Finite Group Databasebeta

← #11904558

Subgroups — #11904558

Order 1152.

3217 conjugacy classes of subgroups.

The subgroup lattice has 897 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic, complemented
2C2×#64315C211yesmaximal, characteristic, complemented
3#10596302C211yesmaximal, characteristic, complemented
4C3×#5834C211yesmaximal, characteristic, complemented
5#10595414C211yesmaximal, characteristic, complemented
6#10595412C211yesmaximal, characteristic, complemented
7#10595347C211yesmaximal, characteristic, complemented
8#10595233C213yesmaximal, complemented
9#10595231C213yesmaximal, complemented
10#10595158C213yesmaximal, complemented
11#10595157C213yesmaximal, complemented
12#10595006C213yesmaximal, complemented
13#10595002C213yesmaximal, complemented
14#10594899C213yesmaximal, complemented
15#10594892C213yesmaximal, complemented
16#87274—31nomaximal
17#86783—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic, complemented
20C3×D3×#41—28no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×#239C2211yescharacteristic, complemented
23C2×C3×D3×Q8C2211yescharacteristic
24C2×C3×#237C2213yes—
25C2×C3×D3×D4C2213yes—
26C2×C3×#235C2213yes—
27C22×C3×C4×D3C2213yes—
28#64315—28no—
29C2×#3798C2213yes—
30C2×#3796C2213yescomplemented
31C2×#3795C2213yes—
32C2×D3×Dic6C2213yescomplemented
33Q8×C3⋊Dic3C2211yescharacteristic, complemented
34#64147C2213yescomplemented
35#64145C2213yescomplemented
36C4×#638C2213yescomplemented
37#64133C2213yescomplemented
38C3×Q8×Dic3C2211yescharacteristic, complemented
39C3×#940C2213yescomplemented
40C3×#938C2213yescomplemented
41C3×#930C2213yescomplemented
42C3×C4×#67C2213yescomplemented
43#63979C2216yescomplemented
44#63978C2213yescomplemented
45#63977C2213yes—
46#63976C2216yes—
47#63976C2213yes—
48Dic3×#67C2216yescomplemented
49#63970C2216yescomplemented
50#63970C2216yescomplemented
51#63964C2213yescomplemented
52#63959C2216yescomplemented
53#63916C2213yescomplemented
54#63914C2213yescomplemented
55#63908C2213yescomplemented
56#63908C2213yescomplemented
57#63906C2213yescomplemented
58#63905C2213yes—
59C4×#626C2213yescomplemented
60C4×#625C2213yescomplemented
61#63879C2216yescomplemented
62#63860C2213yescomplemented
63#63857C2213yescomplemented
64#63855C2213yes—
65#63851C2213yescomplemented
66#63850C2211yescharacteristic
67#63843C2213yescomplemented
68Dic3×Dic6C2213yescomplemented
69#63841C2213yes—
70C22×C3×#41—31no—
71C2×#1010—31no—
72C2×D3×#41D311yescharacteristic, complemented
73C2×#1007—31no—
74C3×#550—31no—
75#5834—31no—
76#5834—31no—
77#5834—33no—
78#5834—33no—
79#5834D311yescharacteristic, complemented
80#5831—31no—
81#5831—31no—
82#5831—31no—
83#5831—33no—
84#5831—33no—
85#5831—61no—
86#5812—31no—
