Finite Group Databasebeta

← #11887526

Subgroups — #11887526

Order 1152.

921 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#10594915C211yesmaximal, characteristic, complemented
2#10594907C211yesmaximal, characteristic
3C2×#63643C211yesmaximal, characteristic, complemented
4C3×#5114C211yesmaximal, characteristic, complemented
5C3×C8×#67C211yesmaximal, characteristic, complemented
6#10591181C211yesmaximal, characteristic, complemented
7#10591126C211yesmaximal, characteristic, complemented
8#10590890C211yesmaximal, characteristic, complemented
9#10590825C211yesmaximal, characteristic, complemented
10#10590822C211yesmaximal, characteristic, complemented
11#10590802C211yesmaximal, characteristic, complemented
12#10590752C211yesmaximal, characteristic, complemented
13#10590744C211yesmaximal, characteristic, complemented
14#10590674C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16#80689—31nomaximal
17#79447—31nomaximal
18C22×#634C2211yescharacteristic
19C2×#3805—21no—
20C2×D3×Dic6C2211yescharacteristic
21C22×C32×C8C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×#930C2211yescharacteristic
24C3×C4×#67C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28#63982—21no—
29#67⋊Dic3—21no—
30#63962—21no—
31#63918C2211yescharacteristic
32#63908C2211yescharacteristic
33#63896—21no—
34#63893—21no—
35Dic3×D12C2211yescharacteristic
36#63891—21no—
37D3×C4⋊Dic3C2211yescharacteristic
38#63866C2211yescharacteristic
39#63857C2211yescharacteristic
40#63844C2211yescharacteristic
41#63840—21no—
42C2×#3716C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44#63643C2211yescharacteristic
45#63643C2211yescharacteristic
46#63643C2211yescharacteristic
47#63643C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#817C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61#5632—31no—
62#5611—31no—
63#5555—31no—
64D4×Dic6—31no—
65C3×#465—31no—
66C3×C8×D4—31no—
67#5170—31no—
68#5162—31no—
69#5114—31no—
70#5114D311yescharacteristic, complemented
71C8×#67D311yescharacteristic, complemented
72C2×#816—31no—
73C2×#816—31no—
74C2×#816—31no—
75C2×#816—61no—
76#5043—31no—
77#5040—31no—
78#4862—31no—
79#4854—31no—
80#4851—31no—
81#4841—31no—
82D3×#103—31no—
83#4792—31no—
84#4778—31no—
85#4758—31no—
86#4738—31no—
87#4738—31no—
88#4721—31no—
89#4721—31no—
90C4×#204—31no—
91#4681—31no—
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3—21no—
94C22×C3⋊Dic3—21no—
95C2×#634—22no—
96C2×#634—21no—
97C2×#634—41no—
98C2×#634C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#627—21no—
107C2×#625—21no—
108#3805—44no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×D3×Dic3—21no—
112D3×Dic6—22no—
113D3×Dic6—41no—
114C2×C32×C8—41no—
115C2×C32×C8C2311yescharacteristic
116C2×C32×C8C2311yescharacteristic
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×#204—41no—
132C3×D3×C8—41no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3716—22no—
144#3716—41no—
145#3298—91noSylow
146C2×D3×Q8—31no—
147C2×#237—61no—
148C2×#237—61no—
149C22×Dic6—31no—
150C22×Dic6—31no—
151C22×Dic6—31no—
152C22×Dic6—61no—
153C2×C3×SD16—31no—
154C22×C3×C8—21no—
155C22×C3×C8—31no—
156C22×C3×C8C2×D311yescharacteristic
157C22×C3×C8C2×D311yescharacteristic
158C3×C22⋊Q8—31no—
159C3×#121—31no—
160C3×C4×D4—31no—
161#944—31no—
162#938—31no—
163#935—61no—
164D4×Dic3—31no—
165D4×Dic3—61no—
166C2×#214—31no—
167C2×#214—31no—
168#930—31no—
169#930C2×D311yescharacteristic
