Finite Group Databasebeta

← #11904217

Subgroups — #11904217

Order 1152.

2337 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C3×#5576C211yesmaximal, characteristic, complemented
3C3×#5569C211yesmaximal, characteristic, complemented
4#10595414C211yesmaximal, characteristic, complemented
5Q8×#626C211yesmaximal, characteristic, complemented
6Dic3×#239C211yesmaximal, characteristic, complemented
7D3×Q8×Dic3C211yesmaximal, characteristic, complemented
8#10594579C213yesmaximal, complemented
9#10594427C213yesmaximal, complemented
10#10594387C213yesmaximal, complemented
11#10594373C213yesmaximal, complemented
12#10593943C213yesmaximal, complemented
13#10593932C213yesmaximal, complemented
14#10593920C213yesmaximal, complemented
15C4×#3796C213yesmaximal, complemented
16#87017—31nomaximal
17#86712—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×#3796C2213yes—
22C32×C4×Q8C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24C4⋊C4×C3⋊D3C2213yes—
25#64096C2213yes—
26C42×C3⋊D3C2213yes—
27C4×#634C2213yes—
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—
39C4×#626C2213yes—
40C4×#626C2213yes—
41#63898C2213yes—
42#63898C2213yes—
43Dic3×D12C2213yes—
44D3×C4⋊Dic3C2213yes—
45#63887C2216yes—
46#63884C2216yes—
47#63881C2211yescharacteristic
48#63881C2213yes—
49#63878C2216yes—
50#63878C2213yes—
51#63878C2213yes—
52C4×D3×Dic3C2213yes—
53C4×D3×Dic3C2213yes—
54#63871C2213yes—
55#63866C2213yes—
56#63862C2216yes—
57#63860C2213yes—
58#63858C2216yes—
59#63857C2213yes—
60#63857C2213yes—
61#63853C2216yes—
62#63849C2213yes—
63#63846C2216yes—
64#63843C2213yes—
65#63843C2213yes—
66Dic3×Dic6C2213yes—
67#63841C2213yes—
68C3×#557—31no—
69C3×#548—31no—
70#5831—31no—
71Dic3×#41—31no—
72Q8×#67—31no—
73C2×Q8×Dic3—31no—
74#5728—33no—
75#5726—33no—
76#5694—33no—
77#5694—33no—
78#5691—33no—
79#5691—33no—
80#5680—33no—
81#5671—33no—
82#5639—33no—
83#5622—33no—
84#5611—33no—
85#5600—33no—
86#5584—33no—
87#5576—31no—
88#5576D311yescharacteristic, complemented
89Q8×D12—31no—
90C4×#239—31no—
91C4×#239—33no—
92C4×D3×Q8—31no—
93C4×D3×Q8—31no—
94C4×D3×Q8—31no—
95C4×D3×Q8—61no—
96#5569D311yescharacteristic, complemented
97#5541—33no—
98C4×#237—33no—
99C2×C32×Q8C2311yescharacteristic
100Q8×C3⋊D3—24no—
101C2×C4×C3⋊D3C2313yes—
102C2×C4×C3⋊D3C2311yescharacteristic
103C2×C4×C3⋊D3C2313yes—
104C2×#634C2313yes—
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×#626C2311yescharacteristic
115C2×D3×Dic3C2313yes—
116C2×D3×Dic3C2313yes—
