Finite Group Databasebeta

← #11904819

Subgroups — #11904819

Order 1152.

3189 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic, complemented
2C2×#64315C211yesmaximal, characteristic, complemented
3#10596047C211yesmaximal, characteristic, complemented
4C3×Q8×D12C211yesmaximal, characteristic, complemented
5C3×#5574C211yesmaximal, characteristic, complemented
6Q8×#626C211yesmaximal, characteristic, complemented
7#10595342C211yesmaximal, characteristic, complemented
8#10594629C213yesmaximal, complemented
9D3×#897C213yesmaximal, complemented
10#10594523C213yesmaximal, complemented
11#10594381C213yesmaximal, complemented
12#10594003C213yesmaximal, complemented
13#10593997C213yesmaximal, complemented
14#10593896C213yesmaximal, complemented
15#10593893C213yesmaximal, complemented
16#86745—31nomaximal
17#85901—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic, complemented
20C2×C3×#239C2211yescharacteristic
21C2×C3×D3×Q8C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic, complemented
23D3×#239—28no—
24#64315—28no—
25C2×D3×D12C2213yes—
26C2×C4×D32C2213yes—
27C2×#3799C2213yes—
28C2×#3798C2213yescomplemented
29C2×#3796C2213yes—
30C2×#3796C2213yescomplemented
31C2×#3795C2213yescomplemented
32C2×D3×Dic6C2213yescomplemented
33C32×C4×Q8C2211yescharacteristic, complemented
34#64106C2213yescomplemented
35#64104C2213yescomplemented
36#64084C2213yescomplemented
37C4×C4⋊(C3⋊D3)C2213yescomplemented
38C3×Q8×Dic3C2211yescharacteristic, complemented
39C3×#897C2213yes—
40C3×#897C2213yescomplemented
41C3×#893C2213yescomplemented
42C3×D3×C4⋊C4C2213yescomplemented
43C3×C4×D12C2213yes—
44C3×C4×D12C2213yescomplemented
45C3×#872C2213yescomplemented
46C3×#869C2213yescomplemented
47#63923C2213yes—
48#63922C2213yes—
49D3×(C2×D3)⋊C4C2216yes—
50#63910C2213yescomplemented
51#63909C2213yescomplemented
52#63909C2216yescomplemented
53#63906C2216yescomplemented
54C4×#626C2213yes—
55C4×#626C2213yescomplemented
56#63895C2216yescomplemented
57#63895C2213yescomplemented
58#63893C2213yes—
59#63891C2213yescomplemented
60#63890C2216yescomplemented
61#63890C2216yescomplemented
62#63890C2213yescomplemented
63D3×C4⋊Dic3C2216yescomplemented
64#63886C2211yescharacteristic
65#63871C2213yescomplemented
66#63871C2213yescomplemented
67#63866C2213yescomplemented
68#63864C2213yescomplemented
69#63857C2213yes—
70C2×#1010—31no—
71C2×D3×#41—31no—
72C2×#1007—31no—
73C22×#239—31no—
74C3×D4×Q8—31no—
75C3×#520—31no—
76#5817—31no—
77Q8×#67—31no—
78#5726—33no—
79#5724—33no—
80#5631—33no—
81#5630—33no—
82#5629—33no—
83D3×C22⋊Q8—33no—
84#5576—31no—
85#5576—31no—
86#5576—31no—
87#5576—61no—
88Q8×D12—31no—
89Q8×D12D311yescharacteristic, complemented
90#5574D311yescharacteristic, complemented
