Finite Group Databasebeta

← #11904697

Subgroups — #11904697

Order 1152.

3472 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×#64320C211yesmaximal, characteristic, complemented
3#10596305C211yesmaximal, characteristic, complemented
4C3×#5834C211yesmaximal, characteristic, complemented
5#10595409C211yesmaximal, characteristic, complemented
6#10595394C211yesmaximal, characteristic, complemented
7#10595342C211yesmaximal, characteristic, complemented
8#10595303C213yesmaximal, complemented
9#10595293C213yesmaximal, complemented
10#10595288C213yesmaximal, complemented
11#10595232C213yesmaximal, complemented
12#10595070C213yesmaximal, complemented
13#10595067C213yesmaximal, complemented
14D3×#930C213yesmaximal, complemented
15#10595002C213yesmaximal, complemented
16#87275—31nomaximal
17#86769—31nomaximal
18C2×C32×#41C2211yescharacteristic, complemented
19C2×#3832C2211yescharacteristic, complemented
20C3×D3×#41—28no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×#239C2211yescharacteristic, complemented
23C2×C3×D3×Q8C2211yescharacteristic, complemented
24C2×C3×#237C2213yescomplemented
25C2×C3×D3×D4C2213yescomplemented
26C2×C3×#235C2213yescomplemented
27C22×C3×C4×D3C2213yescomplemented
28C2×D3×#67C2216yescomplemented
29#64320—28no—
30C2×#3802C2213yescomplemented
31C2×D3×D12C2213yescomplemented
32C2×D3×D12C2213yescomplemented
33C2×#3798C2213yescomplemented
34Q8×C3⋊Dic3C2211yescharacteristic, complemented
35#64149C2213yescomplemented
36#64147C2213yescomplemented
37#64139C2213yescomplemented
38C4×#638C2213yescomplemented
39C3×Q8×Dic3C2211yescharacteristic, complemented
40C3×#940C2213yescomplemented
41C3×#938C2213yescomplemented
42C3×#930C2213yescomplemented
43C3×C4×#67C2213yescomplemented
44#63983C2216yescomplemented
45#63983C2216yescomplemented
46#63978C2216yescomplemented
47#63978C2213yescomplemented
48#63977C2213yescomplemented
49#63976C2213yescomplemented
50#63971C2216yescomplemented
51#63970C2216yescomplemented
52#63964C2213yescomplemented
53D3×(C2×D3)⋊C4C2216yescomplemented
54#63909C2213yescomplemented
55#63908C2213yescomplemented
56#63906C2213yescomplemented
57#63905C2213yescomplemented
58C4×#626C2213yescomplemented
59C4×#625C2213yescomplemented
60#63898C2213yescomplemented
61Dic3×D12C2213yescomplemented
62D3×C4⋊Dic3C2213yescomplemented
63#63871C2213yescomplemented
64#63864C2213yescomplemented
65#63863C2213yescomplemented
66#63856C2213yescomplemented
67#63855C2213yescomplemented
68#63851C2211yescharacteristic, complemented
69#63850C2213yescomplemented
