Finite Group Databasebeta

← #11902850

Subgroups — #11902850

Order 1152.

3452 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic, complemented
2C2×D3×#239C211yesmaximal, characteristic, complemented
3#10596305C211yesmaximal, characteristic, complemented
4C3×#5831C211yesmaximal, characteristic, complemented
5Q8×#625C211yesmaximal, characteristic, complemented
6Dic3×#239C211yesmaximal, characteristic, complemented
7#10595342C211yesmaximal, characteristic, complemented
8#10595301C213yesmaximal, complemented
9#10595288C213yesmaximal, complemented
10#10595229C213yesmaximal, complemented
11#10595153C213yesmaximal, complemented
12#10595067C213yesmaximal, complemented
13C4×D3×#67C213yesmaximal, complemented
14#10595005C213yesmaximal, complemented
15#10594890C213yesmaximal, complemented
16#41×#67—31nomaximal
17#86710—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C2×#3832C2211yescharacteristic, complemented
20C3×D3×#41—28no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic, complemented
23C2×C3×D3×Q8C2211yescharacteristic, complemented
24C2×C3×#237C2213yescomplemented
25C2×C3×D3×D4C2213yescomplemented
26C2×C3×#235C2213yescomplemented
27C22×C3×C4×D3C2213yescomplemented
28C2×D3×#67C2213yes—
29D3×#239—28no—
30C2×D3×D12C2213yescomplemented
31C2×C4×D32C2213yescomplemented
32C2×#3799C2213yescomplemented
33C2×#3796C2213yescomplemented
34Q8×C3⋊Dic3C2211yescharacteristic, complemented
35#64149C2213yescomplemented
36#64147C2213yescomplemented
37#64139C2213yescomplemented
38C4×#638C2213yescomplemented
39C3×Q8×Dic3C2211yescharacteristic, complemented
40C3×#938C2213yescomplemented
41C3×#936C2213yescomplemented
42C3×C4×#67C2213yescomplemented
43C3×#924C2213yescomplemented
44#63983C2216yescomplemented
45#63977C2216yescomplemented
46Dic3×#67C2213yescomplemented
47#63971C2216yescomplemented
48#63971C2216yescomplemented
49#63969C2216yescomplemented
50D3×#217C2213yescomplemented
51#63952C2213yescomplemented
52#63952C2216yescomplemented
53D3×(C2×D3)⋊C4C2213yescomplemented
54#63909C2213yescomplemented
55#63904C2213yescomplemented
56C4×#626C2213yescomplemented
57C4×#625C2213yes—
58#63898C2213yescomplemented
59Dic3×D12C2213yescomplemented
60#63879C2211yescharacteristic
61D3×Dic3⋊C4C2213yescomplemented
62C4×D3×Dic3C2213yescomplemented
63#63873C2213yescomplemented
64#63871C2213yescomplemented
65#63864C2213yescomplemented
66#63856C2213yescomplemented
67#63856C2213yescomplemented
68#63850C2216yescomplemented
69#63841C2213yescomplemented
70C22×C3×#41—31no—
71C2×D3×#41—31no—
72C2×D3×#41D311yescharacteristic, complemented
73C22×#239—31no—
74C3×#548—31no—
75#5834—31no—
