Finite Group Databasebeta

← #25257050

Subgroups — #25257050

Order 11008.

2110 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583451C211yesmaximal, characteristic
2#19137680C211yesmaximal, characteristic
3#19137678C211yesmaximal, characteristic
4#19137676C212yesmaximal
5#19137675C211yesmaximal, characteristic
6#19137673C212yesmaximal
7#19137551C212yesmaximal, complemented
8#19137549C212yesmaximal, complemented
9#19137549C212yesmaximal, complemented
10#19137548C212yesmaximal, complemented
11#19137340C212yesmaximal, complemented
12#19137338C212yesmaximal, complemented
13#19137214C212yesmaximal
14#19137152C212yesmaximal, complemented
15C4×#13063315C212yesmaximal, complemented
16C2×#14582763C211yesmaximal, characteristic
17#19136950C212yesmaximal
18C4×#13063281C211yesmaximal, characteristic
19C43×#2368C211yesmaximal, characteristic
20#14583451C4116yescomplemented
21C2×#13063324C2211yescharacteristic
22C2×#13063323C2211yescharacteristic
23C2×#13063315C2212yes—
24C2×#13063304C2211yescharacteristic
25C2×#13063302C2212yes—
26C2×Q8×Dic43C2211yescharacteristic
27C2×#13063290C2212yes—
28C2×#13063290C2211yescharacteristic
29C2×#13063281C2211yescharacteristic
30C2×#13063281C2212yes—
31C2×#13063281C2211yescharacteristic
32C22×Dic43⋊C4C2212yes—
33C22×C4×Dic43C2211yescharacteristic
34#14582806C2212yes—
35#14582805C2212yes—
36#14582804C2212yes—
37#14582803C2212yes—
38#14582803C2212yes—
39#14582803C2212yes—
40#14582803C2212yes—
41#14582796C2212yes—
42#14582796C2212yes—
43#14582794C2212yes—
44#14582794C2212yes—
45#14582786C2212yes—
46#14582786C2212yes—
47#14582785C2212yes—
48#14582785C2212yes—
49#14582784C2212yes—
50#14582784C2212yes—
51#14582783C2212yes—
52#14582783C2212yes—
53#14582782C2212yes—
54#14582782C2212yes—
55#14582781C2212yes—
56#14582781C2212yes—
57#14582780C2212yes—
58#14582780C2212yes—
59#14582774C2212yes—
60#14582772C2212yes—
61#14582771C2212yes—
62#14582768C2212yes—
63#14582768C2212yes—
64#14582763C2211yescharacteristic
65#14582763C2212yes—
66#14582763C2212yes—
67#14582763C2211yescharacteristic
68#14582763C2212yes—
69#14582763C2212yes—
70#14582763C2211yescharacteristic
71#14582763C2211yescharacteristic
72C4⋊C4×Dic43C2212yes—
73C4⋊C4×Dic43C2212yes—
74C4×Dic43⋊C4C2212yes—
75C4×Dic43⋊C4C2212yes—
76C4×Dic43⋊C4C2212yes—
77C4×Dic43⋊C4C2212yes—
78C4×Dic43⋊C4C2212yes—
79C4×Dic43⋊C4C2212yes—
80C4×Dic43⋊C4C2212yes—
81C4×C4⋊Dic43C2212yes—
82#14582750C2212yes—
83#14582750C2212yes—
84#14582750C2212yes—
85#14582750C2212yes—
86#14582750C2212yes—
87#14582750C2212yes—
88#14582750C2212yes—
89C22⋊C4×Dic43C2211yescharacteristic
90C22⋊C4×Dic43C2212yes—
91C22⋊C4×Dic43C2211yescharacteristic
92C22⋊C4×Dic43C2212yes—
93C4×C22⋊Dic43C2212yes—
94C4×C22⋊Dic43C2211yescharacteristic
95#14582744C2212yes—
96C2×C43⋊#95C2212yes—
97C2×C43⋊#95C2211yescharacteristic
98C42×Dic43C2212yes—
