Finite Group Databasebeta

← #11909769

Subgroups — #11909769

Order 1152.

2353 conjugacy classes of subgroups.

The subgroup lattice has 777 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596288C211yesmaximal, characteristic, complemented
2C3×#5817C211yesmaximal, characteristic, complemented
3C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
4Q8×#627C211yesmaximal, characteristic, complemented
5#10595410C211yesmaximal, characteristic, complemented
6#10595395C213yesmaximal, complemented
7#10595394C211yesmaximal, characteristic, complemented
8#10595388C213yesmaximal, complemented
9#10595371C213yesmaximal, complemented
10#10595353C211yesmaximal, characteristic, complemented
11#10595346C213yesmaximal, complemented
12#10594928C213yesmaximal, complemented
13#10594910C213yesmaximal, complemented
14#10594906C213yesmaximal, complemented
15#10594839C213yesmaximal, complemented
16#86722—31nomaximal
17#85821—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C2×#3832C2211yescharacteristic
20C2×C3×#239C2211yescharacteristic
21C2×#3804C2216yes—
22#64156C2213yes—
23#64155C2213yes—
24Q8×C3⋊Dic3C2211yescharacteristic
25#64139C2213yes—
26C4×#638C2213yes—
27C3×#947C2213yes—
28C3×#946C2213yes—
29C3×Q8×Dic3C2213yes—
30C3×Q8×Dic3C2211yescharacteristic
31C3×Q8×Dic3C2211yescharacteristic
32C3×Q8×Dic3C2213yes—
33C3×Q8×Dic3C2211yescharacteristic
34C3×#930C2213yes—
35C3×C4×#67C2213yes—
36C2×C3×C4⋊Dic3C2213yes—
37C2×C3×C4×Dic3C2213yes—
38#63978C2213yes—
39#63966C2213yes—
40#63964C2211yescharacteristic
41#63961C2213yes—
42#63919C2213yes—
43#63918C2213yes—
44#63918C2213yes—
45C4×#627C2213yes—
46#63916C2213yes—
47#63911C2213yes—
48#63909C2213yes—
49C4×#626C2213yes—
50#63900C2213yes—
51#63899C2216yes—
52#63898C2213yes—
53#63895C2216yes—
54#63894C2213yes—
55#63894C2213yes—
56Dic3×D12C2213yes—
57#63890C2216yes—
58D3×C4⋊Dic3C2213yes—
59#63880C2216yes—
60#63874C2213yes—
61#63868C2213yes—
62#63867C2213yes—
63#63859C2213yes—
64#63855C2213yes—
65#63854C2216yes—
66#63852C2216yes—
67#63852C2213yes—
68C3×#548—31no—
69C2×C3×C4×Q8—31no—
70#5834—31no—
71#5827—31no—
72#5817—31no—
73#5817—31no—
74#5817—61no—
75#5817D311yescharacteristic, complemented
76C2×Q8×Dic3D311yescharacteristic, complemented
77#5682—33no—
78#5681—33no—
79#5643—33no—
80#5635—33no—
81#5611—33no—
82#5596—33no—
83#5585—33no—
84#5582—33no—
85#5582—33no—
86#5579—33no—
87#5577—31no—
88#5574—31no—
89#5574—31no—
90#5574—31no—
91Q8×Dic6—31no—
92Q8×Dic6—31no—
93#5555—33no—
94#5538—33no—
95#5507—33no—
96#5507—33no—
97#5479—33no—
98#5477—33no—
99C2×C32×Q8—24no—
100C2×C32×Q8C2313yes—
101C2×C32×Q8C2311yescharacteristic
102C22×C32×C4C2313yes—
