Finite Group Databasebeta

← #11860945

Subgroups — #11860945

Order 1152.

1115 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596017C211yesmaximal, characteristic, complemented
2C2×#63936C211yesmaximal, characteristic
3#10593889C211yesmaximal, characteristic, complemented
4C3×C4×#214C211yesmaximal, characteristic, complemented
5C3×#5014C211yesmaximal, characteristic, complemented
6#10591445C211yesmaximal, characteristic, complemented
7#10591436C211yesmaximal, characteristic, complemented
8#10591418C211yesmaximal, characteristic, complemented
9#10590612C211yesmaximal, characteristic, complemented
10#10590575C211yesmaximal, characteristic, complemented
11#10590485C211yesmaximal, characteristic, complemented
12#10590460C211yesmaximal, characteristic, complemented
13#10590383C211yesmaximal, characteristic, complemented
14C4×#3716C211yesmaximal, characteristic, complemented
15#10590321C211yesmaximal, characteristic, complemented
16#79868—31nomaximal
17#79650—31nomaximal
18C2×#3830C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic
22C4×#638—21no—
23C2×#3750—21no—
24C4⋊C4×C3⋊D3C2211yescharacteristic
25#64096C2211yescharacteristic
26#64090—21no—
27#64086—21no—
28#64081C2211yescharacteristic
29C4×#634C2211yescharacteristic
30C2×C3×#214C2211yescharacteristic
31C2×C3×#213C2211yescharacteristic
32C3×C4×D12C2211yescharacteristic
33C3×C4×Dic6C2211yescharacteristic
34#63936C418yescomplemented
35#63904—21no—
36#63900C2211yescharacteristic
37#63898C2211yescharacteristic
38#63880—21no—
39#63877—21no—
40D3×Dic3⋊C4—21no—
41#63843C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44C2×#3712C2211yescharacteristic
45C2×#3710C2211yescharacteristic
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#809C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#803C2211yescharacteristic
53C3×C4×C3⋊C8C2211yescharacteristic
54#63573C2211yescharacteristic
55#63573C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63563C2211yescharacteristic
60#63555C2211yescharacteristic
61#63553C2211yescharacteristic
62C2×#916—31no—
63C2×#912—31no—
64#5574—31no—
65#5546—31no—
66#5546—31no—
67#5546—31no—
68#5546—61no—
69C3×#442—31no—
70C3×C4×SD16—31no—
71Dic3×SD16—31no—
72#5152—31no—
73#5030—31no—
74C4×#214—31no—
75C4×#214D311yescharacteristic, complemented
76#5014D311yescharacteristic, complemented
77D3×#106—31no—
78D3×#106—31no—
79#4853—31no—
80#4852—31no—
81#4803—31no—
82#4789—31no—
83#4785—31no—
84#4771—31no—
85#4771—31no—
86#4771—31no—
87#4758—31no—
88#4758—31no—
89#4716—31no—
90#4708—31no—
91C4×#204—31no—
92#4689—31no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4—21no—
95C2×#638—21no—
96C22×C3⋊Dic3—21no—
97C22×C3⋊Dic3—21no—
98#3830—22no—
99#3830C2×C414yescomplemented
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×#634C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3796—22no—
111#3796C2×C414yescomplemented
112C32×C4⋊C4C2311yescharacteristic
113C32×C22⋊C4—21no—
114C32×C42C2311yescharacteristic
115#3757—21no—
116#3752D411yescharacteristic
117#3752D411yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119#3750—21no—
120#3750—21no—
121#3750—21no—
122#3750D411yescharacteristic
123#3750D411yescharacteristic
124C4×C3⋊Dic3—21no—
125C4×C3⋊Dic3—21no—
126C4×C3⋊Dic3C2311yescharacteristic