117C2×D3×Dic3C2311yescharacteristic
118C2×D3×Dic3C2313yes—
119#3796—212no—
120C32×C4⋊C4C2313yes—
121C32×C42C2313yes—
122C4⋊(C3⋊Dic3)C2313yes—
123#3750C2316yes—
124C4×C3⋊Dic3C2313yes—
125C4×C3⋊Dic3C2313yes—
126C4×C3⋊Dic3C2313yes—
127C3×(C2×D3)⋊C4C2316yes—
128C3×(C2×D3)⋊C4C2313yes—
129C3×(C2×D3)⋊C4C2311yescharacteristic
130C3×C4⋊Dic3C2313yes—
131C3×C4⋊Dic3C2313yes—
132C3×C4⋊Dic3C2313yes—
133C3×C4⋊Dic3C2313yes—
134C3×Dic3⋊C4C2316yes—
135C3×Dic3⋊C4C2313yes—
136C3×Dic3⋊C4C2311yescharacteristic
137C3×C4×Dic3C2313yes—
138C3×C4×Dic3C2313yes—
139Dic3⋊Dic3C2316yes—
140Dic3⋊Dic3C2313yes—
141Dic3⋊Dic3C2313yes—
142Dic3⋊Dic3C2316yes—
143#3722C2311yescharacteristic
144#3722C2313yes—
145(C2×D3)⋊Dic3C2316yes—
146(C2×D3)⋊Dic3C2313yes—
147(C2×D3)⋊Dic3C2316yes—
148(C2×D3)⋊Dic3C2313yes—
149Dic32C2313yes—
150Dic32C2313yes—
151Dic32C2311yescharacteristic
152Dic32C2313yes—
153#3482—91noSylow
154C2×C3×#41—31no—
155C22×C3×Q8—31no—
156C2×#239—33no—
157C2×#239C2×D311yescharacteristic
158C2×D3×Q8—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—61no—
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#946—36no—
177#946—33no—
178Q8×Dic3—31no—
179Q8×Dic3—31no—
180Q8×Dic3—33no—
181Q8×Dic3—33no—
182Q8×Dic3—33no—
183Q8×Dic3—61no—
184Q8×Dic3C2×D311yescharacteristic
185Q8×Dic3C2×D311yescharacteristic
186#944—33no—
187#938—33no—
188#936—33no—
189#935—36no—
190D4×Dic3—33no—
191D4×Dic3—33no—
192D4×Dic3—33no—
193C4×#67—33no—
194C4×#67—33no—
195#926—33no—
196C2×C4⋊Dic3—33no—
197#924—33no—
198#924—33no—
199C2×C4×Dic3—33no—
200C2×C4×Dic3—33no—
201#898—36no—
202#898—36no—
203#897—33no—
204#897—33no—
205#897—33no—
206#897C2×D313yes—
207#895—33no—
208#895C2×D313yes—
209#894—36no—
210#894—36no—
211#893—33no—
212#893—33no—
213#893—33no—
214#893—31no—
215#892—33no—
216#892—36no—
217#892—33no—
218#892—33no—
219#892—33no—
220#892—33no—
221D3×C4⋊C4—33no—
222D3×C4⋊C4—33no—
223D3×C4⋊C4—33no—
224D3×C4⋊C4—63no—
225#890—36no—
226#890C2×D313yes—
227#889—36no—
228#888C2×D313yes—
229#887—33no—
230#887—33no—
231#887—33no—
232#887—33no—
233#887—63no—
234#883—36no—
235#67⋊C4—33no—
236#67⋊C4—31no—
237#879—36no—
238#879—36no—
239#878—36no—
240#877—33no—
241#877—36no—
242#877—33no—
243#875—33no—
244#875C2×D313yes—
245C4×D12—33no—
246C4×D12—33no—
247C4×D12—33no—
248C4×D12C2×D313yes—
249C42×D3—33no—
250C42×D3—33no—
251C42×D3—33no—
252C42×D3—33no—
253C42×D3—63no—
254#870C2×D313yes—
255#869—33no—
256C4×Dic6—33no—
257C4×Dic6—33no—
258C4×Dic6—33no—
259C4×Dic6—63no—
