Finite Group Databasebeta

← #11887628

Subgroups — #11887628

Order 1152.

857 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594993C211yesmaximal, characteristic
2#10594915C211yesmaximal, characteristic
3C2×#63643C211yesmaximal, characteristic, complemented
4C3×#5116C211yesmaximal, characteristic, complemented
5C3×C8×#67C211yesmaximal, characteristic
6#10591190C211yesmaximal, characteristic, complemented
7#10591103C211yesmaximal, characteristic, complemented
8#10590949C211yesmaximal, characteristic, complemented
9#10590890C211yesmaximal, characteristic, complemented
10#10590848C211yesmaximal, characteristic, complemented
11#10590805C211yesmaximal, characteristic, complemented
12#10590800C211yesmaximal, characteristic, complemented
13#10590793C211yesmaximal, characteristic, complemented
14#10590684C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16#80781—31nomaximal
17#79448—31nomaximal
18C22×#634C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×C4×#67C2211yescharacteristic
23C3×#924C2211yescharacteristic
24C3×#924C2211yescharacteristic
25C2×C3×Dic12C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27#63982—21no—
28#63982—21no—
29#67⋊Dic3—21no—
30#67⋊Dic3—21no—
31#63918C2211yescharacteristic
32#63896—21no—
33#63893—21no—
34D3×C4⋊Dic3C2211yescharacteristic
35#63866C2211yescharacteristic
36#63857C2211yescharacteristic
37#63856C2211yescharacteristic
38#63845—21no—
39#63844C2211yescharacteristic
40Dic3×Dic6C2211yescharacteristic
41#63840—21no—
42C2×#3719C2211yescharacteristic
43C2×#3719C2211yescharacteristic
44#63643C2211yescharacteristic
45#63643C2211yescharacteristic
46#63643C2211yescharacteristic
47#63643C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#816C2211yescharacteristic
53C3×Dic3⋊C8C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55#63575C2211yescharacteristic
56#63575C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61#5635—31no—
62#5632—31no—
63#5543—31no—
64D4×Dic6—31no—
65C3×#467—31no—
66C3×C8×D4—31no—
67#5186—31no—
68#5182—31no—
69#5116—31no—
70#5116D311yescharacteristic, complemented
71C8×#67D311yescharacteristic
72C2×#816—31no—
73C2×#816—31no—
74C2×#816—31no—
75C2×#816—61no—
76#5050—31no—
77#5044—31no—
78#4884—31no—
79#4875—31no—
80#4850—31no—
81#4849—31no—
82#4813—31no—
83D3×#103—31no—
84#4792—31no—
85#4790—31no—
86#4739—31no—
87#4739—31no—
88#4722—31no—
89#4722—31no—
90C4×Dic12—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×#67D411yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×#627—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108D3×Dic6—22no—
109D3×Dic6—41no—
110C2×C32×C8—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4D411yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×Dic12—41no—
129C3×D3×C8—41no—
130#3724—21no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3719—22no—
143#3719—41no—
144#3299—91noSylow
145C2×D3×Q8—31no—
146C22×Dic6—31no—
147C22×Dic6—31no—
148C22×Dic6—31no—
149C22×Dic6—61no—
150C2×C3×Q16—31no—
151C22×C3×C8—21no—
152C22×C3×C8—31no—
153C22×C3×C8C2×D311yescharacteristic
154C22×C3×C8C2×D311yescharacteristic
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C4×D4—31no—
158#946—31no—
159Q8×Dic3—31no—
160#944—31no—
161C2×#216—31no—
162C2×#216—31no—
163D4×Dic3—61no—
164D4×Dic3—61no—
