Finite Group Databasebeta

← #11906285

Subgroups — #11906285

Order 1152.

2028 conjugacy classes of subgroups.

The subgroup lattice has 1245 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596156C211yesmaximal, characteristic, complemented
2C3×#5689C211yesmaximal, characteristic
3C3×#5685C211yesmaximal, characteristic, complemented
4#10594596C212yesmaximal, complemented
5#10594477C211yesmaximal, characteristic
6#10594391C212yesmaximal
7#10594389C212yesmaximal
8#10594388C212yesmaximal
9#10594385C212yesmaximal
10#10594357C211yesmaximal, characteristic
11D3×#887C211yesmaximal, characteristic
12#10594342C211yesmaximal, characteristic
13#10594324C211yesmaximal, characteristic, complemented
14#10594322C211yesmaximal, characteristic, complemented
15#10594317C211yesmaximal, characteristic, complemented
16#10594315C212yesmaximal, complemented
17#10594314C212yesmaximal, complemented
18#10594313C212yesmaximal, complemented
19#10594313C211yesmaximal, characteristic, complemented
20#10593926C211yesmaximal, characteristic
21#10593885C211yesmaximal, characteristic
22#10593864C211yesmaximal, characteristic, complemented
23#10593856C211yesmaximal, characteristic, complemented
24#87032—31nomaximal
25#86585—31nomaximal
26C2×D3×Dic6C2211yescharacteristic
27C32×#125C2211yescharacteristic
28#64099C2211yescharacteristic
29#64098C2212yes—
30#64098C2212yes—
31#64097C2212yes—
32#64097C2211yescharacteristic
33#64096C2211yescharacteristic
34#64096C2212yes—
35#64096C2211yescharacteristic
36C4×#634C2211yescharacteristic
37C4×#634C2211yescharacteristic
38C3×#897C2212yes—
39C3×#896C2212yes—
40C3×#892C2211yescharacteristic
41C3×D3×C4⋊C4C2211yescharacteristic
42C3×#890C2211yescharacteristic
43C3×#890C2211yescharacteristic
44C3×#889C2212yes—
45C3×#889C2212yes—
46C3×#889C2212yes—
47C3×#888C2212yes—
48C3×#888C2211yescharacteristic
49C3×#888C2211yescharacteristic
50C3×#888C2212yes—
51C3×#887C2211yescharacteristic
52C3×#887C2211yescharacteristic
53C3×#887C2212yes—
54C3×#872C2211yescharacteristic
55C3×#869C2211yescharacteristic
56C3×C4×Dic6C2211yescharacteristic
57C3×C4×Dic6C2211yescharacteristic
58#63919C2212yes—
59#63919C2211yescharacteristic
60#63919C2211yescharacteristic
61#63918C2212yes—
62C4×#627C2211yescharacteristic
63C4×#627C2212yes—
64C4×#627C2211yescharacteristic
65#63899C2211yescharacteristic
66#63899C2212yes—
67#63896C2211yescharacteristic
68#63896C2212yes—
69#63893C2211yescharacteristic
70#63887C2211yescharacteristic
71#63878C2212yes—
72#63878C2212yes—
73#63877C2212yes—
74#63877C2212yes—
75D3×Dic3⋊C4C2212yes—
76C4×D3×Dic3C2212yes—
77C4×D3×Dic3C2211yescharacteristic
