Finite Group Databasebeta

← #11904818

Subgroups — #11904818

Order 1152.

3191 conjugacy classes of subgroups.

The subgroup lattice has 887 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C211yesmaximal, characteristic, complemented
2C2×#64316C211yesmaximal, characteristic, complemented
3#10596045C211yesmaximal, characteristic, complemented
4C3×#5576C211yesmaximal, characteristic, complemented
5C3×Q8×D12C211yesmaximal, characteristic, complemented
6#10595409C211yesmaximal, characteristic, complemented
7Q8×#625C211yesmaximal, characteristic, complemented
8#10594633C213yesmaximal, complemented
9#10594631C213yesmaximal, complemented
10#10594530C213yesmaximal, complemented
11#10594528C213yesmaximal, complemented
12#10594007C213yesmaximal, complemented
13#10594006C213yesmaximal, complemented
14#10593908C213yesmaximal, complemented
15#10593869C213yesmaximal, complemented
16#86745—31nomaximal
17#86714—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×C3×#239C2211yescharacteristic
20C2×C3×D3×Q8C2211yescharacteristic
21C2×C3×D3×Q8C2211yescharacteristic, complemented
22C2×C3×D3×Q8C2211yescharacteristic, complemented
23D3×#239—28no—
24#64316—28no—
25C2×D3×D12C2213yes—
26C2×C4×D32C2213yes—
27C2×#3799C2213yes—
28C2×#3799C2213yescomplemented
29C2×#3799C2213yescomplemented
30C2×#3798C2213yescomplemented
31C2×#3797C2213yescomplemented
32C2×#3796C2213yes—
33C32×C4×Q8C2211yescharacteristic, complemented
34Q8×C3⋊Dic3C2211yescharacteristic, complemented
35#64102C2213yescomplemented
36C4⋊C4×C3⋊D3C2213yescomplemented
37C4×C4⋊(C3⋊D3)C2213yescomplemented
38#64081C2213yescomplemented
39C3×#897C2213yes—
40C3×#897C2213yescomplemented
41C3×#897C2213yescomplemented
42C3×#895C2213yescomplemented
43C3×#875C2213yescomplemented
44C3×C4×D12C2213yes—
45C3×C4×D12C2213yescomplemented
46C3×#869C2213yescomplemented
47#63922C2213yes—
48#63922C2213yes—
49#63921C2216yes—
50#63916C2216yescomplemented
51#63912C2216yescomplemented
52#63908C2213yescomplemented
53C4×#625C2213yes—
54C4×#625C2213yescomplemented
55#63900C2216yescomplemented
56#63899C2213yes—
57#63899C2216yescomplemented
58#63899C2213yescomplemented
59#63885C2211yescharacteristic
60#63885C2213yescomplemented
61#63873C2213yescomplemented
62#63863C2213yescomplemented
63#63856C2213yes—
64#63856C2213yescomplemented
65#63856C2213yescomplemented
66#63854C2216yescomplemented
67#63854C2213yescomplemented
68#63854C2216yescomplemented
69#63854C2213yescomplemented
70C2×D3×#41—31no—
71C2×#1007—31no—
72C2×#1007—31no—
73C22×#239—31no—
74C3×D4×Q8—31no—
75C3×#548—31no—
76#5831—31no—
77#5817—31no—
78Q8×#67—31no—
79Q8×#67—31no—
80#5726—33no—
81#5724—33no—
82#5676—33no—
83#5675—33no—
84#5631—33no—
85#5631—33no—
86#5630—33no—
87#5629—33no—