165C4×#67C2×D311yescharacteristic
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3—61no—
170#924—31no—
171#924—31no—
172#924C2×D311yescharacteristic
173#924C2×D311yescharacteristic
174C2×Dic12—31no—
175C2×Dic12—31no—
176C2×Dic12C2×D311yescharacteristic
177C2×D3×C8C2×D311yescharacteristic
178#897—31no—
179#897—61no—
180#896—61no—
181D3×C4⋊C4—31no—
182#890—61no—
183#889—61no—
184#888—31no—
185#888—61no—
186#888—61no—
187#887—31no—
188#67⋊C4—61no—
189#67⋊C4—61no—
190#878—61no—
191#878—61no—
192#878—61no—
193#878—61no—
194#878—61no—
195#878—61no—
196#869—31no—
197#869—31no—
198C4×Dic6—31no—
199C4×Dic6—31no—
200C3×#107—31no—
201C3×C4⋊C8—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×C4×C8—31no—
207#835—31no—
208#835—31no—
209#830C2×D311yescharacteristic
210(C2×D3)⋊C8C2×D311yescharacteristic
211#818—31no—
212#818—31no—
213#818C2×D311yescharacteristic
214#816—31no—
215#816—31no—
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—61no—
227#816—61no—
228#816—61no—
229#816—61no—
230#816C2×D311yescharacteristic
231#816C2×D311yescharacteristic
232Dic3⋊C8C2×D311yescharacteristic
233C8×Dic3C2×D311yescharacteristic
234#810—31no—
235#810—31no—
236#807—31no—
237#807—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4C2411yescharacteristic
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—42no—
249C2×C3⋊Dic3—81no—
250#634—21no—
251#634—21no—
252#634—21no—
253#634—42no—
254#634#4112yes—
255C3×#67Q1614yescomplemented
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269#627—42no—
270#627—81no—
271D3×Dic3—42no—
272D3×Dic3—81no—
273C32×C8—21no—
274C32×C8—21no—
275C3×C3⋊C8—21no—
276C3×C3⋊C8—21no—
277#554—91no—
278D4×Q8—91no—
279#487—91no—
280#484—91no—
281#484—91no—
282#477—91no—
283#467—31no—
284#467—91no—
285#462—91no—
286#451—91no—
287#451—91no—
288C4×Q16—91no—
289C8×D4—31no—
290C2×#103—91no—
291C2×#103—91no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294C2×C3×D4—31no—
295C22×C3×C4—21no—
296C22×C3×C4—31no—
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C2×#67D1211yescharacteristic
300C22×Dic3—61no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—121no—
307C22×Dic3—121no—
308D3×Q8—62no—
309D3×Q8—121no—
310C2×C4×D3—61no—
311C2×C4×D3—61no—
312C2×C4×D3C22×D311yescharacteristic
313C2×Dic6—31no—
314C2×Dic6—31no—
315C2×Dic6—31no—
316C2×Dic6—31no—
317C2×Dic6—61no—
318C2×Dic6—61no—
319C2×Dic6—62no—
320C2×Dic6—62no—
321C2×Dic6—62no—
322C2×Dic6—64no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6—121no—
330C2×Dic6—121no—
331C2×Dic6—121no—
332C2×Dic6—121no—
333C2×Dic6—122no—
334C2×Dic6C22×D311yescharacteristic
335C2×Dic6C22×D311yescharacteristic
336C3×Q16—121no—
337C2×C3×C8—21no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8—41no—
342C2×C3×C8—41no—
343C2×C3×C8—42no—
344C2×C3×C8—121no—
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—31no—
359#217—21no—
360#217—21no—
361#217—61no—
362#217—61no—
363#217D1211yescharacteristic
364#216—62no—
365#216—121no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4D1211yescharacteristic
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—121no—
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4D1211yescharacteristic
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406Dic12—41no—
407Dic12—62no—