76#5834—31no—
77#5834—61no—
78#5832—33no—
79#5831D311yescharacteristic, complemented
80#5829—33no—
81#5828—33no—
82Dic3×#41—31no—
83#5824—33no—
84#5817—31no—
85Q8×#67—31no—
86Q8×#67—31no—
87#5806—33no—
88D4×#67—33no—
89#5791—33no—
90C2×C4×#67—33no—
91#5676—33no—
92#5668—33no—
93#5631—33no—
94#5627—33no—
95#5609—33no—
96#5606—33no—
97#5576—31no—
98C4×#239—31no—
99#5550—33no—
100C4×D3×D4—33no—
101C23×C3×D3C2313yes—
102C22×D32C2313yes—
103C32×#41—24no—
104C2×C32×Q8C2311yescharacteristic
105C2×C32×D4C2313yes—
106C22×C32×C4C2313yes—
107C2×#638C2313yes—
108C2×#638C2316yes—
109#3832—24no—
110C2×C4⋊(C3⋊D3)C2313yes—
111C2×C4×C3⋊D3C2313yes—
112C2×C3×#67C2313yes—
113C2×C3×#67C2316yes—
114C22×C3×Dic3C2313yes—
115C3×#239D418yescomplemented
116C3×D3×Q8—24no—
117C3×D3×Q8—24no—
118C3×#237—212no—
119C3×D3×D4—212no—
120C3×#235—212no—
121C2×C3×D12C2313yes—
122C2×C3×C4×D3—212no—
123C2×C3×C4×D3C2313yes—
124C2×C3×C4×D3C2311yescharacteristic
125C2×C3×C4×D3C2313yes—
126C2×C3×C4×D3C2313yes—
127C2×C3×C4×D3C2313yes—
128C2×C3×Dic6C2313yes—
129C2×C3×Dic6C2313yes—
130D3×#67—212no—
131C2×#626C2316yes—
132C2×#626C2313yes—
133C2×#625C2311yescharacteristic
134C2×#624C2313yes—
135C2×D3×Dic3C2313yes—
136C2×D3×Dic3C2311yescharacteristic
137C2×D3×Dic3C2313yes—
138C2×D3×Dic3C2313yes—
139D3×D12—212no—
140C4×D32—212no—
141#3799—212no—
142#3796—212no—
143#3757C2313yes—
144#3752C2313yes—
145C4⋊(C3⋊Dic3)C2313yes—
146#3750C2311yescharacteristic
147C4×C3⋊Dic3C2313yes—
148C3×#217C2316yes—
149C3×#217C2313yes—
150C3×(C2×D3)⋊C4C2311yescharacteristic
151C3×C4⋊Dic3C2313yes—
152C3×Dic3⋊C4C2313yes—
153C3×C4×Dic3C2313yes—
154#3724C2316yes—
155#3724C2313yes—
156Dic3⋊Dic3C2313yes—
157#3722C2316yes—
158#3722C2313yes—
159(C2×D3)⋊Dic3C2316yes—
160(C2×D3)⋊Dic3C2313yes—
161(C2×D3)⋊Dic3C2313yes—
162(C2×D3)⋊Dic3C2311yescharacteristic
163Dic32C2313yes—
164Dic32C2311yescharacteristic
165D4×#41—91noSylow
166C2×C3×#41—21no—
167C2×C3×#41—31no—
168C2×C3×#41—33no—
169C2×C3×#41—33no—
170C2×C3×#41—68no—
171C2×C3×#41C2×D311yescharacteristic, complemented
172C2×C3×#41C2×D311yescharacteristic, complemented
173C22×C3×Q8—31no—
174C22×C3×Q8—31no—
175C22×C3×D4—33no—
176C23×C3×C4—33no—
177C22×#67—33no—
178D3×#41—28no—
179D3×#41—68no—
180C2×#239—31no—
181C2×#239—31no—
182C2×#239—33no—
183C2×#239—33no—
184C2×#239—61no—
185C2×#239—68no—
186C2×#239C2×D311yescharacteristic
187C2×D3×Q8C2×D311yescharacteristic, complemented
188C2×D3×Q8C2×D311yescharacteristic, complemented
189C2×#237—33no—
190C2×#237C2×D313yescomplemented
191C2×D3×D4—33no—
192C2×D3×D4—33no—
193C2×D3×D4C2×D313yescomplemented
194C2×#235—33no—
195C2×#235C2×D313yescomplemented
