41no—
541#63227—41no—
542#63227—41no—
543#63227C22×C414yes—
544#63227C22×C414yes—
545#63227C22×C414yes—
546#63227C22×C414yes—
547#63227C22×C414yes—
548#63227C22×C414yes—
549#63227C22×C414yes—
550C4⋊Dic17—22no—
551C4⋊Dic17—41no—
552C4⋊Dic17—41no—
553C4⋊Dic17—41no—
554C4⋊Dic17—41no—
555C4⋊Dic17—41no—
556C4⋊Dic17C22×C414yes—
557C4⋊Dic17C22×C414yes—
558#63225—22no—
559#63225—22no—
560#63225—41no—
561#63225—41no—
562#63225—41no—
563#63225—41no—
564#63225—41no—
565#63225—41no—
566#63225—41no—
567#63225—41no—
568#63225C22×C414yes—
569#63225C22×C414yes—
570#63225C22×C414yes—
571C4×Dic17—22no—
572C4×Dic17—22no—
573C4×Dic17—22no—
574C4×Dic17—22no—
575C4×Dic17—41no—
576C4×Dic17—41no—
577C4×Dic17—41no—
578C4×Dic17—41no—
579C4×Dic17—41no—
580C4×Dic17—41no—
581C4×Dic17—41no—
582C4×Dic17—41no—
583C4×Dic17—41no—
584C4×Dic17—41no—
585C4×Dic17C22×C414yes—
586#34517—171nomaximal, Sylow
587C23×C17—21no—
588C23×C17—21no—
589C23×C17—21no—
590C23×C17—21no—
591C23×C17—21no—
592C23×C17—21no—
593C23×C17—21no—
594C23×C17—21no—
595C23×C17—21no—
596C23×C17—21no—
597C23×C17—21no—
598C23×C17—21no—
599C23×C17—21no—
600C23×C17—21no—
601C23×C17—21no—
602C23×C17—21no—
603C23×C17—21no—
604C23×C17—21no—
605C23×C17C23×C412yes—
606C23×C17C23×C412yes—
607C23×C17C23×C412yes—
608C23×C17C2511yescharacteristic
609C22×D17—21no—
610C22×D17—21no—
611C22×D17—21no—
612C22×D17—21no—
613C22×D17—21no—
614C22×D17—21no—
615C22×D17—21no—
616C22×D17—21no—
617C22×D17—21no—
618C22×D17—21no—
619C22×D17—21no—
620C22×D17—21no—
621C22×D17—21no—
622C22×D17—21no—
623C22×D17—21no—
624C22×D17—21no—
625C22×D17—21no—
626C22×D17—21no—
627C22×D17—44no—
628C22×D17—44no—
629C22×D17—44no—
630C22×D17—82no—
631C22×D17—82no—
632C22×D17—82no—
633C22×D17—82no—
634C22×D17C23×C412yes—
635C22×D17C23×C412yes—
636C22×D17C23×C412yes—
637D4×C17—44no—
638D4×C17—44no—
639D4×C17—44no—
640C2×C4×C17—21no—
641C2×C4×C17—21no—
642C2×C4×C17—21no—
643C2×C4×C17—21no—
644C2×C4×C17—21no—
645C2×C4×C17—21no—
646C2×C4×C17—21no—
647C2×C4×C17—21no—
648C2×C4×C17—21no—
649C2×C4×C17—21no—
650C2×C4×C17—21no—
651C2×C4×C17—21no—
652C2×C4×C17—21no—
653C2×C4×C17—21no—
654C2×C4×C17—21no—
655C2×C4×C17—21no—
656C2×C4×C17—21no—
657C2×C4×C17—21no—
658C2×C4×C17—21no—
659C2×C4×C17—21no—
660C2×C4×C17—21no—
661C2×C4×C17—21no—
662C2×C4×C17—21no—
663C2×C4×C17—21no—
664C2×C4×C17—21no—
665C2×C4×C17—21no—
666C2×C4×C17—21no—
667C2×C4×C17—21no—
668C2×C4×C17—21no—
669C2×C4×C17—21no—
670C2×C4×C17—44no—
671C2×C4×C17—82no—
672C2×C4×C17—82no—
673C2×C4×C17—82no—
674C2×C4×C17—82no—
675C2×C4×C17C23×C412yes—
676C2×C4×C17C23×C412yes—
677C2×C4×C17C23×C412yes—
678C2×C4×C17C23×C412yes—
679C2×C4×C17H(5,𝔽2)12yes—
680C2×C4×C17H(5,𝔽2)12yes—
681C22⋊D17—44no—
682C22⋊D17—44no—
683C22⋊D17—44no—
684C22⋊D17—44no—
685C22⋊D17—44no—
686C22⋊D17—44no—
687C22⋊D17—44no—
688C2×Dic17—21no—
689C2×Dic17—21no—
690C2×Dic17—21no—
691C2×Dic17—21no—
692C2×Dic17—21no—
693C2×Dic17—21no—
694C2×Dic17—21no—
695C2×Dic17—21no—
696C2×Dic17—21no—
697C2×Dic17—21no—
698C2×Dic17—21no—
699C2×Dic17—21no—
700C2×Dic17—21no—
701C2×Dic17—21no—