170C4×#67C2×D311yescharacteristic
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—31no—
173C2×C4⋊Dic3—31no—
174C2×C4⋊Dic3—61no—
175#924—31no—
176#924C2×D311yescharacteristic
177C2×#204—31no—
178C2×#204—31no—
179C2×#204C2×D311yescharacteristic
180C2×D3×C8C2×D311yescharacteristic
181#897—31no—
182#897—61no—
183#896—61no—
184D3×C4⋊C4—31no—
185#888—31no—
186#888—61no—
187#888—61no—
188#887—31no—
189#886—61no—
190#886—61no—
191#883—61no—
192#67⋊C4—61no—
193#878—61no—
194#878—61no—
195#878—61no—
196#878—61no—
197C4×D12—31no—
198#869—31no—
199#869—31no—
200C4×Dic6—31no—
201C3×#106—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#102—31no—
205C3×C22⋊C8—31no—
206C3×C22⋊C8—31no—
207C3×C4×C8—31no—
208#835—31no—
209#835—31no—
210#830C2×D311yescharacteristic
211#821C2×D311yescharacteristic
212(C2×D3)⋊C8C2×D311yescharacteristic
213#817—31no—
214#817—31no—
215#817C2×D311yescharacteristic
216#816—31no—
217#816—31no—
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—31no—
228#816—61no—
229#816—61no—
230#816—61no—
231#816—61no—
232#816C2×D311yescharacteristic
233Dic3⋊C8C2×D311yescharacteristic
234C8×Dic3C2×D311yescharacteristic
235#810—31no—
236#810—31no—
237#808—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
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—42no—
251C2×C3⋊Dic3—42no—
252#634—21no—
253#634—21no—
254#634—21no—
255#634—42no—
256#634#4112yescomplemented
257C3×#67—42no—
258C3×#67SD1614yescomplemented
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#627—42no—
272#627—42no—
273#625—42no—
274D3×Dic3—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—91no—
285#483—91no—
286#475—91no—
287#465—31no—
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—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C22×C3×C4—21no—
301C22×C3×C4—31no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67—21no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67D1211yescharacteristic
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—121no—
316C22×Dic3—121no—
317D3×Q8—62no—
318D3×Q8—121no—
319#237—124no—
320#237—124no—
321C2×D12C22×D311yescharacteristic
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3C22×D311yescharacteristic
326C2×Dic6—31no—
327C2×Dic6—31no—
328C2×Dic6—31no—
329C2×Dic6—31no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6—62no—
333C2×Dic6—62no—
334C2×Dic6—62no—
335C2×Dic6—64no—
336C2×Dic6—61no—
337C2×Dic6—61no—
338C2×Dic6—61no—
339C2×Dic6—61no—
340C2×Dic6—61no—
341C2×Dic6—61no—
342C2×Dic6—121no—
343C2×Dic6—121no—
344C2×Dic6—121no—
345C2×Dic6—121no—
346C2×Dic6—122no—
347C2×Dic6C22×D311yescharacteristic
348C3×SD16—121no—
349C2×C3×C8—21no—
350C2×C3×C8—21no—
351C2×C3×C8—31no—
352C2×C3×C8—31no—
353C2×C3×C8—41no—
354C2×C3×C8—41no—
355C2×C3×C8—42no—
356C2×C3×C8—121no—
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C2×C3×C8C22×D311yescharacteristic
360C2×C3×C8C22×D311yescharacteristic
361C3×C4⋊C4—31no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—31no—
364C3×C4⋊C4—61no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—61no—
368C3×C22⋊C4—61no—
369C3×C42—31no—
370#217—21no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217D1211yescharacteristic
375#214—62no—
376#214—121no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4D1211yescharacteristic
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—121no—
396C4⋊Dic3C22×D311yescharacteristic
