Finite Group Databasebeta

← #11904556

Subgroups — #11904556

Order 1152.

3228 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic, complemented
2C2×#64316C211yesmaximal, characteristic, complemented
3#10596305C211yesmaximal, characteristic, complemented
4C3×#5831C211yesmaximal, characteristic, complemented
5#10595410C211yesmaximal, characteristic, complemented
6#10595409C211yesmaximal, characteristic, complemented
7#10595347C211yesmaximal, characteristic, complemented
8#10595237C213yesmaximal, complemented
9#10595236C213yesmaximal, complemented
10#10595235C213yesmaximal, complemented
11#10595231C213yesmaximal, complemented
12#10595007C213yesmaximal, complemented
13#10595005C213yesmaximal, complemented
14#10595002C213yesmaximal, complemented
15#10594830C213yesmaximal, complemented
16#87274—31nomaximal
17#86736—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×#3832C2211yescharacteristic, complemented
20C3×D3×#41—28no—
21C2×C3×#239C2211yescharacteristic
22C2×C3×D3×Q8C2211yescharacteristic
23C2×C3×D3×Q8C2211yescharacteristic, complemented
24C2×C3×#237C2213yes—
25C2×C3×D3×D4C2213yes—
26C2×C3×#235C2213yes—
27C22×C3×C4×D3C2213yes—
28#64316—28no—
29C2×#3799C2213yes—
30C2×#3799C2213yescomplemented
31C2×#3798C2213yes—
32C2×#3797C2213yescomplemented
33Q8×C3⋊Dic3C2211yescharacteristic, complemented
34#64149C2213yescomplemented
35#64147C2213yescomplemented
36#64139C2213yescomplemented
37C4×#638C2213yescomplemented
38C3×Q8×Dic3C2211yescharacteristic, complemented
39C3×#938C2213yescomplemented
40C3×#936C2213yescomplemented
41C3×C4×#67C2213yescomplemented
42C3×#924C2213yescomplemented
43#63979C2216yescomplemented
44#63978C2213yescomplemented
45#63977C2216yes—
46#63977C2213yes—
47#63976C2213yes—
48#63964C2213yescomplemented
49#63959C2216yescomplemented
50#63958C2216yescomplemented
51#63958C2216yescomplemented
52#63952C2216yescomplemented
53#63916C2213yescomplemented
54#63911C2213yescomplemented
55#63909C2213yescomplemented
56#63908C2213yescomplemented
57#63906C2213yescomplemented
58#63905C2211yescharacteristic
59#63904C2216yescomplemented
60C4×#626C2213yescomplemented
61C4×#625C2213yescomplemented
62#63863C2213yescomplemented
63#63856C2213yescomplemented
64#63855C2213yes—
65#63851C2213yescomplemented
66#63850C2213yes—
67#63843C2213yescomplemented
68Dic3×Dic6C2213yescomplemented
69#63841C2213yes—
70C22×C3×#41—31no—
71C2×D3×#41D311yescharacteristic, complemented
72C2×#1007—31no—
73C2×#1007—31no—
74C3×#548—31no—
75#5834—31no—
76#5834—31no—
77#5834—31no—
78#5834—33no—
79#5834—33no—
80#5834—61no—
81#5831—31no—
82#5831—33no—
83#5831—33no—
84#5831D311yescharacteristic, complemented
85#5817—31no—
86#5812—31no—
