Finite Group Databasebeta

← #11887521

Subgroups — #11887521

Order 1152.

907 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594928C211yesmaximal, characteristic
2#10594803C211yesmaximal, characteristic, complemented
3#10592424C211yesmaximal, characteristic, complemented
4C3×#4738C211yesmaximal, characteristic, complemented
5C3×#4721C211yesmaximal, characteristic, complemented
6#10591179C211yesmaximal, characteristic, complemented
7C2×#63565C211yesmaximal, characteristic, complemented
8#10590901C211yesmaximal, characteristic, complemented
9#10590843C211yesmaximal, characteristic, complemented
10#10590824C211yesmaximal, characteristic, complemented
11#10590816C211yesmaximal, characteristic, complemented
12#10590775C211yesmaximal, characteristic, complemented
13#10590748C211yesmaximal, characteristic, complemented
14#10590686C211yesmaximal, characteristic, complemented
15#10590672C211yesmaximal, characteristic, complemented
16#81450—31nomaximal
17#80049—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C2×#3804—21no—
20C2×#3797C2211yescharacteristic
21C4×#638C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C8×C3⋊D3C2211yescharacteristic
24C3×#930C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C2×C3×#204C2211yescharacteristic
28C2×C3×#204C2211yescharacteristic
29#63964—21no—
30#63961—21no—
31#63952—21no—
32#63919C2211yescharacteristic
33#63916C2211yescharacteristic
34#63900C2211yescharacteristic
35#63899—21no—
36#63898C2211yescharacteristic
37#63888—21no—
38#63873C2211yescharacteristic
39#63871C2211yescharacteristic
40#63854—21no—
41#63843C2211yescharacteristic
42#63839—21no—
43C2×#3715C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45#63647C2211yescharacteristic
46#63641C2211yescharacteristic
47C8×C3⋊Dic3C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×#816C2211yescharacteristic
54#63574C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63565C2211yescharacteristic
60#63562C2211yescharacteristic
61Q8×#67—31no—
62#5632—31no—
63#5611—31no—
64#5507—31no—
65C3×#483—31no—
66C3×#448—31no—
67C2×#835—31no—
68#5171—31no—
69#5170—31no—
70#5162—31no—
71Dic3×SD16—31no—
72#5048—31no—
73#5041—31no—
74C2×#810—31no—
75#4864—31no—
76#4862—31no—
77#4854—31no—
78#4852—31no—
79#4818—31no—
80#4806—31no—
81#4805—31no—
82D3×#103—31no—
83D3×#103—31no—
84#4792—31no—
85#4792—31no—
86#4791—31no—
87#4738D311yescharacteristic, complemented
88#67⋊C8—31no—
89#67⋊C8—31no—
90#67⋊C8—61no—
91#4721D311yescharacteristic, complemented
92C22×C32×C4C2311yescharacteristic
93C2×#638D411yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×Dic6—22no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6—41no—
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#627—21no—
107C2×#626—21no—
108C2×#624—21no—
109C2×#624—21no—
110#3804—44no—
111C2×D3×Dic3—21no—
112#3797—22no—
113#3797—41no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116#3757D411yescharacteristic
117#3752D411yescharacteristic
118#3750D411yescharacteristic
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)—41no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C8×C3⋊D3—41no—
124C3×#217—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×C4⋊Dic3C2311yescharacteristic
131C3×Dic3⋊C4—21no—
132C3×#204—22no—
133C3×#204—41no—
134#3724—21no—
135#3724—21no—
136#3724—21no—
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143Dic32—21no—
144#3715—41no—
145#3298—91noSylow
146C22×C3×Q8—31no—
147C2×D3×Q8—31no—
148C2×D3×Q8—31no—
149C2×#237—61no—
150C2×#235—61no—
151C22×Dic6C2×D311yescharacteristic
152C2×C3×SD16—31no—
153C2×C3×SD16—31no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156C2×C3×C4⋊C4—31no—
157#946—31no—
158#946—61no—
159Q8×Dic3—31no—
160#944—31no—
161#944—31no—
162#944—61no—
163C2×#215—31no—
164#938—31no—
165#935—61no—
166D4×Dic3—31no—
167C2×#214—31no—
168#930C2×D311yescharacteristic
169#929—61no—
170C4×#67—31no—
171C4×#67—31no—
172C4×#67—61no—
173C4×#67—61no—
174C2×C4⋊Dic3C2×D311yescharacteristic
175#924—61no—
176#924C2×D311yescharacteristic
177C22×C3⋊C8—31no—
178C22×C3⋊C8—31no—
179C22×C3⋊C8—61no—
180C2×#204C2×D311yescharacteristic
181C2×#204C2×D311yescharacteristic
182C2×D3×C8—31no—
183C2×D3×C8—31no—
184C2×D3×C8—61no—
185#897—31no—
186#896—61no—
187#896—61no—
188#895—31no—
189#894—61no—
190#893—31no—
191D3×C4⋊C4—31no—
192D3×C4⋊C4—31no—
193#888—31no—
194#888—31no—
195#888—61no—
196#887—31no—
197#883—61no—
198#67⋊C4—61no—
199#878—61no—
200#878—61no—
201C3×#106—31no—
202C3×#106—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×C22⋊C8—21no—
208C3×C22⋊C8C2×D311yescharacteristic