127C3×#214C2×C414yescomplemented
128C3×#213C2×C414yescomplemented
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3C2311yescharacteristic
131C3×C4⋊Dic3C2311yescharacteristic
132C3×Dic3⋊C4—21no—
133C3×C4×Dic3—21no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3724—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3719C2×C414yescomplemented
143#3716C2×C414yescomplemented
144#3712—22no—
145#3710C2×C414yescomplemented
146#2952—91noSylow
147C2×#239—31no—
148C2×#237—31no—
149C2×#237—31no—
150C2×#237—31no—
151C2×#237—61no—
152C2×C3×SD16—31no—
153C2×C3×D8—31no—
154C3×C4×Q8—31no—
155C3×C4×D4—21no—
156C3×C4×D4—31no—
157C3×C4×D4C2×D311yescharacteristic
158C3×C4×D4C2×D311yescharacteristic
159Q8×Dic3—31no—
160C2×#216—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—61no—
165C2×#214—31no—
166C2×#214C2×D311yescharacteristic
167C2×#213C2×D311yescharacteristic
168C4×#67—61no—
169C4×#67—61no—
170C4×#67—61no—
171C4×#67—62no—
172C2×Dic3⋊C4—61no—
173C2×Dic3⋊C4—61no—
174C2×Dic3⋊C4—61no—
175C2×Dic3⋊C4—62no—
176#916—38no—
177#912—38no—
178C2×Dic12—31no—
179C2×#204—31no—
180C2×ΓL(1,𝔽25)—31no—
181C2×ΓL(1,𝔽25)—31no—
182C2×D3×C8—31no—
183C2×D3×C8—31no—
184#893—31no—
185#893—61no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—31no—
190D3×C4⋊C4—61no—
191D3×C4⋊C4—61no—
192#887—31no—
193#887—31no—
194#887—31no—
195#887—61no—
196#67⋊C4—61no—
197#67⋊C4—61no—
198#67⋊C4—61no—
199#67⋊C4—62no—
200#877—61no—
201#877—61no—
202#877—61no—
203#877—62no—
204C4×D12—61no—
205C4×D12C2×D311yescharacteristic
206#872—31no—
207#872—31no—
208#872—61no—
209#872—61no—
210C4×Dic6—31no—
211C4×Dic6—31no—
212C4×Dic6—61no—
213C4×Dic6C2×D311yescharacteristic
214C3×#106—31no—
215C3×#106—31no—
216C3×#103—31no—
217C3×#102—31no—
218C3×#102—31no—
219C3×#102—31no—
220C3×#97—31no—
221C3×C4×C8—31no—
222#835—31no—
223#832—31no—
224#832C2×D311yescharacteristic
225#832C2×D311yescharacteristic
226#821—31no—
227#817—31no—
228#817—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#815—31no—
233#815—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#810—31no—
237#810—31no—
238#810C2×D311yescharacteristic
239#809C2×D311yescharacteristic
240#808—31no—
241#808—31no—
242#808C2×D311yescharacteristic
243#808C2×D311yescharacteristic
244#803C2×D311yescharacteristic
245C4×C3⋊C8C2×D311yescharacteristic
246C23×C32—21no—
247C22×C3⋊D3C2×D411yescharacteristic
248C22×C3×D3—21no—
249C32×D4—21no—
250C32×D4C22×C412yes—
251C2×C32×C4—21no—
252C2×C32×C4—81no—
253C2×C32×C4C2×D411yescharacteristic
254C2×C32×C4C2×D411yescharacteristic
255C2×C32×C4C2411yescharacteristic
256#638—24no—
257C2×C3⋊Dic3—21no—
258C2×C3⋊Dic3—24no—
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—81no—
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C2×C3⋊Dic3C2×D411yescharacteristic
264C4×C3⋊D3—81no—
265C4×C3⋊D3C22×C412yes—
266C4×C3⋊D3#4112yes—
267#634—21no—
268#634C22×C412yes—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C3×D12—21no—
273C3×D12C22×C412yes—
274C3×C4×D3—81no—
275C3×Dic6—21no—
276C3×Dic6C22×C412yes—
277#626—24no—
278#624—81no—
279D3×Dic3—24no—
280D3×Dic3—81no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8C22×C412yes—
284C3×C3⋊C8C22×C412yes—
285C2×#135—91no—
286#520—91no—
287#520—91no—
288#442—31no—
