Finite Group Databasebeta

← #11887622

Subgroups — #11887622

Order 1152.

850 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594988C211yesmaximal, characteristic
2#10594915C211yesmaximal, characteristic
3#10592438C211yesmaximal, characteristic, complemented
4C3×#67⋊C8C211yesmaximal, characteristic
5C3×#4722C211yesmaximal, characteristic, complemented
6#10591187C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8#10590952C211yesmaximal, characteristic, complemented
9#10590890C211yesmaximal, characteristic, complemented
10#10590852C211yesmaximal, characteristic, complemented
11#10590808C211yesmaximal, characteristic, complemented
12#10590807C211yesmaximal, characteristic, complemented
13#10590805C211yesmaximal, characteristic, complemented
14#10590684C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16#81490—31nomaximal
17#79448—31nomaximal
18C22×#634C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20#64133C2211yescharacteristic
21C2×#3746C2211yescharacteristic
22C2×#3746C2211yescharacteristic
23C3×C4×#67C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28#63982—21no—
29#67⋊Dic3—21no—
30Dic3×#67—21no—
31#63964—21no—
32#63918C2211yescharacteristic
33#63899—21no—
34#63896—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36#63866C2211yescharacteristic
37#63857C2211yescharacteristic
38#63857C2211yescharacteristic
39#63846—21no—
40#63844C2211yescharacteristic
41#63844C2211yescharacteristic
42#63840—21no—
43C2×#3719C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45#63643C2211yescharacteristic
46#63643C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×#818C2211yescharacteristic
49C3×#818C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54#63575C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63567C2211yescharacteristic
59#63567C2211yescharacteristic
60#63566C2211yescharacteristic
61#5632—31no—
62#5543—31no—
63D4×Dic6—31no—
64#5511—31no—
65C3×#484—31no—
66C3×C8×D4—31no—
67#5116—31no—
68#5116—31no—
69C2×#816—31no—
70C2×#816—31no—
71#5051—31no—
72C2×#810—31no—
73#4887—31no—
74#4884—31no—
75#4875—31no—
76#4873—31no—
77#4850—31no—
78#4849—31no—
79#4809—31no—
80D3×#103—31no—
81#4795—31no—
82#4792—31no—
83#4739—31no—
84#4739—31no—
85#4739—31no—
86#4739—61no—
87#67⋊C8D311yescharacteristic
88#4722—31no—
89#4722D311yescharacteristic, complemented
90C4×Dic12—31no—
91#4681—31no—
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3—21no—
94C2×#634—22no—
95C2×#634—21no—
96C2×#634—41no—
97C2×#634C2311yescharacteristic
98C2×#634C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C22×C3×Dic3—21no—
102C2×C3×C4×D3C2311yescharacteristic
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×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112#3757—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3746—22no—
116#3746—41no—
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4D411yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8—41no—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D3×C8—41no—
131#3724—21no—
132#3724—21no—
133Dic3⋊Dic3—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—
141Dic32—21no—
142Dic32—21no—
143#3719—41no—
144#3299—91noSylow
145C2×D3×Q8—31no—
146C22×Dic6—31no—
147C22×Dic6—31no—
148C22×Dic6—31no—
149C22×Dic6—61no—
150C22×C3×C8—31no—
151C22×C3×C8—31no—
152C3×C22⋊Q8—31no—
153C3×C4×D4—31no—
154C2×C3×C4⋊C4—31no—
155#944—31no—
156C2×#216—31no—
157D4×Dic3—61no—
158D4×Dic3—61no—
159C4×#67—61no—
160C4×#67C2×D311yescharacteristic
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3C2×D311yescharacteristic
163#924—31no—
164#924—31no—
165#924—31no—
166#924—31no—
167#924—61no—
168#924—61no—
169#924C2×D311yescharacteristic
170C22×C3⋊C8C2×D311yescharacteristic
171C2×Dic12—31no—
172C2×Dic12—31no—
173C2×Dic12—31no—
174C2×Dic12—31no—
175C2×Dic12—31no—
176C2×Dic12—61no—
177C2×Dic12—61no—
178C2×D3×C8C2×D311yescharacteristic
179#897—31no—
180#897—31no—
181#896—61no—
182#896—61no—
183D3×C4⋊C4—31no—
184#890—61no—
185#889—61no—
186#888—31no—
187#888—61no—
188#888—61no—
189#887—31no—
190#887—31no—
191#67⋊C4—61no—
192#878—61no—
193#878—61no—
194#878—61no—
195#878—61no—
196#878—61no—
197#869—31no—
198#869—31no—
199C4×Dic6—31no—
200C4×Dic6—31no—
201C3×#107—31no—
202C3×#107—31no—