209C3×C22⋊C8C2×D311yescharacteristic
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—31no—
215#832—31no—
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—61no—
219#817C2×D311yescharacteristic
220#817C2×D311yescharacteristic
221#816C2×D311yescharacteristic
222#816C2×D311yescharacteristic
223#816C2×D311yescharacteristic
224#816C2×D311yescharacteristic
225Dic3⋊C8—31no—
226Dic3⋊C8—31no—
227Dic3⋊C8—61no—
228C8×Dic3—31no—
229C8×Dic3—31no—
230C8×Dic3—61no—
231#810—31no—
232#810—31no—
233#810—31no—
234#810—31no—
235#810—31no—
236#809—31no—
237#808—31no—
238#808—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246#638SD1614yescomplemented
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252C3×#67—42no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3—42no—
262C3×D12—21no—
263C3×D12—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—42no—
270C3×Dic6#4112yescomplemented
271#627—42no—
272#627—42no—
273#626—42no—
274#624—42no—
275#624—42no—
276D3×Dic3—42no—
277C32×C8—21no—
278C32×C8—21no—
279C3⋊(C3⋊C8)—21no—
280C3⋊(C3⋊C8)—21no—
281D4×Q8—91no—
282#547—91no—
283#487—91no—
284#483—31no—
285#483—91no—
286#475—91no—
287#465—91no—
288#465—91no—
289#461—91no—
290#448—31no—
291#448—91no—
292C4×SD16—91no—
293C8×D4—91no—
294C2×#103—91no—
295C2×#103—91no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×Q8—62no—
300C2×C3×Q8—61no—
301C2×C3×Q8—121no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C22×C3×C4—21no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67—21no—
310C2×#67—31no—
311C2×#67—31no—
312C2×#67—61no—
313C2×#67—61no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—61no—
317D3×Q8—62no—
318D3×Q8—62no—
319D3×Q8—121no—
320D3×Q8—121no—
321#237—124no—
322#235—124no—
323C2×D12—61no—
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—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×Dic6—22no—
334C2×Dic6—21no—
335C2×Dic6—41no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C2×Dic6—61no—
340C2×Dic6C22×D311yescharacteristic
341C2×Dic6C22×D311yescharacteristic
342C2×Dic6C22×D311yescharacteristic
343C3×SD16—62no—
344C3×SD16—121no—
345C2×C3×C8—21no—
346C2×C3×C8—21no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C22×D311yescharacteristic
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359#217—21no—
360#217—31no—
361#217—31no—
362#217—61no—
363#217—61no—
364#217—61no—
365#215—121no—
366#214—121no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375C4⋊Dic3—21no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396C4×Dic3—31no—
397C4×Dic3—31no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—61no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8—122no—
410#204—22no—
411#204—41no—
412D3×C8—121no—
413D3×C8—121no—
414D3×C8—122no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32C2×SD1612yes—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—21no—
420C2×C3⋊D3—21no—
421C2×C3⋊D3C2×SD1612yes—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C32×C4—21no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—21no—
430C3⋊Dic3C2×SD1612yes—
431C3×Dic3—22no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—181no—
439C22×Q8—31no—
440C22×Q8—91no—
441C2×SD16—31no—
442C2×SD16—31no—
443C2×SD16—91no—
444C22×C8—91no—
445C22×C8—91no—
446C4⋊Q8—91no—
447C4⋊Q8—91no—
448C4⋊Q8—181no—
449#123—181no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455C22⋊Q8—181no—
456#121—31no—
457#121—91no—
458C4×Q8—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—91no—
464#106—31no—
465#106—31no—
466#106—91no—
467C4⋊C8—91no—
468#103—31no—
469#103—31no—
470#103—31no—
471#103—31no—
472#103—91no—
473#103—91no—
474#103—91no—
475#103—91no—
476#103—91no—
477#102—91no—
478C22⋊C8—91no—
479C22⋊C8D3211yescharacteristic
480C4×C8—91no—
481C23×C3—21no—
482C23×C3—61no—
483C23×C3D3×D411yescharacteristic
484C23×C3D3×D411yescharacteristic
485C22×D3—21no—
486C22×D3—31no—
487C22×D3—31no—
488C22×D3—61no—
489C3×Q8—32no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—122no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—122no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—122no—
515C2×C3×C4—122no—
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67—34no—
521#67—34no—
522#67—42no—
523#67—64no—
524#67—122no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—42no—
539C2×Dic3—42no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—122no—
544D12—21no—
545D12—21no—
546D12—122no—
547C4×D3—61no—
548C4×D3—61no—
549C4×D3—61no—
550C4×D3—61no—
551C4×D3—121no—
552C4×D3—121no—
553C4×D3—122no—
554C4×D3—122no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—122no—
