Finite Group Databasebeta

← #11887529

Subgroups — #11887529

Order 1152.

919 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#626C211yesmaximal, characteristic, complemented
2#10594517C211yesmaximal, characteristic
3#10592505C211yesmaximal, characteristic, complemented
4C3×D3×#103C211yesmaximal, characteristic, complemented
5C3×#4791C211yesmaximal, characteristic, complemented
6#10591584C211yesmaximal, characteristic, complemented
7#10591552C211yesmaximal, characteristic, complemented
8#10591536C211yesmaximal, characteristic, complemented
9#10590830C211yesmaximal, characteristic, complemented
10#10590760C211yesmaximal, characteristic, complemented
11#10590720C211yesmaximal, characteristic, complemented
12#10590686C211yesmaximal, characteristic, complemented
13#10590560C211yesmaximal, characteristic, complemented
14#10590523C211yesmaximal, characteristic, complemented
15#10590426C211yesmaximal, characteristic, complemented
16#81022—31nomaximal
17#78805—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×#3799—21no—
21C2×#3755C2211yescharacteristic
22C2×#3744C2211yescharacteristic
23#64104C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#888C2211yescharacteristic
28#63909C2211yescharacteristic
29C4×#626—21no—
30C4×#626C2211yescharacteristic
31#63900C2211yescharacteristic
32#63897—21no—
33#63894C2211yescharacteristic
34#63888—21no—
35#63871—21no—
36#63871C2211yescharacteristic
37#63866—21no—
38#63866C2211yescharacteristic
39#63857—21no—
40#63857C2211yescharacteristic
41#63850—21no—
42C2×#3717C2211yescharacteristic
43C2×#3710C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63647C2211yescharacteristic
46#63637C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#817C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×Dic3⋊C8C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#808C2211yescharacteristic
54#63574C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61Q8×#67—31no—
62#5726—31no—
63Q8×D12—31no—
64#5507—31no—
65C3×#475—31no—
66C2×C3×#103—31no—
67#5227—31no—
68#5114—31no—
69C8×#67—31no—
70#5093—31no—
71C4×#215—31no—
72#4971—31no—
73#4864—31no—
74#4864—31no—
75#4862—31no—
76#4862—31no—
77#4841—31no—
78#4834—31no—
79#4818—31no—
80#4807—31no—
81#4806—31no—
82#4806—31no—
83#4806—31no—
84#4806—61no—
85#4805—31no—
86D3×#103—31no—
87D3×#103—31no—
88D3×#103D311yescharacteristic, complemented
89#4792—31no—
90#4791D311yescharacteristic, complemented
91#4788—31no—
92C2×C32×Q8C2311yescharacteristic
93Q8×C3⋊D3—22no—
94Q8×C3⋊D3—41no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4×C3⋊D3—21no—
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634—21no—
100C2×#634C2311yescharacteristic
101C3×D3×Q8—22no—
102C3×D3×Q8—41no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6—21no—
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2311yescharacteristic
109C2×#626—21no—
110C2×#626D411yescharacteristic
111C2×#624—21no—
112C2×#624—21no—
113#3799—44no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116#3755—22no—
117#3752—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119#3744—41no—
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D3×C8—41no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722—21no—
138#3722—21no—
139#3722—21no—
140#3722D411yescharacteristic
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3D411yescharacteristic
143#3717—41no—
144#3710—41no—
145#3298—91noSylow
146C22×C3×Q8—31no—
147C2×#239—61no—
148C2×D3×Q8—31no—
149C2×D3×Q8—31no—
150C2×D3×Q8—61no—
151C2×D3×Q8C2×D311yescharacteristic
