Finite Group Databasebeta

← #11870880

Subgroups — #11870880

Order 1152.

970 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595172C211yesmaximal, characteristic, complemented
2D3×D4×Dic3C211yesmaximal, characteristic, complemented
3#10592852C211yesmaximal, characteristic, complemented
4C3×#5156C211yesmaximal, characteristic
5C3×Dic3×D8C211yesmaximal, characteristic, complemented
6#10591479C211yesmaximal, characteristic, complemented
7#10591459C211yesmaximal, characteristic, complemented
8#10591434C211yesmaximal, characteristic, complemented
9Dic3×#213C211yesmaximal, characteristic, complemented
10#10591415C211yesmaximal, characteristic, complemented
11#10591401C211yesmaximal, characteristic, complemented
12#10590780C211yesmaximal, characteristic, complemented
13#10590744C211yesmaximal, characteristic, complemented
14#10590684C211yesmaximal, characteristic, complemented
15#10590655C211yesmaximal, characteristic, complemented
16#79989—31nomaximal
17#79592—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C22×D3×Dic3—21no—
20C2×C32×D8C2211yescharacteristic
21#64145C2211yescharacteristic, complemented
22D4×C3⋊Dic3C2211yescharacteristic
23C2×#3754C2211yescharacteristic
24C3×#938C2211yescharacteristic
25C3×D4×Dic3C2211yescharacteristic
26C3×D4×Dic3C2211yescharacteristic, complemented
27C2×C3×#213C2211yescharacteristic
28#67⋊Dic3—21no—
29Dic3×#67—21no—
30Dic3×#67—21no—
31#63969—21no—
32D3×#217—21no—
33#63956—21no—
34#63955—21no—
35#63898C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37D3×C4⋊Dic3C2211yescharacteristic
38C4×D3×Dic3C2211yescharacteristic
39#63872C2211yescharacteristic, complemented
40#63857C2211yescharacteristic
41#63844C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
43#63659C2211yescharacteristic, complemented
44#63643C2211yescharacteristic, complemented
45#63641C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#818C2211yescharacteristic, complemented
52C3×C8×Dic3C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C2×D4×Dic3—31no—
62#5600—31no—
63#5557—31no—
64C4×D3×D4—31no—
65C3×#447—31no—
66C3×C4×D8—31no—
67#5218—31no—
68#5156D311yescharacteristic
69#5153—31no—
70#5153—31no—
71#5153—31no—
72#5153—61no—
73Dic3×D8—31no—
74Dic3×D8D311yescharacteristic, complemented
75#5034—31no—
76C4×#214—31no—
77C4×#213—31no—
78#4891—31no—
79#4884—31no—
80#4787—31no—
81#4777—31no—
82#4776—31no—
83#4766—31no—
84#4766—31no—
85#4763—31no—
86#4758—31no—
87#4758—31no—
88#4722—31no—
89#4718—31no—
90C4×#204—31no—
91#4685—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3—21no—
101C3×D3×D4—22no—
102C3×D3×D4—22no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—44no—
109C2×D3×Dic3D411yescharacteristic
110C2×D3×Dic3D411yescharacteristic
111C32×D8—22no—
112C2×C32×C8C2311yescharacteristic
113#3757—21no—
114#3757—21no—
115#3757—21no—
116#3754—22no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×#213—22no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138Dic32—21no—
139Dic32D411yescharacteristic
140Dic32D411yescharacteristic
141#3716—22no—
142#3105—91noSylow
143C22×C3×D4—31no—
144C23×Dic3—61no—
145C2×D3×D4C2×D311yescharacteristic
146C22×C4×D3—61no—
147C2×C3×D8—21no—
148C2×C3×D8—31no—
149C2×C3×D8C2×D311yescharacteristic
150C2×C3×D8C2×D311yescharacteristic
151C3×#121—31no—
152C3×C4×D4—31no—
153C3×C4×D4—31no—
154C2×#217—61no—
155#938C2×D311yescharacteristic
156#936—31no—
157#936—31no—
158#936—61no—
159#935—61no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—31no—
164D4×Dic3—61no—
165D4×Dic3—61no—
