Finite Group Databasebeta

← #11909768

Subgroups — #11909768

Order 1152.

2314 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#634C211yesmaximal, characteristic, complemented
2C3×#5576C211yesmaximal, characteristic, complemented
3C3×#5574C211yesmaximal, characteristic, complemented
4#10595412C211yesmaximal, characteristic, complemented
5#10595409C211yesmaximal, characteristic, complemented
6#10595394C211yesmaximal, characteristic, complemented
7D3×Q8×Dic3C211yesmaximal, characteristic, complemented
8#10594592C213yesmaximal, complemented
9#10594532C213yesmaximal, complemented
10#10594370C213yesmaximal, complemented
11#10594367C213yesmaximal, complemented
12#10593981C213yesmaximal, complemented
13#10593961C213yesmaximal, complemented
14#10593910C213yesmaximal, complemented
15#10593895C213yesmaximal, complemented
16#86722—31nomaximal
17#85908—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×#3795C2216yes—
22C32×C4×Q8C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24Q8×C3⋊Dic3C2211yescharacteristic
25#64097C2213yes—
26#64097C2213yes—
27#64078C2213yes—
28C4×#634C2213yes—
29C3×Q8×Dic3C2211yescharacteristic
30C3×#897C2213yes—
31C3×#895C2213yes—
32C3×#893C2213yes—
33C3×D3×C4⋊C4C2213yes—
34C3×#875C2213yes—
35C3×C4×D12C2213yes—
36C3×C4×D12C2213yes—
37C3×#872C2213yes—
38#63914C2213yes—
39#63913C2216yes—
40#63913C2213yes—
41#63908C2213yes—
42#63908C2213yes—
43#63908C2213yes—
44#63905C2216yes—
45C4×#625C2213yes—
46C4×#625C2213yes—
47#63898C2213yes—
48#63896C2216yes—
49#63896C2211yescharacteristic
50Dic3×D12C2213yes—
51#63891C2213yes—
52#63891C2216yes—
53D3×C4⋊Dic3C2213yes—
54D3×C4⋊Dic3C2213yes—
55#63885C2213yes—
56#63884C2213yes—
57#63879C2216yes—
58C4×D3×Dic3C2213yes—
59#63863C2213yes—
60#63861C2213yes—
61#63858C2213yes—
62#63857C2216yes—
63#63856C2213yes—
64#63855C2213yes—
65#63847C2213yes—
66#63843C2213yes—
67Dic3×Dic6C2213yes—
68C3×#548—31no—
69C3×#520—31no—
70#5834—31no—
71#5834—31no—
72#5831—31no—
73#5827—31no—
74#5817—31no—
75C2×Q8×Dic3—31no—
76#5682—33no—
77#5681—33no—
78#5643—33no—
79#5635—33no—
80#5611—33no—
81#5596—33no—
82#5576D311yescharacteristic, complemented
83#5574—31no—
84#5574D311yescharacteristic, complemented
85C4×D3×Q8—31no—
86Q8×Dic6—31no—
87Q8×Dic6—31no—
88Q8×Dic6—61no—
89#5561—33no—
90#5559—33no—
91#5555—33no—
92#5551—33no—
93#5548—33no—
94#5538—33no—
95#5534—33no—
96#5528—33no—
97#5511—33no—
98#5507—33no—
99C2×C32×Q8C2311yescharacteristic
100C2×#634C2311yescharacteristic
101C2×#634C2316yes—
102C3×#239—24no—
103C3×#239—24no—
104C3×D3×Q8—24no—
105C2×C3×D12C2313yes—
106C2×C3×D12C2313yes—
107C2×C3×D12C2313yes—
