Finite Group Databasebeta

← #11904489

Subgroups — #11904489

Order 1152.

3129 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D32×Q8C211yesmaximal, characteristic, complemented
2C2×#64316C211yesmaximal, characteristic, complemented
3#10596047C211yesmaximal, characteristic, complemented
4C3×Q8×D12C211yesmaximal, characteristic, complemented
5C3×#5572C211yesmaximal, characteristic, complemented
6Q8×#626C211yesmaximal, characteristic, complemented
7#10595342C211yesmaximal, characteristic, complemented
8#10594627C213yesmaximal, complemented
9#10594383C213yesmaximal, complemented
10#10594380C213yesmaximal, complemented
11#10594329C213yesmaximal, complemented
12#10593997C213yesmaximal, complemented
13#10593903C213yesmaximal, complemented
14#10593899C213yesmaximal, complemented
15#10593893C213yesmaximal, complemented
16#86759—31nomaximal
17#85881—31nomaximal
18C2×#3832C2211yescharacteristic, complemented
19C2×Q8×C3⋊D3C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×C3×D3×Q8C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic, complemented
23D32×Q8—28no—
24#64316—28no—
25C2×C4×D32C2213yes—
26C2×#3799C2213yes—
27C2×#3799C2213yescomplemented
28C2×#3798C2213yes—
29C2×#3797C2213yes—
30C2×#3797C2213yescomplemented
31C2×D3×Dic6C2213yes—
32C2×D3×Dic6C2213yes—
33C32×C4×Q8C2211yescharacteristic, complemented
34#64106C2213yescomplemented
35#64104C2213yes—
36#64084C2213yescomplemented
37C4×C4⋊(C3⋊D3)C2213yes—
38C3×Q8×Dic3C2211yescharacteristic, complemented
39C3×#897C2213yes—
40C3×#897C2213yescomplemented
41C3×#892C2213yes—
42C3×#887C2213yescomplemented
43C3×C4×D12C2213yes—
44C3×#872C2213yes—
45C3×#869C2213yescomplemented
46C3×C4×Dic6C2213yescomplemented
47#63923C2213yes—
48#63922C2211yescharacteristic
49#63918C2216yescomplemented
50#63910C2213yes—
51#63909C2213yes—
52C4×#626C2213yes—
53C4×#626C2213yes—
54#63895C2213yes—
55#63895C2216yescomplemented
56#63895C2216yescomplemented
57#63894C2216yes—
58#63893C2213yes—
59#63891C2213yes—
60#63890C2216yes—
61#63890C2213yes—
62#63886C2213yes—
63#63880C2216yes—
64#63871C2213yes—
65#63871C2213yescomplemented
66#63866C2213yescomplemented
67#63864C2213yescomplemented
68#63857C2213yescomplemented
69#63852C2216yescomplemented
70C2×#1007—31no—
71C2×#1007—31no—
72C22×D3×Q8—31no—
73C22×D3×Q8—31no—
74C3×D4×Q8—31no—
75C3×#519—31no—
76#5817—31no—
77Q8×#67—31no—
78#5727—33no—
79#5724—33no—
80#5633—33no—
81#5632—33no—
82#5628—33no—
83#5627—33no—
84#5576—31no—
85#5576—31no—
86#5576—31no—
87#5576—33no—
88#5576—33no—
89#5576—61no—
90Q8×D12—31no—
91Q8×D12—33no—
92Q8×D12—33no—
93Q8×D12D311yescharacteristic, complemented
94#5572D311yescharacteristic, complemented
95#5552—33no—
96#5547—33no—