91#5555—33no—
92#5555—33no—
93#5554—33no—
94#5554—33no—
95#5550—33no—
96#5547—33no—
97#5526—33no—
98#5524—33no—
99#5510—33no—
100C2×#897—33no—
101C22×D32C2313yes—
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×#239D418yescomplemented
111C3×D3×Q8—24no—
112C3×D3×Q8—24no—
113C2×C3×D12C2311yescharacteristic
114C2×C3×D12C2313yes—
115C2×C3×C4×D3C2313yes—
116C2×C3×C4×D3C2313yes—
117C2×C3×C4×D3C2316yes—
118C2×C3×C4×D3C2313yes—
119C2×C3×Dic6C2313yes—
120C2×C3×Dic6C2313yes—
121C2×#627C2313yes—
122C2×#626C2316yes—
123C2×#626C2313yes—
124C2×#626C2311yescharacteristic
125C2×#626C2311yescharacteristic
126C2×#626C2313yes—
127C2×#625C2313yes—
128C2×#624C2313yes—
129C2×D3×Dic3C2316yes—
130C2×D3×Dic3C2313yes—
131C2×D3×Dic3C2311yescharacteristic
132D3×D12—212no—
133C4×D32—212no—
134#3799—212no—
135#3798—212no—
136#3796—212no—
137#3796—212no—
138#3795—212no—
139D3×Dic6—212no—
140C32×C4⋊C4C2313yes—
141C32×C42C2313yes—
142#3752C2311yescharacteristic
143#3752C2313yes—
144#3752C2316yes—
145C4⋊(C3⋊Dic3)C2313yes—
146C3×(C2×D3)⋊C4C2313yes—
147C3×(C2×D3)⋊C4C2313yes—
148C3×(C2×D3)⋊C4C2313yes—
149C3×(C2×D3)⋊C4C2313yes—
150C3×C4⋊Dic3C2313yes—
151C3×C4⋊Dic3C2316yes—
152C3×C4⋊Dic3C2313yes—
153C3×Dic3⋊C4C2313yes—
154C3×Dic3⋊C4C2311yescharacteristic
155C3×C4×Dic3C2313yes—
156Dic3⋊Dic3C2316yes—
157Dic3⋊Dic3C2313yes—
158Dic3⋊Dic3C2313yes—
159#3722C2313yes—
160#3722C2316yes—
161#3722C2313yes—
162(C2×D3)⋊Dic3C2313yes—
163(C2×D3)⋊Dic3C2311yescharacteristic
164#3489—91noSylow
165C2×C3×#41—31no—
166C22×C3×Q8—31no—
167C22×C3×Q8—31no—
168#1010—68no—
169D3×#41—68no—
170#1007—68no—
171C2×#239—31no—
172C2×#239—31no—
173C2×#239—33no—
174C2×#239—33no—
175C2×#239—33no—
176C2×#239—61no—
177C2×#239—68no—
178C2×#239C2×D311yescharacteristic
179C2×D3×Q8—31no—
180C2×D3×Q8—31no—
181C2×D3×Q8—33no—
182C2×D3×Q8—61no—
183C2×D3×Q8C2×D311yescharacteristic
184C2×D3×Q8C2×D311yescharacteristic, complemented
185C2×#237—33no—
186C2×#237—33no—
187C2×#237—33no—
188C2×D3×D4—33no—
189C2×#235—33no—
190C2×#235—33no—
191C2×#235—33no—
192C2×#235—33no—
193C22×D12—33no—
194C22×C4×D3—33no—
195C22×C4×D3—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×Q8C2×D311yescharacteristic, complemented
203C3×C4×Q8C2×D311yescharacteristic, complemented
204C3×C4×D4—33no—
205C3×C4×D4—33no—
206C3×C4×D4—33no—
207C3×#117—33no—
208C2×C3×C4⋊C4—33no—
209#947—33no—
210#946—33no—
211#946—33no—
212Q8×Dic3C2×D311yescharacteristic, complemented
213#944—33no—
214#939—31no—
215#937—33no—
216#930—36no—
217#930—36no—
218#930—33no—
219C4×#67—33no—
220C4×#67—33no—
221C2×(C2×D3)⋊C4—36no—
222C2×C4⋊Dic3—36no—
223#924—33no—
224#897—33no—
225#897—33no—
226#897—33no—
227#897—33no—
228#897—33no—
229#897—33no—
230#897—36no—
231#897—33no—
232#897—63no—