103C2×#638C2313yes—
104#3832—24no—
105C2×C4⋊(C3⋊D3)C2313yes—
106C2×C4×C3⋊D3C2313yes—
107C2×C3×#67C2313yes—
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2313yes—
110C3×#239—24no—
111C2×C3×D12C2313yes—
112C2×C3×C4×D3C2313yes—
113C2×#627C2311yescharacteristic
114C2×#627C2316yes—
115C2×#626C2313yes—
116C2×#626C2316yes—
117C2×#624C2316yes—
118#3804—412no—
119C2×D3×Dic3C2316yes—
120#3757C2311yescharacteristic
121#3752C2313yes—
122#3752C2316yes—
123C4⋊(C3⋊Dic3)C2313yes—
124#3750C2313yes—
125C4×C3⋊Dic3C2313yes—
126C3×#217C2311yescharacteristic
127C3×(C2×D3)⋊C4C2313yes—
128C3×(C2×D3)⋊C4C2316yes—
129C3×C4⋊Dic3C2316yes—
130C3×C4⋊Dic3C2313yes—
131C3×C4⋊Dic3C2313yes—
132C3×C4⋊Dic3C2313yes—
133C3×Dic3⋊C4C2313yes—
134C3×C4×Dic3C2313yes—
135C3×C4×Dic3C2313yes—
136C3×C4×Dic3C2313yes—
137C3×C4×Dic3C2313yes—
138C3×C4×Dic3C2313yes—
139#3724C2313yes—
140#3724C2311yescharacteristic
141#3724C2313yes—
142Dic3⋊Dic3C2311yescharacteristic
143Dic3⋊Dic3C2313yes—
144Dic3⋊Dic3C2313yes—
145Dic3⋊Dic3C2311yescharacteristic
146Dic3⋊Dic3C2313yes—
147#3722C2313yes—
148#3722C2313yes—
149#3722C2313yes—
150(C2×D3)⋊Dic3C2313yes—
151(C2×D3)⋊Dic3C2313yes—
152(C2×D3)⋊Dic3C2313yes—
153#3522—91noSylow
154C2×C3×#41—31no—
155C22×C3×Q8—21no—
156C22×C3×Q8C2×D311yescharacteristic
157C22×C3×Q8C2×D311yescharacteristic
158C2×#239—31no—
159C2×#239—31no—
160C2×#239—61no—
161C2×#239C2×D311yescharacteristic
162C2×#237—36no—
163C2×#235—36no—
164C3×#124—33no—
165C3×C22⋊Q8—33no—
166C3×#121—33no—
167C3×C4×Q8—31no—
168C3×C4×Q8—31no—
169C3×C4×Q8—31no—
170C3×C4×Q8—33no—
171C3×C4×Q8—33no—
172C3×C4×D4—33no—
173C2×C3×C4⋊C4—33no—
174C2×C3×C42—33no—
175#947—33no—
176#947—33no—
177#947—63no—
178#947C2×D313yes—
179#946—33no—
180#946—33no—
181#946—63no—
182#946C2×D313yes—
183Q8×Dic3—31no—
184Q8×Dic3—31no—
185Q8×Dic3—61no—
186Q8×Dic3C2×D313yes—
187Q8×Dic3C2×D313yes—
188Q8×Dic3C2×D311yescharacteristic
189Q8×Dic3C2×D311yescharacteristic
190Q8×Dic3C2×D311yescharacteristic
191#940—33no—
192#939—33no—
193#938—33no—
194#935—33no—
195D4×Dic3—33no—
196D4×Dic3—33no—
197#930—33no—
198#930—33no—
199#930—33no—
200#930—33no—
201#930—63no—
202#930C2×D313yes—
203#929—33no—
204#929—33no—
205C4×#67—33no—
206C4×#67—33no—
207C4×#67—33no—
208C4×#67—63no—
209C4×#67C2×D313yes—
210#926—33no—
211C2×C4⋊Dic3—33no—
212C2×C4⋊Dic3C2×D313yes—
213#924—31no—
214C2×C4×Dic3C2×D313yes—
215#898—33no—
216#897—36no—
217#896—36no—
218#896—36no—
219#895—33no—
220#895—33no—
221#894—36no—
222#894—36no—
223#893—33no—
224#893—33no—
225#893—33no—
226D3×C4⋊C4—33no—
227D3×C4⋊C4—33no—
228D3×C4⋊C4—33no—
229#889—33no—
230#888—33no—
231#888—33no—
232#888—33no—
233#888—33no—
