Finite Group Databasebeta

← #17979195

Subgroups — #17979195

Order 4352.

2036 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14545319C214yesmaximal
2#14545318C212yesmaximal
3#14545313C211yesmaximal, characteristic
4#14545313C212yesmaximal
5#14545304C212yesmaximal
6#14545304C212yesmaximal
7#14545303C211yesmaximal, characteristic
8#14545303C211yesmaximal, characteristic
9#14545284C214yesmaximal
10#14545275C212yesmaximal
11C4⋊Q8×#595C211yesmaximal, characteristic
12#125×#595C212yesmaximal
13#14545243C212yesmaximal
14#14545243C211yesmaximal, characteristic
15#14545224C212yesmaximal
16C4×Q8×#595C211yesmaximal, characteristic
17D17×#557C211yesmaximal, characteristic
18C2×Q8×#595C2211yescharacteristic
19C2×Q8×#595C2211yescharacteristic
20C2×Q8×#595C2212yes—
21C2×Q8×#595C2212yes—
22(C2×#595)⋊Q8C2211yescharacteristic
23(C2×#595)⋊Q8C2212yes—
24(C2×#595)⋊Q8C2211yescharacteristic
25(C2×#595)⋊Q8C2212yes—
26(C2×#595)⋊Q8C2212yes—
27(C2×#595)⋊Q8C2212yes—
28#11763760C2211yescharacteristic
29#11763760C2212yes—
30#11763760C2212yes—
31#11763760C2211yescharacteristic
32#11763760C2212yes—
33#11763760C2214yes—
34#11763758C2214yes—
35#11763758C2212yes—
36#11763758C2214yes—
37#11763758C2212yes—
38#11763758C2214yes—
39#11763758C2214yes—
40#11763758C2214yes—
41#11763758C2214yes—
42#11763758C2214yes—
43#11763758C2214yes—
44#11763758C2214yes—
45#11763758C2214yes—
46#11763758C2214yes—
47#11763755C2211yescharacteristic
48#11763754C2214yes—
49#11763753C2212yes—
50#11763753C2212yes—
51C4⋊C4×#595C2211yescharacteristic
52C4⋊C4×#595C2212yes—
53C4⋊C4×#595C2211yescharacteristic
54C4⋊C4×#595C2212yes—
55C4⋊C4×#595C2214yes—
56C4⋊C4×#595C2212yes—
57C4⋊C4×#595C2214yes—
58C4⋊C4×#595C2212yes—
59C4⋊C4×#595C2212yes—
60C4⋊C4×#595C2214yes—
61C4⋊C4×#595C2212yes—
62C4⋊C4×#595C2212yes—
63C4×C4⋊#595C2211yescharacteristic
64C4×C4⋊#595C2212yes—
65C4×C4⋊#595C2214yes—
66C4×C4⋊#595C2212yes—
67C4×C4⋊#595C2211yescharacteristic
68C4×C4⋊#595C2212yes—
69C4×C4⋊#595C2212yes—
70#11763745C2212yes—
71#11763745C2214yes—
72#11763745C2214yes—
73C42×#595C2212yes—
74C42×#595C2211yescharacteristic
75#11763538C411yescharacteristic, complemented
76#11763537C411yescharacteristic, complemented
77#11763537C412yescomplemented
78#11763536C412yescomplemented
79#11763536C414yescomplemented
80#11763535C412yescomplemented
81#11763534C411yescharacteristic, complemented
82#11763534C412yescomplemented
83C4⋊Q8×D17C2211yescharacteristic
84C4⋊Q8×D17C2212yes—
85#125×D17C2212yes—
86#125×D17C2214yes—
87C4×Q8×D17C2211yescharacteristic
88C4×Q8×D17C2212yes—
89C4×Q8×D17C2211yescharacteristic
90C4×Q8×D17C2212yes—
91C17×#557C411yescharacteristic, complemented
92C2×Q8×D17C2311yescharacteristic