70C22×C3×#41—31no—
71C2×#1009—31no—
72C2×#1009—31no—
73C2×D3×#41D311yescharacteristic, complemented
74C3×#550—31no—
75#5834—31no—
76#5834—31no—
77#5834—61no—
78#5834D311yescharacteristic, complemented
79#5833—33no—
80#5831—31no—
81#5830—33no—
82#5829—33no—
83#5829—33no—
84#5827—31no—
85#5817—31no—
86#5817—31no—
87D4×#67—33no—
88D4×#67—33no—
89#5791—33no—
90C2×#930—33no—
91#5717—33no—
92#5715—33no—
93#5612—33no—
94#5609—33no—
95#5608—33no—
96D3×#121—33no—
97#5576—31no—
98#5574—31no—
99#5550—33no—
100#5547—33no—
101C23×C3×D3C2313yes—
102C22×D32C2316yes—
103C32×#41—24no—
104C2×C32×Q8C2311yescharacteristic
105C2×C32×D4C2313yes—
106C22×C32×C4C2313yes—
107C2×#638C2316yes—
108C2×#638C2313yes—
109#3832—24no—
110C2×C4⋊(C3⋊D3)C2313yes—
111C2×C4×C3⋊D3C2313yes—
112C2×C3×#67C2316yes—
113C2×C3×#67C2313yes—
114C2×C3×#67C2316yes—
115C22×C3×Dic3C2313yes—
116C3×#239—24no—
117C3×#239D418yescomplemented
118C3×D3×Q8—24no—
119C3×#237—212no—
120C3×D3×D4—212no—
121C3×#235—212no—
122C2×C3×D12C2313yes—
123C2×C3×D12C2313yes—
124C2×C3×C4×D3—212no—
125C2×C3×C4×D3C2313yes—
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×C4×D3C2313yes—
128C2×C3×C4×D3C2313yes—
129C2×C3×C4×D3C2313yes—
130C2×C3×Dic6C2313yes—
131D3×#67—412no—
132C2×#627C2311yescharacteristic
133C2×#626C2313yes—
134C2×#626C2313yes—
135C2×#626C2313yes—
136C2×#625C2313yes—
137C2×#625C2313yes—
138C2×D3×Dic3C2316yes—
139#3802—212no—
140D3×D12—212no—
141D3×D12—212no—
142#3798—212no—
143#3757C2313yes—
144#3752C2313yes—
145C4⋊(C3⋊Dic3)C2313yes—
146#3750C2311yescharacteristic
147C4×C3⋊Dic3C2313yes—
148C3×#217C2313yes—
149C3×(C2×D3)⋊C4C2313yes—
150C3×C4⋊Dic3C2313yes—
151C3×Dic3⋊C4C2311yescharacteristic
152C3×C4×Dic3C2313yes—
153#3724C2313yes—
154Dic3⋊Dic3C2311yescharacteristic
155Dic3⋊Dic3C2313yes—
156Dic3⋊Dic3C2313yes—
157#3722C2313yes—
158#3722C2316yes—
159(C2×D3)⋊Dic3C2313yes—
160(C2×D3)⋊Dic3C2311yescharacteristic
161(C2×D3)⋊Dic3C2311yescharacteristic
162(C2×D3)⋊Dic3C2313yes—
163(C2×D3)⋊Dic3C2316yes—
164(C2×D3)⋊Dic3C2313yes—
165#3488—91noSylow
166C2×C3×#41—21no—
167C2×C3×#41—31no—
168C2×C3×#41—31no—
169C2×C3×#41—33no—
170C2×C3×#41—33no—
171C2×C3×#41—68no—
172C2×C3×#41C2×D311yescharacteristic, complemented
173C2×C3×#41C2×D311yescharacteristic, complemented
174C22×C3×Q8—31no—
175C22×C3×D4—33no—
176C23×C3×C4—33no—
177C22×#67—36no—
178#1009—68no—
179#1009—68no—
180D3×#41—28no—
181C2×#239—31no—
182C2×#239—31no—
183C2×#239—61no—
184C2×#239C2×D311yescharacteristic
185C2×#239C2×D311yescharacteristic, complemented