87#5805—33no—
88#5805—33no—
89#5791—33no—
90#5791—33no—
91#5718—33no—
92#5715—33no—
93#5607—33no—
94#5606—33no—
95#5599—33no—
96#5598—33no—
97#5576—31no—
98#5572—31no—
99#5552—33no—
100#5547—33no—
101C23×C3×D3C2313yes—
102C32×#41—24no—
103C2×C32×Q8C2311yescharacteristic
104C2×C32×D4C2313yes—
105C22×C32×C4C2313yes—
106C2×#638C2313yes—
107Q8×C3⋊D3—24no—
108C2×C4×C3⋊D3C2313yes—
109C2×#634C2313yes—
110C2×C3×#67C2316yes—
111C2×C3×#67C2313yes—
112C2×C3×#67C2316yes—
113C22×C3×Dic3C2313yes—
114C3×#239—24no—
115C3×#239—24no—
116C3×D3×Q8D418yescomplemented
117C3×#237—212no—
118C3×D3×D4—212no—
119C3×#235—212no—
120C2×C3×D12C2313yes—
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×#627C2313yes—
130C2×#626C2313yes—
131C2×#626C2311yescharacteristic
132C2×#626C2313yes—
133C2×#625C2313yes—
134C2×#625C2316yes—
135C2×#625C2313yes—
136C2×D3×Dic3C2316yes—
137#3798—212no—
138#3796—212no—
139#3795—212no—
140D3×Dic6—212no—
141#3757C2316yes—
142#3757C2313yes—
143#3752C2311yescharacteristic
144C4⋊(C3⋊Dic3)C2313yes—
145#3750C2313yes—
146C4×C3⋊Dic3C2313yes—
147C3×#217C2313yes—
148C3×(C2×D3)⋊C4C2313yes—
149C3×C4⋊Dic3C2313yes—
150C3×Dic3⋊C4C2311yescharacteristic
151C3×C4×Dic3C2313yes—
152#3724C2311yescharacteristic
153Dic3⋊Dic3C2313yes—
154Dic3⋊Dic3C2313yes—
155Dic3⋊Dic3C2313yes—
156#3722C2311yescharacteristic
157(C2×D3)⋊Dic3C2313yes—
158(C2×D3)⋊Dic3C2311yescharacteristic
159(C2×D3)⋊Dic3C2313yes—
160(C2×D3)⋊Dic3C2313yes—
161(C2×D3)⋊Dic3C2316yes—
162(C2×D3)⋊Dic3C2313yes—
163Dic32C2316yes—
164#3487—91noSylow
165C2×C3×#41—21no—
166C2×C3×#41—31no—
167C2×C3×#41—31no—
168C2×C3×#41—33no—
169C2×C3×#41—33no—
170C2×C3×#41—68no—
171C2×C3×#41C2×D311yescharacteristic
172C2×C3×#41C2×D311yescharacteristic
173C22×C3×Q8—31no—
174C22×C3×D4—33no—
175C23×C3×C4—33no—
176#1010—68no—
177D3×#41—28no—
178#1007—68no—
179C2×#239—33no—
180C2×#239C2×D311yescharacteristic
181C2×#239C2×D311yescharacteristic, complemented
182C2×D3×Q8—31no—
183C2×D3×Q8—31no—
184C2×D3×Q8—33no—
185C2×D3×Q8—61no—
186C2×D3×Q8C2×D311yescharacteristic
187C2×#237—33no—
188C2×#237—33no—
189C2×#237C2×D313yes—
190C2×D3×D4C2×D313yes—
191C2×#235—33no—
192C2×#235—33no—
193C2×#235—33no—
194C2×#235C2×D313yes—
195C22×C4×D3C2×D313yes—
196C22×Dic6—33no—
197C3×#127—33no—
198C3×#121—33no—
199C3×#121—33no—
200C3×C4×Q8—31no—
201C3×C4×D4—33no—
202#953—36no—
203#953—33no—
204#953—33no—
205Q8×Dic3—31no—
206Q8×Dic3—31no—
207Q8×Dic3—33no—
208Q8×Dic3—33no—
209Q8×Dic3—61no—
210Q8×Dic3C2×D311yescharacteristic, complemented
211#940—36no—
212#940—36no—
213#940—33no—
214#940—33no—
215#940C2×D313yescomplemented
216#939—36no—
217#939—36no—
218#939—33no—
219#938—33no—
220#938—33no—
221#938—36no—
222#938—36no—
223#938—33no—
224#938—33no—
225#938—33no—
