Finite Group Databasebeta

← #11909767

Subgroups — #11909767

Order 1152.

2355 conjugacy classes of subgroups.

The subgroup lattice has 771 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596045C211yesmaximal, characteristic, complemented
2C3×#5576C211yesmaximal, characteristic, complemented
3C3×Q8×Dic6C211yesmaximal, characteristic, complemented
4#10595410C211yesmaximal, characteristic, complemented
5#10595394C211yesmaximal, characteristic, complemented
6D3×Q8×Dic3C211yesmaximal, characteristic, complemented
7#10595342C211yesmaximal, characteristic, complemented
8#10594393C213yesmaximal, complemented
9#10594373C213yesmaximal, complemented
10#10594369C213yesmaximal, complemented
11#10594343C213yesmaximal, complemented
12#10593955C213yesmaximal, complemented
13#10593939C213yesmaximal, complemented
14#10593911C213yesmaximal, complemented
15#10593896C213yesmaximal, complemented
16#87043—31nomaximal
17#86722—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×#3796C2216yes—
22C32×C4×Q8C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24#64102C2213yes—
25C4⋊C4×C3⋊D3C2213yes—
26C4×C4⋊(C3⋊D3)C2213yes—
27#64081C2213yes—
28C3×Q8×Dic3C2211yescharacteristic
29C3×Q8×Dic3C2211yescharacteristic
30C3×#897C2213yes—
31C3×#895C2213yes—
32C3×#888C2213yes—
33C3×#888C2213yes—
34C3×#875C2213yes—
35C3×C4×D12C2213yes—
36C3×#869C2213yes—
37C3×C4×Dic6C2213yes—
38#63916C2213yes—
39#63911C2213yes—
40#63909C2213yes—
41#63909C2213yes—
42#63907C2216yes—
43#63907C2213yes—
44C4×#626C2213yes—
45C4×#626C2213yes—
46#63898C2213yes—
47Dic3×D12C2213yes—
48#63890C2213yes—
49#63890C2216yes—
50D3×C4⋊Dic3C2213yes—
51D3×C4⋊Dic3C2213yes—
52#63887C2216yes—
53#63887C2211yescharacteristic
54#63886C2213yes—
55#63884C2213yes—
56#63881C2216yes—
57C4×D3×Dic3C2213yes—
58#63871C2213yes—
59#63871C2216yes—
60#63864C2213yes—
61#63858C2213yes—
62#63855C2213yes—
63#63853C2216yes—
64#63848C2213yes—
65#63846C2213yes—
66#63843C2213yes—
67Dic3×Dic6C2213yes—
68C3×Q82—31no—
69C3×#548—31no—
70#5834—31no—
71#5827—31no—
72#5817—31no—
73C2×Q8×Dic3—31no—
74#5733—33no—
75#5733—33no—
76#5730—33no—
77#5726—33no—
78#5726—33no—
79#5725—33no—
80#5682—33no—
81#5681—33no—
82#5643—33no—
83#5635—33no—
84#5611—33no—
85#5596—33no—
86#5585—33no—
87#5580—33no—
88#5577—31no—
89#5576—31no—
90#5576D311yescharacteristic, complemented
91#5574—31no—
92#5574—31no—
93#5574—31no—
94#5574—61no—
95C4×D3×Q8—31no—
96Q8×Dic6D311yescharacteristic, complemented
97#5555—33no—
98#5538—33no—
99C2×C32×Q8C2311yescharacteristic
100#3832—24no—
101C2×C4⋊(C3⋊D3)C2313yes—
102C2×C4×C3⋊D3C2313yes—
103C2×C4×C3⋊D3C2316yes—
