Finite Group Databasebeta

← #25259867

Subgroups — #25259867

Order 11008.

1990 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583434C211yesmaximal, characteristic
2#19137742C212yesmaximal, complemented
3#19137740C212yesmaximal, complemented
4#19137720C212yesmaximal, complemented
5#19137708C212yesmaximal, complemented
6#19137564C212yesmaximal, complemented
7#19137534C212yesmaximal, complemented
8#19137479C212yesmaximal, complemented
9#19137454C212yesmaximal, complemented
10#19137408C211yesmaximal, characteristic, complemented
11#19137405C211yesmaximal, characteristic, complemented
12#19137401C211yesmaximal, characteristic, complemented
13#19137359C212yesmaximal
14#19137347C212yesmaximal, complemented
15#19137244C212yesmaximal, complemented
16#19137227C212yesmaximal, complemented
17#19136992C211yesmaximal, characteristic, complemented
18#19136991C211yesmaximal, characteristic, complemented
19C43×#2336C211yesmaximal, characteristic, complemented
20#14583434C4116yescomplemented
21C2×#13063320C2212yes—
22C2×#13063313C2211yescharacteristic
23C2×#13063310C2212yes—
24C2×#13063305C2211yescharacteristic
25C2×#13063300C2211yescharacteristic
26C2×#13063290C2211yescharacteristic
27C2×#13063287C2211yescharacteristic
28C2×#13063287C2212yes—
29C2×#13063283C2212yes—
30C2×C42×D43C2211yescharacteristic
31#14582803C2212yes—
32#14582803C2212yes—
33#14582801C2212yes—
34#14582800C2212yes—
35#14582798C2212yes—
36#14582796C2212yes—
37#14582794C2212yes—
38#14582791C2212yes—
39#14582791C2212yes—
40#14582791C2212yes—
41#14582790C2212yes—
42#14582790C2212yes—
43#14582790C2212yes—
44#14582789C2212yes—
45#14582789C2212yes—
46#14582789C2212yes—
47#14582788C2212yes—
48#14582788C2212yes—
49#14582788C2212yes—
50#14582785C2212yes—
51#14582785C2212yes—
52#14582785C2212yes—
53#14582785C2212yes—
54#14582784C2212yes—
55#14582783C2212yes—
56#14582782C2212yes—
57#14582781C2212yes—
58#14582777C2212yes—
59#14582777C2212yes—
60#14582777C2212yes—
61#14582777C2212yes—
62#14582773C2212yes—
63#14582773C2212yes—
64#14582770C2212yes—
65#14582770C2212yes—
66#14582767C2211yescharacteristic
67#14582766C2212yes—
68#14582766C2212yes—
69#14582764C2212yes—
70#14582764C2212yes—
71#14582763C2212yes—
72#14582761C2212yes—
73#14582761C2212yes—
74#14582761C2212yes—
75#14582758C2211yescharacteristic
76#14582758C2211yescharacteristic
77#14582756C2212yes—
78#14582756C2212yes—
79C4⋊C4×Dic43C2212yes—
80C4⋊C4×Dic43C2212yes—
81C4×Dic43⋊C4C2212yes—
82C4×C4⋊Dic43C2212yes—
83C4×C4⋊Dic43C2211yescharacteristic
84#14582750C2212yes—
85C4×(C2×D43)⋊C4C2211yescharacteristic
86C4×(C2×D43)⋊C4C2212yes—
87C4×(C2×D43)⋊C4C2212yes—
88C4×(C2×D43)⋊C4C2212yes—
89C4×(C2×D43)⋊C4C2211yescharacteristic
90#14582746C2212yes—
91#14582746C2212yes—
92#14582746C2212yes—
93#14582745C2211yescharacteristic
94#14582745C2211yescharacteristic
