Finite Group Databasebeta

← #11904692

Subgroups — #11904692

Order 1152.

3765 conjugacy classes of subgroups.

The subgroup lattice has 935 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64366C211yesmaximal, characteristic, complemented
2C2×D3×#239C211yesmaximal, characteristic, complemented
3C3×#5834C211yesmaximal, characteristic, complemented
4C3×#5831C211yesmaximal, characteristic, complemented
5#10595410C211yesmaximal, characteristic, complemented
6#10595353C211yesmaximal, characteristic, complemented
7#10595342C211yesmaximal, characteristic, complemented
8#10595297C213yesmaximal, complemented
9#10595282C213yesmaximal, complemented
10#10595243C213yesmaximal, complemented
11#10595168C213yesmaximal, complemented
12#10595076C213yesmaximal, complemented
13#10595074C213yesmaximal, complemented
14#10595018C213yesmaximal, complemented
15#10594923C213yesmaximal, complemented
16#86769—31nomaximal
17#86713—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19#64366—28no—
20C2×#3832C2211yescharacteristic
21C2×#3832C2211yescharacteristic, complemented
22C2×D4×C3⋊D3C2213yescomplemented
23C2×D4×C3⋊D3C2213yescomplemented
24C2×#3828C2213yescomplemented
25C22×C4⋊(C3⋊D3)C2213yescomplemented
26C2×C3×#239C2211yescharacteristic, complemented
27C2×C3×D3×Q8C2211yescharacteristic, complemented
28C2×#3811C2216yescomplemented
29D3×#239—28no—
30C2×D3×D12C2213yescomplemented
31C2×C4×D32C2213yescomplemented
32C2×#3799C2213yescomplemented
33C2×#3796C2213yescomplemented
34C3×Q8×Dic3C2211yescharacteristic, complemented
35C3×Q8×Dic3C2211yescharacteristic, complemented
36C3×#940C2213yescomplemented
37C3×#938C2213yescomplemented
38C3×#938C2213yescomplemented
39C3×#936C2213yescomplemented
40C3×#930C2213yescomplemented
41C3×C4×#67C2213yescomplemented
42C3×C4×#67C2213yescomplemented
43C3×#924C2213yescomplemented
44#63983C2213yescomplemented
45#63981C2216yescomplemented
46#63981C2216yescomplemented
47#63975C2213yescomplemented
48#63974C2216yescomplemented
49#63971C2213yescomplemented
50#63971C2213yescomplemented
51#63971C2216yescomplemented
52#63958C2216yescomplemented
53#63923C2213yescomplemented
54#63916C2213yescomplemented
55#63911C2213yescomplemented
56#63910C2216yescomplemented
57#63909C2213yescomplemented
58#63909C2213yescomplemented
59C4×#626C2213yescomplemented
60C4×#626C2213yescomplemented
61#63900C2213yescomplemented
62#63897C2213yescomplemented
63#63896C2211yescharacteristic, complemented
64#63896C2213yescomplemented
65#63894C2213yescomplemented
66#63894C2213yescomplemented
67#63874C2213yescomplemented
68#63871C2213yescomplemented
69#63864C2213yescomplemented
70C2×#1009—31no—