702C2×Dic17—21no—
703C2×Dic17—21no—
704C2×Dic17—21no—
705C2×Dic17—21no—
706C2×Dic17—21no—
707C2×Dic17—21no—
708C2×Dic17—21no—
709C2×Dic17—21no—
710C2×Dic17—21no—
711C2×Dic17—21no—
712C2×Dic17—21no—
713C2×Dic17—21no—
714C2×Dic17—21no—
715C2×Dic17—21no—
716C2×Dic17—21no—
717C2×Dic17—21no—
718C2×Dic17—21no—
719C2×Dic17—21no—
720C2×Dic17—21no—
721C2×Dic17—44no—
722C2×Dic17—82no—
723C2×Dic17—82no—
724C2×Dic17C23×C412yes—
725C2×Dic17C23×C412yes—
726C2×Dic17C23×C412yes—
727C2×Dic17C23×C412yes—
728C2×Dic17C23×C412yes—
729C2×Dic17H(5,𝔽2)12yes—
730D68—44no—
731D68—44no—
732C4×D17—44no—
733C4×D17—44no—
734C4×D17—44no—
735C4×D17—82no—
736C4×D17—82no—
737C4×D17—82no—
738C4×D17—82no—
739C2×#560—171no—
740#2377—171no—
741#2377—171no—
742#2376—171no—
743#2373—171no—
744#2373—171no—
745#2366—171no—
746#2364—171no—
747#2364D1711yescharacteristic, complemented
748#2363—171no—
749#2363—171no—
750#2359—171no—
751#2359—171no—
752#2358—171no—
753#2358—171no—
754#2358—171no—
755#2335—171no—
756#2335—171no—
757#2334—171no—
758#2334—171no—
759#2328—171no—
760#2325—171no—
761#2325—171no—
762#2324—171no—
763#2324—171no—
764#2321—171no—
765#2321—171no—
766#2321—171no—
767C4×#123—171no—
768C4×#121—171no—
769C4×#121—171no—
770C22×C17—22no—
771C22×C17—22no—
772C22×C17—22no—
773C22×C17—22no—
774C22×C17—22no—
775C22×C17—22no—
776C22×C17—22no—
777C22×C17—22no—
778C22×C17—22no—
779C22×C17—41no—
780C22×C17—41no—
781C22×C17—41no—
782C22×C17—41no—
783C22×C17—41no—
784C22×C17—41no—
785C22×C17—41no—
786C22×C17—41no—
787C22×C17—41no—
788C22×C17—41no—
789C22×C17—41no—
790C22×C17—41no—
791C22×C17C24×C411yescharacteristic
792C22×C17C2×H(5,𝔽2)11yescharacteristic
793C22×C17C2×H(5,𝔽2)11yescharacteristic
794C22×C17C2×H(5,𝔽2)11yescharacteristic
795C22×C17#58511yescharacteristic
796C22×C17#58511yescharacteristic
797C22×C17#58511yescharacteristic
798C2×D17—22no—
799C2×D17—22no—
800C2×D17—22no—
801C2×D17—22no—
802C2×D17—22no—
803C2×D17—22no—
804C2×D17—22no—
805C2×D17—22no—
806C2×D17—22no—
807C2×D17—41no—
808C2×D17—41no—
809C2×D17—41no—
810C2×D17—41no—
811C2×D17—41no—
812C2×D17—41no—
813C2×D17—41no—
814C2×D17—41no—
815C2×D17—41no—
816C2×D17—41no—
817C2×D17—41no—
818C2×D17—41no—
819C2×D17—88no—
820C4×C17—22no—
821C4×C17—22no—
822C4×C17—22no—
823C4×C17—22no—
824C4×C17—22no—
825C4×C17—22no—
826C4×C17—41no—
827C4×C17—41no—
828C4×C17—41no—
829C4×C17—41no—
830C4×C17—41no—
831C4×C17—41no—
832Dic17—22no—
833Dic17—22no—
834Dic17—22no—
835Dic17—22no—
836Dic17—22no—
837Dic17—22no—
838Dic17—41no—
839Dic17—41no—
840Dic17—41no—
841Dic17—41no—
842Dic17—41no—
843Dic17—41no—
844Dic17—41no—
845#560—1716no—
846C2×#127—171no—
847C2×#126—171no—
848C2×#126—171no—
849C2×#123—171no—
850C2×#123—171no—
851C2×#123—171no—
852C2×#121—171no—
853C2×#121—171no—
854C2×#121—171no—
855C2×#121—171no—
856C2×#121—171no—
857C2×#121C2×D1711yescharacteristic
858C2×#120—171no—
859C2×#120—171no—
860C2×#120—171no—
861C2×C4×D4—171no—
862C2×C4×D4—171no—
863C2×C4×D4—171no—
864C2×C4×D4—171no—
865C2×C4×D4—171no—
866C2×C4×D4—171no—
867C2×C4×D4—171no—
868C2×C4×D4—171no—