95#14582744C2211yescharacteristic
96#14582744C2211yescharacteristic
97#14582744C2212yes—
98#95×D43C2212yes—
99C2×#125×C43C2211yescharacteristic
100C43×#389C2212yes—
101C43×#387C2212yes—
102C43×#387C2212yes—
103C43×#387C2212yes—
104C43×#387C2212yes—
105C43×#383C2211yescharacteristic
106C4×C4⋊C4×C43C2212yes—
107C4×C4⋊C4×C43C2211yescharacteristic
108C22×Dic86C2311yescharacteristic
109C22×D172C2312yes—
110C22×D172C2311yescharacteristic
111C22×C4×D43C2312yes—
112C22×C4×D43C2312yes—
113C22×C4×D43C2311yescharacteristic
114C22×C4×D43C2311yescharacteristic
115C22×C4×D43C2311yescharacteristic
116C22×C4×D43C2312yes—
117#13063320C2×C4116yescomplemented
118#13063313C2×C418yes—
119#13063310C2×C4116yescomplemented
120#13063305C2×C418yescomplemented
121#13063300C2×C418yes—
122#13063290C2×C418yescomplemented
123#13063287C2×C418yes—
124#13063287C2×C4116yescomplemented
125#13063283C2×C4116yescomplemented
126C2×C4⋊Dic43C2312yes—
127C2×C4⋊Dic43C2312yes—
128C2×C4⋊Dic43C2312yes—
129C2×C4⋊Dic43C2312yes—
130C2×Dic43⋊C4C2312yes—
131C2×Dic43⋊C4C2312yes—
132C2×Dic43⋊C4C2312yes—
133C2×Dic43⋊C4C2312yes—
134C2×Dic43⋊C4C2312yes—
135C2×(C2×D43)⋊C4C2312yes—
136C2×(C2×D43)⋊C4C2312yes—
137C2×(C2×D43)⋊C4C2312yes—
138C2×(C2×D43)⋊C4C2312yes—
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×(C2×D43)⋊C4C2312yes—
150C2×C4×Dic43C2312yes—
151C2×C4×Dic43C2312yes—
152C2×C4×Dic43C2311yescharacteristic
153C2×C4×Dic43C2312yes—
154C2×C4×Dic43C2311yescharacteristic
155C2×C4×Dic43C2312yes—
156C2×C4×Dic43C2312yes—
157C2×C4×Dic43C2312yes—
158C2×C4×Dic43C2311yescharacteristic
159C2×C4×Dic43C2311yescharacteristic
160C2×C4×Dic43C2311yescharacteristic
161C2×C4×Dic43C2312yes—
162C42×D43C2×C418yescomplemented
163C43⋊#95C2312yes—
164C43⋊#95C2312yes—
165C43⋊#95C2312yes—
166C43⋊#95C2312yes—
167C43⋊#95C2312yes—
168C43⋊#95C2312yes—
169C43⋊#95C2312yes—
170C43⋊#95C2312yes—
171C43⋊#95C2311yescharacteristic
172C43⋊#95C2312yes—
173C43⋊#95C2312yes—
174C43⋊#95C2312yes—
175C43⋊#95C2312yes—
176C43⋊#95C2311yescharacteristic
177C43⋊#95C2312yes—
178C43⋊#95C2312yes—
179C43⋊#95C2312yes—
180C43⋊#95C2312yes—
181C43⋊#95C2312yes—
182C43⋊#95C2312yes—
183C43⋊#95C2312yes—
184#125×C43C2×C418yescomplemented
185C2×C4⋊C4×C43C2312yes—
186C2×C4⋊C4×C43C2312yes—
187C2×C4⋊C4×C43C2312yes—
188C2×C4⋊C4×C43C2311yescharacteristic
189C2×C4⋊C4×C43C2311yescharacteristic
190C2×C4⋊C4×C43C2312yes—
191C2×C4⋊C4×C43C2312yes—
192C2×C42×C43C2311yescharacteristic
193C2×C42×C43C2312yes—
194C2×C42×C43C2312yes—
195C2×C42×C43C2311yescharacteristic
196C2×C42×C43C2311yescharacteristic
197#95×C43C2312yes—
198#95×C43C2312yes—
199#95×C43C2312yes—
200#95×C43C2311yescharacteristic
201#95×C43C2312yes—
202#95×C43C2312yes—
203#95×C43C2312yes—
204#95×C43C2312yes—
205#95×C43C2311yescharacteristic
206C23×D43C2411yescharacteristic
207C23×D43C2412yes—
208C22×C4×C43C2412yes—
209C22×C4×C43C2412yes—