234#886—33no—
235#886—36no—
236#885—36no—
237#885—33no—
238#883—36no—
239#67⋊C4—36no—
240#879—33no—
241#878—31no—
242#878—36no—
243#876—33no—
244#876—33no—
245#875—36no—
246#875—33no—
247#874—33no—
248C4×D12—33no—
249C4×D12—33no—
250C4×D12—36no—
251C4×D12—33no—
252C4×D12—33no—
253#872—33no—
254#872—33no—
255#872—33no—
256#870—33no—
257#869—33no—
258#869—33no—
259C4×Dic6—33no—
260C4×Dic6—33no—
261C23×C32C2411yescharacteristic
262C22×C3⋊D3C2413yes—
263C22×C3×D3C2413yes—
264C32×Q8—26no—
265C32×Q8#4114yescomplemented
266C2×C32×C4—26no—
267C2×C32×C4C2413yes—
268C2×C32×C4C2413yes—
269#638—26no—
270C2×C3⋊Dic3C2411yescharacteristic
271C2×C3⋊Dic3C2411yescharacteristic
272C2×C3⋊Dic3C2413yes—
273C4⋊(C3⋊D3)—26no—
274C4×C3⋊D3—26no—
275C3×#67—26no—
276C2×C3×Dic3—26no—
277C2×C3×Dic3—22no—
278C2×C3×Dic3C2411yescharacteristic
279C2×C3×Dic3C2413yes—
280C2×C3×Dic3C2413yes—
281C2×C3×Dic3C2411yescharacteristic
282C2×C3×Dic3C2411yescharacteristic
283C2×C3×Dic3C2413yes—
284C2×C3×Dic3C2411yescharacteristic
285C3×D12—26no—
286C3×C4×D3—26no—
287#627—22no—
288#627—46no—
289#626—26no—
290#626—46no—
291#624—46no—
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—91no—
306#520—91no—
307C2×C4×Q8—31no—
308C3×#41—64no—
309C2×C3×Q8—24no—
310C2×C3×Q8—24no—
311C2×C3×Q8—21no—
312C2×C3×Q8—23no—
313C2×C3×Q8—44no—
314C2×C3×Q8C22×D313yes—
315C2×C3×Q8C22×D313yes—
316C2×C3×Q8C22×D311yescharacteristic
317C2×C3×Q8C22×D311yescharacteristic
318C2×C3×D4—33no—
319C2×C3×D4—33no—
320C22×C3×C4—23no—
321C22×C3×C4—31no—
322C22×C3×C4—33no—
323C22×C3×C4—33no—
324C22×C3×C4C22×D313yes—
325C22×C3×C4C22×D313yes—
326C2×#67—33no—
327C2×#67—33no—
328C2×#67—33no—
329C2×#67—36no—
330C2×#67—63no—
331C2×#67C22×D313yes—
332C22×Dic3—36no—
333C22×Dic3C22×D311yescharacteristic
334C22×Dic3C22×D313yes—
335#239—24no—
336#239—64no—
337#239—64no—
338#239—124no—
339#237—1212no—
340#235—1212no—
341C2×D12—33no—
342C2×D12—33no—
343C2×D12—33no—
344C2×D12—36no—
345C2×D12—63no—
346C2×D12C22×D313yes—
347C2×C4×D3—33no—
348C2×C4×D3—33no—
349C2×C4×D3—36no—
350C2×C4×D3—36no—
351C2×C4×D3—36no—
352C2×C4×D3—63no—
353C2×C4×D3C22×D313yes—
354C2×Dic6—31no—
355C2×Dic6—31no—
356C2×Dic6—36no—
357C2×Dic6—36no—
358C3×C4⋊C4—33no—
359C3×C4⋊C4—33no—
360C3×C4⋊C4—33no—
361C3×C4⋊C4—33no—
362C3×C4⋊C4—36no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—36no—
365C3×C22⋊C4—33no—
366C3×C42—33no—
367C3×C42—33no—
368C3×C42—33no—
369C3×C42—33no—
370C3×C42—33no—
371#217—31no—
372#217—31no—
373#217—33no—
374#217—33no—
375#217—33no—
376#217—61no—
377#217C22×D311yescharacteristic
378(C2×D3)⋊C4—33no—
379(C2×D3)⋊C4—33no—
380(C2×D3)⋊C4—33no—
381(C2×D3)⋊C4—36no—
382(C2×D3)⋊C4—33no—