869C2×C4×D4—171no—
870C2×C4×D4—171no—
871C2×C4×D4C2×D1711yescharacteristic
872C2×C4×D4C2×D1711yescharacteristic, complemented
873C2×#117—171no—
874C2×#117—171no—
875C22×C22⋊C4—171no—
876C22×C22⋊C4—171no—
877C22×C22⋊C4—171no—
878C22×C42—171no—
879#390—171no—
880#390—171no—
881#390—171no—
882#390—171no—
883#390—171no—
884#390—171no—
885#390—171no—
886#390—171no—
887#390—171no—
888#390—171no—
889#390—171no—
890#390—171no—
891#389—171no—
892#389—171no—
893#389—171no—
894#389—171no—
895#389—171no—
896#389—171no—
897#388—171no—
898#388—171no—
899#388—171no—
900#388—171no—
901#388—171no—
902#388—171no—
903#388—171no—
904#388—171no—
905#388—171no—
906#388—171no—
907#388—171no—
908#388—171no—
909#388—171no—
910#388—171no—
911#388—171no—
912#388—171no—
913#388—171no—
914#388—171no—
915#388—171no—
916#388—171no—
917#388—171no—
918#388—171no—
919#388C2×D1711yescharacteristic
920#388C2×D1711yescharacteristic, complemented
921#387—171no—
922#387—171no—
923#387—171no—
924#387—171no—
925#387—171no—
926#387—171no—
927#387—171no—
928#387—171no—
929#387—171no—
930#387—171no—
931#387C2×D1711yescharacteristic, complemented
932#387C2×D1711yescharacteristic, complemented
933#386—171no—
934#386—171no—
935#386—171no—
936#386—171no—
937#386—171no—
938#386—171no—
939#386—171no—
940#386—171no—
941#386—171no—
942#386—171no—
943#386—171no—
944#386—171no—
945#386—171no—
946#386—171no—
947#386—171no—
948#386—171no—
949#386—171no—
950#386—171no—
951#386—171no—
952#386—171no—
953#386C2×D1711yescharacteristic
954#386C2×D1711yescharacteristic
955#386C2×D1711yescharacteristic
956#386C2×D1711yescharacteristic, complemented
957#385—171no—
958#385—171no—
959#385—171no—
960#385—171no—
961#385—171no—
962#385—171no—
963#385—171no—
964#385—171no—
965#385—171no—
966#385—171no—
967#385—171no—
968#385—171no—
969#382—171no—
970#381—171no—
971#380—171no—
972#380—171no—
973#380—171no—
974#380—171no—
975#379—171no—
976C4×C4⋊C4—171no—
977C4×C4⋊C4—171no—
978C4×C4⋊C4—171no—
979C4×C4⋊C4—171no—
980C4×C4⋊C4—171no—
981C4×C4⋊C4—171no—
982C4×C4⋊C4—171no—
983C4×C4⋊C4—171no—
984C4×C22⋊C4—171no—
985C4×C22⋊C4—171no—
986C4×C22⋊C4—171no—
987C4×C22⋊C4—171no—
988C4×C22⋊C4—171no—
989C4×C22⋊C4—171no—
990C4×C22⋊C4—171no—
991C4×C22⋊C4—171no—
992C4×C22⋊C4—171no—
993C4×C22⋊C4—171no—
994C4×C22⋊C4—171no—
995C4×C22⋊C4C2×D1711yescharacteristic
996C4×C22⋊C4C2×D1711yescharacteristic, complemented
997C4×C22⋊C4C2×D1711yescharacteristic, complemented
998#376—171no—
999C2×#95—171no—
1000C2×#95C2×D1711yescharacteristic, complemented
1001C2×C17—42no—
1002C2×C17—42no—
1003C2×C17—42no—
1004C2×C17C4×H(5,𝔽2)11yescharacteristic
1005C2×C17C4×H(5,𝔽2)11yescharacteristic
1006C2×C17C4×H(5,𝔽2)11yescharacteristic
1007C2×C17#353411yescharacteristic
1008C2×C17#354211yescharacteristic
1009C2×C17#354611yescharacteristic
1010C2×C17#356611yescharacteristic
1011D17—42no—
1012D17—42no—
1013D17—42no—
1014C25—171no—
1015C22×D4—171no—
1016C22×D4—171no—
1017C22×D4—171no—
1018C22×D4—171no—
1019C22×D4—171no—
1020C22×D4—171no—
1021C22×D4—171no—
1022C22×D4—171no—
1023C22×D4—171no—