166D4×Dic3—61no—
167D4×Dic3—61no—
168D4×Dic3C2×D311yescharacteristic
169D4×Dic3C2×D311yescharacteristic, complemented
170C2×#214—31no—
171C2×#214—31no—
172C2×#214—31no—
173C2×#214—61no—
174C2×#213C2×D311yescharacteristic
175C4×#67—61no—
176C4×#67—61no—
177#926—61no—
178C2×C4⋊Dic3—31no—
179#924—31no—
180C2×C4×Dic3—31no—
181C2×#204—31no—
182#897—31no—
183#893—31no—
184D3×C4⋊C4—31no—
185#890—31no—
186#890—31no—
187#887—31no—
188#883—61no—
189#67⋊C4—61no—
190D3×C22⋊C4—61no—
191#879—61no—
192#879—61no—
193#877—61no—
194C4×D12—31no—
195C42×D3—31no—
196C4×Dic6—31no—
197C3×#107—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×C22⋊C8—31no—
203C3×C4×C8—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—61no—
208#832C2×D311yescharacteristic
209#832C2×D311yescharacteristic
210#832C2×D311yescharacteristic, complemented
211#830—31no—
212#821C2×D311yescharacteristic
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8C2×D311yescharacteristic
215#818—31no—
216#818C2×D311yescharacteristic, complemented
217#817—31no—
218#816—31no—
219#816—31no—
220#816—31no—
221#816—61no—
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227C8×Dic3—31no—
228C8×Dic3C2×D311yescharacteristic, complemented
229#810—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#808—31no—
234#807—31no—
235C4×C3⋊C8—31no—
236C23×C32—21no—
237C23×C32—21no—
238C22×C3×D3—24no—
239C22×C3×D3—21no—
240C22×C3×D3—42no—
241C22×C3×D3—42no—
242C22×C3×D3C2×D411yescharacteristic
243C32×D4—21no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—42no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253#634—21no—
254#634—21no—
255C3×#67—24no—
256C3×#67—42no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269D3×Dic3—22no—
270D3×Dic3—22no—
271D3×Dic3—42no—
272D3×Dic3—42no—
273D3×Dic3—42no—
274C32×C8—21no—
275C3⋊(C3⋊C8)—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#529—91no—
279C2×C4×D4—91no—
280#484—91no—
281#481—91no—
282#478—91no—
283#478—91no—
284#463—91no—
285#463—91no—
286#450—91no—
287#447—31no—
288C4×SD16—91no—
289C4×SD16—91no—
290C4×D8—31no—
291C4×D8—91no—
292#431—91no—
293C24×C3—61no—
294C23×D3—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4—62no—
300C2×C3×D4—62no—
301C2×C3×D4—61no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C2×C3×D4C22×D311yescharacteristic
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C2×#67—21no—
310C2×#67—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—31no—
314C22×Dic3—31no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—121no—
321C22×Dic3—124no—
322D3×D4—22no—
323D3×D4—22no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—124no—
331C2×C4×D3C22×D311yescharacteristic
332C2×Dic6—31no—
333C2×Dic6—31no—
334C2×Dic6—61no—
335C3×D8—22no—
336C3×D8—22no—
337C3×D8—42no—
338C3×D8—62no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—31no—
351#217—21no—
352#217—21no—
353#217—21no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—121no—
364#217—121no—
365#217—121no—
366#214—62no—
367#214—62no—
368#214—62no—
369#214—122no—
370#213—22no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—31no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405#204—62no—
406C22×C32—22no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32—41no—
410C22×C32—41no—
411C22×C32—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—22no—
416C2×C3×D3—48no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3#13512yes—
420C32×C4C2×#4111yescharacteristic
421C32×C4C2×#4111yescharacteristic
422C3⋊Dic3—21no—
423C3⋊Dic3—21no—