108C2×C3×C4×D3C2313yes—
109C2×C3×C4×D3C2313yes—
110C2×C3×C4×D3C2313yes—
111C2×C3×C4×D3C2316yes—
112C2×C3×Dic6C2313yes—
113C2×#625C2313yes—
114C2×#625C2313yes—
115C2×#625C2316yes—
116C2×D3×Dic3C2313yes—
117C2×D3×Dic3C2311yescharacteristic
118C2×D3×Dic3C2316yes—
119#3795—412no—
120C32×C4⋊C4C2313yes—
121C32×C42C2313yes—
122C4⋊(C3⋊Dic3)C2313yes—
123C4⋊(C3⋊Dic3)C2313yes—
124C4⋊(C3⋊Dic3)C2313yes—
125#3750C2313yes—
126#3750C2313yes—
127C4×C3⋊Dic3C2313yes—
128C4×C3⋊Dic3C2313yes—
129C3×(C2×D3)⋊C4C2313yes—
130C3×(C2×D3)⋊C4C2316yes—
131C3×(C2×D3)⋊C4C2313yes—
132C3×(C2×D3)⋊C4C2311yescharacteristic
133C3×(C2×D3)⋊C4C2313yes—
134C3×C4⋊Dic3C2313yes—
135C3×C4⋊Dic3C2313yes—
136C3×Dic3⋊C4C2313yes—
137C3×Dic3⋊C4C2311yescharacteristic
138C3×C4×Dic3C2313yes—
139#3724C2311yescharacteristic
140#3724C2313yes—
141Dic3⋊Dic3C2316yes—
142Dic3⋊Dic3C2313yes—
143Dic3⋊Dic3C2311yescharacteristic
144(C2×D3)⋊Dic3C2313yes—
145(C2×D3)⋊Dic3C2313yes—
146(C2×D3)⋊Dic3C2316yes—
147(C2×D3)⋊Dic3C2313yes—
148(C2×D3)⋊Dic3C2313yes—
149(C2×D3)⋊Dic3C2313yes—
150(C2×D3)⋊Dic3C2311yescharacteristic
151Dic32C2313yes—
152Dic32C2313yes—
153#3522—91noSylow
154C2×C3×#41—31no—
155C2×C3×#41—31no—
156C22×C3×Q8—31no—
157C2×#239C2×D311yescharacteristic
158C2×#239C2×D311yescharacteristic
159C2×D3×Q8C2×D311yescharacteristic
160C2×#237—36no—
161C2×#235—36no—
162C3×#124—33no—
163C3×C22⋊Q8—33no—
164C3×#121—33no—
165C3×C4×Q8—21no—
166C3×C4×Q8—31no—
167C3×C4×Q8C2×D311yescharacteristic
168C3×C4×Q8C2×D311yescharacteristic
169C3×C4×D4—33no—
170C3×C4×D4—33no—
171C3×C4×D4—33no—
172C3×#117—33no—
173C2×C3×C4⋊C4—33no—
174#947—33no—
175#946—33no—
176Q8×Dic3—31no—
177Q8×Dic3—31no—
178Q8×Dic3—31no—
179Q8×Dic3—31no—
180Q8×Dic3—33no—
181Q8×Dic3—33no—
182Q8×Dic3—61no—
183Q8×Dic3—61no—
184Q8×Dic3C2×D311yescharacteristic
185#940—33no—
186#940—33no—
187#939—33no—
188#938—33no—
189#938—33no—
190#938—33no—
191#936—33no—
192#935—33no—
193D4×Dic3—33no—
194D4×Dic3—33no—
195#930—33no—
196#930—33no—
197#930—33no—
198#929—36no—
199C4×#67—33no—
200C4×#67—33no—
201C4×#67—33no—
202C4×#67—33no—
203C4×#67—36no—
204#926—33no—
205C2×C4⋊Dic3—33no—
206C2×C4⋊Dic3—33no—
207#924—33no—
208#924—36no—
209C2×C4×Dic3—33no—
210#898—33no—
211#898—33no—
212#897—36no—
213#897C2×D313yes—
214#896—36no—
215#896—31no—
216#895C2×D313yes—
217#894—33no—
218#893—33no—
219#893C2×D313yes—
220D3×C4⋊C4—33no—
221D3×C4⋊C4—33no—
222D3×C4⋊C4C2×D313yes—
223#889—33no—
224#889—33no—
225#888—33no—
226#888—33no—
227#888—33no—
228#888—33no—
229#888—63no—
230#888—63no—
231#887—33no—
232#886—36no—
233#886—33no—
234#885—36no—
235#885—33no—
236#885—33no—
237#885—36no—
