Finite Group Databasebeta

← #11860618

Subgroups — #11860618

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63811C211yesmaximal, characteristic
2#10593889C211yesmaximal, characteristic
3#10593848C211yesmaximal, characteristic, complemented
4#10592407C211yesmaximal, characteristic, complemented
5C3×#4716C211yesmaximal, characteristic, complemented
6C3×#4710C211yesmaximal, characteristic, complemented
7#10590956C211yesmaximal, characteristic
8#10590818C211yesmaximal, characteristic, complemented
9#10590791C211yesmaximal, characteristic, complemented
10#10590775C211yesmaximal, characteristic, complemented
11#10590743C211yesmaximal, characteristic, complemented
12#10590688C211yesmaximal, characteristic, complemented
13#10590672C211yesmaximal, characteristic, complemented
14C4×#3718C211yesmaximal, characteristic, complemented
15C4×#3715C211yesmaximal, characteristic, complemented
16#79830—31nomaximal
17#79776—31nomaximal
18C2×#3797C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×#3743C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic
22#64081C2211yescharacteristic
23C2×C3×Dic12C2211yescharacteristic
24C2×C3×#204C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27C3×C4×Dic6C2211yescharacteristic
28C3×C4×Dic6C2211yescharacteristic
29#63904—21no—
30#63900C2211yescharacteristic
31#63898C2211yescharacteristic
32#63880—21no—
33#63877—21no—
34D3×Dic3⋊C4—21no—
35#63849C2211yescharacteristic
36#63843C2211yescharacteristic
37#63843C2211yescharacteristic
38#63843C2211yescharacteristic
39#63837—21no—
40#63837—21no—
41#63836—21no—
42#63836—21no—
43C2×#3718C2211yescharacteristic
44C2×#3715C2211yescharacteristic
45#63811C418yescomplemented
46C32×#97C2211yescharacteristic
47#63642C2211yescharacteristic
48C8×C3⋊Dic3C2211yescharacteristic
49C4×C3⋊(C3⋊C8)C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×#817C2211yescharacteristic
53C3×#816C2211yescharacteristic
54C3×#816C2211yescharacteristic
55C3×#816C2211yescharacteristic
56#63576C2211yescharacteristic
57#63574C2211yescharacteristic
58#63565C2211yescharacteristic
59#63565C2211yescharacteristic
60#63565C2211yescharacteristic
61#63562C2211yescharacteristic
62C2×#918—31no—
63C2×#915—31no—
64#5574—31no—
65#5572—31no—
66#5572—31no—
67#5546—31no—
68C3×#441—31no—
69C3×#440—31no—
70Dic3×Q16—31no—
71Dic3×SD16—31no—
72C4×#216—31no—
73C4×#216—31no—
74C4×#215—31no—
75C4×#214—31no—
76#4881—31no—
77#4873—31no—
78#4861—31no—
79#4852—31no—
80#4817—31no—
81#4804—31no—
82D3×#103—31no—
83D3×#103—31no—
84#4789—31no—
85#4789—31no—
86#4772—31no—
87#4757—31no—
88#4716D311yescharacteristic, complemented
89#4710D311yescharacteristic, complemented
90#4708—31no—
91#4708—31no—
92#4708—61no—
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×C3×D12C2311yescharacteristic
95C2×C3×C4×D3—21no—
96C2×C3×Dic6C2311yescharacteristic
97C2×C3×Dic6C2311yescharacteristic
98C2×C3×Dic6C2311yescharacteristic
99C2×#627—21no—
100C2×#626—21no—
101C2×#624—21no—