233#897C2×D313yes—
234#897C2×D313yescomplemented
235#896—33no—
236#896—36no—
237#895—31no—
238#895—36no—
239#895—33no—
240#895—33no—
241#895—33no—
242#895—33no—
243#895—63no—
244#894—36no—
245#894—36no—
246#894—33no—
247#893C2×D313yescomplemented
248D3×C4⋊C4—36no—
249D3×C4⋊C4C2×D313yescomplemented
250#886—33no—
251#886—33no—
252#886—36no—
253#886—36no—
254#884—36no—
255#884—33no—
256#883—33no—
257#882—33no—
258#882—33no—
259#882—33no—
260D3×C22⋊C4—36no—
261#878—33no—
262#875—33no—
263#875—33no—
264#875—33no—
265#875—63no—
266C4×D12—33no—
267C4×D12—33no—
268C4×D12—33no—
269C4×D12—33no—
270C4×D12—63no—
271C4×D12C2×D313yes—
272C4×D12C2×D313yescomplemented
273#872C2×D313yescomplemented
274#869—33no—
275#869C2×D313yescomplemented
276C22×C3⋊D3C2413yes—
277C22×C3⋊D3C2411yescharacteristic
278C22×C3×D3C2411yescharacteristic
279C22×C3×D3C2413yes—
280C22×C3×D3C2411yescharacteristic
281C2×D32—26no—
282C2×D32—26no—
283C2×D32—43no—
284C32×Q8C2×D414yes—
285C2×C32×C4C2411yescharacteristic
286C2×C32×C4C2413yes—
287C2×C32×C4C2413yes—
288C2×C3⋊Dic3C2411yescharacteristic
289C2×C3⋊Dic3C2413yes—
290C4⋊(C3⋊D3)—26no—
291C4⋊(C3⋊D3)—43no—
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×Dic3C2411yescharacteristic
300C3×D12—22no—
301C3×D12C2×D4112yes—
302C3×C4×D3—26no—
303C3×C4×D3—26no—
304C3×C4×D3—46no—
305C3×C4×D3C2×D4112yes—
306C3×Dic6—26no—
307C3×Dic6—26no—
308#627—26no—
309#626—26no—
310#626—212no—
311#626—22no—
312#626—22no—
313#626—43no—
314#625—26no—
315#624—26no—
316D3×Dic3—212no—
317D3×Dic3—26no—
318D3×Dic3—22no—
319C2×2−1+4—91no—
320C22×#41—91no—
321D4×Q8—31no—
322D4×Q8—91no—
323#548—91no—
324#548—91no—
325#547—93no—
326#547—93no—
327#546—93no—
328#546—93no—
329#537—93no—
330#536—93no—
331#525—93no—
332C2×C22⋊Q8—93no—
333#520—31no—
334C23×D3—33no—
335C23×D3—33no—
336C3×#41—38no—
337C2×C3×Q8—21no—
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—33no—
345C2×C3×D4—31no—
346C22×C3×C4—33no—
347C22×C3×C4—33no—
348C22×C3×C4—33no—
349C22×C3×C4—36no—
350C2×#67—33no—
351C2×#67—33no—
352C2×#67—31no—
353C2×#67—33no—
354C2×#67—31no—
355C2×#67—36no—
356C2×#67—33no—
357C22×Dic3—31no—
358C22×Dic3—33no—
359C22×Dic3—36no—
360#239—64no—
361#239—64no—
362#239—612no—
363#239—612no—
364#239—612no—
365#239—124no—
366#239D1218yescomplemented
367D3×Q8—24no—
368D3×Q8—24no—
369D3×Q8—64no—
370D3×Q8—64no—
371D3×Q8—612no—
372D3×Q8—124no—
373#237—612no—
374#237—612no—
375#237—612no—
376D3×D4—612no—
377#235—612no—
378#235—612no—
379#235—612no—
380#235—612no—
381C2×D12—31no—
382C2×D12—33no—
383C2×D12—36no—
384C2×D12—31no—
385C2×D12—33no—
386C2×D12—33no—
387C2×D12—33no—
388C2×D12—33no—
389C2×D12—33no—
390C2×D12—63no—
391C2×D12—63no—
392C2×D12—612no—
393C2×D12C22×D311yescharacteristic