71C2×#1009—31no—
72C2×#1009—61no—
73C2×D3×#41—31no—
74C22×#239—31no—
75C3×#550—31no—
76C3×#548—31no—
77#5834—31no—
78#5834D311yescharacteristic, complemented
79#5831D311yescharacteristic, complemented
80#5817—31no—
81#5717—33no—
82#5715—33no—
83#5676—33no—
84#5674—33no—
85#5630—33no—
86#5629—33no—
87#5612—33no—
88#5609—33no—
89#5609—33no—
90#5608—33no—
91D3×#121—33no—
92D3×#121—33no—
93#5577—31no—
94#5576—31no—
95#5574—31no—
96#5574—31no—
97#5550—33no—
98D4×D12—33no—
99#5547—33no—
100#5547—33no—
101C23×C3⋊D3C2316yes—
102C22×D32C2313yes—
103C32×#41—24no—
104C2×C32×Q8C2311yescharacteristic
105C2×C32×D4C2313yes—
106C22×C32×C4C2313yes—
107C2×#638C2313yes—
108C2×#638C2313yes—
109#3832—24no—
110#3832D418yescomplemented
111D4×C3⋊D3—212no—
112D4×C3⋊D3—212no—
113#3828—212no—
114C2×C4⋊(C3⋊D3)—212no—
115C2×C4⋊(C3⋊D3)C2313yes—
116C2×C4⋊(C3⋊D3)C2313yes—
117C2×C4⋊(C3⋊D3)C2313yes—
118C2×C4×C3⋊D3C2313yes—
119C2×C4×C3⋊D3C2313yes—
120C2×#634C2311yescharacteristic
121C2×C3×#67C2313yes—
122C2×C3×#67C2313yes—
123C2×C3×#67C2316yes—
124C3×#239—24no—
125C3×D3×Q8—24no—
126C2×C3×D12C2313yes—
127C2×C3×C4×D3C2313yes—
128C2×C3×C4×D3C2313yes—
129C2×C3×Dic6C2313yes—
130#3811—412no—
131C2×#626C2316yes—
132C2×#626C2313yes—
133C2×#626C2316yes—
134C2×#626C2313yes—
135C2×#624C2313yes—
136C2×#624C2316yes—
137C2×D3×Dic3C2313yes—
138C2×D3×Dic3C2311yescharacteristic
139D3×D12—212no—
140C4×D32—212no—
141#3799—212no—
142#3796—212no—
143C3×#217C2316yes—
144C3×#217C2313yes—
145C3×#217C2313yes—
146C3×(C2×D3)⋊C4C2311yescharacteristic
147C3×(C2×D3)⋊C4C2313yes—
148C3×C4⋊Dic3C2313yes—
149C3×C4⋊Dic3C2313yes—
150C3×Dic3⋊C4C2313yes—
151C3×Dic3⋊C4C2311yescharacteristic
152C3×C4×Dic3C2313yes—
153C3×C4×Dic3C2313yes—
154#3724C2311yescharacteristic
155#3724C2313yes—
156Dic3⋊Dic3C2313yes—
157Dic3⋊Dic3C2311yescharacteristic
158#3722C2313yes—
159#3722C2316yes—
160#3722C2313yes—
161#3722C2313yes—
162#3722C2313yes—
163(C2×D3)⋊Dic3C2311yescharacteristic
164(C2×D3)⋊Dic3C2313yes—
165#3488—91noSylow
166C2×C3×#41—21no—
167C2×C3×#41—31no—
168C2×C3×#41C2×D311yescharacteristic, complemented
169C2×C3×#41C2×D311yescharacteristic, complemented
170C22×C3×Q8—31no—
171#1009—68no—
172#1009—68no—
173#1009—616no—
174D3×#41—68no—
175C2×#239—31no—
176C2×#239—31no—
177C2×#239—31no—
178C2×#239—31no—
179C2×#239—33no—
180C2×#239—33no—
181C2×#239—61no—
182C2×#239—61no—
183C2×#239—68no—
184C2×#239C2×D311yescharacteristic, complemented
185C2×D3×Q8C2×D311yescharacteristic, complemented
186C2×#237—33no—
187C2×D3×D4—33no—
188C2×D3×D4—33no—
189C2×D3×D4—33no—
190C2×D3×D4—33no—
191C2×D3×D4—36no—
192C2×D3×D4—36no—
193C2×D3×D4—33no—
194C2×D3×D4—63no—
195C2×D3×D4—63no—
