Finite Group Databasebeta

← #11903898

Subgroups — #11903898

Order 1152.

2379 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3832C211yesmaximal, characteristic, complemented
2C3×#5576C211yesmaximal, characteristic, complemented
3C3×#5569C211yesmaximal, characteristic, complemented
4#10595410C211yesmaximal, characteristic, complemented
5Dic3×#239C211yesmaximal, characteristic, complemented
6D3×Q8×Dic3C211yesmaximal, characteristic, complemented
7#10595342C211yesmaximal, characteristic, complemented
8#10594557C213yesmaximal, complemented
9#10594453C213yesmaximal, complemented
10#10594437C213yesmaximal, complemented
11#10594369C213yesmaximal, complemented
12#10593943C213yesmaximal, complemented
13#10593939C213yesmaximal, complemented
14#10593925C213yesmaximal, complemented
15C4×#3796C213yesmaximal, complemented
16#87016—31nomaximal
17#86711—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×#3796C2213yes—
22C32×C4×Q8C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24#64102C2213yes—
25#64101C2213yes—
26C4×C4⋊(C3⋊D3)C2213yes—
27C42×C3⋊D3C2213yes—
28C3×Q8×Dic3C2211yescharacteristic
29C3×Q8×Dic3C2211yescharacteristic
30C3×#897C2213yes—
31C3×#895C2213yes—
32C3×#890C2213yes—
33C3×#888C2213yes—
34C3×#875C2213yes—
35C3×C4×D12C2213yes—
36C3×#870C2213yes—
37C3×C4×Dic6C2213yes—
38#63916C2213yes—
39#63911C2213yes—
40#63909C2213yes—
41#63909C2213yes—
42#63907C2216yes—
43C4×#626C2213yes—
44C4×#626C2213yes—
45#63898C2213yes—
46#63898C2213yes—
47Dic3×D12C2213yes—
48#63890C2216yes—
49D3×C4⋊Dic3C2213yes—
50#63886C2216yes—
51#63881C2216yes—
52#63881C2213yes—
53#63881C2213yes—
54#63878C2211yescharacteristic
55#63878C2213yes—
56C4×D3×Dic3C2213yes—
57C4×D3×Dic3C2213yes—
58#63871C2213yes—
59#63864C2213yes—
60#63862C2216yes—
61#63853C2216yes—
62#63849C2213yes—
63#63848C2216yes—
64#63843C2213yes—
65#63843C2213yes—
66Dic3×Dic6C2213yes—
67#63841C2213yes—
68C3×#557—31no—
69C3×#548—31no—
70#5834—31no—
71Dic3×#41—31no—
72#5817—31no—
73C2×Q8×Dic3—31no—
74#5732—33no—
75#5725—33no—
76#5695—33no—
77#5695—33no—
78#5691—33no—
79#5691—33no—
80#5681—33no—
81#5680—33no—
82#5641—33no—
83#5624—33no—
84#5618—33no—
85#5596—33no—
86#5585—33no—
87#5577—31no—
88#5576—31no—
89#5576D311yescharacteristic, complemented
90C4×#239—31no—
91C4×#239—31no—
92C4×#239—31no—
93C4×#239—33no—
94C4×#239—61no—
95C4×D3×Q8—31no—
96#5569D311yescharacteristic, complemented
97#5565—33no—
98C4×#237—33no—
99C2×C32×Q8C2311yescharacteristic
100#3832—24no—
101C2×C4⋊(C3⋊D3)C2313yes—
102C2×C4×C3⋊D3C2313yes—
103C2×C4×C3⋊D3C2313yes—
104C2×C4×C3⋊D3C2313yes—
105C3×#239—24no—
106C3×D3×Q8—24no—
107C2×C3×D12C2313yes—
108C2×C3×D12C2313yes—
109C2×C3×C4×D3C2313yes—
110C2×C3×C4×D3C2313yes—
111C2×C3×Dic6C2313yes—
112C2×C3×Dic6C2313yes—
113C2×#626C2313yes—
114C2×#626C2313yes—
115C2×#626C2316yes—
116C2×D3×Dic3C2313yes—
117C2×D3×Dic3C2313yes—
118C2×D3×Dic3C2313yes—
119C2×D3×Dic3C2311yescharacteristic
120#3796—212no—
121C32×C4⋊C4C2313yes—
122C32×C42C2313yes—
