Finite Group Databasebeta

← #11889383

Subgroups — #11889383

Order 1152.

826 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×#67C211yesmaximal, characteristic
2#10594939C211yesmaximal, characteristic
3#10592927C211yesmaximal, characteristic, complemented
4C3×#5225C211yesmaximal, characteristic, complemented
5#10591613C211yesmaximal, characteristic, complemented
6#10591596C211yesmaximal, characteristic, complemented
7#10591595C211yesmaximal, characteristic, complemented
8#10591575C211yesmaximal, characteristic, complemented
9#10591549C211yesmaximal, characteristic, complemented
10D3×#835C211yesmaximal, characteristic, complemented
11#10591545C211yesmaximal, characteristic, complemented
12#10591541C211yesmaximal, characteristic, complemented
13#10591147C211yesmaximal, characteristic
14#10591121C211yesmaximal, characteristic, complemented
15#10591102C211yesmaximal, characteristic, complemented
16#83552—31nomaximal
17#78966—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×#3756C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22#64133C2211yescharacteristic
23C3×#946—21no—
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×#944—21no—
27C3×#944C2211yescharacteristic
28C3×C4×#67—21no—
29C3×C4×#67C2211yescharacteristic
30C3×#926C2211yescharacteristic
31C3×#924—21no—
32C3×#924C2211yescharacteristic
33C2×C3×#208C2211yescharacteristic
34#63969—21no—
35#63956—21no—
36D3×C4⋊Dic3C2211yescharacteristic
37#63877—21no—
38#63869C2211yescharacteristic
39#63867—21no—
40#63857C2211yescharacteristic
41#63844C2211yescharacteristic
42C2×#3719C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63657C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51#63576C2211yescharacteristic
52#63574C2211yescharacteristic
53#63573C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61C3×D4×Q8—31no—
62Q8×#67D311yescharacteristic
63#5541—31no—
64#5529—31no—
65C3×#419—31no—
66#5228—31no—
67#5228—31no—
68#5228—31no—
69#5228—61no—
70#5225D311yescharacteristic, complemented
71C2×#835—31no—
72#5137—31no—
73#5127—31no—
74#5090—31no—
75#5082—31no—
76#5052—31no—
77#5051—31no—
78#5045—31no—
79#5043—31no—
80#5030—31no—
81#5022—31no—
82#5011—31no—
83#4996—31no—
84#4813—31no—
85#4809—31no—
86#4805—31no—
87D3×#103—31no—
88#4799—31no—
89#4797—31no—
90#4795—31no—
91#4789—31no—
92C2×C32×Q8—21no—
93C2×C32×Q8—22no—
94C2×C32×Q8—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C3×D3×Q8—22no—
102C3×D3×Q8—41no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×D3×Dic3—21no—
108#3757—21no—
109#3756—22no—
110#3756—41no—
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C3×#217—21no—
116C3×#217—21no—
117C3×#217D411yescharacteristic
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3—21no—
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C3×#208—41no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136#3724—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3719—41no—
143D3×C3⋊C8—41no—
144#3312—91noSylow
145C22×C3×Q8—21no—
146C22×C3×Q8—31no—
147C22×C3×Q8C2×D311yescharacteristic
148C22×C3×Q8C2×D311yescharacteristic
149C2×D3×Q8C2×D311yescharacteristic
150C2×C3×M16—31no—
151C3×C4⋊Q8—31no—
152C3×C4⋊Q8—61no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—61no—
156C3×C22⋊Q8—61no—
157C3×C4×Q8—31no—
158C3×C4×D4—31no—
159C3×C4×D4—61no—
160C3×#117—31no—
161#946—21no—
162#946C2×D311yescharacteristic
163Q8×Dic3C2×D311yescharacteristic
164#944—21no—
165#944C2×D311yescharacteristic
166C2×#216—31no—
167C2×#216—31no—
168C2×#216—31no—
169C2×#216—31no—
170C2×#216—31no—
171C2×#216—61no—
172C2×#216—61no—
173#935—61no—
174C4×#67—21no—
175C4×#67C2×D311yescharacteristic
176#926C2×D311yescharacteristic
177C2×C4⋊Dic3—31no—
178#924—21no—
179#924—31no—
180#924—31no—
181#924—31no—
182#924—61no—
183#924C2×D311yescharacteristic
184C2×#208C2×D311yescharacteristic
185C22×C3⋊C8—31no—
186C2×Dic12—31no—
187C2×D3×C8—31no—
188#897—31no—
189D3×C4⋊C4—31no—
190#890—31no—
191#889—61no—
192#887—31no—
193#883—61no—
194#879—61no—
195#879—61no—
196#877—61no—
197#872—61no—
198#870—31no—
199#870—61no—
200C4×Dic6—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—61no—
213#835—61no—
214#835C2×D311yescharacteristic
