Finite Group Databasebeta

← #25259938

Subgroups — #25259938

Order 11008.

1990 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583435C211yesmaximal, characteristic
2#19137778C212yesmaximal, complemented
3#19137767C212yesmaximal, complemented
4#19137720C212yesmaximal, complemented
5#19137708C212yesmaximal, complemented
6#19137559C212yesmaximal, complemented
7#19137534C212yesmaximal, complemented
8#19137484C212yesmaximal, complemented
9#19137454C212yesmaximal, complemented
10#19137390C212yesmaximal, complemented
11#19137378C212yesmaximal, complemented
12#19137360C211yesmaximal, characteristic
13#19137357C211yesmaximal, characteristic
14#19137353C211yesmaximal, characteristic, complemented
15#19137236C212yesmaximal, complemented
16#19137225C212yesmaximal, complemented
17#19136989C211yesmaximal, characteristic, complemented
18#19136986C211yesmaximal, characteristic, complemented
19C43×#2332C211yesmaximal, characteristic, complemented
20#14583435C4116yescomplemented
21C2×#13063320C2212yes—
22C2×#13063316C2211yescharacteristic
23C2×#13063314C2211yescharacteristic
24C2×#13063309C2212yes—
25C2×#13063299C2211yescharacteristic
26C2×Q8×Dic43C2211yescharacteristic
27C2×#13063287C2211yescharacteristic
28C2×(C22⋊D43)⋊C4C2212yes—
29C2×#13063283C2212yes—
30C22×C4×Dic43C2211yescharacteristic
31#14582806C2212yes—
32#14582799C2212yes—
33#14582799C2212yes—
34#14582797C2212yes—
35#14582796C2212yes—
36#14582795C2212yes—
37#14582794C2212yes—
38#14582792C2212yes—
39#14582792C2212yes—
40#14582791C2212yes—
41#14582790C2212yes—
42#14582790C2212yes—
43#14582790C2212yes—
44#14582789C2212yes—
45#14582788C2212yes—
46#14582788C2212yes—
47#14582788C2212yes—
48#14582785C2212yes—
49#14582785C2212yes—
50#14582784C2212yes—
51#14582784C2212yes—
52#14582784C2212yes—
53#14582783C2212yes—
54#14582782C2212yes—
55#14582782C2212yes—
56#14582782C2212yes—
57#14582781C2212yes—
58#14582777C2212yes—
59#14582777C2212yes—
60#14582775C2212yes—
61#14582775C2212yes—
62#14582773C2212yes—
63#14582773C2212yes—
64#14582770C2212yes—
65#14582770C2212yes—
66#14582766C2212yes—
67#14582766C2212yes—
68#14582766C2212yes—
69#14582764C2212yes—
70#14582763C2212yes—
71#14582763C2212yes—
72#14582762C2211yescharacteristic
73#14582761C2212yes—
74#14582760C2212yes—
75#14582757C2212yes—
76#14582757C2211yescharacteristic
77#14582757C2211yescharacteristic
78#14582756C2212yes—
79C4⋊C4×Dic43C2212yes—
80C4⋊C4×Dic43C2212yes—
81C4×Dic43⋊C4C2212yes—
82C4×Dic43⋊C4C2211yescharacteristic
83C4×Dic43⋊C4C2211yescharacteristic
84C4×C4⋊Dic43C2212yes—
85#14582750C2212yes—
86C22⋊C4×Dic43C2211yescharacteristic
87C22⋊C4×Dic43C2211yescharacteristic
88C4×(C2×D43)⋊C4C2212yes—
89C4×(C2×D43)⋊C4C2212yes—
90C4×(C2×D43)⋊C4C2212yes—
91C4×C22⋊Dic43C2211yescharacteristic
92#14582746C2212yes—
93#14582746C2212yes—
94#14582745C2211yescharacteristic
95#14582745C2211yescharacteristic
96#14582744C2212yes—
97#14582744C2212yes—
98#95×D43C2212yes—