123#3752C2316yes—
124C4⋊(C3⋊Dic3)C2313yes—
125C4×C3⋊Dic3C2311yescharacteristic
126C4×C3⋊Dic3C2313yes—
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⋊C4C2316yes—
136C3×Dic3⋊C4C2313yes—
137C3×Dic3⋊C4C2311yescharacteristic
138C3×C4×Dic3C2313yes—
139C3×C4×Dic3C2313yes—
140Dic3⋊Dic3C2316yes—
141Dic3⋊Dic3C2311yescharacteristic
142Dic3⋊Dic3C2313yes—
143#3722C2313yes—
144#3722C2316yes—
145#3722C2313yes—
146(C2×D3)⋊Dic3C2316yes—
147(C2×D3)⋊Dic3C2313yes—
148(C2×D3)⋊Dic3C2311yescharacteristic
149Dic32C2313yes—
150Dic32C2313yes—
151Dic32C2313yes—
152Dic32C2311yescharacteristic
153#3480—91noSylow
154C2×C3×#41—31no—
155C22×C3×Q8—31no—
156C2×#239—31no—
157C2×#239—31no—
158C2×#239—33no—
159C2×#239—61no—
160C2×#239C2×D311yescharacteristic
161C2×D3×Q8C2×D311yescharacteristic
162C2×#237—33no—
163C3×C4⋊Q8—33no—
164C3×#125—33no—
165C3×#125—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#946—33no—
179Q8×Dic3—31no—
180Q8×Dic3—31no—
181Q8×Dic3—33no—
182Q8×Dic3—33no—
183Q8×Dic3—33no—
184Q8×Dic3—61no—
185Q8×Dic3C2×D311yescharacteristic
186Q8×Dic3C2×D311yescharacteristic
187#940—33no—
188#939—36no—
189#938—33no—
190D4×Dic3—33no—
191D4×Dic3—33no—
192D4×Dic3—33no—
193#930—33no—
194#930—33no—
195C4×#67—33no—
196C4×#67—33no—
197#926—33no—
198C2×C4⋊Dic3—33no—
199C2×C4×Dic3—33no—
200C2×C4×Dic3—33no—
201#898—36no—
202#898—36no—
203#898—36no—
204#897—33no—
205#897C2×D313yes—
206#895—33no—
207#895—36no—
208#895—33no—
209#895—33no—
210#895C2×D313yes—
211#894—36no—
212#894—36no—
213#893—33no—
214#893—33no—
215#893—33no—
216#893—33no—
217#893—36no—
218#893—33no—
219#893—33no—
220#893—63no—
221#892—33no—
222#892—33no—
223#892—33no—
224#892—33no—
225#892—31no—
226#892—33no—
227#892—33no—
228#892—63no—
229D3×C4⋊C4—33no—
230#890C2×D313yes—
231#888C2×D313yes—
232#887—33no—
233#887—33no—
234#886—36no—
235#885—36no—
236#883—36no—
237#67⋊C4—36no—
238#67⋊C4—33no—
239#67⋊C4—33no—
240#879—36no—
241#877—33no—
242#877—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—
253C42×D3—33no—
254C42×D3—33no—
255C42×D3—33no—
256C42×D3—33no—
257C42×D3—63no—
258#870C2×D313yes—
259C4×Dic6—33no—
260C4×Dic6C2×D313yes—
261C22×C3⋊D3C2413yes—
262C22×C3×D3C2413yes—
263C22×C3×D3C2411yescharacteristic
264C32×Q8#4114yescomplemented
265C2×C32×C4C2411yescharacteristic
266C2×C32×C4C2413yes—
267C2×C32×C4C2413yes—
268C2×C3⋊Dic3C2413yes—
269C2×C3⋊Dic3C2411yescharacteristic
270C2×C3⋊Dic3C2411yescharacteristic
271C4⋊(C3⋊D3)—26no—
272C4×C3⋊D3—26no—
273C4×C3⋊D3—26no—
274C4×C3⋊D3—43no—
275C2×C3×Dic3C2411yescharacteristic
276C2×C3×Dic3C2413yes—
277C2×C3×Dic3C2413yes—
278C2×C3×Dic3C2411yescharacteristic
279C2×C3×Dic3C2413yes—
280C2×C3×Dic3C2411yescharacteristic
281C3×D12—26no—
282C3×D12—26no—
283C3×C4×D3—26no—
284C3×C4×D3—26no—
285C3×Dic6—26no—
286C3×Dic6—26no—
287#626—26no—
288#626—26no—
289#626—46no—
290D3×Dic3—26no—
291D3×Dic3—43no—
292D3×Dic3—43no—
293D3×Dic3#4114yescomplemented
294#559—93no—
295#557—31no—
296#556—93no—
297#553—93no—
298#553—93no—
299#550—91no—