152C2×#235—61no—
153C22×C3×C8—31no—
154C3×C4⋊Q8—31no—
155C3×C4×Q8—31no—
156C2×C3×C4⋊C4—31no—
157#946—31no—
158#946—61no—
159#946—61no—
160Q8×Dic3C2×D311yescharacteristic
161#944—31no—
162#944—61no—
163C2×#215—31no—
164C2×#215—31no—
165C2×#215—31no—
166C2×#215—61no—
167#930—31no—
168#929—61no—
169C4×#67—31no—
170C4×#67—61no—
171#924—31no—
172#924—61no—
173C2×#204—31no—
174C2×#204—31no—
175C2×#204—31no—
176C2×#204—61no—
177C2×D3×C8—31no—
178C2×D3×C8—31no—
179C2×D3×C8C2×D311yescharacteristic
180#897—31no—
181#897—31no—
182#897—61no—
183#897—61no—
184#896—61no—
185#895—31no—
186#895—31no—
187#895—31no—
188#895—61no—
189#894—61no—
190#894—61no—
191#894—61no—
192#893—31no—
193D3×C4⋊C4—31no—
194D3×C4⋊C4—31no—
195D3×C4⋊C4C2×D311yescharacteristic
196#888C2×D311yescharacteristic
197C4×D12—31no—
198C4×D12—31no—
199C4×D12—61no—
200#869—31no—
201#869—61no—
202C3×#106—31no—
203C3×#106—31no—
204C3×C4⋊C8—31no—
205C3×#103—21no—
206C3×#103—31no—
207C3×#103—31no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103C2×D311yescharacteristic
211C3×#103C2×D311yescharacteristic
212#835—31no—
213#835C2×D311yescharacteristic
214#835C2×D311yescharacteristic
215#830—31no—
216#821—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—61no—
221#817C2×D311yescharacteristic
222#816—31no—
223#816—31no—
224#816C2×D311yescharacteristic
225Dic3⋊C8C2×D311yescharacteristic
226C8×Dic3—31no—
227#810—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#810—31no—
232#810—61no—
233#810C2×D311yescharacteristic
234#809—31no—
235#808—31no—
236#808—31no—
237#808C2×D311yescharacteristic
238C4×C3⋊C8—31no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8#4112yescomplemented
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3C2×D411yescharacteristic
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—42no—
252C4×C3⋊D3—21no—
253C4×C3⋊D3—21no—
254C4×C3⋊D3—42no—
255#634—21no—
256#634—21no—
257#634—42no—
258C2×C3×Dic3—21no—
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×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—42no—
268C3×C4×D3—42no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—42no—
272C3×Dic6—42no—
273#626—42no—
274#626SD1614yescomplemented
275#624—42no—
276#624—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—91no—
285#483—91no—
286#475—31no—
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—61no—
300C2×C3×Q8—62no—
301C2×C3×Q8—121no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C2×#67—31no—
308C2×#67—61no—
309#239—124no—
310D3×Q8—22no—
311D3×Q8—41no—
312D3×Q8—62no—
313D3×Q8—62no—
314D3×Q8—122no—
315D3×Q8—121no—
316D3×Q8—121no—
317D3×Q8—122no—
318#235—124no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12—121no—
327C2×C4×D3—21no—
328C2×C4×D3—21no—
329C2×C4×D3—31no—
330C2×C4×D3—31no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—121no—
339C2×C4×D3C22×D311yescharacteristic
340C2×Dic6—21no—
341C2×Dic6—21no—
342C2×Dic6—31no—
343C2×Dic6—31no—
344C2×Dic6—61no—
345C2×Dic6—61no—
346C2×Dic6—61no—
347C2×Dic6—121no—
348C2×Dic6C22×D311yescharacteristic
349C2×C3×C8—21no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—121no—
353C2×C3×C8C22×D311yescharacteristic
354C2×C3×C8C22×D311yescharacteristic
355C3×C4⋊C4—21no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C42—31no—
365C3×C42—61no—
366#217—31no—
367#217—61no—
368#215—62no—
369#215—62no—
370#215—122no—
371#215—121no—
372(C2×D3)⋊C4—31no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—121no—
385C4⋊Dic3—21no—
386C4⋊Dic3—31no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3C22×D311yescharacteristic