99C2×C22⋊Q8×C43C2211yescharacteristic
100C43×#391C2212yes—
101C43×#388C2212yes—
102C43×#388C2212yes—
103C43×#387C2212yes—
104C43×#387C2212yes—
105C43×#381C2211yescharacteristic
106C4×C4⋊C4×C43C2212yes—
107C4×C22⋊C4×C43C2211yescharacteristic
108C22×D172C2311yescharacteristic
109C22×C22⋊D43C2312yes—
110C23×Dic43C2311yescharacteristic
111C23×Dic43C2311yescharacteristic
112C22×C4×D43C2312yes—
113C22×C4×D43C2312yes—
114C22×C4×D43C2312yes—
115#13063320C2×C4116yescomplemented
116#13063316C2×C418yescomplemented
117#13063314C2×C418yes—
118#13063309C2×C4116yescomplemented
119#13063299C2×C418yes—
120Q8×Dic43C2×C418yescomplemented
121#13063287C2×C418yes—
122(C22⋊D43)⋊C4C2×C4116yescomplemented
123#13063283C2×C4116yescomplemented
124C2×C4⋊Dic43C2312yes—
125C2×C4⋊Dic43C2312yes—
126C2×C4⋊Dic43C2311yescharacteristic
127C2×C4⋊Dic43C2312yes—
128C2×C4⋊Dic43C2312yes—
129C2×Dic43⋊C4C2312yes—
130C2×Dic43⋊C4C2312yes—
131C2×Dic43⋊C4C2312yes—
132C2×Dic43⋊C4C2312yes—
133C2×Dic43⋊C4C2312yes—
134C2×Dic43⋊C4C2312yes—
135C2×Dic43⋊C4C2312yes—
136C2×C22⋊Dic43C2311yescharacteristic
137C2×C22⋊Dic43C2312yes—
138C2×C22⋊Dic43C2311yescharacteristic
139C2×(C2×D43)⋊C4C2312yes—
140C2×(C2×D43)⋊C4C2312yes—
141C2×(C2×D43)⋊C4C2312yes—
142C2×(C2×D43)⋊C4C2312yes—
143C2×(C2×D43)⋊C4C2312yes—
144C2×(C2×D43)⋊C4C2312yes—
145C2×(C2×D43)⋊C4C2312yes—
146C2×(C2×D43)⋊C4C2312yes—
147C2×(C2×D43)⋊C4C2312yes—
148C2×(C2×D43)⋊C4C2312yes—
149C2×C4×Dic43C2×C418yescomplemented
150C2×C4×Dic43C2312yes—
151C2×C4×Dic43C2312yes—
152C2×C4×Dic43C2312yes—
153C2×C4×Dic43C2311yescharacteristic
154C2×C4×Dic43C2312yes—
155C2×C4×Dic43C2312yes—
156C2×C4×Dic43C2311yescharacteristic
157C2×C4×Dic43C2312yes—
158C2×C4×Dic43C2311yescharacteristic
159C2×C4×Dic43C2311yescharacteristic
160C2×C4×Dic43C2311yescharacteristic
161C2×C4×Dic43C2311yescharacteristic
162C2×C4×Dic43C2312yes—
163C43⋊#95C2312yes—
164C43⋊#95C2312yes—
165C43⋊#95C2312yes—
166C43⋊#95C2312yes—
167C43⋊#95C2312yes—
168C43⋊#95C2312yes—
169C43⋊#95C2312yes—
170C43⋊#95C2312yes—
171C43⋊#95C2312yes—
172C43⋊#95C2312yes—
173C43⋊#95C2312yes—
174C43⋊#95C2312yes—
175C43⋊#95C2312yes—
176C43⋊#95C2312yes—
177C43⋊#95C2312yes—
178C43⋊#95C2312yes—
179C43⋊#95C2312yes—
180C43⋊#95C2312yes—
181C43⋊#95C2312yes—
182C43⋊#95C2312yes—
183C43⋊#95C2312yes—
184C22×Q8×C43C2311yescharacteristic
185C23×C4×C43C2311yescharacteristic
186C22⋊Q8×C43C2×C418yescomplemented
187C2×C4⋊C4×C43C2312yes—
188C2×C4⋊C4×C43C2312yes—
189C2×C4⋊C4×C43C2311yescharacteristic
190C2×C4⋊C4×C43C2312yes—
191C2×C22⋊C4×C43C2311yescharacteristic
192C2×C22⋊C4×C43C2312yes—
193C2×C22⋊C4×C43C2311yescharacteristic
194C2×C22⋊C4×C43C2312yes—
195C2×C42×C43C2311yescharacteristic
196C2×C42×C43C2312yes—
197C2×C42×C43C2312yes—
198C2×C42×C43C2311yescharacteristic
199#95×C43C2312yes—
200#95×C43C2312yes—
201#95×C43C2312yes—
202#95×C43C2312yes—
203#95×C43C2312yes—
204#95×C43C2312yes—
205#95×C43C2312yes—
206C24×C43C2411yescharacteristic
207C23×D43C2412yes—
