Finite Group Databasebeta

← #11887269

Subgroups — #11887269

Order 1152.

883 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594889C211yesmaximal, characteristic
2#10594825C211yesmaximal, characteristic, complemented
3#10592424C211yesmaximal, characteristic, complemented
4C3×#4731C211yesmaximal, characteristic, complemented
5C3×#4721C211yesmaximal, characteristic, complemented
6#10591188C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#10590961C211yesmaximal, characteristic, complemented
9#10590956C211yesmaximal, characteristic, complemented
10#10590868C211yesmaximal, characteristic, complemented
11#10590843C211yesmaximal, characteristic, complemented
12#10590796C211yesmaximal, characteristic, complemented
13#10590782C211yesmaximal, characteristic, complemented
14#10590775C211yesmaximal, characteristic, complemented
15#10590652C211yesmaximal, characteristic, complemented
16#81445—31nomaximal
17#80159—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C4×#638C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C2×C8×C3⋊D3C2211yescharacteristic, complemented
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C3×#924C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28#63977—21no—
29D3×#217—21no—
30#63966—21no—
31#63955—21no—
32#63916C2211yescharacteristic
33#63898C2211yescharacteristic
34#63886—21no—
35#63884—21no—
36#63872C2211yescharacteristic, complemented
37#63871C2211yescharacteristic, complemented
38#63863C2211yescharacteristic
39#63849C2211yescharacteristic, complemented
40#63848—21no—
41#63846—21no—
42#63843C2211yescharacteristic, complemented
43C2×#3718C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic
45#63647C2211yescharacteristic, complemented
46#63641C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#817C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63565C2211yescharacteristic, complemented
56#63565C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61#5806—31no—
62#5642—31no—
63#5630—31no—
64#5513—31no—
65C3×#483—31no—
66C3×#450—31no—
67C2×#832—31no—
68#5173—31no—
69#5171—31no—
70#5166—31no—
71Dic3×SD16—31no—
72#5051—31no—
73#5051—31no—
74C2×#809—31no—
75#4871—31no—
76#4866—31no—
77#4864—31no—
78#4852—31no—
79#4808—31no—
80#4804—31no—
81#4800—31no—
82#4798—31no—
83#4779—31no—
84#4772—31no—
85#4768—31no—
86#4763—31no—
87#4731D311yescharacteristic, complemented
88#67⋊C8—31no—
89#67⋊C8—31no—
90#67⋊C8—61no—
91#4721D311yescharacteristic, complemented
92C23×C3×D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638D411yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C22×C3×Dic3—21no—
97C2×C3×D12—22no—
98C2×C3×D12—21no—
99C2×C3×D12—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3796—22no—
109#3796—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112#3757D411yescharacteristic
113#3752D411yescharacteristic
114#3750D411yescharacteristic
115C4×C3⋊Dic3C2311yescharacteristic
116C2×C3⋊(C3⋊C8)—41no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C8×C3⋊D3—41no—
120C3×#217—21no—
121C3×#217—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×#204—22no—
130C3×#204—41no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142Dic32—21no—
143#3718—41no—
144#3296—91noSylow
145C22×C3×D4—31no—
146C2×#239—31no—
147C2×#237—31no—
148C22×D12C2×D311yescharacteristic
149C2×C3×SD16—31no—
150C2×C3×SD16—31no—
151C3×C22⋊Q8—31no—
152C3×C22⋊Q8—31no—
153C2×C3×C4⋊C4—31no—
154#953—61no—
155C2×#217—61no—
156#947—31no—
157#946—31no—
158Q8×Dic3—31no—
159C2×#216—31no—
160C2×#216—31no—
161#939—61no—
162#938—31no—
163#936—31no—
164#935—61no—
165D4×Dic3—31no—
166#929—61no—
167C4×#67—31no—
168C4×#67—31no—
169C4×#67—61no—
170#926—61no—
171C2×C4⋊Dic3C2×D311yescharacteristic
172#924C2×D311yescharacteristic
173#924C2×D311yescharacteristic
174C22×C3⋊C8—31no—
175C22×C3⋊C8—31no—
176C22×C3⋊C8—61no—
177C2×#204C2×D311yescharacteristic
178C2×#204C2×D311yescharacteristic
179C2×D3×C8—31no—
180C2×D3×C8—31no—
181C2×D3×C8—61no—
182#898—61no—
183#898—61no—
184#897—31no—
185#895—31no—
186#895—61no—
187#894—61no—
188#893—31no—
189#892—31no—
190#892—31no—
191#890—31no—
192#890—31no—
193#890—61no—
194#889—61no—
195#887—31no—
196#886—61no—
197#882—61no—
198D3×C22⋊C4—61no—
199#877—61no—
200C3×#106—31no—
201C3×#106—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—21no—
207C3×C22⋊C8C2×D311yescharacteristic
208C3×C22⋊C8C2×D311yescharacteristic
209#835—31no—
210#835—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—31no—
215#821C2×D311yescharacteristic
216#821C2×D311yescharacteristic
