Finite Group Databasebeta

← #11888681

Subgroups — #11888681

Order 1152.

848 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595357C211yesmaximal, characteristic, complemented
2#10595245C211yesmaximal, characteristic, complemented
3#10592861C211yesmaximal, characteristic, complemented
4C3×#5174C211yesmaximal, characteristic, complemented
5C3×#5172C211yesmaximal, characteristic, complemented
6#10591616C211yesmaximal, characteristic, complemented
7#10591556C211yesmaximal, characteristic, complemented
8#10591549C211yesmaximal, characteristic, complemented
9#10591519C211yesmaximal, characteristic, complemented
10#10591460C211yesmaximal, characteristic, complemented
11#10591436C211yesmaximal, characteristic, complemented
12#10590780C211yesmaximal, characteristic, complemented
13#10590724C211yesmaximal, characteristic, complemented
14#10590708C211yesmaximal, characteristic, complemented
15#10590670C211yesmaximal, characteristic, complemented
16#80819—31nomaximal
17#80107—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×C32×SD16C2211yescharacteristic
21#64153C2211yescharacteristic
22D4×C3⋊Dic3C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#938C2211yescharacteristic
26C3×#938C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
29#67⋊Dic3—21no—
30#63970—21no—
31#63962—21no—
32#63956—21no—
33#63905—21no—
34C4×#625C2211yescharacteristic
35#63898C2211yescharacteristic
36D3×C4⋊Dic3C2211yescharacteristic
37#63885—21no—
38#63884—21no—
39D3×Dic3⋊C4—21no—
40#63872C2211yescharacteristic
41#63857C2211yescharacteristic
42#63841C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63643C2211yescharacteristic
46#63641C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#818C2211yescharacteristic
53#63574C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic
61#5824—31no—
62#5631—31no—
63#5618—31no—
64#5614—31no—
65C3×#468—31no—
66C3×#449—31no—
67#5233—31no—
68#5174D311yescharacteristic, complemented
69#5172D311yescharacteristic, complemented
70#5162—31no—
71#5162—31no—
72#5162—61no—
73#5158—31no—
74#5152—31no—
75#5133—31no—
76#5127—31no—
77#5043—31no—
78#5041—31no—
79#5037—31no—
80#4891—31no—
81#4888—31no—
82#4805—31no—
83#4804—31no—
84#4797—31no—
85#4797—31no—
86#4785—31no—
87#4778—31no—
88#4771—31no—
89#4766—31no—
90#4730—31no—
91#4723—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C3×#239—22no—
99C3×#239—41no—
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×#625—21no—
106C2×#625D411yescharacteristic
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110#3795—22no—
111#3795—41no—
112C32×SD16—41no—
113C2×C32×C8C2311yescharacteristic
114#3757—21no—
115#3754—41no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750—21no—
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×#217—21no—
123C3×#213—22no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×ΓL(1,𝔽25)—41no—
132#3724D411yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143D3×C3⋊C8—41no—
144#3307—91noSylow
145C2×C3×#41—31no—
146C2×#239C2×D311yescharacteristic
147C2×#237—31no—
148C2×#235—31no—
149C2×C3×SD16—21no—
150C2×C3×SD16C2×D311yescharacteristic
151C2×C3×SD16C2×D311yescharacteristic
152C2×C3×D8—31no—
153C2×C3×M16—31no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156C3×#121—31no—
157#946C2×D311yescharacteristic
158#944—31no—
159#944—31no—
160#944—61no—
161#939—61no—
162#939—61no—
163#938—61no—
164#938C2×D311yescharacteristic
165#938C2×D311yescharacteristic
166#935—61no—
167#935—61no—
168D4×Dic3—31no—
169D4×Dic3—31no—
170D4×Dic3—31no—
171D4×Dic3—61no—
172D4×Dic3—61no—
173C2×#214—31no—
174C2×#214—31no—
175C2×#214—61no—
176C2×#213C2×D311yescharacteristic
177#929—61no—
178C4×#67—31no—
179C4×#67—31no—
180#926—31no—
181C2×C4⋊Dic3—31no—
182#924—31no—
183C2×Dic3⋊C4—61no—
184C22×C3⋊C8—31no—
185C2×ΓL(1,𝔽25)C2×D311yescharacteristic
186C2×D3×C8—31no—
187#897—31no—
188#894—61no—
189#893—31no—
190#892—31no—
191D3×C4⋊C4—31no—
192D3×C4⋊C4—61no—
193#890—31no—
194#890—31no—
195#886—61no—
196#884—61no—
197#883—61no—
198#67⋊C4—61no—
199#879—61no—
200#879—61no—
201C3×#107—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—31no—
207#835—31no—
208#835—31no—
209#835—61no—
210#835C2×D311yescharacteristic
211#835C2×D311yescharacteristic
212#832—31no—
213#832—31no—
