Finite Group Databasebeta

← #11887624

Subgroups — #11887624

Order 1152.

828 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594993C211yesmaximal, characteristic
2Dic6×#67C211yesmaximal, characteristic
3#10592421C211yesmaximal, characteristic, complemented
4C3×#4739C211yesmaximal, characteristic, complemented
5C3×#67⋊C8C211yesmaximal, characteristic
6#10591187C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8#10590949C211yesmaximal, characteristic, complemented
9#10590890C211yesmaximal, characteristic, complemented
10#10590851C211yesmaximal, characteristic, complemented
11Dic3×Dic12C211yesmaximal, characteristic, complemented
12#10590804C211yesmaximal, characteristic, complemented
13#10590800C211yesmaximal, characteristic, complemented
14#10590682C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16#80193—31nomaximal
17#79448—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21#64133C2211yescharacteristic
22C3×C4×#67C2211yescharacteristic
23C3×#924C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×C3×Dic12C2211yescharacteristic
26C2×C3×Dic12C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28#63982—21no—
29#67⋊Dic3—21no—
30Dic3×#67—21no—
31#63964—21no—
32#63918C2211yescharacteristic
33#63893—21no—
34D3×C4⋊Dic3C2211yescharacteristic
35#63887—21no—
36#63866C2211yescharacteristic
37#63856C2211yescharacteristic
38#63856C2211yescharacteristic
39#63845—21no—
40Dic3×Dic6C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic
42#63839—21no—
43C2×#3719C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic
45#63645C2211yescharacteristic
46#63645C2211yescharacteristic
47#63643C2211yescharacteristic
48#63643C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54#63575C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63566C2211yescharacteristic
58#63566C2211yescharacteristic
59#63566C2211yescharacteristic
60#63566C2211yescharacteristic
61Q8×#67—31no—
62#5635—31no—
63#5543—31no—
64D4×Dic6—31no—
65C3×#451—31no—
66C3×C8×D4—31no—
67C2×#835—31no—
68#5188—31no—
69#5186—31no—
70#5182—31no—
71Dic3×Q16—31no—
72#5116—31no—
73#5116—31no—
74C2×#816—31no—
75C2×#816—31no—
76#5051—31no—
77#4850—31no—
78#4849—31no—
79#4811—31no—
80D3×#103—31no—
81#4793—31no—
82#4792—31no—
83#4739—31no—
84#4739D311yescharacteristic, complemented
85#67⋊C8D311yescharacteristic
86#4722—31no—
87#4722—31no—
88#4722—31no—
89#4722—61no—
90C4×Dic12—31no—
91#4681—31no—
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3—21no—
94C2×#634C2311yescharacteristic
95C2×C3×#67D411yescharacteristic
96C22×C3×Dic3—21no—
97C2×C3×C4×D3C2311yescharacteristic
98C2×C3×Dic6—22no—
99C2×C3×Dic6—21no—
100C2×C3×Dic6—41no—
101C2×C3×Dic6C2311yescharacteristic
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×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112#3757—21no—
113C4⋊(C3⋊Dic3)—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4D411yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8—41no—
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×Dic12—22no—
129C3×Dic12—41no—
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
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C22×Dic6—31no—
148C22×Dic6C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C22×C3×C8—31no—
152C22×C3×C8—31no—
153C3×C22⋊Q8—31no—
154C3×C4×D4—31no—
155#946—31no—
156#946—31no—
157#946—61no—
158Q8×Dic3—31no—
159Q8×Dic3—31no—
160#944—31no—
161#944—61no—
162C2×#216—31no—
163D4×Dic3—61no—
164D4×Dic3—61no—
165C4×#67—61no—
166C4×#67C2×D311yescharacteristic
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—61no—
171#924—31no—
172#924—31no—
173#924—31no—
174#924—31no—
175#924—61no—
176#924—61no—
177#924C2×D311yescharacteristic
178C22×C3⋊C8C2×D311yescharacteristic
179C2×Dic12—31no—
180C2×Dic12C2×D311yescharacteristic
181C2×Dic12C2×D311yescharacteristic
182C2×D3×C8C2×D311yescharacteristic
183#897—61no—
184D3×C4⋊C4—31no—
185#890—61no—
186#889—61no—
187#888—31no—
188#888—61no—
189#67⋊C4—61no—
190#878—61no—
191#878—61no—
192#878—61no—
193#878—61no—
194#878—61no—
195#869—31no—
196#869—31no—
197C4×Dic6—31no—
198C4×Dic6—31no—
199C3×C4⋊C8—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×C22⋊C8—21no—
203C3×C22⋊C8—31no—
204C3×C22⋊C8C2×D311yescharacteristic
205C3×C22⋊C8C2×D311yescharacteristic
206C3×C4×C8—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212(C2×D3)⋊C8C2×D311yescharacteristic