238#884—33no—
239#883—36no—
240#883—33no—
241#883—36no—
242#67⋊C4—36no—
243#879—33no—
244#879—33no—
245#878—36no—
246#878—31no—
247#875C2×D313yes—
248C4×D12—33no—
249C4×D12C2×D313yes—
250C4×D12C2×D313yes—
251#872—33no—
252#872C2×D313yes—
253C42×D3—33no—
254#869—33no—
255#869—33no—
256#869—63no—
257C4×Dic6—33no—
258C4×Dic6—33no—
259C4×Dic6—33no—
260C4×Dic6—63no—
261C22×C3×D3C2413yes—
262C22×C3×D3C2413yes—
263C22×C3×D3C2411yescharacteristic
264C32×Q8#4114yescomplemented
265C2×C32×C4C2413yes—
266C2×C32×C4C2411yescharacteristic
267C2×C32×C4C2413yes—
268C2×C3⋊Dic3C2413yes—
269C2×C3⋊Dic3C2411yescharacteristic
270C2×C3⋊Dic3C2413yes—
271C2×C3⋊Dic3C2411yescharacteristic
272#634—22no—
273#634—46no—
274C2×C3×Dic3C2411yescharacteristic
275C2×C3×Dic3C2413yes—
276C2×C3×Dic3C2413yes—
277C2×C3×Dic3C2411yescharacteristic
278C2×C3×Dic3C2411yescharacteristic
279C3×D12—26no—
280C3×D12—26no—
281C3×D12—26no—
282C3×C4×D3—26no—
283C3×C4×D3—26no—
284C3×C4×D3—26no—
285C3×C4×D3—46no—
286C3×Dic6—26no—
287#625—26no—
288#625—26no—
289#625—46no—
290D3×Dic3—26no—
291D3×Dic3—22no—
292D3×Dic3—46no—
293#559—93no—
294Q82—91no—
295#554—93no—
296#550—91no—
297#548—31no—
298#548—91no—
299#547—93no—
300#547—93no—
301#542—93no—
302#542—93no—
303#532—93no—
304#529—93no—
305#520—31no—
306#520—91no—
307C2×C4×Q8—91no—
308C3×#41—64no—
309C3×#41—64no—
310C2×C3×Q8—21no—
311C2×C3×Q8—33no—
312C2×C3×Q8—64no—
313C2×C3×Q8C22×D311yescharacteristic
314C2×C3×Q8C22×D311yescharacteristic
315C2×C3×D4—33no—
316C2×C3×D4—33no—
317C2×C3×D4—33no—
318C22×C3×C4—33no—
319C22×C3×C4—33no—
320C22×C3×C4—33no—
321C22×C3×C4—36no—
322C2×#67—33no—
323C2×#67—33no—
324C2×#67—33no—
325C2×#67—33no—
326C2×#67—36no—
327C2×#67—36no—
328C22×Dic3—31no—
329C22×Dic3—33no—
330C22×Dic3—36no—
331#239—24no—
332#239—24no—
333D3×Q8—24no—
334#237—1212no—
335#235—1212no—
336C2×D12C22×D313yes—
337C2×D12C22×D313yes—
338C2×D12C22×D313yes—
339C2×C4×D3—31no—
340C2×C4×D3—33no—
341C2×C4×D3—36no—
342C2×C4×D3C22×D313yes—
343C2×C4×D3C22×D313yes—
344C2×C4×D3C22×D313yes—
345C2×C4×D3C22×D316yes—
346C2×Dic6—31no—
347C2×Dic6—31no—
348C2×Dic6—36no—
349C2×Dic6—36no—
350C2×Dic6—61no—
351C2×Dic6—66no—
352C2×Dic6C22×D313yes—
353C3×C4⋊C4—23no—
354C3×C4⋊C4—33no—
355C3×C4⋊C4—33no—
356C3×C4⋊C4—33no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4C22×D313yes—
359C3×C4⋊C4C22×D313yes—
360C3×C22⋊C4—36no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—33no—
363C3×C22⋊C4—33no—
364C3×C22⋊C4—33no—
365C3×C42—23no—
366C3×C42—33no—
367C3×C42C22×D313yes—
368C3×C42C22×D313yes—
369#217—33no—
370#217—31no—
371#217—33no—
372#217—33no—
373#217—33no—