214#832C2×D311yescharacteristic
215#830—31no—
216#821—31no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8C2×D311yescharacteristic
220#818C2×D311yescharacteristic
221#817—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—31no—
226#816—61no—
227#815—31no—
228#815—31no—
229Dic3⋊C8—31no—
230Dic3⋊C8—31no—
231Dic3⋊C8—61no—
232#810—31no—
233#810—31no—
234#809—31no—
235#808—31no—
236#808—31no—
237#808—31no—
238C23×C32—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C32×D4—21no—
245C32×D4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—81no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253#634—21no—
254#634—21no—
255C3×#67—42no—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—42no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—42no—
270#625—41no—
271#625—42no—
272D3×Dic3—42no—
273D3×Dic3—42no—
274D3×Dic3—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#553—91no—
280#547—91no—
281#491—91no—
282#485—91no—
283#483—91no—
284#478—91no—
285#468—31no—
286#465—91no—
287#461—91no—
288#449—31no—
289#449—91no—
290#442—91no—
291#435—91no—
292#417—91no—
293#416—91no—
294C3×#41—62no—
295C3×#41—121no—
296C2×C3×Q8—21no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×D4—21no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—31no—
307C22×C3×C4—31no—
308C22×C3×C4—61no—
309C2×#67—21no—
310C2×#67—21no—
311C2×#67—31no—
312C2×#67—31no—
313C2×#67—61no—
314C2×#67—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—121no—
321#239—22no—
322#239—41no—
323#237—62no—
324#237—121no—
325#235—62no—
326#235—121no—
327C2×D12—21no—
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—21no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3C22×D311yescharacteristic
334C2×C4×D3C22×D311yescharacteristic
335C2×Dic6—31no—
336C2×Dic6—31no—
337C2×Dic6—61no—
338C3×SD16—41no—
339C3×SD16—41no—
340C3×SD16—42no—
341C3×D8—62no—
342C3×M16—121no—
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355#217—21no—
356#217—21no—
357#217—31no—
358#217—31no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—121no—
365#214—121no—
366#214—121no—
367#214—122no—
368#213—22no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—31no—
371(C2×D3)⋊C4—31no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—121no—
397Dic3⋊C4—121no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409ΓL(1,𝔽25)—41no—
410D3×C8—121no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C32×C4—41no—
425C32×C4C2×#4111yescharacteristic
426C32×C4H(5,𝔽2)11yescharacteristic
427C3⋊Dic3—21no—
428C3⋊Dic3—21no—
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C2×#41—31no—
437C2×#41—91no—
438C2×SD16—91no—
439C2×SD16D3211yescharacteristic
440C2×D8—31no—
441C2×M16—31no—
442C22×C8—91no—
443C4⋊Q8—91no—
444#126—181no—
445#125—91no—
446#123—181no—
447#123—181no—
448#123—181no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451#121—31no—
452#121—31no—
453#121—181no—
454#121—181no—
455C4×D4—91no—
456C4×D4—91no—
457C4×D4—91no—
458C4×D4—181no—
459#117—91no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4—181no—
462#107—31no—
463#106—91no—
464#106—91no—
465C4⋊C8—91no—
466#103—31no—
467#103—31no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476C22⋊C8—31no—
477C22⋊C8—91no—
478#97—91no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—31no—
483C23×C3—41no—
484C23×C3—61no—
485C22×D3—21no—
486C22×D3D3×D411yescharacteristic
487C22×D3D3×D411yescharacteristic
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—41no—
493C3×Q8—41no—
494C3×D4—22no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—32no—
500C3×D4—41no—
501C3×D4—61no—
502C3×D4—122no—
503C3×D4—122no—
504C3×D4—241no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—122no—
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—42no—
522#67—81no—
523#67—121no—
524#67—121no—
525#67—122no—
526#67—122no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—122no—
543C2×Dic3—122no—
544C2×Dic3—241no—
545C2×Dic3—241no—
546C2×Dic3—241no—
547C2×Dic3—242no—
548C2×Dic3D3×D411yescharacteristic
549C2×Dic3D3×D411yescharacteristic
550D12—21no—
551D12—42no—
552D12#23712yes—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—42no—
558C4×D3—122no—
559C4×D3—122no—
560C4×D3—241no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—121no—