408Dic12—121no—
409D3×C8—41no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32C2×Q1612yes—
413C22×C32C22×D411yescharacteristic
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3C2×Q1612yes—
417C32×C4—21no—
418C32×C4C2×#4111yescharacteristic
419C32×C4H(5,𝔽2)11yescharacteristic
420C3⋊Dic3—22no—
421C3⋊Dic3—41no—
422C3⋊Dic3—41no—
423C3⋊Dic3—41no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3C2×Q1612yes—
431C22×Q8—91no—
432C22×Q8—91no—
433C2×Q16—31no—
434C2×Q16—91no—
435C2×Q16—91no—
436C22×C8—31no—
437C22×C8D3211yescharacteristic
438C4⋊Q8—91no—
439C4⋊Q8—91no—
440C4⋊Q8—181no—
441#125—181no—
442C22⋊Q8—31no—
443C22⋊Q8—31no—
444C22⋊Q8—91no—
445C22⋊Q8—91no—
446C22⋊Q8—181no—
447C22⋊Q8—181no—
448C22⋊Q8—181no—
449C22⋊Q8—181no—
450C4×Q8—91no—
451C4×Q8—91no—
452C4×D4—31no—
453C4×D4—181no—
454C4×D4—181no—
455C2×C4⋊C4—91no—
456C2×C4⋊C4—91no—
457#107—31no—
458#107—91no—
459#107—91no—
460C4⋊C8—31no—
461#103—31no—
462#103—31no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471C22⋊C8—31no—
472C22⋊C8—31no—
473C4×C8—31no—
474C23×C3—21no—
475C23×C3—31no—
476C23×C3C2×D1211yescharacteristic
477C23×C3D3×D411yescharacteristic
478C22×D3C2×D1211yescharacteristic
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8—61no—
482C3×Q8—61no—
483C3×D4—34no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—31no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4C2×D1211yescharacteristic
502C2×C3×C4D3×D411yescharacteristic
503C2×C3×C4C23×D311yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505#67Dic1214yescomplemented
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—121no—
519C2×Dic3—121no—
520C2×Dic3—121no—
521C2×Dic3—121no—
522C2×Dic3—122no—
523C2×Dic3—122no—
524C2×Dic3—122no—
525C2×Dic3—124no—
526C2×Dic3—241no—
527C2×Dic3—241no—
528C2×Dic3—241no—
529C2×Dic3—242no—
530C2×Dic3C2×D1211yescharacteristic
531C2×Dic3C2×D1211yescharacteristic
532C2×Dic3C2×D1211yescharacteristic
533C4×D3—21no—
534C4×D3—21no—
535C4×D3—122no—
536C4×D3—241no—
537Dic6—21no—
538Dic6—21no—
539Dic6—21no—
540Dic6—21no—
541Dic6—32no—
542Dic6—32no—
543Dic6—62no—
544Dic6—61no—
545Dic6—61no—
546Dic6—62no—
547Dic6—61no—
548Dic6—61no—
549Dic6—61no—
550Dic6—61no—
551Dic6—121no—
552Dic6—121no—
553Dic6—122no—
554Dic6—122no—
555Dic6—122no—
556Dic6—122no—
557Dic6—124no—
558Dic6—241no—
559Dic6—241no—
560C3×C8—21no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—41no—
565C3×C8—41no—
566C3×C8—61no—
567C3×C8—61no—
568C3⋊C8—21no—
569C3⋊C8—21no—
570C2×C32—22no—
571C2×C32#54611yescharacteristic
572C2×C32C22×Q1611yescharacteristic
573C2×C32#57711yescharacteristic
574C3×D3—22no—
575C2×Q8—31no—
576C2×Q8—31no—
577C2×Q8—91no—
578C2×Q8—91no—
579C2×Q8—182no—
580C2×Q8—181no—
581C2×Q8—181no—
582C2×Q8—182no—
583C2×Q8—181no—
584C2×Q8—361no—
585C2×Q8—361no—
586C2×D4—31no—
587C22×C4—31no—
588C22×C4—181no—
589C22×C4—181no—
590C22×C4—181no—
591C22×C4—181no—
592C22×C4C2×D3211yescharacteristic
593Q16—121no—
594Q16—182no—
595Q16—361no—
596C2×C8—31no—
597C2×C8—31no—
598C2×C8—41no—
599C2×C8—121no—
600C2×C8C2×D3211yescharacteristic
601C2×C8C2×D3211yescharacteristic
602C4⋊C4—31no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—91no—
608C4⋊C4—91no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C22⋊C4—31no—
619C22⋊C4—31no—
620C22⋊C4—61no—
