Finite Group Databasebeta

← #11889392

Subgroups — #11889392

Order 1152.

797 conjugacy classes of subgroups.

The subgroup lattice has 743 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×D12C211yesmaximal, characteristic
2#10593917C211yesmaximal, characteristic
3#10592721C211yesmaximal, characteristic, complemented
4C3×#5030C211yesmaximal, characteristic, complemented
5#10591594C211yesmaximal, characteristic, complemented
6#10591594C211yesmaximal, characteristic, complemented
7#10591557C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9#10590520C211yesmaximal, characteristic, complemented
10#10590518C211yesmaximal, characteristic, complemented
11#10590447C211yesmaximal, characteristic, complemented
12#10590439C211yesmaximal, characteristic, complemented
13#10590384C211yesmaximal, characteristic, complemented
14#10590326C211yesmaximal, characteristic
15#10590289C211yesmaximal, characteristic, complemented
16#83552—31nomaximal
17#79841—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic
21#64079C2211yescharacteristic
22C2×C3×#216C2211yescharacteristic
23C3×#897—21no—
24C3×#897—21no—
25C3×#897C2211yescharacteristic
26C3×#897C2211yescharacteristic
27C3×C4×D12—21no—
28C3×C4×D12C2211yescharacteristic
29C3×#869—21no—
30C3×#869C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32D3×C4⋊Dic3C2211yescharacteristic
33#63884—21no—
34#63877—21no—
35#63859—21no—
36#63856C2211yescharacteristic
37#63856C2211yescharacteristic
38#63847—21no—
39#63841C2211yescharacteristic
40C2×#3718C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63635C2211yescharacteristic
47#63634C2211yescharacteristic
48C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#808C2211yescharacteristic
52C3×#803C2211yescharacteristic
53#63566C2211yescharacteristic
54#63566C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×D4×Q8—31no—
62#5581—31no—
63Q8×D12D311yescharacteristic
64#5541—31no—
65C3×#441—31no—
66#5228—31no—
67#5228—31no—
68#5225—31no—
69C2×#835—31no—
70#5186—31no—
71#5186—31no—
72#5090—31no—
73#5082—31no—
74#5052—31no—
75#5051—31no—
76#5045—31no—
77#5043—31no—
78#5031—31no—
79#5030D311yescharacteristic, complemented
80#5022—31no—
81#5022—31no—
82#5022—61no—
83#5011—31no—
84#4868—31no—
85#4862—31no—
86#4816—31no—
87#4813—31no—
88#4802—31no—
89D3×#103—31no—
90#4706—31no—
91#4703—31no—
92C2×C32×Q8C2311yescharacteristic
93C3×D3×Q8—22no—
94C3×D3×Q8—22no—
95C3×D3×Q8—41no—
96C3×D3×Q8—41no—
97C2×C3×D12D411yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×D3×Dic3—21no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C42—21no—
111C32×C42C2311yescharacteristic
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#216—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3D411yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140#3718—41no—
141#3718—41no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3312—91noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C2×D311yescharacteristic
148C2×D3×Q8C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C3×C4⋊Q8—31no—
151C3×C4⋊Q8—61no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—61no—
155C3×C22⋊Q8—61no—
156C3×C4×Q8—21no—