210C22×C4×C43C2412yes—
211C22×C4×C43C2412yes—
212C22×C4×C43C2411yescharacteristic
213C22×C4×C43C2411yescharacteristic
214C22×C4×C43C2412yes—
215C22×C4×C43C2412yes—
216C22×C4×C43C2411yescharacteristic
217C22×Dic43C2412yes—
218C22×Dic43C2412yes—
219C22×Dic43C2412yes—
220C22×Dic43C2412yes—
221C22×Dic43C2411yescharacteristic
222C22×Dic43C2411yescharacteristic
223C22×Dic43C2412yes—
224C22×Dic43C2411yescharacteristic
225C2×D172—42no—
226C2×D172—42no—
227C2×D172—42no—
228C2×D172C22×C414yes—
229C2×D172C22×C418yes—
230C2×C4×D43—42no—
231C2×C4×D43—41no—
232C2×C4×D43—41no—
233C2×C4×D43—42no—
234C2×C4×D43—42no—
235C2×C4×D43—42no—
236C2×C4×D43—42no—
237C2×C4×D43—42no—
238C2×C4×D43—42no—
239C2×C4×D43—42no—
240C2×C4×D43—42no—
241C2×C4×D43—42no—
242C2×C4×D43C22×C414yes—
243C2×C4×D43C22×C414yes—
244C2×C4×D43C22×C414yes—
245C2×C4×D43C22×C418yes—
246C2×Dic86—42no—
247C2×Dic86C22×C414yes—
248C4⋊C4×C43—42no—
249C4⋊C4×C43—42no—
250C4⋊C4×C43—42no—
251C4⋊C4×C43C22×C418yes—
252C4⋊C4×C43C22×C414yes—
253C4⋊C4×C43C22×C418yes—
254C4⋊C4×C43C22×C414yes—
255C42×C43—42no—
256C42×C43—41no—
257C42×C43—41no—
258C42×C43—42no—
259C42×C43C22×C414yes—
260(C2×D43)⋊C4—42no—
261(C2×D43)⋊C4—42no—
262(C2×D43)⋊C4—42no—
263(C2×D43)⋊C4—42no—
264(C2×D43)⋊C4—42no—
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)⋊C4C22×C418yes—
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⋊Dic43—42no—
278C4⋊Dic43C22×C418yes—
279Dic43⋊C4—42no—
280Dic43⋊C4—42no—
281Dic43⋊C4—42no—
282Dic43⋊C4—42no—
283Dic43⋊C4C22×C418yes—
284C4×Dic43—42no—
285C4×Dic43—42no—
286C4×Dic43—42no—
287C4×Dic43—42no—
288C4×Dic43—41no—
289C4×Dic43—42no—
290C4×Dic43—42no—
291C4×Dic43—41no—
292C4×Dic43C22×C414yes—
293C4×Dic43C22×C414yes—
294C4×Dic43C22×C414yes—
295C4×Dic43C22×C418yes—
296C23×C43C2511yescharacteristic
297C22×D43—21no—
298C22×D43—21no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43C23×C414yes—
308C22×D43C23×C412yes—
309C2×C4×C43—21no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—21no—
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—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×C43C23×C414yes—
330C2×C4×C43C23×C412yes—
331C2×C4×C43C23×C412yes—
332C2×C4×C43C23×C412yes—
333C2×C4×C43C23×C414yes—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—21no—
339C2×Dic43—21no—
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×Dic43C23×C412yes—
353C2×Dic43C23×C412yes—
354C2×Dic43C23×C412yes—
355C2×Dic43C23×C414yes—
356D172—44no—
357D172—48no—
358C4×D43—44no—
359C4×D43—48no—
360C4×D43—44no—
361C4×D43—44no—
362C4×D43—84no—
363C4×D43—84no—
364Dic86—44no—
365#34400—431nomaximal, Sylow
366C22×C43C24×C411yescharacteristic
367C22×C43#58511yescharacteristic
368C22×C43#58512yes—
369C22×C43#58511yescharacteristic
370C22×C43#58512yes—
371C2×D43—22no—
372C2×D43—24no—
373C2×D43—22no—
374C2×D43—22no—
375C2×D43—24no—