102C2×#624—21no—
103C2×D3×Dic3—21no—
104C2×D3×Dic3—21no—
105#3797—22no—
106#3797C2×C414yescomplemented
107#3796—22no—
108#3796C2×C414yes—
109C2×C32×C8C2311yescharacteristic
110C2×C32×C8C2311yescharacteristic
111C32×C42C2311yescharacteristic
112#3752D411yescharacteristic
113#3752D411yescharacteristic
114#3750D411yescharacteristic
115#3750D411yescharacteristic
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119#3743C2×C414yescomplemented
120C8×C3⋊D3—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×Dic12C2×C414yescomplemented
133C3×#204C2×C414yescomplemented
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142Dic32—21no—
143Dic32—21no—
144#3718C2×C414yescomplemented
145#3715C2×C414yescomplemented
146#2947—91noSylow
147C2×#239—31no—
148C2×D3×Q8—31no—
149C2×D3×Q8—31no—
150C2×#237—31no—
151C2×C3×Q16—31no—
152C2×C3×SD16—31no—
153C3×C4×Q8—31no—
154C3×C4×Q8—31no—
155C3×C4×Q8—31no—
156C3×C4×D4—31no—
157Q8×Dic3—31no—
158Q8×Dic3—31no—
159Q8×Dic3—31no—
160C2×#216—31no—
161C2×#216—31no—
162C2×#215—31no—
163D4×Dic3—31no—
164C2×#214—31no—
165C4×#67—61no—
166C2×Dic3⋊C4—61no—
167#918—38no—
168#915—38no—
169C2×Dic12C2×D311yescharacteristic
170C2×#204C2×D311yescharacteristic
171C2×ΓL(1,𝔽25)—31no—
172C2×ΓL(1,𝔽25)—31no—
173C2×ΓL(1,𝔽25)—61no—
174C2×D3×C8—31no—
175C2×D3×C8—31no—
176C2×D3×C8—61no—
177#893—31no—
178#893—61no—
179#892—31no—
180#892—31no—
181#892—61no—
182#892—61no—
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185D3×C4⋊C4—61no—
186#887—31no—
187#887—31no—
188#887—31no—
189#887—61no—
190#887—61no—
191#67⋊C4—61no—
192#877—61no—
193C4×D12—61no—
194C4×D12C2×D311yescharacteristic
195#872—31no—
196#872—31no—
197#872—61no—
198#872—61no—
199#872—61no—
200#872—61no—
201C4×Dic6—61no—
202C4×Dic6—61no—
203C4×Dic6C2×D311yescharacteristic
204C4×Dic6C2×D311yescharacteristic
205C4×Dic6C2×D311yescharacteristic
206C3×#107—31no—
207C3×#106—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#102—31no—
212C3×#97—21no—
213C3×#97C2×D311yescharacteristic
214C3×#97C2×D311yescharacteristic
215#835—31no—
216#835—31no—
217#835—31no—
218#832—31no—
219#821C2×D311yescharacteristic
220#818C2×D311yescharacteristic
221#817C2×D311yescharacteristic
222#816C2×D311yescharacteristic
223#816C2×D311yescharacteristic
224#816C2×D311yescharacteristic
225#815—31no—
226#815—31no—
227#815—61no—
228C8×Dic3—31no—
229C8×Dic3—31no—
230C8×Dic3—61no—
231#810—31no—
232#810—31no—
233#810—31no—
234#809—31no—
235#808—31no—
236#808—31no—
237#807—31no—
238#807—31no—
239C4×C3⋊C8—31no—
240C4×C3⋊C8—31no—
241C4×C3⋊C8—61no—
242C22×C3⋊D3C2×D411yescharacteristic
243C22×C3×D3—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4×C3⋊D3C22×C412yes—
251C4×C3⋊D3#4112yes—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C3×D12—21no—
260C3×D12C22×C412yes—
261C3×C4×D3—81no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6C22×C412yes—
266C3×Dic6C22×C412yes—
267C3×Dic6C22×C412yes—
268#627—24no—
269#626—24no—
270#624—24no—