196C2×#235—33no—
197C2×#235—33no—
198C2×#235—33no—
199C2×#235—63no—
200C22×D12—33no—
201C22×D12—33no—
202C22×D12—33no—
203C22×D12—63no—
204C22×C4×D3—33no—
205C22×C4×D3—33no—
206C3×#127—33no—
207C3×#124—33no—
208C3×C22⋊Q8—33no—
209C3×#121—33no—
210C3×#121—33no—
211C3×#121—33no—
212C3×C4×Q8—31no—
213C3×C4×Q8—31no—
214C3×C4×D4—33no—
215C3×C4×D4—33no—
216#947—33no—
217#946—33no—
218Q8×Dic3C2×D311yescharacteristic, complemented
219Q8×Dic3C2×D311yescharacteristic, complemented
220#940—33no—
221#940C2×D313yescomplemented
222#939—33no—
223#939—36no—
224#939—33no—
225#938—36no—
226#938—33no—
227#938C2×D313yescomplemented
228#938C2×D313yescomplemented
229#937—33no—
230#937—33no—
231#937—36no—
232#937—36no—
233#936C2×D313yescomplemented
234#930—33no—
235#930—33no—
236#930C2×D313yescomplemented
237C4×#67—33no—
238C4×#67—33no—
239C4×#67C2×D313yescomplemented
240C4×#67C2×D313yescomplemented
241#924C2×D313yescomplemented
242#897—33no—
243#896—31no—
244#896—33no—
245#895—33no—
246#895—33no—
247#895—33no—
248#895—36no—
249#894—33no—
250#894—33no—
251#893—33no—
252#893—33no—
253D3×C4⋊C4—33no—
254D3×C4⋊C4—33no—
255#884—33no—
256#884—36no—
257#884—36no—
258#884—33no—
259#884—36no—
260#883—33no—
261#883—33no—
262#882—36no—
263#882—36no—
264#882—33no—
265#882—33no—
266D3×C22⋊C4—36no—
267D3×C22⋊C4—36no—
268#878—31no—
269#878—33no—
270#875—33no—
271#874—33no—
272C4×D12—33no—
273C4×D12—33no—
274C4×D12—33no—
275C4×D12—33no—
276#872—33no—
277#872—33no—
278C23×C32C2413yes—
279C22×C3⋊D3—212no—
280C22×C3⋊D3—46no—
281C22×C3⋊D3—46no—
282C22×C3⋊D3C2413yes—
283C22×C3⋊D3C2413yes—
284C22×C3×D3C2413yes—
285C22×C3×D3C2411yescharacteristic
286C2×D32—26no—
287C2×D32—26no—
288C2×D32—43no—
289C32×Q8C2×D414yescomplemented
290C32×D4—26no—
291C2×C32×C4—26no—
292C2×C32×C4C2411yescharacteristic
293C2×C32×C4C2413yes—
294#638—26no—
295#638—26no—
296C2×C3⋊Dic3C2411yescharacteristic
297C2×C3⋊Dic3C2411yescharacteristic
298C4⋊(C3⋊D3)—26no—
299C4⋊(C3⋊D3)—26no—
300C4⋊(C3⋊D3)C2×D4112yescomplemented
301C4×C3⋊D3—26no—
302C4×C3⋊D3C2×D4112yescomplemented
303#634—22no—
304C3×#67—26no—
305C3×#67—46no—
306C3×#67—43no—
307C2×C3×Dic3C2411yescharacteristic
308C2×C3×Dic3C2413yes—
309C2×C3×Dic3C2411yescharacteristic
310C2×C3×Dic3C2413yes—
311C2×C3×Dic3C2411yescharacteristic
312C2×C3×Dic3C2413yes—
313C3×D12—26no—
314C3×C4×D3—26no—
315C3×C4×D3—26no—
316C3×Dic6—26no—
317#626—212no—
318#626—26no—
319#626—43no—
320#626—46no—
321#624—26no—
322#624—46no—
323D3×Dic3—26no—
324D3×Dic3—22no—
325C2×H(5,𝔽2)—91no—
326C22×#41—91no—
327#550—31no—
328#550—91no—
329#548—31no—
330#548—91no—
331#546—93no—
332#546—93no—
333D42—93no—
334D42—93no—