78#63873C2212yes—
79#63873C2212yes—
80#63869C2211yescharacteristic
81#63869C2211yescharacteristic
82#63867C2212yes—
83#63867C2212yes—
84#63856C2212yes—
85#63855C2211yescharacteristic
86#63851C2212yes—
87#63847C2212yes—
88#63847C2212yes—
89#63847C2212yes—
90#63847C2212yes—
91#63846C2211yescharacteristic
92#63846C2212yes—
93#63845C2212yes—
94#63845C2212yes—
95#63845C2211yescharacteristic
96#63844C2212yes—
97#63844C2212yes—
98#63844C2211yescharacteristic
99#63844C2211yescharacteristic
100#63844C2212yes—
101#63844C2211yescharacteristic
102#63843C2212yes—
103#63843C2211yescharacteristic
104#63843C2211yescharacteristic
105Dic3×Dic6C2212yes—
106Dic3×Dic6C2211yescharacteristic
107#63841C2211yescharacteristic
108#63840C2211yescharacteristic
109#63840C2212yes—
110#63839C2211yescharacteristic
111#63839C2212yes—
112#63839C2212yes—
113#63839C2212yes—
114#63839C2212yes—
115#63839C2212yes—
116#63839C2212yes—
117#63838C2212yes—
118#63838C2212yes—
119#63838C2212yes—
120#63838C2212yes—
121#63837C2212yes—
122#63837C2212yes—
123#63837C2212yes—
124#63837C2212yes—
125C3×#557—31no—
126C3×#544—31no—
127#5729—32no—
128#5729—31no—
129#5722—31no—
130#5722—32no—
131#5722—31no—
132#5722—32no—
133#5722—31no—
134#5721—32no—
135#5721—31no—
136#5721—31no—
137#5689—32no—
138#5689D311yescharacteristic
139#5688—32no—
140#5688—31no—
141#5685—31no—
142#5685—31no—
143#5685—31no—
144#5685—31no—
145#5685—32no—
146#5685—32no—
147#5685—32no—
148#5685—31no—
149#5685—32no—
150#5685—61no—
151#5685D311yescharacteristic, complemented
152#5623—32no—
153#5623—32no—
154#5622—32no—
155#5622—32no—
156#5578—32no—
157#5578—31no—
158#5572—31no—
159#5572—31no—
160C4×D3×Q8—31no—
161#5569—31no—
162#5569—31no—
163#5567—32no—
164#5567—31no—
165Q8×Dic6—31no—
166#5517—31no—
167#5517—31no—
168#5516—31no—
169#5516—31no—
170#5500—31no—
171C2×#887—31no—
172C2×#634C2311yescharacteristic
173C2×#634C2312yes—
174C2×#634C2311yescharacteristic
175C2×C3×C4×D3C2312yes—
176C2×C3×C4×D3C2311yescharacteristic
177C2×C3×Dic6C2312yes—
178C2×C3×Dic6C2312yes—
179C2×C3×Dic6C2311yescharacteristic
180C2×C3×Dic6C2312yes—
181C2×C3×Dic6C2311yescharacteristic
182C2×#627C2311yescharacteristic
183C2×#627C2312yes—
184C2×#627C2312yes—
185C2×#627C2311yescharacteristic
186C2×#627C2312yes—
187C2×D3×Dic3C2311yescharacteristic
188C2×D3×Dic3C2311yescharacteristic
189C2×D3×Dic3C2312yes—
190D3×Dic6Q818yescomplemented
191C32×C4⋊C4C2311yescharacteristic
192C32×C4⋊C4C2312yes—
193C32×C4⋊C4C2311yescharacteristic
194C32×C4⋊C4C2312yes—
195C32×C42C2311yescharacteristic
196C4⋊(C3⋊Dic3)C2311yescharacteristic
197C4⋊(C3⋊Dic3)C2311yescharacteristic
198C4⋊(C3⋊Dic3)C2312yes—