394C2×D12C22×D313yes—
395C2×C4×D3—36no—
396C2×C4×D3—33no—
397C2×C4×D3—31no—
398C2×C4×D3—33no—
399C2×C4×D3—33no—
400C2×C4×D3—33no—
401C2×C4×D3—33no—
402C2×C4×D3—33no—
403C2×C4×D3—33no—
404C2×C4×D3—63no—
405C2×C4×D3—63no—
406C2×C4×D3—612no—
407C2×C4×D3—612no—
408C2×C4×D3C22×D313yes—
409C2×C4×D3C22×D313yes—
410C2×C4×D3C22×D316yes—
411C2×C4×D3C22×D313yes—
412C2×Dic6—33no—
413C2×Dic6—33no—
414C2×Dic6—33no—
415C2×Dic6—33no—
416C2×Dic6—63no—
417C2×Dic6—612no—
418C2×Dic6C22×D313yes—
419C2×Dic6C22×D313yes—
420C3×C4⋊C4—23no—
421C3×C4⋊C4—36no—
422C3×C4⋊C4—33no—
423C3×C4⋊C4—33no—
424C3×C4⋊C4—31no—
425C3×C4⋊C4—33no—
426C3×C4⋊C4C22×D313yes—
427C3×C4⋊C4C22×D313yes—
428C3×C22⋊C4—33no—
429C3×C22⋊C4—33no—
430C3×C22⋊C4—33no—
431C3×C22⋊C4—33no—
432C3×C42—23no—
433C3×C42—33no—
434C3×C42C22×D313yes—
435C3×C42C22×D313yes—
436#217—33no—
437#217—31no—
438(C2×D3)⋊C4—31no—
439(C2×D3)⋊C4—33no—
440(C2×D3)⋊C4—31no—
441(C2×D3)⋊C4—31no—
442(C2×D3)⋊C4—33no—
443(C2×D3)⋊C4—33no—
444(C2×D3)⋊C4—36no—
445(C2×D3)⋊C4—36no—
446(C2×D3)⋊C4—33no—
447(C2×D3)⋊C4—33no—
448(C2×D3)⋊C4—36no—
449(C2×D3)⋊C4—36no—
450(C2×D3)⋊C4—33no—
451(C2×D3)⋊C4—33no—
452(C2×D3)⋊C4—61no—
453(C2×D3)⋊C4—63no—
454(C2×D3)⋊C4—66no—
455(C2×D3)⋊C4C22×D313yes—
456(C2×D3)⋊C4C22×D313yes—
457(C2×D3)⋊C4C22×D313yes—
458(C2×D3)⋊C4C22×D313yes—
459C4⋊Dic3—33no—
460C4⋊Dic3—33no—
461C4⋊Dic3—33no—
462C4⋊Dic3—36no—
463C4⋊Dic3—33no—
464C4⋊Dic3—63no—
465C4⋊Dic3C22×D313yes—
466C4⋊Dic3C22×D316yes—
467C4⋊Dic3C22×D313yes—
468Dic3⋊C4—33no—
469Dic3⋊C4—33no—
470Dic3⋊C4—36no—
471Dic3⋊C4C22×D311yescharacteristic
472Dic3⋊C4C22×D313yes—
473C4×Dic3C22×D313yes—
474C22×C32C2511yescharacteristic
475C2×C3⋊D3—21no—
476C2×C3⋊D3—23no—
477C2×C3⋊D3—21no—
478C2×C3⋊D3—21no—
479C2×C3⋊D3—23no—
480C2×C3⋊D3—23no—
481C2×C3×D3—21no—
482C2×C3×D3—23no—
483C2×C3×D3—23no—
484C2×C3×D3—21no—
485C2×C3×D3—21no—
486C2×C3×D3—21no—
487C2×C3×D3—21no—
488C2×C3×D3C22×D416yes—
489C2×C3×D32−1+412yescomplemented
490D32—412no—
491C32×C4—21no—
492C32×C4—23no—
493C32×C4C22×D416yes—
494C3⋊Dic3—21no—
495C3⋊Dic3—23no—
496C3×Dic3—23no—
497C3×Dic3—23no—
498C3×Dic3—21no—
499C3×Dic3—23no—
500C3×Dic3C22×D412yes—
5012−1+4—188no—
502C2×#41—31no—
503C2×#41—93no—
504C2×#41—93no—
505C2×#41—93no—
506C2×#41—93no—
507C2×#41—93no—
508C2×#41—91no—
509C2×#41—188no—
510C22×Q8—31no—
511C22×Q8—31no—
512C22×Q8—93no—
513C22×Q8—91no—
514C22×D4—93no—
515C23×C4—93no—
516C4⋊Q8—33no—
517C4⋊Q8—93no—
518#124—93no—
519#124—93no—
520#123—93no—
521#123—93no—
522#123—96no—
523#123—96no—
524C22⋊Q8—33no—
525C22⋊Q8—33no—
526C22⋊Q8—93no—
527C22⋊Q8—96no—
528C22⋊Q8—93no—
529C22⋊Q8—93no—
530C22⋊Q8—93no—
531C22⋊Q8—93no—
532C22⋊Q8—93no—
533#121—93no—
534#121—96no—
535#121—96no—
536#121—93no—
537#121—91no—
538#121—93no—