335#537—93no—
336#535—93no—
337#525—93no—
338C2×#121—93no—
339#520—91no—
340C23×D3—36no—
341C23×D3—36no—
342C23×D3—33no—
343C23×D3—33no—
344C23×D3—66no—
345C3×#41—28no—
346C3×#41—24no—
347C3×#41—24no—
348C3×#41—64no—
349C2×C3×Q8—21no—
350C2×C3×Q8—33no—
351C2×C3×Q8—64no—
352C2×C3×Q8C22×D311yescharacteristic
353C2×C3×Q8C22×D311yescharacteristic
354C2×C3×D4—23no—
355C2×C3×D4—33no—
356C2×C3×D4—33no—
357C2×C3×D4—36no—
358C2×C3×D4—33no—
359C2×C3×D4C22×D313yes—
360C2×C3×D4C22×D313yes—
361C22×C3×C4—23no—
362C22×C3×C4—33no—
363C22×C3×C4—33no—
364C22×C3×C4C22×D313yes—
365C22×C3×C4C22×D313yes—
366C2×#67—33no—
367C2×#67—33no—
368C2×#67—33no—
369C2×#67—33no—
370C2×#67—33no—
371C2×#67—36no—
372C2×#67—33no—
373C2×#67—36no—
374C2×#67—63no—
375C2×#67—63no—
376C2×#67C22×D313yes—
377C2×#67C22×D313yes—
378C2×#67C22×D316yes—
379C22×Dic3—31no—
380C22×Dic3—33no—
381#239—24no—
382#239—38no—
383#239—38no—
384#239—68no—
385#239—612no—
386#239—612no—
387#239—68no—
388#239—64no—
389#239—64no—
390D3×Q8—24no—
391#237—612no—
392D3×D4—612no—
393D3×D4—612no—
394D3×D4—612no—
395D3×D4—612no—
396D3×D4—612no—
397D3×D4—624no—
398D3×D4—624no—
399D3×D4—1212no—
400D3×D4—1212no—
401#235—612no—
402#235—612no—
403#235—612no—
404#235—624no—
405C2×D12—33no—
406C2×D12—33no—
407C2×D12—33no—
408C2×D12—36no—
409C2×D12—33no—
410C2×D12—33no—
411C2×D12—33no—
412C2×D12—33no—
413C2×D12—33no—
414C2×D12—36no—
415C2×D12—63no—
416C2×D12—63no—
417C2×D12—63no—
418C2×D12—612no—
419C2×D12—612no—
420C2×D12—612no—
421C2×D12—624no—
422C2×D12C22×D313yes—
423C2×C4×D3—33no—
424C2×C4×D3—33no—
425C2×C4×D3—31no—
426C2×C4×D3—33no—
427C2×C4×D3—33no—
428C2×C4×D3—33no—
429C2×C4×D3—33no—
430C2×C4×D3—33no—
431C2×C4×D3—36no—
432C2×C4×D3—36no—
433C2×C4×D3—63no—
434C2×C4×D3—63no—
435C2×C4×D3—612no—
436C2×C4×D3—612no—
437C2×C4×D3C22×D313yes—
438C2×C4×D3C22×D313yes—
439C2×Dic6—31no—
440C2×Dic6—31no—
441C2×Dic6—61no—
442C2×Dic6C22×D313yes—
443C3×C4⋊C4—33no—
444C3×C4⋊C4—33no—
445C3×C4⋊C4—31no—
446C3×C4⋊C4—33no—
447C3×C22⋊C4—33no—
448C3×C22⋊C4—36no—
449C3×C22⋊C4—33no—
450C3×C22⋊C4—31no—
451C3×C22⋊C4—33no—
452C3×C42—33no—
453C3×C42—33no—
454#217—31no—
455#217—33no—
456#217C22×D313yes—
457#217C22×D316yes—
458#217C22×D313yes—
459(C2×D3)⋊C4—31no—
460(C2×D3)⋊C4—33no—
461(C2×D3)⋊C4—33no—
462(C2×D3)⋊C4—33no—
463(C2×D3)⋊C4—33no—
464(C2×D3)⋊C4—33no—
465(C2×D3)⋊C4—33no—
466(C2×D3)⋊C4—33no—
467(C2×D3)⋊C4—36no—
468(C2×D3)⋊C4—33no—
469(C2×D3)⋊C4—36no—
470(C2×D3)⋊C4—33no—
471(C2×D3)⋊C4C22×D311yescharacteristic
472(C2×D3)⋊C4C22×D313yes—
473C4⋊Dic3—31no—
474C4⋊Dic3—33no—
475C4⋊Dic3C22×D313yes—
476C4⋊Dic3C22×D313yes—
477Dic3⋊C4—31no—
478Dic3⋊C4—31no—
479Dic3⋊C4—33no—