199#3750C2312yes—
200#3750C2311yescharacteristic
201#3750C2311yescharacteristic
202#3750C2312yes—
203#3750C2312yes—
204#3750C2312yes—
205#3750C2312yes—
206C4×C3⋊Dic3C2312yes—
207C4×C3⋊Dic3C2311yescharacteristic
208C4×C3⋊Dic3C2311yescharacteristic
209C4×C3⋊Dic3C2312yes—
210C4×C3⋊Dic3C2312yes—
211C3×(C2×D3)⋊C4C2312yes—
212C3×(C2×D3)⋊C4C2311yescharacteristic
213C3×(C2×D3)⋊C4C2311yescharacteristic
214C3×C4⋊Dic3C2312yes—
215C3×C4⋊Dic3C2312yes—
216C3×C4⋊Dic3C2311yescharacteristic
217C3×C4⋊Dic3C2311yescharacteristic
218C3×C4⋊Dic3C2311yescharacteristic
219C3×C4⋊Dic3C2312yes—
220C3×C4⋊Dic3C2311yescharacteristic
221C3×Dic3⋊C4C2311yescharacteristic
222C3×Dic3⋊C4C2312yes—
223C3×Dic3⋊C4C2312yes—
224C3×Dic3⋊C4C2312yes—
225C3×Dic3⋊C4C2311yescharacteristic
226C3×Dic3⋊C4C2312yes—
227C3×Dic3⋊C4C2312yes—
228C3×Dic3⋊C4C2312yes—
229C3×Dic3⋊C4C2312yes—
230C3×Dic3⋊C4C2311yescharacteristic
231C3×Dic3⋊C4C2311yescharacteristic
232C3×Dic3⋊C4C2312yes—
233C3×C4×Dic3C2312yes—
234C3×C4×Dic3C2312yes—
235C3×C4×Dic3C2311yescharacteristic
236C3×C4×Dic3C2312yes—
237C3×C4×Dic3C2311yescharacteristic
238C3×C4×Dic3C2312yes—
239C3×C4×Dic3C2311yescharacteristic
240#3724C2311yescharacteristic
241#3724C2312yes—
242#3724C2312yes—
243#3724C2312yes—
244#3724C2311yescharacteristic
245#3724C2312yes—
246#3724C2312yes—
247#3724C2312yes—
248#3724C2312yes—
249Dic3⋊Dic3C2311yescharacteristic
250Dic3⋊Dic3C2312yes—
251Dic3⋊Dic3C2312yes—
252Dic3⋊Dic3C2312yes—
253Dic3⋊Dic3C2311yescharacteristic
254Dic3⋊Dic3C2312yes—
255Dic3⋊Dic3C2311yescharacteristic
256Dic3⋊Dic3C2311yescharacteristic
257Dic3⋊Dic3C2312yes—
258Dic3⋊Dic3C2311yescharacteristic
259Dic3⋊Dic3C2311yescharacteristic
260(C2×D3)⋊Dic3C2312yes—
261(C2×D3)⋊Dic3C2311yescharacteristic
262(C2×D3)⋊Dic3C2311yescharacteristic
263Dic32C2311yescharacteristic
264Dic32C2312yes—
265Dic32C2312yes—
266Dic32C2312yes—
267Dic32C2312yes—
268Dic32C2312yes—
269Dic32C2311yescharacteristic
270Dic32C2312yes—
271Dic32C2312yes—
272#3502—91noSylow
273C2×D3×Q8—31no—
274C22×Dic6—31no—
275C3×C4⋊Q8—32no—
276C3×C4⋊Q8—31no—
277C3×C4⋊Q8—32no—
278C3×C4⋊Q8—31no—
279C3×C4⋊Q8—31no—
280C3×#125—21no—
281C3×#125—32no—
282C3×#125—32no—
283C3×#125—32no—
284C3×#125—31no—
285C3×#125—31no—
286C3×#125C2×D311yescharacteristic
287C3×#125C2×D311yescharacteristic
288C3×C22⋊Q8—32no—
289C3×C22⋊Q8—32no—
290C3×C4×Q8—32no—
291C3×C4×Q8—31no—
292C3×C4×Q8—31no—
293C3×C4×Q8—31no—
294C3×C4×Q8—31no—
295C3×#117—31no—
296C3×#117—31no—
297C2×C3×C4⋊C4—31no—
298#946—32no—
299#946—31no—
300Q8×Dic3—32no—
301Q8×Dic3—31no—
302Q8×Dic3—31no—
303Q8×Dic3—32no—
304Q8×Dic3—31no—
305#944—32no—
306#944—32no—
307#944—32no—
308#944—32no—