87#5805—33no—
88#5805—33no—
89#5791—33no—
90#5791—33no—
91#5677—33no—
92#5674—33no—
93#5633—33no—
94#5627—33no—
95#5607—33no—
96#5599—33no—
97#5577—31no—
98#5572—31no—
99#5553—33no—
100#5547—33no—
101C23×C3×D3C2313yes—
102C32×#41—24no—
103C2×C32×Q8C2311yescharacteristic
104C2×C32×D4C2313yes—
105C22×C32×C4C2313yes—
106C2×#638C2313yes—
107C2×#638C2316yes—
108#3832—24no—
109C2×C4⋊(C3⋊D3)C2313yes—
110C2×C4×C3⋊D3C2313yes—
111C2×C3×#67C2316yes—
112C2×C3×#67C2313yes—
113C22×C3×Dic3C2313yes—
114C3×#239—24no—
115C3×D3×Q8—24no—
116C3×D3×Q8D418yescomplemented
117C3×#237—212no—
118C3×D3×D4—212no—
119C3×#235—212no—
120C2×C3×D12C2313yes—
121C2×C3×C4×D3—212no—
122C2×C3×C4×D3C2313yes—
123C2×C3×C4×D3C2311yescharacteristic
124C2×C3×C4×D3C2313yes—
125C2×C3×C4×D3C2313yes—
126C2×C3×C4×D3C2313yes—
127C2×C3×Dic6C2313yes—
128C2×C3×Dic6C2313yes—
129C2×#627C2313yes—
130C2×#626C2313yes—
131C2×#626C2313yes—
132C2×#626C2313yes—
133C2×#626C2316yes—
134C2×#625C2311yescharacteristic
135C2×#625C2313yes—
136C2×#624C2316yes—
137#3799—212no—
138#3799—212no—
139#3798—212no—
140#3797—212no—
141#3757C2313yes—
142#3752C2313yes—
143C4⋊(C3⋊Dic3)C2313yes—
144#3750C2311yescharacteristic
145C4×C3⋊Dic3C2313yes—
146C3×#217C2316yes—
147C3×#217C2313yes—
148C3×(C2×D3)⋊C4C2311yescharacteristic
149C3×C4⋊Dic3C2313yes—
150C3×Dic3⋊C4C2313yes—
151C3×C4×Dic3C2313yes—
152#3724C2313yes—
153Dic3⋊Dic3C2313yes—
154Dic3⋊Dic3C2313yes—
155Dic3⋊Dic3C2311yescharacteristic
156#3722C2313yes—
157(C2×D3)⋊Dic3C2313yes—
158(C2×D3)⋊Dic3C2313yes—
159(C2×D3)⋊Dic3C2313yes—
160(C2×D3)⋊Dic3C2311yescharacteristic
161(C2×D3)⋊Dic3C2316yes—
162(C2×D3)⋊Dic3C2311yescharacteristic
163Dic32C2316yes—
164#3487—91noSylow
165C2×C3×#41—21no—
166C2×C3×#41—31no—
167C2×C3×#41—33no—
168C2×C3×#41—33no—
169C2×C3×#41—68no—
170C2×C3×#41C2×D311yescharacteristic
171C2×C3×#41C2×D311yescharacteristic
172C22×C3×Q8—31no—
173C22×C3×Q8—31no—
174C22×C3×D4—33no—
175C23×C3×C4—33no—
176D3×#41—28no—
177#1007—68no—
178#1007—68no—
179C2×#239—31no—
180C2×#239—31no—
181C2×#239—33no—
182C2×#239—33no—
183C2×#239—61no—
184C2×#239C2×D311yescharacteristic
185C2×D3×Q8—33no—
186C2×D3×Q8—33no—
187C2×D3×Q8C2×D311yescharacteristic
188C2×D3×Q8C2×D311yescharacteristic, complemented
189C2×#237C2×D313yes—
190C2×D3×D4C2×D313yes—
191C2×#235—33no—
192C2×#235—33no—
193C2×#235—33no—
194C2×#235—33no—
195C2×#235C2×D313yes—
196C22×C4×D3C2×D313yes—
197C3×#124—33no—
198C3×C22⋊Q8—33no—
199C3×#121—33no—
200C3×C4×Q8—31no—
201C3×C4×D4—33no—
202#953—33no—
203#953—33no—
204#953—36no—
205#947—33no—
206#946—33no—
207Q8×Dic3—31no—
208Q8×Dic3—31no—
209Q8×Dic3—33no—
210Q8×Dic3—33no—
211Q8×Dic3—61no—
212Q8×Dic3C2×D311yescharacteristic, complemented
213#940—33no—