383(C2×D3)⋊C4—36no—
384(C2×D3)⋊C4—33no—
385(C2×D3)⋊C4—33no—
386(C2×D3)⋊C4—33no—
387(C2×D3)⋊C4—33no—
388(C2×D3)⋊C4—33no—
389(C2×D3)⋊C4—33no—
390(C2×D3)⋊C4—33no—
391(C2×D3)⋊C4—63no—
392(C2×D3)⋊C4—66no—
393(C2×D3)⋊C4C22×D316yes—
394(C2×D3)⋊C4C22×D313yes—
395C4⋊Dic3—33no—
396C4⋊Dic3—33no—
397C4⋊Dic3—33no—
398C4⋊Dic3—33no—
399C4⋊Dic3—31no—
400C4⋊Dic3—31no—
401C4⋊Dic3—33no—
402C4⋊Dic3—63no—
403C4⋊Dic3C22×D313yes—
404C4⋊Dic3C22×D313yes—
405C4⋊Dic3C22×D313yes—
406C4⋊Dic3C22×D316yes—
407Dic3⋊C4—33no—
408Dic3⋊C4—33no—
409Dic3⋊C4—33no—
410Dic3⋊C4—33no—
411Dic3⋊C4—33no—
412Dic3⋊C4—33no—
413Dic3⋊C4—33no—
414Dic3⋊C4—33no—
415Dic3⋊C4—31no—
416Dic3⋊C4—31no—
417Dic3⋊C4—31no—
418Dic3⋊C4—33no—
419Dic3⋊C4—31no—
420Dic3⋊C4—63no—
421Dic3⋊C4C22×D313yes—
422C4×Dic3—33no—
423C4×Dic3—33no—
424C4×Dic3—63no—
425C4×Dic3C22×D313yes—
426C4×Dic3C22×D313yes—
427C4×Dic3C22×D313yes—
428C4×Dic3C22×D313yes—
429C4×Dic3C22×D313yes—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32H(5,𝔽2)12yes—
433C22×C32C2511yescharacteristic
434C2×C3⋊D3—23no—
435C2×C3⋊D3—23no—
436C2×C3⋊D3—23no—
437C2×C3×D3—23no—
438C2×C3×D3—23no—
439C2×C3×D3—23no—
440C32×C4—23no—
441C32×C4C2×#4116yes—
442C3⋊Dic3—21no—
443C3⋊Dic3—23no—
444C3⋊Dic3—21no—
445C3×Dic3—21no—
446C3×Dic3—23no—
447C3×Dic3—23no—
448C3×Dic3—23no—
449C3×Dic3—21no—
450C3×Dic3—21no—
451C3×Dic32−1+412yes—
452C2×#41—31no—
453C2×#41—96no—
454C2×#41—91no—
455C22×Q8D3211yescharacteristic
456C4⋊Q8—93no—
457C4⋊Q8—93no—
458C4⋊Q8—93no—
459#127—93no—
460#126—93no—
461#126—93no—
462#125—93no—
463#124—33no—
464#124—93no—
465#124—96no—
466#124—93no—
467#123—96no—
468#123—96no—
469#123—93no—
470#123—93no—
471C22⋊Q8—33no—
472C22⋊Q8—96no—
473C22⋊Q8—91no—
474C22⋊Q8—96no—
475C22⋊Q8—93no—
476#121—33no—
477#121—93no—
478#121—93no—
479#121—93no—
480#121—93no—
481C4×Q8—31no—
482C4×Q8—33no—
483C4×Q8—31no—
484C4×Q8—33no—
485C4×Q8—31no—
486C4×Q8—93no—
487C4×Q8—91no—
488C4×D4—33no—
489C4×D4—96no—
490C4×D4—93no—
491C4×D4—93no—
492C4×D4—93no—
493C4×D4—93no—
494C4×D4—93no—
495C4×D4—93no—
496#117—93no—
497#117—93no—
498C2×C4⋊C4—33no—
499C2×C4⋊C4—93no—
500C2×C4⋊C4—93no—
501C2×C42—33no—
502C23×C3—21no—
503C23×C3—33no—
504C23×C3C23×D311yescharacteristic
505C23×C3C23×D311yescharacteristic
506C22×D3—33no—
507C22×D3—33no—
508C22×D3—63no—
509C22×D3C23×D313yes—
510C3×Q8—26no—
511C3×Q8—26no—
512C3×Q8—24no—
513C3×Q8—46no—
514C3×Q8#23514yescomplemented
515C3×Q8#23714yescomplemented
516C3×D4—66no—
517C3×D4—66no—
518C2×C3×C4—26no—
519C2×C3×C4—26no—
520C2×C3×C4—23no—
521C2×C3×C4—23no—
522C2×C3×C4—31no—
523C2×C3×C4—33no—
524C2×C3×C4—31no—
525C2×C3×C4—33no—
526C2×C3×C4—33no—
527C2×C3×C4—31no—
528C2×C3×C4—31no—