196C22×D12—33no—
197C22×C4×D3—33no—
198C22×C4×D3—33no—
199C22×C4×D3C2×D313yescomplemented
200C3×#124—33no—
201C3×C22⋊Q8—33no—
202C3×#121—33no—
203C3×C4×Q8—31no—
204C3×C4×D4—33no—
205#953—36no—
206C2×#217—33no—
207#947—33no—
208#946—33no—
209#946—33no—
210#946—33no—
211Q8×Dic3—31no—
212Q8×Dic3—31no—
213Q8×Dic3—61no—
214Q8×Dic3C2×D311yescharacteristic, complemented
215#944—33no—
216#944—33no—
217#940—33no—
218#940—33no—
219#940—63no—
220#939—36no—
221#939—36no—
222#938—33no—
223#938—33no—
224#938—63no—
225#938C2×D313yescomplemented
226#937—36no—
227#937—36no—
228#936C2×D313yescomplemented
229#935—36no—
230D4×Dic3—33no—
231D4×Dic3—33no—
232D4×Dic3—33no—
233#930—33no—
234#930—33no—
235#930—33no—
236#930—63no—
237#929—36no—
238C4×#67—33no—
239C4×#67—33no—
240C4×#67—33no—
241C4×#67—33no—
242C4×#67—33no—
243C4×#67—33no—
244C4×#67—36no—
245C4×#67—31no—
246C4×#67—33no—
247C4×#67—33no—
248C4×#67—63no—
249C4×#67C2×D313yescomplemented
250C2×(C2×D3)⋊C4—33no—
251#926—33no—
252#924—33no—
253#924—33no—
254#924C2×D313yescomplemented
255C2×Dic3⋊C4—33no—
256C2×C4×Dic3—33no—
257#897—33no—
258#895—33no—
259#894—36no—
260#893—33no—
261#893—33no—
262#892—33no—
263D3×C4⋊C4—33no—
264#884—36no—
265#884—36no—
266#883—36no—
267#882—36no—
268#67⋊C4—33no—
269#67⋊C4—36no—
270#67⋊C4—31no—
271D3×C22⋊C4—33no—
272D3×C22⋊C4—33no—
273#875—33no—
274C4×D12—33no—
275C4×D12—33no—
276C42×D3—33no—
277C23×C32C2413yes—
278C22×C3⋊D3C2413yes—
279C22×C3×D3—26no—
280C22×C3×D3—26no—
281C22×C3×D3—43no—
282C22×C3×D3C2413yes—
283C22×C3×D3C2411yescharacteristic
284C22×C3×D3C2411yescharacteristic
285C2×D32—26no—
286C2×D32—26no—
287C2×D32—43no—
288C32×Q8C2×D414yescomplemented
289C32×D4—26no—
290C2×C32×C4—26no—
291C2×C32×C4C2411yescharacteristic
292C2×C32×C4C2413yes—
293#638—26no—
294#638—46no—
295C2×C3⋊Dic3C2413yes—
296C2×C3⋊Dic3C2411yescharacteristic
297C2×C3⋊Dic3C2411yescharacteristic
298C4⋊(C3⋊D3)—26no—
299C4×C3⋊D3—26no—
300C3×#67—212no—
301C3×#67—26no—
302C2×C3×Dic3—26no—
303C2×C3×Dic3C2413yes—
304C2×C3×Dic3C2411yescharacteristic
305C2×C3×Dic3C2413yes—
306C2×C3×Dic3C2413yes—
307C2×C3×Dic3C2411yescharacteristic
308C3×D12C2×D4112yescomplemented
309C3×C4×D3—26no—
310C3×C4×D3—26no—
311C3×C4×D3—26no—
312C3×C4×D3—22no—
313C3×C4×D3C2×D4112yescomplemented
314C3×Dic6—26no—
315C3×Dic6—26no—
316#626—212no—
317#626—26no—
318#625#4114yescomplemented
319#624—26no—
320D3×Dic3—26no—
321D3×Dic3—26no—
322D3×Dic3—22no—
323D3×Dic3—43no—
324C22×#41—31no—
325C22×#41—91no—
326#550—91no—
327D4×Q8—91no—
328#548—31no—
329#548—91no—
330#547—93no—
331#546—93no—
332#546—93no—
333D42—93no—
334#532—93no—
335#525—93no—
336#525—93no—