214#940—33no—
215#940—36no—
216#940—36no—
217#940—33no—
218#940—63no—
219#939—33no—
220#938—33no—
221#938—33no—
222#938—33no—
223#938—36no—
224#938—36no—
225#938—33no—
226#938—63no—
227#938C2×D313yescomplemented
228#937—33no—
229#936—33no—
230#936—36no—
231#936C2×D313yescomplemented
232#930—33no—
233#930—33no—
234#930—33no—
235#930—33no—
236#930—33no—
237#930—33no—
238#930—63no—
239#929—31no—
240#929—33no—
241C4×#67—33no—
242C4×#67—33no—
243C4×#67—33no—
244C4×#67—33no—
245C4×#67—36no—
246C4×#67—36no—
247C4×#67—33no—
248C4×#67—63no—
249C4×#67C2×D313yescomplemented
250#926—33no—
251#926—33no—
252#924—33no—
253#924—33no—
254#924—33no—
255#924C2×D313yescomplemented
256#896—33no—
257#895—33no—
258#895—33no—
259#894—33no—
260#893—36no—
261#892—33no—
262#887—33no—
263#885—36no—
264#884—36no—
265#884—36no—
266#884—33no—
267#883—31no—
268#882—33no—
269#882—36no—
270#67⋊C4—36no—
271#878—33no—
272#874—33no—
273C4×D12—33no—
274#872—33no—
275C4×Dic6—33no—
276C23×C32C2413yes—
277C22×C3⋊D3C2413yes—
278C22×C3×D3—26no—
279C22×C3×D3—43no—
280C22×C3×D3—43no—
281C22×C3×D3C2413yes—
282C22×C3×D3C2411yescharacteristic
283C22×C3×D3C2411yescharacteristic
284C32×Q8C2×D414yes—
285C32×D4—26no—
286C2×C32×C4—26no—
287C2×C32×C4C2411yescharacteristic
288C2×C32×C4C2413yes—
289#638—43no—
290#638—46no—
291C2×C3⋊Dic3C2413yes—
292C2×C3⋊Dic3C2411yescharacteristic
293C2×C3⋊Dic3C2411yescharacteristic
294C4⋊(C3⋊D3)—26no—
295C4×C3⋊D3—26no—
296C3×#67—212no—
297C3×#67—43no—
298C2×C3×Dic3—26no—
299C2×C3×Dic3C2413yes—
300C2×C3×Dic3C2413yes—
301C2×C3×Dic3C2411yescharacteristic
302C2×C3×Dic3C2411yescharacteristic
303C2×C3×Dic3C2413yes—
304C3×D12—26no—
305C3×C4×D3—22no—
306C3×C4×D3—26no—
307C3×C4×D3—26no—
308C3×C4×D3—26no—
309C3×C4×D3C2×D4112yes—
310C3×Dic6—26no—
311C3×Dic6C2×D4112yes—
312#627—26no—
313#626—26no—
314#626—26no—
315#626—43no—
316#626—46no—
317#625—22no—
318#625—43no—
319#624—212no—
320C2×2−1+4—91no—
321C22×#41—31no—
322#550—93no—
323#550—91no—
324#550—93no—
325#550—91no—
326#548—31no—
327#548—93no—
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—
343C2×C3×Q8—21no—
344C2×C3×Q8—38no—
345C2×C3×Q8—33no—
346C2×C3×Q8—33no—
347C2×C3×Q8—64no—
348C2×C3×Q8C22×D311yescharacteristic
349C2×C3×Q8C22×D311yescharacteristic
350C2×C3×D4—23no—
351C2×C3×D4—36no—
352C2×C3×D4—33no—
353C2×C3×D4—33no—
354C2×C3×D4—612no—
355C2×C3×D4C22×D313yes—
356C2×C3×D4C22×D313yes—
357C22×C3×C4—23no—
358C22×C3×C4—33no—
359C22×C3×C4—33no—
360C22×C3×C4—33no—
361C22×C3×C4—33no—
362C22×C3×C4—33no—
363C22×C3×C4—31no—
364C22×C3×C4—612no—
365C22×C3×C4C22×D313yes—
366C22×C3×C4C22×D313yes—
367C2×#67—31no—
368C2×#67—31no—
369C2×#67—36no—
370C2×#67—33no—
371C2×#67—33no—
372C2×#67—36no—