88D3×C22⋊Q8—33no—
89D3×C22⋊Q8—33no—
90#5612—33no—
91#5608—33no—
92#5576D311yescharacteristic, complemented
93Q8×D12D311yescharacteristic, complemented
94#5574—31no—
95#5574—31no—
96#5574—61no—
97#5551—33no—
98#5550—33no—
99#5547—33no—
100#5547—33no—
101C22×D32C2313yes—
102C2×C32×Q8C2311yescharacteristic
103#3832D418yescomplemented
104C2×C4⋊(C3⋊D3)C2313yes—
105C2×C4×C3⋊D3C2316yes—
106C2×C4×C3⋊D3C2313yes—
107C3×#239—24no—
108C3×D3×Q8—24no—
109C3×D3×Q8—24no—
110C3×D3×Q8—24no—
111C2×C3×D12C2313yes—
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2313yes—
114C2×C3×C4×D3C2313yes—
115C2×C3×C4×D3C2313yes—
116C2×C3×C4×D3C2313yes—
117C2×C3×C4×D3C2313yes—
118C2×C3×Dic6C2313yes—
119C2×C3×Dic6C2313yes—
120C2×C3×Dic6C2313yes—
121C2×#627C2313yes—
122C2×#626C2316yes—
123C2×#626C2313yes—
124C2×#626C2313yes—
125C2×#625C2311yescharacteristic
126C2×#625C2311yescharacteristic
127C2×#625C2313yes—
128C2×#624C2316yes—
129C2×#624C2313yes—
130C2×D3×Dic3C2313yes—
131C2×D3×Dic3C2311yescharacteristic
132D3×D12—212no—
133C4×D32—212no—
134#3799—212no—
135#3799—212no—
136#3799—212no—
137#3798—212no—
138#3797—212no—
139#3796—212no—
140C32×C4⋊C4C2313yes—
141C32×C42C2313yes—
142#3752C2313yes—
143#3752C2313yes—
144C4⋊(C3⋊Dic3)C2313yes—
145#3750C2311yescharacteristic
146#3750C2313yes—
147C4×C3⋊Dic3C2313yes—
148C3×(C2×D3)⋊C4C2316yes—
149C3×(C2×D3)⋊C4C2313yes—
150C3×(C2×D3)⋊C4C2313yes—
151C3×(C2×D3)⋊C4C2311yescharacteristic
152C3×(C2×D3)⋊C4C2313yes—
153C3×C4⋊Dic3C2316yes—
154C3×C4⋊Dic3C2313yes—
155C3×C4⋊Dic3C2313yes—
156#3724C2313yes—
157#3724C2316yes—
158#3724C2313yes—
159(C2×D3)⋊Dic3C2311yescharacteristic
160(C2×D3)⋊Dic3C2313yes—
161(C2×D3)⋊Dic3C2313yes—
162(C2×D3)⋊Dic3C2316yes—
163(C2×D3)⋊Dic3C2313yes—
164#3489—91noSylow
165C2×C3×#41—31no—
166C22×C3×Q8—31no—
167C22×C3×Q8—31no—
168C22×C3×Q8—31no—
169D3×#41—68no—
170#1007—68no—
171#1007—68no—
172C2×#239—31no—
173C2×#239—31no—
174C2×#239—33no—
175C2×#239—33no—
176C2×#239—33no—
177C2×#239—33no—
178C2×#239—61no—
179C2×#239—68no—
180C2×#239C2×D311yescharacteristic
181C2×D3×Q8—33no—
182C2×D3×Q8—33no—
183C2×D3×Q8C2×D311yescharacteristic
184C2×D3×Q8C2×D311yescharacteristic, complemented
185C2×D3×Q8C2×D311yescharacteristic, complemented
186C2×#237—33no—
187C2×D3×D4—33no—
188C2×#235—33no—
189C2×#235—33no—
190C2×#235—33no—
191C2×#235—33no—
192C2×#235—33no—
193C22×D12—33no—
194C22×C4×D3—33no—
195C22×C4×D3—33no—
196C3×C4⋊Q8—33no—
197C3×#124—33no—
198C3×C22⋊Q8—33no—
199C3×C22⋊Q8—33no—
200C3×C22⋊Q8—33no—
201C3×#121—33no—
202C3×C4×Q8—21no—
203C3×C4×Q8C2×D311yescharacteristic, complemented
204C3×C4×Q8C2×D311yescharacteristic, complemented
205C3×C4×D4—33no—
206C3×C4×D4—33no—
207#947—33no—
208#946—33no—
209#946—33no—
210#946—33no—
211Q8×Dic3—31no—