529C2×C3×C4—46no—
530C2×C3×C4—62no—
531C2×C3×C4—66no—
532C2×C3×C4—66no—
533C2×C3×C4C23×D313yes—
534C2×C3×C4C23×D313yes—
535C2×C3×C4C23×D313yes—
536C2×C3×C4C23×D313yes—
537#67—26no—
538#67—66no—
539#67—66no—
540#67—66no—
541#67—126no—
542#67—126no—
543C2×Dic3—26no—
544C2×Dic3—22no—
545C2×Dic3—31no—
546C2×Dic3—31no—
547C2×Dic3—33no—
548C2×Dic3—33no—
549C2×Dic3—31no—
550C2×Dic3—31no—
551C2×Dic3—61no—
552C2×Dic3—63no—
553C2×Dic3—61no—
554C2×Dic3—126no—
555C2×Dic3C23×D311yescharacteristic
556C2×Dic3C23×D311yescharacteristic
557C2×Dic3C23×D313yes—
558C2×Dic3C23×D313yes—
559C2×Dic3C23×D313yes—
560C2×Dic3C23×D311yescharacteristic
561C2×Dic3C23×D311yescharacteristic
562D12—26no—
563D12—66no—
564D12—66no—
565D12—66no—
566D12—126no—
567D12—126no—
568C4×D3—26no—
569C4×D3—66no—
570C4×D3—66no—
571C4×D3—126no—
572C4×D3—126no—
573C4×D3—126no—
574C4×D3—126no—
575Dic6—62no—
576Dic6—62no—
577Dic6—126no—
578Dic6—126no—
579C2×C32—22no—
580C2×C32C22×#4111yescharacteristic
581C2×C32C2×H(5,𝔽2)11yescharacteristic
582C2×C32C2×2−1+411yescharacteristic
583C3⋊D3—43no—
584C3×D3—43no—
585#41—64no—
586#41—184no—
587#41—3612no—
588C2×Q8—24no—
589C2×Q8—91no—
590C2×Q8—96no—
591C2×Q8C2×D3213yes—
592C2×Q8C2×D3211yescharacteristic
593C2×D4—33no—
594C2×D4—33no—
595C2×D4—93no—
596C2×D4—96no—
597C2×D4—93no—
598C2×D4—93no—
599C22×C4—31no—
600C22×C4—33no—
601C22×C4—33no—
602C22×C4—96no—
603C22×C4—96no—
604C22×C4—93no—
605C22×C4C2×D3213yes—
606C4⋊C4—33no—
607C4⋊C4—33no—
608C4⋊C4—36no—
609C4⋊C4—33no—
610C4⋊C4—33no—
611C4⋊C4—93no—
612C4⋊C4—93no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4—91no—
616C4⋊C4—93no—
617C4⋊C4—93no—
618C4⋊C4—93no—
619C4⋊C4—93no—
620C4⋊C4—93no—
621C22⋊C4—31no—
622C22⋊C4—33no—
623C22⋊C4—36no—
624C22⋊C4—93no—
625C22⋊C4—93no—
626C22⋊C4—93no—
627C22⋊C4—93no—
628C22⋊C4—93no—
629C22⋊C4—93no—
630C22⋊C4—91no—
631C22⋊C4—96no—
632C22⋊C4—93no—
633C42—33no—
634C42—33no—
635C42—33no—
636C42—33no—
637C42—33no—
638C42—93no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—22no—
644C22×C3—21no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—63no—
648C22×C3—63no—
649C22×C3—63no—
650C22×C3#100912yes—
651C22×C3#100912yes—
652C22×C3C24×D311yescharacteristic
653C22×C3C24×D311yescharacteristic
654C2×D3—23no—
655C2×D3—23no—
656C2×D3—23no—
657C2×D3—63no—
658C2×D3—63no—
659C2×D3—63no—
660C2×D3—63no—
661C2×D3—63no—
662C2×D3—63no—
663C2×D3—123no—
664C2×D3—123no—
665C2×D3—123no—
666C3×C4—23no—
667C3×C4—23no—
668C3×C4—26no—
669C3×C4—32no—
670C3×C4—43no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—63no—
674C3×C4—63no—
675C3×C4—63no—
676C3×C4—61no—
677C3×C4C2×#23516yes—
678C3×C4C2×#23716yes—