1024C22×D4C22×D1711yescharacteristic
1025C22×D4C22×D1711yescharacteristic
1026C22×D4C22×D1711yescharacteristic
1027C23×C4—171no—
1028C23×C4—171no—
1029C23×C4—171no—
1030C23×C4—171no—
1031C23×C4—171no—
1032C23×C4—171no—
1033C23×C4—171no—
1034C23×C4—171no—
1035C23×C4—171no—
1036C23×C4—171no—
1037C23×C4C22×D1711yescharacteristic
1038C23×C4C22×D1711yescharacteristic
1039C23×C4C22×D1711yescharacteristic
1040C23×C4C22×D1711yescharacteristic
1041C23×C4C22×D1711yescharacteristic
1042#127—178no—
1043#126—178no—
1044#126—178no—
1045#123—178no—
1046#123—178no—
1047#123—178no—
1048#121—178no—
1049#121—178no—
1050#121—178no—
1051#121—178no—
1052#121—178no—
1053#121C4×D1718yescomplemented
1054#120—178no—
1055#120—178no—
1056#120—178no—
1057C4×D4—42no—
1058C4×D4—42no—
1059C4×D4—682no—
1060C4×D4—682no—
1061C4×D4—682no—
1062C4×D4—682no—
1063C4×D4—682no—
1064C4×D4—682no—
1065C4×D4—682no—
1066C4×D4—682no—
1067C4×D4—682no—
1068C4×D4—682no—
1069#117—682no—
1070#117—682no—
1071C2×C4⋊C4—171no—
1072C2×C4⋊C4—171no—
1073C2×C4⋊C4—171no—
1074C2×C4⋊C4—171no—
1075C2×C4⋊C4—171no—
1076C2×C4⋊C4—171no—
1077C2×C4⋊C4—171no—
1078C2×C4⋊C4—171no—
1079C2×C4⋊C4—171no—
1080C2×C4⋊C4—171no—
1081C2×C4⋊C4—171no—
1082C2×C4⋊C4—171no—
1083C2×C4⋊C4—171no—
1084C2×C4⋊C4—171no—
1085C2×C4⋊C4—171no—
1086C2×C4⋊C4—171no—
1087C2×C4⋊C4—171no—
1088C2×C4⋊C4—171no—
1089C2×C4⋊C4—171no—
1090C2×C4⋊C4—171no—
1091C2×C4⋊C4—171no—
1092C2×C4⋊C4C22×D1711yescharacteristic
1093C2×C4⋊C4C22×D1711yescharacteristic
1094C2×C4⋊C4C22×D1711yescharacteristic
1095C2×C22⋊C4—171no—
1096C2×C22⋊C4—171no—
1097C2×C22⋊C4—171no—
1098C2×C22⋊C4—171no—
1099C2×C22⋊C4—171no—
1100C2×C22⋊C4—171no—
1101C2×C22⋊C4—171no—
1102C2×C22⋊C4—171no—
1103C2×C22⋊C4—171no—
1104C2×C22⋊C4—171no—
1105C2×C22⋊C4—171no—
1106C2×C22⋊C4—171no—
1107C2×C22⋊C4—171no—
1108C2×C22⋊C4—171no—
1109C2×C22⋊C4—171no—
1110C2×C22⋊C4—171no—
1111C2×C22⋊C4—171no—
1112C2×C22⋊C4—171no—
1113C2×C22⋊C4—171no—
1114C2×C22⋊C4—171no—
1115C2×C22⋊C4—171no—
1116C2×C22⋊C4—171no—
1117C2×C22⋊C4—171no—
1118C2×C22⋊C4—171no—
1119C2×C22⋊C4—171no—
1120C2×C22⋊C4—171no—
1121C2×C22⋊C4—171no—
1122C2×C22⋊C4—171no—
1123C2×C22⋊C4—171no—
1124C2×C22⋊C4—171no—
1125C2×C22⋊C4—171no—
1126C2×C22⋊C4—171no—
1127C2×C22⋊C4—171no—
1128C2×C22⋊C4—171no—
1129C2×C22⋊C4—171no—
1130C2×C22⋊C4—171no—
1131C2×C22⋊C4—171no—
1132C2×C22⋊C4—171no—
1133C2×C22⋊C4—682no—
1134C2×C22⋊C4—682no—
1135C2×C22⋊C4—682no—
1136C2×C22⋊C4C22×D1711yescharacteristic
1137C2×C22⋊C4C22×D1711yescharacteristic
1138C2×C22⋊C4C22×D1711yescharacteristic
1139C2×C22⋊C4C22×D1711yescharacteristic
1140C2×C22⋊C4C22×D1711yescharacteristic
1141C2×C22⋊C4C22×D1711yescharacteristic
1142C2×C22⋊C4C22×D1711yescharacteristic
1143C2×C22⋊C4C22×D1711yescharacteristic
1144C2×C22⋊C4C22×D1711yescharacteristic
1145C2×C22⋊C4C22×D1711yescharacteristic
1146C2×C42—171no—
1147C2×C42—171no—
1148C2×C42—171no—
1149C2×C42—171no—
1150C2×C42—171no—
1151C2×C42—171no—
1152C2×C42—171no—
1153C2×C42—171no—
1154C2×C42—171no—
1155C2×C42—171no—
1156C2×C42—171no—
1157C2×C42—171no—
1158C2×C42—171no—
1159C2×C42—171no—