373C2×#67—33no—
374C2×#67—33no—
375C2×#67—33no—
376C2×#67—33no—
377C2×#67—36no—
378C2×#67—33no—
379C2×#67—63no—
380C2×#67—66no—
381C2×#67C22×D316yes—
382C2×#67C22×D313yes—
383C22×Dic3C22×D313yes—
384#239—24no—
385#239—612no—
386#239—64no—
387#239—64no—
388#239—612no—
389#239—124no—
390D3×Q8—24no—
391D3×Q8—612no—
392D3×Q8—612no—
393D3×Q8#6718yescomplemented
394#237—212no—
395D3×D4—212no—
396#235—212no—
397#235—612no—
398#235—612no—
399#235—612no—
400#235—612no—
401C2×D12—33no—
402C2×D12—33no—
403C2×D12—33no—
404C2×D12—33no—
405C2×D12—33no—
406C2×D12—36no—
407C2×D12—63no—
408C2×D12C22×D313yes—
409C2×C4×D3—212no—
410C2×C4×D3—33no—
411C2×C4×D3—33no—
412C2×C4×D3—36no—
413C2×C4×D3—36no—
414C2×C4×D3—63no—
415C2×C4×D3C22×D313yes—
416C2×C4×D3C22×D311yescharacteristic
417C2×C4×D3C22×D313yes—
418C2×C4×D3C22×D313yes—
419C2×C4×D3C22×D313yes—
420C2×Dic6—33no—
421C2×Dic6—33no—
422C2×Dic6C22×D313yes—
423C2×Dic6C22×D313yes—
424C3×C4⋊C4—33no—
425C3×C4⋊C4—33no—
426C3×C22⋊C4—33no—
427C3×C22⋊C4—36no—
428C3×C22⋊C4—31no—
429C3×C42—33no—
430#217—33no—
431#217—33no—
432#217—31no—
433#217—33no—
434#217—36no—
435#217—33no—
436#217—33no—
437#217—31no—
438#217—63no—
439#217C22×D313yes—
440#217C22×D316yes—
441(C2×D3)⋊C4—31no—
442(C2×D3)⋊C4—33no—
443(C2×D3)⋊C4—33no—
444(C2×D3)⋊C4—33no—
445(C2×D3)⋊C4—36no—
446(C2×D3)⋊C4—31no—
447(C2×D3)⋊C4—33no—
448(C2×D3)⋊C4—33no—
449(C2×D3)⋊C4—33no—
450(C2×D3)⋊C4—33no—
451(C2×D3)⋊C4—63no—
452(C2×D3)⋊C4C22×D311yescharacteristic
453C4⋊Dic3—33no—
454C4⋊Dic3—33no—
455C4⋊Dic3—31no—
456C4⋊Dic3—33no—
457C4⋊Dic3—33no—
458C4⋊Dic3—63no—
459C4⋊Dic3C22×D313yes—
460Dic3⋊C4—31no—
461Dic3⋊C4—31no—
462Dic3⋊C4—33no—
463Dic3⋊C4—33no—
464Dic3⋊C4—33no—
465Dic3⋊C4—31no—
466Dic3⋊C4—33no—
467Dic3⋊C4—61no—
468Dic3⋊C4C22×D313yes—
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—23no—
480C2×C3⋊D3—23no—
481C2×C3⋊D3—23no—
482C2×C3×D3—21no—
483C2×C3×D3—21no—
484C2×C3×D3—21no—
485C2×C3×D3—23no—
486C2×C3×D3—21no—
487C2×C3×D3—23no—
488C2×C3×D3—23no—
489C2×C3×D3—21no—
490C2×C3×D3—412no—
491C2×C3×D3C22×D412yes—
492C32×C4—21no—
493C32×C4C22×D416yes—
494C3⋊Dic3—21no—
495C3⋊Dic3—21no—
496C3⋊Dic3—23no—
497C3×Dic3—23no—
498C3×Dic3—21no—
499C3×Dic3—21no—
500C3×Dic3—23no—
501C3×Dic3C22×D416yes—
5022−1+4—188no—
503C2×#41—31no—
504C2×#41—33no—
505C2×#41—33no—
506C2×#41—68no—
507C2×#41—93no—
508C2×#41—93no—
509C2×#41—93no—
510C2×#41—91no—
511C2×#41D3211yescharacteristic
512C22×Q8—31no—
513C22×Q8—31no—
514C22×Q8—93no—
515C22×D4—33no—
516C23×C4—33no—
517#127—93no—
518#127—96no—
519#127—93no—
520#124—33no—
521#124—96no—
522#124—93no—
523#123—91no—
524#123—93no—
525C22⋊Q8—33no—
526C22⋊Q8—93no—
527C22⋊Q8—93no—
528C22⋊Q8—93no—
529#121—33no—