300#548—31no—
301#548—91no—
302#532—93no—
303#529—93no—
304#529—93no—
305C4×#41—93no—
306C4×#41—91no—
307C4×#41—91no—
308C2×C4×Q8—91no—
309C3×#41—64no—
310C2×C3×Q8—21no—
311C2×C3×Q8—33no—
312C2×C3×Q8—33no—
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—33no—
326C22×Dic3—33no—
327#239—24no—
328#239—612no—
329#239—68no—
330#239—64no—
331#239—64no—
332D3×Q8—24no—
333#237—612no—
334C2×D12—33no—
335C2×D12—33no—
336C2×D12—33no—
337C2×D12—33no—
338C2×D12—36no—
339C2×D12—63no—
340C2×D12C22×D313yes—
341C2×D12C22×D313yes—
342C2×C4×D3—31no—
343C2×C4×D3—33no—
344C2×C4×D3—33no—
345C2×C4×D3—33no—
346C2×C4×D3—33no—
347C2×C4×D3—33no—
348C2×C4×D3—33no—
349C2×C4×D3—33no—
350C2×C4×D3—33no—
351C2×C4×D3—33no—
352C2×C4×D3—63no—
353C2×C4×D3—63no—
354C2×C4×D3—63no—
355C2×C4×D3C22×D313yes—
356C2×C4×D3C22×D313yes—
357C2×Dic6C22×D313yes—
358C2×Dic6C22×D313yes—
359C3×C4⋊C4—23no—
360C3×C4⋊C4—33no—
361C3×C4⋊C4—33no—
362C3×C4⋊C4—31no—
363C3×C4⋊C4—33no—
364C3×C4⋊C4—33no—
365C3×C4⋊C4—33no—
366C3×C4⋊C4—36no—
367C3×C4⋊C4C22×D313yes—
368C3×C4⋊C4C22×D313yes—
369C3×C22⋊C4—31no—
370C3×C22⋊C4—33no—
371C3×C22⋊C4—36no—
372C3×C42—23no—
373C3×C42—33no—
374C3×C42—33no—
375C3×C42C22×D313yes—
376C3×C42C22×D313yes—
377#217—33no—
378#217—31no—
379#217—36no—
380(C2×D3)⋊C4—31no—
381(C2×D3)⋊C4—36no—
382(C2×D3)⋊C4—33no—
383(C2×D3)⋊C4—36no—
384(C2×D3)⋊C4—36no—
385(C2×D3)⋊C4—33no—
386(C2×D3)⋊C4—33no—
387(C2×D3)⋊C4—36no—
388(C2×D3)⋊C4—36no—
389(C2×D3)⋊C4—33no—
390(C2×D3)⋊C4—33no—
391(C2×D3)⋊C4—66no—
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—63no—
401C4⋊Dic3C22×D313yes—
402C4⋊Dic3C22×D313yes—
403C4⋊Dic3C22×D313yes—
404C4⋊Dic3C22×D313yes—
405Dic3⋊C4—36no—
406Dic3⋊C4—33no—
407Dic3⋊C4—31no—
408Dic3⋊C4C22×D311yescharacteristic
409Dic3⋊C4C22×D313yes—
410Dic3⋊C4C22×D316yes—
411C4×Dic3—31no—
412C4×Dic3—33no—
413C4×Dic3—31no—
414C4×Dic3—33no—
415C4×Dic3—33no—
416C4×Dic3—33no—
417C4×Dic3—33no—
418C4×Dic3—31no—
419C4×Dic3—33no—
420C4×Dic3—33no—
421C4×Dic3—33no—
422C4×Dic3—31no—
423C4×Dic3—33no—
424C4×Dic3—33no—
425C4×Dic3—61no—
426C4×Dic3—63no—
427C4×Dic3—63no—
428C4×Dic3C22×D313yes—
429C4×Dic3C22×D313yes—
430C22×C32C2511yescharacteristic
431C2×C3⋊D3—23no—
432C2×C3⋊D3—23no—
433C2×C3⋊D3—23no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—23no—
437C2×C3×D3—23no—
438C2×C3×D3—23no—
439C2×C3×D3C2×#4112yes—
440C32×C4—21no—
441C32×C4—23no—
442C32×C4C2×#4116yes—
443C3⋊Dic3—21no—
444C3⋊Dic3—23no—
445C3⋊Dic3C2×#4112yes—
446C3×Dic3—23no—
447C3×Dic3—23no—
448C3×Dic3—21no—
449C3×Dic3—21no—
450C3×Dic3—23no—
451C3×Dic3C2×#4112yes—
452C2×#41—31no—
453C2×#41—93no—
454C2×#41—91no—
455C22×Q8—31no—
456C4⋊Q8—33no—
457#127—93no—
458#126—96no—
459#126—96no—
460#125—33no—
461#125—33no—
462#124—33no—
463#124—93no—
464#124—96no—
465#123—96no—
466#123—96no—
467C22⋊Q8—33no—
468C22⋊Q8—93no—
469#121—33no—
470#121—93no—
471#121—93no—
472#121—93no—
473#121—96no—
474C4×Q8—31no—
475C4×Q8—31no—
476C4×Q8—33no—
477C4×Q8—93no—
478C4×Q8—93no—
479C4×Q8—93no—