309#944—32no—
310#944—32no—
311#944—32no—
312#944—31no—
313#944—32no—
314#944—32no—
315#944—32no—
316#926—31no—
317#926—31no—
318#924—32no—
319#924—32no—
320C2×Dic3⋊C4—32no—
321C2×C4×Dic3—31no—
322C2×C4×Dic3—32no—
323#897—31no—
324#897C2×D312yes—
325#896—32no—
326#896—32no—
327#896—31no—
328#896—32no—
329#896—31no—
330#896C2×D312yes—
331#892—31no—
332#892—32no—
333#892—32no—
334#892C2×D311yescharacteristic
335D3×C4⋊C4—32no—
336D3×C4⋊C4C2×D311yescharacteristic
337#890—31no—
338#890—31no—
339#890—32no—
340#890—31no—
341#890—31no—
342#890—32no—
343#890—32no—
344#890—31no—
345#890—31no—
346#890—61no—
347#890C2×D311yescharacteristic
348#890C2×D311yescharacteristic
349#889—32no—
350#889—32no—
351#889—32no—
352#889—32no—
353#889—32no—
354#889—32no—
355#889—32no—
356#889—32no—
357#889—32no—
358#889—32no—
359#889—31no—
360#889—32no—
361#889—32no—
362#889—32no—
363#889—32no—
364#889—32no—
365#889—31no—
366#889—32no—
367#889—32no—
368#889—62no—
369#889—62no—
370#889C2×D312yes—
371#889C2×D312yes—
372#889C2×D312yes—
373#888—32no—
374#888—32no—
375#888—32no—
376#888—32no—
377#888—32no—
378#888—32no—
379#888—31no—
380#888—31no—
381#888—32no—
382#888—32no—
383#888—31no—
384#888—32no—
385#888—31no—
386#888—32no—
387#888—31no—
388#888—31no—
389#888—31no—
390#888—31no—
391#888—31no—
392#888—32no—
393#888—32no—
394#888—32no—
395#888—61no—
396#888—62no—
397#888C2×D312yes—
398#888C2×D311yescharacteristic
399#888C2×D312yes—
400#888C2×D311yescharacteristic
401#887—32no—
402#887—31no—
403#887—31no—
404#887—31no—
405#887—31no—
406#887—32no—
407#887—31no—
408#887—31no—
409#887—32no—
410#887—32no—
411#887—32no—
412#887—32no—
413#887—32no—
414#887—32no—
415#887—32no—
416#887—32no—
417#887—32no—
418#887—32no—
419#887—32no—
420#887—32no—
421#887—32no—
422#887—32no—
423#887—31no—
424#887—31no—
425#887—32no—
426#887—32no—
427#887—31no—
428#887—61no—
429#887—61no—
430#887—62no—
431#887C2×D311yescharacteristic
432#887C2×D312yes—
433#887C2×D311yescharacteristic
434#878—31no—
435#878—31no—
436#878—32no—
437#878—31no—
438#878—32no—
439#878—31no—
440#877—32no—
441#877—32no—
442#877—32no—
443#877—32no—
444#872—31no—
445#872—32no—
446#872—32no—
447#872C2×D311yescharacteristic
448C42×D3—31no—
449C42×D3—32no—
450#870—31no—
451#870—31no—
452#870—32no—
453#870—32no—
454#869—32no—
455#869C2×D311yescharacteristic
456C4×Dic6—31no—
457C4×Dic6—32no—
458C4×Dic6—31no—
459C4×Dic6—31no—
460C4×Dic6—31no—
461C4×Dic6—31no—
462C4×Dic6—31no—
463C4×Dic6—32no—
464C4×Dic6—32no—
465C4×Dic6—31no—
466C4×Dic6—31no—
467C4×Dic6—32no—
468C4×Dic6—32no—
469C4×Dic6—32no—
470C4×Dic6—32no—
471C4×Dic6—32no—
472C4×Dic6—31no—