260C4×Dic6C2×D313yes—
261C22×C3⋊D3C2411yescharacteristic
262C22×C3×D3C2413yes—
263C22×C3×D3C2411yescharacteristic
264C32×Q8#4114yescomplemented
265C2×C32×C4C2411yescharacteristic
266C2×C32×C4C2413yes—
267C2×C32×C4C2413yes—
268C2×C3⋊Dic3C2413yes—
269C2×C3⋊Dic3C2413yes—
270C2×C3⋊Dic3C2411yescharacteristic
271C4×C3⋊D3—26no—
272C4×C3⋊D3—22no—
273C4×C3⋊D3—26no—
274#634—26no—
275C2×C3×Dic3C2411yescharacteristic
276C2×C3×Dic3C2411yescharacteristic
277C2×C3×Dic3C2413yes—
278C2×C3×Dic3C2413yes—
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#4114yescomplemented
289D3×Dic3—26no—
290D3×Dic3—22no—
291D3×Dic3—26no—
292D3×Dic3—26no—
293#557—31no—
294#556—93no—
295#552—93no—
296#552—93no—
297D4×Q8—91no—
298#548—31no—
299#548—91no—
300#547—93no—
301#533—93no—
302#529—93no—
303#529—93no—
304C4×#41—93no—
305C4×#41—91no—
306C2×C4×Q8—91no—
307C2×C4×Q8—91no—
308C3×#41—64no—
309C2×C3×Q8—21no—
310C2×C3×Q8—33no—
311C2×C3×Q8—33no—
312C2×C3×Q8—64no—
313C2×C3×Q8C22×D311yescharacteristic
314C2×C3×Q8C22×D311yescharacteristic
315C2×C3×D4—33no—
316C2×C3×D4—33no—
317C22×C3×C4—33no—
318C22×C3×C4—33no—
319C2×#67—31no—
320C2×#67—33no—
321C22×Dic3—33no—
322C22×Dic3—33no—
323C22×Dic3—33no—
324C22×Dic3—31no—
325#239—24no—
326#239—612no—
327D3×Q8—24no—
328D3×Q8—68no—
329D3×Q8—64no—
330D3×Q8—64no—
331#237—612no—
332C2×D12—31no—
333C2×D12—33no—
334C2×D12C22×D313yes—
335C2×D12C22×D313yes—
336C2×C4×D3—31no—
337C2×C4×D3—33no—
338C2×C4×D3—33no—
339C2×C4×D3—33no—
340C2×C4×D3—31no—
341C2×C4×D3—31no—
342C2×C4×D3—33no—
343C2×C4×D3—33no—
344C2×C4×D3—33no—
345C2×C4×D3—33no—
346C2×C4×D3—61no—
347C2×C4×D3—63no—
348C2×C4×D3—63no—
349C2×C4×D3C22×D313yes—
350C2×C4×D3C22×D313yes—
351C2×Dic6—33no—
352C2×Dic6—33no—
353C2×Dic6—63no—
354C2×Dic6C22×D313yes—
355C2×Dic6C22×D313yes—
356C3×C4⋊C4—23no—
357C3×C4⋊C4—33no—
358C3×C4⋊C4—33no—
359C3×C4⋊C4—36no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—33no—
362C3×C4⋊C4—33no—
363C3×C4⋊C4—33no—
364C3×C4⋊C4C22×D313yes—
365C3×C4⋊C4C22×D313yes—
366C3×C22⋊C4—31no—
367C3×C22⋊C4—36no—
368C3×C22⋊C4—33no—
369C3×C42—23no—
370C3×C42—33no—
371C3×C42—33no—
372C3×C42C22×D313yes—
373C3×C42C22×D313yes—
374#217—36no—
375#217—33no—
376#217—33no—
377#217—36no—
378(C2×D3)⋊C4—33no—
379(C2×D3)⋊C4—33no—
380(C2×D3)⋊C4—36no—
381(C2×D3)⋊C4—36no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—33no—
384(C2×D3)⋊C4—33no—
385(C2×D3)⋊C4—31no—
386(C2×D3)⋊C4C22×D311yescharacteristic
387(C2×D3)⋊C4C22×D313yes—
388(C2×D3)⋊C4C22×D316yes—
389C4⋊Dic3—33no—