226#938—63no—
227#938C2×D313yescomplemented
228#937—33no—
229#937—36no—
230#936—33no—
231#936—33no—
232#936—36no—
233#936—33no—
234#936—63no—
235D4×Dic3—36no—
236#930—33no—
237#930—33no—
238#930—33no—
239#930—33no—
240#930C2×D313yescomplemented
241#929—33no—
242#929—31no—
243C4×#67—33no—
244C4×#67—33no—
245C4×#67—36no—
246C4×#67—33no—
247C4×#67—33no—
248C4×#67—36no—
249C4×#67—33no—
250C4×#67—63no—
251C4×#67C2×D313yescomplemented
252#926—33no—
253#926—33no—
254#924—33no—
255#924—33no—
256#924—33no—
257#924—33no—
258#924—33no—
259#924—63no—
260#897—33no—
261#896—33no—
262#895—33no—
263#894—31no—
264#892—33no—
265#887—33no—
266#885—36no—
267#884—33no—
268#883—33no—
269#882—33no—
270#67⋊C4—36no—
271#878—33no—
272#875—33no—
273C4×D12—33no—
274#872—33no—
275C4×Dic6—33no—
276C23×C32C2413yes—
277C22×C3⋊D3C2411yescharacteristic
278C22×C3×D3—26no—
279C22×C3×D3—43no—
280C22×C3×D3—43no—
281C22×C3×D3C2413yes—
282C22×C3×D3C2413yes—
283C22×C3×D3C2411yescharacteristic
284C32×Q8C2×D414yes—
285C32×D4—26no—
286C2×C32×C4—26no—
287C2×C32×C4C2411yescharacteristic
288C2×C32×C4C2413yes—
289#638—43no—
290C2×C3⋊Dic3C2413yes—
291C2×C3⋊Dic3C2413yes—
292C2×C3⋊Dic3C2411yescharacteristic
293C4×C3⋊D3—26no—
294#634—26no—
295C3×#67—212no—
296C3×#67—46no—
297C3×#67—43no—
298C2×C3×Dic3—26no—
299C2×C3×Dic3C2413yes—
300C2×C3×Dic3C2411yescharacteristic
301C2×C3×Dic3C2411yescharacteristic
302C2×C3×Dic3C2411yescharacteristic
303C2×C3×Dic3C2413yes—
304C3×D12—26no—
305C3×D12—26no—
306C3×C4×D3—22no—
307C3×C4×D3—26no—
308C3×C4×D3—26no—
309C3×C4×D3—26no—
310C3×C4×D3C2×D4112yes—
311C3×Dic6C2×D4112yes—
312#627—26no—
313#626—22no—
314#626—26no—
315#626—43no—
316#625—26no—
317#625—43no—
318#625—46no—
319D3×Dic3—212no—
320C2×2−1+4—91no—
321C22×#41—31no—
322#550—31no—
323#550—93no—
324#550—93no—
325#550—91no—
326#548—93no—
327#548—91no—
328#548—93no—
329#548—91no—
330#535—93no—
331#535—93no—
332#525—93no—
333#525—93no—
334#519—91no—
335C24×C3—33no—
336C23×D3C22×D313yes—
337C3×#41—24no—
338C3×#41—24no—
339C3×#41—44no—
340C3×#41—612no—
341C3×#41—612no—
342C3×#41—64no—
343C3×#41—64no—
344C2×C3×Q8—21no—
345C2×C3×Q8—38no—
346C2×C3×Q8—33no—
347C2×C3×Q8C22×D311yescharacteristic
348C2×C3×Q8C22×D311yescharacteristic
349C2×C3×D4—23no—
350C2×C3×D4—36no—
351C2×C3×D4—36no—
352C2×C3×D4—33no—
353C2×C3×D4—33no—
354C2×C3×D4—33no—
355C2×C3×D4—612no—
356C2×C3×D4C22×D313yes—
357C2×C3×D4C22×D313yes—
358C22×C3×C4—23no—
359C22×C3×C4—33no—
360C22×C3×C4—33no—
361C22×C3×C4—33no—
362C22×C3×C4—33no—
363C22×C3×C4—33no—
364C22×C3×C4—31no—
365C22×C3×C4—612no—
366C22×C3×C4C22×D313yes—
367C22×C3×C4C22×D313yes—
368C2×#67—33no—
369C2×#67—33no—
370C2×#67—33no—
371C2×#67—33no—
372C2×#67—36no—
373C2×#67—33no—
374C2×#67—33no—