566Dic6—121no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—41no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C2×C32—81no—
578C2×C32#54611yescharacteristic
579C2×C32#57511yescharacteristic
580C2×C32#57711yescharacteristic
581C3×D3—41no—
582C3×D3—41no—
583C3×D3—42no—
584#41—62no—
585#41—121no—
586#41—182no—
587#41—361no—
588C2×Q8—91no—
589C2×Q8C2×D3211yescharacteristic
590C2×D4—31no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—91no—
595C2×D4—181no—
596C2×D4C2×D3211yescharacteristic
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—61no—
600C22×C4—181no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4—181no—
604SD16—41no—
605SD16—361no—
606D8—62no—
607M16—121no—
608C2×C8—31no—
609C2×C8—31no—
610C2×C8—91no—
611C2×C8—361no—
612C2×C8C2×D3211yescharacteristic
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—91no—
618C4⋊C4—91no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—91no—
629C22⋊C4—91no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—91no—
635C42—181no—
636C22×C3—21no—
637C22×C3—42no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—62no—
650C22×C3—61no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3C2×D3×D411yescharacteristic
656C22×C3C2×D3×D411yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—22no—
663C2×D3—21no—
664C2×D3—41no—
665C2×D3—41no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—81no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4C2×#23711yescharacteristic
677C3×C4#100411yescharacteristic
678C3×C4#100411yescharacteristic
679C3×C4D3×#4111yescharacteristic
680Dic3—21no—
681Dic3—21no—
682Dic3—41no—
683Dic3—41no—
684Dic3—41no—
685Dic3—62no—
686Dic3—61no—
687Dic3—61no—
688Dic3—61no—
689Dic3—61no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—241no—
696Dic3—241no—
697C32#330711yescharacteristic, complemented, Sylow
698C23—21no—
699C23—31no—
700C23—31no—
701C23—61no—
702Q8—21no—
703Q8—21no—
704Q8—181no—
705Q8—181no—
706D4—21no—
707D4—21no—
708D4—32no—
709D4—61no—
710D4—122no—
711D4—122no—
712D4—241no—
713D4—361no—
714D4—362no—
715C2×C4—21no—
716C2×C4—31no—
717C2×C4—31no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—91no—
726C2×C4—91no—
727C2×C4—122no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—362no—
731C2×C4—362no—
732C2×C4—721no—
733C2×C4—721no—
734C2×C4C22×D3211yescharacteristic
735C8—21no—
736C8—61no—
737C8—61no—
738C8—181no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—82no—
743C2×C3—81no—
744C2×C3—81no—
745C2×C3—121no—
746C2×C3—122no—
747C2×C3—121no—
748C2×C3#559111yescharacteristic
749C2×C3#561011yescharacteristic
750C2×C3#576811yescharacteristic
751C2×C3#577311yescharacteristic
752C2×C3#577511yescharacteristic
753C2×C3#577811yescharacteristic
754D3—41no—
755D3—41no—
756D3—42no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—61no—
766C22—62no—
767C22—121no—
768C22—121no—
769C22D32×D411yescharacteristic
770C4—41no—
771C4—61no—
772C4—61no—
773C4—121no—
774C4—121no—
775C4—121no—
776C4—181no—
777C4—181no—
778C4—361no—
779C4—361no—
780C4D3×#23711yescharacteristic
781C4#6433011yescharacteristic
782C3—21no—
783C3#8010711yescharacteristic, complemented
784C3#8081911yescharacteristic, complemented
785C2—81no—
786C2—121no—
787C2—121no—
788C2—122no—
789C2#1059474511yescharacteristic
790C2#1059475411yescharacteristic
791C2#1059529011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×SD16C22
socleC22×C32C22×D4
hypercenterC2×SD16D32
hypocenterC32#3307
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10595357C2semidirect
2. #10595245C2semidirect
3. #10592861C2semidirect
4. C3×#5174C2semidirect
5. C3×#5172C2semidirect
6. #10591616C2semidirect
7. #10591556C2semidirect
8. #10591549C2semidirect
9. #10591519C2semidirect
10. #10591460C2semidirect
11. #10591436C2semidirect
12. #10590780C2semidirect
13. #10590724C2semidirect
14. #10590708C2semidirect
15. #10590670C2semidirect
68. #5174D3semidirect
69. #5172D3semidirect
697. C32#3307semidirect
783. C3#80107semidirect
784. C3#80819semidirect

Maximal subgroups

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

subgroupindex
#105953572
#105952452
#105928612
C3×#51742
C3×#51722
#105916162
#105915562
#105915492
#105915192
#105914602
#105914362
#105907802
#105907242
#105907082
#105906702
#808193
#801073