186C2×D3×Q8C2×D311yescharacteristic, complemented
187C2×#237C2×D313yescomplemented
188C2×D3×D4—36no—
189C2×D3×D4—33no—
190C2×D3×D4—33no—
191C2×D3×D4—33no—
192C2×D3×D4—33no—
193C2×D3×D4C2×D313yescomplemented
194C2×#235—33no—
195C2×#235—33no—
196C2×#235C2×D313yescomplemented
197C22×D12—33no—
198C22×D12—33no—
199C22×C4×D3C2×D313yescomplemented
200C3×#127—33no—
201C3×#121—33no—
202C3×#121—33no—
203C3×C4×Q8—31no—
204C3×C4×D4—33no—
205#953—33no—
206#953—33no—
207#947—33no—
208#947—33no—
209#946—33no—
210#946—33no—
211Q8×Dic3—31no—
212Q8×Dic3—31no—
213Q8×Dic3—61no—
214Q8×Dic3C2×D311yescharacteristic, complemented
215#940—33no—
216#940—33no—
217#940—63no—
218#940C2×D313yescomplemented
219#939—36no—
220#939—33no—
221#939—36no—
222#939—36no—
223#938—33no—
224#938—33no—
225#938—36no—
226#938—33no—
227#938—63no—
228#938C2×D313yescomplemented
229#937—33no—
230#937—36no—
231#937—36no—
232#937—36no—
233#937—36no—
234#936—33no—
235D4×Dic3—33no—
236D4×Dic3—33no—
237#930—33no—
238#930—33no—
239#930—36no—
240#930—33no—
241#930—33no—
242#930—33no—
243#930—33no—
244#930—63no—
245#930C2×D313yescomplemented
246#929—33no—
247#929—33no—
248C4×#67—33no—
249C4×#67—33no—
250C4×#67—33no—
251C4×#67—33no—
252C4×#67—33no—
253C4×#67—63no—
254C4×#67C2×D313yescomplemented
255C2×(C2×D3)⋊C4—36no—
256#926—33no—
257C2×C4⋊Dic3—33no—
258#924—33no—
259#924—33no—
260#924—31no—
261#897—33no—
262#896—31no—
263#895—33no—
264#894—33no—
265#893—33no—
266D3×C4⋊C4—33no—
267#884—36no—
268#884—33no—
269#883—33no—
270#882—33no—
271D3×C22⋊C4—36no—
272#878—33no—
273#875—33no—
274C4×D12—33no—
275C4×D12—33no—
276#872—33no—
277C23×C32C2413yes—
278C22×C3⋊D3C2413yes—
279C22×C3×D3—26no—
280C22×C3×D3—26no—
281C22×C3×D3—43no—
282C22×C3×D3C2413yes—
283C22×C3×D3C2413yes—
284C22×C3×D3C2411yescharacteristic
285C2×D32—212no—
286C2×D32—46no—
287C2×D32—46no—
288C32×Q8C2×D414yescomplemented
289C32×D4—26no—
290C2×C32×C4—26no—
291C2×C32×C4C2411yescharacteristic
292C2×C32×C4C2413yes—
293#638—43no—
294#638—46no—
295C2×C3⋊Dic3C2411yescharacteristic
296C2×C3⋊Dic3C2413yes—
297C2×C3⋊Dic3C2411yescharacteristic
298C4⋊(C3⋊D3)—26no—
299C4×C3⋊D3—26no—
300C3×#67—212no—
301C3×#67—46no—
302C3×#67—43no—
303C2×C3×Dic3—26no—
304C2×C3×Dic3C2411yescharacteristic
305C2×C3×Dic3C2413yes—
306C2×C3×Dic3C2413yes—
307C2×C3×Dic3C2411yescharacteristic
308C2×C3×Dic3C2411yescharacteristic
309C3×D12—26no—
310C3×D12C2×D4112yescomplemented
311C3×C4×D3—26no—
312C3×C4×D3—26no—
313C3×C4×D3—26no—
314C3×C4×D3—22no—
315C3×C4×D3C2×D4112yescomplemented