375C2×#67—36no—
376C2×#67—33no—
377C2×#67—31no—
378C2×#67—33no—
379C2×#67—63no—
380C2×#67C22×D316yes—
381C2×#67C22×D316yes—
382C2×#67C22×D313yes—
383C22×Dic3—36no—
384C22×Dic3C22×D313yes—
385#239—24no—
386#239—24no—
387#239—612no—
388D3×Q8—612no—
389D3×Q8—64no—
390D3×Q8—64no—
391D3×Q8—124no—
392D3×Q8#6718yescomplemented
393#237—212no—
394#237—612no—
395#237—612no—
396D3×D4—212no—
397#235—212no—
398#235—612no—
399#235—612no—
400#235—612no—
401C2×D12—31no—
402C2×D12—33no—
403C2×D12—33no—
404C2×D12C22×D313yes—
405C2×D12C22×D313yes—
406C2×C4×D3—212no—
407C2×C4×D3—36no—
408C2×C4×D3—33no—
409C2×C4×D3—33no—
410C2×C4×D3—63no—
411C2×C4×D3C22×D313yes—
412C2×C4×D3C22×D313yes—
413C2×C4×D3C22×D311yescharacteristic
414C2×C4×D3C22×D313yes—
415C2×C4×D3C22×D313yes—
416C2×Dic6—33no—
417C2×Dic6—33no—
418C2×Dic6—33no—
419C2×Dic6—33no—
420C2×Dic6—63no—
421C2×Dic6—612no—
422C2×Dic6C22×D313yes—
423C3×C4⋊C4—33no—
424C3×C4⋊C4—31no—
425C3×C22⋊C4—33no—
426C3×C22⋊C4—33no—
427C3×C42—33no—
428#217—33no—
429#217—36no—
430#217—36no—
431#217—33no—
432#217—33no—
433#217—33no—
434#217—36no—
435#217—33no—
436#217—33no—
437#217—31no—
438#217—66no—
439#217—63no—
440#217C22×D313yes—
441(C2×D3)⋊C4—31no—
442(C2×D3)⋊C4—33no—
443(C2×D3)⋊C4—33no—
444(C2×D3)⋊C4—36no—
445(C2×D3)⋊C4—33no—
446(C2×D3)⋊C4—33no—
447(C2×D3)⋊C4—31no—
448(C2×D3)⋊C4—31no—
449(C2×D3)⋊C4—31no—
450(C2×D3)⋊C4—31no—
451(C2×D3)⋊C4—61no—
452(C2×D3)⋊C4C22×D313yes—
453C4⋊Dic3—33no—
454C4⋊Dic3—33no—
455C4⋊Dic3—33no—
456C4⋊Dic3—33no—
457C4⋊Dic3—33no—
458C4⋊Dic3—63no—
459C4⋊Dic3C22×D313yes—
460Dic3⋊C4—33no—
461Dic3⋊C4—33no—
462Dic3⋊C4—33no—
463Dic3⋊C4—33no—
464Dic3⋊C4—31no—
465Dic3⋊C4—33no—
466Dic3⋊C4—31no—
467Dic3⋊C4—63no—
468Dic3⋊C4C22×D311yescharacteristic
469C4×Dic3—33no—
470C4×Dic3—33no—
471C4×Dic3—36no—
472C4×Dic3—36no—
473C4×Dic3—63no—
474C4×Dic3C22×D313yes—
475C22×C32—23no—
476C22×C32—23no—
477C22×C32—23no—
478C22×C32C2511yescharacteristic
479C2×C3⋊D3—21no—
480C2×C3⋊D3—21no—
481C2×C3⋊D3—21no—
482C2×C3×D3—21no—
483C2×C3×D3—21no—
484C2×C3×D3—23no—
485C2×C3×D3—23no—
486C2×C3×D3—23no—
487C2×C3×D3—23no—
488C2×C3×D3—23no—
489C2×C3×D3—23no—
490C2×C3×D3—412no—
491C2×C3×D3C22×D412yes—
492C32×C4—21no—
493C32×C4C22×D416yes—
494C3⋊Dic3—23no—
495C3⋊Dic3—21no—
496C3⋊Dic3—23no—
497C3×Dic3—21no—
498C3×Dic3—21no—
499C3×Dic3—23no—
500C3×Dic3—21no—
501C3×Dic3C22×D416yes—
5022−1+4—188no—
503C2×#41—31no—
504C2×#41—31no—
505C2×#41—33no—
506C2×#41—33no—
507C2×#41—68no—
508C2×#41—93no—
509C2×#41—93no—
510C2×#41—93no—
511C2×#41D3211yescharacteristic
512C22×Q8—31no—
513C22×Q8—93no—
514C22×Q8—91no—
515C22×D4—33no—
516C23×C4—33no—
517#127—33no—
518#127—96no—
519#127—93no—
520#124—93no—
521#124—96no—
522#124—93no—
523#123—93no—
524#123—91no—