212Q8×Dic3—31no—
213Q8×Dic3—61no—
214#944—33no—
215#944—33no—
216#939—31no—
217#939—33no—
218#938—33no—
219#938—36no—
220#937—33no—
221#937—33no—
222#936—33no—
223#930—33no—
224C4×#67—33no—
225C4×#67—33no—
226C4×#67—33no—
227C4×#67—33no—
228#924—33no—
229#924—33no—
230#924—33no—
231#897C2×D313yes—
232#897C2×D313yescomplemented
233#897C2×D313yescomplemented
234#896—33no—
235#896—36no—
236#896—33no—
237#895—36no—
238#895C2×D313yescomplemented
239#894—36no—
240#894—36no—
241#894—33no—
242#894—33no—
243#893—33no—
244#893—33no—
245#893—63no—
246D3×C4⋊C4—33no—
247D3×C4⋊C4—33no—
248D3×C4⋊C4—36no—
249D3×C4⋊C4—36no—
250D3×C4⋊C4—63no—
251#884—31no—
252#884—33no—
253#884—36no—
254#884—36no—
255#883—36no—
256#883—36no—
257#883—33no—
258#883—33no—
259#882—33no—
260#882—33no—
261D3×C22⋊C4—36no—
262D3×C22⋊C4—36no—
263#878—33no—
264#878—36no—
265#878—33no—
266#875C2×D313yescomplemented
267C4×D12—33no—
268C4×D12—33no—
269C4×D12—63no—
270C4×D12C2×D313yes—
271C4×D12C2×D313yescomplemented
272#872—33no—
273#872—33no—
274#872—63no—
275#869C2×D313yescomplemented
276C22×C3⋊D3C2413yes—
277C22×C3×D3C2413yes—
278C22×C3×D3C2411yescharacteristic
279C22×C3×D3C2411yescharacteristic
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—
290C2×C3⋊Dic3C2411yescharacteristic
291C4⋊(C3⋊D3)C2×D4112yes—
292C4×C3⋊D3—46no—
293C4×C3⋊D3C2×D4112yes—
294C2×C3×Dic3C2413yes—
295C2×C3×Dic3C2411yescharacteristic
296C2×C3×Dic3C2413yes—
297C2×C3×Dic3C2413yes—
298C3×D12—22no—
299C3×D12—26no—
300C3×D12—43no—
301C3×C4×D3—26no—
302C3×C4×D3—26no—
303C3×C4×D3—26no—
304C3×C4×D3—26no—
305C3×Dic6—26no—
306C3×Dic6—26no—
307C3×Dic6—26no—
308#627—26no—
309#626—212no—
310#626—26no—
311#626—26no—
312#625—22no—
313#625—22no—
314#625—43no—
315#624—212no—
316#624—26no—
317D3×Dic3—26no—
318D3×Dic3—22no—
319C2×2−1+4—91no—
320C22×#41—91no—
321D4×Q8—31no—
322D4×Q8—91no—
323#548—31no—
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—91no—
334C23×D3—33no—
335C23×D3—33no—
336C3×#41—64no—
337C2×C3×Q8—21no—
338C2×C3×Q8—33no—
339C2×C3×Q8—33no—
340C2×C3×Q8—33no—
341C2×C3×Q8—64no—
342C2×C3×Q8—64no—
343C2×C3×Q8—64no—
344C2×C3×Q8C22×D311yescharacteristic
345C2×C3×Q8C22×D311yescharacteristic
346C2×C3×D4—33no—
347C2×C3×D4—31no—
348C2×C3×D4—33no—
349C22×C3×C4—33no—
350C22×C3×C4—33no—
351C22×C3×C4—33no—
352C22×C3×C4—33no—
353C2×#67—31no—
354C2×#67—31no—
355C2×#67—31no—
356C2×#67—31no—
357C2×#67—33no—
358C2×#67—33no—
359C2×#67—36no—
360C2×#67—33no—
361C2×#67—33no—
362C22×Dic3—31no—
363C22×Dic3—33no—
364#239—24no—
365#239—38no—
366#239—38no—
367#239—68no—
368#239—612no—
369#239—612no—
370#239—612no—
371#239—612no—
372D3×Q8—24no—
373D3×Q8—24no—
374D3×Q8—24no—
375D3×Q8—612no—
376D3×Q8—612no—
377#237—612no—
378D3×D4—612no—
379#235—612no—