157C3×C4×Q8—31no—
158C3×C4×Q8C2×D311yescharacteristic
159C3×C4×Q8C2×D311yescharacteristic
160C3×C4×D4—31no—
161C3×C4×D4—61no—
162#946—31no—
163#946—31no—
164C2×#216—31no—
165C2×#216—31no—
166C2×#216—31no—
167C2×#216—31no—
168C2×#216C2×D311yescharacteristic
169#935—61no—
170#926—31no—
171C2×C4⋊Dic3—31no—
172#924—31no—
173#924—31no—
174C2×#208—31no—
175C22×C3⋊C8—31no—
176C2×ΓL(1,𝔽25)—31no—
177C2×D3×C8—31no—
178#897—21no—
179#897—21no—
180#897C2×D311yescharacteristic
181#897C2×D311yescharacteristic
182#894—61no—
183#892—31no—
184D3×C4⋊C4—31no—
185#889—61no—
186#889—61no—
187#879—61no—
188#877—61no—
189#876—61no—
190C4×D12—21no—
191C4×D12C2×D311yescharacteristic
192#872—61no—
193#870—31no—
194#870—31no—
195#870—61no—
196#869—21no—
197#869C2×D311yescharacteristic
198C4×Dic6C2×D311yescharacteristic
199C3×#106—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×#97—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—61no—
214#835—61no—
215#835C2×D311yescharacteristic
216#830—31no—
217#830—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#810—31no—
225#810—31no—
226#810C2×D311yescharacteristic
227#808—31no—
228#808—31no—
229#808—61no—
230#808C2×D311yescharacteristic
231#807—31no—
232#807—31no—
233#807—61no—
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—61no—
237#803C2×D311yescharacteristic
238C22×C3×D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8#4112yes—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C3×D12—22no—
256C3×C4×D3—21no—
257C3×C4×D3—21no—
258C3×C4×D3—21no—
259C3×C4×D3—21no—
260C3×C4×D3—42no—
261C3×C4×D3—42no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—42no—
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—31no—
287#435—91no—
288#419—91no—
289C2×#103—91no—
290C2×C3×Q8—21no—
291C2×C3×Q8—31no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C2×C3×Q8—61no—
296C2×C3×Q8—62no—
297C2×C3×Q8—62no—
298C2×C3×Q8—121no—
299C2×C3×Q8—121no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×Dic3—61no—
308D3×Q8—22no—
309D3×Q8—22no—
310D3×Q8—41no—
311D3×Q8—41no—
312C2×D12#6711yescharacteristic
313C2×C4×D3—21no—
314C2×C4×D3—21no—
315C2×C4×D3—61no—
316C2×C4×D3C22×D311yescharacteristic
317C2×C4×D3C22×D311yescharacteristic
318C2×Dic6—21no—
319C2×Dic6—21no—
320C2×Dic6C22×D311yescharacteristic
321C2×Dic6C22×D311yescharacteristic
322C2×Dic6C22×D311yescharacteristic
323C3×Q16—62no—
324C2×C3×C8—31no—
325C2×C3×C8—31no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—31no—
331C3×C4⋊C4—41no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4C22×D311yescharacteristic
338C3×C4⋊C4C22×D311yescharacteristic
339C3×C22⋊C4—31no—
340C3×C22⋊C4—31no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C42—21no—
344C3×C42—21no—
345C3×C42—21no—
346C3×C42—41no—
347C3×C42—61no—
348C3×C42C22×D311yescharacteristic
349C3×C42C22×D311yescharacteristic
350#217—61no—
351#217—61no—
352#217—61no—
353#216—22no—
354#216—121no—
355#216—121no—
356#216—121no—
357#216—121no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4#6711yescharacteristic
364(C2×D3)⋊C4#6711yescharacteristic
365C4⋊Dic3—21no—
366C4⋊Dic3—21no—
367C4⋊Dic3—21no—
368C4⋊Dic3—21no—