97#5526—33no—
98#5526—33no—
99#5524—33no—
100#5524—33no—
101C22×D32C2311yescharacteristic
102C2×C32×Q8C2311yescharacteristic
103#3832—24no—
104Q8×C3⋊D3—24no—
105C2×C4⋊(C3⋊D3)C2313yes—
106C2×C4⋊(C3⋊D3)C2313yes—
107C2×C4×C3⋊D3C2313yes—
108C2×C4×C3⋊D3C2313yes—
109C2×#634C2313yes—
110C3×D3×Q8—24no—
111C3×D3×Q8—24no—
112C3×D3×Q8D418yescomplemented
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3C2313yes—
115C2×C3×C4×D3C2313yes—
116C2×C3×C4×D3C2313yes—
117C2×C3×Dic6C2313yes—
118C2×C3×Dic6C2313yes—
119C2×C3×Dic6C2313yes—
120C2×#627C2316yes—
121C2×#627C2313yes—
122C2×#626C2313yes—
123C2×#626C2313yes—
124C2×#626C2313yes—
125C2×#626C2311yescharacteristic
126C2×#625C2311yescharacteristic
127C2×#624C2313yes—
128C2×#624C2316yes—
129C2×D3×Dic3C2313yes—
130C2×D3×Dic3C2313yes—
131C4×D32—212no—
132#3799—212no—
133#3799—212no—
134#3798—212no—
135#3797—212no—
136#3797—212no—
137D3×Dic6—212no—
138D3×Dic6—212no—
139C32×C4⋊C4C2313yes—
140C32×C42C2313yes—
141#3752C2311yescharacteristic
142#3752C2313yes—
143#3752C2316yes—
144C4⋊(C3⋊Dic3)C2313yes—
145C3×(C2×D3)⋊C4C2313yes—
146C3×(C2×D3)⋊C4C2313yes—
147C3×(C2×D3)⋊C4C2313yes—
148C3×(C2×D3)⋊C4C2311yescharacteristic
149C3×C4⋊Dic3C2313yes—
150C3×C4⋊Dic3C2316yes—
151C3×C4⋊Dic3C2313yes—
152C3×Dic3⋊C4C2313yes—
153C3×Dic3⋊C4C2313yes—
154C3×C4×Dic3C2316yes—
155C3×C4×Dic3C2313yes—
156Dic3⋊Dic3C2316yes—
157Dic3⋊Dic3C2313yes—
158Dic3⋊Dic3C2313yes—
159#3722C2316yes—
160#3722C2313yes—
161#3722C2313yes—
162(C2×D3)⋊Dic3C2313yes—
163(C2×D3)⋊Dic3C2311yescharacteristic
164#3486—91noSylow
165C22×C3×Q8—31no—
166C22×C3×Q8—31no—
167C22×C3×Q8—31no—
168#1007—68no—
169#1007—68no—
170C2×#239—31no—
171C2×#239—31no—
172C2×#239—33no—
173C2×#239—33no—
174C2×#239—61no—
175C2×D3×Q8—31no—
176C2×D3×Q8—31no—
177C2×D3×Q8—33no—
178C2×D3×Q8—33no—
179C2×D3×Q8—33no—
180C2×D3×Q8—33no—
181C2×D3×Q8—33no—
182C2×D3×Q8—33no—
183C2×D3×Q8—61no—
184C2×D3×Q8—68no—
185C2×D3×Q8—68no—
186C2×D3×Q8C2×D311yescharacteristic
187C2×D3×Q8C2×D311yescharacteristic
188C2×D3×Q8C2×D311yescharacteristic, complemented
189C2×#235—33no—
190C2×#235—33no—
191C2×#235—33no—
192C2×#235—33no—
193C22×C4×D3—33no—
194C22×C4×D3—33no—
195C22×Dic6—33no—
196C22×Dic6—33no—
197C3×C4⋊Q8—33no—
198C3×C22⋊Q8—33no—
199C3×C22⋊Q8—33no—
200C3×C4×Q8—21no—
201C3×C4×Q8—31no—
202C3×C4×Q8—33no—
203C3×C4×Q8—33no—
204C3×C4×Q8C2×D311yescharacteristic, complemented
205C3×C4×Q8C2×D311yescharacteristic, complemented
206C3×C4×D4—33no—
207C3×#117—33no—
208C3×#117—33no—
209#947—33no—
210#946—33no—
211#946—33no—
212Q8×Dic3C2×D311yescharacteristic, complemented
213#944—33no—
214#939—33no—
215#937—31no—
216#930—33no—
217C4×#67—33no—
218C4×#67—33no—
219#924—33no—
220#897—33no—
221#897—33no—