480Dic3⋊C4—33no—
481Dic3⋊C4—31no—
482Dic3⋊C4—33no—
483Dic3⋊C4C22×D313yes—
484Dic3⋊C4C22×D311yescharacteristic
485C4×Dic3C22×D313yes—
486C4×Dic3C22×D313yes—
487C22×C32—23no—
488C22×C32—23no—
489C22×C32—23no—
490C22×C32C2511yescharacteristic
491C2×C3⋊D3—23no—
492C2×C3⋊D3—23no—
493C2×C3⋊D3—23no—
494C2×C3⋊D3—23no—
495C2×C3⋊D3—23no—
496C2×C3⋊D3—812no—
497C2×C3⋊D3C22×D416yes—
498C2×C3×D3—21no—
499C2×C3×D3—21no—
500C2×C3×D3—23no—
501C2×C3×D3—23no—
502C2×C3×D3—23no—
503C2×C3×D3H(5,𝔽2)12yescomplemented
504D32—412no—
505C32×C4—21no—
506C32×C4C22×D416yes—
507C3⋊Dic3—21no—
508C3⋊Dic3C22×D412yes—
509C3×Dic3—21no—
510C3×Dic3—23no—
511C3×Dic3—23no—
512C3×Dic3—23no—
513C3×Dic3—21no—
514C3×Dic3—21no—
515H(5,𝔽2)—188no—
516C2×#41—31no—
517C2×#41—93no—
518C2×#41—93no—
519C2×#41—91no—
520C2×#41—91no—
521C2×#41—93no—
522C2×#41—188no—
523C2×#41D3211yescharacteristic, complemented
524C22×Q8—31no—
525C22×D4—93no—
526C22×D4—96no—
527C22×D4—93no—
528C22×D4—93no—
529C22×D4—93no—
530C23×C4—93no—
531#127—33no—
532#127—93no—
533#124—33no—
534#124—93no—
535#123—93no—
536#123—93no—
537C22⋊Q8—33no—
538C22⋊Q8—91no—
539C22⋊Q8—93no—
540C22⋊Q8—93no—
541#121—33no—
542#121—33no—
543#121—33no—
544#121—96no—
545#121—93no—
546#121—96no—
547#121—93no—
548#121—96no—
549#121—93no—
550#121—93no—
551#121—93no—
552#120—93no—
553#120—96no—
554#120—96no—
555#120—93no—
556C4×Q8—31no—
557C4×Q8—31no—
558C4×D4—33no—
559C4×D4—33no—
560C4×D4—93no—
561C4×D4—93no—
562C4×D4—93no—
563C4×D4—93no—
564#117—93no—
565C2×C4⋊C4—93no—
566C2×C22⋊C4—96no—
567C23×C3—23no—
568C23×C3—31no—
569C23×C3—33no—
570C23×C3C23×D313yes—
571C23×C3C23×D313yes—
572C22×D3—33no—
573C22×D3—33no—
574C22×D3—33no—
575C22×D3—33no—
576C22×D3—63no—
577C22×D3—63no—
578C22×D3—66no—
579C22×D3—66no—
580C22×D3—66no—
581C22×D3—612no—
582C22×D3—612no—
583C22×D3—624no—
584C22×D3—66no—
585C22×D3—123no—
586C22×D3—123no—
587C22×D3—126no—
588C22×D3—126no—
589C22×D3—126no—
590C22×D3—126no—
591C22×D3—246no—
592C22×D3—246no—
593C22×D3C23×D313yes—
594C22×D3C23×D311yescharacteristic
595C3×Q8—24no—
596C3×Q8—66no—
597C3×Q8D3×D414yescomplemented
598C3×Q8D3×D414yescomplemented
599C3×D4—212no—
600C3×D4—26no—
601C3×D4—26no—
602C3×D4—66no—
603C3×D4—66no—
604C3×D4—126no—
605C3×D4—123no—
606C2×C3×C4—212no—
607C2×C3×C4—26no—
608C2×C3×C4—26no—
609C2×C3×C4—21no—
610C2×C3×C4—23no—
611C2×C3×C4—31no—
612C2×C3×C4—33no—
613C2×C3×C4—31no—
614C2×C3×C4—33no—
615C2×C3×C4—31no—
616C2×C3×C4—33no—
617C2×C3×C4—66no—
618C2×C3×C4—66no—
619C2×C3×C4C23×D311yescharacteristic
620C2×C3×C4C23×D311yescharacteristic
621C2×C3×C4C23×D313yes—
622C2×C3×C4C23×D313yes—
623#67—26no—
624#67—46no—
625#67—43no—
626#67—612no—