99C2×C22⋊Q8×C43C2211yescharacteristic
100C43×#391C2212yes—
101C43×#387C2212yes—
102C43×#387C2212yes—
103C43×#385C2212yes—
104C4×C4⋊C4×C43C2212yes—
105C4×C22⋊C4×C43C2212yes—
106C4×C22⋊C4×C43C2211yescharacteristic
107C2×#95×C43C2211yescharacteristic
108C22×Dic86C2311yescharacteristic
109C22×Dic86C2312yes—
110C23×Dic43C2312yes—
111C23×Dic43C2311yescharacteristic
112C23×Dic43C2311yescharacteristic
113#13063324C2×C418yescomplemented
114#13063323C2×C418yescomplemented
115#13063315C2×C4116yescomplemented
116#13063304C2×C418yes—
117#13063302C2×C4116yes—
118Q8×Dic43C2×C418yescomplemented
119#13063290C2×C4116yescomplemented
120#13063290C2×C418yescomplemented
121#13063281—24no—
122#13063281C2×C4116yes—
123#13063281Q818yescomplemented
124C2×C4⋊Dic43C2312yes—
125C2×C4⋊Dic43C2312yes—
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2312yes—
128C2×Dic43⋊C4—28no—
129C2×Dic43⋊C4C2312yes—
130C2×Dic43⋊C4C2312yes—
131C2×Dic43⋊C4C2312yes—
132C2×Dic43⋊C4C2312yes—
133C2×Dic43⋊C4C2312yes—
134C2×Dic43⋊C4C2312yes—
135C2×Dic43⋊C4C2312yes—
136C2×Dic43⋊C4C2312yes—
137C2×Dic43⋊C4C2312yes—
138C2×Dic43⋊C4C2312yes—
139C2×Dic43⋊C4C2312yes—
140C2×Dic43⋊C4C2312yes—
141C2×Dic43⋊C4C2312yes—
142C2×Dic43⋊C4C2312yes—
143C2×Dic43⋊C4C2312yes—
144C2×C22⋊Dic43C2311yescharacteristic
145C2×C22⋊Dic43C2312yes—
146C2×C22⋊Dic43C2311yescharacteristic
147C2×C4×Dic43C2×C418yes—
148C2×C4×Dic43C2312yes—
149C2×C4×Dic43C2312yes—
150C2×C4×Dic43C2312yes—
151C2×C4×Dic43C2312yes—
152C2×C4×Dic43C2312yes—
153C2×C4×Dic43C2312yes—
154C2×C4×Dic43C2312yes—
155C2×C4×Dic43C2312yes—
156C2×C4×Dic43C2312yes—
157C2×C4×Dic43C2312yes—
158C2×C4×Dic43C2311yescharacteristic
159C2×C4×Dic43C2311yescharacteristic
160C2×C4×Dic43C2311yescharacteristic
161C2×C4×Dic43C2311yescharacteristic
162C2×C4×Dic43C2312yes—
163C2×C4×Dic43C2312yes—
164C2×C4×Dic43C2312yes—
165C43⋊#95C2312yes—
166C43⋊#95C2312yes—
167C43⋊#95C2312yes—
168C43⋊#95C2312yes—
169C43⋊#95C2312yes—
170C43⋊#95C2312yes—
171C43⋊#95C2312yes—
172C43⋊#95C2311yescharacteristic
173C43⋊#95C2312yes—
174C43⋊#95C2312yes—
175C43⋊#95C2312yes—
176C43⋊#95C2312yes—
177C43⋊#95C2312yes—
178C43⋊#95C2312yes—
179C43⋊#95C2312yes—
180C43⋊#95C2312yes—
181C43⋊#95C2312yes—
182C43⋊#95C2312yes—
183C43⋊#95C2312yes—
184C43⋊#95C2312yes—
185C43⋊#95C2312yes—
186C43⋊#95C2311yescharacteristic
187C22×Q8×C43C2311yescharacteristic
188C23×C4×C43C2312yes—
189C23×C4×C43C2311yescharacteristic
190C22⋊Q8×C43C2×C418yes—
191C2×C4⋊C4×C43C2312yes—
192C2×C4⋊C4×C43C2312yes—
193C2×C4⋊C4×C43C2311yescharacteristic
194C2×C4⋊C4×C43C2312yes—
195C2×C22⋊C4×C43C2311yescharacteristic
196C2×C22⋊C4×C43C2312yes—
197C2×C22⋊C4×C43C2311yescharacteristic
198C2×C42×C43C2312yes—
199C2×C42×C43C2312yes—
200C2×C42×C43C2312yes—
201#95×C43C2312yes—
202#95×C43C2312yes—
203#95×C43C2312yes—
204#95×C43C2312yes—
205#95×C43C2312yes—
206#95×C43C2312yes—
207#95×C43C2311yescharacteristic