621C22⋊C4—61no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C42—31no—
625C42—181no—
626C42—181no—
627C22×C3—22no—
628C22×C3—22no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—22no—
635C22×C3—32no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3C2×Dic1212yes—
639C22×C3D3×Q1612yes—
640C22×C3C22×D1211yescharacteristic
641C22×C3C2×D3×D411yescharacteristic
642C2×D3—21no—
643C2×D3—21no—
644C2×D3C2×Dic1212yes—
645C3×C4—22no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—32no—
651C3×C4—61no—
652C3×C4—61no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4#100411yescharacteristic
658C3×C4#100411yescharacteristic
659C3×C4D3×#4111yescharacteristic
660C3×C4D3×#4111yescharacteristic
661Dic3—21no—
662Dic3—21no—
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666Dic3—41no—
667Dic3—62no—
668Dic3—62no—
669Dic3—122no—
670Dic3—122no—
671Dic3—121no—
672Dic3—121no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—241no—
678Dic3—241no—
679Dic3C2×Dic1212yes—
680C32#329911yescharacteristic, complemented, Sylow
681C23—31no—
682C23D3×D1211yescharacteristic
683Q8—61no—
684Q8—61no—
685Q8—61no—
686Q8—61no—
687Q8—92no—
688Q8—181no—
689Q8—181no—
690Q8—181no—
691Q8—362no—
692Q8—362no—
693Q8—721no—
694D4—34no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—181no—
707C2×C4—181no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—362no—
711C2×C4—362no—
712C2×C4—721no—
713C2×C4—721no—
714C2×C4D3×D1211yescharacteristic
715C2×C4C22×D3211yescharacteristic
716C8—21no—
717C8—21no—
718C8—61no—
719C8—61no—
720C2×C3—24no—
721C2×C3—22no—
722C2×C3—22no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—62no—
727C2×C3#555411yescharacteristic
728C2×C3#561011yescharacteristic
729C2×C3C22×Dic1211yescharacteristic
730C2×C3#575111yescharacteristic
731C2×C3C2×D3×Q1611yescharacteristic
732C2×C3#577011yescharacteristic
733D3—22no—
734C22—21no—
735C22—21no—
736C22—32no—
737C22—61no—
738C22—61no—
739C22D3×Dic1212yes—
740C22C2×D3×D1211yescharacteristic
741C4—21no—
742C4—32no—
743C4—61no—
744C4—61no—
745C4—121no—
746C4—121no—
747C4—121no—
748C4—121no—
749C4—182no—
750C4—361no—
751C4—361no—
752C4—361no—
753C4#6430611yescharacteristic
754C4#6433011yescharacteristic
755C3—21no—
756C3#7944811yescharacteristic, complemented
757C3#8078111yescharacteristic, complemented
758C2—22no—
759C2—62no—
760C2#1059467911yescharacteristic
761C2C2×D3×Dic1211yescharacteristic
762C2#1059507511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC22×C8D32
hypocenterC32#3299
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
3. C2×#63643C2semidirect
4. C3×#5116C2semidirect
6. #10591190C2semidirect
7. #10591103C2semidirect
8. #10590949C2semidirect
9. #10590890C2semidirect
10. #10590848C2semidirect
11. #10590805C2semidirect
12. #10590800C2semidirect
13. #10590793C2semidirect
14. #10590684C2semidirect
15. D3×#816C2semidirect
70. #5116D3semidirect
255. C3×#67Q16semidirect
505. #67Dic12semidirect
680. C32#3299semidirect
756. C3#79448semidirect
757. C3#80781semidirect

Maximal subgroups

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

subgroupindex
#105949932
#105949152
C2×#636432
C3×#51162
C3×C8×#672
#105911902
#105911032
#105909492
#105908902
#105908482
#105908052
#105908002
#105907932
#105906842
D3×#8162
#807813
#794483