93C2×Q8×D17C2312yes—
94C2×Q8×D17C2311yescharacteristic
95Q8×#595—24no—
96Q8×#595—28no—
97Q8×#595—24no—
98Q8×#595—28no—
99C2×C4⋊#595C2311yescharacteristic
100C2×C4⋊#595C2311yescharacteristic
101C2×C4⋊#595C2312yes—
102C2×C4⋊#595C2312yes—
103C2×C4⋊#595C2311yescharacteristic
104C2×C4⋊#595C2312yes—
105C2×C4⋊#595C2312yes—
106C2×C4⋊#595C2312yes—
107C2×C4⋊#595C2314yes—
108C2×C4⋊#595C2314yes—
109C2×C4⋊#595C2312yes—
110C2×C4⋊#595C2312yes—
111C2×C4⋊#595C2311yescharacteristic
112C2×C4×#595C2311yescharacteristic
113C2×C4×#595C2312yes—
114C2×C4×#595C2311yescharacteristic
115C2×C4×#595C2312yes—
116C2×C4×#595C2311yescharacteristic
117C2×C4×#595C2311yescharacteristic
118C2×C4×#595C2312yes—
119C2×C4×#595C2312yes—
120C2×C4×#595C2312yes—
121C2×C4×#595C2314yes—
122C2×C4×#595C2314yes—
123C2×C4×#595C2312yes—
124C2×C4×#595C2311yescharacteristic
125C2×C4×#595C2314yes—
126C2×C4×#595C2314yes—
127C2×C4×#595C2311yescharacteristic
128C17×C4⋊Q8C2×C411yescharacteristic
129C17×C4⋊Q8C2×C412yes—
130C17×#125C2×C412yes—
131C17×#125C2×C414yes—
132C4×Q8×C17C2×C412yes—
133C4×Q8×C17C2×C411yescharacteristic
134C4×Q8×C17C2×C412yes—
135C4×Q8×C17C2×C411yescharacteristic
136Q8×Dic17C2×C411yescharacteristic
137Q8×Dic17C2×C412yes—
138Q8×Dic17C2×C411yescharacteristic
139Q8×Dic17C2×C412yes—
140#10587630C2×C412yes—
141#10587630C2×C412yes—
142#10587630C2×C412yes—
143C4⋊C4×D17C2311yescharacteristic
144C4⋊C4×D17C2312yes—
145C4⋊C4×D17C2314yes—
146C4⋊C4×D17C2311yescharacteristic
147C4⋊C4×D17C2312yes—
148C4⋊C4×D17C2314yes—
149C4⋊C4×D17C2312yes—
150C4⋊C4×D17C2312yes—
151C4⋊C4×D17C2314yes—
152#10587576C2×C412yes—
153#10587576C2×C414yes—
154#10587576C2×C412yes—
155#10587576C2×C414yes—
156#10587575C2×C414yes—
157#10587575C2×C414yes—
158#10587575C2×C414yes—
159#10587575C2×C414yes—
160#10587575C2×C414yes—
161#10587575C2×C414yes—
162#10587574C2×C412yes—
163#10587574C2×C414yes—
164#10587574C2×C412yes—
165#10587574C2×C414yes—
166#10587573C2×C414yes—
167#10587573C2×C412yes—
168#10587573C2×C412yes—
169#10587573C2×C414yes—
170#10587573C2×C412yes—
171#10587573C2×C411yescharacteristic
172#10587573C2×C411yescharacteristic
173#10587573C2×C412yes—
174C42×D17C2312yes—
175C42×D17C2311yescharacteristic
176C42×D17C2314yes—
177C42×D17C2312yes—
178#10587556C2×C412yes—
179#10587556C2×C414yes—
180#10587555C2×C411yescharacteristic
181#10587555C2×C412yes—
182C4×Dic34C2×C412yes—
183C4×Dic34C2×C411yescharacteristic
184C4×Dic34C2×C411yescharacteristic
185C4×Dic34C2×C412yes—
186C4×Dic34C2×C412yes—
187C4×Dic34C2×C414yes—
188C4×Dic34C2×C414yes—
189C4×Dic34C2×C412yes—
190(C2×#595)⋊C4C2312yes—
191(C2×#595)⋊C4C2312yes—
192(C2×#595)⋊C4C2312yes—
193(C2×#595)⋊C4C2312yes—
194(C2×#595)⋊C4C2314yes—