222#897—33no—
223#897—33no—
224#897—33no—
225#897—33no—
226#897—33no—
227#897—36no—
228#897—36no—
229#897—63no—
230#897C2×D313yes—
231#897C2×D313yescomplemented
232#896—36no—
233#896—36no—
234#896—33no—
235#895—33no—
236#895—33no—
237#895—33no—
238#895—33no—
239#895—33no—
240#895—63no—
241#894—33no—
242#894—36no—
243#893—36no—
244#892C2×D313yes—
245#888—36no—
246#887C2×D313yescomplemented
247#886—33no—
248#886—36no—
249#886—33no—
250#885—36no—
251#884—33no—
252#883—33no—
253#882—31no—
254#882—33no—
255#882—33no—
256#67⋊C4—36no—
257#878—33no—
258#875—33no—
259#875—33no—
260#875—33no—
261#875—36no—
262#875—63no—
263C4×D12—33no—
264C4×D12—33no—
265C4×D12—33no—
266C4×D12—33no—
267C4×D12—36no—
268C4×D12—36no—
269C4×D12—63no—
270C4×D12C2×D313yes—
271#872C2×D313yes—
272#869—33no—
273#869—36no—
274#869C2×D313yescomplemented
275C4×Dic6C2×D313yescomplemented
276C22×C3⋊D3C2413yes—
277C22×C3⋊D3C2411yescharacteristic
278C22×C3×D3C2411yescharacteristic
279C22×C3×D3C2411yescharacteristic
280C22×C3×D3C2411yescharacteristic
281C2×D32—22no—
282C2×D32—22no—
283C2×D32—22no—
284C32×Q8C2×D414yes—
285C2×C32×C4C2413yes—
286C2×C32×C4C2411yescharacteristic
287C2×C32×C4C2413yes—
288C2×C3⋊Dic3C2411yescharacteristic
289C2×C3⋊Dic3C2413yes—
290C4⋊(C3⋊D3)—26no—
291C4⋊(C3⋊D3)—26no—
292C4×C3⋊D3—26no—
293C4×C3⋊D3—26no—
294#634—26no—
295C2×C3×Dic3C2411yescharacteristic
296C2×C3×Dic3C2413yes—
297C2×C3×Dic3C2413yes—
298C2×C3×Dic3C2413yes—
299C2×C3×Dic3C2413yes—
300C3×D12—22no—
301C3×C4×D3—26no—
302C3×C4×D3—26no—
303C3×C4×D3C2×D4112yes—
304C3×Dic6—26no—
305C3×Dic6—26no—
306C3×Dic6C2×D4112yes—
307#627—212no—
308#627—26no—
309#626—22no—
310#626—26no—
311#626—26no—
312#626—26no—
313#625—22no—
314#624—26no—
315#624—212no—
316D3×Dic3—26no—
317D3×Dic3—26no—
318C2×2−1+4—91no—
319C23×Q8—91no—
320D4×Q8—31no—
321D4×Q8—93no—
322D4×Q8—93no—
323D4×Q8—91no—
324#548—93no—
325#548—93no—
326#548—91no—
327#548—91no—
328#536—93no—
329#536—93no—
330#525—93no—
331#525—93no—
332#519—31no—
333C23×D3—31no—
334C23×D3—31no—
335C2×C3×Q8—21no—
336C2×C3×Q8—38no—
337C2×C3×Q8—33no—
338C2×C3×Q8—33no—
339C2×C3×Q8—33no—
340C2×C3×Q8—64no—
341C2×C3×Q8—64no—
342C2×C3×Q8C22×D311yescharacteristic
343C2×C3×Q8C22×D311yescharacteristic
344C2×C3×D4—31no—
345C22×C3×C4—33no—
346C22×C3×C4—33no—
347C22×C3×C4—33no—
348C2×#67—31no—
349C2×#67—31no—
350C2×#67—33no—
351C2×#67—33no—
352C2×#67—31no—
353C2×#67—33no—
354C22×Dic3—33no—
355C22×Dic3—33no—
356#239—612no—
357#239—64no—
358#239—64no—
359#239—612no—
360#239—124no—
361D3×Q8—24no—
362D3×Q8—24no—
363D3×Q8—612no—
364D3×Q8—612no—
365D3×Q8—612no—
366D3×Q8—64no—
367D3×Q8—64no—
368D3×Q8—612no—
369D3×Q8—612no—
370D3×Q8—612no—
371D3×Q8—124no—
372D3×Q8D1218yescomplemented