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—31no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403C4×Dic3—21no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410#204—121no—
411#204—121no—
412#204—122no—
413#204—121no—
414D3×C8—41no—
415D3×C8—121no—
416D3×C8—121no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3C2×SD1612yes—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3C2×SD1612yes—
427C32×C4—22no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—21no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3C2×SD1612yes—
440C2×#41—181no—
441C22×Q8—31no—
442C22×Q8—91no—
443C2×SD16—91no—
444C2×SD16—91no—
445C2×SD16—91no—
446C22×C8—31no—
447C22×C8—91no—
448C4⋊Q8—31no—
449C4⋊Q8—91no—
450C4⋊Q8—181no—
451#123—181no—
452#123—181no—
453C22⋊Q8—91no—
454C22⋊Q8—91no—
455C22⋊Q8—181no—
456C22⋊Q8—181no—
457C22⋊Q8—181no—
458#121—91no—
459#121—91no—
460C4×Q8—31no—
461C4×D4—91no—
462C4×D4—91no—
463C4×D4—181no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—91no—
466#106—31no—
467#106—31no—
468#106—91no—
469C4⋊C8—31no—
470#103—31no—
471#103—31no—
472#103—31no—
473#103—31no—
474#103—91no—
475#103—91no—
476#103—91no—
477#103—91no—
478#103D3211yescharacteristic
479#102—91no—
480C22⋊C8—91no—
481C22⋊C8—91no—
482C4×C8—91no—
483C23×C3—31no—
484C22×D3—31no—
485C22×D3—31no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—121no—
490C22×D3D3×D411yescharacteristic
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—22no—
494C3×Q8—41no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—122no—
498C3×Q8—122no—
499C3×Q8#23512yescomplemented
500C3×Q8#23912yescomplemented
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—122no—
518C2×C3×C4—122no—
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—34no—
522#67—122no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—121no—
533C2×Dic3D3×D411yescharacteristic
534C2×Dic3D3×D411yescharacteristic
535C2×Dic3D3×D411yescharacteristic
536D12—34no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12—61no—
541D12—121no—
542D12—121no—
543D12—122no—
544D12—122no—
545D12—122no—
546D12—242no—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—42no—
550C4×D3—42no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—61no—
555C4×D3—121no—
556C4×D3—121no—
557C4×D3—122no—
558C4×D3—122no—
559C4×D3—122no—
560C4×D3—122no—
561C4×D3—122no—
562C4×D3—124no—
563C4×D3—122no—
564Dic6—21no—
565Dic6—21no—
566Dic6—42no—
567Dic6—42no—
568Dic6—62no—
569Dic6—61no—
570Dic6—61no—
571Dic6—61no—
572Dic6—61no—
573Dic6—121no—
574Dic6—122no—
575Dic6—122no—
576Dic6—124no—
577C3×C8—21no—
578C3×C8—21no—
579C3×C8—41no—
580C3×C8—61no—
581C3×C8—61no—
582C3⋊C8—21no—
583C3⋊C8—21no—
584C3⋊C8—61no—
585C3⋊C8—61no—
586C3⋊C8—121no—
587C2×C32#54611yescharacteristic
588C2×C32C22×SD1611yescharacteristic
589C2×C32#57811yescharacteristic
590C3⋊D3—22no—
591C3⋊D3—81no—
592C3×D3—22no—
593#41—364no—
594C2×Q8—31no—
595C2×Q8—61no—
596C2×Q8—61no—
597C2×Q8—62no—
598C2×Q8—91no—
599C2×Q8—121no—
600C2×Q8—181no—
601C2×Q8—182no—
602C2×Q8—361no—
603C2×Q8C2×D3211yescharacteristic
604C2×D4—91no—
605C2×D4—91no—
606C2×D4—181no—
607C2×D4—181no—
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—91no—
612C22×C4—181no—
613C22×C4—181no—
614C22×C4—181no—
615SD16—182no—
616SD16—361no—
617SD16—361no—
618C2×C8—31no—
619C2×C8—31no—
620C2×C8—91no—
621C2×C8—121no—
622C2×C8—361no—
623C2×C8C2×D3211yescharacteristic
624C4⋊C4—31no—
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—91no—