390C4⋊Dic3—33no—
391C4⋊Dic3—33no—
392C4⋊Dic3—36no—
393C4⋊Dic3—33no—
394C4⋊Dic3—36no—
395C4⋊Dic3—63no—
396C4⋊Dic3C22×D313yes—
397C4⋊Dic3C22×D313yes—
398C4⋊Dic3C22×D313yes—
399C4⋊Dic3C22×D313yes—
400Dic3⋊C4—36no—
401Dic3⋊C4—36no—
402Dic3⋊C4—36no—
403Dic3⋊C4—33no—
404Dic3⋊C4—36no—
405Dic3⋊C4—33no—
406Dic3⋊C4—66no—
407Dic3⋊C4C22×D311yescharacteristic
408Dic3⋊C4C22×D313yes—
409Dic3⋊C4C22×D316yes—
410C4×Dic3—33no—
411C4×Dic3—33no—
412C4×Dic3—33no—
413C4×Dic3—33no—
414C4×Dic3—33no—
415C4×Dic3—33no—
416C4×Dic3—33no—
417C4×Dic3—31no—
418C4×Dic3—33no—
419C4×Dic3—33no—
420C4×Dic3—33no—
421C4×Dic3—33no—
422C4×Dic3—33no—
423C4×Dic3—31no—
424C4×Dic3—63no—
425C4×Dic3—63no—
426C4×Dic3—63no—
427C4×Dic3C22×D313yes—
428C4×Dic3C22×D313yes—
429C22×C32C2511yescharacteristic
430C2×C3⋊D3—21no—
431C2×C3⋊D3—21no—
432C2×C3⋊D3C2×#4112yes—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—23no—
436C2×C3×D3—23no—
437C2×C3×D3—23no—
438C2×C3×D3C2×#4112yes—
439C32×C4—21no—
440C32×C4—23no—
441C32×C4C2×#4116yes—
442C3⋊Dic3—23no—
443C3⋊Dic3—23no—
444C3⋊Dic32−1+412yes—
445C3×Dic3—23no—
446C3×Dic3—23no—
447C3×Dic3—21no—
448C3×Dic3—21no—
449C3×Dic3—23no—
450C3×Dic3C2×#4112yes—
451C2×#41—31no—
452C2×#41—93no—
453C22×Q8—31no—
454C22×Q8—91no—
455C4⋊Q8—33no—
456C4⋊Q8—93no—
457#126—96no—
458#126—96no—
459#125—33no—
460#125—33no—
461#125—96no—
462#124—33no—
463#124—93no—
464#123—96no—
465#123—96no—
466C22⋊Q8—33no—
467C22⋊Q8—96no—
468C22⋊Q8—93no—
469C22⋊Q8—93no—
470C22⋊Q8—93no—
471#121—33no—
472#121—93no—
473C4×Q8—31no—
474C4×Q8—31no—
475C4×Q8—33no—
476C4×Q8—93no—
477C4×Q8—93no—
478C4×Q8—93no—
479C4×Q8—91no—
480C4×Q8—93no—
481C4×Q8—93no—
482C4×Q8D3211yescharacteristic
483C4×D4—33no—
484C4×D4—93no—
485C4×D4—93no—
486C4×D4—93no—
487C4×D4—91no—
488C4×D4—93no—
489C4×D4—93no—
490C4×D4—93no—
491#117—93no—
492#117—93no—
493#117—96no—
494#117—93no—
495#117—93no—
496C2×C4⋊C4—93no—
497C2×C4⋊C4—93no—
498C2×C42—93no—
499C2×C42—93no—
500C2×C42—93no—
501C23×C3—31no—
502C23×C3—33no—
503C22×D3—31no—
504C22×D3—31no—
505C22×D3—61no—
506C22×D3C23×D313yes—
507C22×D3C23×D311yescharacteristic
508C3×Q8—24no—
509C3×Q8—66no—
510C3×Q8—66no—
511C3×Q8#23714yescomplemented
512C3×Q8#23914yescomplemented
513C3×D4—66no—
514C3×D4—66no—
515C2×C3×C4—21no—
516C2×C3×C4—23no—
517C2×C3×C4—23no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—33no—
522C2×C3×C4—33no—
523C2×C3×C4—33no—
524C2×C3×C4—66no—
525C2×C3×C4—66no—
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D313yes—