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—61no—
220#817C2×D311yescharacteristic, complemented
221#817C2×D311yescharacteristic, complemented
222#816C2×D311yescharacteristic, complemented
223#816C2×D311yescharacteristic, complemented
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227C8×Dic3—31no—
228C8×Dic3—31no—
229C8×Dic3—61no—
230#810—31no—
231#810—31no—
232#809—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#807—31no—
237#807—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249#638—22no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—42no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—42no—
266C3×D12#4112yes—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—42no—
272#626—81no—
273D3×Dic3—42no—
274D3×Dic3—81no—
275C32×C8—21no—
276C32×C8—21no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)—21no—
279#552—91no—
280#546—91no—
281#488—91no—
282#483—31no—
283#482—91no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—31no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C24×C3—61no—
295C23×D3—21no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×D4—31no—
299C2×C3×D4—31no—
300C2×C3×D4—62no—
301C2×C3×D4—61no—
302C2×C3×D4—121no—
303C22×C3×C4—21no—
304C22×C3×C4—61no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—31no—
308C2×#67—31no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C22×Dic3—21no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315#239—62no—
316#239—121no—
317#237—62no—
318#237—121no—
319C2×D12—22no—
320C2×D12—21no—
321C2×D12—41no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12C22×D311yescharacteristic
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—31no—
327C2×C4×D3—31no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×Dic6C22×D311yescharacteristic
332C2×Dic6C22×D311yescharacteristic
333C3×SD16—62no—
334C3×SD16—121no—
335C2×C3×C8—21no—
336C2×C3×C8—21no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350#217—21no—
351#217—21no—
352#217—31no—
353#217—31no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#216—121no—
360#216—121no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372C4⋊Dic3—21no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—121no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8—122no—
406#204—22no—
407#204—41no—
408D3×C8—121no—
409D3×C8—121no—
410D3×C8—122no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32#13512yes—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3×D3—22no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—84no—
425C32×C4—21no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C22×D4—31no—
439C2×Q16—91no—
440C2×SD16—31no—
441C2×SD16—31no—
442C22×C8—91no—
443C22×C8—91no—
444#126—181no—
445#125—91no—
446#125—181no—
447#124—91no—
448#123—181no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—31no—
452C22⋊Q8—91no—
453#121—91no—
454#121—181no—
455#120—181no—
456C4×Q8—91no—
457C4×D4—91no—
458C4×D4—91no—
459#117—91no—
460#117—181no—
461C2×C4⋊C4—31no—
462C2×C22⋊C4—181no—
463#107—91no—
464#106—31no—
465#106—31no—
466C4⋊C8—91no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—91no—
478C22⋊C8D3211yescharacteristic
479C4×C8—91no—
480C23×C3—21no—
481C23×C3—61no—
482C23×C3—61no—
483C23×C3—122no—
484C23×C3—122no—
485C23×C3—241no—
486C23×C3D3×D411yescharacteristic
487C23×C3D3×D411yescharacteristic
488C22×D3—21no—
489C22×D3—21no—
490C22×D3—31no—
491C22×D3—31no—
492C22×D3—42no—
493C22×D3—42no—
494C22×D3—61no—
495C22×D3—81no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×D4—32no—
501C3×D4—61no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—122no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—122no—
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—64no—
525#67—62no—
526#67—62no—
527#67—122no—
528#67—241no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—42no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—122no—
546C2×Dic3—241no—
547D12—21no—
548D12—21no—
549D12—21no—
550D12—42no—
551D12—122no—
552D12—241no—
553D12#23712yes—
554C4×D3—61no—
555C4×D3—61no—
556C4×D3—61no—
557C4×D3—61no—
558C4×D3—121no—
559C4×D3—121no—
560C4×D3—122no—
561C4×D3—241no—
562Dic6—21no—
563Dic6—21no—
564Dic6—21no—
565Dic6—21no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—41no—
571C3×C8—41no—
572C3⋊C8—62no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C3⋊C8—121no—
578C2×C32—22no—
579C2×C32#54611yescharacteristic
580C2×C32C2×#13511yescharacteristic
581C2×C32#57711yescharacteristic
582C3⋊D3—41no—
583C3×D3—42no—