289#442—91no—
290#441—91no—
291#441—91no—
292C4×SD16—31no—
293C4×SD16—91no—
294C4×SD16—91no—
295C4×SD16—91no—
296C2×#106—91no—
297#417—91no—
298#417—91no—
299#405—91no—
300C2×C3×Q8—31no—
301C2×C3×D4—21no—
302C2×C3×D4—31no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C22×C3×C4—22no—
306C22×C3×C4—21no—
307C22×C3×C4—21no—
308C22×C3×C4—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—62no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—62no—
320C22×Dic3—62no—
321#239—34no—
322#239—62no—
323#237—34no—
324#237—34no—
325#237—34no—
326#237—64no—
327#237—62no—
328#237—62no—
329#237—62no—
330#237—64no—
331C2×D12—61no—
332C2×D12C22×D311yescharacteristic
333C2×C4×D3—21no—
334C2×C4×D3—31no—
335C2×C4×D3—31no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—62no—
344C2×Dic6—31no—
345C2×Dic6—31no—
346C2×Dic6—61no—
347C2×Dic6C22×D311yescharacteristic
348C3×SD16—34no—
349C3×D8—34no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C3×C4⋊C4—21no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C22⋊C4—22no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—61no—
364C3×C42—21no—
365C3×C42—61no—
366C3×C42C22×D311yescharacteristic
367C3×C42C22×D311yescharacteristic
368#217—61no—
369#217—61no—
370#217—61no—
371#217—62no—
372#216—34no—
373#214—34no—
374#214C4×D314yescomplemented
375#213C4×D314yescomplemented
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—21no—
391Dic3⋊C4—31no—
392Dic3⋊C4—31no—
393Dic3⋊C4—31no—
394Dic3⋊C4—31no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—62no—
405Dic3⋊C4—62no—
406Dic3⋊C4—62no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409C4×Dic3—21no—
410C4×Dic3—31no—
411C4×Dic3—31no—
412C4×Dic3—61no—
413C4×Dic3—61no—
414C4×Dic3—61no—
415C4×Dic3—61no—
416C4×Dic3—61no—
417C4×Dic3—62no—
418C4×Dic3—62no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C2×C3⋊C8C22×D311yescharacteristic
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425Dic12—34no—
426#204—34no—
427ΓL(1,𝔽25)—62no—
428ΓL(1,𝔽25)—62no—
429D3×C8—34no—
430D3×C8—34no—
431C22×C32—22no—
432C22×C32—41no—
433C22×C32—41no—
434C22×C32C22×D411yescharacteristic
435C2×C3⋊D3—21no—
436C2×C3⋊D3—21no—
437C2×C3⋊D3C4×D412yes—
438C2×C3×D3—22no—
439C2×C3×D3—41no—
440C2×C3×D3—41no—
441C32×C4—21no—
442C32×C4—21no—
443C32×C4—41no—
444C32×C4C23×C411yescharacteristic
445C32×C4C2×#4111yescharacteristic
446C3⋊Dic3—22no—
447C3⋊Dic3—21no—
448C3⋊Dic3—21no—
449C3⋊Dic3—41no—
450C3⋊Dic3C4×D412yes—
451C3×Dic3—22no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C2×#41—91no—
455C2×#41—91no—
456#135—98no—
457C2×Q16—91no—
458C2×SD16—31no—
459C2×SD16—91no—
460C2×D8—31no—
461C2×M16—91no—
462C22×C8—91no—
463C4×Q8—31no—
464C4×Q8—91no—
465C4×Q8—91no—
466C4×Q8—91no—
467C4×D4—31no—
468C4×D4—91no—
469C4×D4—91no—
470C4×D4—181no—
471C4×D4—181no—
472C4×D4—181no—
473C4×D4—181no—
474C4×D4D3211yescharacteristic
475#117—91no—
476#117—181no—
477#117—181no—
478C2×C4⋊C4—91no—
479C2×C4⋊C4—91no—
480C2×C4⋊C4—181no—
481C2×C4⋊C4—181no—
482#106—31no—
483#106—31no—
484#106—91no—
485#106—91no—
486#103—31no—
487#103—91no—
488#103—91no—
489#103—91no—
490#102—31no—
491#102—31no—
492#102—31no—
493#102—91no—
494#97—31no—
495#97—91no—
496C4×C8—31no—
497C4×C8—91no—
498C23×C3—22no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—61no—