104C3×#239—24no—
105C3×D3×Q8—24no—
106C2×C3×D12C2313yes—
107C2×C3×D12C2313yes—
108C2×C3×C4×D3C2313yes—
109C2×C3×C4×D3C2313yes—
110C2×C3×Dic6C2313yes—
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2316yes—
113C2×#626C2313yes—
114C2×#626C2313yes—
115C2×#626C2316yes—
116C2×D3×Dic3C2313yes—
117C2×D3×Dic3C2311yescharacteristic
118C2×D3×Dic3C2316yes—
119#3796—412no—
120C32×C4⋊C4C2313yes—
121C32×C42C2313yes—
122#3752C2313yes—
123#3752C2313yes—
124C4⋊(C3⋊Dic3)C2313yes—
125#3750C2311yescharacteristic
126#3750C2313yes—
127C4×C3⋊Dic3C2313yes—
128C3×(C2×D3)⋊C4C2316yes—
129C3×(C2×D3)⋊C4C2313yes—
130C3×(C2×D3)⋊C4C2311yescharacteristic
131C3×C4⋊Dic3C2313yes—
132C3×C4⋊Dic3C2313yes—
133C3×C4⋊Dic3C2313yes—
134C3×C4⋊Dic3C2313yes—
135C3×Dic3⋊C4C2313yes—
136C3×Dic3⋊C4C2313yes—
137C3×C4×Dic3C2313yes—
138C3×C4×Dic3C2313yes—
139Dic3⋊Dic3C2316yes—
140Dic3⋊Dic3C2311yescharacteristic
141Dic3⋊Dic3C2313yes—
142Dic3⋊Dic3C2313yes—
143Dic3⋊Dic3C2311yescharacteristic
144#3722C2313yes—
145#3722C2313yes—
146#3722C2316yes—
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—
155C22×C3×Q8—31no—
156C2×#239—31no—
157C2×#239—31no—
158C2×#239—36no—
159C2×#239—61no—
160C2×#239C2×D311yescharacteristic
161C2×D3×Q8C2×D311yescharacteristic
162C2×#237—36no—
163C3×C4⋊Q8—33no—
164C3×C4⋊Q8—33no—
165C3×C4⋊Q8—33no—
166C3×#124—33no—
167C3×C22⋊Q8—33no—
168C3×#121—33no—
169C3×C4×Q8—21no—
170C3×C4×Q8—31no—
171C3×C4×Q8—31no—
172C3×C4×Q8—33no—
173C3×C4×Q8C2×D311yescharacteristic
174C3×C4×Q8C2×D311yescharacteristic
175C3×C4×D4—33no—
176#947—36no—
177#947—33no—
178#947—33no—
179#946—36no—
180#946—31no—
181#946—33no—
182#946—36no—
183Q8×Dic3—31no—
184Q8×Dic3—31no—
185Q8×Dic3—33no—
186Q8×Dic3—33no—
187Q8×Dic3—61no—
188Q8×Dic3C2×D311yescharacteristic
189Q8×Dic3C2×D311yescharacteristic
190#940—33no—
191#939—33no—
192#938—33no—
193#935—33no—
194D4×Dic3—33no—
195D4×Dic3—33no—
196#930—33no—
197#930—33no—
198C4×#67—33no—
199C4×#67—33no—
200#926—33no—
201C2×C4⋊Dic3—33no—
202C2×C4⋊Dic3—33no—
203C2×C4×Dic3—33no—
204#898—33no—
205#898—33no—
206#898—33no—
207#897—36no—
208#897—33no—
209#897C2×D313yes—
210#895—33no—
211#895—33no—
212#895—33no—
213#895—33no—
214#895C2×D313yes—
215#894—33no—
216#894—33no—
217#894—36no—
218#894—36no—
219#893—33no—
220#893—33no—
221#893—33no—
222#893—36no—
223#893—63no—
224D3×C4⋊C4—33no—
225D3×C4⋊C4—33no—
226D3×C4⋊C4—33no—
227D3×C4⋊C4—33no—
228D3×C4⋊C4—63no—
229#890—33no—
230#889—33no—
231#888C2×D313yes—
232#888C2×D313yes—
233#887—33no—
234#886—36no—
235#886—33no—
236#885—36no—
237#885—33no—
238#883—36no—
239#67⋊C4—36no—
240#879—33no—
241#878—36no—
242#878—31no—
243#875—33no—