529C2×C3×C4C23×D313yes—
530C2×C3×C4C23×D313yes—
531C2×C3×C4C23×D313yes—
532#67—34no—
533#67—66no—
534C2×Dic3—31no—
535C2×Dic3—31no—
536C2×Dic3—33no—
537C2×Dic3—33no—
538C2×Dic3—33no—
539C2×Dic3—33no—
540C2×Dic3—61no—
541C2×Dic3—63no—
542C2×Dic3—63no—
543C2×Dic3—62no—
544C2×Dic3—66no—
545C2×Dic3—66no—
546C2×Dic3—66no—
547C2×Dic3C23×D311yescharacteristic
548C2×Dic3C23×D311yescharacteristic
549C2×Dic3C23×D313yes—
550C2×Dic3C23×D313yes—
551C2×Dic3C23×D313yes—
552C2×Dic3C23×D311yescharacteristic
553D12—26no—
554D12—26no—
555D12—34no—
556D12—66no—
557C4×D3—26no—
558C4×D3—26no—
559C4×D3—62no—
560C4×D3—62no—
561C4×D3—62no—
562C4×D3—66no—
563C4×D3—66no—
564C4×D3—66no—
565C4×D3—64no—
566C4×D3—612no—
567C4×D3—66no—
568C4×D3—66no—
569C4×D3—66no—
570C4×D3—66no—
571C4×D3—126no—
572Dic6—26no—
573Dic6—26no—
574Dic6—612no—
575Dic6—66no—
576Dic6—66no—
577C2×C32C22×#4111yescharacteristic
578C2×C32C22×#4111yescharacteristic
579C2×C32C2×2−1+411yescharacteristic
580C3⋊D3—22no—
581C3×D3—22no—
582C3×D3—43no—
583#41—64no—
584#41—1812no—
585C2×Q8—33no—
586C2×Q8—33no—
587C2×Q8—64no—
588C2×Q8—93no—
589C2×Q8—184no—
590C2×Q8C2×D3211yescharacteristic
591C2×D4—33no—
592C2×D4—33no—
593C2×D4—91no—
594C2×D4—93no—
595C22×C4—33no—
596C22×C4—33no—
597C22×C4—91no—
598C22×C4—93no—
599C22×C4—93no—
600C22×C4—93no—
601C22×C4—91no—
602C22×C4—93no—
603C22×C4—93no—
604C4⋊C4—33no—
605C4⋊C4—31no—
606C4⋊C4—33no—
607C4⋊C4—33no—
608C4⋊C4—33no—
609C4⋊C4—33no—
610C4⋊C4—36no—
611C4⋊C4—96no—
612C4⋊C4—93no—
613C4⋊C4—93no—
614C4⋊C4—96no—
615C4⋊C4—93no—
616C4⋊C4—96no—
617C4⋊C4C2×D3213yes—
618C22⋊C4—31no—
619C22⋊C4—33no—
620C22⋊C4—36no—
621C22⋊C4—91no—
622C22⋊C4—93no—
623C22⋊C4—93no—
624C22⋊C4—96no—
625C22⋊C4—93no—
626C22⋊C4—96no—
627C42—33no—
628C42—33no—
629C42—91no—
630C42—93no—
631C42—93no—
632C42—93no—
633C42—93no—
634C42—93no—
635C42—93no—
636C42C2×D3213yes—
637C22×C3—21no—
638C22×C3—32no—
639C22×C3—61no—
640C22×C3—61no—
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—32no—
652C2×D3—32no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3D3×#4112yes—
661C3×C4—22no—
662C3×C4—23no—
663C3×C4—23no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—26no—
667C3×C4—32no—
668C3×C4—43no—
669C3×C4—61no—
670C3×C4—63no—
671C3×C4—63no—
672C3×C4—61no—
673C3×C4—63no—
674C3×C4C2×#23716yes—
675C3×C4C2×#23916yes—
676Dic3—23no—
677Dic3—21no—
678Dic3—23no—
679Dic3—21no—
680Dic3—23no—
681Dic3—32no—
682Dic3—32no—
683Dic3—62no—
684Dic3—66no—
685Dic3—63no—