376C2×D43—24no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C4×C43—22no—
384C4×C43—22no—
385C4×C43—22no—
386C4×C43—24no—
387C4×C43—24no—
388C4×C43—42no—
389C4×C43—42no—
390C4×C43—42no—
391C4×C43—42no—
392Dic43—24no—
393Dic43—22no—
394Dic43—22no—
395Dic43—22no—
396Dic43—42no—
397Dic43—42no—
398Dic43—42no—
399Dic43—42no—
400C2×#529—431no—
401#2376—432no—
402#2376—432no—
403#2373—432no—
404#2373—432no—
405#2357—432no—
406#2353—432no—
407#2346—432no—
408#2343—432no—
409#2337—431no—
410#2337—431no—
411#2336—431no—
412#2336D4311yescharacteristic, complemented
413#2333—432no—
414#2332—432no—
415#2320—432no—
416#2318—432no—
417#2283—431no—
418#2283—431no—
419C2×C43#342811yescharacteristic
420C2×C43#342811yescharacteristic
421C2×C43#342811yescharacteristic
422C2×C43#356612yes—
423C2×C43#356612yes—
424D43—42no—
425D43—44no—
426#529—4316no—
427C2×#126—432no—
428C2×#125C2×D4311yescharacteristic
429C2×#124—431no—
430C2×#123—432no—
431C2×C22⋊Q8—431no—
432C2×#121—431no—
433C2×C4×Q8—431no—
434C2×C4×D4—431no—
435C2×C4×D4—432no—
436C2×#117—432no—
437C22×C42—431no—
438#391—432no—
439#391—432no—
440#390—432no—
441#390—432no—
442#389—432no—
443#389—432no—
444#389—432no—
445#389C2×D4312yes—
446#388—432no—
447#388—432no—
448#388—432no—
449#388—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#387—432no—
459#387—432no—
460#387—432no—
461#387—432no—
462#387—432no—
463#387—432no—
464#387—432no—
465#387—432no—
466#387C2×D4312yes—
467#387C2×D4312yes—
468#387C2×D4312yes—
469#387C2×D4312yes—
470#386—432no—
471#386—432no—
472#386—432no—
473#386—432no—
474#385—432no—
475#385—432no—
476#385—432no—
477#385—432no—
478#383—431no—
479#383—432no—
480#383—432no—
481#383C2×D4311yescharacteristic
482#382—432no—
483#382—432no—
484#382—432no—
485#381—432no—
486#381—432no—
487#381—432no—
488#380—432no—
489#380—432no—
490#380—431no—
491#380—431no—
492C4×C4⋊C4—432no—
493C4×C4⋊C4—432no—
494C4×C4⋊C4—432no—
495C4×C4⋊C4—432no—
496C4×C4⋊C4—431no—
497C4×C4⋊C4—432no—
498C4×C4⋊C4C2×D4311yescharacteristic
499C4×C4⋊C4C2×D4312yes—
500C4×C22⋊C4—432no—
501C4×C22⋊C4—432no—
502C4×C22⋊C4—432no—
503C4×C22⋊C4—431no—
504C4×C22⋊C4—431no—
505C4×C22⋊C4—432no—
506C4×C22⋊C4—432no—
507C4×C22⋊C4—432no—
508#376—431no—
509#376—431no—
510#376—432no—
511#376—431no—
512#376—431no—
513C2×#95—432no—
514C43#3440011yescharacteristic, complemented, Sylow
515C22×Q8—431no—
516C22×D4—432no—
517C22×D4—431no—
518C23×C4—432no—
519C23×C4—431no—
520C23×C4—431no—
521C23×C4—431no—
522C23×C4—432no—
523C23×C4—432no—
524#126—4316no—
525#125C4×D4318yescomplemented
526#124—438no—
527#123—4316no—
528C22⋊Q8—438no—
529#121—438no—
530C4×Q8—438no—
531C4×D4—438no—
532C4×D4—4316no—
533#117—4316no—
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⋊C4C22×D4312yes—
544C2×C4⋊C4C22×D4312yes—
545C2×C4⋊C4C22×D4312yes—
546C2×C4⋊C4C22×D4312yes—
