Finite Group Databasebeta

← #11887556

Subgroups — #11887556

Order 1152.

900 conjugacy classes of subgroups.

The subgroup lattice has 789 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595400C211yesmaximal, characteristic, complemented
2#10594512C211yesmaximal, characteristic
3#10592517C211yesmaximal, characteristic, complemented
4C3×#4805C211yesmaximal, characteristic, complemented
5C3×D3×#103C211yesmaximal, characteristic, complemented
6#10591585C211yesmaximal, characteristic, complemented
7#10591584C211yesmaximal, characteristic, complemented
8#10591538C211yesmaximal, characteristic, complemented
9#10590951C211yesmaximal, characteristic, complemented
10#10590830C211yesmaximal, characteristic, complemented
11#10590816C211yesmaximal, characteristic, complemented
12#10590717C211yesmaximal, characteristic, complemented
13D3×#810C211yesmaximal, characteristic, complemented
14#10590483C211yesmaximal, characteristic, complemented
15#10590426C211yesmaximal, characteristic, complemented
16#81450—31nomaximal
17#78805—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3798—21no—
20C2×D3×Dic6C2211yescharacteristic
21#64153C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23C2×#3744C2211yescharacteristic
24#64102C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27C3×D3×C4⋊C4C2211yescharacteristic
28C3×D3×C4⋊C4C2211yescharacteristic
29#63919C2211yescharacteristic
30#63909C2211yescharacteristic
31#63909C2211yescharacteristic
32C4×#625C2211yescharacteristic
33#63887—21no—
34#63879—21no—
35#63865—21no—
36#63857C2211yescharacteristic
37#63851—21no—
38#63850—21no—
39#63850—21no—
40#63843C2211yescharacteristic
41#63839—21no—
42C2×#3717C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63641C2211yescharacteristic
46#63637C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#817C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#808C2211yescharacteristic
54#63574C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic
61Q8×#67—31no—
62#5632—31no—
63#5507—31no—
64#5507—31no—
65C3×#483—31no—
66C2×C3×#103—31no—
67#5227—31no—
68#5114—31no—
69C8×#67—31no—
70#5048—31no—
71#4971—31no—
72C2×#810—31no—
73#4864—31no—
74#4862—31no—
75#4854—31no—
76#4852—31no—
77#4818—31no—
78#4818—31no—
79#4818—61no—
80#4807—31no—
81#4806—31no—
82#4806—31no—
83#4805D311yescharacteristic, complemented
84D3×#103—31no—
85D3×#103D311yescharacteristic, complemented
86#4792—31no—
87#4792—31no—
88#4791—31no—
89#4788—31no—
90#4738—31no—
91#67⋊C8—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×#634C2311yescharacteristic
96C3×D3×Q8—22no—
97C3×D3×Q8—41no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#627—21no—
107C2×#626—21no—
108C2×#626—21no—
109C2×#625D411yescharacteristic
110C2×D3×Dic3—21no—
111#3798—44no—
112D3×Dic6—22no—
113D3×Dic6—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3755—41no—
117#3752—21no—
118#3750—21no—
119#3750—21no—
120C4×C3⋊Dic3C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122#3744—41no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×D3×C8—41no—
133#3724—21no—
134#3724D411yescharacteristic
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143#3717—22no—
144D3×C3⋊C8—41no—
145#3298—91noSylow
146C22×C3×Q8—31no—
147C2×D3×Q8—31no—
148C2×D3×Q8C2×D311yescharacteristic
149C2×#235—61no—
150C2×#235—61no—
151C22×Dic6—31no—
152C22×C3×C8—31no—
153C3×C22⋊Q8—31no—
154C2×C3×C4⋊C4—31no—
155C2×C3×C4⋊C4—31no—
156#946—61no—
157#946C2×D311yescharacteristic
158Q8×Dic3—31no—
159#944—31no—
160#944—31no—
161#944—61no—
162#944—61no—
163C2×#215—31no—
164C2×#215—31no—
165C2×#215—31no—
166C2×#215—61no—
167#930—31no—
168#930—31no—
169#929—61no—
170#929—61no—
171C4×#67—31no—
172C4×#67—31no—
173C4×#67—61no—
174#924—31no—
175#924—61no—
176C22×C3⋊C8—31no—
177C2×#204—31no—
178C2×#204—31no—
179C2×#204—31no—
180C2×#204—61no—
181C2×D3×C8—31no—
182C2×D3×C8C2×D311yescharacteristic
183#897—31no—
184#896—61no—
185#896—61no—
186#896—61no—
187#895—31no—
188#895—31no—
189#894—61no—
190#894—61no—
191#893—31no—
192#893—31no—
193#893—61no—
194D3×C4⋊C4C2×D311yescharacteristic
195D3×C4⋊C4C2×D311yescharacteristic
196#888—31no—
197#888—31no—
198#888—61no—
199#887—31no—
200#67⋊C4—61no—
201#878—61no—
202C3×#106—31no—
203C3×#106—31no—
204C3×#103—21no—
205C3×#103—31no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103C2×D311yescharacteristic
210C3×#103C2×D311yescharacteristic
211C3×C22⋊C8—31no—
212#835—31no—
213#835C2×D311yescharacteristic
214#835C2×D311yescharacteristic