631C4⋊C4—181no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4C2×D3211yescharacteristic
637C22⋊C4—91no—
638C22⋊C4—91no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C42—31no—
645C42—61no—
646C22×C3—21no—
647C22×C3—32no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C2×D3×D411yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—32no—
655C2×D3—32no—
656C2×D3—62no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—241no—
670C2×D3—241no—
671C2×D3—241no—
672C2×D3D3×SD1612yes—
673C3×C4—22no—
674C3×C4—22no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—32no—
678C3×C4—42no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—61no—
682C3×C4—61no—
683C3×C4—81no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4C2×#23511yescharacteristic
689C3×C4#100411yescharacteristic
690C3×C4C2×#23911yescharacteristic
691C3×C4#100911yescharacteristic
692Dic3—21no—
693Dic3—21no—
694Dic3—41no—
695Dic3—41no—
696Dic3—41no—
697Dic3—41no—
698Dic3—61no—
699Dic3—61no—
700Dic3—121no—
701Dic3—122no—
702Dic3—121no—
703Dic3—121no—
704Dic3D3×SD1612yes—
705C32#329811yescharacteristic, complemented, Sylow
706C23—31no—
707C23—91no—
708C23—181no—
709Q8—21no—
710Q8—61no—
711Q8—61no—
712Q8—122no—
713Q8—122no—
714Q8—181no—
715Q8—181no—
716Q8—362no—
717Q8#379912yescomplemented
718D4—94no—
719D4—181no—
720D4—181no—
721D4—362no—
722D4—362no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—91no—
735C2×C4—122no—
736C2×C4—122no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—362no—
741C2×C4—362no—
742C2×C4—362no—
743C2×C4C22×D3211yescharacteristic
744C8—21no—
745C8—61no—
746C8—61no—
747C8—181no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3—62no—
752C2×C3#549011yescharacteristic
753C2×C3#563011yescharacteristic
754C2×C3C2×D3×SD1611yescharacteristic
755C2×C3C2×D3×SD1611yescharacteristic
756C2×C3#576611yescharacteristic
757C2×C3#577911yescharacteristic
758D3—22no—
759D3—62no—
760D3—62no—
761D3—122no—
762D3—241no—
763D3—241no—
764D3—481no—
765C22—32no—
766C22—61no—
767C22—61no—
768C22—92no—
769C22—181no—
770C22—181no—
771C22—361no—
772C22—361no—
773C22—361no—
774C22D32×D411yescharacteristic
775C4—22no—
776C4—32no—
777C4—41no—
778C4—61no—
779C4—61no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—181no—
785C4—361no—
786C4C2×#379911yescharacteristic
787C4#6431411yescharacteristic
788C3—21no—
789C3#7880511yescharacteristic, complemented
790C3#8102211yescharacteristic, complemented
791C2—62no—
792C2—182no—
793C2—721no—
794C2#1059418711yescharacteristic
795C2D32×SD1611yescharacteristic
796C2#1059476611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594517C2
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. Q8×#626C2semidirect
3. #10592505C2semidirect
4. C3×D3×#103C2semidirect
5. C3×#4791C2semidirect
6. #10591584C2semidirect
7. #10591552C2semidirect
8. #10591536C2semidirect
9. #10590830C2semidirect
10. #10590760C2semidirect
11. #10590720C2semidirect
12. #10590686C2semidirect
13. #10590560C2semidirect
14. #10590523C2semidirect
15. #10590426C2semidirect
88. D3×#103D3semidirect
90. #4791D3semidirect
243. C32×Q8#41semidirect
274. #626SD16semidirect
499. C3×Q8#235semidirect
500. C3×Q8#239semidirect
705. C32#3298semidirect
717. Q8#3799semidirect
789. C3#78805semidirect
790. C3#81022semidirect

Maximal subgroups

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

subgroupindex
Q8×#6262
#105945172
#105925052
C3×D3×#1032
C3×#47912
#105915842
#105915522
#105915362
#105908302
#105907602
#105907202
#105906862
#105905602
#105905232
#105904262
#810223
#788053