374#217—33no—
375#217—36no—
376(C2×D3)⋊C4—33no—
377(C2×D3)⋊C4—33no—
378(C2×D3)⋊C4—36no—
379(C2×D3)⋊C4—33no—
380(C2×D3)⋊C4—33no—
381(C2×D3)⋊C4—31no—
382(C2×D3)⋊C4—33no—
383(C2×D3)⋊C4C22×D313yes—
384(C2×D3)⋊C4C22×D313yes—
385(C2×D3)⋊C4C22×D311yescharacteristic
386(C2×D3)⋊C4C22×D313yes—
387(C2×D3)⋊C4C22×D316yes—
388C4⋊Dic3—33no—
389C4⋊Dic3—33no—
390C4⋊Dic3—33no—
391C4⋊Dic3—33no—
392C4⋊Dic3—33no—
393C4⋊Dic3—33no—
394C4⋊Dic3—36no—
395C4⋊Dic3—31no—
396C4⋊Dic3—33no—
397C4⋊Dic3—63no—
398C4⋊Dic3—63no—
399C4⋊Dic3—63no—
400C4⋊Dic3C22×D313yes—
401C4⋊Dic3C22×D313yes—
402Dic3⋊C4—33no—
403Dic3⋊C4—33no—
404Dic3⋊C4—33no—
405Dic3⋊C4—33no—
406Dic3⋊C4—36no—
407Dic3⋊C4—31no—
408Dic3⋊C4—33no—
409Dic3⋊C4—33no—
410Dic3⋊C4—31no—
411Dic3⋊C4—31no—
412Dic3⋊C4—33no—
413Dic3⋊C4—63no—
414Dic3⋊C4—63no—
415Dic3⋊C4C22×D311yescharacteristic
416Dic3⋊C4C22×D313yes—
417C4×Dic3—33no—
418C4×Dic3—33no—
419C4×Dic3—33no—
420C4×Dic3—33no—
421C4×Dic3—33no—
422C4×Dic3—33no—
423C4×Dic3—33no—
424C4×Dic3—33no—
425C4×Dic3—63no—
426C4×Dic3—63no—
427C4×Dic3C22×D313yes—
428C22×C32C2511yescharacteristic
429C2×C3×D3—21no—
430C2×C3×D3—21no—
431C2×C3×D3—23no—
432C2×C3×D3—23no—
433C2×C3×D3—23no—
434C2×C3×D3—23no—
435C2×C3×D3—23no—
436C2×C3×D3—23no—
437C2×C3×D3H(5,𝔽2)12yes—
438C32×C4—21no—
439C32×C4—23no—
440C32×C4C2×#4116yes—
441C3⋊Dic3—21no—
442C3⋊Dic3—23no—
443C3⋊Dic3—23no—
444C3⋊Dic32−1+412yes—
445C3×Dic3—23no—
446C3×Dic3—21no—
447C3×Dic3—21no—
448C3×Dic3—23no—
449C3×Dic3—21no—
450C2×#41—31no—
451C2×#41—31no—
452C2×#41—96no—
453C22×Q8—31no—
454C4⋊Q8—93no—
455C4⋊Q8—93no—
456C4⋊Q8—93no—
457#127—93no—
458#126—93no—
459#126—93no—
460#125—93no—
461#124—33no—
462#124—93no—
463#124—96no—
464#124—93no—
465#123—93no—
466#123—96no—
467#123—96no—
468#123—93no—
469C22⋊Q8—33no—
470C22⋊Q8—91no—
471C22⋊Q8—96no—
472C22⋊Q8—96no—
473C22⋊Q8—93no—
474#121—33no—
475#121—93no—
476#121—93no—
477#121—93no—
478#121—93no—
479C4×Q8—31no—
480C4×Q8—93no—
481C4×Q8—93no—
482C4×Q8—91no—
483C4×Q8—91no—
484C4×Q8—93no—
485C4×Q8D3211yescharacteristic
486C4×D4—33no—
487C4×D4—33no—
488C4×D4—33no—
489C4×D4—93no—
490C4×D4—96no—
491C4×D4—93no—
492C4×D4—93no—
493C4×D4—93no—
494#117—33no—
495#117—93no—
496C2×C4⋊C4—33no—
497C2×C4⋊C4—93no—
498C2×C4⋊C4—93no—
499C2×C42—93no—
500C23×C3—31no—
501C23×C3—33no—
502C23×C3—33no—
503C22×D3C23×D313yes—
504C22×D3C23×D313yes—
505C22×D3C23×D311yescharacteristic
506C3×Q8—24no—
507C3×Q8—66no—
508C3×Q8#23514yescomplemented
509C3×Q8#23714yescomplemented
510C3×D4—66no—
511C3×D4—66no—
512C3×D4—66no—
513C2×C3×C4—23no—
514C2×C3×C4—21no—
515C2×C3×C4—23no—
516C2×C3×C4—31no—
517C2×C3×C4—33no—