208C2×Q8×C43—41no—
209C2×Q8×C43—41no—
210C2×Q8×C43C22×C414yes—
211C22×C4×C43—41no—
212C22×C4×C43—41no—
213C22×C4×C43C22×C414yes—
214C22×C4×C43C2412yes—
215C22×C4×C43C2412yes—
216C22×C4×C43C2412yes—
217C22×C4×C43C2412yes—
218C22×C4×C43C2411yescharacteristic
219C22×C4×C43C2411yescharacteristic
220C22×C4×C43C2412yes—
221C22×C4×C43C2412yes—
222C2×C22⋊D43—42no—
223C2×C22⋊D43—42no—
224C2×C22⋊D43C22×C418yes—
225C22×Dic43—42no—
226C22×Dic43—42no—
227C22×Dic43C22×C414yes—
228C22×Dic43C22×C414yes—
229C22×Dic43C2412yes—
230C22×Dic43C2412yes—
231C22×Dic43C2412yes—
232C22×Dic43C2412yes—
233C22×Dic43C2411yescharacteristic
234C22×Dic43C2411yescharacteristic
235C22×Dic43C2412yes—
236C22×Dic43C2411yescharacteristic
237C22×Dic43C2411yescharacteristic
238C2×D172—41no—
239C2×D172—41no—
240C2×D172C22×C414yes—
241C2×C4×D43—42no—
242C2×C4×D43—42no—
243C2×C4×D43—42no—
244C2×C4×D43—42no—
245C2×C4×D43—42no—
246C2×C4×D43—42no—
247C2×C4×D43—42no—
248C2×C4×D43—42no—
249C2×C4×D43C22×C418yes—
250C4⋊C4×C43—42no—
251C4⋊C4×C43—42no—
252C4⋊C4×C43C22×C418yes—
253C4⋊C4×C43C22×C414yes—
254C22⋊C4×C43—42no—
255C22⋊C4×C43—41no—
256C22⋊C4×C43—41no—
257C22⋊C4×C43C22×C418yes—
258C42×C43—41no—
259C42×C43—41no—
260C42×C43—42no—
261C42×C43—42no—
262C22⋊Dic43—42no—
263C22⋊Dic43—41no—
264C22⋊Dic43—41no—
265(C2×D43)⋊C4—42no—
266(C2×D43)⋊C4—42no—
267(C2×D43)⋊C4—42no—
268(C2×D43)⋊C4—42no—
269(C2×D43)⋊C4—42no—
270(C2×D43)⋊C4—42no—
271(C2×D43)⋊C4C22×C418yes—
272(C2×D43)⋊C4C22×C418yes—
273(C2×D43)⋊C4C22×C418yes—
274(C2×D43)⋊C4C22×C418yes—
275C4⋊Dic43—42no—
276C4⋊Dic43—42no—
277C4⋊Dic43C22×C418yes—
278C4⋊Dic43C22×C414yes—
279C4⋊Dic43C22×C418yes—
280Dic43⋊C4—42no—
281Dic43⋊C4—42no—
282Dic43⋊C4—42no—
283Dic43⋊C4—42no—
284Dic43⋊C4—42no—
285Dic43⋊C4—42no—
286Dic43⋊C4C22×C418yes—
287C4×Dic43—42no—
288C4×Dic43—42no—
289C4×Dic43—42no—
290C4×Dic43—42no—
291C4×Dic43—41no—
292C4×Dic43—42no—
293C4×Dic43—42no—
294C4×Dic43—41no—
295C4×Dic43C22×C414yes—
296C4×Dic43C22×C414yes—
297C4×Dic43C22×C414yes—
298C4×Dic43C22×C414yes—
299C4×Dic43C22×C418yes—
300C23×C43—22no—
301C23×C43—21no—
302C23×C43—21no—
303C23×C43—22no—
304C23×C43C23×C412yes—
305C23×C43C2511yescharacteristic
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—22no—
312C22×D43C23×C414yes—
313Q8×C43—44no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—22no—
320C2×C4×C43—21no—
321C2×C4×C43—21no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—44no—
335C2×C4×C43C23×C412yes—
336C2×C4×C43C23×C412yes—
337C2×C4×C43C23×C414yes—
338C2×C4×C43C23×C414yes—
339C22⋊D43—48no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—44no—
359C2×Dic43—44no—
360C2×Dic43C23×C412yes—
361C2×Dic43C23×C412yes—
362C2×Dic43C23×C412yes—
363C2×Dic43C23×C412yes—
364C2×Dic43C23×C414yes—
365D172—44no—
366C4×D43—48no—
367C4×D43—84no—
368C4×D43—84no—
369#34405—431nomaximal, Sylow
370C22×C43—22no—
371C22×C43—22no—
372C22×C43—22no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43C24×C411yescharacteristic