539#120—93no—
540#120—93no—
541C4×Q8—31no—
542C4×Q8D3211yescharacteristic, complemented
543C4×D4—33no—
544C4×D4—33no—
545C4×D4—33no—
546C4×D4—93no—
547C4×D4—93no—
548C4×D4—93no—
549#117—33no—
550C2×C4⋊C4—33no—
551C2×C4⋊C4—96no—
552C2×C22⋊C4—96no—
553C23×C3—31no—
554C23×C3—33no—
555C23×C3—31no—
556C22×D3—33no—
557C22×D3—33no—
558C22×D3—31no—
559C22×D3—31no—
560C22×D3—61no—
561C22×D3—63no—
562C22×D3—66no—
563C22×D3—66no—
564C22×D3—66no—
565C22×D3—66no—
566C22×D3—123no—
567C22×D3—123no—
568C22×D3C23×D311yescharacteristic
569C22×D3C23×D313yes—
570C22×D3C23×D311yescharacteristic
571C3×Q8—24no—
572C3×Q8—66no—
573C3×Q8—66no—
574C3×Q8C2×D1214yes—
575C3×Q8D3×D414yes—
576C3×D4—312no—
577C3×D4—62no—
578C2×C3×C4—23no—
579C2×C3×C4—23no—
580C2×C3×C4—21no—
581C2×C3×C4—31no—
582C2×C3×C4—312no—
583C2×C3×C4—33no—
584C2×C3×C4—33no—
585C2×C3×C4—31no—
586C2×C3×C4—33no—
587C2×C3×C4—66no—
588C2×C3×C4—66no—
589C2×C3×C4—126no—
590C2×C3×C4C23×D313yes—
591C2×C3×C4C23×D311yescharacteristic
592C2×C3×C4C23×D313yes—
593C2×C3×C4C23×D311yescharacteristic
594C2×C3×C4C23×D313yes—
595C2×C3×C4C23×D313yes—
596#67—612no—
597#67—66no—
598#67—62no—
599#67—66no—
600#67—66no—
601#67—62no—
602#67—123no—
603C2×Dic3—31no—
604C2×Dic3—33no—
605C2×Dic3—31no—
606C2×Dic3—33no—
607C2×Dic3—61no—
608C2×Dic3—63no—
609C2×Dic3—612no—
610C2×Dic3—66no—
611C2×Dic3—62no—
612C2×Dic3C23×D311yescharacteristic
613C2×Dic3C23×D313yes—
614C2×Dic3C23×D313yes—
615C2×Dic3C23×D313yes—
616C2×Dic3C23×D311yescharacteristic
617D12—22no—
618D12—62no—
619D12—612no—
620D12—66no—
621D12—62no—
622D12—66no—
623D12—66no—
624D12—126no—
625D12—123no—
626D12—123no—
627D12—126no—
628D12—123no—
629D12C2×D12112yes—
630C4×D3—26no—
631C4×D3—26no—
632C4×D3—46no—
633C4×D3—66no—
634C4×D3—62no—
635C4×D3—66no—
636C4×D3—612no—
637C4×D3—66no—
638C4×D3—66no—
639C4×D3—66no—
640C4×D3—66no—
641C4×D3—66no—
642C4×D3—126no—
643C4×D3—126no—
644C4×D3C2×D12112yes—
645Dic6—26no—
646Dic6—26no—
647Dic6—66no—
648Dic6—66no—
649Dic6—66no—
650Dic6—66no—
651Dic6—126no—
652C2×C32C23×D411yescharacteristic
653C2×C32C2×2−1+411yescharacteristic
654C2×C32#58511yescharacteristic
655C3⋊D3—41no—
656C3⋊D3—43no—
657C3×D3—22no—
658C3×D3—26no—
659C3×D3—41no—
660C24—93no—
661#41—38no—
662#41—1812no—
663#41—1812no—
664#41—1812no—
665#41—1812no—
666#41—1812no—
667#41—184no—
668C2×Q8—33no—
669C2×Q8—33no—
670C2×Q8—64no—
671C2×Q8—64no—
672C2×Q8—93no—
673C2×Q8—93no—
674C2×Q8—1812no—
675C2×Q8—184no—
676C2×Q8C2×D3211yescharacteristic
677C2×D4—33no—
678C2×D4—31no—
679C2×D4—91no—
680C2×D4—93no—
681C2×D4—91no—
682C2×D4—96no—
683C2×D4—93no—
684C2×D4—93no—
685C2×D4—93no—
686C2×D4—93no—
687C2×D4—1812no—
688C22×C4—33no—
689C22×C4—33no—
690C22×C4—33no—
691C22×C4—36no—
692C22×C4—93no—