480C4×Q8—91no—
481C4×Q8D3211yescharacteristic
482C4×D4—33no—
483C4×D4—93no—
484C4×D4—93no—
485C4×D4—93no—
486C4×D4—93no—
487C4×D4—93no—
488C4×D4—96no—
489C4×D4—93no—
490C4×D4—93no—
491C4×D4—93no—
492C4×D4—93no—
493#117—91no—
494#117—93no—
495#117—93no—
496#117—93no—
497#117—93no—
498C2×C4⋊C4—93no—
499C2×C42—93no—
500C2×C42—93no—
501C2×C42—93no—
502C23×C3—31no—
503C23×C3—33no—
504C22×D3—33no—
505C22×D3—33no—
506C22×D3—63no—
507C22×D3C23×D313yes—
508C22×D3C23×D311yescharacteristic
509C3×Q8—24no—
510C3×Q8—66no—
511C3×Q8—66no—
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—31no—
521C2×C3×C4—33no—
522C2×C3×C4—33no—
523C2×C3×C4—33no—
524C2×C3×C4—31no—
525C2×C3×C4—66no—
526C2×C3×C4—66no—
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D313yes—
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—34no—
539C2×Dic3—31no—
540C2×Dic3—33no—
541C2×Dic3—31no—
542C2×Dic3—33no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—63no—
546C2×Dic3—66no—
547C2×Dic3—123no—
548C2×Dic3—123no—
549C2×Dic3C23×D311yescharacteristic
550C2×Dic3C23×D313yes—
551C2×Dic3C23×D311yescharacteristic
552C2×Dic3C23×D313yes—
553C2×Dic3C23×D313yes—
554C2×Dic3C23×D311yescharacteristic
555D12—26no—
556D12—26no—
557D12—612no—
558D12—66no—
559D12—66no—
560D12—66no—
561D12—66no—
562D12—126no—
563C4×D3—26no—
564C4×D3—26no—
565C4×D3—34no—
566C4×D3—66no—
567C4×D3—66no—
568C4×D3—66no—
569C4×D3—612no—
570C4×D3—66no—
571C4×D3—66no—
572C4×D3—126no—
573C4×D3—123no—
574C4×D3—123no—
575C4×D3—123no—
576C4×D3—123no—
577C4×D3—126no—
578Dic6—26no—
579Dic6—26no—
580C2×C32C22×#4111yescharacteristic
581C2×C32C22×#4111yescharacteristic
582C2×C32#58511yescharacteristic
583C3⋊D3—43no—
584C3×D3—22no—
585C3×D3—43no—
586#41—64no—
587#41—1812no—
588#41—184no—
589C2×Q8—33no—
590C2×Q8—33no—
591C2×Q8—64no—
592C2×Q8C2×D3211yescharacteristic
593C2×D4—33no—
594C2×D4—33no—
595C2×D4—93no—
596C2×D4—93no—
597C2×D4—96no—
598C2×D4—93no—
599C22×C4—33no—
600C22×C4—33no—
601C22×C4—91no—
602C22×C4—93no—
603C22×C4—93no—
604C22×C4—93no—
605C22×C4—93no—
606C22×C4—93no—
607C22×C4—93no—
608C4⋊C4—33no—
609C4⋊C4—33no—
610C4⋊C4—31no—
611C4⋊C4—33no—
612C4⋊C4—33no—
613C4⋊C4—33no—
614C4⋊C4—36no—
615C4⋊C4—96no—
616C4⋊C4—91no—
617C4⋊C4—93no—
618C4⋊C4—93no—
619C4⋊C4C2×D3213yes—
620C22⋊C4—31no—
621C22⋊C4—33no—
622C22⋊C4—36no—
623C22⋊C4—93no—
624C22⋊C4—93no—
625C22⋊C4—96no—
626C22⋊C4—91no—
627C22⋊C4—93no—
628C22⋊C4—96no—
629C22⋊C4—96no—
630C42—33no—
631C42—33no—
632C42—91no—
633C42—93no—
634C42—93no—
635C42—93no—
636C42—91no—
637C42—93no—
638C42—93no—
639C42C2×D3213yes—
640C22×C3—21no—
641C22×C3—32no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—63no—
645C22×C3—63no—
646C22×C3—63no—
647C22×C3C24×D311yescharacteristic
648C22×C3C24×D311yescharacteristic
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—23no—
652C2×D3—23no—
653C2×D3—23no—
654C2×D3—66no—
655C2×D3—63no—
656C2×D3—63no—
657C2×D3—63no—
658C2×D3—63no—
659C2×D3—63no—
660C2×D3—63no—
661C2×D3—123no—
662C2×D3—123no—