473C4×Dic6—32no—
474C4×Dic6—31no—
475C4×Dic6—31no—
476C4×Dic6—32no—
477C4×Dic6—31no—
478C4×Dic6—61no—
479C4×Dic6—61no—
480C4×Dic6C2×D311yescharacteristic
481C4×Dic6C2×D311yescharacteristic
482C22×C3×D3C2411yescharacteristic
483C2×C32×C4C2412yes—
484C2×C32×C4C2411yescharacteristic
485C2×C32×C4C2412yes—
486C2×C32×C4C2411yescharacteristic
487C2×C32×C4C2411yescharacteristic
488C2×C3⋊Dic3C2412yes—
489C2×C3⋊Dic3C2411yescharacteristic
490C2×C3⋊Dic3C2411yescharacteristic
491C2×C3⋊Dic3C2411yescharacteristic
492C2×C3⋊Dic3C2412yes—
493C2×C3⋊Dic3C2411yescharacteristic
494#634—22no—
495#634—24no—
496#634C2×Q814yes—
497C2×C3×Dic3C2411yescharacteristic
498C2×C3×Dic3C2411yescharacteristic
499C2×C3×Dic3C2412yes—
500C2×C3×Dic3C2411yescharacteristic
501C2×C3×Dic3C2412yes—
502C2×C3×Dic3C2411yescharacteristic
503C2×C3×Dic3C2412yes—
504C2×C3×Dic3C2411yescharacteristic
505C2×C3×Dic3C2411yescharacteristic
506C2×C3×Dic3C2411yescharacteristic
507C2×C3×Dic3C2412yes—
508C3×C4×D3—42no—
509C3×C4×D3C2×Q814yes—
510C3×Dic6—41no—
511C3×Dic6—42no—
512C3×Dic6—42no—
513C3×Dic6—42no—
514C3×Dic6C2×Q814yes—
515#627—22no—
516#627—41no—
517#627—42no—
518#627—42no—
519#627C2×Q818yes—
520D3×Dic3—22no—
521D3×Dic3—41no—
522D3×Dic3C2×Q818yes—
523Q82—91no—
524Q82—92no—
525Q82—91no—
526#557—31no—
527#557—92no—
528#557—91no—
529#557—91no—
530#557—91no—
531#557—91no—
532#557—92no—
533#557—92no—
534#557—91no—
535#544—31no—
536#544—91no—
537#544—92no—
538#544—92no—
539#533—91no—
540#533—91no—
541#533—92no—
542#533—92no—
543#519—91no—
544#519—91no—
545C2×C4×Q8—91no—
546C2×C3×Q8—31no—
547C2×C3×Q8—32no—
548C2×C3×Q8—32no—
549C2×C3×Q8—32no—
550C2×C3×Q8—31no—
551C22×C3×C4—31no—
552C22×C3×C4—32no—
553C22×Dic3—32no—
554C22×Dic3—31no—
555C22×Dic3—31no—
556D3×Q8—38no—
557C2×C4×D3—32no—
558C2×C4×D3—31no—
559C2×C4×D3—31no—
560C2×C4×D3C22×D312yes—
561C2×C4×D3C22×D311yescharacteristic
562C2×Dic6—31no—
563C2×Dic6—31no—
564C2×Dic6—32no—
565C2×Dic6—32no—
566C2×Dic6—38no—
567C2×Dic6—31no—
568C2×Dic6—32no—
569C2×Dic6—31no—
570C2×Dic6—32no—
571C2×Dic6—31no—
572C2×Dic6—31no—
573C2×Dic6—31no—
574C2×Dic6—32no—
575C2×Dic6—31no—
576C2×Dic6—32no—
577C2×Dic6—32no—
578C2×Dic6—32no—
579C2×Dic6—61no—
580C2×Dic6—61no—
581C2×Dic6—62no—
582C2×Dic6C22×D312yes—
583C2×Dic6C22×D311yescharacteristic
584C2×Dic6C22×D312yes—
585C2×Dic6C22×D312yes—
586C2×Dic6C22×D311yescharacteristic
587C3×C4⋊C4—21no—
588C3×C4⋊C4—22no—
589C3×C4⋊C4—21no—
590C3×C4⋊C4—22no—
591C3×C4⋊C4—32no—
592C3×C4⋊C4—31no—
593C3×C4⋊C4—31no—
594C3×C4⋊C4—31no—
595C3×C4⋊C4—31no—
596C3×C4⋊C4—32no—
597C3×C4⋊C4—31no—
598C3×C4⋊C4—32no—
599C3×C4⋊C4—31no—
600C3×C4⋊C4—32no—
601C3×C4⋊C4—32no—