373#235—612no—
374#235—612no—
375#235—612no—
376#235—612no—
377C2×D12—31no—
378C2×D12—33no—
379C2×D12—33no—
380C2×D12—33no—
381C2×D12—33no—
382C2×D12—33no—
383C2×D12—33no—
384C2×D12—33no—
385C2×D12—63no—
386C2×D12—63no—
387C2×D12C22×D311yescharacteristic
388C2×C4×D3—33no—
389C2×C4×D3—33no—
390C2×C4×D3—33no—
391C2×C4×D3—33no—
392C2×C4×D3—33no—
393C2×C4×D3—33no—
394C2×C4×D3—33no—
395C2×C4×D3—36no—
396C2×C4×D3—36no—
397C2×C4×D3—33no—
398C2×C4×D3—63no—
399C2×C4×D3—63no—
400C2×C4×D3—612no—
401C2×C4×D3—612no—
402C2×C4×D3C22×D313yes—
403C2×C4×D3C22×D313yes—
404C2×C4×D3C22×D313yes—
405C2×Dic6—33no—
406C2×Dic6—33no—
407C2×Dic6—33no—
408C2×Dic6—36no—
409C2×Dic6—33no—
410C2×Dic6—36no—
411C2×Dic6—63no—
412C2×Dic6—612no—
413C2×Dic6—612no—
414C2×Dic6C22×D313yes—
415C2×Dic6C22×D313yes—
416C2×Dic6C22×D313yes—
417C3×C4⋊C4—23no—
418C3×C4⋊C4—36no—
419C3×C4⋊C4—33no—
420C3×C4⋊C4—33no—
421C3×C4⋊C4—33no—
422C3×C4⋊C4—33no—
423C3×C4⋊C4C22×D313yes—
424C3×C4⋊C4C22×D313yes—
425C3×C22⋊C4—33no—
426C3×C22⋊C4—33no—
427C3×C22⋊C4—31no—
428C3×C22⋊C4—33no—
429C3×C42—23no—
430C3×C42—36no—
431C3×C42—33no—
432C3×C42C22×D313yes—
433C3×C42C22×D313yes—
434#217—31no—
435#217—33no—
436(C2×D3)⋊C4—31no—
437(C2×D3)⋊C4—33no—
438(C2×D3)⋊C4—31no—
439(C2×D3)⋊C4—31no—
440(C2×D3)⋊C4—36no—
441(C2×D3)⋊C4—33no—
442(C2×D3)⋊C4—33no—
443(C2×D3)⋊C4—36no—
444(C2×D3)⋊C4—33no—
445(C2×D3)⋊C4—33no—
446(C2×D3)⋊C4—36no—
447(C2×D3)⋊C4—33no—
448(C2×D3)⋊C4—33no—
449(C2×D3)⋊C4—36no—
450(C2×D3)⋊C4—61no—
451(C2×D3)⋊C4—63no—
452(C2×D3)⋊C4—66no—
453(C2×D3)⋊C4C22×D311yescharacteristic
454(C2×D3)⋊C4C22×D313yes—
455(C2×D3)⋊C4C22×D313yes—
456(C2×D3)⋊C4C22×D313yes—
457C4⋊Dic3—33no—
458C4⋊Dic3—33no—
459C4⋊Dic3—33no—
460C4⋊Dic3—33no—
461C4⋊Dic3—36no—
462C4⋊Dic3—63no—
463C4⋊Dic3C22×D313yes—
464C4⋊Dic3C22×D316yes—
465C4⋊Dic3C22×D313yes—
466Dic3⋊C4—33no—
467Dic3⋊C4—36no—
468Dic3⋊C4—33no—
469Dic3⋊C4C22×D313yes—
470Dic3⋊C4C22×D313yes—
471C4×Dic3C22×D316yes—
472C4×Dic3C22×D313yes—
473C22×C32C2511yescharacteristic
474C2×C3⋊D3—21no—
475C2×C3⋊D3—21no—
476C2×C3⋊D3—23no—
477C2×C3⋊D3—23no—
478C2×C3⋊D3—23no—
479C2×C3⋊D32−1+412yescomplemented
480C2×C3×D3—21no—
481C2×C3×D3—21no—
482C2×C3×D3—21no—
483C2×C3×D3—21no—
484C2×C3×D3—21no—
485C2×C3×D3—21no—
486C2×C3×D3—21no—
487C2×C3×D3C22×D412yes—
488C2×C3×D32−1+412yescomplemented
489D32—28no—
490C32×C4—21no—
491C32×C4—23no—
492C32×C4C22×D416yes—
493C3⋊Dic3—23no—
494C3⋊Dic3—21no—
495C3×Dic3—23no—
496C3×Dic3—23no—
497C3×Dic3—23no—
498C3×Dic3—21no—
499C3×Dic3C22×D416yes—
5002−1+4—188no—
501C2×#41—93no—
502C2×#41—93no—
503C2×#41—93no—
504C2×#41—91no—
505C22×Q8—31no—
506C22×Q8—31no—
507C22×Q8—31no—
508C22×Q8—93no—
509C22×Q8—93no—
510C22×Q8—93no—
511C22×Q8—93no—