208#95×C43C2311yescharacteristic
209C24×C43C2411yescharacteristic
210C2×Q8×C43—42no—
211C2×Q8×C43C22×C414yes—
212C22×C4×C43—24no—
213C22×C4×C43—42no—
214C22×C4×C43—42no—
215C22×C4×C43—42no—
216C22×C4×C43C22×C414yes—
217C22×C4×C43C2412yes—
218C22×C4×C43C2412yes—
219C22×C4×C43C2412yes—
220C22×C4×C43C2411yescharacteristic
221C22×C4×C43C2411yescharacteristic
222C22×C4×C43C2412yes—
223C22×C4×C43C2412yes—
224C22×C4×C43C2412yes—
225C22×Dic43—24no—
226C22×Dic43—42no—
227C22×Dic43—42no—
228C22×Dic43—42no—
229C22×Dic43C22×C414yes—
230C22×Dic43C22×C414yes—
231C22×Dic43C2×Q814yes—
232C22×Dic43#4114yes—
233C22×Dic43C2412yes—
234C22×Dic43C2412yes—
235C22×Dic43C2412yes—
236C22×Dic43C2411yescharacteristic
237C22×Dic43C2411yescharacteristic
238C22×Dic43C2412yes—
239C22×Dic43C2412yes—
240C22×Dic43C2412yes—
241C22×Dic43C2411yescharacteristic
242C22×Dic43C2411yescharacteristic
243C2×Dic86—42no—
244C2×Dic86—42no—
245C2×Dic86—42no—
246C2×Dic86C22×C418yes—
247C2×Dic86C22×C414yes—
248C4⋊C4×C43—42no—
249C4⋊C4×C43—42no—
250C4⋊C4×C43C22×C418yes—
251C4⋊C4×C43C22×C414yes—
252C22⋊C4×C43—22no—
253C22⋊C4×C43C22×C418yes—
254C22⋊C4×C43C2×Q814yes—
255C42×C43—42no—
256C42×C43—42no—
257C42×C43—42no—
258C22⋊Dic43—22no—
259C22⋊Dic43C22×C418yes—
260C22⋊Dic43C2×Q814yes—
261C4⋊Dic43—42no—
262C4⋊Dic43—42no—
263C4⋊Dic43C22×C418yes—
264C4⋊Dic43C22×C414yes—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267Dic43⋊C4—24no—
268Dic43⋊C4—24no—
269Dic43⋊C4—24no—
270Dic43⋊C4—42no—
271Dic43⋊C4—42no—
272Dic43⋊C4—42no—
273Dic43⋊C4—42no—
274Dic43⋊C4C22×C418yes—
275Dic43⋊C4C22×C418yes—
276Dic43⋊C4C22×C418yes—
277Dic43⋊C4C22×C418yes—
278Dic43⋊C4C22×C418yes—
279Dic43⋊C4C2×Q818yes—
280C4×Dic43—24no—
281C4×Dic43—42no—
282C4×Dic43—42no—
283C4×Dic43—42no—
284C4×Dic43—42no—
285C4×Dic43—42no—
286C4×Dic43—42no—
287C4×Dic43—42no—
288C4×Dic43—42no—
289C4×Dic43—42no—
290C4×Dic43C22×C414yes—
291C4×Dic43C22×C414yes—
292C4×Dic43C22×C414yes—
293C4×Dic43C22×C414yes—
294C4×Dic43C22×C418yes—
295C4×Dic43C22×C418yes—
296C4×Dic43C2×Q818yes—
297C23×C43—22no—
298C23×C43—22no—
299C23×C43C23×C412yes—
300C23×C43C22×Q812yes—
301C23×C43C2×#4112yes—
302C23×C43C2511yescharacteristic
303Q8×C43—44no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—44no—
322C2×C4×C43—84no—
323C2×C4×C43C23×C412yes—
324C2×C4×C43C23×C412yes—
325C2×C4×C43C23×C414yes—
326C2×C4×C43C23×C414yes—
327C2×C4×C43C22×Q814yes—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—44no—
346C2×Dic43—84no—
347C2×Dic43C4×Q8116yes—
348C2×Dic43C23×C412yes—
349C2×Dic43C23×C412yes—
350C2×Dic43C23×C414yes—
351C2×Dic43C23×C414yes—
352C2×Dic43C23×C412yes—
353C2×Dic43C23×C412yes—
354C2×Dic43C22×Q814yes—
355C2×Dic43C22×Q812yes—
356C2×Dic43C22×Q812yes—
357C2×Dic43C2×#4112yes—
358C2×Dic43C2×#4112yes—
359Dic86—48no—
360Dic86—44no—
361#34215—431nomaximal, Sylow
362C22×C43—22no—
363C22×C43—22no—