337C4×#41—91no—
338C2×C4×D4—93no—
339C24×C3—33no—
340C23×D3—33no—
341C23×D3—33no—
342C23×D3C22×D313yes—
343C3×#41—24no—
344C3×#41—24no—
345C3×#41—38no—
346C3×#41—44no—
347C3×#41—612no—
348C3×#41—612no—
349C2×C3×Q8—21no—
350C2×C3×Q8—33no—
351C2×C3×Q8—33no—
352C2×C3×Q8—64no—
353C2×C3×Q8—64no—
354C2×C3×Q8C22×D311yescharacteristic
355C2×C3×Q8C22×D311yescharacteristic
356C2×C3×D4—23no—
357C2×C3×D4—33no—
358C2×C3×D4—36no—
359C2×C3×D4—33no—
360C2×C3×D4—612no—
361C2×C3×D4C22×D313yes—
362C2×C3×D4C22×D313yes—
363C22×C3×C4—23no—
364C22×C3×C4—33no—
365C22×C3×C4—33no—
366C22×C3×C4—33no—
367C22×C3×C4—33no—
368C22×C3×C4—33no—
369C22×C3×C4—31no—
370C22×C3×C4—612no—
371C22×C3×C4C22×D313yes—
372C22×C3×C4C22×D313yes—
373C2×#67—31no—
374C2×#67—31no—
375C2×#67—33no—
376C2×#67—33no—
377C2×#67—36no—
378C2×#67—36no—
379C2×#67—33no—
380C2×#67—36no—
381C2×#67—63no—
382C2×#67—66no—
383C2×#67—612no—
384C2×#67C22×D316yes—
385C2×#67C22×D313yes—
386C22×Dic3—31no—
387C22×Dic3—33no—
388C22×Dic3—33no—
389C22×Dic3—33no—
390C22×Dic3C22×D313yes—
391#239—64no—
392#239—64no—
393#239—612no—
394#239—612no—
395#239—124no—
396#239#6718yescomplemented
397D3×Q8—24no—
398D3×Q8—24no—
399#237—212no—
400#237—612no—
401D3×D4—212no—
402D3×D4—612no—
403D3×D4—612no—
404#235—212no—
405#235—612no—
406C2×D12—33no—
407C2×D12—36no—
408C2×D12—33no—
409C2×D12—33no—
410C2×D12—63no—
411C2×D12—612no—
412C2×D12C22×D313yes—
413C2×C4×D3—212no—
414C2×C4×D3—33no—
415C2×C4×D3—33no—
416C2×C4×D3—31no—
417C2×C4×D3—33no—
418C2×C4×D3—33no—
419C2×C4×D3—33no—
420C2×C4×D3—33no—
421C2×C4×D3—33no—
422C2×C4×D3—63no—
423C2×C4×D3—612no—
424C2×C4×D3—612no—
425C2×C4×D3C22×D313yes—
426C2×C4×D3C22×D313yes—
427C2×C4×D3C22×D311yescharacteristic
428C2×C4×D3C22×D313yes—
429C2×C4×D3C22×D313yes—
430C2×Dic6C22×D313yes—
431C2×Dic6C22×D313yes—
432C3×C4⋊C4—33no—
433C3×C4⋊C4—33no—
434C3×C22⋊C4—33no—
435C3×C22⋊C4—36no—
436C3×C22⋊C4—31no—
437C3×C42—33no—
438#217—33no—
439#217—33no—
440#217—33no—
441#217—33no—
442#217—36no—
443#217—31no—
444#217—63no—
445#217C22×D316yes—
446#217C22×D313yes—
447(C2×D3)⋊C4—31no—
448(C2×D3)⋊C4—36no—
449(C2×D3)⋊C4—33no—
450(C2×D3)⋊C4—33no—
451(C2×D3)⋊C4—33no—
452(C2×D3)⋊C4—33no—
453(C2×D3)⋊C4—33no—
454(C2×D3)⋊C4—36no—
455(C2×D3)⋊C4—33no—
456(C2×D3)⋊C4—36no—
457(C2×D3)⋊C4—63no—
458(C2×D3)⋊C4C22×D311yescharacteristic
459C4⋊Dic3—33no—
460C4⋊Dic3—33no—
461C4⋊Dic3—33no—
462C4⋊Dic3—63no—
463C4⋊Dic3C22×D313yes—
464Dic3⋊C4—31no—
465Dic3⋊C4—31no—
466Dic3⋊C4—36no—
467Dic3⋊C4—33no—
468Dic3⋊C4—33no—
469Dic3⋊C4—33no—
470Dic3⋊C4—36no—
471Dic3⋊C4—61no—
472Dic3⋊C4C22×D313yes—
473C4×Dic3—33no—
474C4×Dic3—33no—
475C4×Dic3—31no—
476C4×Dic3—33no—