195(C2×#595)⋊C4C2314yes—
196(C2×#595)⋊C4C2312yes—
197(C2×#595)⋊C4C2312yes—
198(C2×#595)⋊C4C2314yes—
199(C2×#595)⋊C4C2314yes—
200(C2×#595)⋊C4C2314yes—
201(C2×#595)⋊C4C2312yes—
202(C2×#595)⋊C4C2312yes—
203(C2×#595)⋊C4C2312yes—
204(C2×#595)⋊C4C2312yes—
205(C2×#595)⋊C4C2314yes—
206(C2×#595)⋊C4C2314yes—
207(C2×#595)⋊C4C2314yes—
208(C2×#595)⋊C4C2314yes—
209(C2×#595)⋊C4C2314yes—
210C22×#595C2411yescharacteristic
211C22×#595C2412yes—
212C22×#595C2414yes—
213C22×#595C2412yes—
214C22×#595C2412yes—
215C22×#595C2412yes—
216C22×#595C2411yescharacteristic
217C22×#595C2411yescharacteristic
218C22×#595C2411yescharacteristic
219C2×Q8×C17C22×C412yes—
220C2×Q8×C17C22×C411yescharacteristic
221C2×Q8×C17C22×C411yescharacteristic
222Q8×D17—22no—
223Q8×D17—24no—
224Q8×D17—22no—
225Q8×D17—24no—
226Q8×D17—22no—
227Q8×D17—22no—
228C2×C4×D17C2412yes—
229C2×C4×D17C2412yes—
230C2×C4×D17C2414yes—
231C2×C4×D17C2411yescharacteristic
232C2×C4×D17C2412yes—
233C2×C4×D17C2412yes—
234C2×C4×D17C2411yescharacteristic
235C2×C4×D17C2411yescharacteristic
236C2×Dic34C22×C411yescharacteristic
237C2×Dic34C22×C412yes—
238C2×Dic34C22×C412yes—
239C2×Dic34C22×C411yescharacteristic
240C2×Dic34C22×C414yes—
241C2×Dic34C22×C412yes—
242C4⋊#595—24no—
243C4⋊#595—24no—
244C4⋊#595—28no—
245C4⋊#595—28no—
246C4⋊#595—24no—
247C4⋊#595—22no—
248C4⋊#595—24no—
249C4⋊#595—22no—
250C4⋊#595—22no—
251C4⋊#595—24no—
252C4⋊#595—42no—
253C4⋊#595—42no—
254C4⋊#595#4114yes—
255C4×#595—24no—
256C4×#595—28no—
257C4×#595—28no—
258C4×#595—24no—
259C4×#595—22no—
260C4×#595—24no—
261C4×#595—22no—
262C4×#595—24no—
263C4×#595—22no—
264C4×#595—24no—
265C4×#595—22no—
266C4×#595—42no—
267C4×#595—44no—
268C4×#595—44no—
269C4×#595—41no—
270C4×#595#4114yes—
271C4⋊C4×C17C22×C414yes—
272C4⋊C4×C17C22×C412yes—
273C4⋊C4×C17C22×C414yes—
274C4⋊C4×C17C22×C412yes—
275C4⋊C4×C17C22×C412yes—
276C4⋊C4×C17C22×C411yescharacteristic
277C4⋊C4×C17C22×C414yes—
278C4⋊C4×C17C22×C412yes—
279C4⋊C4×C17C22×C411yescharacteristic
280C42×C17C22×C414yes—
281C42×C17C22×C412yes—
282C42×C17C22×C412yes—
283C42×C17C22×C411yescharacteristic
284C4⋊Dic17C22×C411yescharacteristic
285C4⋊Dic17C22×C414yes—
286C4⋊Dic17C22×C412yes—
287C4⋊Dic17C22×C412yes—
288C4⋊Dic17C22×C411yescharacteristic
289C4⋊Dic17C22×C412yes—
290C4⋊Dic17C22×C414yes—
291C4⋊Dic17C22×C412yes—
292C4⋊Dic17C22×C414yes—
293#63225C22×C412yes—
294#63225C22×C412yes—
295#63225C22×C414yes—
296#63225C22×C414yes—
297#63225C22×C414yes—
298#63225C22×C414yes—
299#63225C22×C412yes—
300#63225C22×C412yes—
301#63225C22×C412yes—
302#63225C22×C412yes—
303#63225C22×C414yes—
304#63225C22×C414yes—
305#63225C22×C414yes—
306#63225C22×C414yes—
307C4×Dic17C22×C414yes—
308C4×Dic17C22×C412yes—