203C3×C4⋊C8—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×C22⋊C8—21no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8C2×D311yescharacteristic
209C3×C22⋊C8C2×D311yescharacteristic
210C3×C4×C8—31no—
211#835—31no—
212(C2×D3)⋊C8C2×D311yescharacteristic
213#818—31no—
214#818C2×D311yescharacteristic
215#818C2×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—61no—
227#816—61no—
228#816C2×D311yescharacteristic
229#816C2×D311yescharacteristic
230Dic3⋊C8C2×D311yescharacteristic
231C8×Dic3C2×D311yescharacteristic
232#810—31no—
233#810—31no—
234#810—31no—
235#810—31no—
236#810—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—
249#634—21no—
250#634—21no—
251#634—21no—
252#634—21no—
253#634—21no—
254#634—42no—
255#634#4112yes—
256C3×#67Q1614yescomplemented
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—81no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×C4×D3—21no—
266C3×C4×D3—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—31no—
281#484—91no—
282#477—91no—
283#467—91no—
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×D4—31no—
294C22×C3×C4—21no—
295C22×C3×C4—31no—
296C22×C3×C4—61no—
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C2×#67D1211yescharacteristic
300C22×Dic3—21no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305C22×Dic3—121no—
306D3×Q8—62no—
307D3×Q8—121no—
308C2×C4×D3—61no—
309C2×C4×D3—61no—
310C2×C4×D3C22×D311yescharacteristic
311C2×Dic6—31no—
312C2×Dic6—31no—
313C2×Dic6—31no—
314C2×Dic6—31no—
315C2×Dic6—31no—
316C2×Dic6—31no—
317C2×Dic6—61no—
318C2×Dic6—61no—
319C2×Dic6—61no—
320C2×Dic6—62no—
321C2×Dic6—62no—
322C2×Dic6—62no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—61no—
328C2×Dic6—61no—
329C2×Dic6—122no—
330C2×Dic6—121no—
331C2×Dic6—121no—
332C2×Dic6—121no—
333C2×Dic6—121no—
334C2×Dic6—122no—
335C2×Dic6C22×D311yescharacteristic
336C2×C3×C8—21no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8—121no—
341C2×C3×C8—121no—
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—61no—
355C3×C42—31no—
356#217—21no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—121no—
362#217D1211yescharacteristic
363#216—121no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4D1211yescharacteristic
367C4⋊Dic3—21no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
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—121no—
394Dic3⋊C4D1211yescharacteristic
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—41no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403Dic12—62no—
404Dic12—62no—
405Dic12—122no—
406Dic12—121no—
407Dic12—121no—
408Dic12—122no—
409Dic12—121no—
410D3×C8—41no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32C2×Q1612yes—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3C2×Q1612yes—
418C32×C4—21no—
419C32×C4C2×#4111yescharacteristic
420C32×C4H(5,𝔽2)11yescharacteristic
421C3⋊Dic3—22no—
422C3⋊Dic3—41no—
423C3⋊Dic3—41no—
424C3⋊Dic3—41no—
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3C2×Q1612yes—
432C22×Q8—91no—
433C22×Q8—91no—
434C2×Q16—91no—
435C2×Q16—91no—
436C2×Q16—91no—
437C22×C8—31no—
438C22×C8—31no—
439C4⋊Q8—91no—
440C4⋊Q8—91no—
441C4⋊Q8—181no—
442#125—181no—
443C22⋊Q8—31no—
444C22⋊Q8—91no—
445C22⋊Q8—91no—
446C22⋊Q8—91no—
447C22⋊Q8—181no—
448C22⋊Q8—181no—
449C22⋊Q8—181no—
450C22⋊Q8—181no—
451C4×Q8—91no—
452C4×Q8—91no—
453C4×D4—31no—
454C4×D4—181no—
455C4×D4—181no—
456C2×C4⋊C4—31no—
457C2×C4⋊C4—91no—
458#107—31no—
459#107—31no—
460#107—91no—
461C4⋊C8—31no—
462#103—31no—
463#103—31no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472C22⋊C8—31no—
473C22⋊C8D3211yescharacteristic
474C4×C8—31no—
475C23×C3—21no—
476C23×C3—31no—
477C23×C3C2×D1211yescharacteristic
478C23×C3D3×D411yescharacteristic
479C22×D3C2×D1211yescharacteristic
480C3×Q8—61no—
481C3×Q8—61no—
482C3×D4—34no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—31no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—241no—
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—81no—
519C2×Dic3—121no—
520C2×Dic3—121no—
521C2×Dic3—121no—
522C2×Dic3—121no—
523C2×Dic3—122no—
524C2×Dic3—122no—
525C2×Dic3—122no—
526C2×Dic3—124no—
527C2×Dic3—241no—
528C2×Dic3C2×D1211yescharacteristic
529C2×Dic3C2×D1211yescharacteristic
530C2×Dic3C2×D1211yescharacteristic
531C4×D3—21no—
532C4×D3—21no—
533C4×D3—122no—
534C4×D3—241no—
535Dic6—21no—
536Dic6—21no—
537Dic6—32no—
538Dic6—32no—
539Dic6—62no—
540Dic6—61no—
541Dic6—61no—