558Dic6—21no—
559Dic6—21no—
560Dic6—21no—
561Dic6—21no—
562Dic6—21no—
563Dic6—42no—
564Dic6—122no—
565Dic6—122no—
566Dic6—122no—
567Dic6—122no—
568Dic6#23712yescomplemented
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—41no—
574C3×C8—41no—
575C3⋊C8—62no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—121no—
581C2×C32—22no—
582C2×C32#54611yescharacteristic
583C2×C32C22×SD1611yescharacteristic
584C2×C32#57811yescharacteristic
585C3⋊D3—22no—
586C3×D3—81no—
587#41—364no—
588C2×Q8—31no—
589C2×Q8—31no—
590C2×Q8—31no—
591C2×Q8—62no—
592C2×Q8—61no—
593C2×Q8—121no—
594C2×Q8—181no—
595C2×Q8—181no—
596C2×Q8—182no—
597C2×Q8—361no—
598C2×D4—31no—
599C2×D4—61no—
600C2×D4—91no—
601C2×D4—181no—
602C22×C4—61no—
603C22×C4—61no—
604C22×C4—91no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4C2×D3211yescharacteristic
609SD16—62no—
610SD16—121no—
611SD16—361no—
612C2×C8—91no—
613C2×C8—91no—
614C2×C8—361no—
615C2×C8—361no—
616C2×C8C2×D3211yescharacteristic
617C2×C8C2×D3211yescharacteristic
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—91no—
634C22⋊C4—91no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—91no—
639C42—181no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—22no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3D3×SD1612yes—
652C22×C3D3×SD1612yes—
653C22×C3C2×D3×D411yescharacteristic
654C22×C3C2×D3×D411yescharacteristic
655C2×D3—32no—
656C2×D3—32no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—62no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—121no—
666C2×D3—121no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—41no—
672C3×C4—62no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4C2×#23711yescharacteristic
680C3×C4#100411yescharacteristic
681C3×C4D3×#4111yescharacteristic
682C3×C4#100911yescharacteristic
683Dic3—22no—
684Dic3—32no—
685Dic3—32no—
686Dic3—41no—
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—41no—
691Dic3—41no—
692Dic3—62no—
693Dic3—61no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—121no—
698Dic3—121no—
699C32#329811yescharacteristic, complemented, Sylow
700C23—61no—
701C23—91no—
702C23#380211yescharacteristic
703Q8—32no—
704Q8—61no—
705Q8—61no—
706Q8—61no—
707Q8—61no—
708Q8—61no—
709Q8—122no—
710Q8—362no—
711Q8—362no—
712D4—61no—
713D4—61no—
714D4—94no—
715D4—122no—
716D4—362no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—91no—
727C2×C4—91no—
728C2×C4—91no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—362no—
734C2×C4—362no—
735C2×C4—362no—
736C2×C4#380211yescharacteristic
737C2×C4C22×D3211yescharacteristic
738C8—21no—
739C8—21no—
740C8—181no—
741C8—181no—
742C2×C3—22no—
743C2×C3—22no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—42no—
748C2×C3—241no—
749C2×C3#559111yescharacteristic
750C2×C3#565411yescharacteristic
751C2×C3C2×D3×SD1611yescharacteristic
752C2×C3C2×D3×SD1611yescharacteristic
753C2×C3#577911yescharacteristic
754C2×C3#577911yescharacteristic
755D3—62no—
756D3—62no—
757D3—81no—
758D3—122no—
759C22—21no—
760C22—21no—
761C22—92no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22—181no—
766C22—181no—
767C22#6379612yes—
768C22C2×#380211yescharacteristic
769C4—21no—
770C4—62no—
771C4—92no—
772C4—121no—
773C4—121no—
774C4—121no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4—181no—
779C4—181no—
780C4D3×#23711yescharacteristic
781C4#6431411yescharacteristic
782C3—21no—
783C3#8004911yescharacteristic, complemented
784C3#8145011yescharacteristic, complemented
785C2—22no—
786C2—182no—
787C2—241no—
788C2#1059429411yescharacteristic
789C2C2×#6379611yescharacteristic
790C2#1059472311yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10594928C2
hypercenterC22⋊C8D32
hypocenterC32#3298
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. #10594803C2semidirect
3. #10592424C2semidirect
4. C3×#4738C2semidirect
5. C3×#4721C2semidirect
6. #10591179C2semidirect
7. C2×#63565C2semidirect
8. #10590901C2semidirect
9. #10590843C2semidirect
10. #10590824C2semidirect
11. #10590816C2semidirect
12. #10590775C2semidirect
13. #10590748C2semidirect
14. #10590686C2semidirect
15. #10590672C2semidirect
87. #4738D3semidirect
91. #4721D3semidirect
246. #638SD16semidirect
270. C3×Dic6#41semidirect
568. Dic6#237semidirect
699. C32#3298semidirect
783. C3#80049semidirect
784. C3#81450semidirect

Maximal subgroups

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

subgroupindex
#105949282
#105948032
#105924242
C3×#47382
C3×#47212
#105911792
C2×#635652
#105909012
#105908432
#105908242
#105908162
#105907752
#105907482
#105906862
#105906722
#814503
#800493