627#67—66no—
628#67—66no—
629#67—66no—
630#67—66no—
631#67—66no—
632#67—612no—
633#67—612no—
634#67—126no—
635#67—123no—
636C2×Dic3—31no—
637C2×Dic3—31no—
638C2×Dic3—31no—
639C2×Dic3—31no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—62no—
643C2×Dic3—66no—
644C2×Dic3C23×D311yescharacteristic
645C2×Dic3C23×D311yescharacteristic
646C2×Dic3C23×D313yes—
647C2×Dic3C23×D313yes—
648C2×Dic3C23×D313yes—
649C2×Dic3C23×D311yescharacteristic
650D12—26no—
651D12—312no—
652D12—312no—
653D12—612no—
654D12—66no—
655D12—66no—
656D12—612no—
657D12—612no—
658D12—612no—
659D12—66no—
660D12—66no—
661D12—66no—
662D12—123no—
663D12—126no—
664C4×D3—26no—
665C4×D3—26no—
666C4×D3—312no—
667C4×D3—312no—
668C4×D3—612no—
669C4×D3—66no—
670C4×D3—66no—
671C4×D3—62no—
672C4×D3—66no—
673C4×D3—612no—
674C4×D3—66no—
675C4×D3—66no—
676C4×D3—126no—
677C4×D3—126no—
678Dic6—26no—
679Dic6—62no—
680Dic6—62no—
681Dic6—64no—
682C2×C32—43no—
683C2×C32C23×D411yescharacteristic
684C2×C32C2×H(5,𝔽2)11yescharacteristic
685C2×C32#58511yescharacteristic
686C3⋊D3—26no—
687C3⋊D3—43no—
688C3×D3—22no—
689C3×D3—43no—
690C24—93no—
691C24—96no—
692#41—24no—
693#41—64no—
694#41—98no—
695#41—1812no—
696#41—1812no—
697#41—1812no—
698#41—184no—
699C2×Q8—33no—
700C2×Q8—64no—
701C2×Q8—91no—
702C2×Q8C2×D3211yescharacteristic
703C2×D4—33no—
704C2×D4—33no—
705C2×D4—36no—
706C2×D4—33no—
707C2×D4—93no—
708C2×D4—96no—
709C2×D4—93no—
710C2×D4—96no—
711C2×D4—93no—
712C2×D4—93no—
713C2×D4—93no—
714C2×D4—93no—
715C2×D4—93no—
716C2×D4—1812no—
717C2×D4—1812no—
718C2×D4—1812no—
719C2×D4—1812no—
720C2×D4—3612no—
721C2×D4C2×D3213yes—
722C22×C4—33no—
723C22×C4—33no—
724C22×C4—93no—
725C22×C4—96no—
726C22×C4—91no—
727C22×C4—93no—
728C22×C4—93no—
729C22×C4—93no—
730C22×C4—1812no—
731C22×C4C2×D3213yes—
732C4⋊C4—33no—
733C4⋊C4—33no—
734C4⋊C4—31no—
735C4⋊C4—33no—
736C4⋊C4—93no—
737C4⋊C4—91no—
738C4⋊C4—91no—
739C4⋊C4—93no—
740C22⋊C4—33no—
741C22⋊C4—36no—
742C22⋊C4—33no—
743C22⋊C4—31no—
744C22⋊C4—33no—
745C22⋊C4—93no—
746C22⋊C4—96no—
747C22⋊C4—93no—
748C22⋊C4—93no—
749C22⋊C4—93no—
750C22⋊C4—91no—
751C22⋊C4—93no—
752C42—33no—
753C42—33no—
754C22×C3—26no—
755C22×C3—23no—
756C22×C3—23no—
757C22×C3—23no—
758C22×C3—23no—
759C22×C3—23no—
760C22×C3—23no—
761C22×C3—21no—
762C22×C3—32no—
763C22×C3—43no—
764C22×C3—43no—
765C22×C3—61no—
766C22×C3—61no—
767C22×C3—63no—
768C22×C3—63no—
769C22×C3—63no—
770C22×C3C24×D311yescharacteristic
771C22×C3C24×D311yescharacteristic
772C2×D3—21no—
773C2×D3—21no—
774C2×D3—23no—
775C2×D3—23no—
776C2×D3—23no—
777C2×D3—36no—
778C2×D3—36no—
779C2×D3—66no—
780C2×D3—63no—
781C2×D3—63no—
782C2×D3—63no—
783C2×D3—63no—