525C22⋊Q8—93no—
526C22⋊Q8—93no—
527C22⋊Q8—93no—
528C22⋊Q8—93no—
529#121—33no—
530#121—33no—
531#121—93no—
532#121—93no—
533#121—93no—
534#121—93no—
535#121—93no—
536#121—96no—
537#121—96no—
538#121—93no—
539#120—93no—
540#120—93no—
541#120—96no—
542C4×Q8—31no—
543C4×Q8—93no—
544C4×Q8—93no—
545C4×Q8—91no—
546C4×D4—33no—
547C4×D4—93no—
548C4×D4—96no—
549C4×D4—93no—
550C4×D4—96no—
551C4×D4—93no—
552#117—93no—
553#117—93no—
554C23×C3—23no—
555C23×C3—31no—
556C23×C3—33no—
557C23×C3—33no—
558C23×C3—66no—
559C23×C3—123no—
560C23×C3—123no—
561C23×C3C23×D313yes—
562C23×C3C23×D313yes—
563C22×D3—26no—
564C22×D3—31no—
565C22×D3—31no—
566C22×D3—43no—
567C22×D3—43no—
568C22×D3—61no—
569C22×D3C23×D313yes—
570C22×D3C23×D313yes—
571C22×D3C23×D311yescharacteristic
572C3×Q8—24no—
573C3×Q8—312no—
574C3×Q8D3×D414yes—
575C3×Q8C2×#6714yes—
576C3×D4—26no—
577C3×D4—26no—
578C3×D4—46no—
579C3×D4—612no—
580C3×D4—66no—
581C3×D4—66no—
582C3×D4—126no—
583C3×D4—123no—
584C2×C3×C4—26no—
585C2×C3×C4—26no—
586C2×C3×C4—23no—
587C2×C3×C4—21no—
588C2×C3×C4—33no—
589C2×C3×C4—312no—
590C2×C3×C4—33no—
591C2×C3×C4—31no—
592C2×C3×C4—31no—
593C2×C3×C4—31no—
594C2×C3×C4—46no—
595C2×C3×C4—66no—
596C2×C3×C4—62no—
597C2×C3×C4—66no—
598C2×C3×C4—66no—
599C2×C3×C4—66no—
600C2×C3×C4C23×D311yescharacteristic
601C2×C3×C4C23×D311yescharacteristic
602C2×C3×C4C23×D313yes—
603C2×C3×C4C23×D313yes—
604#67—212no—
605#67—43no—
606#67—46no—
607#67—62no—
608#67—66no—
609#67—66no—
610#67—66no—
611#67—123no—
612#67—123no—
613#67—126no—
614#67—126no—
615#67—123no—
616#67—123no—
617#67—123no—
618#67—126no—
619C2×Dic3—26no—
620C2×Dic3—31no—
621C2×Dic3—33no—
622C2×Dic3—33no—
623C2×Dic3—31no—
624C2×Dic3—33no—
625C2×Dic3—33no—
626C2×Dic3—61no—
627C2×Dic3—63no—
628C2×Dic3—63no—
629C2×Dic3—612no—
630C2×Dic3C23×D313yes—
631C2×Dic3C23×D311yescharacteristic
632C2×Dic3C23×D311yescharacteristic
633C2×Dic3C23×D311yescharacteristic
634C2×Dic3C23×D313yes—
635D12—26no—
636D12—26no—
637D12—66no—
638D12—62no—
639D12—123no—
640C4×D3—22no—
641C4×D3—26no—
642C4×D3—26no—
643C4×D3—26no—
644C4×D3—612no—
645C4×D3—66no—
646C4×D3—66no—
647C4×D3—126no—
648C4×D3C2×#67112yes—
649Dic6—66no—
650Dic6—66no—
651Dic6—66no—
652Dic6—66no—
653Dic6—126no—
654Dic6C2×#67112yes—
655C2×C32—43no—
656C2×C32C23×D411yescharacteristic
657C2×C32#58511yescharacteristic
658C2×C32#58511yescharacteristic
659C3⋊D3—41no—
660C3×D3—22no—
661C3×D3—43no—
662C3×D3—43no—
663C24—33no—
664#41—24no—
665#41—612no—
666#41—612no—
667#41—64no—
668#41—64no—
669#41—1812no—
670#41—1812no—
671#41—1812no—
672C2×Q8—38no—
673C2×Q8—33no—
674C2×Q8—93no—
675C2×Q8—93no—
676C2×Q8—1812no—
677C2×Q8—184no—
678C2×Q8C2×D3211yescharacteristic
679C2×D4—36no—
680C2×D4—33no—
681C2×D4—36no—
682C2×D4—33no—