376C22×C43#58511yescharacteristic
377C22×C43#58511yescharacteristic
378C22×C43#58512yes—
379C22×C43#58512yes—
380C2×D43—24no—
381C2×D43—24no—
382C2×D43—24no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—42no—
386C2×D43—42no—
387C4×C43—24no—
388C4×C43—22no—
389C4×C43—22no—
390C4×C43—24no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43—42no—
394C4×C43—42no—
395Dic43—22no—
396Dic43—22no—
397Dic43—22no—
398Dic43—22no—
399Dic43—24no—
400Dic43—42no—
401Dic43—42no—
402Dic43—42no—
403Dic43—42no—
404C2×#529—431no—
405#2382—432no—
406#2379—432no—
407#2373—432no—
408#2373—432no—
409#2356—432no—
410#2353—432no—
411#2347—432no—
412#2343—432no—
413#2335—432no—
414#2335—432no—
415#2333—431no—
416#2333—431no—
417#2332—431no—
418#2332D4311yescharacteristic, complemented
419#2319—432no—
420#2318—432no—
421#2283—431no—
422#2283—431no—
423C2×C43—42no—
424C2×C43#342811yescharacteristic
425C2×C43#342811yescharacteristic
426C2×C43#342811yescharacteristic
427C2×C43#356712yes—
428C2×C43#356812yes—
429D43—44no—
430#529—4316no—
431C2×#126—432no—
432C2×#125—431no—
433C2×#124—431no—
434C2×#123—432no—
435C2×C22⋊Q8C2×D4311yescharacteristic
436C2×#121—431no—
437C2×C4×Q8—431no—
438C2×C4×D4—431no—
439C2×C4×D4—432no—
440C2×#117—432no—
441C22×C42—431no—
442#391—432no—
443#391C2×D4312yes—
444#390—432no—
445#390—432no—
446#389—432no—
447#389—432no—
448#389—432no—
449#389—432no—
450#388—432no—
451#388—432no—
452#388—432no—
453#388—432no—
454#388—432no—
455#388—432no—
456#388—432no—
457#388—432no—
458#388—432no—
459#388—432no—
460#388C2×D4312yes—
461#388C2×D4312yes—
462#387—432no—
463#387—432no—
464#387—432no—
465#387—432no—
466#387—432no—
467#387—432no—
468#387—432no—
469#387—432no—
470#387—432no—
471#387—432no—
472#387C2×D4312yes—
473#387C2×D4312yes—
474#386—432no—
475#386—432no—
476#386—432no—
477#386—432no—
478#385—432no—
479#385—432no—
480#385—432no—
481#385—432no—
482#383—432no—
483#383—432no—
484#383—432no—
485#382—432no—
486#382—432no—
487#382—432no—
488#381—431no—
489#381—432no—
490#381—432no—
491#381C2×D4311yescharacteristic
492#380—432no—
493#380—431no—
494#380—431no—
495#380—432no—
496C4×C4⋊C4—432no—
497C4×C4⋊C4—432no—
498C4×C4⋊C4—432no—
499C4×C4⋊C4—432no—
500C4×C4⋊C4—431no—
501C4×C4⋊C4—431no—
502C4×C4⋊C4—432no—
503C4×C4⋊C4C2×D4312yes—
504C4×C22⋊C4—431no—
505C4×C22⋊C4—431no—
506C4×C22⋊C4—431no—
507C4×C22⋊C4—432no—
508C4×C22⋊C4—432no—
509C4×C22⋊C4—432no—
510C4×C22⋊C4—432no—
511C4×C22⋊C4—432no—
512C4×C22⋊C4C2×D4311yescharacteristic
513#376—431no—
514#376—431no—
515#376—432no—
516#376—432no—
517C2×#95—432no—
518C43#3440511yescharacteristic, complemented, Sylow
519C22×Q8C22×D4311yescharacteristic
520C22×D4—432no—
521C22×D4—431no—
522C23×C4—431no—
523C23×C4—431no—
524C23×C4—432no—
525C23×C4—432no—
526C23×C4—432no—
527C23×C4C22×D4311yescharacteristic
528#126—4316no—
529#125—438no—
530#124—438no—
531#123—4316no—
532C22⋊Q8C4×D4318yescomplemented