215#830—31no—
216#821—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8C2×D311yescharacteristic
219#817C2×D311yescharacteristic
220#816—31no—
221#816—31no—
222#816C2×D311yescharacteristic
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—61no—
226C8×Dic3—31no—
227C8×Dic3—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—31no—
233#810—61no—
234#810C2×D311yescharacteristic
235#809—31no—
236#808—31no—
237#808—31no—
238#808C2×D311yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4×C3⋊D3—42no—
253#634—21no—
254#634—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—42no—
266C3×C4×D3—42no—
267C3×C4×D3—42no—
268C3×Dic6—21no—
269C3×Dic6—42no—
270C3×Dic6#4112yescomplemented
271#627—42no—
272#627—42no—
273#626—42no—
274#626—42no—
275#625SD1614yescomplemented
276D3×Dic3—42no—
277C32×C8—21no—
278C3⋊(C3⋊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—91no—
294C2×#103—31no—
295C2×#103—91no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C2×C3×Q8—62no—
300C2×C3×Q8—121no—
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—31no—
309C2×#67—31no—
310C2×#67—61no—
311C2×#67—61no—
312C22×Dic3—61no—
313D3×Q8—22no—
314D3×Q8—41no—
315D3×Q8—62no—
316D3×Q8—121no—
317#235—124no—
318#235—124no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—61no—
324C2×C4×D3—21no—
325C2×C4×D3—21no—
326C2×C4×D3—21no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—121no—
331C2×C4×D3C22×D311yescharacteristic
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—21no—
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—61no—
337C2×Dic6—62no—
338C2×Dic6—61no—
339C2×Dic6—61no—
340C2×Dic6—61no—
341C2×Dic6—61no—
342C2×Dic6—121no—
343C2×Dic6C22×D311yescharacteristic
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8—121no—
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C3×C4⋊C4—21no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C22⋊C4—61no—
360#217—31no—
361#217—31no—
362#217—61no—
363#215—62no—
364#215—121no—
365#215—121no—
366#215—122no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—121no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
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—121no—
397Dic3⋊C4—121no—
398C4×Dic3—31no—
399C4×Dic3—31no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409#204—62no—
410#204—121no—
411#204—121no—
412#204—122no—
413D3×C8—41no—
414D3×C8—121no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—41no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—21no—
423C2×C3×D3C2×SD1612yes—
424C2×C3×D3C2×SD1612yes—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—41no—
431C3⋊Dic3C2×SD1612yes—
432C3×Dic3—22no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—181no—
439C22×Q8—31no—
440C22×Q8—91no—
441C2×SD16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C22×C8—31no—
445C22×C8—91no—
446C4⋊Q8—91no—
447C4⋊Q8—91no—
448C4⋊Q8—181no—
449#123—181no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—91no—
453C22⋊Q8—181no—
454C22⋊Q8—181no—
455C22⋊Q8—181no—
456#121—91no—
457#121—91no—
458C4×Q8—91no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—181no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—31no—
464#106—31no—
465#106—31no—
466#106—91no—
467C4⋊C8—91no—
468#103—31no—
469#103—31no—
470#103—31no—
471#103—31no—
472#103—91no—
473#103—91no—
474#103—91no—
475#103—91no—
476#103D3211yescharacteristic
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8—91no—
480C4×C8—91no—
481C23×C3—31no—
482C23×C3—31no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—121no—
486C22×D3D3×D411yescharacteristic
487C22×D3D3×D411yescharacteristic
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—32no—
493C3×Q8—41no—
494C3×Q8—41no—
495C3×Q8—61no—
496C3×Q8—122no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—122no—
515C2×C3×C4—122no—
516C2×C3×C4—122no—
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519#67—34no—
520#67—34no—
521#67—122no—
522#67—122no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—121no—
536C2×Dic3—122no—
537C2×Dic3D3×D411yescharacteristic
538C2×Dic3D3×D411yescharacteristic
539D12—62no—
540D12—61no—
541D12—61no—
542D12—61no—
543D12—61no—
544D12—121no—
545D12—122no—
546D12—122no—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—42no—
552C4×D3—42no—
553C4×D3—42no—
554C4×D3—122no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—242no—
558Dic6—21no—
559Dic6—42no—
560Dic6—61no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—121no—
565Dic6—121no—
566Dic6—122no—