679Dic3—21no—
680Dic3—21no—
681Dic3—23no—
682Dic3—23no—
683Dic3—23no—
684Dic3—21no—
685Dic3—61no—
686Dic3—61no—
687Dic3—61no—
688Dic3—63no—
689Dic3—63no—
690Dic3—61no—
691Dic3—121no—
692Dic3—123no—
693Dic3—121no—
694Dic3#100712yes—
695C32#352211yescharacteristic, complemented, Sylow
696C23—33no—
697C23—93no—
698C23C22×D3211yescharacteristic
699Q8—26no—
700Q8—182no—
701Q8—366no—
702Q8#380414yescomplemented
703D4—66no—
704D4—66no—
705D4—186no—
706D4—186no—
707D4—186no—
708D4—366no—
709C2×C4—26no—
710C2×C4—31no—
711C2×C4—31no—
712C2×C4—31no—
713C2×C4—33no—
714C2×C4—33no—
715C2×C4—33no—
716C2×C4—31no—
717C2×C4—62no—
718C2×C4—66no—
719C2×C4—66no—
720C2×C4—91no—
721C2×C4—93no—
722C2×C4—91no—
723C2×C4—186no—
724C2×C4—366no—
725C2×C4—366no—
726C2×C4C22×D3213yes—
727C2×C4C22×D3213yes—
728C2×C3—22no—
729C2×C3—22no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—42no—
734C2×C3—123no—
735C2×C3C22×#23511yescharacteristic
736C2×C3C22×#23711yescharacteristic
737C2×C3C2×#100711yescharacteristic
738C2×C3C2×#100911yescharacteristic
739C2×C3C2×#100911yescharacteristic
740C2×C3D3×2−1+411yescharacteristic
741D3—43no—
742D3—123no—
743D3—123no—
744D3—243no—
745C22—21no—
746C22—21no—
747C22—63no—
748C22—63no—
749C22—63no—
750C22—183no—
751C22—183no—
752C22—183no—
753C22#6432012yes—
754C22C23×D3211yescharacteristic
755C4—23no—
756C4—32no—
757C4—63no—
758C4—63no—
759C4—63no—
760C4—61no—
761C4—61no—
762C4—61no—
763C4—183no—
764C4—181no—
765C4—181no—
766C4C2×#380416yes—
767C3—21no—
768C3#8582111yescharacteristic, complemented
769C3#8672211yescharacteristic, complemented
770C2—22no—
771C2—123no—
772C2—363no—
773C2C2×#6432011yescharacteristic
774C2D3×#100711yescharacteristic
775C2C22×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. #10596288C2semidirect
2. C3×#5817C2semidirect
3. C2×C3×Q8×Dic3C2semidirect
4. Q8×#627C2semidirect
5. #10595410C2semidirect
6. #10595395C2semidirect
7. #10595394C2semidirect
8. #10595388C2semidirect
9. #10595371C2semidirect
10. #10595353C2semidirect
11. #10595346C2semidirect
12. #10594928C2semidirect
13. #10594910C2semidirect
14. #10594906C2semidirect
15. #10594839C2semidirect
75. #5817D3semidirect
76. C2×Q8×Dic3D3semidirect
265. C32×Q8#41semidirect
514. C3×Q8#235semidirect
515. C3×Q8#237semidirect
695. C32#3522semidirect
702. Q8#3804semidirect
768. C3#85821semidirect
769. C3#86722semidirect

Maximal subgroups

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

subgroupindex
#105962882
C3×#58172
C2×C3×Q8×Dic32
Q8×#6272
#105954102
#105953952
#105953942
#105953882
#105953712
#105953532
#105953462
#105949282
#105949102
#105949062
#105948392
#867223
#858213