693C22×C4—96no—
694C22×C4—93no—
695C22×C4—91no—
696C22×C4—93no—
697C22×C4—93no—
698C22×C4—1812no—
699C4⋊C4—33no—
700C4⋊C4—33no—
701C4⋊C4—36no—
702C4⋊C4—31no—
703C4⋊C4—33no—
704C4⋊C4—93no—
705C4⋊C4—96no—
706C4⋊C4—93no—
707C4⋊C4—93no—
708C4⋊C4C2×D3213yes—
709C22⋊C4—33no—
710C22⋊C4—33no—
711C22⋊C4—33no—
712C22⋊C4—33no—
713C22⋊C4—96no—
714C22⋊C4—93no—
715C22⋊C4—93no—
716C22⋊C4—93no—
717C22⋊C4—91no—
718C22⋊C4—96no—
719C22⋊C4—91no—
720C22⋊C4—93no—
721C42—33no—
722C42C2×D3213yes—
723C22×C3—21no—
724C22×C3—36no—
725C22×C3—32no—
726C22×C3—61no—
727C22×C3—63no—
728C22×C3—61no—
729C22×C3—63no—
730C22×C3—61no—
731C22×C3—61no—
732C22×C3—61no—
733C22×C3C24×D311yescharacteristic
734C22×C3C24×D311yescharacteristic
735C2×D3—21no—
736C2×D3—23no—
737C2×D3—23no—
738C2×D3—21no—
739C2×D3—21no—
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—62no—
743C2×D3—61no—
744C2×D3—63no—
745C2×D3—61no—
746C2×D3—63no—
747C2×D3—61no—
748C2×D3—63no—
749C2×D3—61no—
750C2×D3—63no—
751C2×D3—61no—
752C2×D3—63no—
753C2×D3—61no—
754C2×D3—63no—
755C2×D3—121no—
756C2×D3—121no—
757C2×D3—123no—
758C2×D3—123no—
759C2×D3—123no—
760C2×D3—1212no—
761C2×D3—1212no—
762C2×D3C22×D1216yes—
763C2×D3#100712yescomplemented
764C3×C4—21no—
765C3×C4—23no—
766C3×C4—21no—
767C3×C4—23no—
768C3×C4—26no—
769C3×C4—32no—
770C3×C4—43no—
771C3×C4—41no—
772C3×C4—63no—
773C3×C4—63no—
774C3×C4—61no—
775C3×C4—63no—
776C3×C4C22×D1216yes—
777C3×C4C2×D3×D416yes—
778Dic3—23no—
779Dic3—23no—
780Dic3—23no—
781Dic3—21no—
782Dic3—63no—
783Dic3—61no—
784Dic3—63no—
785Dic3—61no—
786Dic3—123no—
787Dic3—121no—
788Dic3C22×D1212yes—
789C32#348911yescharacteristic, complemented, Sylow
790C23—31no—
791C23—33no—
792C23—31no—
793C23—93no—
794C23—91no—
795C23—186no—
796C23—186no—
797C23—363no—
798Q8—66no—
799Q8—66no—
800Q8—186no—
801Q8—186no—
802Q8D3×D1214yes—
803D4—312no—
804D4—62no—
805D4—182no—
806D4—1812no—
807D4—186no—
808D4—182no—
809D4—186no—
810D4—186no—
811D4—363no—
812D4—363no—
813C2×C4—31no—
814C2×C4—312no—
815C2×C4—31no—
816C2×C4—33no—
817C2×C4—33no—
818C2×C4—33no—
819C2×C4—66no—
820C2×C4—66no—
821C2×C4—93no—
822C2×C4—91no—
823C2×C4—126no—
824C2×C4—186no—
825C2×C4—182no—
826C2×C4—186no—
827C2×C4—1812no—
828C2×C4—186no—
829C2×C4—186no—
830C2×C4C22×D3211yescharacteristic
831C2×C4C22×D3213yes—
832C2×C4C22×D3213yes—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—62no—
837C2×C3—66no—
838C2×C3—121no—
839C2×C3C23×D1211yescharacteristic
840C2×C3C22×D3×D411yescharacteristic
841C2×C3C2×#100711yescharacteristic
842C2×C3#596611yescharacteristic
843C2×C3D3×2−1+411yescharacteristic
844C2×C3#596811yescharacteristic
845D3—26no—
846D3—22no—
847D3—41no—
848D3—122no—
849D3—123no—
850D3—121no—
851D3—123no—
852D3—121no—
853D3—243no—