686Dic3—63no—
687Dic3—63no—
688Dic3—63no—
689Dic3—123no—
690Dic3D3×#4112yes—
691C32#348211yescharacteristic, complemented, Sylow
692C23—31no—
693C23—33no—
694C23—91no—
695Q8—66no—
696Q8—66no—
697Q8—186no—
698Q8#379614yescomplemented
699D4—66no—
700D4—66no—
701D4—94no—
702D4—186no—
703C2×C4—31no—
704C2×C4—31no—
705C2×C4—33no—
706C2×C4—33no—
707C2×C4—31no—
708C2×C4—33no—
709C2×C4—66no—
710C2×C4—66no—
711C2×C4—91no—
712C2×C4—93no—
713C2×C4—93no—
714C2×C4—182no—
715C2×C4—186no—
716C2×C4—186no—
717C2×C4—182no—
718C2×C4—186no—
719C2×C4—186no—
720C2×C4—186no—
721C2×C4C22×D3211yescharacteristic
722C2×C4C22×D3213yes—
723C2×C4C22×D3213yes—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—62no—
728C2×C3—123no—
729C2×C3C22×#23711yescharacteristic
730C2×C3C22×#23911yescharacteristic
731C2×C3C2×D3×#4111yescharacteristic
732C2×C3C2×D3×#4111yescharacteristic
733C2×C3D3×2−1+411yescharacteristic
734C2×C3D3×2−1+411yescharacteristic
735D3—22no—
736D3—43no—
737D3—64no—
738D3—62no—
739D3—62no—
740C22—32no—
741C22—61no—
742C22—61no—
743C22—63no—
744C22—63no—
745C22—63no—
746C22—92no—
747C22—181no—
748C22—181no—
749C22C23×D3211yescharacteristic
750C4—21no—
751C4—23no—
752C4—32no—
753C4—61no—
754C4—63no—
755C4—61no—
756C4—63no—
757C4—63no—
758C4—92no—
759C4—183no—
760C4—183no—
761C4C2×#379616yes—
762C3—21no—
763C3#8671211yescharacteristic, complemented
764C3#8701711yescharacteristic, complemented
765C2—62no—
766C2—123no—
767C2—182no—
768C2C22×#379611yescharacteristic
769C2#1059668711yescharacteristic
770C2D32×#4111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3482
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×Q8×C3⋊D3C2semidirect
2. C3×#5576C2semidirect
3. C3×#5569C2semidirect
4. #10595414C2semidirect
5. Q8×#626C2semidirect
6. Dic3×#239C2semidirect
7. D3×Q8×Dic3C2semidirect
8. #10594579C2semidirect
9. #10594427C2semidirect
10. #10594387C2semidirect
11. #10594373C2semidirect
12. #10593943C2semidirect
13. #10593932C2semidirect
14. #10593920C2semidirect
15. C4×#3796C2semidirect
88. #5576D3semidirect
96. #5569D3semidirect
264. C32×Q8#41semidirect
288. #626#41semidirect
511. C3×Q8#237semidirect
512. C3×Q8#239semidirect
691. C32#3482semidirect
698. Q8#3796semidirect
763. C3#86712semidirect
764. C3#87017semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C3×#55762
C3×#55692
#105954142
Q8×#6262
Dic3×#2392
D3×Q8×Dic32
#105945792
#105944272
#105943872
#105943732
#105939432
#105939322
#105939202
C4×#37962
#870173
#867123