215#835C2×D311yescharacteristic
216#835C2×D311yescharacteristic
217#835C2×D311yescharacteristic
218#830—31no—
219#830—31no—
220#830—31no—
221#830—61no—
222(C2×D3)⋊C8—31no—
223#817—31no—
224#816—31no—
225#816—31no—
226#815—31no—
227Dic3⋊C8—31no—
228#810—31no—
229#810—31no—
230#810—31no—
231#808—31no—
232#808—31no—
233#808—31no—
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—42no—
244C32×Q8#4112yes—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—42no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254#634—21no—
255#634—21no—
256C3×#67—22no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—42no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—42no—
270D3×Dic3—42no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#552—91no—
276D4×Q8—31no—
277#491—91no—
278#485—91no—
279#483—91no—
280#479—91no—
281#470—91no—
282#467—91no—
283#462—91no—
284#451—91no—
285#451—91no—
286#441—91no—
287#435—91no—
288#419—31no—
289C2×#103—91no—
290C2×C3×Q8—21no—
291C2×C3×Q8—21no—
292C2×C3×Q8—22no—
293C2×C3×Q8—22no—
294C2×C3×Q8—21no—
295C2×C3×Q8—21no—
296C2×C3×Q8—31no—
297C2×C3×Q8—41no—
298C2×C3×Q8—42no—
299C2×C3×Q8—41no—
300C2×C3×Q8—41no—
301C2×C3×Q8—42no—
302C2×C3×Q8—61no—
303C2×C3×Q8—62no—
304C2×C3×Q8—121no—
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×D4—31no—
310C22×C3×C4—21no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—31no—
314C22×C3×C4—41no—
315C22×C3×C4—61no—
316C22×C3×C4C22×D311yescharacteristic
317C22×C3×C4C22×D311yescharacteristic
318C2×#67#6711yescharacteristic
319C22×Dic3—61no—
320D3×Q8—22no—
321D3×Q8—41no—
322C2×C4×D3—21no—
323C2×C4×D3—61no—
324C2×C4×D3C22×D311yescharacteristic
325C2×Dic6—21no—
326C2×Dic6—31no—
327C2×Dic6—31no—
328C2×Dic6—61no—
329C2×Dic6C22×D311yescharacteristic
330C3×M16—121no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C22⋊C4—31no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C42—31no—
348C3×C42—61no—
349C3×C42—61no—
350#217—21no—
351#217—21no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—121no—
356#217#6711yescharacteristic
357#216—62no—
358#216—62no—
359#216—122no—
360#216—121no—
361#216—121no—
362#216—121no—
363#216—122no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4#6711yescharacteristic
367C4⋊Dic3—21no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
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—121no—
391Dic3⋊C4#6711yescharacteristic
392C4×Dic3—21no—
393C4×Dic3—21no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3C22×D311yescharacteristic
397#208—41no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407Dic12—121no—
408D3×C8—121no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3#13712yes—
416C32×C4—22no—
417C32×C4—21no—
418C32×C4—41no—
419C32×C4C2×#4111yescharacteristic
420C32×C4H(5,𝔽2)11yescharacteristic
421C3⋊Dic3—41no—
422C3⋊Dic3—41no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C22×Q8—31no—
431C22×Q8D3211yescharacteristic
432C2×Q16—91no—
433C2×Q16—91no—
434C2×Q16—91no—
435C2×M16—31no—
436C22×C8—91no—
437C4⋊Q8—31no—
438C4⋊Q8—61no—
439#126—181no—
440#125—91no—
441#125—181no—
442#123—181no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—61no—
446C22⋊Q8—61no—
447C22⋊Q8—91no—
448C22⋊Q8—91no—
449C4×Q8—31no—
450C4×Q8—91no—
451C4×D4—31no—
452C4×D4—61no—
453#117—31no—
454#117—181no—
455C2×C4⋊C4—91no—
456#107—91no—
457#106—91no—
458#106—91no—
459C4⋊C8—91no—
460#103—31no—
461#103—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—
470C22⋊C8—91no—
471C22⋊C8—91no—
472#97—91no—
473C23×C3—21no—
474C23×C3—31no—
475C23×C3D3×D411yescharacteristic
476C23×C3C2×#6711yescharacteristic
477C22×D3C2×#6711yescharacteristic
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—22no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—22no—
486C3×Q8—41no—
487C3×Q8—41no—
488C3×Q8—42no—
489C3×Q8—42no—
490C3×Q8—44no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—122no—
494C3×Q8#23512yes—
495C3×Q8#23712yes—
496C3×D4—62no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—42no—
515C2×C3×C4—42no—
516C2×C3×C4—44no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—122no—
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4C2×#6711yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—22no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—122no—