244#875C2×D313yes—
245#874—33no—
246C4×D12—33no—
247C4×D12—33no—
248C4×D12—33no—
249C4×D12—33no—
250C4×D12—33no—
251C4×D12—63no—
252C4×D12C2×D313yes—
253#872—33no—
254#872—33no—
255#872—33no—
256#872—63no—
257C42×D3—33no—
258#869C2×D313yes—
259C4×Dic6—33no—
260C4×Dic6C2×D313yes—
261C22×C3⋊D3C2413yes—
262C22×C3×D3C2413yes—
263C22×C3×D3C2411yescharacteristic
264C32×Q8#4114yescomplemented
265C2×C32×C4C2413yes—
266C2×C32×C4C2411yescharacteristic
267C2×C32×C4C2413yes—
268C2×C3⋊Dic3C2411yescharacteristic
269C2×C3⋊Dic3C2413yes—
270C2×C3⋊Dic3C2411yescharacteristic
271C4⋊(C3⋊D3)—26no—
272C4×C3⋊D3—26no—
273C4×C3⋊D3—46no—
274C2×C3×Dic3C2413yes—
275C2×C3×Dic3C2413yes—
276C2×C3×Dic3C2411yescharacteristic
277C2×C3×Dic3C2413yes—
278C2×C3×Dic3C2411yescharacteristic
279C2×C3×Dic3C2411yescharacteristic
280C3×D12—26no—
281C3×D12—26no—
282C3×C4×D3—26no—
283C3×C4×D3—26no—
284C3×Dic6—26no—
285C3×Dic6—22no—
286C3×Dic6—46no—
287#626—26no—
288#626—26no—
289#626—46no—
290D3×Dic3—26no—
291D3×Dic3—22no—
292D3×Dic3—46no—
293#559—93no—
294Q82—31no—
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—91no—
308C3×#41—64no—
309C2×C3×Q8—21no—
310C2×C3×Q8—33no—
311C2×C3×Q8—31no—
312C2×C3×Q8—36no—
313C2×C3×Q8—64no—
314C2×C3×Q8C22×D311yescharacteristic
315C2×C3×Q8C22×D311yescharacteristic
316C2×C3×D4—33no—
317C2×C3×D4—33no—
318C22×C3×C4—33no—
319C22×C3×C4—33no—
320C2×#67—33no—
321C2×#67—33no—
322C2×#67—36no—
323C22×Dic3—31no—
324C22×Dic3—33no—
325C22×Dic3—36no—
326#239—24no—
327#239—68no—
328#239—64no—
329#239—64no—
330#239—1212no—
331D3×Q8—24no—
332#237—1212no—
333C2×D12—33no—
334C2×D12—33no—
335C2×D12—33no—
336C2×D12—33no—
337C2×D12—36no—
338C2×D12—63no—
339C2×D12C22×D313yes—
340C2×D12C22×D313yes—
341C2×C4×D3—31no—
342C2×C4×D3—33no—
343C2×C4×D3—33no—
344C2×C4×D3—33no—
345C2×C4×D3—36no—
346C2×C4×D3—36no—
347C2×C4×D3—36no—
348C2×C4×D3—63no—
349C2×C4×D3—66no—
350C2×C4×D3C22×D313yes—
351C2×C4×D3C22×D313yes—
352C2×Dic6C22×D313yes—
353C2×Dic6C22×D311yescharacteristic
354C2×Dic6C22×D316yes—
355C3×C4⋊C4—23no—
356C3×C4⋊C4—33no—
357C3×C4⋊C4—33no—
358C3×C4⋊C4—33no—
359C3×C4⋊C4—33no—
360C3×C4⋊C4—33no—
361C3×C4⋊C4—33no—
362C3×C4⋊C4C22×D313yes—
363C3×C4⋊C4C22×D313yes—
364C3×C22⋊C4—36no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—33no—
367C3×C42—23no—
368C3×C42—33no—
369C3×C42—33no—
370C3×C42C22×D313yes—
371C3×C42C22×D313yes—
372#217—33no—
373#217—31no—
374#217—33no—
375#217—33no—
376(C2×D3)⋊C4—33no—
377(C2×D3)⋊C4—33no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—33no—
380(C2×D3)⋊C4—33no—
381(C2×D3)⋊C4—33no—
382(C2×D3)⋊C4—33no—
383(C2×D3)⋊C4—33no—
384(C2×D3)⋊C4—33no—