380#235—612no—
381#235—612no—
382#235—612no—
383#235—612no—
384C2×D12—33no—
385C2×D12—33no—
386C2×D12—33no—
387C2×D12—33no—
388C2×D12—36no—
389C2×D12—63no—
390C2×D12—612no—
391C2×D12C22×D311yescharacteristic
392C2×D12C22×D313yes—
393C2×D12C22×D313yes—
394C2×C4×D3—33no—
395C2×C4×D3—33no—
396C2×C4×D3—31no—
397C2×C4×D3—33no—
398C2×C4×D3—36no—
399C2×C4×D3—36no—
400C2×C4×D3—33no—
401C2×C4×D3—33no—
402C2×C4×D3—36no—
403C2×C4×D3—36no—
404C2×C4×D3—63no—
405C2×C4×D3—66no—
406C2×C4×D3—612no—
407C2×C4×D3—612no—
408C2×C4×D3C22×D313yes—
409C2×C4×D3C22×D313yes—
410C2×C4×D3C22×D313yes—
411C2×C4×D3C22×D313yes—
412C2×Dic6—33no—
413C2×Dic6—33no—
414C2×Dic6C22×D313yes—
415C2×Dic6C22×D313yes—
416C2×Dic6C22×D313yes—
417C3×C4⋊C4—23no—
418C3×C4⋊C4—33no—
419C3×C4⋊C4—36no—
420C3×C4⋊C4—33no—
421C3×C4⋊C4C22×D313yes—
422C3×C4⋊C4C22×D313yes—
423C3×C22⋊C4—33no—
424C3×C22⋊C4—36no—
425C3×C22⋊C4—33no—
426C3×C22⋊C4—31no—
427C3×C22⋊C4—33no—
428C3×C42—23no—
429C3×C42C22×D313yes—
430C3×C42C22×D313yes—
431#217—33no—
432#217—36no—
433#217—33no—
434#217—31no—
435#217—33no—
436(C2×D3)⋊C4—33no—
437(C2×D3)⋊C4—36no—
438(C2×D3)⋊C4—33no—
439(C2×D3)⋊C4—31no—
440(C2×D3)⋊C4—33no—
441(C2×D3)⋊C4—33no—
442(C2×D3)⋊C4—33no—
443(C2×D3)⋊C4—33no—
444(C2×D3)⋊C4—33no—
445(C2×D3)⋊C4—63no—
446(C2×D3)⋊C4—63no—
447(C2×D3)⋊C4C22×D313yes—
448(C2×D3)⋊C4C22×D313yes—
449(C2×D3)⋊C4C22×D311yescharacteristic
450(C2×D3)⋊C4C22×D313yes—
451(C2×D3)⋊C4C22×D316yes—
452C4⋊Dic3—33no—
453C4⋊Dic3—33no—
454C4⋊Dic3—63no—
455C4⋊Dic3C22×D313yes—
456C4⋊Dic3C22×D316yes—
457C4⋊Dic3C22×D313yes—
458Dic3⋊C4—31no—
459Dic3⋊C4—31no—
460Dic3⋊C4—33no—
461Dic3⋊C4—33no—
462Dic3⋊C4—33no—
463Dic3⋊C4—36no—
464Dic3⋊C4—33no—
465Dic3⋊C4—33no—
466Dic3⋊C4—33no—
467Dic3⋊C4—36no—
468Dic3⋊C4—61no—
469Dic3⋊C4—63no—
470C4×Dic3—33no—
471C4×Dic3—33no—
472C4×Dic3—63no—
473C22×C32C2511yescharacteristic
474C2×C3⋊D3—23no—
475C2×C3⋊D3—23no—
476C2×C3⋊D3C22×D416yes—
477C2×C3×D3—21no—
478C2×C3×D3—21no—
479C2×C3×D3—23no—
480C2×C3×D3—21no—
481C2×C3×D3—21no—
482C2×C3×D3—21no—
483C2×C3×D3—21no—
484C2×C3×D3—23no—
485C2×C3×D3—21no—
486C2×C3×D3—23no—
487C2×C3×D3—21no—
488C2×C3×D32−1+412yescomplemented
489D32—412no—
490C32×C4—21no—
491C32×C4—23no—
492C32×C4C22×D416yes—
493C3⋊Dic3—21no—
494C3⋊Dic3—23no—
495C3⋊Dic3C22×D412yes—
496C3×Dic3—21no—
497C3×Dic3—23no—
498C3×Dic3—23no—
499C3×Dic3—23no—
5002−1+4—188no—
501C2×#41—31no—
502C2×#41—93no—
503C2×#41—93no—
504C2×#41—93no—
505C2×#41—93no—
506C2×#41—93no—
507C2×#41—91no—
508C2×#41—188no—
509C22×Q8—31no—
510C22×Q8—31no—
511C22×Q8—31no—
512C22×Q8—93no—
513C22×D4—93no—
514C23×C4—93no—
515C4⋊Q8—33no—
516C4⋊Q8—93no—
517#124—33no—
518#124—93no—
519#123—93no—
520#123—93no—
521#123—96no—
522#123—96no—
523C22⋊Q8—33no—
524C22⋊Q8—33no—