602C3×C4⋊C4—32no—
603C3×C4⋊C4—32no—
604C3×C4⋊C4—32no—
605C3×C4⋊C4—32no—
606C3×C4⋊C4—32no—
607C3×C4⋊C4—32no—
608C3×C4⋊C4—31no—
609C3×C4⋊C4—31no—
610C3×C4⋊C4C22×D311yescharacteristic
611C3×C4⋊C4C22×D311yescharacteristic
612C3×C4⋊C4C22×D311yescharacteristic
613C3×C4⋊C4C22×D312yes—
614C3×C4⋊C4C22×D312yes—
615C3×C4⋊C4C22×D311yescharacteristic
616C3×C4⋊C4C22×D312yes—
617C3×C4⋊C4C22×D312yes—
618C3×C22⋊C4—31no—
619C3×C22⋊C4—32no—
620C3×C22⋊C4—31no—
621C3×C42—21no—
622C3×C42—32no—
623C3×C42—31no—
624C3×C42—32no—
625C3×C42—32no—
626C3×C42—31no—
627C3×C42—32no—
628C3×C42—31no—
629C3×C42C22×D311yescharacteristic
630C3×C42C22×D311yescharacteristic
631#217—32no—
632#217—31no—
633#217—31no—
634(C2×D3)⋊C4—31no—
635(C2×D3)⋊C4—31no—
636(C2×D3)⋊C4—32no—
637(C2×D3)⋊C4C22×D311yescharacteristic
638(C2×D3)⋊C4C22×D312yes—
639(C2×D3)⋊C4C22×D311yescharacteristic
640C4⋊Dic3—31no—
641C4⋊Dic3—31no—
642C4⋊Dic3—31no—
643C4⋊Dic3—31no—
644C4⋊Dic3—32no—
645C4⋊Dic3—32no—
646C4⋊Dic3—31no—
647C4⋊Dic3—31no—
648C4⋊Dic3—32no—
649C4⋊Dic3—32no—
650C4⋊Dic3—32no—
651C4⋊Dic3—31no—
652C4⋊Dic3—32no—
653C4⋊Dic3—31no—
654C4⋊Dic3—31no—
655C4⋊Dic3—31no—
656C4⋊Dic3—32no—
657C4⋊Dic3—61no—
658C4⋊Dic3—61no—
659C4⋊Dic3—62no—
660C4⋊Dic3C22×D311yescharacteristic
661C4⋊Dic3C22×D312yes—
662C4⋊Dic3C22×D311yescharacteristic
663C4⋊Dic3C22×D311yescharacteristic
664C4⋊Dic3C22×D312yes—
665C4⋊Dic3C22×D312yes—
666C4⋊Dic3C22×D311yescharacteristic
667Dic3⋊C4—32no—
668Dic3⋊C4—32no—
669Dic3⋊C4—32no—
670Dic3⋊C4—31no—
671Dic3⋊C4—32no—
672Dic3⋊C4—31no—
673Dic3⋊C4—31no—
674Dic3⋊C4—32no—
675Dic3⋊C4—31no—
676Dic3⋊C4—32no—
677Dic3⋊C4—32no—
678Dic3⋊C4—32no—
679Dic3⋊C4—32no—
680Dic3⋊C4—32no—
681Dic3⋊C4—31no—
682Dic3⋊C4—31no—
683Dic3⋊C4—31no—
684Dic3⋊C4—32no—
685Dic3⋊C4—32no—
686Dic3⋊C4—31no—
687Dic3⋊C4—31no—
688Dic3⋊C4—32no—
689Dic3⋊C4—32no—
690Dic3⋊C4—32no—
691Dic3⋊C4—32no—
692Dic3⋊C4—32no—
693Dic3⋊C4—32no—
694Dic3⋊C4—31no—
695Dic3⋊C4—31no—
696Dic3⋊C4—31no—
697Dic3⋊C4—31no—
698Dic3⋊C4—32no—
699Dic3⋊C4—32no—
700Dic3⋊C4—32no—
701Dic3⋊C4—32no—
702Dic3⋊C4—32no—
703Dic3⋊C4—32no—
704Dic3⋊C4—32no—
705Dic3⋊C4—31no—
706Dic3⋊C4—32no—
707Dic3⋊C4—32no—
708Dic3⋊C4—32no—
709Dic3⋊C4—32no—
710Dic3⋊C4—61no—
711Dic3⋊C4—62no—
712Dic3⋊C4—61no—
713Dic3⋊C4—62no—
714Dic3⋊C4—62no—
715Dic3⋊C4—62no—
716Dic3⋊C4—62no—
717Dic3⋊C4C22×D311yescharacteristic
718Dic3⋊C4C22×D312yes—
719Dic3⋊C4C22×D312yes—
720Dic3⋊C4C22×D312yes—
721Dic3⋊C4C22×D312yes—
722Dic3⋊C4C22×D311yescharacteristic
723Dic3⋊C4C22×D311yescharacteristic
724Dic3⋊C4C22×D312yes—
725Dic3⋊C4C22×D312yes—
726Dic3⋊C4C22×D311yescharacteristic
727Dic3⋊C4C22×D312yes—
728Dic3⋊C4C22×D312yes—
729C4×Dic3—31no—
730C4×Dic3—31no—