530#121—93no—
531#121—96no—
532#121—96no—
533#121—93no—
534#121—93no—
535#121—93no—
536#121—93no—
537#121—93no—
538#121—93no—
539#120—93no—
540#120—96no—
541#120—93no—
542C4×Q8—31no—
543C4×Q8—93no—
544C4×Q8—93no—
545C4×Q8—91no—
546C4×D4—33no—
547C4×D4—93no—
548C4×D4—96no—
549C4×D4—96no—
550C4×D4—93no—
551C4×D4—93no—
552#117—93no—
553#117—93no—
554C23×C3—23no—
555C23×C3—31no—
556C23×C3—33no—
557C23×C3—31no—
558C23×C3—66no—
559C23×C3—123no—
560C23×C3—123no—
561C23×C3C23×D313yes—
562C23×C3C23×D313yes—
563C22×D3—26no—
564C22×D3—33no—
565C22×D3—33no—
566C22×D3—43no—
567C22×D3—43no—
568C22×D3—63no—
569C22×D3C23×D313yes—
570C22×D3C23×D311yescharacteristic
571C22×D3C23×D311yescharacteristic
572C3×Q8—24no—
573C3×Q8—312no—
574C3×Q8—66no—
575C3×Q8D3×D414yes—
576C3×Q8C2×#6714yes—
577C3×D4—26no—
578C3×D4—26no—
579C3×D4—46no—
580C3×D4—612no—
581C3×D4—66no—
582C3×D4—123no—
583C2×C3×C4—26no—
584C2×C3×C4—26no—
585C2×C3×C4—23no—
586C2×C3×C4—21no—
587C2×C3×C4—33no—
588C2×C3×C4—312no—
589C2×C3×C4—33no—
590C2×C3×C4—31no—
591C2×C3×C4—31no—
592C2×C3×C4—33no—
593C2×C3×C4—46no—
594C2×C3×C4—66no—
595C2×C3×C4—62no—
596C2×C3×C4—66no—
597C2×C3×C4—66no—
598C2×C3×C4—66no—
599C2×C3×C4C23×D311yescharacteristic
600C2×C3×C4C23×D311yescharacteristic
601C2×C3×C4C23×D313yes—
602C2×C3×C4C23×D313yes—
603#67—212no—
604#67—43no—
605#67—66no—
606#67—62no—
607#67—62no—
608#67—66no—
609#67—126no—
610#67—123no—
611#67—123no—
612#67—123no—
613#67—123no—
614#67—123no—
615#67—126no—
616#67—126no—
617#67—126no—
618#67—246no—
619C2×Dic3—26no—
620C2×Dic3—31no—
621C2×Dic3—33no—
622C2×Dic3—31no—
623C2×Dic3—33no—
624C2×Dic3—31no—
625C2×Dic3—31no—
626C2×Dic3—61no—
627C2×Dic3—63no—
628C2×Dic3—61no—
629C2×Dic3C23×D313yes—
630C2×Dic3C23×D311yescharacteristic
631C2×Dic3C23×D311yescharacteristic
632C2×Dic3C23×D313yes—
633C2×Dic3C23×D313yes—
634D12—26no—
635D12—66no—
636D12—66no—
637D12—66no—
638D12—66no—
639D12—126no—
640D12—123no—
641D12—126no—
642C4×D3—22no—
643C4×D3—26no—
644C4×D3—26no—
645C4×D3—26no—
646C4×D3—612no—
647C4×D3—66no—
648C4×D3—66no—
649C4×D3—612no—
650C4×D3—126no—
651C4×D3C2×#67112yes—
652Dic6—26no—
653Dic6—66no—
654Dic6—66no—
655Dic6C2×#67112yes—
656C2×C32—43no—
657C2×C32C23×D411yescharacteristic
658C2×C32#58511yescharacteristic
659C2×C32#58511yescharacteristic
660C3⋊D3—43no—
661C3×D3—22no—
662C3×D3—41no—
663C3×D3—43no—
664C24—33no—
665#41—24no—
666#41—612no—
667#41—612no—
668#41—64no—
669#41—1812no—
670#41—1812no—
671#41—1812no—
672#41—184no—
673C2×Q8—38no—
674C2×Q8—33no—
675C2×Q8—33no—
676C2×Q8—64no—
677C2×Q8—93no—
678C2×Q8—1812no—
679C2×Q8C2×D3211yescharacteristic
680C2×D4—36no—
681C2×D4—33no—
682C2×D4—33no—
683C2×D4—612no—
684C2×D4—93no—