316C3×Dic6—26no—
317#627—22no—
318#626—26no—
319#626—26no—
320#626—26no—
321#625—26no—
322#625—26no—
323D3×Dic3—46no—
324C2×H(5,𝔽2)—91no—
325C22×#41—31no—
326#550—31no—
327#550—91no—
328#548—91no—
329#548—91no—
330#546—93no—
331#546—93no—
332D42—93no—
333D42—93no—
334#537—93no—
335#535—93no—
336#525—93no—
337C2×#121—93no—
338#520—91no—
339C24×C3—33no—
340C23×D3—36no—
341C23×D3—36no—
342C23×D3C22×D313yes—
343C3×#41—24no—
344C3×#41—24no—
345C3×#41—38no—
346C3×#41—44no—
347C3×#41—612no—
348C3×#41—612no—
349C3×#41—64no—
350C2×C3×Q8—21no—
351C2×C3×Q8—33no—
352C2×C3×Q8—64no—
353C2×C3×Q8C22×D311yescharacteristic
354C2×C3×Q8C22×D311yescharacteristic
355C2×C3×D4—23no—
356C2×C3×D4—36no—
357C2×C3×D4—33no—
358C2×C3×D4—36no—
359C2×C3×D4—33no—
360C2×C3×D4—33no—
361C2×C3×D4—612no—
362C2×C3×D4C22×D313yes—
363C2×C3×D4C22×D313yes—
364C22×C3×C4—23no—
365C22×C3×C4—33no—
366C22×C3×C4—33no—
367C22×C3×C4—33no—
368C22×C3×C4—31no—
369C22×C3×C4—33no—
370C22×C3×C4—33no—
371C22×C3×C4—612no—
372C22×C3×C4C22×D313yes—
373C22×C3×C4C22×D313yes—
374C2×#67—33no—
375C2×#67—33no—
376C2×#67—33no—
377C2×#67—33no—
378C2×#67—33no—
379C2×#67—36no—
380C2×#67—33no—
381C2×#67—36no—
382C2×#67—33no—
383C2×#67—33no—
384C2×#67—33no—
385C2×#67—63no—
386C2×#67—66no—
387C2×#67—1212no—
388C2×#67C22×D316yes—
389C2×#67C22×D313yes—
390C2×#67C22×D316yes—
391C22×Dic3—36no—
392C22×Dic3C22×D313yes—
393#239—24no—
394#239—64no—
395#239—64no—
396#239—124no—
397#239#6718yescomplemented
398D3×Q8—24no—
399#237—212no—
400D3×D4—212no—
401D3×D4—612no—
402D3×D4—612no—
403D3×D4—612no—
404D3×D4—612no—
405D3×D4—1212no—
406#235—212no—
407#235—612no—
408#235—612no—
409C2×D12—33no—
410C2×D12—33no—
411C2×D12—33no—
412C2×D12—33no—
413C2×D12—33no—
414C2×D12—63no—
415C2×D12—612no—
416C2×D12—612no—
417C2×D12C22×D313yes—
418C2×D12C22×D313yes—
419C2×C4×D3—212no—
420C2×C4×D3—33no—
421C2×C4×D3—33no—
422C2×C4×D3—36no—
423C2×C4×D3—63no—
424C2×C4×D3C22×D313yes—
425C2×C4×D3C22×D313yes—
426C2×C4×D3C22×D311yescharacteristic
427C2×C4×D3C22×D313yes—
428C2×C4×D3C22×D313yes—
429C2×Dic6—31no—
430C2×Dic6—31no—
431C2×Dic6C22×D313yes—
432C3×C4⋊C4—33no—
433C3×C4⋊C4—31no—
434C3×C22⋊C4—33no—
435C3×C22⋊C4—33no—
436C3×C42—33no—
437#217—33no—
438#217—33no—
439#217—36no—
440#217—33no—
441#217—31no—
442#217—31no—
443#217—33no—
444#217—33no—
445#217—63no—
446#217C22×D313yes—
447(C2×D3)⋊C4—33no—
448(C2×D3)⋊C4—33no—
449(C2×D3)⋊C4—31no—
450(C2×D3)⋊C4—31no—
451(C2×D3)⋊C4—36no—
452(C2×D3)⋊C4—33no—
453(C2×D3)⋊C4—33no—
454(C2×D3)⋊C4—33no—
455(C2×D3)⋊C4—33no—