364C22×C43—24no—
365C22×C43—24no—
366C22×C43C2×C4×Q814yes—
367C22×C43C24×C411yescharacteristic
368C22×C43C23×Q811yescharacteristic
369C22×C43C22×#4111yescharacteristic
370C22×C43#58512yes—
371C22×C43#58512yes—
372C4×C43—22no—
373C4×C43—24no—
374C4×C43—22no—
375C4×C43—24no—
376C4×C43—24no—
377C4×C43—42no—
378C4×C43—42no—
379C4×C43—42no—
380Dic43—22no—
381Dic43—24no—
382Dic43—24no—
383Dic43—22no—
384Dic43—24no—
385Dic43—42no—
386Dic43—42no—
387Dic43—42no—
388Dic43C2×C4×Q814yes—
389Dic43C2×C4×Q814yes—
390C2×#533—431no—
391#2368—432no—
392#2368—432no—
393#2368—431no—
394#2368—431no—
395#2368—431no—
396#2368D4311yescharacteristic
397#2355—432no—
398#2355—432no—
399#2355—432no—
400#2355—432no—
401#2331—432no—
402#2331—432no—
403#2317—432no—
404C4×#125—432no—
405C4×#125—432no—
406C2×#382—431no—
407#2274—432no—
408C4×#117—431no—
409C2×C43—24no—
410C2×C43C22×C4×Q811yescharacteristic
411C2×C43#342811yescharacteristic
412C2×C43#342811yescharacteristic
413C2×C43#350412yes—
414C2×C43#351012yes—
415#533—4316no—
416C2×C4⋊Q8—431no—
417C2×C4⋊Q8—431no—
418C2×#125—432no—
419C2×C22⋊Q8—431no—
420C2×C22⋊Q8—432no—
421C2×C22⋊Q8C2×D4311yescharacteristic
422C2×C4×Q8—431no—
423C2×C4×Q8—431no—
424C2×C4×Q8—432no—
425C2×#117—432no—
426C2×#117—431no—
427C2×#117—431no—
428C22×C4⋊C4—432no—
429C22×C42—431no—
430#391—432no—
431#391—432no—
432#391—432no—
433#391—432no—
434#391—432no—
435#391—432no—
436#391—432no—
437#391C2×D4312yes—
438#389—432no—
439#389—432no—
440#389—432no—
441#389—432no—
442#387—432no—
443#387—432no—
444#387—432no—
445#387—432no—
446#387—432no—
447#387—432no—
448#387—432no—
449#387—432no—
450#387—432no—
451#387—432no—
452#387—432no—
453#387—432no—
454#387—432no—
455#387—432no—
456#387C2×D4312yes—
457#387C2×D4312yes—
458#385—432no—
459#385—432no—
460#385—432no—
461#385C2×D4312yes—
462#384—432no—
463#384—432no—
464#382—431no—
465#382—431no—
466#382—432no—
467#382—432no—
468#382—432no—
469#382—432no—
470#382—431no—
471#382—431no—
472C4×C4⋊C4—432no—
473C4×C4⋊C4—432no—
474C4×C4⋊C4—432no—
475C4×C4⋊C4—432no—
476C4×C4⋊C4—432no—
477C4×C4⋊C4—432no—
478C4×C4⋊C4—432no—
479C4×C4⋊C4—432no—
480C4×C4⋊C4—432no—
481C4×C4⋊C4—432no—
482C4×C4⋊C4—432no—
483C4×C4⋊C4—432no—
484C4×C4⋊C4—432no—
485C4×C4⋊C4—432no—
486C4×C4⋊C4—432no—
487C4×C4⋊C4—432no—
488C4×C4⋊C4—432no—
489C4×C4⋊C4C2×D4312yes—
490C4×C22⋊C4—431no—
491C4×C22⋊C4—432no—
492C4×C22⋊C4—431no—
493C4×C22⋊C4—431no—
494C4×C22⋊C4—432no—
495C4×C22⋊C4—432no—
496C4×C22⋊C4C2×D4311yescharacteristic
497C4×C22⋊C4C2×D4312yes—
498#376—432no—
499C2×#95—432no—
500C2×#95—431no—
501C2×#95C2×D4311yescharacteristic
502C43—432no—
503C43#3421511yescharacteristic, complemented, Sylow
504C22×Q8—432no—
505C22×Q8—431no—
506C22×Q8C22×D4311yescharacteristic
507C23×C4—431no—
508C23×C4—431no—
509C23×C4—432no—
510C23×C4C22×D4312yes—
511C23×C4C22×D4311yescharacteristic
512C4⋊Q8—438no—