525C22⋊Q8—33no—
526C22⋊Q8—93no—
527C22⋊Q8—96no—
528C22⋊Q8—93no—
529C22⋊Q8—93no—
530C22⋊Q8—93no—
531C22⋊Q8—93no—
532#121—33no—
533#121—96no—
534#121—91no—
535#121—93no—
536#121—96no—
537#121—93no—
538#120—93no—
539#120—93no—
540C4×Q8—91no—
541C4×Q8D3211yescharacteristic, complemented
542C4×D4—33no—
543C4×D4—33no—
544C4×D4—93no—
545C4×D4—93no—
546C4×D4—93no—
547C4×D4—93no—
548#117—93no—
549C2×C4⋊C4—96no—
550C2×C4⋊C4—93no—
551C2×C22⋊C4—96no—
552C23×C3—31no—
553C23×C3—33no—
554C23×C3—31no—
555C23×C3—31no—
556C22×D3—33no—
557C22×D3—33no—
558C22×D3—63no—
559C22×D3—66no—
560C22×D3—66no—
561C22×D3—66no—
562C22×D3—66no—
563C22×D3—123no—
564C22×D3—123no—
565C22×D3C23×D313yes—
566C22×D3C23×D311yescharacteristic
567C22×D3C23×D311yescharacteristic
568C22×D3C23×D311yescharacteristic
569C3×Q8—24no—
570C3×Q8—66no—
571C3×Q8—66no—
572C3×Q8—66no—
573C3×Q8D3×D414yes—
574C3×Q8D3×D414yes—
575C3×D4—62no—
576C3×D4—66no—
577C3×D4—123no—
578C2×C3×C4—23no—
579C2×C3×C4—21no—
580C2×C3×C4—23no—
581C2×C3×C4—33no—
582C2×C3×C4—31no—
583C2×C3×C4—33no—
584C2×C3×C4—33no—
585C2×C3×C4—66no—
586C2×C3×C4—66no—
587C2×C3×C4—66no—
588C2×C3×C4—66no—
589C2×C3×C4C23×D311yescharacteristic
590C2×C3×C4C23×D313yes—
591C2×C3×C4C23×D313yes—
592C2×C3×C4C23×D311yescharacteristic
593C2×C3×C4C23×D313yes—
594C2×C3×C4C23×D313yes—
595#67—66no—
596#67—66no—
597#67—612no—
598#67—62no—
599#67—62no—
600#67—62no—
601#67—62no—
602#67—123no—
603#67—123no—
604C2×Dic3—31no—
605C2×Dic3—31no—
606C2×Dic3—31no—
607C2×Dic3—31no—
608C2×Dic3—33no—
609C2×Dic3—33no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—63no—
613C2×Dic3—62no—
614C2×Dic3—66no—
615C2×Dic3C23×D313yes—
616C2×Dic3C23×D311yescharacteristic
617C2×Dic3C23×D313yes—
618C2×Dic3C23×D313yes—
619D12—22no—
620D12—26no—
621D12—312no—
622D12—312no—
623D12—43no—
624D12—612no—
625D12—612no—
626D12—66no—
627D12—66no—
628C4×D3—26no—
629C4×D3—26no—
630C4×D3—26no—
631C4×D3—26no—
632C4×D3—312no—
633C4×D3—312no—
634C4×D3—612no—
635C4×D3—66no—
636C4×D3—66no—
637C4×D3—612no—
638C4×D3—612no—
639C4×D3—62no—
640C4×D3—66no—
641C4×D3—126no—
642C4×D3—126no—
643C4×D3—246no—
644Dic6—26no—
645Dic6—26no—
646Dic6—26no—
647Dic6—66no—
648Dic6—66no—
649C2×C32C23×D411yescharacteristic
650C2×C32C2×2−1+411yescharacteristic
651C2×C32#58511yescharacteristic
652C3⋊D3—26no—
653C3×D3—22no—
654C3×D3—43no—
655C3×D3—41no—
656C3×D3—41no—
657C24—93no—
658#41—64no—
659#41—98no—
660#41—1812no—
661#41—1812no—
662#41—1812no—
663#41—1812no—
664#41—1812no—
665C2×Q8—33no—
666C2×Q8—33no—
667C2×Q8—33no—
668C2×Q8—64no—
669C2×Q8—64no—
670C2×Q8—64no—
671C2×Q8—93no—
672C2×Q8—1812no—
673C2×Q8C2×D3211yescharacteristic
674C2×D4—31no—
675C2×D4—33no—
676C2×D4—33no—
677C2×D4—93no—
678C2×D4—93no—
679C2×D4—96no—