533#121—438no—
534C4×Q8—438no—
535C4×D4—438no—
536C4×D4—4316no—
537#117—4316no—
538C2×C4⋊C4—432no—
539C2×C4⋊C4—432no—
540C2×C4⋊C4—431no—
541C2×C4⋊C4—432no—
542C2×C4⋊C4—432no—
543C2×C4⋊C4—432no—
544C2×C4⋊C4—432no—
545C2×C4⋊C4—432no—
546C2×C4⋊C4—432no—
547C2×C4⋊C4—432no—
548C2×C4⋊C4—432no—
549C2×C4⋊C4—432no—
550C2×C4⋊C4C22×D4312yes—
551C2×C4⋊C4C22×D4312yes—
552C2×C4⋊C4C22×D4312yes—
553C2×C4⋊C4C22×D4311yescharacteristic
554C2×C22⋊C4—432no—
555C2×C22⋊C4—432no—
556C2×C22⋊C4—432no—
557C2×C22⋊C4—432no—
558C2×C22⋊C4—431no—
559C2×C22⋊C4—432no—
560C2×C22⋊C4—431no—
561C2×C22⋊C4—432no—
562C2×C22⋊C4—432no—
563C2×C22⋊C4—432no—
564C2×C22⋊C4—432no—
565C2×C22⋊C4—432no—
566C2×C22⋊C4—432no—
567C2×C22⋊C4C22×D4311yescharacteristic
568C2×C22⋊C4C22×D4311yescharacteristic
569C2×C22⋊C4C22×D4312yes—
570C2×C22⋊C4C22×D4312yes—
571C2×C42—438no—
572C2×C42—431no—
573C2×C42—432no—
574C2×C42—431no—
575C2×C42—431no—
576C2×C42—431no—
577C2×C42—431no—
578C2×C42—432no—
579C2×C42—432no—
580C2×C42—431no—
581C2×C42—432no—
582C2×C42—432no—
583C2×C42—432no—
584C2×C42—432no—
585C2×C42C22×D4311yescharacteristic
586C2×C42C22×D4311yescharacteristic
587C2×C42C22×D4312yes—
588C2×C42C22×D4312yes—
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#95—432no—
598#95—432no—
599#95—432no—
600#95—432no—
601#95—432no—
602#95—432no—
603#95—432no—
604#95—432no—
605#95—432no—
606#95—432no—
607#95—432no—
608#95—432no—
609#95—432no—
610#95C22×D4312yes—
611#95C22×D4312yes—
612#95C22×D4312yes—
613#95C22×D4312yes—
614#95C22×D4312yes—
615#95C22×D4312yes—
616#95C22×D4312yes—
617C24—432no—
618C24C23×D4311yescharacteristic
619C2×Q8—41no—
620C2×Q8—41no—
621C2×Q8C2×C4×D4314yes—
622C2×D4—438no—
623C2×D4—434no—
624C2×D4—1721no—
625C2×D4—1721no—
626C2×D4—1722no—
627C2×D4—1722no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—432no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—434no—
636C22×C4—434no—
637C22×C4—438no—
638C22×C4—432no—
639C22×C4—432no—
640C22×C4—432no—
641C22×C4—432no—
642C22×C4—1722no—
643C22×C4—1722no—
644C22×C4—1722no—
645C22×C4—1722no—
646C22×C4—1722no—
647C22×C4—1722no—
648C22×C4—1722no—
649C22×C4—1722no—
650C22×C4—1722no—
651C22×C4—1722no—
652C22×C4C2×C4×D4314yes—
653C22×C4C23×D4312yes—
654C22×C4C23×D4312yes—
655C22×C4C23×D4312yes—
656C22×C4C23×D4312yes—
657C22×C4C23×D4311yescharacteristic
658C22×C4C23×D4311yescharacteristic
659C22×C4C23×D4312yes—
660C22×C4C23×D4312yes—
661C4⋊C4—42no—
662C4⋊C4—42no—
663C4⋊C4—438no—
664C4⋊C4—438no—
665C4⋊C4—434no—
666C4⋊C4—438no—
667C4⋊C4—1722no—
668C4⋊C4—1722no—
669C4⋊C4—1722no—
670C4⋊C4—1722no—
671C4⋊C4—1722no—
672C4⋊C4—1722no—
673C4⋊C4—1722no—
674C4⋊C4—1722no—
675C4⋊C4C2×C4×D4318yes—
676C4⋊C4C2×C4×D4314yes—
677C22⋊C4—41no—
678C22⋊C4—41no—
679C22⋊C4—42no—
680C22⋊C4—438no—
681C22⋊C4—438no—
682C22⋊C4—438no—
683C22⋊C4—438no—
684C22⋊C4—1722no—
685C22⋊C4—1722no—
686C22⋊C4—1722no—
687C22⋊C4—1722no—
688C22⋊C4—1722no—
689C22⋊C4—1722no—
690C22⋊C4—1721no—
691C22⋊C4—1721no—