397C4⋊Dic3C22×D311yescharacteristic
398Dic3⋊C4—21no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4D1211yescharacteristic
407C4×Dic3—61no—
408C4×Dic3—61no—
409C4×Dic3C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412#204—41no—
413#204—62no—
414#204—121no—
415D3×C8—41no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32C2×SD1612yes—
419C22×C32C22×D411yescharacteristic
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3C2×SD1612yes—
426C32×C4—21no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—22no—
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3C2×SD1612yes—
439C2×#41—181no—
440C22×Q8—91no—
441C22×Q8—91no—
442C2×SD16—31no—
443C2×SD16—91no—
444C2×SD16—91no—
445C22×C8—31no—
446C22×C8D3211yescharacteristic
447C4⋊Q8—91no—
448C4⋊Q8—91no—
449C4⋊Q8—181no—
450#123—181no—
451#123—181no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454C22⋊Q8—181no—
455C22⋊Q8—181no—
456C22⋊Q8—181no—
457#121—31no—
458#121—91no—
459C4×Q8—91no—
460C4×D4—31no—
461C4×D4—91no—
462C4×D4—181no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—91no—
465#106—31no—
466#106—91no—
467#106—91no—
468C4⋊C8—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#103—91no—
476#103—91no—
477#103—91no—
478#102—31no—
479C22⋊C8—31no—
480C22⋊C8—31no—
481C4×C8—31no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—61no—
485C23×C3C2×D1211yescharacteristic
486C23×C3D3×D411yescharacteristic
487C22×D3—21no—
488C22×D3C2×D1211yescharacteristic
489C3×Q8—61no—
490C3×Q8—61no—
491C3×D4—34no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—122no—
495C2×C3×C4—22no—
496C2×C3×C4—22no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4C2×D1211yescharacteristic
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—42no—
516#67—122no—
517#67—122no—
518#67#20414yescomplemented
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—122no—
535C2×Dic3—122no—
536C2×Dic3—122no—
537C2×Dic3—122no—
538C2×Dic3—124no—
539C2×Dic3—122no—
540C2×Dic3—122no—
541C2×Dic3—122no—
542C2×Dic3—242no—
543C2×Dic3C2×D1211yescharacteristic
544C2×Dic3C2×D1211yescharacteristic
545C2×Dic3C2×D1211yescharacteristic
546D12—21no—
547D12—21no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—122no—
551C4×D3—122no—
552C4×D3—122no—
553Dic6—21no—
554Dic6—21no—
555Dic6—32no—
556Dic6—32no—
557Dic6—62no—
558Dic6—61no—
559Dic6—61no—
560Dic6—62no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—121no—
566Dic6—121no—
567Dic6—122no—
568Dic6—122no—
569Dic6—122no—
570Dic6—122no—
571Dic6—122no—
572Dic6—124no—
573Dic6—122no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—21no—
578C3×C8—41no—
579C3×C8—41no—
580C3×C8—61no—
581C3×C8—61no—
582C3⋊C8—21no—
583C3⋊C8—21no—
584C2×C32—22no—
585C2×C32#54611yescharacteristic
586C2×C32C22×SD1611yescharacteristic
587C2×C32#57811yescharacteristic
588C3×D3—22no—
589C3×D3—81no—
590#41—364no—
591C2×Q8—31no—
592C2×Q8—91no—
593C2×Q8—91no—
594C2×Q8—182no—
595C2×Q8—181no—
596C2×Q8—181no—
597C2×Q8—182no—
598C2×Q8—181no—
599C2×Q8—361no—
600C2×Q8—361no—
601C2×D4—31no—
602C2×D4—31no—
603C2×D4—61no—
604C2×D4—181no—
605C22×C4—31no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4C2×D3211yescharacteristic
612SD16—121no—
613SD16—182no—
614SD16—361no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—41no—
618C2×C8—121no—
619C2×C8C2×D3211yescharacteristic
620C2×C8C2×D3211yescharacteristic
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—61no—