540C2×Dic3C2×#6711yescharacteristic
541C2×Dic3C2×#6711yescharacteristic
542C2×Dic3C2×#6711yescharacteristic
543C4×D3—21no—
544C4×D3—21no—
545C4×D3—42no—
546C4×D3—122no—
547Dic6—21no—
548Dic6—21no—
549Dic6—42no—
550Dic6—61no—
551Dic6—61no—
552Dic6—61no—
553Dic6—61no—
554Dic6—121no—
555Dic6—121no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—121no—
565C3⋊C8—121no—
566C2×C32—41no—
567C2×C32#54611yescharacteristic
568C2×C32C2×#13711yescharacteristic
569C2×C32#57811yescharacteristic
570C3×D3—22no—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×Q8—31no—
574C2×Q8—41no—
575C2×Q8—61no—
576C2×Q8—62no—
577C2×Q8—91no—
578C2×Q8—121no—
579C2×Q8C2×D3211yescharacteristic
580C2×Q8C2×D3211yescharacteristic
581C2×D4—31no—
582C22×C4—21no—
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—181no—
586C22×C4C2×D3211yescharacteristic
587Q16—182no—
588Q16—361no—
589Q16—361no—
590M16—121no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—91no—
594C2×C8—91no—
595C2×C8—361no—
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C22⋊C4—31no—
613C22⋊C4—31no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C42—31no—
620C42—61no—
621C42—61no—
622C42—181no—
623C22×C3—22no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—32no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3C2×D3×D411yescharacteristic
637C22×C3C22×#6711yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3#94212yes—
641C3×C4—21no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—41no—
648C3×C4—42no—
649C3×C4—42no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—61no—
653C3×C4—61no—
654C3×C4—61no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4C2×#23511yescharacteristic
660C3×C4C2×#23711yescharacteristic
661C3×C4#100411yescharacteristic
662C3×C4#100411yescharacteristic
663Dic3—21no—
664Dic3—21no—
665Dic3—21no—
666Dic3—41no—
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—121no—
671Dic3—121no—
672Dic3—121no—
673Dic3—121no—
674Dic3—241no—
675Dic3—241no—
676C32#331211yescharacteristic, complemented, Sylow
677C23—31no—
678C23D3×#6711yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8—61no—
684Q8—61no—
685Q8—122no—
686Q8—181no—
687Q8—181no—
688Q8#380412yes—
689D4—62no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—42no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—122no—
705C2×C4—181no—
706C2×C4—181no—
707C2×C4—362no—
708C2×C4D3×#6711yescharacteristic
709C2×C4C22×D3211yescharacteristic
710C8—61no—
711C8—61no—
712C8—181no—
713C8—181no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—42no—
718C2×C3—41no—
719C2×C3—41no—
720C2×C3—62no—
721C2×C3#549011yescharacteristic
722C2×C3D3×#13711yescharacteristic
723C2×C3#577911yescharacteristic
724C2×C3#580611yescharacteristic
725C2×C3C2×#94211yescharacteristic
726C2×C3#583811yescharacteristic
727D3—22no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—32no—
732C22—61no—
733C22—61no—
734C22C2×D3×#6711yescharacteristic
735C4—21no—
736C4—22no—
737C4—41no—
738C4—61no—
739C4—61no—
740C4—61no—
741C4—121no—
742C4—121no—
743C4—121no—
744C4—121no—
745C4—361no—
746C4—361no—
747C4C2×#380411yescharacteristic
748C4#6433011yescharacteristic
749C3—21no—
750C3#7896611yescharacteristic, complemented
751C3#8355211yescharacteristic, complemented
752C2—41no—
753C2—62no—
754C2D3×#94211yescharacteristic
755C2#1059532811yescharacteristic
756C2#1059549311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC22×Q8D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. #10592927C2semidirect
4. C3×#5225C2semidirect
5. #10591613C2semidirect
6. #10591596C2semidirect
7. #10591595C2semidirect
8. #10591575C2semidirect
9. #10591549C2semidirect
10. D3×#835C2semidirect
11. #10591545C2semidirect
12. #10591541C2semidirect
14. #10591121C2semidirect
15. #10591102C2semidirect
70. #5225D3semidirect
676. C32#3312semidirect
750. C3#78966semidirect
751. C3#83552semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×#672
#105949392
#105929272
C3×#52252
#105916132
#105915962
#105915952
#105915752
#105915492
D3×#8352
#105915452
#105915412
#105911472
#105911212
#105911022
#835523
#789663