512C22×Q8—91no—
513C22×Q8—188no—
514C23×C4—93no—
515C4⋊Q8—33no—
516C4⋊Q8—96no—
517C4⋊Q8—93no—
518#124—96no—
519#124—93no—
520#124—93no—
521#123—93no—
522#123—93no—
523#123—96no—
524C22⋊Q8—33no—
525C22⋊Q8—33no—
526C22⋊Q8—93no—
527C22⋊Q8—93no—
528C22⋊Q8—96no—
529C22⋊Q8—96no—
530C22⋊Q8—93no—
531C22⋊Q8—93no—
532C22⋊Q8—93no—
533C22⋊Q8—93no—
534#121—93no—
535#121—93no—
536#121—93no—
537#121—93no—
538#120—93no—
539#120—91no—
540C4×Q8—31no—
541C4×Q8—33no—
542C4×Q8—33no—
543C4×Q8D3211yescharacteristic, complemented
544C4×D4—33no—
545C4×D4—96no—
546C4×D4—96no—
547C4×D4—93no—
548C4×D4—93no—
549C4×D4—93no—
550#117—33no—
551#117—33no—
552C23×C3—31no—
553C23×C3—31no—
554C23×C3—31no—
555C22×D3—31no—
556C22×D3—31no—
557C22×D3—33no—
558C22×D3—33no—
559C22×D3—61no—
560C22×D3—63no—
561C22×D3—62no—
562C22×D3—62no—
563C22×D3—62no—
564C22×D3—62no—
565C22×D3—62no—
566C22×D3—62no—
567C22×D3C23×D311yescharacteristic
568C22×D3C23×D311yescharacteristic
569C22×D3C23×D311yescharacteristic
570C3×Q8—24no—
571C3×Q8—312no—
572C3×Q8—66no—
573C3×Q8—66no—
574C3×Q8C2×D1214yes—
575C3×Q8D3×D414yes—
576C3×D4—62no—
577C2×C3×C4—23no—
578C2×C3×C4—23no—
579C2×C3×C4—21no—
580C2×C3×C4—33no—
581C2×C3×C4—312no—
582C2×C3×C4—33no—
583C2×C3×C4—33no—
584C2×C3×C4—33no—
585C2×C3×C4—31no—
586C2×C3×C4—66no—
587C2×C3×C4—66no—
588C2×C3×C4C23×D313yes—
589C2×C3×C4C23×D311yescharacteristic
590C2×C3×C4C23×D313yes—
591C2×C3×C4C23×D311yescharacteristic
592C2×C3×C4C23×D313yes—
593C2×C3×C4C23×D313yes—
594#67—62no—
595#67—66no—
596#67—66no—
597#67—62no—
598#67—62no—
599#67—66no—
600C2×Dic3—31no—
601C2×Dic3—33no—
602C2×Dic3—31no—
603C2×Dic3—33no—
604C2×Dic3—61no—
605C2×Dic3—63no—
606C2×Dic3—66no—
607C2×Dic3—66no—
608C2×Dic3C23×D311yescharacteristic
609C2×Dic3C23×D313yes—
610C2×Dic3C23×D313yes—
611C2×Dic3C23×D313yes—
612C2×Dic3C23×D313yes—
613D12—22no—
614D12—66no—
615D12—66no—
616D12—66no—
617D12—62no—
618D12—66no—
619D12—66no—
620D12—66no—
621D12—66no—
622D12—126no—
623D12—126no—
624C4×D3—26no—
625C4×D3—26no—
626C4×D3—66no—
627C4×D3—612no—
628C4×D3—66no—
629C4×D3—66no—
630C4×D3—66no—
631C4×D3—66no—
632C4×D3—66no—
633C4×D3—66no—
634C4×D3—66no—
635C4×D3—612no—
636C4×D3—126no—
637C4×D3—126no—
638C4×D3C2×D12112yes—
639Dic6—26no—
640Dic6—26no—
641Dic6—612no—
642Dic6—66no—
643Dic6—66no—
644Dic6—66no—
645Dic6—612no—
646Dic6—66no—
647Dic6—126no—
648Dic6C2×D12112yes—
649C2×C32C23×D411yescharacteristic
650C2×C32C2×2−1+411yescharacteristic
651C2×C32C2×2−1+411yescharacteristic
652C3⋊D3—22no—
653C3⋊D3—43no—
654C3×D3—22no—
655C3×D3—22no—
656C3×D3—41no—
657C24—91no—
658#41—1812no—
659#41—1812no—
660#41—1812no—
661#41—184no—
662C2×Q8—38no—
663C2×Q8—33no—
664C2×Q8—33no—
665C2×Q8—33no—
666C2×Q8—64no—
