Finite Group Databasebeta

← #25259933

Subgroups — #25259933

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×#14583430C211yesmaximal, characteristic
2#19137778C212yesmaximal, complemented
3#19137765C212yesmaximal, complemented
4#19137716C212yesmaximal, complemented
5#19137712C212yesmaximal, complemented
6#19137557C212yesmaximal, complemented
7#19137533C212yesmaximal, complemented
8#19137485C212yesmaximal, complemented
9#19137449C212yesmaximal, complemented
10#19137386C212yesmaximal, complemented
11#19137382C212yesmaximal, complemented
12#19137362C211yesmaximal, characteristic
13#19137351C211yesmaximal, characteristic, complemented
14#19137348C211yesmaximal, characteristic, complemented
15#19137232C212yesmaximal, complemented
16#19137221C212yesmaximal, complemented
17#19136989C211yesmaximal, characteristic, complemented
18#19136986C211yesmaximal, characteristic, complemented
19C43×#2333C211yesmaximal, characteristic
20#14583430C4116yescomplemented
21C2×#13063318C2212yes—
22C2×#13063316C2211yescharacteristic
23C2×#13063312C2211yescharacteristic
24C2×#13063306C2212yes—
25C2×#13063304C2211yescharacteristic
26C2×#13063290C2211yescharacteristic
27C2×D4×Dic43C2211yescharacteristic
28C2×D4×Dic43C2212yes—
29C2×#13063281C2212yes—
30C22×C4×Dic43C2211yescharacteristic
31#14582803C2212yes—
32#14582803C2212yes—
33#14582802C2212yes—
34#14582797C2212yes—
35#14582796C2212yes—
36#14582795C2212yes—
37#14582794C2212yes—
38#14582793C2212yes—
39#14582793C2212yes—
40#14582793C2212yes—
41#14582793C2212yes—
42#14582793C2212yes—
43#14582792C2212yes—
44#14582787C2212yes—
45#14582787C2212yes—
46#14582787C2212yes—
47#14582787C2212yes—
48#14582787C2212yes—
49#14582786C2212yes—
50#14582785C2212yes—
51#14582784C2212yes—
52#14582784C2212yes—
53#14582783C2212yes—
54#14582783C2212yes—
55#14582782C2212yes—
56#14582782C2212yes—
57#14582781C2212yes—
58#14582781C2212yes—
59#14582780C2212yes—
60#14582779C2212yes—
61#14582779C2212yes—
62#14582772C2212yes—
63#14582772C2212yes—
64#14582771C2212yes—
65#14582771C2212yes—
66#14582766C2212yes—
67#14582766C2212yes—
68#14582766C2212yes—
69#14582763C2212yes—
70#14582763C2212yes—
71#14582763C2212yes—
72#14582762C2211yescharacteristic
73#14582760C2212yes—
74#14582760C2212yes—
75#14582757C2212yes—
76#14582757C2211yescharacteristic
77#14582757C2212yes—
78#14582757C2211yescharacteristic
79C4⋊C4×Dic43C2212yes—
80C4×Dic43⋊C4C2212yes—
81C4×Dic43⋊C4C2212yes—
82C4×Dic43⋊C4C2211yescharacteristic
83C4×Dic43⋊C4C2211yescharacteristic
84#14582750C2212yes—
85#14582750C2212yes—
86#14582750C2212yes—
87C22⋊C4×Dic43C2212yes—
88C22⋊C4×Dic43C2211yescharacteristic
89C22⋊C4×Dic43C2212yes—
90C22⋊C4×Dic43C2211yescharacteristic
91C22⋊C4×Dic43C2212yes—
92C4×C22⋊Dic43C2211yescharacteristic
93C4×C22⋊Dic43C2212yes—
94#14582745C2212yes—
95#14582745C2211yescharacteristic
96#14582745C2211yescharacteristic
97#14582744C2212yes—
98C2×C43⋊#95C2212yes—
99C2×#121×C43C2211yescharacteristic
100C43×#390C2212yes—
101C43×#388C2212yes—
102C43×#387C2212yes—
103C43×#386C2212yes—