784C2×D3—66no—
785C2×D3—63no—
786C2×D3—63no—
787C2×D3—63no—
788C2×D3—63no—
789C2×D3—63no—
790C2×D3—63no—
791C2×D3—123no—
792C2×D3—123no—
793C2×D3—123no—
794C2×D3—123no—
795C2×D3—1212no—
796C2×D3—1212no—
797C2×D3—2412no—
798C2×D3—2412no—
799C2×D3—2424no—
800C2×D3#100912yescomplemented
801C3×C4—22no—
802C3×C4—21no—
803C3×C4—21no—
804C3×C4—26no—
805C3×C4—61no—
806C3×C4—63no—
807C3×C4—63no—
808C3×C4—61no—
809C3×C4—63no—
810C3×C4—61no—
811C3×C4C2×D3×D416yes—
812C3×C4C2×D3×D416yes—
813Dic3—23no—
814Dic3—21no—
815Dic3—23no—
816Dic3—21no—
817Dic3—23no—
818Dic3—21no—
819Dic3—32no—
820Dic3—32no—
821Dic3—62no—
822Dic3—62no—
823Dic3—61no—
824Dic3—61no—
825C32#348811yescharacteristic, complemented, Sylow
826C23—31no—
827C23—33no—
828C23—93no—
829C23—93no—
830C23—1812no—
831C23—186no—
832C23—186no—
833C23—366no—
834C23—366no—
835C23—363no—
836C23C22×D3213yes—
837Q8—66no—
838Q8—182no—
839Q8#381114yescomplemented
840D4—26no—
841D4—66no—
842D4—66no—
843D4—912no—
844D4—126no—
845D4—123no—
846D4—186no—
847D4—186no—
848D4—1812no—
849D4—186no—
850D4—186no—
851D4—186no—
852D4—366no—
853D4—363no—
854C2×C4—26no—
855C2×C4—31no—
856C2×C4—31no—
857C2×C4—33no—
858C2×C4—33no—
859C2×C4—31no—
860C2×C4—33no—
861C2×C4—66no—
862C2×C4—66no—
863C2×C4—91no—
864C2×C4—912no—
865C2×C4—91no—
866C2×C4—186no—
867C2×C4—182no—
868C2×C4—186no—
869C2×C4—186no—
870C2×C4—366no—
871C2×C4C22×D3211yescharacteristic
872C2×C4C22×D3213yes—
873C2×C3—21no—
874C2×C3—21no—
875C2×C3—21no—
876C2×C3—46no—
877C2×C3—43no—
878C2×C3—43no—
879C2×C3—62no—
880C2×C3—123no—
881C2×C3C22×D3×D411yescharacteristic
882C2×C3C22×D3×D411yescharacteristic
883C2×C3C2×#100911yescharacteristic
884C2×C3#596411yescharacteristic
885C2×C3D3×H(5,𝔽2)11yescharacteristic
886C2×C3#596811yescharacteristic
887D3—22no—
888D3—43no—
889D3—66no—
890D3—66no—
891D3—126no—
892D3—126no—
893D3—123no—
894D3—123no—
895C22—23no—
896C22—23no—
897C22—23no—
898C22—32no—
899C22—61no—
900C22—61no—
901C22—63no—
902C22—63no—
903C22—63no—
904C22—96no—
905C22—183no—
906C22—183no—
907C22—183no—
908C22—183no—
909C22—183no—
910C22—3612no—
911C22—7212no—
912C22C23×D3211yescharacteristic
913C4—21no—
914C4—63no—
915C4—63no—
916C4—61no—
917C4—61no—
918C4—61no—
919C4—63no—
920C4—92no—
921C4—181no—
922C4C2×#381116yes—
923C3—21no—
924C3#8671311yescharacteristic, complemented
925C3#8676911yescharacteristic, complemented
926C2—43no—
927C2—62no—
928C2—123no—
929C2—186no—
930C2—363no—
931C2D3×#100911yescharacteristic
932C2#1059669711yescharacteristic
933C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3488
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64366C2semidirect
2. C2×D3×#239C2semidirect