667C2×Q8—64no—
668C2×Q8—96no—
669C2×Q8—93no—
670C2×Q8—93no—
671C2×Q8—1812no—
672C2×Q8—1812no—
673C2×Q8—1812no—
674C2×Q8—1812no—
675C2×Q8—184no—
676C2×Q8C2×D3211yescharacteristic
677C2×D4—31no—
678C2×D4—93no—
679C2×D4—91no—
680C2×D4—93no—
681C2×D4—93no—
682C2×D4—91no—
683C2×D4—93no—
684C2×D4—93no—
685C22×C4—33no—
686C22×C4—33no—
687C22×C4—33no—
688C22×C4—93no—
689C22×C4—96no—
690C22×C4—93no—
691C22×C4—93no—
692C22×C4—93no—
693C22×C4—93no—
694C22×C4—1812no—
695C4⋊C4—33no—
696C4⋊C4—33no—
697C4⋊C4—33no—
698C4⋊C4—33no—
699C4⋊C4—36no—
700C4⋊C4—93no—
701C4⋊C4—96no—
702C4⋊C4—93no—
703C4⋊C4—93no—
704C4⋊C4C2×D3213yes—
705C22⋊C4—33no—
706C22⋊C4—31no—
707C22⋊C4—33no—
708C22⋊C4—33no—
709C22⋊C4—93no—
710C22⋊C4—96no—
711C22⋊C4—93no—
712C22⋊C4—91no—
713C22⋊C4—93no—
714C22⋊C4—91no—
715C22⋊C4—96no—
716C22⋊C4—93no—
717C42—36no—
718C42—33no—
719C42C2×D3213yes—
720C22×C3—21no—
721C22×C3—32no—
722C22×C3—32no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3C24×D311yescharacteristic
731C22×C3C24×D311yescharacteristic
732C2×D3—21no—
733C2×D3—21no—
734C2×D3—21no—
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—32no—
740C2×D3—32no—
741C2×D3—62no—
742C2×D3—68no—
743C2×D3—68no—
744C2×D3—61no—
745C2×D3—61no—
746C2×D3—61no—
747C2×D3—61no—
748C2×D3—63no—
749C2×D3—63no—
750C2×D3—63no—
751C2×D3—63no—
752C2×D3—63no—
753C2×D3—63no—
754C2×D3—121no—
755C2×D3—121no—
756C2×D3—123no—
757C2×D3—123no—
758C2×D3—123no—
759C2×D3C22×D1212yes—
760C2×D3#100712yescomplemented
761C3×C4—21no—
762C3×C4—23no—
763C3×C4—23no—
764C3×C4—21no—
765C3×C4—26no—
766C3×C4—36no—
767C3×C4—43no—
768C3×C4—41no—
769C3×C4—63no—
770C3×C4—63no—
771C3×C4—63no—
772C3×C4—61no—
773C3×C4C22×D1216yes—
774C3×C4C2×D3×D416yes—
775Dic3—23no—
776Dic3—23no—
777Dic3—23no—
778Dic3—21no—
779Dic3—63no—
780Dic3—61no—
781Dic3—63no—
782Dic3—61no—
783Dic3—123no—
784Dic3—121no—
785Dic3C22×D1216yes—
786C32#348611yescharacteristic, complemented, Sylow
787C23—31no—
788C23—31no—
789C23—31no—
790C23—91no—
791C23—93no—
792C23—182no—
793C23—182no—
794C23—182no—
795Q8—312no—
796Q8—66no—
797Q8—66no—
798Q8—1812no—
799Q8—186no—
800Q8—186no—
801Q8D3×D1214yes—
802D4—62no—
803D4—186no—
804D4—186no—
805D4—186no—
806D4—186no—
807D4—182no—
808D4—182no—
809D4—186no—
810C2×C4—33no—
811C2×C4—312no—
812C2×C4—33no—
813C2×C4—31no—
814C2×C4—33no—
815C2×C4—33no—
816C2×C4—66no—
817C2×C4—66no—
818C2×C4—93no—
819C2×C4—91no—
820C2×C4—186no—
821C2×C4—1812no—
822C2×C4—186no—
823C2×C4—186no—
824C2×C4—186no—
825C2×C4—186no—
826C2×C4C22×D3213yes—
827C2×C4C22×D3211yescharacteristic
828C2×C4C22×D3213yes—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—62no—
833C2×C3—62no—
834C2×C3—121no—
835C2×C3C23×D1211yescharacteristic
