Finite Group Databasebeta

← #11887520

Subgroups — #11887520

Order 1152.

919 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594915C211yesmaximal, characteristic, complemented
2#10594906C211yesmaximal, characteristic
3#10592437C211yesmaximal, characteristic, complemented
4C3×#67⋊C8C211yesmaximal, characteristic, complemented
5C3×#4721C211yesmaximal, characteristic, complemented
6#10591177C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8#10590951C211yesmaximal, characteristic, complemented
9#10590890C211yesmaximal, characteristic, complemented
10#10590830C211yesmaximal, characteristic, complemented
11#10590802C211yesmaximal, characteristic, complemented
12#10590760C211yesmaximal, characteristic, complemented
13#10590758C211yesmaximal, characteristic, complemented
14#10590674C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16#81450—31nomaximal
17#79447—31nomaximal
18C22×#634C2211yescharacteristic
19C2×#3804—21no—
20C2×D3×Dic6C2211yescharacteristic
21#64139C2211yescharacteristic
22C2×#3744C2211yescharacteristic
23C2×#3744C2211yescharacteristic
24C3×C4×#67C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29#63982—21no—
30#67⋊Dic3—21no—
31#63966—21no—
32#63918C2211yescharacteristic
33#63909C2211yescharacteristic
34#63896—21no—
35#63895—21no—
36#63894C2211yescharacteristic
37#63890—21no—
38D3×C4⋊Dic3C2211yescharacteristic
39#63866C2211yescharacteristic
40#63857C2211yescharacteristic
41#63844C2211yescharacteristic
42#63840—21no—
43C2×#3717C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45#63643C2211yescharacteristic
46#63643C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×#817C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63564C2211yescharacteristic
61#5632—31no—
62#5555—31no—
63D4×Dic6—31no—
64#5507—31no—
65C3×#483—31no—
66C3×C8×D4—31no—
67#5114—31no—
68#5114—31no—
69C2×#816—31no—
70C2×#816—31no—
71#5048—31no—
72C2×#810—31no—
73#4864—31no—
74#4862—31no—
75#4854—31no—
76#4852—31no—
77#4851—31no—
78#4841—31no—
79#4818—31no—
80#4806—31no—
81D3×#103—31no—
82#4792—31no—
83#4738—31no—
84#4738—31no—
85#4738—31no—
86#4738—61no—
87#67⋊C8D311yescharacteristic, complemented
88#4721—31no—
89#4721D311yescharacteristic, complemented
90C4×#204—31no—
91#4681—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94C22×C3⋊Dic3—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×#634—22no—
97C2×#634—21no—
98C2×#634—41no—
99C2×#634C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×C3×#67D411yescharacteristic
102C22×C3×Dic3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#627—21no—
107C2×#626—21no—
108C2×#624—21no—
109#3804—44no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112D3×Dic6—22no—
113D3×Dic6—41no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3744—22no—
119#3744—41no—
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8—41no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×D3×C8—41no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141#3722—21no—
142(C2×D3)⋊Dic3—21no—
143Dic32—21no—
144#3717—41no—
145#3298—91noSylow
146C2×D3×Q8—31no—
147C2×#237—61no—
148C2×#235—61no—
149C22×Dic6—31no—
150C22×Dic6—31no—
151C22×Dic6—31no—
152C22×Dic6—61no—
153C22×C3×C8—31no—
154C22×C3×C8—31no—
155C3×C22⋊Q8—31no—
156C3×C4×D4—31no—
157C2×C3×C4⋊C4—31no—
158#944—31no—
159C2×#215—31no—
160D4×Dic3—61no—
161#930—31no—
162#930—31no—
163#930—31no—
164#930—61no—
165#929—61no—
166C4×#67C2×D311yescharacteristic