271#624—81no—
272D3×Dic3—24no—
273D3×Dic3—81no—
274C32×C8—21no—
275C32×C8C22×C412yes—
276C3⋊(C3⋊C8)—21no—
277C3⋊(C3⋊C8)C22×C412yes—
278C2×#137—91no—
279#520—91no—
280#519—91no—
281#441—31no—
282#441—91no—
283#440—31no—
284#440—91no—
285C4×Q16—91no—
286C4×Q16—91no—
287C4×SD16—91no—
288C4×SD16—91no—
289#428—91no—
290#416—91no—
291C2×#103—91no—
292#405—91no—
293C2×C3×Q8—31no—
294C2×C3×Q8—31no—
295C2×C3×Q8—31no—
296C2×C3×D4—31no—
297C22×C3×C4—61no—
298C2×#67—61no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301#239—34no—
302#239—62no—
303D3×Q8—34no—
304D3×Q8—34no—
305D3×Q8—62no—
306D3×Q8—62no—
307#237—34no—
308#237—62no—
309C2×D12—61no—
310C2×D12C22×D311yescharacteristic
311C2×C4×D3—21no—
312C2×C4×D3—31no—
313C2×C4×D3—31no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—61no—
318C2×C4×D3—61no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×Dic6—61no—
322C2×Dic6—61no—
323C2×Dic6C22×D311yescharacteristic
324C2×Dic6C22×D311yescharacteristic
325C2×Dic6C22×D311yescharacteristic
326C3×Q16—34no—
327C3×SD16—34no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8C22×D311yescharacteristic
331C2×C3×C8C22×D311yescharacteristic
332C2×C3×C8C22×D311yescharacteristic
333C2×C3×C8C22×D311yescharacteristic
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C42—21no—
343C3×C42—61no—
344C3×C42—61no—
345C3×C42—61no—
346C3×C42C22×D311yescharacteristic
347C3×C42C22×D311yescharacteristic
348#217—61no—
349#216—34no—
350#216—34no—
351#215—34no—
352#214—34no—
353(C2×D3)⋊C4—21no—
354(C2×D3)⋊C4—31no—
355(C2×D3)⋊C4—31no—
356(C2×D3)⋊C4—31no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3C22×D311yescharacteristic
367C4⋊Dic3C22×D311yescharacteristic
368C4⋊Dic3C22×D311yescharacteristic
369C4⋊Dic3C22×D311yescharacteristic
370Dic3⋊C4—21no—
371Dic3⋊C4—21no—
372Dic3⋊C4—21no—
373Dic3⋊C4—31no—
374Dic3⋊C4—31no—
375Dic3⋊C4—31no—
376Dic3⋊C4—31no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3—21no—
387C4×Dic3—31no—
388C4×Dic3—31no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—61no—
404Dic12C4×D314yescomplemented
405#204C4×D314yescomplemented
406ΓL(1,𝔽25)—34no—
407ΓL(1,𝔽25)—34no—
408ΓL(1,𝔽25)—64no—
409D3×C8—62no—
410D3×C8—62no—
411D3×C8—64no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3C4×D412yes—
416C2×C3×D3—22no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C32×C4—21no—
420C32×C4—21no—
421C32×C4C23×C411yescharacteristic
422C32×C4C2×#4111yescharacteristic
423C3⋊Dic3—21no—
424C3⋊Dic3—21no—
425C3⋊Dic3C4×D412yes—
426C3×Dic3—22no—
427C3×Dic3—22no—
428C3×Dic3—22no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C2×#41—91no—
434C22×Q8—91no—
435#137—98no—
436C2×Q16—31no—
437C2×Q16—91no—
438C2×SD16—31no—
439C2×SD16—91no—
440C2×M16—91no—
441C22×C8—91no—
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8—31no—
445C4×Q8—91no—
446C4×Q8—91no—
447C4×Q8—91no—
448C4×Q8—181no—
449C4×Q8—181no—
450C4×D4—31no—
451C4×D4—91no—
452C4×D4—181no—
453C4×D4—181no—
454#117—91no—
455#117—91no—