385(C2×D3)⋊C4—33no—
386(C2×D3)⋊C4—36no—
387(C2×D3)⋊C4—36no—
388(C2×D3)⋊C4—33no—
389(C2×D3)⋊C4—33no—
390(C2×D3)⋊C4—63no—
391(C2×D3)⋊C4—63no—
392(C2×D3)⋊C4C22×D311yescharacteristic
393(C2×D3)⋊C4C22×D313yes—
394(C2×D3)⋊C4C22×D316yes—
395C4⋊Dic3—33no—
396C4⋊Dic3—33no—
397C4⋊Dic3—31no—
398C4⋊Dic3—33no—
399C4⋊Dic3—36no—
400C4⋊Dic3—31no—
401C4⋊Dic3—33no—
402C4⋊Dic3—63no—
403C4⋊Dic3C22×D313yes—
404C4⋊Dic3C22×D313yes—
405C4⋊Dic3C22×D313yes—
406C4⋊Dic3C22×D313yes—
407Dic3⋊C4—31no—
408Dic3⋊C4—31no—
409Dic3⋊C4—33no—
410Dic3⋊C4—33no—
411Dic3⋊C4—36no—
412Dic3⋊C4—31no—
413Dic3⋊C4—33no—
414Dic3⋊C4—33no—
415Dic3⋊C4—31no—
416Dic3⋊C4—61no—
417Dic3⋊C4—63no—
418Dic3⋊C4C22×D313yes—
419Dic3⋊C4C22×D313yes—
420C4×Dic3—33no—
421C4×Dic3—33no—
422C4×Dic3—33no—
423C4×Dic3—33no—
424C4×Dic3—33no—
425C4×Dic3—33no—
426C4×Dic3—63no—
427C4×Dic3C22×D313yes—
428C4×Dic3C22×D313yes—
429C22×C32C2511yescharacteristic
430C2×C3⋊D3—23no—
431C2×C3⋊D3—23no—
432C2×C3⋊D3—23no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—23no—
436C2×C3×D3—23no—
437C2×C3×D3—23no—
438C2×C3×D3H(5,𝔽2)12yes—
439C32×C4—23no—
440C32×C4—21no—
441C32×C4C2×#4116yes—
442C3⋊Dic3—21no—
443C3⋊Dic3—23no—
444C3⋊Dic3—21no—
445C3×Dic3—23no—
446C3×Dic3—21no—
447C3×Dic3—23no—
448C3×Dic3—23no—
449C3×Dic3—21no—
450C3×Dic32−1+412yes—
451C2×#41—31no—
452C2×#41—96no—
453C2×#41—91no—
454C22×Q8—31no—
455C4⋊Q8—33no—
456C4⋊Q8—33no—
457C4⋊Q8—33no—
458#127—93no—
459#126—93no—
460#126—93no—
461#125—93no—
462#124—33no—
463#124—93no—
464#124—93no—
465#124—96no—
466#123—93no—
467#123—96no—
468#123—96no—
469#123—93no—
470C22⋊Q8—33no—
471C22⋊Q8—91no—
472C22⋊Q8—96no—
473C22⋊Q8—96no—
474C22⋊Q8—93no—
475#121—33no—
476#121—93no—
477#121—93no—
478#121—93no—
479#121—93no—
480C4×Q8—31no—
481C4×Q8—31no—
482C4×Q8—33no—
483C4×Q8—93no—
484C4×Q8—93no—
485C4×Q8—91no—
486C4×Q8D3211yescharacteristic
487C4×D4—33no—
488C4×D4—93no—
489C4×D4—93no—
490C4×D4—93no—
491C4×D4—96no—
492C4×D4—93no—
493C4×D4—93no—
494C4×D4—93no—
495#117—93no—
496#117—93no—
497C2×C4⋊C4—93no—
498C2×C4⋊C4—93no—
499C2×C4⋊C4—93no—
500C2×C42—93no—
501C23×C3—31no—
502C23×C3—33no—
503C22×D3—33no—
504C22×D3—33no—
505C22×D3—63no—
506C22×D3C23×D313yes—
507C22×D3C23×D311yescharacteristic
508C3×Q8—24no—
509C3×Q8—62no—
510C3×Q8—66no—
511C3×Q8—126no—
512C3×Q8#23714yescomplemented
513C3×Q8#23914yescomplemented
514C3×D4—66no—
515C3×D4—66no—
516C2×C3×C4—23no—
517C2×C3×C4—21no—
518C2×C3×C4—23no—
519C2×C3×C4—31no—
520C2×C3×C4—33no—
521C2×C3×C4—33no—
522C2×C3×C4—31no—
523C2×C3×C4—33no—
524C2×C3×C4—31no—
525C2×C3×C4—66no—
526C2×C3×C4—66no—
527C2×C3×C4C23×D313yes—