104C43×#386C2212yes—
105C43×#381C2211yescharacteristic
106C4×C22⋊C4×C43C2211yescharacteristic
107C4×C22⋊C4×C43C2212yes—
108C22×Dic86C2311yescharacteristic
109C23×Dic43C2312yes—
110C23×Dic43C2311yescharacteristic
111C23×Dic43C2311yescharacteristic
112C23×Dic43C2312yes—
113#13063318C2×C4116yescomplemented
114#13063316C2×C418yescomplemented
115#13063312C2×C418yes—
116#13063306C2×C4116yescomplemented
117#13063304C2×C418yescomplemented
118#13063290C2×C418yescomplemented
119D4×Dic43C2×C418yes—
120D4×Dic43C2×C4116yescomplemented
121#13063281C2×C4116yescomplemented
122C2×C4⋊Dic43C2312yes—
123C2×C4⋊Dic43C2311yescharacteristic
124C2×C4⋊Dic43C2312yes—
125C2×Dic43⋊C4C2312yes—
126C2×Dic43⋊C4C2312yes—
127C2×Dic43⋊C4C2312yes—
128C2×Dic43⋊C4C2312yes—
129C2×Dic43⋊C4C2312yes—
130C2×Dic43⋊C4C2312yes—
131C2×Dic43⋊C4C2312yes—
132C2×Dic43⋊C4C2312yes—
133C2×Dic43⋊C4C2312yes—
134C2×Dic43⋊C4C2312yes—
135C2×Dic43⋊C4C2312yes—
136C2×C22⋊Dic43C2312yes—
137C2×C22⋊Dic43C2311yescharacteristic
138C2×C22⋊Dic43C2312yes—
139C2×C22⋊Dic43C2312yes—
140C2×C22⋊Dic43C2312yes—
141C2×C22⋊Dic43C2311yescharacteristic
142C2×C22⋊Dic43C2312yes—
143C2×C22⋊Dic43C2312yes—
144C2×C22⋊Dic43C2312yes—
145C2×C22⋊Dic43C2312yes—
146C2×C4×Dic43C2×C418yescomplemented
147C2×C4×Dic43C2312yes—
148C2×C4×Dic43C2312yes—
149C2×C4×Dic43C2312yes—
150C2×C4×Dic43C2312yes—
151C2×C4×Dic43C2312yes—
152C2×C4×Dic43C2312yes—
153C2×C4×Dic43C2311yescharacteristic
154C2×C4×Dic43C2312yes—
155C2×C4×Dic43C2311yescharacteristic
156C2×C4×Dic43C2311yescharacteristic
157C2×C4×Dic43C2311yescharacteristic
158C2×C4×Dic43C2311yescharacteristic
159C2×C4×Dic43C2311yescharacteristic
160C2×C4×Dic43C2312yes—
161C43⋊#95C2312yes—
162C43⋊#95C2312yes—
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×D4×C43C2312yes—
185C22×D4×C43C2311yescharacteristic
186C23×C4×C43C2312yes—
187C23×C4×C43C2311yescharacteristic
188#121×C43C2×C418yes—
189C2×C4⋊C4×C43C2312yes—
190C2×C4⋊C4×C43C2311yescharacteristic
191C2×C22⋊C4×C43C2311yescharacteristic
192C2×C22⋊C4×C43C2312yes—
193C2×C22⋊C4×C43C2312yes—
194C2×C22⋊C4×C43C2312yes—
195C2×C22⋊C4×C43C2312yes—
196C2×C22⋊C4×C43C2311yescharacteristic
197C2×C22⋊C4×C43C2312yes—
198C2×C42×C43C2312yes—
199C2×C42×C43C2311yescharacteristic
200C2×C42×C43C2311yescharacteristic
201#95×C43C2312yes—
202#95×C43C2312yes—
203#95×C43C2312yes—
204#95×C43C2312yes—
205#95×C43C2312yes—
206C24×C43C2411yescharacteristic
207C24×C43C2412yes—
208C2×D4×C43—41no—
209C2×D4×C43—42no—
210C2×D4×C43—42no—
211C2×D4×C43—41no—
212C2×D4×C43C22×C414yes—
213C2×D4×C43C22×C418yes—
214C22×C4×C43—41no—
215C22×C4×C43—41no—
216C22×C4×C43—42no—
217C22×C4×C43—42no—
218C22×C4×C43—42no—
219C22×C4×C43C22×C414yes—
220C22×C4×C43C2412yes—
221C22×C4×C43C2412yes—
222C22×C4×C43C2412yes—
223C22×C4×C43C2412yes—
224C22×C4×C43C2411yescharacteristic
225C22×C4×C43C2411yescharacteristic
226C22×C4×C43C2412yes—
227C22×Dic43—42no—
228C22×Dic43—42no—
229C22×Dic43—42no—
230C22×Dic43—42no—
231C22×Dic43—42no—
232C22×Dic43—42no—
233C22×Dic43—42no—
234C22×Dic43C22×C414yes—
235C22×Dic43C22×C414yes—