1160C2×C42—171no—
1161C2×C42—682no—
1162C2×C42C22×D1711yescharacteristic
1163C2×C42C22×D1711yescharacteristic
1164C2×C42C22×D1711yescharacteristic
1165C2×C42C22×D1711yescharacteristic
1166#95—171no—
1167#95—171no—
1168#95—171no—
1169#95—171no—
1170#95—171no—
1171#95—171no—
1172#95—171no—
1173#95—171no—
1174#95—171no—
1175#95—171no—
1176#95—171no—
1177#95—171no—
1178#95—171no—
1179#95—171no—
1180#95—171no—
1181#95—171no—
1182#95—171no—
1183#95—171no—
1184#95—171no—
1185#95—171no—
1186#95—171no—
1187#95—171no—
1188#95—171no—
1189#95—171no—
1190#95—171no—
1191#95—171no—
1192#95C22×D1711yescharacteristic
1193#95C22×D1711yescharacteristic
1194#95C22×D1711yescharacteristic
1195#95C22×D1711yescharacteristic
1196#95C22×D1711yescharacteristic
1197#95C22×D1711yescharacteristic
1198#95C22×D1711yescharacteristic
1199#95C22×D1711yescharacteristic
1200#95C22×D1711yescharacteristic
1201#95C22×D1711yescharacteristic
1202C17#3451711yescharacteristic, complemented, Sylow
1203C24—171no—
1204C24—171no—
1205C24—171no—
1206C24—174no—
1207C24—681no—
1208C24—681no—
1209C24—681no—
1210C24—681no—
1211C24—681no—
1212C24—681no—
1213C24C23×D1711yescharacteristic
1214C24C23×D1711yescharacteristic
1215C24C23×D1711yescharacteristic
1216C2×D4—41no—
1217C2×D4—41no—
1218C2×D4—41no—
1219C2×D4—41no—
1220C2×D4—41no—
1221C2×D4—41no—
1222C2×D4—174no—
1223C2×D4—174no—
1224C2×D4—174no—
1225C2×D4—174no—
1226C2×D4—174no—
1227C2×D4—174no—
1228C2×D4—174no—
1229C2×D4—174no—
1230C2×D4—174no—
1231C2×D4—681no—
1232C2×D4—681no—
1233C2×D4—681no—
1234C2×D4—681no—
1235C2×D4—681no—
1236C2×D4—681no—
1237C2×D4—681no—
1238C2×D4—681no—
1239C2×D4—681no—
1240C2×D4—681no—
1241C2×D4—681no—
1242C2×D4—681no—
1243C2×D4—681no—
1244C2×D4—681no—
1245C2×D4—681no—
1246C2×D4—681no—
1247C2×D4—681no—
1248C2×D4—681no—
1249C2×D4C2×C4×D1714yes—
1250C2×D4C2×C4×D1714yes—
1251C2×D4C2×C4×D1714yes—
1252C22×C4—22no—
1253C22×C4—22no—
1254C22×C4—22no—
1255C22×C4—41no—
1256C22×C4—41no—
1257C22×C4—41no—
1258C22×C4—41no—
1259C22×C4—41no—
1260C22×C4—41no—
1261C22×C4—41no—
1262C22×C4—41no—
1263C22×C4—41no—
1264C22×C4—41no—
1265C22×C4—41no—
1266C22×C4—171no—
1267C22×C4—171no—
1268C22×C4—171no—
1269C22×C4—171no—
1270C22×C4—171no—
1271C22×C4—171no—
1272C22×C4—174no—
1273C22×C4—174no—
1274C22×C4—171no—
1275C22×C4—171no—
1276C22×C4—171no—
1277C22×C4—171no—
1278C22×C4—171no—
1279C22×C4—171no—
1280C22×C4—171no—
1281C22×C4—342no—
1282C22×C4—342no—
1283C22×C4—342no—
1284C22×C4—342no—
1285C22×C4—342no—
1286C22×C4—681no—
1287C22×C4—681no—
1288C22×C4—681no—
1289C22×C4—681no—
1290C22×C4—681no—
1291C22×C4—681no—
1292C22×C4—681no—
1293C22×C4—681no—
1294C22×C4—681no—
1295C22×C4—681no—
1296C22×C4—681no—
1297C22×C4—681no—
1298C22×C4—681no—
1299C22×C4—681no—
1300C22×C4—681no—
1301C22×C4—681no—
1302C22×C4—681no—
1303C22×C4—681no—
1304C22×C4—681no—
1305C22×C4—681no—
1306C22×C4—681no—
1307C22×C4—681no—
1308C22×C4—681no—
1309C22×C4C2×C4×D1714yes—
1310C22×C4C23×D1711yescharacteristic
1311C22×C4C23×D1711yescharacteristic
1312C22×C4C23×D1711yescharacteristic
1313C22×C4C23×D1711yescharacteristic