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D313yes—
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D313yes—
532C2×C3×C4C23×D313yes—
533#67—66no—
534#67—66no—
535#67—126no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—33no—
539C2×Dic3—33no—
540C2×Dic3—31no—
541C2×Dic3—31no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—63no—
545C2×Dic3—66no—
546C2×Dic3—62no—
547C2×Dic3—126no—
548C2×Dic3C23×D313yes—
549C2×Dic3C23×D313yes—
550C2×Dic3C23×D311yescharacteristic
551C2×Dic3C23×D313yes—
552C2×Dic3C23×D311yescharacteristic
553C2×Dic3C23×D311yescharacteristic
554D12—26no—
555D12—26no—
556D12—612no—
557D12—66no—
558D12—66no—
559D12—66no—
560D12—66no—
561D12—126no—
562C4×D3—26no—
563C4×D3—26no—
564C4×D3—612no—
565C4×D3—62no—
566C4×D3—66no—
567C4×D3—66no—
568C4×D3—66no—
569C4×D3—126no—
570C4×D3—126no—
571C4×D3—126no—
572C4×D3—246no—
573Dic6—26no—
574Dic6—22no—
575Dic6—46no—
576C2×C32C22×#4111yescharacteristic
577C2×C32C2×H(5,𝔽2)11yescharacteristic
578C2×C32C2×2−1+411yescharacteristic
579C3⋊D3—43no—
580C3×D3—22no—
581C3×D3—43no—
582#41—64no—
583#41—184no—
584#41—3612no—
585C2×Q8—31no—
586C2×Q8—33no—
587C2×Q8—36no—
588C2×Q8—64no—
589C2×Q8C2×D3211yescharacteristic
590C2×D4—33no—
591C2×D4—33no—
592C2×D4—93no—
593C2×D4—93no—
594C2×D4—96no—
595C2×D4—93no—
596C22×C4—33no—
597C22×C4—33no—
598C22×C4—91no—
599C22×C4—93no—
600C22×C4—96no—
601C22×C4—93no—
602C22×C4—96no—
603C4⋊C4—33no—
604C4⋊C4—33no—
605C4⋊C4—33no—
606C4⋊C4—33no—
607C4⋊C4—33no—
608C4⋊C4—33no—
609C4⋊C4—93no—
610C4⋊C4—96no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—93no—
614C4⋊C4—93no—
615C4⋊C4—93no—
616C4⋊C4—91no—
617C4⋊C4C2×D3213yes—
618C22⋊C4—31no—
619C22⋊C4—33no—
620C22⋊C4—36no—
621C22⋊C4—93no—
622C22⋊C4—96no—
623C22⋊C4—93no—
624C22⋊C4—93no—
625C22⋊C4—93no—
626C22⋊C4—91no—
627C22⋊C4—93no—
628C22⋊C4—93no—
629C22⋊C4—93no—
630C42—33no—
631C42—33no—
632C42—93no—
633C42—93no—
634C42—93no—
635C42C2×D3213yes—
636C22×C3—21no—
637C22×C3—32no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—63no—
641C22×C3—63no—
642C22×C3—63no—
643C22×C3C24×D311yescharacteristic
644C22×C3C24×D311yescharacteristic
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—23no—
648C2×D3—23no—
649C2×D3—23no—
650C2×D3—66no—
651C2×D3—63no—
652C2×D3—63no—
653C2×D3—63no—
654C2×D3—63no—
655C2×D3—63no—
656C2×D3—63no—
657C2×D3—123no—
658C2×D3—123no—
659C2×D3#100912yes—
660C3×C4—21no—
661C3×C4—23no—
662C3×C4—23no—
663C3×C4—21no—
664C3×C4—26no—
665C3×C4—32no—
666C3×C4—43no—
667C3×C4—41no—
668C3×C4—61no—
669C3×C4—63no—
670C3×C4—63no—
671C3×C4—63no—
672C3×C4—61no—
673C3×C4C2×#23716yes—
674C3×C4C2×#23916yes—