513C4⋊Q8—438no—
514#125—4316no—
515C22⋊Q8—438no—
516C22⋊Q8—4316no—
517C22⋊Q8C4×D4318yes—
518C4×Q8—438no—
519C4×Q8—438no—
520C4×Q8—4316no—
521#117—4316no—
522#117—438no—
523#117—864no—
524C2×C4⋊C4—432no—
525C2×C4⋊C4—432no—
526C2×C4⋊C4—432no—
527C2×C4⋊C4—432no—
528C2×C4⋊C4—432no—
529C2×C4⋊C4—432no—
530C2×C4⋊C4—432no—
531C2×C4⋊C4—431no—
532C2×C4⋊C4—432no—
533C2×C4⋊C4—432no—
534C2×C4⋊C4—432no—
535C2×C4⋊C4—432no—
536C2×C4⋊C4—432no—
537C2×C4⋊C4—432no—
538C2×C4⋊C4—432no—
539C2×C4⋊C4—432no—
540C2×C4⋊C4—432no—
541C2×C4⋊C4—432no—
542C2×C4⋊C4—432no—
543C2×C4⋊C4—868no—
544C2×C4⋊C4C22×D4312yes—
545C2×C4⋊C4C22×D4312yes—
546C2×C4⋊C4C22×D4312yes—
547C2×C4⋊C4C22×D4311yescharacteristic
548C2×C22⋊C4—432no—
549C2×C22⋊C4—431no—
550C2×C22⋊C4—431no—
551C2×C22⋊C4C22×D4311yescharacteristic
552C2×C22⋊C4C22×D4312yes—
553C2×C22⋊C4C22×D4311yescharacteristic
554C2×C42—438no—
555C2×C42—432no—
556C2×C42—432no—
557C2×C42—432no—
558C2×C42—431no—
559C2×C42—431no—
560C2×C42—431no—
561C2×C42—431no—
562C2×C42—432no—
563C2×C42—432no—
564C2×C42—432no—
565C2×C42—432no—
566C2×C42—432no—
567C2×C42—432no—
568C2×C42—432no—
569C2×C42—432no—
570C2×C42—432no—
571C2×C42—432no—
572C2×C42C22×D4312yes—
573C2×C42C22×D4312yes—
574C2×C42C22×D4312yes—
575#95—432no—
576#95—432no—
577#95—431no—
578#95—431no—
579#95—432no—
580#95—432no—
581#95—432no—
582#95—432no—
583#95—432no—
584#95—432no—
585#95—432no—
586#95—432no—
587#95—432no—
588#95—432no—
589#95—432no—
590#95—432no—
591#95—432no—
592#95—432no—
593#95—432no—
594#95—432no—
595#95—432no—
596#95—432no—
597#95C22×D4311yescharacteristic
598#95C22×D4311yescharacteristic
599#95C22×D4312yes—
600#95C22×D4312yes—
601#95C22×D4312yes—
602#95C22×D4312yes—
603#95C22×D4312yes—
604#95C22×D4312yes—
605C24C23×D4311yescharacteristic
606C2×Q8—42no—
607C2×Q8—438no—
608C2×Q8—434no—
609C2×Q8—1722no—
610C2×Q8—1722no—
611C2×Q8—1722no—
612C2×Q8C2×C4×D4314yes—
613C22×C4—24no—
614C22×C4—42no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—434no—
618C22×C4—434no—
619C22×C4—434no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—432no—
624C22×C4—431no—
625C22×C4—432no—
626C22×C4—432no—
627C22×C4—434no—
628C22×C4—432no—
629C22×C4—432no—
630C22×C4—432no—
631C22×C4—864no—
632C22×C4—1722no—
633C22×C4—1722no—
634C22×C4—1722no—
635C22×C4C2×C4×D4314yes—
636C22×C4C23×D4312yes—
637C22×C4C23×D4312yes—
638C22×C4C23×D4312yes—
639C22×C4C23×D4311yescharacteristic
640C22×C4C23×D4311yescharacteristic
641C22×C4C23×D4312yes—
642C22×C4C23×D4312yes—
643C22×C4C23×D4312yes—
644C4⋊C4—42no—
645C4⋊C4—42no—
646C4⋊C4—438no—
647C4⋊C4—438no—
648C4⋊C4—438no—
649C4⋊C4—438no—
650C4⋊C4—438no—
651C4⋊C4—438no—
652C4⋊C4—434no—
653C4⋊C4—438no—
654C4⋊C4—864no—
655C4⋊C4—864no—
656C4⋊C4—864no—
657C4⋊C4—864no—
658C4⋊C4—864no—
659C4⋊C4—1722no—
660C4⋊C4—1722no—
661C4⋊C4—1722no—
662C4⋊C4—1722no—
663C4⋊C4—1722no—
664C4⋊C4—1722no—