854C22—36no—
855C22—32no—
856C22—61no—
857C22—63no—
858C22—63no—
859C22—61no—
860C22—61no—
861C22—61no—
862C22—61no—
863C22—181no—
864C22—183no—
865C22—181no—
866C22—183no—
867C22—181no—
868C22—183no—
869C22—3612no—
870C22C23×D3211yescharacteristic
871C4—21no—
872C4—23no—
873C4—32no—
874C4—63no—
875C4—63no—
876C4—61no—
877C4—63no—
878C4—181no—
879C4—183no—
880C4C2×D3×D1216yes—
881C3—21no—
882C3#8590111yescharacteristic, complemented
883C3#8674511yescharacteristic, complemented
884C2—62no—
885C2—66no—
886C2—121no—
887C2—363no—
888C2—361no—
889C2C22×D3×D1211yescharacteristic
890C2D3×#100711yescharacteristic
891C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3489
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×D3×#239C2semidirect
2. C2×#64315C2semidirect
3. #10596047C2semidirect
4. C3×Q8×D12C2semidirect
5. C3×#5574C2semidirect
6. Q8×#626C2semidirect
7. #10595342C2semidirect
8. #10594629C2semidirect
9. D3×#897C2semidirect
10. #10594523C2semidirect
11. #10594381C2semidirect
12. #10594003C2semidirect
13. #10593997C2semidirect
14. #10593896C2semidirect
15. #10593893C2semidirect
19. C2×Q8×C3⋊D3C22semidirect
22. C2×C3×D3×Q8C22semidirect
28. C2×#3798C22semidirect
30. C2×#3796C22semidirect
31. C2×#3795C22semidirect
32. C2×D3×Dic6C22semidirect
33. C32×C4×Q8C22semidirect
34. #64106C22semidirect
35. #64104C22semidirect
36. #64084C22semidirect
37. C4×C4⋊(C3⋊D3)C22semidirect
38. C3×Q8×Dic3C22semidirect
40. C3×#897C22semidirect
41. C3×#893C22semidirect
42. C3×D3×C4⋊C4C22semidirect
44. C3×C4×D12C22semidirect
45. C3×#872C22semidirect
46. C3×#869C22semidirect
50. #63910C22semidirect
51. #63909C22semidirect
52. #63909C22semidirect
53. #63906C22semidirect
55. C4×#626C22semidirect
56. #63895C22semidirect
57. #63895C22semidirect
59. #63891C22semidirect
60. #63890C22semidirect
61. #63890C22semidirect
62. #63890C22semidirect
63. D3×C4⋊Dic3C22semidirect
65. #63871C22semidirect
66. #63871C22semidirect
67. #63866C22semidirect
68. #63864C22semidirect
89. Q8×D12D3semidirect
90. #5574D3semidirect
110. C3×#239D4semidirect
184. C2×D3×Q8C2×D3semidirect
202. C3×C4×Q8C2×D3semidirect
203. C3×C4×Q8C2×D3semidirect
212. Q8×Dic3C2×D3semidirect
234. #897C2×D3semidirect
247. #893C2×D3semidirect
249. D3×C4⋊C4C2×D3semidirect
272. C4×D12C2×D3semidirect
273. #872C2×D3semidirect
275. #869C2×D3semidirect
366. #239D12semidirect
489. C2×C3×D32−1+4semidirect
542. C4×Q8D32semidirect
763. C2×D3#1007semidirect
789. C32#3489semidirect
882. C3#85901semidirect
883. C3#86745semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×#643152
#105960472
C3×Q8×D122
C3×#55742
Q8×#6262
#105953422
#105946292
D3×#8972
#105945232
#105943812
#105940032
#105939972
#105938962
#105938932
#867453
#859013