547C2×C4⋊C4C22×D4311yescharacteristic
548C2×C4⋊C4C22×D4312yes—
549C2×C4⋊C4C22×D4311yescharacteristic
550C2×C22⋊C4—432no—
551C2×C22⋊C4—432no—
552C2×C22⋊C4—432no—
553C2×C22⋊C4—432no—
554C2×C22⋊C4—432no—
555C2×C22⋊C4—432no—
556C2×C22⋊C4—432no—
557C2×C22⋊C4—432no—
558C2×C22⋊C4—432no—
559C2×C22⋊C4—432no—
560C2×C22⋊C4—432no—
561C2×C22⋊C4—432no—
562C2×C22⋊C4—432no—
563C2×C22⋊C4—432no—
564C2×C22⋊C4—432no—
565C2×C42—431no—
566C2×C42—432no—
567C2×C42—431no—
568C2×C42—431no—
569C2×C42—438no—
570C2×C42—432no—
571C2×C42—431no—
572C2×C42—432no—
573C2×C42—431no—
574C2×C42—432no—
575C2×C42—432no—
576C2×C42—432no—
577C2×C42—432no—
578C2×C42C22×D4311yescharacteristic
579C2×C42C22×D4311yescharacteristic
580C2×C42C22×D4312yes—
581C2×C42C22×D4312yes—
582C2×C42C22×D4311yescharacteristic
583#95—432no—
584#95—432no—
585#95—432no—
586#95—432no—
587#95—432no—
588#95—432no—
589#95—431no—
590#95—432no—
591#95—432no—
592#95—431no—
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#95C22×D4312yes—
605#95C22×D4311yescharacteristic
606#95C22×D4311yescharacteristic
607#95C22×D4312yes—
608#95C22×D4312yes—
609#95C22×D4312yes—
610#95C22×D4312yes—
611#95C22×D4312yes—
612#95C22×D4312yes—
613C24—432no—
614C24—431no—
615C2×Q8—434no—
616C2×Q8—1722no—
617C2×D4—438no—
618C2×D4—434no—
619C2×D4—1722no—
620C2×D4—1722no—
621C2×D4—1722no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—432no—
625C22×C4—431no—
626C22×C4—434no—
627C22×C4—434no—
628C22×C4—434no—
629C22×C4—438no—
630C22×C4—432no—
631C22×C4—432no—
632C22×C4—432no—
633C22×C4—432no—
634C22×C4—1722no—
635C22×C4—1722no—
636C22×C4—1722no—
637C22×C4—1722no—
638C22×C4—1722no—
639C22×C4—1722no—
640C22×C4—1721no—
641C22×C4—1722no—
642C22×C4—1722no—
643C22×C4—1721no—
644C22×C4—1722no—
645C22×C4—1722no—
646C22×C4C23×D4312yes—
647C22×C4C23×D4312yes—
648C22×C4C23×D4312yes—
649C22×C4C23×D4312yes—
650C22×C4C23×D4311yescharacteristic
651C22×C4C23×D4311yescharacteristic
652C22×C4C23×D4312yes—
653C22×C4C23×D4312yes—
654C22×C4C23×D4311yescharacteristic
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—438no—
659C4⋊C4—438no—
660C4⋊C4—1722no—
661C4⋊C4—1722no—
662C4⋊C4—1722no—
663C4⋊C4—1722no—
664C4⋊C4—1722no—
665C4⋊C4—1722no—
666C4⋊C4—1722no—
667C4⋊C4C2×C4×D4318yes—
668C4⋊C4C2×C4×D4314yes—
669C4⋊C4C2×C4×D4318yes—
670C4⋊C4C2×C4×D4314yes—
671C22⋊C4—438no—
672C22⋊C4—438no—
673C22⋊C4—438no—
674C22⋊C4—438no—
675C22⋊C4—438no—
676C22⋊C4—1722no—
677C22⋊C4—1722no—
678C22⋊C4—1722no—
679C22⋊C4—1722no—
680C22⋊C4—1722no—
681C22⋊C4—1722no—
682C22⋊C4—1722no—
683C22⋊C4—1722no—
684C22⋊C4—1722no—
685C22⋊C4—1722no—
686C42—41no—
687C42—41no—
688C42—42no—
689C42—42no—
690C42—434no—
691C42—434no—
692C42—434no—
693C42—438no—
694C42—1722no—
695C42—1721no—
696C42—1721no—
697C42—1722no—
698C42—1722no—
699C42—1722no—
700C42—1722no—
701C42—1722no—
702C42C2×C4×D4314yes—
703C23—434no—
704C23—432no—