1314C22×C4C23×D1711yescharacteristic
1315C22×C4C23×D1711yescharacteristic
1316C22×C4C23×D1711yescharacteristic
1317C22×C4C23×D1711yescharacteristic
1318C22×C4C23×D1711yescharacteristic
1319C22×C4C23×D1711yescharacteristic
1320C22×C4C23×D1711yescharacteristic
1321C22×C4C23×D1711yescharacteristic
1322C4⋊C4—22no—
1323C4⋊C4—41no—
1324C4⋊C4—174no—
1325C4⋊C4—174no—
1326C4⋊C4—174no—
1327C4⋊C4—174no—
1328C4⋊C4—174no—
1329C4⋊C4—342no—
1330C4⋊C4—342no—
1331C4⋊C4—342no—
1332C4⋊C4—681no—
1333C4⋊C4—681no—
1334C4⋊C4—681no—
1335C4⋊C4—681no—
1336C4⋊C4—681no—
1337C4⋊C4—681no—
1338C4⋊C4—681no—
1339C4⋊C4—681no—
1340C4⋊C4—681no—
1341C4⋊C4—681no—
1342C4⋊C4—681no—
1343C4⋊C4—681no—
1344C4⋊C4—681no—
1345C4⋊C4C2×C4×D1714yes—
1346C22⋊C4—22no—
1347C22⋊C4—22no—
1348C22⋊C4—22no—
1349C22⋊C4—41no—
1350C22⋊C4—41no—
1351C22⋊C4—41no—
1352C22⋊C4—41no—
1353C22⋊C4—41no—
1354C22⋊C4—174no—
1355C22⋊C4—174no—
1356C22⋊C4—174no—
1357C22⋊C4—174no—
1358C22⋊C4—174no—
1359C22⋊C4—174no—
1360C22⋊C4—174no—
1361C22⋊C4—174no—
1362C22⋊C4—174no—
1363C22⋊C4—174no—
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⋊C4C2×C4×D1714yes—
1393C22⋊C4C2×C4×D1714yes—
1394C42—22no—
1395C42—41no—
1396C42—41no—
1397C42—41no—
1398C42—174no—
1399C42—342no—
1400C42—342no—
1401C42—342no—
1402C42—342no—
1403C42—681no—
1404C42—681no—
1405C42—681no—
1406C42—681no—
1407C42—681no—
1408C42—681no—
1409C42—681no—
1410C42—681no—
1411C42—681no—
1412C42—681no—
1413C23—21no—
1414C23—21no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—21no—
1419C23—21no—
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—172no—
1432C23—172no—
1433C23—172no—
1434C23—341no—
1435C23—341no—
1436C23—341no—
1437C23—341no—
1438C23—341no—
1439C23—341no—
1440C23—341no—
1441C23—341no—
1442C23—341no—
1443C23—341no—
1444C23—341no—
1445C23—341no—
1446C23—341no—
1447C23—341no—
1448C23—341no—
1449C23—341no—
1450C23—341no—
1451C23—341no—
1452C23—684no—
1453C23—684no—
1454C23—684no—
1455C23—1362no—
1456C23—1362no—
1457C23—1362no—
1458C23—1362no—
1459C23C22×C4×D1712yes—
1460C23C22×C4×D1712yes—
1461C23C22×C4×D1712yes—
1462C23C24×D1711yescharacteristic
1463D4—44no—
1464D4—44no—
1465D4—44no—
1466D4—684no—
1467D4—684no—
1468D4—684no—
1469D4—684no—
1470D4—684no—
1471D4—684no—
1472D4—684no—
1473D4—684no—
1474D4—684no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—44no—
1506C2×C4—82no—
1507C2×C4—82no—
1508C2×C4—82no—
1509C2×C4—82no—
1510C2×C4—172no—
1511C2×C4—172no—
1512C2×C4—172no—
1513C2×C4—172no—
1514C2×C4—172no—
1515C2×C4—172no—
1516C2×C4—341no—
1517C2×C4—341no—
1518C2×C4—341no—
1519C2×C4—341no—
1520C2×C4—341no—
1521C2×C4—341no—
1522C2×C4—341no—
1523C2×C4—341no—
1524C2×C4—341no—
1525C2×C4—341no—
1526C2×C4—341no—
1527C2×C4—341no—
1528C2×C4—341no—
1529C2×C4—341no—
1530C2×C4—341no—
1531C2×C4—341no—
1532C2×C4—341no—
1533C2×C4—341no—
1534C2×C4—341no—
1535C2×C4—341no—
1536C2×C4—341no—
1537C2×C4—341no—
1538C2×C4—341no—
1539C2×C4—341no—
1540C2×C4—341no—
1541C2×C4—341no—
1542C2×C4—341no—
1543C2×C4—341no—
1544C2×C4—341no—
1545C2×C4—341no—
1546C2×C4—341no—