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3C2×D311yescharacteristic
169#924—31no—
170#924C2×D311yescharacteristic
171C22×C3⋊C8C2×D311yescharacteristic
172C2×#204—31no—
173C2×#204—31no—
174C2×#204—31no—
175C2×#204—31no—
176C2×#204—31no—
177C2×#204—61no—
178C2×#204—61no—
179C2×D3×C8C2×D311yescharacteristic
180#897—31no—
181#897—61no—
182#896—61no—
183#896—61no—
184#895—31no—
185#894—61no—
186#893—31no—
187D3×C4⋊C4—31no—
188#888—31no—
189#888—61no—
190#888—61no—
191#887—31no—
192#886—61no—
193#886—61no—
194#67⋊C4—61no—
195#878—61no—
196#878—61no—
197#878—61no—
198C4×D12—31no—
199#869—31no—
200#869—31no—
201C4×Dic6—31no—
202C3×#106—31no—
203C3×#106—31no—
204C3×C4⋊C8—31no—
205C3×#103—31no—
206C3×#103—31no—
207C3×C22⋊C8—21no—
208C3×C22⋊C8—31no—
209C3×C22⋊C8C2×D311yescharacteristic
210C3×C22⋊C8C2×D311yescharacteristic
211C3×C4×C8—31no—
212#835—31no—
213#821—31no—
214(C2×D3)⋊C8C2×D311yescharacteristic
215#817—31no—
216#817C2×D311yescharacteristic
217#817C2×D311yescharacteristic
218#816—31no—
219#816—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—61no—
228#816—61no—
229#816C2×D311yescharacteristic
230#816C2×D311yescharacteristic
231Dic3⋊C8C2×D311yescharacteristic
232C8×Dic3C2×D311yescharacteristic
233#810—31no—
234#810—31no—
235#810—31no—
236#810—31no—
237#809—31no—
238#808—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246#638—42no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—42no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253#634—21no—
254#634—21no—
255#634—21no—
256#634—42no—
257#634#4112yescomplemented
258C3×#67SD1614yescomplemented
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—42no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#627—42no—
272#627—42no—
273#626—42no—
274#624—42no—
275D3×Dic3—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—91no—
291#448—91no—
292C4×SD16—91no—
293C8×D4—31no—
294C2×#103—91no—
295C2×#103—91no—
296C2×C3×Q8—31no—
297C2×C3×D4—31no—
298C22×C3×C4—21no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—121no—
307C2×#67D1211yescharacteristic
308C22×Dic3—21no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—121no—
314D3×Q8—62no—
315D3×Q8—121no—
316#237—124no—
317#235—124no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—61no—
321C2×D12—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3C22×D311yescharacteristic
327C2×Dic6—31no—
328C2×Dic6—31no—
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—61no—
332C2×Dic6—61no—
333C2×Dic6—62no—
334C2×Dic6—62no—
335C2×Dic6—62no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C2×Dic6—61no—
340C2×Dic6—61no—
341C2×Dic6—61no—
342C2×Dic6—122no—
343C2×Dic6—121no—
344C2×Dic6—121no—
345C2×Dic6—121no—
346C2×Dic6—121no—
347C2×Dic6—122no—
348C2×Dic6C22×D311yescharacteristic
349C2×C3×C8—21no—
350C2×C3×C8—21no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—121no—
354C2×C3×C8—121no—
355C2×C3×C8C22×D311yescharacteristic
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—61no—
364C3×C4⋊C4—61no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—61no—
368C3×C42—31no—
369#217—21no—
370#217—61no—
371#217D1211yescharacteristic
372#215—121no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—121no—
381(C2×D3)⋊C4D1211yescharacteristic
382C4⋊Dic3—21no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4D1211yescharacteristic
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3C22×D311yescharacteristic