663C2×D3D3×#4112yes—
664C3×C4—22no—
665C3×C4—23no—
666C3×C4—23no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—26no—
670C3×C4—32no—
671C3×C4—43no—
672C3×C4—61no—
673C3×C4—63no—
674C3×C4—63no—
675C3×C4—61no—
676C3×C4—63no—
677C3×C4C2×#23716yes—
678C3×C4C2×#23916yes—
679Dic3—23no—
680Dic3—21no—
681Dic3—23no—
682Dic3—21no—
683Dic3—23no—
684Dic3—32no—
685Dic3—32no—
686Dic3—62no—
687Dic3—62no—
688Dic3—61no—
689Dic3—61no—
690Dic3—63no—
691Dic3—63no—
692Dic3—123no—
693Dic3D3×#4112yes—
694C32#348011yescharacteristic, complemented, Sylow
695C23—31no—
696C23—33no—
697C23—93no—
698Q8—66no—
699Q8—66no—
700Q8#379614yescomplemented
701D4—66no—
702D4—66no—
703D4—186no—
704D4—186no—
705D4—186no—
706D4—366no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—33no—
710C2×C4—33no—
711C2×C4—31no—
712C2×C4—33no—
713C2×C4—66no—
714C2×C4—66no—
715C2×C4—94no—
716C2×C4—91no—
717C2×C4—91no—
718C2×C4—93no—
719C2×C4—186no—
720C2×C4—186no—
721C2×C4—186no—
722C2×C4—363no—
723C2×C4—363no—
724C2×C4—363no—
725C2×C4C22×D3211yescharacteristic
726C2×C4C22×D3213yes—
727C2×C4C22×D3213yes—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—62no—
732C2×C3—123no—
733C2×C3C22×#23711yescharacteristic
734C2×C3C22×#23911yescharacteristic
735C2×C3C2×D3×#4111yescharacteristic
736C2×C3C2×D3×#4111yescharacteristic
737C2×C3#596811yescharacteristic
738C2×C3#596811yescharacteristic
739D3—22no—
740D3—43no—
741D3—126no—
742D3—123no—
743D3—123no—
744C22—32no—
745C22—61no—
746C22—61no—
747C22—63no—
748C22—63no—
749C22—63no—
750C22—183no—
751C22—183no—
752C22—183no—
753C22C23×D3211yescharacteristic
754C4—21no—
755C4—23no—
756C4—32no—
757C4—61no—
758C4—63no—
759C4—61no—
760C4—63no—
761C4—63no—
762C4—92no—
763C4—181no—
764C4—183no—
765C4C2×#379616yes—
766C3—21no—
767C3#8671111yescharacteristic, complemented
768C3#8701611yescharacteristic, complemented
769C2—62no—
770C2—123no—
771C2—363no—
772C2C22×#379611yescharacteristic
773C2#1059668911yescharacteristic
774C2D32×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3480
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×#3832C2semidirect
2. C3×#5576C2semidirect
3. C3×#5569C2semidirect
4. #10595410C2semidirect
5. Dic3×#239C2semidirect
6. D3×Q8×Dic3C2semidirect
7. #10595342C2semidirect
8. #10594557C2semidirect
9. #10594453C2semidirect
10. #10594437C2semidirect
11. #10594369C2semidirect
12. #10593943C2semidirect
13. #10593939C2semidirect
14. #10593925C2semidirect
15. C4×#3796C2semidirect
89. #5576D3semidirect
96. #5569D3semidirect
264. C32×Q8#41semidirect
293. D3×Dic3#41semidirect
512. C3×Q8#237semidirect
513. C3×Q8#239semidirect
694. C32#3480semidirect
700. Q8#3796semidirect
767. C3#86711semidirect
768. C3#87016semidirect

Maximal subgroups

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

subgroupindex
C4×#38322
C3×#55762
C3×#55692
#105954102
Dic3×#2392
D3×Q8×Dic32
#105953422
#105945572
#105944532
#105944372
#105943692
#105939432
#105939392
#105939252
C4×#37962
#870163
#867113