477C4×Dic3—31no—
478C4×Dic3—33no—
479C4×Dic3—63no—
480C4×Dic3C22×D313yes—
481C22×C32—23no—
482C22×C32—23no—
483C22×C32—23no—
484C22×C32C2511yescharacteristic
485C2×C3⋊D3—23no—
486C2×C3⋊D3—23no—
487C2×C3⋊D3—23no—
488C2×C3×D3—21no—
489C2×C3×D3—21no—
490C2×C3×D3—23no—
491C2×C3×D3—23no—
492C2×C3×D3—21no—
493C2×C3×D3—21no—
494C2×C3×D3—412no—
495C2×C3×D3C22×D416yes—
496C2×C3×D3C2×#4112yescomplemented
497C2×C3×D3C2×#4112yescomplemented
498D32—412no—
499C32×C4—21no—
500C32×C4C22×D416yes—
501C3⋊Dic3—21no—
502C3⋊Dic3—23no—
503C3⋊Dic3C2×#4112yescomplemented
504C3×Dic3—23no—
505C3×Dic3—23no—
506C3×Dic3—23no—
507C3×Dic3—21no—
508C3×Dic3C22×D412yes—
509C2×#41—31no—
510C2×#41—33no—
511C2×#41—33no—
512C2×#41—68no—
513C2×#41—93no—
514C2×#41—93no—
515C2×#41—91no—
516C2×#41—188no—
517C2×#41D3211yescharacteristic, complemented
518C22×Q8—31no—
519C22×Q8—31no—
520C22×D4—33no—
521C22×D4—93no—
522C22×D4—93no—
523C23×C4—33no—
524C23×C4—93no—
525C4⋊Q8—93no—
526#127—93no—
527#124—33no—
528#124—93no—
529#123—96no—
530#123—96no—
531C22⋊Q8—33no—
532C22⋊Q8—93no—
533C22⋊Q8—93no—
534C22⋊Q8—93no—
535#121—33no—
536#121—96no—
537#121—96no—
538#121—93no—
539#121—93no—
540#121—93no—
541#120—96no—
542#120—96no—
543C4×Q8—31no—
544C4×Q8—91no—
545C4×D4—33no—
546C4×D4—93no—
547C4×D4—93no—
548C4×D4—91no—
549C4×D4—93no—
550C4×D4—96no—
551C4×D4—93no—
552C4×D4—93no—
553C4×D4—93no—
554C4×D4—93no—
555C4×D4—93no—
556#117—93no—
557C2×C4⋊C4—93no—
558C2×C22⋊C4—93no—
559C2×C22⋊C4—93no—
560C2×C42—93no—
561C23×C3—23no—
562C23×C3—31no—
563C23×C3—31no—
564C23×C3—33no—
565C23×C3—66no—
566C23×C3—66no—
567C23×C3—123no—
568C23×C3C23×D313yes—
569C23×C3C23×D313yes—
570C22×D3—26no—
571C22×D3—26no—
572C22×D3—33no—
573C22×D3—33no—
574C22×D3—43no—
575C22×D3—63no—
576C22×D3—66no—
577C22×D3—66no—
578C22×D3—66no—
579C22×D3—66no—
580C22×D3—123no—
581C22×D3—123no—
582C22×D3C23×D311yescharacteristic
583C22×D3C23×D311yescharacteristic
584C22×D3C23×D313yes—
585C3×Q8—24no—
586C3×Q8—66no—
587C3×Q8—66no—
588C3×Q8D3×D414yescomplemented
589C3×Q8C2×#6714yescomplemented
590C3×D4—26no—
591C3×D4—26no—
592C3×D4—312no—
593C3×D4—46no—
594C3×D4—66no—
595C3×D4—612no—
596C2×C3×C4—26no—
597C2×C3×C4—26no—
598C2×C3×C4—23no—
599C2×C3×C4—21no—
600C2×C3×C4—31no—
601C2×C3×C4—312no—
602C2×C3×C4—33no—
603C2×C3×C4—31no—
604C2×C3×C4—33no—
605C2×C3×C4—33no—
606C2×C3×C4—46no—
607C2×C3×C4—62no—
608C2×C3×C4—66no—
609C2×C3×C4—66no—
610C2×C3×C4—66no—
611C2×C3×C4—66no—
612C2×C3×C4C23×D311yescharacteristic
613C2×C3×C4C23×D311yescharacteristic
614C2×C3×C4C23×D313yes—
615C2×C3×C4C23×D313yes—
616#67—26no—
617#67—212no—
618#67—34no—
619#67—34no—
620#67—612no—