836C2×C3C22×D3×D411yescharacteristic
837C2×C3C2×#100711yescharacteristic
838C2×C3D3×2−1+411yescharacteristic
839C2×C3D3×2−1+411yescharacteristic
840C2×C3D3×2−1+411yescharacteristic
841D3—22no—
842D3—22no—
843D3—41no—
844D3—62no—
845D3—62no—
846D3—122no—
847D3—123no—
848D3—123no—
849D3—243no—
850C22—32no—
851C22—32no—
852C22—61no—
853C22—61no—
854C22—61no—
855C22—61no—
856C22—61no—
857C22—61no—
858C22—61no—
859C22—92no—
860C22—188no—
861C22—181no—
862C22—181no—
863C22—183no—
864C22—183no—
865C22—183no—
866C22C23×D3211yescharacteristic
867C4—21no—
868C4—23no—
869C4—36no—
870C4—63no—
871C4—63no—
872C4—63no—
873C4—61no—
874C4—181no—
875C4—183no—
876C4C2×D3×D1216yes—
877C3—21no—
878C3#8588111yescharacteristic, complemented
879C3#8675911yescharacteristic, complemented
880C2—62no—
881C2—62no—
882C2—121no—
883C2—182no—
884C2—363no—
885C2C22×D3×D1211yescharacteristic
886C2D3×#100711yescharacteristic
887C2#1059669411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3486
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×D32×Q8C2semidirect
2. C2×#64316C2semidirect
3. #10596047C2semidirect
4. C3×Q8×D12C2semidirect
5. C3×#5572C2semidirect
6. Q8×#626C2semidirect
7. #10595342C2semidirect
8. #10594627C2semidirect
9. #10594383C2semidirect
10. #10594380C2semidirect
11. #10594329C2semidirect
12. #10593997C2semidirect
13. #10593903C2semidirect
14. #10593899C2semidirect
15. #10593893C2semidirect
18. C2×#3832C22semidirect
22. C2×C3×D3×Q8C22semidirect
27. C2×#3799C22semidirect
30. C2×#3797C22semidirect
33. C32×C4×Q8C22semidirect
34. #64106C22semidirect
36. #64084C22semidirect
38. C3×Q8×Dic3C22semidirect
40. C3×#897C22semidirect
42. C3×#887C22semidirect
45. C3×#869C22semidirect
46. C3×C4×Dic6C22semidirect
49. #63918C22semidirect
55. #63895C22semidirect
56. #63895C22semidirect
65. #63871C22semidirect
66. #63866C22semidirect
67. #63864C22semidirect
68. #63857C22semidirect
69. #63852C22semidirect
93. Q8×D12D3semidirect
94. #5572D3semidirect
112. C3×D3×Q8D4semidirect
188. C2×D3×Q8C2×D3semidirect
204. C3×C4×Q8C2×D3semidirect
205. C3×C4×Q8C2×D3semidirect
212. Q8×Dic3C2×D3semidirect
231. #897C2×D3semidirect
246. #887C2×D3semidirect
274. #869C2×D3semidirect
275. C4×Dic6C2×D3semidirect
372. D3×Q8D12semidirect
479. C2×C3⋊D32−1+4semidirect
488. C2×C3×D32−1+4semidirect
543. C4×Q8D32semidirect
760. C2×D3#1007semidirect
786. C32#3486semidirect
878. C3#85881semidirect
879. C3#86759semidirect

Maximal subgroups

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

subgroupindex
C2×D32×Q82
C2×#643162
#105960472
C3×Q8×D122
C3×#55722
Q8×#6262
#105953422
#105946272
#105943832
#105943802
#105943292
#105939972
#105939032
#105938992
#105938932
#867593
#858813