1547C2×C4—341no—
1548C2×C4—341no—
1549C2×C4—684no—
1550C2×C4—684no—
1551C2×C4—684no—
1552C2×C4—684no—
1553C2×C4—1362no—
1554C2×C4—1362no—
1555C2×C4—1362no—
1556C2×C4—1362no—
1557C2×C4—1362no—
1558C2×C4—1362no—
1559C2×C4C22×C4×D1712yes—
1560C2×C4C22×C4×D1712yes—
1561C2×C4C22×C4×D1712yes—
1562C2×C4C22×C4×D1712yes—
1563C2×C4#1058769112yes—
1564C2×C4#1058769612yes—
1565C22—22no—
1566C22—22no—
1567C22—22no—
1568C22—22no—
1569C22—22no—
1570C22—22no—
1571C22—22no—
1572C22—22no—
1573C22—22no—
1574C22—41no—
1575C22—41no—
1576C22—41no—
1577C22—41no—
1578C22—41no—
1579C22—41no—
1580C22—41no—
1581C22—41no—
1582C22—41no—
1583C22—41no—
1584C22—41no—
1585C22—41no—
1586C22—342no—
1587C22—342no—
1588C22—342no—
1589C22—342no—
1590C22—342no—
1591C22—342no—
1592C22—342no—
1593C22—342no—
1594C22—342no—
1595C22—681no—
1596C22—681no—
1597C22—681no—
1598C22—681no—
1599C22—681no—
1600C22—681no—
1601C22—681no—
1602C22—681no—
1603C22—681no—
1604C22—681no—
1605C22—681no—
1606C22—681no—
1607C22—1368no—
1608C22C23×C4×D1711yescharacteristic
1609C22H(5,𝔽2)×D1711yescharacteristic
1610C22C2×#1058769111yescharacteristic
1611C22C2×#1058769611yescharacteristic
1612C22#1176364411yescharacteristic
1613C22#1176364511yescharacteristic
1614C22#1176364511yescharacteristic
1615C4—22no—
1616C4—22no—
1617C4—22no—
1618C4—22no—
1619C4—22no—
1620C4—22no—
1621C4—41no—
1622C4—41no—
1623C4—41no—
1624C4—41no—
1625C4—41no—
1626C4—41no—
1627C4—342no—
1628C4—342no—
1629C4—342no—
1630C4—342no—
1631C4—342no—
1632C4—342no—
1633C4—681no—
1634C4—681no—
1635C4—681no—
1636C4—681no—
1637C4—681no—
1638C4—681no—
1639C4—681no—
1640C2—42no—
1641C2—42no—
1642C2—42no—
1643C2—682no—
1644C2—682no—
1645C2—682no—
1646C2#1454198811yescharacteristic
1647C2C4×#1058769111yescharacteristic
1648C2C4×#1058769611yescharacteristic
1649C2#1454296611yescharacteristic
1650C2#1454308611yescharacteristic
1651C2#1454315511yescharacteristic
1652C2#1454345811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D17
commutatorC22×C17C24×C4
FittingC17×#2364C2
socle, cosocleC23×C17C25
prime radicalC2×#11763547C2
hypercenter#2364D17
hypocenterC17#34517
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C23 ◁ #2364

Complements

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

NH ≅ G/Ntype
2. #14531937C2semidirect
3. #14531936C2semidirect
4. #14531931C2semidirect
5. #14531906C2semidirect
6. #14531903C2semidirect
7. #14531846C2semidirect
8. #14531832C2semidirect
9. #14531825C2semidirect
10. #14531820C2semidirect
11. #14531778C2semidirect
12. #14531772C2semidirect
13. #14531764C2semidirect
14. #14531762C2semidirect
15. #14531761C2semidirect
16. #14531579C2semidirect
17. #14531574C2semidirect
18. #14531565C2semidirect
19. #14531556C2semidirect
20. #14531505C2semidirect
21. #14531487C2semidirect
22. #14531482C2semidirect
23. #14531479C2semidirect
24. #14531474C2semidirect
25. #14531444C2semidirect
26. #14531440C2semidirect
27. #14531440C2semidirect
28. #14531305C2semidirect
29. C4×#10587570C2semidirect
30. C4×#10587624C2semidirect
31. C17×#2364C2semidirect