369C4⋊Dic3—31no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3#6711yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—121no—
389Dic3⋊C4—121no—
390C4×Dic3—21no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393#208—121no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—121no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403ΓL(1,𝔽25)—121no—
404D3×C8—121no—
405C22×C32C22×D411yescharacteristic
406C2×C3×D3—21no—
407C2×C3×D3—21no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3#13712yes—
412C32×C4—22no—
413C32×C4—21no—
414C32×C4—21no—
415C32×C4—41no—
416C32×C4C2×#4111yescharacteristic
417C32×C4H(5,𝔽2)11yescharacteristic
418C3⋊Dic3—41no—
419C3⋊Dic3—41no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C22×Q8—31no—
427C22×Q8—31no—
428C2×Q16—31no—
429C2×Q16—91no—
430C2×Q16—91no—
431C2×M16—91no—
432C22×C8—91no—
433C4⋊Q8—31no—
434C4⋊Q8—61no—
435#126—181no—
436#125—91no—
437#125—181no—
438#123—181no—
439C22⋊Q8—31no—
440C22⋊Q8—31no—
441C22⋊Q8—61no—
442C22⋊Q8—61no—
443C22⋊Q8—91no—
444C22⋊Q8—91no—
445C4×Q8—31no—
446C4×Q8D3211yescharacteristic
447C4×D4—31no—
448C4×D4—61no—
449#117—91no—
450#117—181no—
451C2×C4⋊C4—91no—
452#107—91no—
453#106—31no—
454#106—91no—
455C4⋊C8—91no—
456#103—31no—
457#103—31no—
458#103—91no—
459#103—91no—
460#103—91no—
461#103—91no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468#97—31no—
469C23×C3—31no—
470C23×C3—31no—
471C22×D3C2×#6711yescharacteristic
472C22×D3C2×#6711yescharacteristic
473C3×Q8—21no—
474C3×Q8—21no—
475C3×Q8—22no—
476C3×Q8—41no—
477C3×Q8—61no—
478C3×Q8—61no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8—61no—
482C3×Q8—61no—
483C3×Q8—122no—
484C3×Q8—122no—
485C3×Q8#23512yes—
486C3×Q8#23712yes—
487C3×D4—62no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—31no—
496C2×C3×C4—31no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—122no—
508C2×C3×C4—122no—
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4C2×#6711yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3—122no—
526C2×Dic3C2×#6711yescharacteristic
527C2×Dic3C2×#6711yescharacteristic
528D12—22no—
529C4×D3—21no—
530C4×D3—21no—
531C4×D3—21no—
532C4×D3—21no—
533C4×D3—42no—
534C4×D3—42no—
535C4×D3—122no—
536Dic6—21no—
537Dic6—21no—
538Dic6—21no—
539Dic6—21no—
540Dic6—21no—
541Dic6—21no—
542Dic6—42no—
543Dic6—42no—
544C3×C8—61no—
545C3×C8—61no—
546C3⋊C8—21no—
547C3⋊C8—21no—
548C3⋊C8—61no—
549C3⋊C8—61no—
550C3⋊C8—61no—
551C3⋊C8—61no—
552C3⋊C8—121no—
553C3⋊C8—121no—
554C2×C32#54611yescharacteristic
555C2×C32C2×#13711yescharacteristic
556C2×C32#57811yescharacteristic
557C3×D3—22no—
558C3×D3—41no—
559C2×Q8—31no—
560C2×Q8—31no—
561C2×Q8—31no—
562C2×Q8—61no—
563C2×Q8—61no—
564C2×Q8—62no—
565C2×Q8—62no—
566C2×Q8—121no—
567C2×Q8—121no—
568C2×Q8C2×D3211yescharacteristic
569C2×D4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—181no—
575Q16—62no—
576Q16—361no—
577Q16—361no—
578M16—361no—
579C2×C8—31no—
580C2×C8—31no—
581C2×C8—91no—
582C2×C8—91no—
583C2×C8—361no—
584C4⋊C4—21no—
585C4⋊C4—31no—
586C4⋊C4—31no—
587C4⋊C4—61no—
588C4⋊C4—61no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—91no—
593C4⋊C4—91no—
594C4⋊C4—181no—
595C4⋊C4—181no—