680C2×D4—91no—
681C2×D4—91no—
682C2×D4—93no—
683C2×D4—93no—
684C2×D4—1812no—
685C22×C4—33no—
686C22×C4—33no—
687C22×C4—33no—
688C22×C4—33no—
689C22×C4—96no—
690C22×C4—93no—
691C22×C4—91no—
692C22×C4—93no—
693C22×C4—93no—
694C22×C4—96no—
695C22×C4—1812no—
696C4⋊C4—33no—
697C4⋊C4—36no—
698C4⋊C4—33no—
699C4⋊C4—93no—
700C4⋊C4—96no—
701C4⋊C4—93no—
702C4⋊C4—93no—
703C4⋊C4—93no—
704C4⋊C4—91no—
705C4⋊C4C2×D3213yes—
706C22⋊C4—33no—
707C22⋊C4—36no—
708C22⋊C4—31no—
709C22⋊C4—33no—
710C22⋊C4—33no—
711C22⋊C4—93no—
712C22⋊C4—96no—
713C22⋊C4—91no—
714C22⋊C4—93no—
715C22⋊C4—93no—
716C22⋊C4—93no—
717C22⋊C4—93no—
718C42—93no—
719C42C2×D3213yes—
720C22×C3—21no—
721C22×C3—32no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—63no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—63no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—63no—
732C22×C3—61no—
733C22×C3C24×D311yescharacteristic
734C22×C3C24×D311yescharacteristic
735C2×D3—21no—
736C2×D3—21no—
737C2×D3—21no—
738C2×D3—21no—
739C2×D3—23no—
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—23no—
743C2×D3—21no—
744C2×D3—23no—
745C2×D3—21no—
746C2×D3—36no—
747C2×D3—36no—
748C2×D3—66no—
749C2×D3—63no—
750C2×D3—63no—
751C2×D3—63no—
752C2×D3—63no—
753C2×D3—123no—
754C2×D3—123no—
755C2×D3—1212no—
756C2×D3—1212no—
757C2×D3#100712yescomplemented
758C3×C4—21no—
759C3×C4—23no—
760C3×C4—21no—
761C3×C4—23no—
762C3×C4—26no—
763C3×C4—43no—
764C3×C4—41no—
765C3×C4—63no—
766C3×C4—63no—
767C3×C4—61no—
768C3×C4—63no—
769C3×C4C2×D3×D416yes—
770C3×C4C2×D3×D416yes—
771Dic3—23no—
772Dic3—23no—
773Dic3—23no—
774Dic3—21no—
775Dic3—32no—
776Dic3—32no—
777Dic3—62no—
778Dic3—61no—
779Dic3—63no—
780Dic3—61no—
781Dic3—63no—
782Dic3—123no—
783Dic3—121no—
784C32#348911yescharacteristic, complemented, Sylow
785C23—31no—
786C23—33no—
787C23—31no—
788C23—31no—
789C23—93no—
790C23—186no—
791C23—186no—
792C23—363no—
793Q8—66no—
794Q8—66no—
795Q8—66no—
796Q8—186no—
797Q8#380214yes—
798D4—62no—
799D4—66no—
800D4—912no—
801D4—123no—
802D4—1812no—
803D4—186no—
804D4—186no—
805D4—182no—
806D4—182no—
807D4—363no—
808C2×C4—33no—
809C2×C4—33no—
810C2×C4—31no—
811C2×C4—33no—
812C2×C4—66no—
813C2×C4—66no—
814C2×C4—66no—
815C2×C4—66no—
816C2×C4—91no—
817C2×C4—912no—
818C2×C4—91no—
819C2×C4—93no—
820C2×C4—186no—
821C2×C4—1812no—
822C2×C4—182no—
823C2×C4—186no—
824C2×C4—366no—
825C2×C4C22×D3211yescharacteristic
826C2×C4C22×D3213yes—
827C2×C4C22×D3213yes—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—62no—
832C2×C3—121no—
833C2×C3—123no—
834C2×C3—121no—
835C2×C3C22×D3×D411yescharacteristic
836C2×C3C22×D3×D411yescharacteristic
837C2×C3C2×#100711yescharacteristic
838C2×C3#596411yescharacteristic
839C2×C3D3×2−1+411yescharacteristic