685C2×D4—93no—
686C2×D4—93no—
687C2×D4—96no—
688C2×D4—91no—
689C2×D4—93no—
690C2×D4—93no—
691C2×D4—96no—
692C2×D4—93no—
693C2×D4C2×D3213yes—
694C22×C4—33no—
695C22×C4—33no—
696C22×C4—33no—
697C22×C4—33no—
698C22×C4—33no—
699C22×C4—31no—
700C22×C4—612no—
701C22×C4—96no—
702C22×C4—93no—
703C22×C4C2×D3213yes—
704C4⋊C4—33no—
705C4⋊C4—33no—
706C4⋊C4—93no—
707C4⋊C4—93no—
708C4⋊C4—93no—
709C4⋊C4—91no—
710C4⋊C4—93no—
711C4⋊C4—91no—
712C22⋊C4—33no—
713C22⋊C4—36no—
714C22⋊C4—31no—
715C22⋊C4—93no—
716C22⋊C4—91no—
717C22⋊C4—93no—
718C22⋊C4—91no—
719C22⋊C4—93no—
720C22⋊C4—96no—
721C22⋊C4—93no—
722C22⋊C4—93no—
723C22⋊C4—93no—
724C42—33no—
725C42—96no—
726C42—93no—
727C22×C3—23no—
728C22×C3—23no—
729C22×C3—23no—
730C22×C3—23no—
731C22×C3—23no—
732C22×C3—23no—
733C22×C3—21no—
734C22×C3—32no—
735C22×C3—43no—
736C22×C3—43no—
737C22×C3—43no—
738C22×C3—61no—
739C22×C3—61no—
740C22×C3—63no—
741C22×C3—61no—
742C22×C3—63no—
743C22×C3—61no—
744C22×C3—63no—
745C22×C3—61no—
746C22×C3—1212no—
747C22×C3C24×D311yescharacteristic
748C22×C3C24×D311yescharacteristic
749C2×D3—21no—
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—23no—
753C2×D3—23no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—23no—
757C2×D3—412no—
758C2×D3—63no—
759C2×D3—63no—
760C2×D3—63no—
761C2×D3—63no—
762C2×D3—63no—
763C2×D3—63no—
764C2×D3—123no—
765C2×D3—123no—
766C2×D3—123no—
767C2×D3C22×#6712yes—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—26no—
771C3×C4—36no—
772C3×C4—41no—
773C3×C4—61no—
774C3×C4—61no—
775C3×C4—63no—
776C3×C4—63no—
777C3×C4C2×D3×D416yes—
778C3×C4C22×#6716yes—
779Dic3—23no—
780Dic3—23no—
781Dic3—21no—
782Dic3—21no—
783Dic3—62no—
784Dic3—61no—
785Dic3—61no—
786Dic3—61no—
787Dic3—63no—
788Dic3—63no—
789Dic3—61no—
790Dic3—121no—
791Dic3—123no—
792Dic3C22×#6716yes—
793C32#348711yescharacteristic, complemented, Sylow
794C23—31no—
795C23—31no—
796C23—33no—
797C23—66no—
798C23—93no—
799C23—123no—
800C23—123no—
801C23C22×D3213yes—
802Q8—312no—
803Q8—66no—
804Q8—186no—
805Q8D3×#6714yes—
806D4—26no—
807D4—612no—
808D4—66no—
809D4—123no—
810D4—186no—
811D4—186no—
812D4—182no—
813D4—186no—
814D4—366no—
815D4—363no—
816D4—363no—
817D4—366no—
818D4—363no—
819C2×C4—26no—
820C2×C4—33no—
821C2×C4—312no—
822C2×C4—31no—
823C2×C4—33no—
824C2×C4—33no—
825C2×C4—31no—
826C2×C4—66no—
827C2×C4—62no—
828C2×C4—66no—
829C2×C4—66no—
830C2×C4—66no—
831C2×C4—91no—
832C2×C4—93no—
833C2×C4—91no—
834C2×C4—1812no—
835C2×C4—186no—
836C2×C4C22×D3211yescharacteristic
837C2×C4C22×D3213yes—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—21no—
841C2×C3—43no—
842C2×C3—43no—
843C2×C3—62no—
844C2×C3—83no—
845C2×C3—123no—
846C2×C3—121no—
847C2×C3C22×D3×D411yescharacteristic