518C2×C3×C4—33no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—66no—
522C2×C3×C4—66no—
523C2×C3×C4—66no—
524C2×C3×C4—126no—
525C2×C3×C4C23×D313yes—
526C2×C3×C4C23×D313yes—
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D313yes—
530C2×C3×C4C23×D313yes—
531#67—66no—
532#67—66no—
533#67—66no—
534#67—66no—
535#67—126no—
536#67—126no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—33no—
542C2×Dic3—33no—
543C2×Dic3—33no—
544C2×Dic3—33no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—63no—
548C2×Dic3—63no—
549C2×Dic3—62no—
550C2×Dic3—66no—
551C2×Dic3—126no—
552C2×Dic3C23×D311yescharacteristic
553C2×Dic3C23×D313yes—
554C2×Dic3C23×D313yes—
555C2×Dic3C23×D311yescharacteristic
556C2×Dic3C23×D311yescharacteristic
557D12—26no—
558D12—26no—
559D12—26no—
560C4×D3—26no—
561C4×D3—26no—
562C4×D3—26no—
563C4×D3—46no—
564C4×D3—62no—
565C4×D3—66no—
566C4×D3—126no—
567Dic6—26no—
568Dic6—62no—
569Dic6—62no—
570Dic6—64no—
571Dic6—126no—
572Dic6—126no—
573Dic6—246no—
574C2×C32C22×#4111yescharacteristic
575C2×C32C2×H(5,𝔽2)11yescharacteristic
576C2×C32C2×2−1+411yescharacteristic
577C3×D3—22no—
578C3×D3—43no—
579C3×D3—43no—
580#41—64no—
581#41—64no—
582#41—3612no—
583C2×Q8—33no—
584C2×Q8—64no—
585C2×Q8—91no—
586C2×Q8—96no—
587C2×Q8C2×D3211yescharacteristic
588C2×D4—33no—
589C2×D4—33no—
590C2×D4—33no—
591C2×D4—93no—
592C2×D4—93no—
593C2×D4—96no—
594C22×C4—33no—
595C22×C4—33no—
596C22×C4—33no—
597C22×C4—36no—
598C22×C4—91no—
599C22×C4—93no—
600C22×C4—96no—
601C4⋊C4—33no—
602C4⋊C4—33no—
603C4⋊C4—31no—
604C4⋊C4—33no—
605C4⋊C4—93no—
606C4⋊C4—96no—
607C4⋊C4—91no—
608C4⋊C4—91no—
609C4⋊C4—93no—
610C4⋊C4—93no—
611C4⋊C4—93no—
612C4⋊C4—93no—
613C4⋊C4—93no—
614C4⋊C4—93no—
615C4⋊C4C2×D3213yes—
616C22⋊C4—33no—
617C22⋊C4—33no—
618C22⋊C4—31no—
619C22⋊C4—33no—
620C22⋊C4—36no—
621C22⋊C4—93no—
622C22⋊C4—93no—
623C22⋊C4—91no—
624C22⋊C4—93no—
625C22⋊C4—93no—
626C22⋊C4—96no—
627C22⋊C4—93no—
628C42—33no—
629C42—93no—
630C42—93no—
631C42—93no—
632C42—93no—
633C42C2×D3213yes—
634C22×C3—21no—
635C22×C3—32no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—63no—
639C22×C3—63no—
640C22×C3—63no—
641C22×C3—63no—
642C22×C3—63no—
643C22×C3—63no—
644C22×C3C24×D311yescharacteristic
645C22×C3C24×D311yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—23no—
649C2×D3—23no—
650C2×D3—23no—
651C2×D3—23no—
652C2×D3—23no—
653C2×D3—23no—
654C2×D3#100912yes—
655C3×C4—22no—
656C3×C4—23no—
657C3×C4—23no—
658C3×C4—21no—
659C3×C4—21no—
660C3×C4—26no—
661C3×C4—43no—
662C3×C4—61no—
663C3×C4—63no—
664C3×C4—61no—
665C3×C4—63no—
666C3×C4—61no—
667C3×C4C2×#23516yes—
668C3×C4C2×#23716yes—