406C2×C3⋊C8—41no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409#204—62no—
410#204—62no—
411#204—122no—
412#204—121no—
413#204—121no—
414#204—122no—
415#204—121no—
416D3×C8—41no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32C2×SD1612yes—
420C22×C32C22×D411yescharacteristic
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3C2×SD1612yes—
427C32×C4—21no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—22no—
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3C2×SD1612yes—
440C2×#41—181no—
441C22×Q8—91no—
442C22×Q8—91no—
443C2×SD16—91no—
444C2×SD16—91no—
445C2×SD16—91no—
446C22×C8—31no—
447C22×C8—31no—
448C4⋊Q8—91no—
449C4⋊Q8—91no—
450C4⋊Q8—181no—
451#123—181no—
452#123—181no—
453C22⋊Q8—31no—
454C22⋊Q8—91no—
455C22⋊Q8—181no—
456C22⋊Q8—181no—
457C22⋊Q8—181no—
458#121—91no—
459#121—91no—
460C4×Q8—91no—
461C4×D4—31no—
462C4×D4—91no—
463C4×D4—181no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—91no—
466#106—31no—
467#106—31no—
468#106—91no—
469C4⋊C8—31no—
470#103—31no—
471#103—31no—
472#103—91no—
473#103—91no—
474#103—91no—
475#103—91no—
476#103—91no—
477#103—91no—
478#103—91no—
479#102—91no—
480C22⋊C8—31no—
481C22⋊C8D3211yescharacteristic
482C4×C8—31no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3C2×D1211yescharacteristic
486C23×C3D3×D411yescharacteristic
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—121no—
490C22×D3C2×D1211yescharacteristic
491C3×Q8—61no—
492C3×Q8—61no—
493C3×D4—34no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—122no—
512C2×C3×C4C2×D1211yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516#67—122no—
517#67—122no—
518#67—122no—
519#67—242no—
520#67#20414yescomplemented
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—42no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3—122no—
536C2×Dic3—122no—
537C2×Dic3—122no—
538C2×Dic3—122no—
539C2×Dic3—124no—
540C2×Dic3C2×D1211yescharacteristic
541C2×Dic3C2×D1211yescharacteristic
542C2×Dic3C2×D1211yescharacteristic
543D12—61no—
544D12—61no—
545D12—61no—
546D12—61no—
547D12—121no—
548D12—121no—
549D12—122no—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—122no—
555C4×D3—122no—
556Dic6—21no—
557Dic6—21no—
558Dic6—32no—
559Dic6—32no—
560Dic6—62no—
561Dic6—61no—
562Dic6—61no—
563Dic6—62no—
564Dic6—61no—
565Dic6—61no—
566Dic6—61no—
567Dic6—61no—
568Dic6—121no—
569Dic6—121no—
570Dic6—122no—
571Dic6—122no—
572Dic6—122no—
573Dic6—122no—
574Dic6—122no—
575Dic6—124no—
576Dic6—122no—
577C3×C8—21no—
578C3×C8—21no—
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—41no—
582C3×C8—41no—
583C3×C8—61no—
584C3×C8—61no—
585C3⋊C8—21no—
586C3⋊C8—21no—
587C2×C32—22no—
588C2×C32#54611yescharacteristic
589C2×C32C22×SD1611yescharacteristic
590C2×C32#57811yescharacteristic
591C3⋊D3—81no—
592C3×D3—22no—
593#41—364no—
594C2×Q8—31no—
595C2×Q8—91no—
596C2×Q8—91no—
597C2×Q8—182no—
598C2×Q8—181no—
599C2×Q8—181no—
600C2×Q8—182no—
601C2×Q8—181no—
602C2×Q8—361no—
603C2×Q8—361no—
604C2×D4—31no—
605C2×D4—91no—
606C2×D4—181no—
607C2×D4—181no—
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—181no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4—181no—
614C22×C4C2×D3211yescharacteristic
615SD16—182no—
616SD16—361no—
617SD16—361no—
618C2×C8—31no—
619C2×C8—31no—
620C2×C8—121no—
621C2×C8—121no—
622C2×C8C2×D3211yescharacteristic
623C2×C8C2×D3211yescharacteristic
624C4⋊C4—31no—
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—91no—
631C4⋊C4—181no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C22⋊C4—31no—