683C2×D4—33no—
684C2×D4—612no—
685C2×D4—91no—
686C2×D4—93no—
687C2×D4—93no—
688C2×D4—93no—
689C2×D4—96no—
690C2×D4—93no—
691C2×D4—93no—
692C2×D4C2×D3213yes—
693C22×C4—33no—
694C22×C4—33no—
695C22×C4—33no—
696C22×C4—33no—
697C22×C4—33no—
698C22×C4—31no—
699C22×C4—612no—
700C22×C4—96no—
701C22×C4—93no—
702C22×C4C2×D3213yes—
703C4⋊C4—33no—
704C4⋊C4—31no—
705C4⋊C4—93no—
706C4⋊C4—93no—
707C4⋊C4—91no—
708C4⋊C4—93no—
709C4⋊C4—93no—
710C4⋊C4—93no—
711C22⋊C4—33no—
712C22⋊C4—33no—
713C22⋊C4—91no—
714C22⋊C4—91no—
715C22⋊C4—93no—
716C22⋊C4—93no—
717C22⋊C4—93no—
718C22⋊C4—96no—
719C22⋊C4—93no—
720C22⋊C4—96no—
721C22⋊C4—93no—
722C22⋊C4—91no—
723C42—33no—
724C42—96no—
725C42—93no—
726C22×C3—23no—
727C22×C3—23no—
728C22×C3—23no—
729C22×C3—23no—
730C22×C3—23no—
731C22×C3—23no—
732C22×C3—21no—
733C22×C3—32no—
734C22×C3—43no—
735C22×C3—43no—
736C22×C3—43no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—63no—
740C22×C3—63no—
741C22×C3—63no—
742C22×C3—63no—
743C22×C3—63no—
744C22×C3—63no—
745C22×C3—1212no—
746C22×C3C24×D311yescharacteristic
747C22×C3C24×D311yescharacteristic
748C2×D3—21no—
749C2×D3—21no—
750C2×D3—23no—
751C2×D3—23no—
752C2×D3—23no—
753C2×D3—23no—
754C2×D3—23no—
755C2×D3—23no—
756C2×D3—412no—
757C2×D3—62no—
758C2×D3—61no—
759C2×D3—61no—
760C2×D3—61no—
761C2×D3—61no—
762C2×D3—61no—
763C2×D3—61no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3C22×#6712yes—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—26no—
770C3×C4—36no—
771C3×C4—41no—
772C3×C4—61no—
773C3×C4—63no—
774C3×C4—61no—
775C3×C4—61no—
776C3×C4C2×D3×D416yes—
777C3×C4C22×#6716yes—
778Dic3—21no—
779Dic3—21no—
780Dic3—23no—
781Dic3—21no—
782Dic3—63no—
783Dic3—63no—
784Dic3—63no—
785Dic3—61no—
786Dic3—61no—
787Dic3—63no—
788Dic3—123no—
789Dic3—123no—
790Dic3—121no—
791Dic3C22×#6716yes—
792C32#348711yescharacteristic, complemented, Sylow
793C23—31no—
794C23—33no—
795C23—33no—
796C23—66no—
797C23—91no—
798C23—123no—
799C23—123no—
800C23C22×D3213yes—
801Q8—312no—
802Q8—186no—
803Q8—186no—
804Q8D3×#6714yes—
805D4—26no—
806D4—612no—
807D4—66no—
808D4—66no—
809D4—123no—
810D4—126no—
811D4—186no—
812D4—182no—
813D4—186no—
814D4—363no—
815D4—363no—
816D4—366no—
817D4—363no—
818C2×C4—26no—
819C2×C4—33no—
820C2×C4—312no—
821C2×C4—31no—
822C2×C4—33no—
823C2×C4—31no—
824C2×C4—31no—
825C2×C4—66no—
826C2×C4—62no—
827C2×C4—66no—
828C2×C4—66no—
829C2×C4—66no—
830C2×C4—93no—
831C2×C4—91no—
832C2×C4—93no—
833C2×C4—1812no—
834C2×C4—186no—
835C2×C4C22×D3211yescharacteristic
836C2×C4C22×D3213yes—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—43no—
841C2×C3—43no—
842C2×C3—62no—
843C2×C3—83no—
844C2×C3—123no—
845C2×C3—123no—
846C2×C3C22×D3×D411yescharacteristic
847C2×C3#596411yescharacteristic