456(C2×D3)⋊C4—36no—
457(C2×D3)⋊C4—36no—
458(C2×D3)⋊C4—33no—
459(C2×D3)⋊C4—63no—
460(C2×D3)⋊C4C22×D313yes—
461C4⋊Dic3—33no—
462C4⋊Dic3—33no—
463C4⋊Dic3—33no—
464C4⋊Dic3—33no—
465C4⋊Dic3—31no—
466C4⋊Dic3—63no—
467C4⋊Dic3C22×D313yes—
468Dic3⋊C4—31no—
469Dic3⋊C4—31no—
470Dic3⋊C4—31no—
471Dic3⋊C4—33no—
472Dic3⋊C4—33no—
473Dic3⋊C4—33no—
474Dic3⋊C4—33no—
475Dic3⋊C4—61no—
476Dic3⋊C4C22×D311yescharacteristic
477C4×Dic3—33no—
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—23no—
490C2×C3×D3—23no—
491C2×C3×D3—21no—
492C2×C3×D3—23no—
493C2×C3×D3—23no—
494C2×C3×D3—23no—
495C2×C3×D3—412no—
496C2×C3×D3C22×D416yes—
497C2×C3×D3H(5,𝔽2)12yescomplemented
498D32—812no—
499C32×C4—21no—
500C32×C4C22×D416yes—
501C3⋊Dic3—21no—
502C3⋊Dic3—21no—
503C3⋊Dic3—23no—
504C3×Dic3—21no—
505C3×Dic3—23no—
506C3×Dic3—23no—
507C3×Dic3—21no—
508C3×Dic3C22×D412yes—
509H(5,𝔽2)—188no—
510C2×#41—31no—
511C2×#41—31no—
512C2×#41—33no—
513C2×#41—33no—
514C2×#41—68no—
515C2×#41—93no—
516C2×#41—91no—
517C2×#41D3211yescharacteristic, complemented
518C22×Q8—31no—
519C22×D4—33no—
520C22×D4—93no—
521C22×D4—93no—
522C22×D4—93no—
523C22×D4—96no—
524C23×C4—33no—
525#127—33no—
526#127—93no—
527#124—93no—
528#124—93no—
529#123—93no—
530#123—93no—
531C22⋊Q8—93no—
532C22⋊Q8—91no—
533C22⋊Q8—93no—
534C22⋊Q8—93no—
535#121—33no—
536#121—33no—
537#121—93no—
538#121—96no—
539#121—93no—
540#121—96no—
541#121—93no—
542#121—93no—
543#121—96no—
544#121—93no—
545#121—93no—
546#120—93no—
547#120—96no—
548#120—96no—
549#120—93no—
550C4×Q8—31no—
551C4×Q8—91no—
552C4×D4—33no—
553C4×D4—93no—
554C4×D4—93no—
555C4×D4—93no—
556C4×D4—93no—
557C4×D4—93no—
558#117—93no—
559C2×C4⋊C4—93no—
560C2×C22⋊C4—96no—
561C23×C3—23no—
562C23×C3—33no—
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—612no—
577C22×D3—612no—
578C22×D3—126no—
579C22×D3—126no—
580C22×D3—126no—
581C22×D3—126no—
582C22×D3C23×D313yes—
583C22×D3C23×D311yescharacteristic
584C22×D3C23×D313yes—
585C3×Q8—24no—
586C3×Q8—66no—
587C3×Q8D3×D414yescomplemented
588C3×Q8C2×#6714yescomplemented
589C3×D4—26no—
590C3×D4—26no—
591C3×D4—312no—
592C3×D4—46no—
593C3×D4—612no—
594C3×D4—66no—
595C3×D4—126no—
596C3×D4—123no—
597C2×C3×C4—26no—
598C2×C3×C4—26no—
599C2×C3×C4—23no—
600C2×C3×C4—21no—
601C2×C3×C4—31no—
602C2×C3×C4—312no—
603C2×C3×C4—31no—
604C2×C3×C4—33no—
605C2×C3×C4—33no—
606C2×C3×C4—31no—
607C2×C3×C4—46no—
608C2×C3×C4—62no—
609C2×C3×C4—66no—
610C2×C3×C4—66no—
611C2×C3×C4—66no—
612C2×C3×C4—66no—
613C2×C3×C4C23×D311yescharacteristic
614C2×C3×C4C23×D311yescharacteristic