567Dic6—122no—
568Dic6—122no—
569Dic6—122no—
570Dic6#23512yescomplemented
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—41no—
574C3×C8—61no—
575C3×C8—61no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—121no—
581C2×C32#54611yescharacteristic
582C2×C32C22×SD1611yescharacteristic
583C2×C32#57811yescharacteristic
584C3⋊D3—81no—
585C3×D3—22no—
586C3×D3—22no—
587#41—364no—
588C2×Q8—31no—
589C2×Q8—61no—
590C2×Q8—62no—
591C2×Q8—91no—
592C2×Q8—121no—
593C2×Q8—181no—
594C2×Q8—181no—
595C2×Q8—182no—
596C2×Q8—361no—
597C2×Q8C2×D3211yescharacteristic
598C2×D4—91no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—181no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—61no—
607C22×C4—181no—
608C22×C4—181no—
609SD16—182no—
610SD16—361no—
611SD16—361no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—91no—
615C2×C8—121no—
616C2×C8—361no—
617C2×C8C2×D3211yescharacteristic
618C4⋊C4—31no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—61no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—61no—
632C22⋊C4—91no—
633C22⋊C4—91no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—91no—
639C42—181no—
640C22×C3—21no—
641C22×C3—32no—
642C22×C3—32no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3C2×D3×D411yescharacteristic
648C22×C3C2×D3×D411yescharacteristic
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—122no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—241no—
661C2×D3—241no—
662C2×D3D3×SD1612yes—
663C2×D3D3×SD1612yes—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—62no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—81no—
674C3×C4—81no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4C2×#23511yescharacteristic
679C3×C4#100411yescharacteristic
680C3×C4D3×#4111yescharacteristic
681C3×C4#100911yescharacteristic
682Dic3—21no—
683Dic3—22no—
684Dic3—21no—
685Dic3—32no—
686Dic3—32no—
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—62no—
691Dic3—61no—
692Dic3—61no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697C32#329811yescharacteristic, complemented, Sylow
698C23—31no—
699C23—31no—
700C23—181no—
701Q8—21no—
702Q8—21no—
703Q8—32no—
704Q8—61no—
705Q8—122no—
706Q8—181no—
707Q8—181no—
708Q8—362no—
709Q8—362no—
710D4—94no—
711D4—181no—
712D4—181no—
713D4—362no—
714D4—362no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—31no—
718C2×C4—31no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—91no—
728C2×C4—91no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—181no—
733C2×C4—362no—
734C2×C4—362no—
735C2×C4C22×D3211yescharacteristic
736C8—21no—
737C8—61no—
738C8—61no—
739C8—181no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—62no—
744C2×C3—62no—
745C2×C3#549011yescharacteristic
746C2×C3#565411yescharacteristic
747C2×C3C2×D3×SD1611yescharacteristic
748C2×C3C2×D3×SD1611yescharacteristic
749C2×C3#576611yescharacteristic
750C2×C3#577911yescharacteristic
751D3—22no—
752D3—22no—
753D3—242no—
754D3—241no—
755D3—241no—
756C22—32no—
757C22—32no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—361no—
763C22—361no—
764C22—361no—
765C22D32×D411yescharacteristic
766C4—41no—
767C4—41no—
768C4—61no—
769C4—61no—
770C4—62no—
771C4—92no—
772C4—121no—
773C4—121no—
774C4—121no—
775C4—181no—
776C4—361no—
777C4D3×#23511yescharacteristic
778C4#6431411yescharacteristic
779C3—21no—
780C3#7880511yescharacteristic, complemented
781C3#8145011yescharacteristic, complemented
782C2—62no—
783C2—62no—
784C2—721no—
785C2#1059427211yescharacteristic
786C2D32×SD1611yescharacteristic
787C2#1059476611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594512C2
hypercenter#103D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #10595400C2semidirect
3. #10592517C2semidirect
4. C3×#4805C2semidirect
5. C3×D3×#103C2semidirect
6. #10591585C2semidirect
7. #10591584C2semidirect
8. #10591538C2semidirect
9. #10590951C2semidirect
10. #10590830C2semidirect
11. #10590816C2semidirect
12. #10590717C2semidirect
13. D3×#810C2semidirect
14. #10590483C2semidirect
15. #10590426C2semidirect
83. #4805D3semidirect
85. D3×#103D3semidirect
270. C3×Dic6#41semidirect
275. #625SD16semidirect
570. Dic6#235semidirect
697. C32#3298semidirect
780. C3#78805semidirect
781. C3#81450semidirect

Maximal subgroups

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

subgroupindex
#105954002
#105945122
#105925172
C3×#48052
C3×D3×#1032
#105915852
#105915842
#105915382
#105909512
#105908302
#105908162
#105907172
D3×#8102
#105904832
#105904262
#814503
#788053