625C4⋊C4—91no—
626C4⋊C4—91no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4—181no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C22⋊C4—31no—
635C22⋊C4—31no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—31no—
642C42—181no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—22no—
651C22×C3—32no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3C2×#20412yes—
658C22×C3D3×SD1612yes—
659C22×C3C22×D1211yescharacteristic
660C22×C3C2×D3×D411yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3C2×#20412yes—
667C3×C4—22no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—32no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4#100411yescharacteristic
679C3×C4#100411yescharacteristic
680C3×C4D3×#4111yescharacteristic
681C3×C4D3×#4111yescharacteristic
682Dic3—21no—
683Dic3—21no—
684Dic3—41no—
685Dic3—41no—
686Dic3—41no—
687Dic3—62no—
688Dic3—62no—
689Dic3—122no—
690Dic3—122no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—241no—
698Dic3—241no—
699Dic3C2×#20412yes—
700C32#329811yescharacteristic, complemented, Sylow
701C23—31no—
702C23—61no—
703C23D3×D1211yescharacteristic
704Q8—61no—
705Q8—61no—
706Q8—92no—
707Q8—181no—
708Q8—181no—
709Q8—181no—
710Q8—362no—
711Q8—362no—
712Q8—362no—
713D4—34no—
714D4—61no—
715D4—61no—
716D4—122no—
717D4—362no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—362no—
733C2×C4—362no—
734C2×C4—362no—
735C2×C4—362no—
736C2×C4—362no—
737C2×C4D3×D1211yescharacteristic
738C2×C4C22×D3211yescharacteristic
739C8—21no—
740C8—21no—
741C8—61no—
742C8—61no—
743C2×C3—24no—
744C2×C3—22no—
745C2×C3—22no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—62no—
750C2×C3—241no—
751C2×C3#555411yescharacteristic
752C2×C3#561011yescharacteristic
753C2×C3C22×#20411yescharacteristic
754C2×C3#575311yescharacteristic
755C2×C3C2×D3×SD1611yescharacteristic
756C2×C3#577111yescharacteristic
757D3—22no—
758D3—81no—
759C22—21no—
760C22—21no—
761C22—32no—
762C22—61no—
763C22—61no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22D3×#20412yes—
768C22C2×D3×D1211yescharacteristic
769C4—21no—
770C4—32no—
771C4—61no—
772C4—61no—
773C4—121no—
774C4—121no—
775C4—121no—
776C4—182no—
777C4—361no—
778C4—361no—
779C4—361no—
780C4#6430611yescharacteristic
781C4#6433011yescharacteristic
782C3—21no—
783C3#7944711yescharacteristic, complemented
784C3#8068911yescharacteristic, complemented
785C2—22no—
786C2—62no—
787C2—241no—
788C2C2×D3×#20411yescharacteristic
789C2#1059469211yescharacteristic
790C2#1059507511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10594907C2
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. C2×#63643C2semidirect
4. C3×#5114C2semidirect
5. C3×C8×#67C2semidirect
6. #10591181C2semidirect
7. #10591126C2semidirect
8. #10590890C2semidirect
9. #10590825C2semidirect
10. #10590822C2semidirect
11. #10590802C2semidirect
12. #10590752C2semidirect
13. #10590744C2semidirect
14. #10590674C2semidirect
15. D3×#816C2semidirect
70. #5114D3semidirect
71. C8×#67D3semidirect
256. #634#41semidirect
258. C3×#67SD16semidirect
518. #67#204semidirect
700. C32#3298semidirect
783. C3#79447semidirect
784. C3#80689semidirect

Maximal subgroups

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

subgroupindex
#105949152
#105949072
C2×#636432
C3×#51142
C3×C8×#672
#105911812
#105911262
#105908902
#105908252
#105908222
#105908022
#105907522
#105907442
#105906742
D3×#8162
#806893
#794473