3. C3×#5834C2semidirect
4. C3×#5831C2semidirect
5. #10595410C2semidirect
6. #10595353C2semidirect
7. #10595342C2semidirect
8. #10595297C2semidirect
9. #10595282C2semidirect
10. #10595243C2semidirect
11. #10595168C2semidirect
12. #10595076C2semidirect
13. #10595074C2semidirect
14. #10595018C2semidirect
15. #10594923C2semidirect
18. C2×C32×#41C22semidirect
21. C2×#3832C22semidirect
22. C2×D4×C3⋊D3C22semidirect
23. C2×D4×C3⋊D3C22semidirect
24. C2×#3828C22semidirect
25. C22×C4⋊(C3⋊D3)C22semidirect
26. C2×C3×#239C22semidirect
27. C2×C3×D3×Q8C22semidirect
28. C2×#3811C22semidirect
30. C2×D3×D12C22semidirect
31. C2×C4×D32C22semidirect
32. C2×#3799C22semidirect
33. C2×#3796C22semidirect
34. C3×Q8×Dic3C22semidirect
35. C3×Q8×Dic3C22semidirect
36. C3×#940C22semidirect
37. C3×#938C22semidirect
38. C3×#938C22semidirect
39. C3×#936C22semidirect
40. C3×#930C22semidirect
41. C3×C4×#67C22semidirect
42. C3×C4×#67C22semidirect
43. C3×#924C22semidirect
44. #63983C22semidirect
45. #63981C22semidirect
46. #63981C22semidirect
47. #63975C22semidirect
48. #63974C22semidirect
49. #63971C22semidirect
50. #63971C22semidirect
51. #63971C22semidirect
52. #63958C22semidirect
53. #63923C22semidirect
54. #63916C22semidirect
55. #63911C22semidirect
56. #63910C22semidirect
57. #63909C22semidirect
58. #63909C22semidirect
59. C4×#626C22semidirect
60. C4×#626C22semidirect
61. #63900C22semidirect
62. #63897C22semidirect
63. #63896C22semidirect
64. #63896C22semidirect
65. #63894C22semidirect
66. #63894C22semidirect
67. #63874C22semidirect
68. #63871C22semidirect
69. #63864C22semidirect
78. #5834D3semidirect
79. #5831D3semidirect
110. #3832D4semidirect
168. C2×C3×#41C2×D3semidirect
169. C2×C3×#41C2×D3semidirect
184. C2×#239C2×D3semidirect
185. C2×D3×Q8C2×D3semidirect
218. Q8×Dic3C2×D3semidirect
219. Q8×Dic3C2×D3semidirect
221. #940C2×D3semidirect
227. #938C2×D3semidirect
228. #938C2×D3semidirect
233. #936C2×D3semidirect
236. #930C2×D3semidirect
239. C4×#67C2×D3semidirect
240. C4×#67C2×D3semidirect
241. #924C2×D3semidirect
289. C32×Q8C2×D4semidirect
300. C4⋊(C3⋊D3)C2×D4semidirect
302. C4×C3⋊D3C2×D4semidirect
503. C2×C3×D3H(5,𝔽2)semidirect
523. C2×#41D32semidirect
597. C3×Q8D3×D4semidirect
598. C3×Q8D3×D4semidirect
800. C2×D3#1009semidirect
825. C32#3488semidirect
839. Q8#3811semidirect
924. C3#86713semidirect
925. C3#86769semidirect

Maximal subgroups

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

subgroupindex
C2×#643662
C2×D3×#2392
C3×#58342
C3×#58312
#105954102
#105953532
#105953422
#105952972
#105952822
#105952432
#105951682
#105950762
#105950742
#105950182
#105949232
#867693
#867133