621#67—66no—
622#67—66no—
623#67—66no—
624#67—126no—
625#67—126no—
626#67—126no—
627#67—246no—
628C2×Dic3—26no—
629C2×Dic3—31no—
630C2×Dic3—31no—
631C2×Dic3—33no—
632C2×Dic3—33no—
633C2×Dic3—31no—
634C2×Dic3—31no—
635C2×Dic3—61no—
636C2×Dic3—63no—
637C2×Dic3—61no—
638C2×Dic3—66no—
639C2×Dic3—66no—
640C2×Dic3—62no—
641C2×Dic3—123no—
642C2×Dic3C23×D311yescharacteristic
643C2×Dic3C23×D313yes—
644C2×Dic3C23×D313yes—
645C2×Dic3C23×D313yes—
646C2×Dic3C23×D311yescharacteristic
647D12—66no—
648D12—612no—
649D12—66no—
650D12—66no—
651D12—126no—
652D12C2×#67112yescomplemented
653C4×D3—26no—
654C4×D3—26no—
655C4×D3—26no—
656C4×D3—22no—
657C4×D3—66no—
658C4×D3—66no—
659C4×D3—62no—
660C4×D3—66no—
661C4×D3—66no—
662C4×D3—66no—
663C4×D3—66no—
664C4×D3—126no—
665C4×D3—123no—
666C4×D3C2×#67112yescomplemented
667Dic6—26no—
668Dic6—26no—
669C2×C32—43no—
670C2×C32C23×D411yescharacteristic
671C2×C32C22×#4111yescharacteristic
672C2×C32#58511yescharacteristic
673C3⋊D3—43no—
674C3×D3—22no—
675C3×D3—26no—
676C3×D3—22no—
677C24—33no—
678C24—93no—
679#41—24no—
680#41—38no—
681#41—612no—
682#41—612no—
683#41—1812no—
684#41—1812no—
685#41—184no—
686C2×Q8—33no—
687C2×Q8—33no—
688C2×Q8—64no—
689C2×Q8—64no—
690C2×Q8C2×D3211yescharacteristic
691C2×D4—33no—
692C2×D4—36no—
693C2×D4—33no—
694C2×D4—612no—
695C2×D4—93no—
696C2×D4—96no—
697C2×D4—91no—
698C2×D4—93no—
699C2×D4—96no—
700C2×D4—93no—
701C2×D4—1812no—
702C2×D4—1812no—
703C2×D4C2×D3213yes—
704C22×C4—33no—
705C22×C4—33no—
706C22×C4—33no—
707C22×C4—33no—
708C22×C4—31no—
709C22×C4—33no—
710C22×C4—612no—
711C22×C4—93no—
712C22×C4—93no—
713C22×C4—93no—
714C22×C4—91no—
715C22×C4—93no—
716C22×C4—93no—
717C22×C4—1812no—
718C22×C4C2×D3213yes—
719C4⋊C4—33no—
720C4⋊C4—33no—
721C4⋊C4—93no—
722C4⋊C4—93no—
723C4⋊C4—96no—
724C4⋊C4—91no—
725C4⋊C4—93no—
726C22⋊C4—33no—
727C22⋊C4—36no—
728C22⋊C4—31no—
729C22⋊C4—93no—
730C22⋊C4—96no—
731C22⋊C4—91no—
732C22⋊C4—93no—
733C22⋊C4—93no—
734C22⋊C4—96no—
735C22⋊C4—93no—
736C22⋊C4—93no—
737C42—33no—
738C42—91no—
739C42—93no—
740C42—93no—
741C22×C3—23no—
742C22×C3—23no—
743C22×C3—23no—
744C22×C3—23no—
745C22×C3—23no—
746C22×C3—23no—
747C22×C3—21no—
748C22×C3—36no—
749C22×C3—32no—
750C22×C3—32no—
751C22×C3—43no—
752C22×C3—43no—
753C22×C3—43no—
754C22×C3—61no—
755C22×C3—63no—
756C22×C3—61no—
757C22×C3—63no—
758C22×C3—61no—
759C22×C3—61no—
760C22×C3—1212no—
761C22×C3C24×D311yescharacteristic
762C22×C3C24×D311yescharacteristic
763C2×D3—21no—
764C2×D3—23no—
765C2×D3—23no—
766C2×D3—21no—
767C2×D3—21no—
768C2×D3—21no—
769C2×D3—412no—
770C2×D3—63no—
771C2×D3—63no—
772C2×D3—63no—
773C2×D3—63no—
774C2×D3—63no—
775C2×D3—63no—