615C2×C3×C4C23×D313yes—
616C2×C3×C4C23×D313yes—
617#67—212no—
618#67—46no—
619#67—43no—
620#67—66no—
621#67—66no—
622#67—66no—
623#67—66no—
624#67—66no—
625#67—66no—
626#67—66no—
627#67—126no—
628#67—123no—
629#67—123no—
630#67—126no—
631#67—126no—
632#67—246no—
633C2×Dic3—26no—
634C2×Dic3—31no—
635C2×Dic3—31no—
636C2×Dic3—33no—
637C2×Dic3—33no—
638C2×Dic3—31no—
639C2×Dic3—31no—
640C2×Dic3—61no—
641C2×Dic3—63no—
642C2×Dic3—61no—
643C2×Dic3—126no—
644C2×Dic3C23×D311yescharacteristic
645C2×Dic3C23×D313yes—
646C2×Dic3C23×D311yescharacteristic
647C2×Dic3C23×D313yes—
648C2×Dic3C23×D311yescharacteristic
649D12—26no—
650D12—66no—
651D12—66no—
652D12—66no—
653D12—66no—
654D12—66no—
655D12—126no—
656D12C2×#67112yescomplemented
657C4×D3—26no—
658C4×D3—26no—
659C4×D3—26no—
660C4×D3—22no—
661C4×D3—66no—
662C4×D3—66no—
663C4×D3—126no—
664C4×D3—126no—
665C4×D3C2×#67112yescomplemented
666Dic6—26no—
667Dic6—62no—
668Dic6—62no—
669C2×C32—43no—
670C2×C32C23×D411yescharacteristic
671C2×C32C2×H(5,𝔽2)11yescharacteristic
672C2×C32#58511yescharacteristic
673C3⋊D3—43no—
674C3×D3—26no—
675C3×D3—22no—
676C3×D3—43no—
677C24—33no—
678C24—96no—
679#41—24no—
680#41—38no—
681#41—612no—
682#41—612no—
683#41—64no—
684#41—1812no—
685#41—184no—
686C2×Q8—33no—
687C2×Q8—64no—
688C2×Q8—91no—
689C2×Q8C2×D3211yescharacteristic
690C2×D4—36no—
691C2×D4—33no—
692C2×D4—36no—
693C2×D4—33no—
694C2×D4—33no—
695C2×D4—612no—
696C2×D4—93no—
697C2×D4—93no—
698C2×D4—93no—
699C2×D4—93no—
700C2×D4—93no—
701C2×D4—93no—
702C2×D4—96no—
703C2×D4—93no—
704C2×D4—1812no—
705C2×D4—1812no—
706C2×D4—1812no—
707C2×D4—3612no—
708C2×D4C2×D3213yes—
709C22×C4—33no—
710C22×C4—33no—
711C22×C4—33no—
712C22×C4—33no—
713C22×C4—33no—
714C22×C4—31no—
715C22×C4—612no—
716C22×C4—96no—
717C22×C4—93no—
718C22×C4C2×D3213yes—
719C4⋊C4—33no—
720C4⋊C4—31no—
721C4⋊C4—93no—
722C4⋊C4—91no—
723C4⋊C4—93no—
724C4⋊C4—93no—
725C4⋊C4—93no—
726C4⋊C4—91no—
727C22⋊C4—33no—
728C22⋊C4—33no—
729C22⋊C4—96no—
730C22⋊C4—93no—
731C22⋊C4—96no—
732C22⋊C4—93no—
733C22⋊C4—93no—
734C22⋊C4—91no—
735C22⋊C4—91no—
736C22⋊C4—93no—
737C22⋊C4—93no—
738C22⋊C4—93no—
739C42—33no—
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—43no—
751C22×C3—43no—
752C22×C3—43no—
753C22×C3—61no—
754C22×C3—63no—
755C22×C3—61no—
756C22×C3—63no—
757C22×C3—63no—
758C22×C3—63no—
759C22×C3—63no—
760C22×C3—1212no—
761C22×C3C24×D311yescharacteristic
762C22×C3C24×D311yescharacteristic
763C2×D3—23no—
764C2×D3—21no—
765C2×D3—23no—
766C2×D3—21no—
767C2×D3—23no—
768C2×D3—23no—