236C22×Dic43C22×C418yes—
237C22×Dic43C2412yes—
238C22×Dic43C2412yes—
239C22×Dic43C2412yes—
240C22×Dic43C2412yes—
241C22×Dic43C2411yescharacteristic
242C22×Dic43C2411yescharacteristic
243C22×Dic43C2412yes—
244C22×Dic43C2411yescharacteristic
245C22×Dic43C2412yes—
246C22×Dic43C2411yescharacteristic
247C2×Dic86—41no—
248C2×Dic86—41no—
249C2×Dic86C22×C414yes—
250C4⋊C4×C43—42no—
251C4⋊C4×C43C22×C414yes—
252C22⋊C4×C43—42no—
253C22⋊C4×C43—41no—
254C22⋊C4×C43—41no—
255C22⋊C4×C43—42no—
256C22⋊C4×C43—42no—
257C22⋊C4×C43—42no—
258C22⋊C4×C43C22×C418yes—
259C42×C43—41no—
260C42×C43—41no—
261C42×C43—42no—
262C22⋊Dic43—42no—
263C22⋊Dic43—41no—
264C22⋊Dic43—41no—
265C22⋊Dic43—42no—
266C22⋊Dic43—42no—
267C22⋊Dic43—42no—
268C22⋊Dic43C22×C418yes—
269C22⋊Dic43C22×C418yes—
270C22⋊Dic43C22×C418yes—
271C22⋊Dic43C22×C418yes—
272C4⋊Dic43—42no—
273C4⋊Dic43C22×C414yes—
274C4⋊Dic43C22×C418yes—
275Dic43⋊C4—42no—
276Dic43⋊C4—42no—
277Dic43⋊C4—42no—
278Dic43⋊C4—42no—
279Dic43⋊C4—42no—
280Dic43⋊C4—42no—
281Dic43⋊C4—42no—
282Dic43⋊C4—42no—
283Dic43⋊C4C22×C418yes—
284Dic43⋊C4C22×C418yes—
285Dic43⋊C4C22×C418yes—
286C4×Dic43—42no—
287C4×Dic43—42no—
288C4×Dic43—42no—
289C4×Dic43—42no—
290C4×Dic43—42no—
291C4×Dic43—42no—
292C4×Dic43—42no—
293C4×Dic43—41no—
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×C43—22no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—22no—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43C23×C414yes—
311C23×C43C23×C412yes—
312C23×C43C2511yescharacteristic
313D4×C43—44no—
314D4×C43—48no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—21no—
320C2×C4×C43—21no—
321C2×C4×C43—22no—
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—44no—
334C2×C4×C43—84no—
335C2×C4×C43C23×C412yes—
336C2×C4×C43C23×C412yes—
337C2×C4×C43C23×C414yes—
338C2×Dic43—22no—
339C2×Dic43—22no—
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—48no—
360C2×Dic43—44no—
361C2×Dic43—84no—
362C2×Dic43C23×C412yes—
363C2×Dic43C23×C412yes—
364C2×Dic43C23×C412yes—
365C2×Dic43C23×C412yes—
366C2×Dic43C23×C414yes—
367C2×Dic43C23×C414yes—
368Dic86—44no—
369#34405—431nomaximal, Sylow
370C22×C43—22no—
371C22×C43—24no—
372C22×C43—22no—
373C22×C43—22no—
374C22×C43—24no—
375C22×C43—24no—
376C22×C43—42no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—42no—
380C22×C43—42no—
381C22×C43—42no—
382C22×C43C24×C411yescharacteristic
383C22×C43#58511yescharacteristic
384C22×C43#58512yes—
385C22×C43#58511yescharacteristic
386C22×C43#58512yes—
387C4×C43—22no—
388C4×C43—22no—
389C4×C43—24no—
390C4×C43—42no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43—42no—
394Dic43—24no—
395Dic43—22no—
396Dic43—22no—
397Dic43—22no—
398Dic43—24no—
399Dic43—22no—
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#2333D4311yescharacteristic
417#2332—431no—
418#2332—431no—
419#2319—432no—
420#2318—432no—
421#2283—431no—
422#2283—431no—
423C2×C43—42no—
424C2×C43—44no—
425C2×C43#342811yescharacteristic
426C2×C43#342811yescharacteristic
427C2×C43#342811yescharacteristic
428C2×C43#356712yes—
429C2×C43#356812yes—