776C2×D3—123no—
777C2×D3—123no—
778C2×D3—123no—
779C2×D3—1212no—
780C2×D3—1212no—
781C2×D3D3×#4112yescomplemented
782C2×D3D3×#4112yescomplemented
783C2×D3C22×#6716yes—
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—26no—
787C3×C4—32no—
788C3×C4—41no—
789C3×C4—63no—
790C3×C4—63no—
791C3×C4—61no—
792C3×C4—63no—
793C3×C4C2×D3×D416yes—
794C3×C4C22×#6716yes—
795Dic3—23no—
796Dic3—23no—
797Dic3—21no—
798Dic3—23no—
799Dic3—32no—
800Dic3—32no—
801Dic3—62no—
802Dic3—61no—
803Dic3—63no—
804Dic3—63no—
805Dic3—61no—
806Dic3—121no—
807Dic3—123no—
808Dic3C22×#6712yes—
809C32D4×#4111yescharacteristic, complemented, Sylow
810C23—31no—
811C23—31no—
812C23—33no—
813C23—66no—
814C23—66no—
815C23—93no—
816C23—123no—
817C23—186no—
818C23—186no—
819C23—363no—
820C23C22×D3213yes—
821Q8—66no—
822Q8—66no—
823Q8D3×#6714yescomplemented
824D4—26no—
825D4—312no—
826D4—612no—
827D4—66no—
828D4—94no—
829D4—1812no—
830D4—186no—
831D4—186no—
832D4—186no—
833D4—366no—
834C2×C4—26no—
835C2×C4—31no—
836C2×C4—312no—
837C2×C4—31no—
838C2×C4—33no—
839C2×C4—33no—
840C2×C4—33no—
841C2×C4—62no—
842C2×C4—66no—
843C2×C4—66no—
844C2×C4—66no—
845C2×C4—66no—
846C2×C4—91no—
847C2×C4—93no—
848C2×C4—91no—
849C2×C4—186no—
850C2×C4—182no—
851C2×C4—186no—
852C2×C4—186no—
853C2×C4—186no—
854C2×C4—363no—
855C2×C4C22×D3211yescharacteristic
856C2×C4C22×D3213yes—
857C2×C3—21no—
858C2×C3—21no—
859C2×C3—21no—
860C2×C3—43no—
861C2×C3—43no—
862C2×C3—66no—
863C2×C3—62no—
864C2×C3—62no—
865C2×C3—83no—
866C2×C3C22×D3×D411yescharacteristic
867C2×C3C2×D3×#4111yescharacteristic
868C2×C3C2×D3×#4111yescharacteristic
869C2×C3#596411yescharacteristic
870C2×C3#596811yescharacteristic
871C2×C3C23×#6711yescharacteristic
872D3—22no—
873D3—22no—
874D3—26no—
875D3—123no—
876D3—123no—
877D3—243no—
878C22—23no—
879C22—23no—
880C22—23no—
881C22—32no—
882C22—32no—
883C22—36no—
884C22—63no—
885C22—63no—
886C22—61no—
887C22—61no—
888C22—61no—
889C22—61no—
890C22—1212no—
891C22—183no—
892C22—183no—
893C22—183no—
894C22—3612no—
895C22C23×D3211yescharacteristic
896C4—21no—
897C4—32no—
898C4—63no—
899C4—61no—
900C4—63no—
901C4—63no—
902C4—92no—
903C4—183no—
904C4—181no—
905C4C2×D3×#6716yes—
906C3—21no—
907C3#8671011yescharacteristic, complemented
908C3#41×#6711yescharacteristic, complemented
909C2—43no—
910C2—62no—
911C2—66no—
912C2—62no—
913C2—363no—
914C2D32×#4111yescharacteristic
915C2#1059669711yescharacteristic
916C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32D4×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×#41C2semidirect
2. C2×D3×#239C2semidirect
3. #10596305C2semidirect
4. C3×#5831C2semidirect
5. Q8×#625C2semidirect