456#117—181no—
457#117—181no—
458#117—181no—
459C2×C4⋊C4—91no—
460C2×C4⋊C4—181no—
461#107—31no—
462#107—91no—
463#106—31no—
464#106—91no—
465#103—31no—
466#103—31no—
467#103—31no—
468#103—91no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—91no—
473#97—91no—
474#97D3211yescharacteristic
475C4×C8—91no—
476C4×C8—91no—
477C23×C3—61no—
478C22×D3—21no—
479C22×D3—31no—
480C22×D3—31no—
481C22×D3—61no—
482C3×Q8—32no—
483C3×Q8—32no—
484C3×Q8—32no—
485C3×Q8—61no—
486C3×Q8—61no—
487C3×Q8—61no—
488C3×D4—32no—
489C3×D4—61no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—241no—
501C2×C3×C4D3×D411yescharacteristic
502C2×C3×C4D3×D411yescharacteristic
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506C2×C3×C4C23×D311yescharacteristic
507#67—64no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—31no—
518C2×Dic3—31no—
519C2×Dic3—31no—
520C2×Dic3—31no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—64no—
525C2×Dic3—241no—
526D12—21no—
527D12—64no—
528D12C2×C4×D312yes—
529C4×D3—32no—
530C4×D3—32no—
531C4×D3—32no—
532C4×D3—32no—
533C4×D3—62no—
534C4×D3—62no—
535C4×D3—64no—
536C4×D3—64no—
537C4×D3—64no—
538C4×D3—81no—
539C4×D3—241no—
540C4×D3—241no—
541C4×D3—241no—
542Dic6—21no—
543Dic6—21no—
544Dic6—21no—
545Dic6—64no—
546Dic6—64no—
547Dic6C2×C4×D312yes—
548Dic6C2×C4×D312yes—
549Dic6C2×C4×D312yes—
550C3×C8—22no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—22no—
554C3×C8C2×C4×D312yes—
555C3×C8C2×C4×D312yes—
556C3⋊C8—32no—
557C3⋊C8—32no—
558C3⋊C8—62no—
559C3⋊C8—62no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C2×C32C2×C4×D411yescharacteristic
563C2×C32#57711yescharacteristic
564C2×C32#57811yescharacteristic
565C3⋊D3—22no—
566C3×D3—42no—
567#41—94no—
568#41—182no—
569C2×Q8—31no—
570C2×Q8—31no—
571C2×Q8—31no—
572C2×Q8—94no—
573C2×Q8—181no—
574C2×Q8—182no—
575C2×D4—31no—
576C2×D4—181no—
577C22×C4—61no—
578C22×C4—91no—
579C22×C4—181no—
580C22×C4—181no—
581C22×C4—181no—
582C22×C4—181no—
583Q16—34no—
584Q16—94no—
585SD16—34no—
586SD16—94no—
587M16—94no—
588C2×C8—91no—
589C2×C8—91no—
590C2×C8—182no—
591C2×C8C2×D3211yescharacteristic
592C2×C8C2×D3211yescharacteristic
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—91no—
601C4⋊C4—91no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C22⋊C4—61no—
607C22⋊C4—91no—
608C22⋊C4—91no—
609C22⋊C4—181no—
610C22⋊C4—181no—
611C42—61no—
612C42—61no—
613C42—61no—
614C42—91no—
615C42—181no—
616C42—181no—
617C42—181no—
618C42—181no—
619C42C2×D3211yescharacteristic
620C22×C3—21no—
621C22×C3—62no—
622C22×C3—121no—
623C22×C3—121no—
624C22×C3C2×D3×D411yescharacteristic
625C22×C3C2×D3×D411yescharacteristic
626C2×D3—22no—
627C2×D3—32no—
628C2×D3—32no—
629C2×D3—41no—
630C2×D3—41no—
631C2×D3—62no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—61no—
636C2×D3—121no—
637C2×D3—121no—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—62no—
647C3×C4—62no—
648C3×C4—62no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4C22×C4×D311yescharacteristic