213#818—31no—
214#818—31no—
215#818—31no—
216#818—31no—
217#818—31no—
218#818—61no—
219#818—61no—
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—31no—
229#816—31no—
230#816—61no—
231#816—61no—
232#816C2×D311yescharacteristic
233#816C2×D311yescharacteristic
234Dic3⋊C8C2×D311yescharacteristic
235C8×Dic3C2×D311yescharacteristic
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—81no—
249#634—21no—
250#634—21no—
251C3×#67Q1614yescomplemented
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—42no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—42no—
268C3×Dic6#4112yes—
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—91no—
284#467—91no—
285#462—91no—
286#451—31no—
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×Q8—31no—
295C2×C3×Q8—62no—
296C2×C3×Q8—61no—
297C2×C3×Q8—121no—
298C2×C3×D4—31no—
299C22×C3×C4—21no—
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67D1211yescharacteristic
305C22×Dic3—21no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—121no—
311D3×Q8—62no—
312D3×Q8—121no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3C22×D311yescharacteristic
316C2×Dic6—22no—
317C2×Dic6—21no—
318C2×Dic6—31no—
319C2×Dic6—31no—
320C2×Dic6—41no—
321C2×Dic6—61no—
322C2×Dic6—62no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—121no—
328C2×Dic6C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C2×Dic6C22×D311yescharacteristic
331C3×Q16—62no—
332C3×Q16—121no—
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—121no—
338C2×C3×C8—121no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—61no—
349C3×C42—31no—
350#217—21no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—121no—
356#217D1211yescharacteristic
357#216—121no—
358(C2×D3)⋊C4—61no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4D1211yescharacteristic
361C4⋊Dic3—31no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—121no—
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—22no—
404Dic12—41no—
405Dic12—121no—
406D3×C8—41no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32C2×Q1612yes—
410C22×C32C22×D411yescharacteristic
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3C2×Q1612yes—
414C32×C4—21no—
415C32×C4C2×#4111yescharacteristic
416C32×C4H(5,𝔽2)11yescharacteristic
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—22no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3C2×Q1612yes—
428C22×Q8—31no—
429C22×Q8—91no—
430C2×Q16—31no—
431C2×Q16—31no—
432C2×Q16—91no—
433C22×C8—31no—
434C22×C8—31no—
435C4⋊Q8—91no—
436C4⋊Q8—91no—
437C4⋊Q8—181no—
438#125—181no—
439C22⋊Q8—31no—
440C22⋊Q8—91no—
441C22⋊Q8—91no—
442C22⋊Q8—91no—
443C22⋊Q8—181no—
444C22⋊Q8—181no—
445C22⋊Q8—181no—
446C22⋊Q8—181no—
447C4×Q8—91no—
448C4×Q8—91no—
449C4×D4—31no—
450C4×D4—181no—
451C4×D4—181no—
452C2×C4⋊C4—91no—
453C2×C4⋊C4—91no—
454#107—91no—
455#107—91no—
456#107—91no—
457C4⋊C8—31no—
458#103—31no—
459#103—31no—
460#103—91no—
461#103—91no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468C22⋊C8—31no—
469C22⋊C8D3211yescharacteristic
470C4×C8—31no—
471C23×C3—21no—
472C23×C3—31no—
473C23×C3C2×D1211yescharacteristic
474C23×C3D3×D411yescharacteristic
475C22×D3C2×D1211yescharacteristic
476C3×Q8—32no—
477C3×Q8—61no—
478C3×Q8—61no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8—61no—
482C3×Q8—122no—
483C3×D4—34no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—31no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
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×C4—122no—
502C2×C3×C4C2×D1211yescharacteristic
503C2×C3×C4D3×D411yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505C2×C3×C4C23×D311yescharacteristic
506#67Dic1214yescomplemented
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—21no—
510C2×Dic3—21no—
511C2×Dic3—42no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—121no—
521C2×Dic3—121no—
522C2×Dic3—121no—
523C2×Dic3—121no—
524C2×Dic3—122no—
525C2×Dic3—241no—
526C2×Dic3—241no—
527C2×Dic3—241no—
528C2×Dic3—242no—
529C2×Dic3C2×D1211yescharacteristic
530C2×Dic3C2×D1211yescharacteristic
531C2×Dic3C2×D1211yescharacteristic
532C4×D3—21no—
533C4×D3—21no—
534C4×D3—122no—
535C4×D3—241no—
536Dic6—21no—
537Dic6—21no—
538Dic6—21no—
539Dic6—21no—
540Dic6—21no—
541Dic6—42no—
542Dic6—61no—
543Dic6—61no—
544Dic6—61no—
545Dic6—61no—
546Dic6—121no—