424C3⋊Dic3—41no—
425C3⋊Dic3—41no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3AGL(1,ℤ/8)12yes—
432C22×D4—31no—
433C23×C4—181no—
434C2×SD16—91no—
435C2×SD16—91no—
436C2×D8—31no—
437C2×D8D3211yescharacteristic
438#126—181no—
439#125—91no—
440#124—91no—
441#123—181no—
442C22⋊Q8—91no—
443#121—31no—
444C4×Q8—91no—
445C4×D4—31no—
446C4×D4—31no—
447C4×D4—91no—
448C4×D4—91no—
449C4×D4—91no—
450C4×D4—181no—
451C4×D4—181no—
452C4×D4—181no—
453#117—181no—
454C2×C4⋊C4—91no—
455C2×C22⋊C4—181no—
456C2×C42—91no—
457#107—31no—
458#107—91no—
459#106—91no—
460#106—91no—
461C4⋊C8—91no—
462C4⋊C8—91no—
463#103—91no—
464#103—91no—
465#102—31no—
466#102—31no—
467#102—31no—
468#102—31no—
469#102—91no—
470#102—91no—
471C22⋊C8—31no—
472C22⋊C8—91no—
473C4×C8—31no—
474C4×C8—91no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—31no—
480C23×C3—41no—
481C23×C3—41no—
482C23×C3—64no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C22×D3—24no—
487C22×D3—21no—
488C22×D3—42no—
489C22×D3—42no—
490C22×D3D3×D411yescharacteristic
491C3×D4—21no—
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—22no—
498C3×D4—32no—
499C3×D4—41no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—64no—
503C3×D4—61no—
504C3×D4—122no—
505C3×D4#23512yes—
506C3×D4#23712yes—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—122no—
517C2×C3×C4—122no—
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67—24no—
521#67—42no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—42no—
530C2×Dic3—42no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—62no—
534C2×Dic3—62no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—122no—
542C2×Dic3—122no—
543C2×Dic3—122no—
544C2×Dic3—122no—
545C2×Dic3—122no—
546C2×Dic3—242no—
547C2×Dic3D3×D411yescharacteristic
548C2×Dic3D3×D411yescharacteristic
549C2×Dic3D3×D411yescharacteristic
550D12—21no—
551D12#23712yes—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—62no—
555C4×D3—62no—
556C4×D3—122no—
557C4×D3—122no—
558C4×D3—122no—
559Dic6—61no—
560Dic6—61no—
561Dic6—61no—
562Dic6—61no—
563Dic6—121no—
564Dic6—121no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—41no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—121no—
575C2×C32—42no—
576C2×C32—81no—
577C2×C32#52511yescharacteristic
578C2×C32C2×#13511yescharacteristic
579C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
580C3×D3—22no—
581C3×D3—42no—
582C24—61no—
583C2×Q8—91no—
584C2×D4—31no—
585C2×D4—61no—
586C2×D4—62no—
587C2×D4—62no—
588C2×D4—61no—
589C2×D4C2×D3211yescharacteristic
590C2×D4C2×D3211yescharacteristic
591C22×C4—31no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—91no—
595C22×C4—91no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4—181no—
600C22×C4—364no—
601SD16—182no—
602SD16—182no—
603D8—22no—
604D8—62no—
605C2×C8—31no—
606C2×C8—31no—
607C2×C8—91no—
608C2×C8C2×D3211yescharacteristic
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—91no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C42—31no—
628C42—91no—
629C42—91no—
630C42—91no—
631C42—181no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—32no—
636C22×C3—42no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—62no—
650C22×C3—81no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—128no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3C2×D3×D411yescharacteristic
659C22×C3C2×D3×D411yescharacteristic
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—22no—