654C3×C4C22×C4×D311yescharacteristic
655C3×C4D3×#4111yescharacteristic
656C3×C4D3×#4111yescharacteristic
657Dic3—22no—
658Dic3—22no—
659Dic3—22no—
660Dic3—32no—
661Dic3—32no—
662Dic3—41no—
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666Dic3—62no—
667Dic3—61no—
668Dic3—61no—
669Dic3—61no—
670Dic3—61no—
671Dic3—121no—
672Dic3—121no—
673C32#294711yescharacteristic, complemented, Sylow
674C23—61no—
675C23—91no—
676Q8—32no—
677Q8—32no—
678Q8—32no—
679Q8—61no—
680Q8—61no—
681Q8—61no—
682Q8—184no—
683D4—32no—
684D4—61no—
685D4—184no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—91no—
694C2×C4—92no—
695C2×C4—92no—
696C2×C4—91no—
697C2×C4—91no—
698C2×C4—184no—
699C2×C4—184no—
700C2×C4—241no—
701C2×C4—721no—
702C2×C4—721no—
703C2×C4#380211yescharacteristic
704C2×C4#380211yescharacteristic
705C2×C4C22×D3211yescharacteristic
706C8—21no—
707C8—92no—
708C8—181no—
709C8C4×D3212yes—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—122no—
714C2×C3C4×D3×D411yescharacteristic
715C2×C3C4×D3×D411yescharacteristic
716C2×C3#577511yescharacteristic
717C2×C3#577811yescharacteristic
718C2×C3#577911yescharacteristic
719C2×C3#577911yescharacteristic
720D3—42no—
721D3—62no—
722D3—62no—
723D3—122no—
724C22—62no—
725C22—92no—
726C22—121no—
727C22—121no—
728C22—181no—
729C22—181no—
730C22C2×#380211yescharacteristic
731C4—21no—
732C4—21no—
733C4—62no—
734C4—62no—
735C4—62no—
736C4—92no—
737C4—121no—
738C4—121no—
739C4—121no—
740C4—121no—
741C4—181no—
742C4—181no—
743C4C2×C4×D3211yescharacteristic
744C4#6430611yescharacteristic
745C3—21no—
746C3#7977611yescharacteristic, complemented
747C3#7983011yescharacteristic, complemented
748C2—122no—
749C2—182no—
750C2C4×#380211yescharacteristic
751C2#1059471911yescharacteristic
752C2#1059472311yescharacteristic
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#97C22
socleC22×C32C22×D4
prime radicalC2×#3796C22
cosocleC2×C32×C4C24
hypercenter#97D32
hypocenterC32#2947
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
3. #10593848C2semidirect
4. #10592407C2semidirect
5. C3×#4716C2semidirect
6. C3×#4710C2semidirect
8. #10590818C2semidirect
9. #10590791C2semidirect
10. #10590775C2semidirect
11. #10590743C2semidirect
12. #10590688C2semidirect
13. #10590672C2semidirect
14. C4×#3718C2semidirect
15. C4×#3715C2semidirect
45. #63811C4semidirect
88. #4716D3semidirect
89. #4710D3semidirect
106. #3797C2×C4semidirect
119. #3743C2×C4semidirect
132. C3×Dic12C2×C4semidirect
133. C3×#204C2×C4semidirect
144. #3718C2×C4semidirect
145. #3715C2×C4semidirect
404. Dic12C4×D3semidirect
405. #204C4×D3semidirect
673. C32#2947semidirect
746. C3#79776semidirect
747. C3#79830semidirect

Maximal subgroups

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

subgroupindex
C2×#638112
#105938892
#105938482
#105924072
C3×#47162
C3×#47102
#105909562
#105908182
#105907912
#105907752
#105907432
#105906882
#105906722
C4×#37182
C4×#37152
#798303
#797763