430#529—4316no—
431C2×#126—432no—
432C2×#125—431no—
433C2×#124—431no—
434C2×#123—432no—
435C2×C22⋊Q8—431no—
436C2×#121C2×D4311yescharacteristic
437C2×C4×Q8—431no—
438C2×C4×D4—432no—
439C2×C4×D4—431no—
440C2×#117—432no—
441C22×C42—431no—
442#391—432no—
443#391—432no—
444#390—432no—
445#390C2×D4312yes—
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#388—432no—
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#387—432no—
473#387C2×D4312yes—
474#386—432no—
475#386—432no—
476#386C2×D4312yes—
477#386C2×D4312yes—
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—431no—
493#380—431no—
494#380—432no—
495#380—432no—
496C4×C4⋊C4—432no—
497C4×C4⋊C4—432no—
498C4×C4⋊C4—432no—
499C4×C4⋊C4—431no—
500C4×C4⋊C4—431no—
501C4×C4⋊C4—432no—
502C4×C4⋊C4—432no—
503C4×C4⋊C4—432no—
504C4×C22⋊C4—431no—
505C4×C22⋊C4—432no—
506C4×C22⋊C4—432no—
507C4×C22⋊C4—432no—
508C4×C22⋊C4—431no—
509C4×C22⋊C4—431no—
510C4×C22⋊C4—432no—
511C4×C22⋊C4C2×D4311yescharacteristic
512C4×C22⋊C4C2×D4312yes—
513#376—432no—
514#376—431no—
515#376—431no—
516#376—432no—
517C2×#95—432no—
518C43#3440511yescharacteristic, complemented, Sylow
519C22×Q8—431no—
520C22×D4C22×D4312yes—
521C22×D4C22×D4311yescharacteristic
522C23×C4—432no—
523C23×C4—431no—
524C23×C4—431no—
525C23×C4—432no—
526C23×C4C22×D4312yes—
527C23×C4C22×D4311yescharacteristic
528#126—4316no—
529#125—438no—
530#124—438no—
531#123—4316no—
532C22⋊Q8—438no—
533#121C4×D4318yes—
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⋊C4—432no—
551C2×C4⋊C4—432no—
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⋊C4C22×D4311yescharacteristic
565C2×C22⋊C4C22×D4311yescharacteristic
566C2×C22⋊C4C22×D4312yes—
567C2×C22⋊C4C22×D4312yes—
568C2×C22⋊C4C22×D4312yes—
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×C42—432no—
586C2×C42C22×D4311yescharacteristic
587C2×C42C22×D4311yescharacteristic
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#95—432no—
611#95—432no—
612#95C22×D4312yes—
613#95C22×D4312yes—
614#95C22×D4312yes—
615#95C22×D4312yes—
616#95C22×D4312yes—
617C24C23×D4311yescharacteristic
618C24C23×D4312yes—
619C2×Q8—434no—
620C2×Q8—1721no—
621C2×Q8—1721no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4C2×C4×D4318yes—
627C2×D4C2×C4×D4314yes—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—432no—
636C22×C4—431no—
637C22×C4—431no—
638C22×C4—432no—
639C22×C4—434no—
640C22×C4—434no—
641C22×C4—438no—
642C22×C4—432no—
643C22×C4—432no—
644C22×C4—432no—
645C22×C4—432no—
646C22×C4—1722no—
647C22×C4—1722no—
648C22×C4—1722no—
649C22×C4—1722no—
650C22×C4—1722no—
651C22×C4—1722no—
652C22×C4—1722no—
653C22×C4C2×C4×D4314yes—
654C22×C4C23×D4312yes—
655C22×C4C23×D4312yes—
656C22×C4C23×D4312yes—
657C22×C4C23×D4312yes—
658C22×C4C23×D4311yescharacteristic
659C22×C4C23×D4311yescharacteristic
660C22×C4C23×D4312yes—
661C4⋊C4—42no—
662C4⋊C4—438no—
663C4⋊C4—438no—
664C4⋊C4—434no—
665C4⋊C4—438no—
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⋊C4—1722no—
676C4⋊C4C2×C4×D4314yes—
677C22⋊C4—42no—
678C22⋊C4—41no—
679C22⋊C4—42no—