663C2×D3—48no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3#91212yes—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—32no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4C2×#23511yescharacteristic
676C3×C4C2×#23711yescharacteristic
677C3×C4C2×#23711yescharacteristic
678C3×C4D3×#4111yescharacteristic
679Dic3—21no—
680Dic3—21no—
681Dic3—41no—
682Dic3—41no—
683Dic3—41no—
684Dic3—61no—
685Dic3—61no—
686Dic3—61no—
687Dic3—61no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—241no—
695Dic3—241no—
696Dic3#91112yes—
697C32#310511yescharacteristic, complemented, Sylow
698C23—21no—
699C23—21no—
700C23—31no—
701C23—64no—
702C23—61no—
703C23—122no—
704C23—122no—
705Q8—181no—
706Q8—181no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—32no—
711D4—64no—
712D4—61no—
713D4—122no—
714D4#380412yes—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—31no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—122no—
726C2×C4—122no—
727C2×C4—182no—
728C2×C4—182no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—362no—
732C2×C4—362no—
733C2×C4—362no—
734C2×C4—362no—
735C2×C4C22×D3211yescharacteristic
736C8—21no—
737C8—61no—
738C8—61no—
739C8—181no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—42no—
744C2×C3—42no—
745C2×C3—62no—
746C2×C3—82no—
747C2×C3—81no—
748C2×C3—81no—
749C2×C3—122no—
750C2×C3—161no—
751C2×C3#554711yescharacteristic
752C2×C3#558611yescharacteristic
753C2×C3C2×#91111yescharacteristic
754C2×C3C2×#91211yescharacteristic
755C2×C3D3×#13511yescharacteristic
756C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
757D3—22no—
758D3—42no—
759C22—22no—
760C22—32no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—61no—
767C22—61no—
768C22—62no—
769C22—128no—
770C22—121no—
771C22—121no—
772C22D32×D411yescharacteristic
773C4—32no—
774C4—61no—
775C4—61no—
776C4—121no—
777C4—121no—
778C4—121no—
779C4—181no—
780C4—181no—
781C4—361no—
782C4—361no—
783C4D3×#23711yescharacteristic
784C4C2×#380411yescharacteristic
785C3—21no—
786C3#7959211yescharacteristic, complemented
787C3#7998911yescharacteristic, complemented
788C2—42no—
789C2—62no—
790C2—81no—
791C2—122no—
792C2D3×#91111yescharacteristic
793C2D3×#91211yescharacteristic
794C2#1059512911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
prime radicalC3×#5156C2
hypercenterC2×D8D32
hypocenterC32#3105
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595172C2semidirect
2. D3×D4×Dic3C2semidirect
3. #10592852C2semidirect
5. C3×Dic3×D8C2semidirect
6. #10591479C2semidirect
7. #10591459C2semidirect
8. #10591434C2semidirect
9. Dic3×#213C2semidirect
10. #10591415C2semidirect
11. #10591401C2semidirect
12. #10590780C2semidirect
13. #10590744C2semidirect
14. #10590684C2semidirect
15. #10590655C2semidirect
21. #64145C22semidirect
26. C3×D4×Dic3C22semidirect
39. #63872C22semidirect
41. #63844C22semidirect
43. #63659C22semidirect
44. #63643C22semidirect
45. #63641C22semidirect
48. C3×#832C22semidirect
51. C3×#818C22semidirect
52. C3×C8×Dic3C22semidirect
53. #63575C22semidirect
54. #63574C22semidirect
55. #63573C22semidirect
56. #63572C22semidirect
57. #63567C22semidirect
60. Dic3×C3⋊C8C22semidirect
74. Dic3×D8D3semidirect
169. D4×Dic3C2×D3semidirect
210. #832C2×D3semidirect
216. #818C2×D3semidirect
228. C8×Dic3C2×D3semidirect
697. C32#3105semidirect
786. C3#79592semidirect
787. C3#79989semidirect

Maximal subgroups

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

subgroupindex
#105951722
D3×D4×Dic32
#105928522
C3×#51562
C3×Dic3×D82
#105914792
#105914592
#105914342
Dic3×#2132
#105914152
#105914012
#105907802
#105907442
#105906842
#105906552
#799893
#795923