542Dic6—62no—
543Dic6—61no—
544Dic6—61no—
545Dic6—61no—
546Dic6—61no—
547Dic6—61no—
548Dic6—61no—
549Dic6—61no—
550Dic6—61no—
551Dic6—121no—
552Dic6—121no—
553Dic6—121no—
554Dic6—121no—
555Dic6—122no—
556Dic6—122no—
557Dic6—122no—
558Dic6—122no—
559Dic6—124no—
560Dic6—241no—
561Dic6—241no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—41no—
567C3×C8—41no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C2×C32—22no—
573C2×C32#54611yescharacteristic
574C2×C32C22×Q1611yescharacteristic
575C2×C32#57711yescharacteristic
576C3×D3—22no—
577C2×Q8—31no—
578C2×Q8—91no—
579C2×Q8—91no—
580C2×Q8—91no—
581C2×Q8—182no—
582C2×Q8—181no—
583C2×Q8—181no—
584C2×Q8—182no—
585C2×Q8—181no—
586C2×Q8—361no—
587C2×Q8—361no—
588C2×D4—31no—
589C22×C4—31no—
590C22×C4—61no—
591C22×C4—181no—
592C22×C4—181no—
593C22×C4—181no—
594C22×C4C2×D3211yescharacteristic
595Q16—182no—
596Q16—361no—
597Q16—361no—
598C2×C8—31no—
599C2×C8—31no—
600C2×C8—121no—
601C2×C8—121no—
602C2×C8C2×D3211yescharacteristic
603C2×C8C2×D3211yescharacteristic
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—31no—
608C4⋊C4—61no—
609C4⋊C4—61no—
610C4⋊C4—91no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C22⋊C4—31no—
621C22⋊C4—31no—
622C22⋊C4—61no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C42—31no—
627C42—181no—
628C42—181no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—22no—
635C22×C3—32no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3C2×Dic1212yes—
641C22×C3D3×Q1612yes—
642C22×C3C22×D1211yescharacteristic
643C22×C3C2×D3×D411yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3C2×Dic1212yes—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—32no—
652C3×C4—41no—
653C3×C4—61no—
654C3×C4—61no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4#100411yescharacteristic
660C3×C4D3×#4111yescharacteristic
661C3×C4D3×#4111yescharacteristic
662C3×C4#100911yescharacteristic
663Dic3—21no—
664Dic3—21no—
665Dic3—41no—
666Dic3—41no—
667Dic3—41no—
668Dic3—41no—
669Dic3—62no—
670Dic3—62no—
671Dic3—122no—
672Dic3—122no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—241no—
680Dic3—241no—
681Dic3C2×Dic1212yes—
682C32#329911yescharacteristic, complemented, Sylow
683C23—31no—
684C23D3×D1211yescharacteristic
685Q8—61no—
686Q8—61no—
687Q8—92no—
688Q8—181no—
689Q8—181no—
690Q8—181no—
691Q8—181no—
692Q8—181no—
693Q8—362no—
694Q8—362no—
695Q8—721no—
696D4—34no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—241no—
713C2×C4—362no—
714C2×C4—362no—
715C2×C4—721no—
716C2×C4D3×D1211yescharacteristic
717C2×C4C22×D3211yescharacteristic
718C8—21no—
719C8—21no—
720C8—61no—
721C8—61no—
722C2×C3—22no—
723C2×C3—22no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—42no—
728C2×C3—62no—
729C2×C3#555411yescharacteristic
730C2×C3#565411yescharacteristic
731C2×C3C22×Dic1211yescharacteristic
732C2×C3#575111yescharacteristic
733C2×C3C2×D3×Q1611yescharacteristic
734C2×C3#577511yescharacteristic
735D3—22no—
736C22—21no—
737C22—21no—
738C22—32no—
739C22—61no—
740C22—61no—
741C22D3×Dic1212yes—
742C22C2×D3×D1211yescharacteristic
743C4—21no—
744C4—32no—
745C4—61no—
746C4—61no—
747C4—121no—
748C4—121no—
749C4—121no—
750C4—121no—
751C4—182no—
752C4—361no—
753C4—361no—
754C4—361no—
755C4#6431211yescharacteristic
756C4#6431411yescharacteristic
757C3—21no—
758C3#7944811yescharacteristic, complemented
759C3#8149011yescharacteristic, complemented
760C2—22no—
761C2—62no—
762C2#1059429311yescharacteristic
763C2C2×D3×Dic1211yescharacteristic
764C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊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. #10592438C2semidirect
5. C3×#4722C2semidirect
6. #10591187C2semidirect
7. C2×#63567C2semidirect
8. #10590952C2semidirect
9. #10590890C2semidirect
10. #10590852C2semidirect
11. #10590808C2semidirect
12. #10590807C2semidirect
13. #10590805C2semidirect
14. #10590684C2semidirect
15. D3×#816C2semidirect
89. #4722D3semidirect
256. C3×#67Q16semidirect
505. #67Dic12semidirect
682. C32#3299semidirect
758. C3#79448semidirect
759. C3#81490semidirect

Maximal subgroups

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

subgroupindex
#105949882
#105949152
#105924382
C3×#67⋊C82
C3×#47222
#105911872
C2×#635672
#105909522
#105908902
#105908522
#105908082
#105908072
#105908052
#105906842
D3×#8162
#814903
#794483