32. #11763547C4semidirect
54. C2×C4×C22⋊D17C22semidirect
55. C2×C4×C22⋊D17C22semidirect
57. C2×#10587612C22semidirect
58. C2×#10587563C22semidirect
62. C2×C42×D17C22semidirect
65. #11762712C22semidirect
73. #11762709C22semidirect
74. #11762709C22semidirect
75. #11762708C22semidirect
76. #11762707C22semidirect
77. #11762706C22semidirect
78. #11762706C22semidirect
79. #11762706C22semidirect
80. #11762705C22semidirect
81. #11762703C22semidirect
83. #11762702C22semidirect
89. #11762701C22semidirect
97. #11762698C22semidirect
102. #11762697C22semidirect
103. #11762696C22semidirect
104. #11762696C22semidirect
105. #11762694C22semidirect
106. #11762694C22semidirect
107. #11762694C22semidirect
108. #11762693C22semidirect
109. #11762693C22semidirect
110. #11762692C22semidirect
111. #11762691C22semidirect
112. #11762690C22semidirect
114. #11762689C22semidirect
118. #11762688C22semidirect
125. #11762686C22semidirect
131. #11762685C22semidirect
132. #11762685C22semidirect
134. #11762684C22semidirect
139. #11762683C22semidirect
141. #11762682C22semidirect
145. #11762673C22semidirect
146. #11762671C22semidirect
147. #11762669C22semidirect
148. #11762668C22semidirect
149. #11762667C22semidirect
150. #11762666C22semidirect
152. C4⋊C4×Dic17C22semidirect
153. C4⋊C4×Dic17C22semidirect
154. C4×#63225C22semidirect
155. C4×#63225C22semidirect
156. C4×C4⋊Dic17C22semidirect
157. C4×C4⋊Dic17C22semidirect
158. #11762660C22semidirect
159. #11762660C22semidirect
161. C22⋊C4×Dic17C22semidirect
165. C4×C22⋊Dic17C22semidirect
170. #11762656C22semidirect
171. #11762654C22semidirect
172. C2×#10587502C22semidirect
175. C2×C4×D4×C17C22semidirect
177. C17×#388C22semidirect
178. C17×#387C22semidirect
179. C17×#387C22semidirect
183. C17×#386C22semidirect
185. C4×C22⋊C4×C17C22semidirect
186. C4×C22⋊C4×C17C22semidirect
187. C2×C17×#95C22semidirect
216. C17×#121C2×C4semidirect
249. #10587626C2×C4semidirect
250. #10587625C2×C4semidirect
251. #10587625C2×C4semidirect
252. #10587624C2×C4semidirect
253. #10587623C2×C4semidirect
254. #10587623C2×C4semidirect
256. #10587616C2×C4semidirect
257. #10587615C2×C4semidirect
327. #10587584C2×C4semidirect
328. #10587580C2×C4semidirect
330. #10587572C2×C4semidirect
331. #10587570C2×C4semidirect
332. #10587568C2×C4semidirect
336. #10587565C2×C4semidirect
747. #2364D17semidirect
872. C2×C4×D4C2×D17semidirect
920. #388C2×D17semidirect
931. #387C2×D17semidirect
932. #387C2×D17semidirect
956. #386C2×D17semidirect
996. C4×C22⋊C4C2×D17semidirect
997. C4×C22⋊C4C2×D17semidirect
1000. C2×#95C2×D17semidirect
1053. #121C4×D17semidirect
1202. C17#34517semidirect

Maximal subgroups

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

subgroupindex
C2×#117635472
#145319372
#145319362
#145319312
#145319062
#145319032
#145318462
#145318322
#145318252
#145318202
#145317782
#145317722
#145317642
#145317622
#145317612
#145315792
#145315742
#145315652
#145315562
#145315052
#145314872
#145314822
#145314792
#145314742
#145314442
#145314402
#145313052
C4×#105875702
C4×#105876242
C17×#23642
#3451717