502C22×D3—21no—
503C22×D3—31no—
504C22×D3—31no—
505C22×D3—61no—
506C3×Q8—32no—
507C3×Q8—61no—
508C3×D4—22no—
509C3×D4—21no—
510C3×D4—21no—
511C3×D4—22no—
512C3×D4—32no—
513C3×D4—61no—
514C3×D4C2×C4×D312yes—
515C3×D4C2×C4×D312yes—
516C2×C3×C4—22no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—81no—
526C2×C3×C4—81no—
527C2×C3×C4—82no—
528C2×C3×C4—241no—
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4D3×D411yescharacteristic
531C2×C3×C4D3×D411yescharacteristic
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535#67—64no—
536#67—64no—
537#67—64no—
538#67—68no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—31no—
543C2×Dic3—31no—
544C2×Dic3—31no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—31no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—64no—
552C2×Dic3—64no—
553C2×Dic3—64no—
554C2×Dic3—62no—
555C2×Dic3—68no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—62no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—241no—
562C2×Dic3—241no—
563C2×Dic3—241no—
564C2×Dic3—242no—
565D12—21no—
566D12—64no—
567D12C2×C4×D312yes—
568C4×D3—32no—
569C4×D3—32no—
570C4×D3—32no—
571C4×D3—32no—
572C4×D3—62no—
573C4×D3—62no—
574C4×D3—64no—
575C4×D3—81no—
576C4×D3—241no—
577C4×D3—241no—
578C4×D3—241no—
579C4×D3—241no—
580C4×D3—241no—
581C4×D3—242no—
582Dic6—21no—
583Dic6—32no—
584Dic6—32no—
585Dic6—62no—
586Dic6—62no—
587Dic6—61no—
588Dic6—61no—
589Dic6C2×C4×D312yes—
590C3×C8—32no—
591C3×C8—32no—
592C3×C8—61no—
593C3×C8—61no—
594C3⋊C8—21no—
595C3⋊C8—21no—
596C3⋊C8C2×C4×D312yes—
597C3⋊C8C2×C4×D312yes—
598C2×C32—42no—
599C2×C32C2×C4×D411yescharacteristic
600C2×C32#57711yescharacteristic
601C2×C32#57711yescharacteristic
602C3⋊D3—22no—
603C3×D3—42no—
604#41—94no—
605#41—94no—
606#41—182no—
607#41—182no—
608C2×Q8—31no—
609C2×Q8—91no—
610C2×D4—31no—
611C2×D4—181no—
612C2×D4—181no—
613C2×D4C2×D3211yescharacteristic
614C22×C4—21no—
615C22×C4—61no—
616C22×C4—91no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623Q16—94no—
624SD16—34no—
625SD16—94no—
626D8—34no—
627M16—182no—
628C2×C8—31no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—31no—
632C2×C8—94no—
633C4⋊C4—31no—
634C4⋊C4—31no—
635C4⋊C4—61no—
636C4⋊C4—91no—
637C4⋊C4—91no—
638C4⋊C4—91no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C4⋊C4—181no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C4⋊C4C2×D3211yescharacteristic
645C22⋊C4—21no—
646C22⋊C4—61no—
647C22⋊C4—91no—
648C22⋊C4—91no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C42—61no—
652C42—91no—
653C42—181no—
654C42—181no—
655C42—181no—
656C42C2×D3211yescharacteristic
657C22×C3—24no—
658C22×C3—22no—
659C22×C3—22no—
660C22×C3—21no—
661C22×C3—42no—
662C22×C3—42no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—62no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3C2×D3×D411yescharacteristic
671C22×C3C2×D3×D411yescharacteristic
672C2×D3—22no—
673C2×D3—32no—
674C2×D3—32no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—62no—
678C2×D3—61no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—61no—
682C2×D3—121no—
683C2×D3—121no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—21no—