669Dic3—21no—
670Dic3—23no—
671Dic3—21no—
672Dic3—23no—
673Dic3—21no—
674Dic3—32no—
675Dic3—32no—
676Dic3—62no—
677Dic3—62no—
678Dic3—63no—
679Dic3—63no—
680Dic3—63no—
681Dic3—63no—
682Dic3—61no—
683Dic3—61no—
684Dic3—123no—
685Dic3—123no—
686C32#352211yescharacteristic, complemented, Sylow
687C23—31no—
688C23—33no—
689C23—33no—
690Q8—66no—
691Q8—182no—
692Q8—366no—
693Q8#379514yescomplemented
694D4—66no—
695D4—66no—
696D4—66no—
697D4—186no—
698D4—186no—
699D4—366no—
700C2×C4—31no—
701C2×C4—33no—
702C2×C4—33no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—66no—
706C2×C4—66no—
707C2×C4—66no—
708C2×C4—91no—
709C2×C4—91no—
710C2×C4—93no—
711C2×C4—93no—
712C2×C4—126no—
713C2×C4—182no—
714C2×C4—186no—
715C2×C4—366no—
716C2×C4C22×D3211yescharacteristic
717C2×C4C22×D3213yes—
718C2×C4C22×D3213yes—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—62no—
723C2×C3—123no—
724C2×C3—123no—
725C2×C3C22×#23511yescharacteristic
726C2×C3C22×#23711yescharacteristic
727C2×C3C2×#100911yescharacteristic
728C2×C3D3×H(5,𝔽2)11yescharacteristic
729C2×C3D3×2−1+411yescharacteristic
730C2×C3D3×2−1+411yescharacteristic
731D3—22no—
732D3—43no—
733D3—43no—
734C22—32no—
735C22—61no—
736C22—61no—
737C22—63no—
738C22—63no—
739C22—63no—
740C22—63no—
741C22—63no—
742C22—63no—
743C22C23×D3211yescharacteristic
744C4—21no—
745C4—23no—
746C4—61no—
747C4—61no—
748C4—63no—
749C4—61no—
750C4—63no—
751C4—92no—
752C4—181no—
753C4—183no—
754C4—183no—
755C4C2×#379516yes—
756C3—21no—
757C3#8590811yescharacteristic, complemented
758C3#8672211yescharacteristic, complemented
759C2—62no—
760C2—123no—
761C2—123no—
762C2C22×#379511yescharacteristic
763C2#1059668711yescharacteristic
764C2D3×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. Q8×#634C2semidirect
2. C3×#5576C2semidirect
3. C3×#5574C2semidirect
4. #10595412C2semidirect
5. #10595409C2semidirect
6. #10595394C2semidirect
7. D3×Q8×Dic3C2semidirect
8. #10594592C2semidirect
9. #10594532C2semidirect
10. #10594370C2semidirect
11. #10594367C2semidirect
12. #10593981C2semidirect
13. #10593961C2semidirect
14. #10593910C2semidirect
15. #10593895C2semidirect
82. #5576D3semidirect
84. #5574D3semidirect
264. C32×Q8#41semidirect
508. C3×Q8#235semidirect
509. C3×Q8#237semidirect
686. C32#3522semidirect
693. Q8#3795semidirect
757. C3#85908semidirect
758. C3#86722semidirect

Maximal subgroups

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

subgroupindex
Q8×#6342
C3×#55762
C3×#55742
#105954122
#105954092
#105953942
D3×Q8×Dic32
#105945922
#105945322
#105943702
#105943672
#105939812
#105939612
#105939102
#105938952
#867223
#859083