840C2×C3#596811yescharacteristic
841D3—22no—
842D3—43no—
843D3—41no—
844D3—41no—
845D3—66no—
846D3—66no—
847D3—126no—
848C22—32no—
849C22—61no—
850C22—61no—
851C22—61no—
852C22—61no—
853C22—63no—
854C22—61no—
855C22—61no—
856C22—63no—
857C22—61no—
858C22—63no—
859C22—61no—
860C22—96no—
861C22—183no—
862C22—183no—
863C22—3612no—
864C22C23×D3211yescharacteristic
865C4—21no—
866C4—23no—
867C4—61no—
868C4—63no—
869C4—63no—
870C4—63no—
871C4—92no—
872C4—181no—
873C4—183no—
874C4C2×#380216yes—
875C3—21no—
876C3#8671411yescharacteristic, complemented
877C3#8674511yescharacteristic, complemented
878C2—62no—
879C2—123no—
880C2—121no—
881C2—121no—
882C2—186no—
883C2C22×#380211yescharacteristic
884C2D3×#100711yescharacteristic
885C2#1059669711yescharacteristic
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×#64316C2semidirect
3. #10596045C2semidirect
4. C3×#5576C2semidirect
5. C3×Q8×D12C2semidirect
6. #10595409C2semidirect
7. Q8×#625C2semidirect
8. #10594633C2semidirect
9. #10594631C2semidirect
10. #10594530C2semidirect
11. #10594528C2semidirect
12. #10594007C2semidirect
13. #10594006C2semidirect
14. #10593908C2semidirect
15. #10593869C2semidirect
21. C2×C3×D3×Q8C22semidirect
22. C2×C3×D3×Q8C22semidirect
28. C2×#3799C22semidirect
29. C2×#3799C22semidirect
30. C2×#3798C22semidirect
31. C2×#3797C22semidirect
33. C32×C4×Q8C22semidirect
34. Q8×C3⋊Dic3C22semidirect
35. #64102C22semidirect
36. C4⋊C4×C3⋊D3C22semidirect
37. C4×C4⋊(C3⋊D3)C22semidirect
38. #64081C22semidirect
40. C3×#897C22semidirect
41. C3×#897C22semidirect
42. C3×#895C22semidirect
43. C3×#875C22semidirect
45. C3×C4×D12C22semidirect
46. C3×#869C22semidirect
50. #63916C22semidirect
51. #63912C22semidirect
52. #63908C22semidirect
54. C4×#625C22semidirect
55. #63900C22semidirect
57. #63899C22semidirect
58. #63899C22semidirect
60. #63885C22semidirect
61. #63873C22semidirect
62. #63863C22semidirect
64. #63856C22semidirect
65. #63856C22semidirect
66. #63854C22semidirect
67. #63854C22semidirect
68. #63854C22semidirect
69. #63854C22semidirect
92. #5576D3semidirect
93. Q8×D12D3semidirect
103. #3832D4semidirect
184. C2×D3×Q8C2×D3semidirect
185. C2×D3×Q8C2×D3semidirect
203. C3×C4×Q8C2×D3semidirect
204. C3×C4×Q8C2×D3semidirect
232. #897C2×D3semidirect
233. #897C2×D3semidirect
238. #895C2×D3semidirect
266. #875C2×D3semidirect
271. C4×D12C2×D3semidirect
275. #869C2×D3semidirect
488. C2×C3×D32−1+4semidirect
541. C4×Q8D32semidirect
757. C2×D3#1007semidirect
784. C32#3489semidirect
876. C3#86714semidirect
877. 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×#643162
#105960452
C3×#55762
C3×Q8×D122
#105954092
Q8×#6252
#105946332
#105946312
#105945302
#105945282
#105940072
#105940062
#105939082
#105938692
#867453
#867143