309C4×Dic17C22×C412yes—
310C4×Dic17C22×C411yescharacteristic
311C4×Dic17C22×C414yes—
312C4×Dic17C22×C412yes—
313C4×Dic17C22×C412yes—
314C4×Dic17C22×C411yescharacteristic
315C4×Dic17C22×C412yes—
316C4×Dic17C22×C411yescharacteristic
317C4×Dic17C22×C414yes—
318C4×Dic17C22×C412yes—
319#34328—171nomaximal, Sylow
320C22×D17C2511yescharacteristic
321C2×#595—21no—
322C2×#595—21no—
323C2×#595—21no—
324C2×#595—21no—
325C2×#595—22no—
326C2×#595—21no—
327C2×#595—21no—
328C2×#595—22no—
329C2×#595—22no—
330C2×#595—24no—
331C2×#595—22no—
332C2×#595—21no—
333C2×#595—22no—
334C2×#595—22no—
335C2×#595—22no—
336C2×#595—21no—
337C2×#595—24no—
338C2×#595—22no—
339C2×#595—22no—
340C2×#595—22no—
341C2×#595—24no—
342C2×#595—22no—
343C2×#595—21no—
344C2×#595C2×#4112yes—
345C2×#595C2×#4114yes—
346C2×#595C2×#4112yes—
347C2×#5952−1+412yes—
348Q8×C17—22no—
349Q8×C17—24no—
350Q8×C17—22no—
351C2×C4×C17C23×C412yes—
352C2×C4×C17C23×C412yes—
353C2×C4×C17C23×C411yescharacteristic
354C2×C4×C17C23×C412yes—
355C2×C4×C17C23×C414yes—
356C2×C4×C17C23×C412yes—
357C2×C4×C17C23×C411yescharacteristic
358C2×C4×C17C23×C411yescharacteristic
359C2×Dic17C23×C412yes—
360C2×Dic17C23×C412yes—
361C2×Dic17C23×C414yes—
362C2×Dic17C23×C412yes—
363C2×Dic17C23×C411yescharacteristic
364C2×Dic17C23×C412yes—
365C2×Dic17C23×C411yescharacteristic
366C2×Dic17C23×C411yescharacteristic
367C4×D17—24no—
368C4×D17—22no—
369C4×D17—22no—
370C4×D17—24no—
371C4×D17—22no—
372C4×D17—21no—
373C4×D17—22no—
374C4×D17—22no—
375C4×D17—22no—
376C4×D17—22no—
377C4×D17—22no—
378C4×D17—21no—
379C4×D17C2×#4112yes—
380C4×D17C2×#4112yes—
381C4×D172−1+412yes—
382C4×D172−1+412yes—
383Dic34—24no—
384Dic34—22no—
385Dic34—22no—
386Dic34—28no—
387Dic34—24no—
388Dic34—24no—
389C2×#557—171no—
390#2371—174no—
391#2370—172no—
392#2365—172no—
393#2365—171no—
394#2356—172no—
395#2356—172no—
396#2355—171no—
397#2355—171no—
398#2336—174no—
399#2327—172no—
400C4×C4⋊Q8—171no—
401C4×#125—172no—
402#2295—171no—
403#2295—172no—
404#2276—172no—
405C42×Q8—171no—
406C22×C17C24×C411yescharacteristic
407C2×D17C22×#4111yescharacteristic
408C2×D17C22×#4111yescharacteristic
409C2×D17C2×2−1+411yescharacteristic
410C2×D17C2×2−1+411yescharacteristic
411C2×D17C2×2−1+411yescharacteristic
412C2×D17#58511yescharacteristic
413#595—22no—
414#595—22no—
415#595—24no—
416#595—22no—
417#595—44no—
418#595—42no—
419#595—41no—
420#595—42no—
421#595—42no—
422C4×C17—24no—
423C4×C17—22no—
424C4×C17—22no—
425C4×C17—22no—
426C4×C17—21no—
427C4×C17—22no—
428C4×C17C4×#4112yes—
429C4×C17#51912yes—
430Dic17—24no—
431Dic17—22no—
432Dic17—22no—
433Dic17—22no—
434Dic17—21no—
435Dic17—22no—
436Dic17C4×#4112yes—
437Dic17#51912yes—
438#557—172no—