584C3×D3—81no—
585C24—61no—
586#41—182no—
587#41—361no—
588C2×Q8—31no—
589C2×Q8—31no—
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—62no—
593C2×D4—61no—
594C2×D4—91no—
595C2×D4—121no—
596C2×D4—181no—
597C2×D4—181no—
598C22×C4—61no—
599C22×C4—91no—
600C22×C4—181no—
601C22×C4—181no—
602C22×C4C2×D3211yescharacteristic
603Q16—361no—
604SD16—62no—
605SD16—121no—
606C2×C8—91no—
607C2×C8—91no—
608C2×C8—361no—
609C2×C8—361no—
610C2×C8C2×D3211yescharacteristic
611C2×C8C2×D3211yescharacteristic
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—91no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—91no—
635C42—181no—
636C42—181no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—22no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—62no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—244no—
652C22×C3#91612yes—
653C22×C3#91612yes—
654C22×C3C2×D3×D411yescharacteristic
655C22×C3C2×D3×D411yescharacteristic
656C2×D3—22no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—62no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—84no—
670C2×D3—121no—
671C2×D3—121no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—41no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4C2×#23711yescharacteristic
684C3×C4#100411yescharacteristic
685C3×C4D3×#4111yescharacteristic
686C3×C4#100911yescharacteristic
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—62no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—61no—
700Dic3—121no—
701Dic3—121no—
702C32#329611yescharacteristic, complemented, Sylow
703C23—61no—
704C23—61no—
705C23—91no—
706C23—122no—
707C23—122no—
708C23—241no—
709C23#380211yescharacteristic
710Q8—61no—
711Q8—61no—
712Q8—61no—
713Q8—61no—
714D4—32no—
715D4—61no—
716D4—61no—
717D4—61no—
718D4—122no—
719D4—182no—
720D4—362no—
721D4—721no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—91no—
731C2×C4—91no—
732C2×C4—91no—
733C2×C4—122no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—362no—
737C2×C4—721no—
738C2×C4#380211yescharacteristic
739C2×C4C22×D3211yescharacteristic
740C8—21no—
741C8—21no—
742C8—181no—
743C8—181no—
744C2×C3—22no—
745C2×C3—22no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—42no—
750C2×C3—122no—
751C2×C3—241no—
752C2×C3#559111yescharacteristic
753C2×C3#565411yescharacteristic
754C2×C3C2×#91611yescharacteristic
755C2×C3C2×#91611yescharacteristic
756C2×C3#577511yescharacteristic
757C2×C3#577811yescharacteristic
758D3—42no—
759D3—81no—
760D3—122no—
761D3—121no—
762D3—121no—
763C22—21no—
764C22—21no—
765C22—62no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—181no—
772C22—181no—
773C22—181no—
774C22—244no—
775C22#6380912yes—
776C22C2×#380211yescharacteristic
777C4—21no—
778C4—121no—
779C4—121no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—181no—
785C4—181no—
786C4—181no—
787C4D3×#23711yescharacteristic
788C4#6431411yescharacteristic
789C3—21no—
790C3#8015911yescharacteristic, complemented
791C3#8144511yescharacteristic, complemented
792C2—22no—
793C2—122no—
794C2—241no—
795C2—361no—
796C2#1059429411yescharacteristic
797C2C2×#6380911yescharacteristic
798C2#1059471911yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10594889C2
hypercenterC22⋊C8D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10594825C2semidirect
3. #10592424C2semidirect
4. C3×#4731C2semidirect
5. C3×#4721C2semidirect
6. #10591188C2semidirect
7. C2×#63562C2semidirect
8. #10590961C2semidirect
9. #10590956C2semidirect
10. #10590868C2semidirect
11. #10590843C2semidirect
12. #10590796C2semidirect
13. #10590782C2semidirect
14. #10590775C2semidirect
15. #10590652C2semidirect
22. C2×C8×C3⋊D3C22semidirect
36. #63872C22semidirect
37. #63871C22semidirect
39. #63849C22semidirect
42. #63843C22semidirect
43. C2×#3718C22semidirect
45. #63647C22semidirect
46. #63641C22semidirect
47. C8×C3⋊Dic3C22semidirect
50. C3×#817C22semidirect
51. C3×#817C22semidirect
52. C3×#816C22semidirect
53. C3×#816C22semidirect
54. #63576C22semidirect
55. #63565C22semidirect
56. #63565C22semidirect
87. #4731D3semidirect
91. #4721D3semidirect
220. #817C2×D3semidirect
221. #817C2×D3semidirect
222. #816C2×D3semidirect
223. #816C2×D3semidirect
702. C32#3296semidirect
790. C3#80159semidirect
791. C3#81445semidirect

Maximal subgroups

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

subgroupindex
#105948892
#105948252
#105924242
C3×#47312
C3×#47212
#105911882
C2×#635622
#105909612
#105909562
#105908682
#105908432
#105907962
#105907822
#105907752
#105906522
#814453
#801593