680C22⋊C4—41no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—438no—
684C22⋊C4—438no—
685C22⋊C4—438no—
686C22⋊C4—438no—
687C22⋊C4—1722no—
688C22⋊C4—1721no—
689C22⋊C4—1722no—
690C22⋊C4—1721no—
691C22⋊C4—1722no—
692C22⋊C4—1722no—
693C22⋊C4C2×C4×D4318yes—
694C42—41no—
695C42—41no—
696C42—42no—
697C42—434no—
698C42—434no—
699C42—434no—
700C42—434no—
701C42—438no—
702C42—1721no—
703C42—1721no—
704C42—1722no—
705C42—1722no—
706C42—1722no—
707C42—1722no—
708C42—1722no—
709C42—1722no—
710C42—1722no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23C22×C4×D4314yes—
722C23C22×C4×D4312yes—
723C23C24×D4311yescharacteristic
724Q8—1724no—
725D4—44no—
726D4—48no—
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—44no—
746C2×C4—84no—
747C2×C4—432no—
748C2×C4—432no—
749C2×C4—432no—
750C2×C4—432no—
751C2×C4—434no—
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—862no—
772C2×C4—862no—
773C2×C4—3444no—
774C2×C4—1724no—
775C2×C4—1724no—
776C2×C4—1728no—
777C2×C4C22×C4×D4312yes—
778C2×C4C22×C4×D4312yes—
779C2×C4C22×C4×D4314yes—
780C22—22no—
781C22—22no—
782C22—24no—
783C22—24no—
784C22—22no—
785C22—24no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22C23×C4×D4311yescharacteristic
793C22#1458373411yescharacteristic
794C22#1458373412yes—
795C22#1458373411yescharacteristic
796C22#1458373512yes—
797C4—22no—
798C4—22no—
799C4—24no—
800C4—42no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—862no—
805C4—862no—
806C4—864no—
807C4—862no—
808C4—862no—
809C4—864no—
810C4—1722no—
811C4—1722no—
812C4—1722no—
813C4—1722no—
814C2—42no—
815C2—44no—
816C2#1914779311yescharacteristic
817C2#1914779311yescharacteristic
818C2#1914779411yescharacteristic
819C2#1914928012yes—
820C2#1914928812yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2333C2
socle, cosocleC23×C43C25
prime radicalC2×#121×C43C22
hypercenter#2333D43
hypocenterC43#34405
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2333

Complements

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

NH ≅ G/Ntype
2. #19137778C2semidirect
3. #19137765C2semidirect
4. #19137716C2semidirect
5. #19137712C2semidirect
6. #19137557C2semidirect
7. #19137533C2semidirect
8. #19137485C2semidirect
9. #19137449C2semidirect
10. #19137386C2semidirect
11. #19137382C2semidirect
13. #19137351C2semidirect
14. #19137348C2semidirect
15. #19137232C2semidirect
16. #19137221C2semidirect
17. #19136989C2semidirect
18. #19136986C2semidirect
20. #14583430C4semidirect
113. #13063318C2×C4semidirect
114. #13063316C2×C4semidirect
116. #13063306C2×C4semidirect
117. #13063304C2×C4semidirect
118. #13063290C2×C4semidirect
120. D4×Dic43C2×C4semidirect
121. #13063281C2×C4semidirect
146. C2×C4×Dic43C2×C4semidirect
518. C43#34405semidirect

Maximal subgroups

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

subgroupindex
C2×#145834302
#191377782
#191377652
#191377162
#191377122
#191375572
#191375332
#191374852
#191374492
#191373862
#191373822
#191373622
#191373512
#191373482
#191372322
#191372212
#191369892
#191369862
C43×#23332
#3440543