675Dic3—23no—
676Dic3—21no—
677Dic3—21no—
678Dic3—23no—
679Dic3—23no—
680Dic3—62no—
681Dic3—61no—
682Dic3—61no—
683Dic3—61no—
684Dic3—63no—
685Dic3—63no—
686Dic3—61no—
687Dic3—123no—
688Dic3—121no—
689Dic3#100712yes—
690C32#352211yescharacteristic, complemented, Sylow
691C23—31no—
692C23—33no—
693C23—93no—
694Q8—62no—
695Q8—66no—
696Q8—126no—
697Q8#379614yescomplemented
698D4—66no—
699D4—66no—
700D4—186no—
701D4—186no—
702D4—186no—
703D4—366no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—33no—
707C2×C4—33no—
708C2×C4—33no—
709C2×C4—31no—
710C2×C4—66no—
711C2×C4—66no—
712C2×C4—91no—
713C2×C4—93no—
714C2×C4—91no—
715C2×C4—182no—
716C2×C4—186no—
717C2×C4—186no—
718C2×C4—366no—
719C2×C4—366no—
720C2×C4C22×D3211yescharacteristic
721C2×C4C22×D3213yes—
722C2×C4C22×D3213yes—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—62no—
727C2×C3—123no—
728C2×C3C22×#23711yescharacteristic
729C2×C3C22×#23911yescharacteristic
730C2×C3C2×#100711yescharacteristic
731C2×C3C2×#100911yescharacteristic
732C2×C3D3×H(5,𝔽2)11yescharacteristic
733C2×C3D3×2−1+411yescharacteristic
734D3—22no—
735D3—43no—
736D3—126no—
737D3—123no—
738D3—123no—
739C22—32no—
740C22—61no—
741C22—61no—
742C22—63no—
743C22—63no—
744C22—63no—
745C22—183no—
746C22—183no—
747C22—183no—
748C22C23×D3211yescharacteristic
749C4—21no—
750C4—23no—
751C4—32no—
752C4—61no—
753C4—63no—
754C4—61no—
755C4—63no—
756C4—63no—
757C4—181no—
758C4—181no—
759C4—183no—
760C4C2×#379616yes—
761C3—21no—
762C3#8672211yescharacteristic, complemented
763C3#8704311yescharacteristic, complemented
764C2—62no—
765C2—123no—
766C2—363no—
767C2C22×#379611yescharacteristic
768C2D3×#100711yescharacteristic
769C2D3×#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. #10596045C2semidirect
2. C3×#5576C2semidirect
3. C3×Q8×Dic6C2semidirect
4. #10595410C2semidirect
5. #10595394C2semidirect
6. D3×Q8×Dic3C2semidirect
7. #10595342C2semidirect
8. #10594393C2semidirect
9. #10594373C2semidirect
10. #10594369C2semidirect
11. #10594343C2semidirect
12. #10593955C2semidirect
13. #10593939C2semidirect
14. #10593911C2semidirect
15. #10593896C2semidirect
90. #5576D3semidirect
96. Q8×Dic6D3semidirect
264. C32×Q8#41semidirect
512. C3×Q8#237semidirect
513. C3×Q8#239semidirect
690. C32#3522semidirect
697. Q8#3796semidirect
762. C3#86722semidirect
763. C3#87043semidirect

Maximal subgroups

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

subgroupindex
#105960452
C3×#55762
C3×Q8×Dic62
#105954102
#105953942
D3×Q8×Dic32
#105953422
#105943932
#105943732
#105943692
#105943432
#105939552
#105939392
#105939112
#105938962
#870433
#867223