439#557—171no—
440#557—174no—
441#557—172no—
442#557—172no—
443#557—172no—
444#557—171no—
445#557—171no—
446#557#59511yescharacteristic, complemented
447C2×C4⋊Q8—171no—
448C2×C4⋊Q8—172no—
449C2×#125—172no—
450C2×#125—174no—
451C2×C4×Q8—171no—
452C2×C4×Q8—171no—
453C2×C4×Q8—172no—
454C2×C4×Q8—172no—
455C2×C4×Q8—172no—
456C2×C4×Q8—171no—
457C2×C4×Q8—171no—
458C2×C4×Q8—172no—
459#391—172no—
460#391—172no—
461#391—172no—
462#391—172no—
463#391—171no—
464#391—171no—
465#389—171no—
466#389—172no—
467#389—172no—
468#389—174no—
469#389—172no—
470#389—171no—
471#387—174no—
472#387—174no—
473#387—174no—
474#387—174no—
475#387—174no—
476#387—172no—
477#387—174no—
478#387—174no—
479#387—174no—
480#387—174no—
481#387—174no—
482#387—174no—
483#387—172no—
484#384—171no—
485#383—174no—
486#382—172no—
487#382—172no—
488C4×C4⋊C4—174no—
489C4×C4⋊C4—172no—
490C4×C4⋊C4—172no—
491C4×C4⋊C4—174no—
492C4×C4⋊C4—172no—
493C4×C4⋊C4—172no—
494C4×C4⋊C4—172no—
495C4×C4⋊C4—174no—
496C4×C4⋊C4—171no—
497C4×C4⋊C4—172no—
498C4×C4⋊C4—171no—
499C4×C4⋊C4—172no—
500C4×C4⋊C4—172no—
501C4×C4⋊C4—172no—
502C4×C4⋊C4—172no—
503C4×C4⋊C4—171no—
504C4×C4⋊C4—174no—
505C4×C4⋊C4—172no—
506C4×C4⋊C4—171no—
507#376—172no—
508#376—174no—
509#376—174no—
510C43—172no—
511C43—171no—
512C2×C17C2×C4×#4111yescharacteristic
513C2×C17C2×#51911yescharacteristic
514C2×C17C4×2−1+411yescharacteristic
515D17#350711yescharacteristic
516D17#350911yescharacteristic
517D17#351511yescharacteristic
518D17#352311yescharacteristic
519C22×Q8—171no—
520C22×Q8—172no—
521C22×Q8—171no—
522C4⋊Q8—172no—
523C4⋊Q8—172no—
524C4⋊Q8—172no—
525C4⋊Q8—172no—
526C4⋊Q8—174no—
527C4⋊Q8—172no—
528C4⋊Q8—174no—
529C4⋊Q8—171no—
530C4⋊Q8—172no—
531C4⋊Q8C2×#59511yescharacteristic
532C4⋊Q8C2×#59512yes—
533#125—174no—
534#125—174no—
535#125—174no—
536#125—174no—
537#125—174no—
538#125—174no—
539#125—172no—
540#125—174no—
541#125—172no—
542#125—174no—
543#125—172no—
544#125—174no—
545#125C2×#59512yes—
546#125C2×#59514yes—
547C4×Q8—172no—
548C4×Q8—171no—
549C4×Q8—172no—
550C4×Q8—171no—
551C4×Q8—174no—
552C4×Q8—172no—
553C4×Q8—172no—
554C4×Q8—174no—
555C4×Q8—171no—
556C4×Q8—172no—
557C4×Q8—172no—
558C4×Q8—171no—
559C4×Q8—174no—
560C4×Q8—172no—
561C4×Q8—171no—
562C4×Q8—172no—
563C4×Q8—172no—
564C4×Q8—174no—
565C4×Q8—172no—
566C4×Q8—171no—
567C4×Q8—348no—
568C4×Q8—344no—
569C4×Q8—344no—
570C4×Q8—348no—
571C4×Q8C2×#59512yes—
572C4×Q8C2×#59511yescharacteristic
573C4×Q8C2×#59512yes—
574C4×Q8C2×#59511yescharacteristic
575C2×C4⋊C4—171no—
576C2×C4⋊C4—171no—
577C2×C4⋊C4—172no—
578C2×C4⋊C4—174no—
579C2×C4⋊C4—171no—
580C2×C4⋊C4—172no—
581C2×C4⋊C4—172no—
582C2×C4⋊C4—174no—
583C2×C4⋊C4—174no—
584C2×C4⋊C4—172no—