769C2×D3—23no—
770C2×D3—412no—
771C2×D3—63no—
772C2×D3—63no—
773C2×D3—63no—
774C2×D3—63no—
775C2×D3—63no—
776C2×D3—63no—
777C2×D3—123no—
778C2×D3—123no—
779C2×D3—123no—
780C2×D3—2412no—
781C2×D3—2412no—
782C2×D3#100912yescomplemented
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—61no—
793C3×C4C2×D3×D416yes—
794C3×C4C22×#6716yes—
795Dic3—21no—
796Dic3—21no—
797Dic3—23no—
798Dic3—23no—
799Dic3—62no—
800Dic3—61no—
801Dic3—63no—
802Dic3—61no—
803Dic3—61no—
804Dic3—63no—
805Dic3—61no—
806Dic3—121no—
807Dic3—123no—
808Dic3C22×#6712yes—
809C32#348811yescharacteristic, complemented, Sylow
810C23—31no—
811C23—33no—
812C23—33no—
813C23—66no—
814C23—66no—
815C23—93no—
816C23—123no—
817C23—1812no—
818C23—366no—
819C23—366no—
820C23C22×D3213yes—
821Q8—66no—
822Q8—182no—
823Q8D3×#6714yescomplemented
824D4—26no—
825D4—312no—
826D4—612no—
827D4—66no—
828D4—126no—
829D4—123no—
830D4—186no—
831D4—186no—
832D4—186no—
833D4—186no—
834D4—186no—
835D4—186no—
836D4—366no—
837D4—363no—
838C2×C4—26no—
839C2×C4—31no—
840C2×C4—312no—
841C2×C4—31no—
842C2×C4—33no—
843C2×C4—31no—
844C2×C4—33no—
845C2×C4—62no—
846C2×C4—66no—
847C2×C4—66no—
848C2×C4—66no—
849C2×C4—66no—
850C2×C4—91no—
851C2×C4—93no—
852C2×C4—91no—
853C2×C4—186no—
854C2×C4—366no—
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—83no—
865C2×C3—123no—
866C2×C3C22×D3×D411yescharacteristic
867C2×C3C2×#100911yescharacteristic
868C2×C3#596411yescharacteristic
869C2×C3#596411yescharacteristic
870C2×C3D3×H(5,𝔽2)11yescharacteristic
871C2×C3C23×#6711yescharacteristic
872D3—22no—
873D3—26no—
874D3—43no—
875D3—123no—
876D3—123no—
877D3—243no—
878C22—23no—
879C22—23no—
880C22—23no—
881C22—32no—
882C22—36no—
883C22—63no—
884C22—61no—
885C22—63no—
886C22—61no—
887C22—63no—
888C22—63no—
889C22—63no—
890C22—1212no—
891C22—183no—
892C22—183no—
893C22—183no—
894C22—7212no—
895C22C23×D3211yescharacteristic
896C4—21no—
897C4—32no—
898C4—63no—
899C4—61no—
900C4—63no—
901C4—61no—
902C4—183no—
903C4—181no—
904C4—181no—
905C4C2×D3×#6716yes—
906C3—21no—
907C3#8676911yescharacteristic, complemented
908C3#8727511yescharacteristic, complemented
909C2—43no—
910C2—62no—
911C2—66no—
912C2—123no—
913C2—363no—
914C2D3×#100911yescharacteristic
915C2#1059669511yescharacteristic
916C2C22×D3×#6711yescharacteristic
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×C3×D3×#41C2semidirect
2. C2×#64320C2semidirect
3. #10596305C2semidirect
4. C3×#5834C2semidirect
5. #10595409C2semidirect
6. #10595394C2semidirect
7. #10595342C2semidirect