848C2×C3#596411yescharacteristic
849C2×C3#596411yescharacteristic
850C2×C3#596411yescharacteristic
851C2×C3#596811yescharacteristic
852C2×C3C23×#6711yescharacteristic
853D3—22no—
854D3—41no—
855D3—43no—
856D3—123no—
857D3—123no—
858D3—243no—
859C22—23no—
860C22—23no—
861C22—23no—
862C22—32no—
863C22—61no—
864C22—61no—
865C22—61no—
866C22—63no—
867C22—61no—
868C22—63no—
869C22—61no—
870C22—63no—
871C22—1212no—
872C22—183no—
873C22—183no—
874C22—183no—
875C22C23×D3211yescharacteristic
876C4—21no—
877C4—36no—
878C4—63no—
879C4—61no—
880C4—61no—
881C4—63no—
882C4—181no—
883C4—183no—
884C4—181no—
885C4C2×D3×#6716yes—
886C3—21no—
887C3#8673611yescharacteristic, complemented
888C3#8727411yescharacteristic, complemented
889C2—43no—
890C2—62no—
891C2—123no—
892C2—121no—
893C2—363no—
894C2#1059669511yescharacteristic
895C2#1059669711yescharacteristic
896C2C22×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×#64316C2semidirect
3. #10596305C2semidirect
4. C3×#5831C2semidirect
5. #10595410C2semidirect
6. #10595409C2semidirect
7. #10595347C2semidirect
8. #10595237C2semidirect
9. #10595236C2semidirect
10. #10595235C2semidirect
11. #10595231C2semidirect
12. #10595007C2semidirect
13. #10595005C2semidirect
14. #10595002C2semidirect
15. #10594830C2semidirect
19. C2×#3832C22semidirect
23. C2×C3×D3×Q8C22semidirect
30. C2×#3799C22semidirect
32. C2×#3797C22semidirect
33. Q8×C3⋊Dic3C22semidirect
34. #64149C22semidirect
35. #64147C22semidirect
36. #64139C22semidirect
37. C4×#638C22semidirect
38. C3×Q8×Dic3C22semidirect
39. C3×#938C22semidirect
40. C3×#936C22semidirect
41. C3×C4×#67C22semidirect
42. C3×#924C22semidirect
43. #63979C22semidirect
44. #63978C22semidirect
48. #63964C22semidirect
49. #63959C22semidirect
50. #63958C22semidirect
51. #63958C22semidirect
52. #63952C22semidirect
53. #63916C22semidirect
54. #63911C22semidirect
55. #63909C22semidirect
56. #63908C22semidirect
57. #63906C22semidirect
59. #63904C22semidirect
60. C4×#626C22semidirect
61. C4×#625C22semidirect
62. #63863C22semidirect
63. #63856C22semidirect
65. #63851C22semidirect
67. #63843C22semidirect
68. Dic3×Dic6C22semidirect
71. C2×D3×#41D3semidirect
84. #5831D3semidirect
116. C3×D3×Q8D4semidirect
188. C2×D3×Q8C2×D3semidirect
212. Q8×Dic3C2×D3semidirect
227. #938C2×D3semidirect
231. #936C2×D3semidirect
249. C4×#67C2×D3semidirect
255. #924C2×D3semidirect
393. D3×Q8#67semidirect
793. C32#3487semidirect
887. C3#86736semidirect
888. 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×#643162
#105963052
C3×#58312
#105954102
#105954092
#105953472
#105952372
#105952362
#105952352
#105952312
#105950072
#105950052
#105950022
#105948302
#872743
#867363