585C2×C4⋊C4—171no—
586C2×C4⋊C4—172no—
587C2×C4⋊C4—172no—
588C2×C4⋊C4—174no—
589C2×C4⋊C4—172no—
590C2×C4⋊C4—174no—
591C2×C4⋊C4—171no—
592C2×C4⋊C4—172no—
593C2×C4⋊C4—172no—
594C2×C4⋊C4—171no—
595C2×C4⋊C4—172no—
596C2×C4⋊C4—172no—
597C2×C42—171no—
598C2×C42—172no—
599C2×C42—174no—
600C2×C42—171no—
601C2×C42—172no—
602C2×C42—172no—
603C2×C42—171no—
604C2×C42—172no—
605C2×C42—174no—
606C2×C42—174no—
607C2×C42—172no—
608C2×C42—171no—
609C2×C42—172no—
610C2×C42—171no—
611C2×C42—171no—
612C2×C42—172no—
613C2×C42—172no—
614C2×C42—171no—
615C2×C42—174no—
616C2×C42—174no—
617#95—172no—
618#95—172no—
619#95—172no—
620#95—174no—
621#95—172no—
622#95—172no—
623#95—172no—
624#95—174no—
625#95—174no—
626#95—174no—
627#95—174no—
628#95—172no—
629#95—172no—
630#95—174no—
631#95—174no—
632#95—172no—
633#95—174no—
634#95—174no—
635#95—172no—
636#95—174no—
637C17#3432811yescharacteristic, complemented, Sylow
638C2×Q8—172no—
639C2×Q8—171no—
640C2×Q8—172no—
641C2×Q8—174no—
642C2×Q8—171no—
643C2×Q8—172no—
644C2×Q8—344no—
645C2×Q8—342no—
646C2×Q8—342no—
647C2×Q8—344no—
648C2×Q8—342no—
649C2×Q8—342no—
650C2×Q8C22×#59511yescharacteristic
651C2×Q8C22×#59511yescharacteristic
652C2×Q8C22×#59512yes—
653C22×C4—171no—
654C22×C4—171no—
655C22×C4—171no—
656C22×C4—171no—
657C22×C4—171no—
658C22×C4—172no—
659C22×C4—172no—
660C22×C4—172no—
661C22×C4—171no—
662C22×C4—172no—
663C22×C4—174no—
664C22×C4—172no—
665C22×C4—172no—
666C22×C4—172no—
667C22×C4—171no—
668C22×C4—172no—
669C22×C4—174no—
670C4⋊C4—174no—
671C4⋊C4—172no—
672C4⋊C4—171no—
673C4⋊C4—172no—
674C4⋊C4—172no—
675C4⋊C4—174no—
676C4⋊C4—172no—
677C4⋊C4—172no—
678C4⋊C4—172no—
679C4⋊C4—174no—
680C4⋊C4—172no—
681C4⋊C4—174no—
682C4⋊C4—172no—
683C4⋊C4—171no—
684C4⋊C4—174no—
685C4⋊C4—174no—
686C4⋊C4—174no—
687C4⋊C4—174no—
688C4⋊C4—172no—
689C4⋊C4—174no—
690C4⋊C4—174no—
691C4⋊C4—174no—
692C4⋊C4—174no—
693C4⋊C4—172no—
694C4⋊C4—342no—
695C4⋊C4—342no—
696C4⋊C4—344no—
697C4⋊C4—344no—
698C4⋊C4—342no—
699C4⋊C4—344no—
700C4⋊C4—344no—
701C4⋊C4—348no—
702C4⋊C4—344no—
703C4⋊C4—348no—
704C4⋊C4—682no—
705C4⋊C4—682no—
706C4⋊C4C22×#59511yescharacteristic
707C4⋊C4C22×#59512yes—
708C4⋊C4C22×#59514yes—
709C4⋊C4C22×#59512yes—
710C4⋊C4C22×#59511yescharacteristic
711C4⋊C4C22×#59514yes—
712C4⋊C4C22×#59512yes—
713C4⋊C4C22×#59514yes—
714C4⋊C4C22×#59512yes—
715C42—174no—
716C42—172no—
717C42—172no—
718C42—174no—
719C42—174no—
720C42—172no—
721C42—174no—
722C42—171no—
723C42—171no—
724C42—172no—
725C42—172no—
726C42—171no—
727C42—172no—
728C42—342no—
729C42—344no—
730C42—342no—
731C42—342no—
732C42—344no—
733C42—342no—
734C42—344no—
735C42—348no—
736C42—344no—
737C42—344no—
738C42—348no—
739C42—682no—
740C42—684no—