638C22⋊C4—31no—
639C22⋊C4—61no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C42—31no—
645C42—181no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—22no—
652C22×C3—32no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3C2×#20412yes—
658C22×C3D3×SD1612yes—
659C22×C3C22×D1211yescharacteristic
660C22×C3C2×D3×D411yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—241no—
670C2×D3—241no—
671C2×D3—241no—
672C2×D3C2×#20412yes—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—32no—
678C3×C4—41no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4#100411yescharacteristic
686C3×C4D3×#4111yescharacteristic
687C3×C4D3×#4111yescharacteristic
688C3×C4#100911yescharacteristic
689Dic3—21no—
690Dic3—21no—
691Dic3—41no—
692Dic3—41no—
693Dic3—41no—
694Dic3—41no—
695Dic3—62no—
696Dic3—62no—
697Dic3—122no—
698Dic3—122no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—241no—
704Dic3C2×#20412yes—
705C32#329811yescharacteristic, complemented, Sylow
706C23—31no—
707C23—181no—
708C23D3×D1211yescharacteristic
709Q8—61no—
710Q8—61no—
711Q8—92no—
712Q8—181no—
713Q8—181no—
714Q8—181no—
715Q8—362no—
716Q8—362no—
717Q8—362no—
718D4—34no—
719D4—181no—
720D4—181no—
721D4—362no—
722D4—362no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—122no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—362no—
739C2×C4—362no—
740C2×C4—362no—
741C2×C4—362no—
742C2×C4D3×D1211yescharacteristic
743C2×C4C22×D3211yescharacteristic
744C8—21no—
745C8—21no—
746C8—61no—
747C8—61no—
748C2×C3—22no—
749C2×C3—22no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—42no—
754C2×C3—62no—
755C2×C3#555411yescharacteristic
756C2×C3#565411yescharacteristic
757C2×C3C22×#20411yescharacteristic
758C2×C3#575311yescharacteristic
759C2×C3C2×D3×SD1611yescharacteristic
760C2×C3#577911yescharacteristic
761D3—22no—
762D3—241no—
763D3—241no—
764D3—481no—
765C22—21no—
766C22—21no—
767C22—32no—
768C22—61no—
769C22—61no—
770C22—361no—
771C22—361no—
772C22—361no—
773C22D3×#20412yes—
774C22C2×D3×D1211yescharacteristic
775C4—21no—
776C4—32no—
777C4—61no—
778C4—61no—
779C4—121no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4—182no—
784C4—361no—
785C4—361no—
786C4#6431211yescharacteristic
787C4#6431411yescharacteristic
788C3—21no—
789C3#7944711yescharacteristic, complemented
790C3#8145011yescharacteristic, complemented
791C2—22no—
792C2—62no—
793C2—721no—
794C2#1059429311yescharacteristic
795C2C2×D3×#20411yescharacteristic
796C2#1059472111yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10594906C2
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
1. #10594915C2semidirect
3. #10592437C2semidirect
4. C3×#67⋊C8C2semidirect
5. C3×#4721C2semidirect
6. #10591177C2semidirect
7. C2×#63567C2semidirect
8. #10590951C2semidirect
9. #10590890C2semidirect
10. #10590830C2semidirect
11. #10590802C2semidirect
12. #10590760C2semidirect
13. #10590758C2semidirect
14. #10590674C2semidirect
15. D3×#816C2semidirect
87. #67⋊C8D3semidirect
89. #4721D3semidirect
257. #634#41semidirect
258. C3×#67SD16semidirect
520. #67#204semidirect
705. C32#3298semidirect
789. C3#79447semidirect
790. C3#81450semidirect

Maximal subgroups

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

subgroupindex
#105949152
#105949062
#105924372
C3×#67⋊C82
C3×#47212
#105911772
C2×#635672
#105909512
#105908902
#105908302
#105908022
#105907602
#105907582
#105906742
D3×#8162
#814503
#794473