596C4⋊C4—181no—
597C4⋊C4—181no—
598C4⋊C4—181no—
599C4⋊C4C2×D3211yescharacteristic
600C22⋊C4—31no—
601C22⋊C4—31no—
602C22⋊C4—61no—
603C22⋊C4—61no—
604C22⋊C4—181no—
605C22⋊C4—181no—
606C22⋊C4—181no—
607C42—21no—
608C42—61no—
609C42—181no—
610C42C2×D3211yescharacteristic
611C22×C3—21no—
612C22×C3—32no—
613C22×C3—61no—
614C22×C3—61no—
615C22×C3—61no—
616C22×C3—61no—
617C22×C3—61no—
618C22×C3C2×D3×D411yescharacteristic
619C22×C3C22×#6711yescharacteristic
620C2×D3—21no—
621C2×D3—21no—
622C2×D3—21no—
623C2×D3—21no—
624C2×D3—21no—
625C2×D3#94212yes—
626C3×C4—21no—
627C3×C4—21no—
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—42no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—61no—
640C3×C4—61no—
641C3×C4—81no—
642C3×C4—121no—
643C3×C4—121no—
644C3×C4—121no—
645C3×C4—121no—
646C3×C4C2×#23511yescharacteristic
647C3×C4C2×#23711yescharacteristic
648C3×C4#100411yescharacteristic
649C3×C4#100911yescharacteristic
650Dic3—21no—
651Dic3—21no—
652Dic3—41no—
653Dic3—41no—
654Dic3—41no—
655Dic3—41no—
656Dic3—121no—
657Dic3—121no—
658Dic3—121no—
659Dic3—121no—
660Dic3—241no—
661Dic3—241no—
662C32#331211yescharacteristic, complemented, Sylow
663C23—31no—
664C23—31no—
665Q8—21no—
666Q8—61no—
667Q8—61no—
668Q8—61no—
669Q8—61no—
670Q8—61no—
671Q8—61no—
672Q8—122no—
673Q8—122no—
674Q8#379512yes—
675D4—62no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—122no—
689C2×C4—122no—
690C2×C4—181no—
691C2×C4—181no—
692C2×C4—362no—
693C2×C4D3×#6711yescharacteristic
694C2×C4D3×#6711yescharacteristic
695C2×C4C22×D3211yescharacteristic
696C8—61no—
697C8—61no—
698C8—181no—
699C8—181no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—62no—
704C2×C3—121no—
705C2×C3#555011yescharacteristic
706C2×C3D3×#13711yescharacteristic
707C2×C3#577911yescharacteristic
708C2×C3#580611yescharacteristic
709C2×C3C2×#94211yescharacteristic
710C2×C3#583811yescharacteristic
711D3—22no—
712D3—41no—
713C22—32no—
714C22—61no—
715C22—61no—
716C22—61no—
717C22—61no—
718C22—61no—
719C22C2×D3×#6711yescharacteristic
720C4—22no—
721C4—21no—
722C4—21no—
723C4—41no—
724C4—61no—
725C4—61no—
726C4—121no—
727C4—121no—
728C4—121no—
729C4—121no—
730C4—361no—
731C4—361no—
732C4C2×#379511yescharacteristic
733C4#6430711yescharacteristic
734C3—21no—
735C3#7984111yescharacteristic, complemented
736C3#8355211yescharacteristic, complemented
737C2—62no—
738C2—121no—
739C2#1059488611yescharacteristic
740C2D3×#94211yescharacteristic
741C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC4×Q8D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #10592721C2semidirect
4. C3×#5030C2semidirect
5. #10591594C2semidirect
6. #10591594C2semidirect
7. #10591557C2semidirect
8. D3×#835C2semidirect
9. #10590520C2semidirect
10. #10590518C2semidirect
11. #10590447C2semidirect
12. #10590439C2semidirect
13. #10590384C2semidirect
15. #10590289C2semidirect
79. #5030D3semidirect
662. C32#3312semidirect
735. C3#79841semidirect
736. C3#83552semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×D122
#105939172
#105927212
C3×#50302
#105915942
#105915572
D3×#8352
#105905202
#105905182
#105904472
#105904392
#105903842
#105903262
#105902892
#835523
#798413