8. #10595303C2semidirect
9. #10595293C2semidirect
10. #10595288C2semidirect
11. #10595232C2semidirect
12. #10595070C2semidirect
13. #10595067C2semidirect
14. D3×#930C2semidirect
15. #10595002C2semidirect
18. C2×C32×#41C22semidirect
19. C2×#3832C22semidirect
22. C2×C3×#239C22semidirect
23. C2×C3×D3×Q8C22semidirect
24. C2×C3×#237C22semidirect
25. C2×C3×D3×D4C22semidirect
26. C2×C3×#235C22semidirect
27. C22×C3×C4×D3C22semidirect
28. C2×D3×#67C22semidirect
30. C2×#3802C22semidirect
31. C2×D3×D12C22semidirect
32. C2×D3×D12C22semidirect
33. C2×#3798C22semidirect
34. Q8×C3⋊Dic3C22semidirect
35. #64149C22semidirect
36. #64147C22semidirect
37. #64139C22semidirect
38. C4×#638C22semidirect
39. C3×Q8×Dic3C22semidirect
40. C3×#940C22semidirect
41. C3×#938C22semidirect
42. C3×#930C22semidirect
43. C3×C4×#67C22semidirect
44. #63983C22semidirect
45. #63983C22semidirect
46. #63978C22semidirect
47. #63978C22semidirect
48. #63977C22semidirect
49. #63976C22semidirect
50. #63971C22semidirect
51. #63970C22semidirect
52. #63964C22semidirect
53. D3×(C2×D3)⋊C4C22semidirect
54. #63909C22semidirect
55. #63908C22semidirect
56. #63906C22semidirect
57. #63905C22semidirect
58. C4×#626C22semidirect
59. C4×#625C22semidirect
60. #63898C22semidirect
61. Dic3×D12C22semidirect
62. D3×C4⋊Dic3C22semidirect
63. #63871C22semidirect
64. #63864C22semidirect
65. #63863C22semidirect
66. #63856C22semidirect
67. #63855C22semidirect
68. #63851C22semidirect
69. #63850C22semidirect
73. C2×D3×#41D3semidirect
78. #5834D3semidirect
117. C3×#239D4semidirect
172. C2×C3×#41C2×D3semidirect
173. C2×C3×#41C2×D3semidirect
185. C2×#239C2×D3semidirect
186. C2×D3×Q8C2×D3semidirect
187. C2×#237C2×D3semidirect
193. C2×D3×D4C2×D3semidirect
196. C2×#235C2×D3semidirect
199. C22×C4×D3C2×D3semidirect
214. Q8×Dic3C2×D3semidirect
218. #940C2×D3semidirect
228. #938C2×D3semidirect
245. #930C2×D3semidirect
254. C4×#67C2×D3semidirect
288. C32×Q8C2×D4semidirect
310. C3×D12C2×D4semidirect
315. C3×C4×D3C2×D4semidirect
397. #239#67semidirect
497. C2×C3×D3H(5,𝔽2)semidirect
517. C2×#41D32semidirect
587. C3×Q8D3×D4semidirect
588. C3×Q8C2×#67semidirect
656. D12C2×#67semidirect
665. C4×D3C2×#67semidirect
782. C2×D3#1009semidirect
809. C32#3488semidirect
823. Q8D3×#67semidirect
907. C3#86769semidirect
908. C3#87275semidirect

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×#643202
#105963052
C3×#58342
#105954092
#105953942
#105953422
#105953032
#105952932
#105952882
#105952322
#105950702
#105950672
D3×#9302
#105950022
#872753
#867693