692C22⋊C4—1722no—
693C22⋊C4C2×C4×D4318yes—
694C42—41no—
695C42—41no—
696C42—42no—
697C42—42no—
698C42—434no—
699C42—434no—
700C42—434no—
701C42—434no—
702C42—438no—
703C42—1721no—
704C42—1721no—
705C42—1722no—
706C42—1722no—
707C42—1722no—
708C42—1722no—
709C42—1722no—
710C42—1722no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—434no—
716C23—862no—
717C23—862no—
718C23—862no—
719C23—862no—
720C23—862no—
721C23—862no—
722C23C22×C4×D4312yes—
723C23C24×D4311yescharacteristic
724Q8—44no—
725D4—1724no—
726D4—1728no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—44no—
748C2×C4—432no—
749C2×C4—432no—
750C2×C4—432no—
751C2×C4—432no—
752C2×C4—434no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—3444no—
772C2×C4—3444no—
773C2×C4—1728no—
774C2×C4—1724no—
775C2×C4—1724no—
776C2×C4C22×C4×D4312yes—
777C2×C4C22×C4×D4312yes—
778C2×C4C22×C4×D4314yes—
779C2×C4C22×C4×D4314yes—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—42no—
784C22—42no—
785C22—864no—
786C22—864no—
787C22—864no—
788C22—1722no—
789C22—1722no—
790C22—1722no—
791C22—1722no—
792C22C23×C4×D4311yescharacteristic
793C22#1458373411yescharacteristic
794C22#1458373411yescharacteristic
795C22#1458373512yes—
796C22#1458373612yes—
797C4—22no—
798C4—22no—
799C4—24no—
800C4—24no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—862no—
806C4—862no—
807C4—862no—
808C4—862no—
809C4—864no—
810C4—1722no—
811C4—1722no—
812C4—1722no—
813C4—1722no—
814C2—42no—
815C2—1724no—
816C2#1914779311yescharacteristic
817C2#1914779411yescharacteristic
818C2#1914779711yescharacteristic
819C2#1914928112yes—
820C2#1914928712yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2332C2
socle, cosocleC23×C43C25
prime radicalC2×#13063299C22
hypercenter#2332D43
hypocenterC43#34405
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2332

Complements

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

NH ≅ G/Ntype
2. #19137778C2semidirect
3. #19137767C2semidirect
4. #19137720C2semidirect
5. #19137708C2semidirect
6. #19137559C2semidirect
7. #19137534C2semidirect
8. #19137484C2semidirect
9. #19137454C2semidirect
10. #19137390C2semidirect
11. #19137378C2semidirect
14. #19137353C2semidirect
15. #19137236C2semidirect
16. #19137225C2semidirect
17. #19136989C2semidirect
18. #19136986C2semidirect
19. C43×#2332C2semidirect
20. #14583435C4semidirect
115. #13063320C2×C4semidirect
116. #13063316C2×C4semidirect
118. #13063309C2×C4semidirect
120. Q8×Dic43C2×C4semidirect
122. (C22⋊D43)⋊C4C2×C4semidirect
123. #13063283C2×C4semidirect
149. C2×C4×Dic43C2×C4semidirect
186. C22⋊Q8×C43C2×C4semidirect
418. #2332D43semidirect
518. C43#34405semidirect
532. C22⋊Q8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834352
#191377782
#191377672
#191377202
#191377082
#191375592
#191375342
#191374842
#191374542
#191373902
#191373782
#191373602
#191373572
#191373532
#191372362
#191372252
#191369892
#191369862
C43×#23322
#3440543