848C2×C3#596411yescharacteristic
849C2×C3#596411yescharacteristic
850C2×C3#596611yescharacteristic
851C2×C3C23×#6711yescharacteristic
852D3—22no—
853D3—43no—
854D3—43no—
855D3—122no—
856D3—121no—
857D3—121no—
858C22—23no—
859C22—23no—
860C22—23no—
861C22—32no—
862C22—61no—
863C22—61no—
864C22—63no—
865C22—63no—
866C22—63no—
867C22—63no—
868C22—63no—
869C22—63no—
870C22—1212no—
871C22—181no—
872C22—181no—
873C22—181no—
874C22C23×D3211yescharacteristic
875C4—21no—
876C4—36no—
877C4—61no—
878C4—63no—
879C4—61no—
880C4—61no—
881C4—183no—
882C4—181no—
883C4—183no—
884C4C2×D3×#6716yes—
885C3—21no—
886C3#8678311yescharacteristic, complemented
887C3#8727411yescharacteristic, complemented
888C2—43no—
889C2—62no—
890C2—123no—
891C2—123no—
892C2—361no—
893C2#1059669511yescharacteristic
894C2#1059669611yescharacteristic
895C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3487
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×#64315C2semidirect
3. #10596302C2semidirect
4. C3×#5834C2semidirect
5. #10595414C2semidirect
6. #10595412C2semidirect
7. #10595347C2semidirect
8. #10595233C2semidirect
9. #10595231C2semidirect
10. #10595158C2semidirect
11. #10595157C2semidirect
12. #10595006C2semidirect
13. #10595002C2semidirect
14. #10594899C2semidirect
15. #10594892C2semidirect
19. C2×Q8×C3⋊D3C22semidirect
22. C2×C3×#239C22semidirect
30. C2×#3796C22semidirect
32. C2×D3×Dic6C22semidirect
33. Q8×C3⋊Dic3C22semidirect
34. #64147C22semidirect
35. #64145C22semidirect
36. C4×#638C22semidirect
37. #64133C22semidirect
38. C3×Q8×Dic3C22semidirect
39. C3×#940C22semidirect
40. C3×#938C22semidirect
41. C3×#930C22semidirect
42. C3×C4×#67C22semidirect
43. #63979C22semidirect
44. #63978C22semidirect
48. Dic3×#67C22semidirect
49. #63970C22semidirect
50. #63970C22semidirect
51. #63964C22semidirect
52. #63959C22semidirect
53. #63916C22semidirect
54. #63914C22semidirect
55. #63908C22semidirect
56. #63908C22semidirect
57. #63906C22semidirect
59. C4×#626C22semidirect
60. C4×#625C22semidirect
61. #63879C22semidirect
62. #63860C22semidirect
63. #63857C22semidirect
65. #63851C22semidirect
67. #63843C22semidirect
68. Dic3×Dic6C22semidirect
72. C2×D3×#41D3semidirect
79. #5834D3semidirect
116. C3×D3×Q8D4semidirect
181. C2×#239C2×D3semidirect
210. Q8×Dic3C2×D3semidirect
215. #940C2×D3semidirect
227. #938C2×D3semidirect
240. #930C2×D3semidirect
251. C4×#67C2×D3semidirect
392. D3×Q8#67semidirect
792. C32#3487semidirect
886. C3#86783semidirect
887. C3#87274semidirect

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×#643152
#105963022
C3×#58342
#105954142
#105954122
#105953472
#105952332
#105952312
#105951582
#105951572
#105950062
#105950022
#105948992
#105948922
#872743
#867833