547Dic6—121no—
548Dic6—122no—
549Dic6—122no—
550Dic6—241no—
551Dic6—241no—
552Dic6#23712yes—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—41no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C2×C32—22no—
564C2×C32#54611yescharacteristic
565C2×C32C22×Q1611yescharacteristic
566C2×C32#57711yescharacteristic
567C3×D3—22no—
568C2×Q8—31no—
569C2×Q8—31no—
570C2×Q8—31no—
571C2×Q8—62no—
572C2×Q8—61no—
573C2×Q8—91no—
574C2×Q8—121no—
575C2×Q8—181no—
576C2×Q8—181no—
577C2×Q8—182no—
578C2×Q8—361no—
579C2×D4—31no—
580C22×C4—31no—
581C22×C4—61no—
582C22×C4—181no—
583C22×C4—181no—
584C22×C4—181no—
585C22×C4C2×D3211yescharacteristic
586Q16—62no—
587Q16—121no—
588Q16—361no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—121no—
592C2×C8—121no—
593C2×C8C2×D3211yescharacteristic
594C2×C8C2×D3211yescharacteristic
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—91no—
599C4⋊C4—91no—
600C4⋊C4—91no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C22⋊C4—31no—
612C22⋊C4—31no—
613C22⋊C4—61no—
614C22⋊C4—181no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C42—31no—
618C42—181no—
619C42—181no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—22no—
626C22×C3—32no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3C2×Dic1212yes—
632C22×C3D3×Q1612yes—
633C22×C3C22×D1211yescharacteristic
634C22×C3C2×D3×D411yescharacteristic
635C2×D3—21no—
636C2×D3—21no—
637C2×D3C2×Dic1212yes—
638C3×C4—21no—
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—32no—
643C3×C4—41no—
644C3×C4—61no—
645C3×C4—62no—
646C3×C4—61no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4C2×#23711yescharacteristic
651C3×C4#100411yescharacteristic
652C3×C4#100411yescharacteristic
653C3×C4D3×#4111yescharacteristic
654Dic3—21no—
655Dic3—21no—
656Dic3—22no—
657Dic3—41no—
658Dic3—41no—
659Dic3—41no—
660Dic3—121no—
661Dic3—121no—
662Dic3—121no—
663Dic3—121no—
664Dic3—121no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668Dic3—241no—
669Dic3—241no—
670Dic3—241no—
671Dic3—241no—
672Dic3C2×Dic1212yes—
673C32#329911yescharacteristic, complemented, Sylow
674C23—31no—
675C23D3×D1211yescharacteristic
676Q8—32no—
677Q8—61no—
678Q8—61no—
679Q8—61no—
680Q8—61no—
681Q8—61no—
682Q8—122no—
683Q8—181no—
684Q8—181no—
685Q8—362no—
686Q8—721no—
687D4—34no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—31no—
691C2×C4—31no—
692C2×C4—31no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—122no—
700C2×C4—181no—
701C2×C4—181no—
702C2×C4—181no—
703C2×C4—181no—
704C2×C4—362no—
705C2×C4—721no—
706C2×C4—721no—
707C2×C4D3×D1211yescharacteristic
708C2×C4C22×D3211yescharacteristic
709C8—21no—
710C8—21no—
711C8—61no—
712C8—61no—
713C2×C3—22no—
714C2×C3—22no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—42no—
719C2×C3—62no—
720C2×C3#555411yescharacteristic
721C2×C3#559111yescharacteristic
722C2×C3C22×Dic1211yescharacteristic
723C2×C3#575111yescharacteristic
724C2×C3C2×D3×Q1611yescharacteristic
725C2×C3#577811yescharacteristic
726D3—22no—
727C22—21no—
728C22—21no—
729C22—32no—
730C22—61no—
731C22—61no—
732C22D3×Dic1212yes—
733C22C2×D3×D1211yescharacteristic
734C4—21no—
735C4—32no—
736C4—61no—
737C4—61no—
738C4—62no—
739C4—121no—
740C4—121no—
741C4—121no—
742C4—361no—
743C4—361no—
744C4—361no—
745C4—361no—
746C4D3×#23711yescharacteristic
747C4#6431311yescharacteristic
748C3—21no—
749C3#7944811yescharacteristic, complemented
750C3#8019311yescharacteristic, complemented
751C2—22no—
752C2—62no—
753C2#1059429211yescharacteristic
754C2C2×D3×Dic1211yescharacteristic
755C2#1059471511yescharacteristic
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. #10592421C2semidirect
4. C3×#4739C2semidirect
6. #10591187C2semidirect
7. C2×#63566C2semidirect
8. #10590949C2semidirect
9. #10590890C2semidirect
10. #10590851C2semidirect
11. Dic3×Dic12C2semidirect
12. #10590804C2semidirect
13. #10590800C2semidirect
14. #10590682C2semidirect
15. D3×#816C2semidirect
84. #4739D3semidirect
251. C3×#67Q16semidirect
506. #67Dic12semidirect
673. C32#3299semidirect
749. C3#79448semidirect
750. C3#80193semidirect

Maximal subgroups

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

subgroupindex
#105949932
Dic6×#672
#105924212
C3×#47392
C3×#67⋊C82
#105911872
C2×#635662
#105909492
#105908902
#105908512
Dic3×Dic122
#105908042
#105908002
#105906822
D3×#8162
#801933
#794483