705C23—861no—
706C23—862no—
707C23—862no—
708C23—862no—
709C23—862no—
710C23—861no—
711C23—862no—
712C23—862no—
713C23—862no—
714C23—862no—
715C23C24×D4311yescharacteristic
716Q8—1724no—
717D4—1728no—
718D4—1724no—
719C2×C4—21no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—432no—
740C2×C4—432no—
741C2×C4—432no—
742C2×C4—434no—
743C2×C4—861no—
744C2×C4—862no—
745C2×C4—862no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—861no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
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—3444no—
762C2×C4—3444no—
763C2×C4—1724no—
764C2×C4—1724no—
765C2×C4—1728no—
766C2×C4—1724no—
767C2×C4C22×C4×D4312yes—
768C2×C4C22×C4×D4312yes—
769C2×C4C22×C4×D4312yes—
770C2×C4C22×C4×D4314yes—
771C2×C4C22×C4×D4314yes—
772C22—862no—
773C22—864no—
774C22—864no—
775C22—862no—
776C22—862no—
777C22—864no—
778C22—1722no—
779C22—1722no—
780C22—1722no—
781C22—1722no—
782C22—1722no—
783C22—1722no—
784C22C23×C4×D4311yescharacteristic
785C22#1458373411yescharacteristic
786C22#1458373512yes—
787C22#1458373611yescharacteristic
788C22#1458373612yes—
789C4—22no—
790C4—24no—
791C4—22no—
792C4—24no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—862no—
799C4—862no—
800C4—862no—
801C4—864no—
802C4—1722no—
803C4—1722no—
804C4—1722no—
805C4—1722no—
806C2—1722no—
807C2—1724no—
808C2#1914779411yescharacteristic
809C2#1914779511yescharacteristic
810C2#1914779711yescharacteristic
811C2#1914925412yes—
812C2#1914927812yes—
subgroupG/H
center, FrattiniC23C24×D43
commutatorC22×C43C24×C4
FittingC43×#2336C2
socle, cosocleC23×C43C25
prime radicalC2×#13063300C22
hypercenter#2336D43
hypocenterC43#34400
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #2336

Complements

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

NH ≅ G/Ntype
2. #19137742C2semidirect
3. #19137740C2semidirect
4. #19137720C2semidirect
5. #19137708C2semidirect
6. #19137564C2semidirect
7. #19137534C2semidirect
8. #19137479C2semidirect
9. #19137454C2semidirect
10. #19137408C2semidirect
11. #19137405C2semidirect
12. #19137401C2semidirect
14. #19137347C2semidirect
15. #19137244C2semidirect
16. #19137227C2semidirect
17. #19136992C2semidirect
18. #19136991C2semidirect
19. C43×#2336C2semidirect
20. #14583434C4semidirect
117. #13063320C2×C4semidirect
119. #13063310C2×C4semidirect
120. #13063305C2×C4semidirect
122. #13063290C2×C4semidirect
124. #13063287C2×C4semidirect
125. #13063283C2×C4semidirect
162. C42×D43C2×C4semidirect
184. #125×C43C2×C4semidirect
412. #2336D43semidirect
514. C43#34400semidirect
525. #125C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145834342
#191377422
#191377402
#191377202
#191377082
#191375642
#191375342
#191374792
#191374542
#191374082
#191374052
#191374012
#191373592
#191373472
#191372442
#191372272
#191369922
#191369912
C43×#23362
#3440043