665C4⋊C4C2×C4×D4318yes—
666C4⋊C4C2×C4×D4314yes—
667C22⋊C4—22no—
668C22⋊C4—438no—
669C22⋊C4—434no—
670C22⋊C4—862no—
671C22⋊C4C2×C4×D4318yes—
672C22⋊C4Q8×D4314yes—
673C42—42no—
674C42—42no—
675C42—42no—
676C42—434no—
677C42—434no—
678C42—434no—
679C42—434no—
680C42—438no—
681C42—438no—
682C42—438no—
683C42—864no—
684C42—1722no—
685C42—1722no—
686C42—1722no—
687C42—1722no—
688C42—1722no—
689C42—1722no—
690C42—1722no—
691C42—1722no—
692C42—1722no—
693C23—22no—
694C23—22no—
695C23C22×C4×D4312yes—
696C23C2×Q8×D4312yes—
697C23#41×D4312yes—
698C23C24×D4311yescharacteristic
699Q8—44no—
700Q8—1724no—
701Q8—1728no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—44no—
720C2×C4—84no—
721C2×C4—4316no—
722C2×C4—432no—
723C2×C4—432no—
724C2×C4—432no—
725C2×C4—432no—
726C2×C4—432no—
727C2×C4—432no—
728C2×C4—432no—
729C2×C4—432no—
730C2×C4—434no—
731C2×C4—434no—
732C2×C4—434no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—862no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—3444no—
751C2×C4—1724no—
752C2×C4C22×C4×D4312yes—
753C2×C4C22×C4×D4312yes—
754C2×C4C22×C4×D4314yes—
755C2×C4C22×C4×D4314yes—
756C2×C4C2×Q8×D4314yes—
757C22—22no—
758C22—22no—
759C22—24no—
760C22—24no—
761C22C4×Q8×D4314yes—
762C22C23×C4×D4311yescharacteristic
763C22C22×Q8×D4311yescharacteristic
764C22C2×#41×D4311yescharacteristic
765C22#1458373412yes—
766C22#1458373512yes—
767C4—22no—
768C4—22no—
769C4—24no—
770C4—24no—
771C4—24no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—434no—
776C4—434no—
777C4—864no—
778C4—862no—
779C4—862no—
780C4—864no—
781C4—864no—
782C4—1722no—
783C4—1722no—
784C4—1722no—
785C2—24no—
786C2C2×C4×Q8×D4311yescharacteristic
787C2#1914779311yescharacteristic
788C2#1914779411yescharacteristic
789C2#1914841512yes—
790C2#1914848312yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2368C2
socle, cosocleC23×C43C25
prime radicalC24×C43C24
hypercenter#2368D43
hypocenterC43#34215
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2368

Complements

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

NH ≅ G/Ntype
7. #19137551C2semidirect
8. #19137549C2semidirect
9. #19137549C2semidirect
10. #19137548C2semidirect
11. #19137340C2semidirect
12. #19137338C2semidirect
14. #19137152C2semidirect
15. C4×#13063315C2semidirect
20. #14583451C4semidirect
113. #13063324C2×C4semidirect
114. #13063323C2×C4semidirect
115. #13063315C2×C4semidirect
118. Q8×Dic43C2×C4semidirect
119. #13063290C2×C4semidirect
120. #13063290C2×C4semidirect
123. #13063281Q8semidirect
503. C43#34215semidirect

Maximal subgroups

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

subgroupindex
C2×#145834512
#191376802
#191376782
#191376762
#191376752
#191376732
#191375512
#191375492
#191375482
#191373402
#191373382
#191372142
#191371522
C4×#130633152
C2×#145827632
#191369502
C4×#130632812
C43×#23682
#3421543