689C3×C4—21no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—42no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—62no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4C22×C4×D311yescharacteristic
699C3×C4C22×C4×D311yescharacteristic
700C3×C4D3×#4111yescharacteristic
701C3×C4D3×#4111yescharacteristic
702Dic3—22no—
703Dic3—32no—
704Dic3—32no—
705Dic3—41no—
706Dic3—41no—
707Dic3—62no—
708Dic3—64no—
709Dic3—61no—
710Dic3—61no—
711Dic3—61no—
712Dic3—61no—
713Dic3—62no—
714Dic3—62no—
715Dic3—121no—
716Dic3—121no—
717Dic3—122no—
718Dic3—121no—
719Dic3—121no—
720C32#295211yescharacteristic, complemented, Sylow
721C23—21no—
722C23—61no—
723C23—91no—
724Q8—32no—
725Q8—61no—
726Q8—92no—
727Q8—181no—
728D4—21no—
729D4—32no—
730D4—61no—
731D4—184no—
732D4—184no—
733D4C4×D3212yes—
734C2×C4—21no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—81no—
739C2×C4—91no—
740C2×C4—92no—
741C2×C4—92no—
742C2×C4—91no—
743C2×C4—91no—
744C2×C4—184no—
745C2×C4—184no—
746C2×C4—181no—
747C2×C4—181no—
748C2×C4—241no—
749C2×C4—721no—
750C2×C4—721no—
751C2×C4—721no—
752C2×C4—721no—
753C2×C4#381111yescharacteristic
754C2×C4#381111yescharacteristic
755C2×C4C22×D3211yescharacteristic
756C8—32no—
757C8—32no—
758C8—61no—
759C8—61no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—44no—
764C2×C3—42no—
765C2×C3—42no—
766C2×C3—122no—
767C2×C3C4×D3×D411yescharacteristic
768C2×C3C4×D3×D411yescharacteristic
769C2×C3#576211yescharacteristic
770C2×C3#577011yescharacteristic
771C2×C3#577511yescharacteristic
772C2×C3#577511yescharacteristic
773D3—42no—
774D3—62no—
775D3—62no—
776D3—122no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—62no—
781C22—92no—
782C22—121no—
783C22—121no—
784C22—181no—
785C22—181no—
786C22C2×#381111yescharacteristic
787C4—21no—
788C4—21no—
789C4—41no—
790C4—62no—
791C4—92no—
792C4—121no—
793C4—121no—
794C4—181no—
795C4—181no—
796C4—182no—
797C4—361no—
798C4C2×C4×D3211yescharacteristic
799C4#6430611yescharacteristic
800C3—21no—
801C3#7965011yescharacteristic, complemented
802C3#7986811yescharacteristic, complemented
803C2—42no—
804C2—122no—
805C2—182no—
806C2C4×#381111yescharacteristic
807C2#1059511511yescharacteristic
808C2#1059546211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×#63936C2
cosocleC2×C32×C4C24
hypercenterC4×D4D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596017C2semidirect
3. #10593889C2semidirect
4. C3×C4×#214C2semidirect
5. C3×#5014C2semidirect
6. #10591445C2semidirect
7. #10591436C2semidirect
8. #10591418C2semidirect
9. #10590612C2semidirect
10. #10590575C2semidirect
11. #10590485C2semidirect
12. #10590460C2semidirect
13. #10590383C2semidirect
14. C4×#3716C2semidirect
15. #10590321C2semidirect
34. #63936C4semidirect
75. C4×#214D3semidirect
76. #5014D3semidirect
99. #3830C2×C4semidirect
111. #3796C2×C4semidirect
127. C3×#214C2×C4semidirect
128. C3×#213C2×C4semidirect
142. #3719C2×C4semidirect
143. #3716C2×C4semidirect
145. #3710C2×C4semidirect
374. #214C4×D3semidirect
375. #213C4×D3semidirect
720. C32#2952semidirect
801. C3#79650semidirect
802. C3#79868semidirect

Maximal subgroups

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

subgroupindex
#105960172
C2×#639362
#105938892
C3×C4×#2142
C3×#50142
#105914452
#105914362
#105914182
#105906122
#105905752
#105904852
#105904602
#105903832
C4×#37162
#105903212
#798683
#796503