6. Dic3×#239C2semidirect
7. #10595342C2semidirect
8. #10595301C2semidirect
9. #10595288C2semidirect
10. #10595229C2semidirect
11. #10595153C2semidirect
12. #10595067C2semidirect
13. C4×D3×#67C2semidirect
14. #10595005C2semidirect
15. #10594890C2semidirect
18. C2×C32×#41C22semidirect
19. C2×#3832C22semidirect
22. C2×C3×D3×Q8C22semidirect
23. C2×C3×D3×Q8C22semidirect
24. C2×C3×#237C22semidirect
25. C2×C3×D3×D4C22semidirect
26. C2×C3×#235C22semidirect
27. C22×C3×C4×D3C22semidirect
30. C2×D3×D12C22semidirect
31. C2×C4×D32C22semidirect
32. C2×#3799C22semidirect
33. C2×#3796C22semidirect
34. Q8×C3⋊Dic3C22semidirect
35. #64149C22semidirect
36. #64147C22semidirect
37. #64139C22semidirect
38. C4×#638C22semidirect
39. C3×Q8×Dic3C22semidirect
40. C3×#938C22semidirect
41. C3×#936C22semidirect
42. C3×C4×#67C22semidirect
43. C3×#924C22semidirect
44. #63983C22semidirect
45. #63977C22semidirect
46. Dic3×#67C22semidirect
47. #63971C22semidirect
48. #63971C22semidirect
49. #63969C22semidirect
50. D3×#217C22semidirect
51. #63952C22semidirect
52. #63952C22semidirect
53. D3×(C2×D3)⋊C4C22semidirect
54. #63909C22semidirect
55. #63904C22semidirect
56. C4×#626C22semidirect
58. #63898C22semidirect
59. Dic3×D12C22semidirect
61. D3×Dic3⋊C4C22semidirect
62. C4×D3×Dic3C22semidirect
63. #63873C22semidirect
64. #63871C22semidirect
65. #63864C22semidirect
66. #63856C22semidirect
67. #63856C22semidirect
68. #63850C22semidirect
69. #63841C22semidirect
72. C2×D3×#41D3semidirect
79. #5831D3semidirect
115. C3×#239D4semidirect
171. C2×C3×#41C2×D3semidirect
172. C2×C3×#41C2×D3semidirect
187. C2×D3×Q8C2×D3semidirect
188. C2×D3×Q8C2×D3semidirect
190. C2×#237C2×D3semidirect
193. C2×D3×D4C2×D3semidirect
195. C2×#235C2×D3semidirect
199. C22×C4×D3C2×D3semidirect
214. Q8×Dic3C2×D3semidirect
225. #938C2×D3semidirect
228. #936C2×D3semidirect
249. C4×#67C2×D3semidirect
254. #924C2×D3semidirect
288. C32×Q8C2×D4semidirect
308. C3×D12C2×D4semidirect
313. C3×C4×D3C2×D4semidirect
318. #625#41semidirect
396. #239#67semidirect
496. C2×C3×D3C2×#41semidirect
497. C2×C3×D3C2×#41semidirect
503. C3⋊Dic3C2×#41semidirect
517. C2×#41D32semidirect
588. C3×Q8D3×D4semidirect
589. C3×Q8C2×#67semidirect
652. D12C2×#67semidirect
666. C4×D3C2×#67semidirect
781. C2×D3D3×#41semidirect
782. C2×D3D3×#41semidirect
809. C32D4×#41semidirect
823. Q8D3×#67semidirect
907. C3#86710semidirect
908. C3#41×#67semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×D3×#2392
#105963052
C3×#58312
Q8×#6252
Dic3×#2392
#105953422
#105953012
#105952882
#105952292
#105951532
#105950672
C4×D3×#672
#105950052
#105948902
#41×#673
#867103