741C42—684no—
742C42—681no—
743C42C22×#59514yes—
744C42C22×#59512yes—
745C42C22×#59512yes—
746C42C22×#59511yescharacteristic
747C23—171no—
748Q8—24no—
749Q8—22no—
750Q8—22no—
751Q8—344no—
752Q8—348no—
753Q8—344no—
754Q8—342no—
755Q8—344no—
756Q8—342no—
757C2×C4—171no—
758C2×C4—171no—
759C2×C4—172no—
760C2×C4—172no—
761C2×C4—172no—
762C2×C4—172no—
763C2×C4—172no—
764C2×C4—172no—
765C2×C4—174no—
766C2×C4—172no—
767C2×C4—172no—
768C2×C4—172no—
769C2×C4—171no—
770C2×C4—172no—
771C2×C4—172no—
772C2×C4—174no—
773C2×C4—342no—
774C2×C4—344no—
775C2×C4—344no—
776C2×C4—342no—
777C2×C4—342no—
778C2×C4—341no—
779C2×C4—342no—
780C2×C4—342no—
781C2×C4—341no—
782C2×C4—342no—
783C2×C4—342no—
784C2×C4—342no—
785C2×C4—341no—
786C2×C4—341no—
787C2×C4—341no—
788C2×C4—342no—
789C2×C4—341no—
790C2×C4—341no—
791C2×C4—342no—
792C2×C4—341no—
793C2×C4—342no—
794C2×C4—342no—
795C2×C4—341no—
796C2×C4—342no—
797C2×C4—344no—
798C2×C4—342no—
799C2×C4—341no—
800C2×C4—342no—
801C2×C4—342no—
802C2×C4—344no—
803C2×C4—341no—
804C2×C4—342no—
805C2×C4—342no—
806C2×C4—344no—
807C2×C4—342no—
808C2×C4C23×#59512yes—
809C2×C4C23×#59512yes—
810C2×C4C23×#59511yescharacteristic
811C2×C4C23×#59512yes—
812C2×C4C23×#59512yes—
813C2×C4C23×#59514yes—
814C2×C4C23×#59511yescharacteristic
815C2×C4C23×#59511yescharacteristic
816C22—171no—
817C22—171no—
818C22—171no—
819C22—171no—
820C22—171no—
821C22—171no—
822C22C24×#59511yescharacteristic
823C4—22no—
824C4—24no—
825C4—22no—
826C4—22no—
827C4—21no—
828C4—22no—
829C4—172no—
830C4—172no—
831C4—344no—
832C4—342no—
833C4—342no—
834C4—342no—
835C4—342no—
836C4—344no—
837C4—342no—
838C4—342no—
839C4—341no—
840C4—342no—
841C4—681no—
842C4—682no—
843C4—684no—
844C4—682no—
845C4—682no—
846C4#41×#59512yes—
847C4#1176387712yes—
848C2—171no—
849C2—171no—
850C2—171no—
851C2—171no—
852C2C2×#41×#59511yescharacteristic
853C2C2×#1176387711yescharacteristic
854C22−1+4×#59511yescharacteristic
subgroupG/H
center, FrattiniC22C24×#595
commutator, socleC22×C17C24×C4
FittingC17×#557C4
prime radical, cosocleC22×D17C25
hypercenter#557#595
hypocenterC17#34328
LCSG ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
75. #11763538C4semidirect
76. #11763537C4semidirect
77. #11763537C4semidirect
78. #11763536C4semidirect
79. #11763536C4semidirect
80. #11763535C4semidirect
81. #11763534C4semidirect
82. #11763534C4semidirect
91. C17×#557C4semidirect
446. #557#595semidirect
637. C17#34328semidirect

Maximal subgroups

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

subgroupindex
#145453192
#145453182
#145453132
#145453042
#145453032
#145452842
#145452752
C4⋊Q8×#5952
#125×#5952
#145452432
#145452242
C4×Q8×#5952
D17×#5572
#3432817