731C4×Dic3—31no—
732C4×Dic3—31no—
733C4×Dic3—32no—
734C4×Dic3—32no—
735C4×Dic3—32no—
736C4×Dic3—32no—
737C4×Dic3—32no—
738C4×Dic3—32no—
739C4×Dic3—32no—
740C4×Dic3—31no—
741C4×Dic3—32no—
742C4×Dic3—32no—
743C4×Dic3—32no—
744C4×Dic3—31no—
745C4×Dic3—32no—
746C4×Dic3—31no—
747C4×Dic3—32no—
748C4×Dic3—32no—
749C4×Dic3—32no—
750C4×Dic3—32no—
751C4×Dic3—32no—
752C4×Dic3—32no—
753C4×Dic3—32no—
754C4×Dic3—31no—
755C4×Dic3—32no—
756C4×Dic3—32no—
757C4×Dic3—61no—
758C4×Dic3—62no—
759C4×Dic3—61no—
760C4×Dic3—62no—
761C4×Dic3—62no—
762C4×Dic3C22×D311yescharacteristic
763C4×Dic3C22×D311yescharacteristic
764C4×Dic3C22×D311yescharacteristic
765C4×Dic3C22×D312yes—
766C4×Dic3C22×D312yes—
767C4×Dic3C22×D312yes—
768C4×Dic3C22×D312yes—
769C22×C32C2511yescharacteristic
770C2×C3×D3—21no—
771C2×C3×D3—21no—
772C2×C3×D3C22×Q812yes—
773C32×C4—22no—
774C32×C4—21no—
775C32×C4—21no—
776C32×C4—22no—
777C32×C4C22×Q812yes—
778C3⋊Dic3—21no—
779C3⋊Dic3—22no—
780C3⋊Dic3—21no—
781C3⋊Dic3—21no—
782C3⋊Dic3C22×Q814yes—
783C3⋊Dic32−1+412yes—
784C3×Dic3—21no—
785C3×Dic3—21no—
786C3×Dic3—21no—
787C3×Dic3—21no—
788C3×Dic3—22no—
789C3×Dic3—21no—
790C3×Dic3—22no—
791C3×Dic3—22no—
792C3×Dic3—21no—
793C3×Dic3C22×Q814yes—
794C3×Dic3C22×Q812yes—
795C22×Q8—91no—
796C4⋊Q8—32no—
797C4⋊Q8—31no—
798C4⋊Q8—32no—
799C4⋊Q8—31no—
800C4⋊Q8—31no—
801C4⋊Q8—92no—
802C4⋊Q8—91no—
803C4⋊Q8—92no—
804C4⋊Q8—91no—
805C4⋊Q8—91no—
806C4⋊Q8—92no—
807C4⋊Q8—91no—
808C4⋊Q8—92no—
809C4⋊Q8—92no—
810C4⋊Q8—92no—
811C4⋊Q8—92no—
812C4⋊Q8—92no—
813C4⋊Q8—92no—
814C4⋊Q8—92no—
815C4⋊Q8—92no—
816C4⋊Q8—92no—
817C4⋊Q8—91no—
818#125—32no—
819#125—31no—
820#125—32no—
821#125—31no—
822#125—32no—
823#125—92no—
824#125—91no—
825#125—92no—
826#125—91no—
827#125—92no—
828#125—92no—
829#125—91no—
830#125—91no—
831#125—92no—
832#125—92no—
833#125—92no—
834#125—92no—
835#125—92no—
836#125—92no—
837#125—92no—
838#125—91no—
839#125D3211yescharacteristic
840C22⋊Q8—32no—
841C22⋊Q8—32no—
842C22⋊Q8—91no—
843C22⋊Q8—92no—
844C22⋊Q8—91no—
845C22⋊Q8—92no—
846C22⋊Q8—91no—
847C22⋊Q8—91no—
848C22⋊Q8—92no—
849C22⋊Q8—92no—
850C4×Q8—31no—
851C4×Q8—31no—
852C4×Q8—32no—
853C4×Q8—31no—
854C4×Q8—31no—
855C4×Q8—92no—
856C4×Q8—91no—
857C4×Q8—91no—
858C4×Q8—92no—
859C4×Q8—91no—
860C4×Q8—92no—
861C4×Q8—92no—
862C4×Q8—91no—
863C4×Q8—91no—
864C4×Q8—92no—
865C4×Q8—92no—
866C4×Q8—92no—
867C4×Q8—92no—
868C4×Q8—91no—
869C4×Q8—92no—
870C4×Q8—92no—
871C4×Q8—92no—
872C4×Q8—92no—
873C4×Q8—92no—
874C4×Q8—91no—
875C4×Q8—91no—
876C4×Q8—92no—
877C4×Q8—91no—
878C4×Q8—91no—
879C4×Q8—92no—
880C4×Q8—91no—
881C4×Q8—91no—
882#117—31no—
883#117—31no—
884#117—92no—
885#117—92no—
886#117—91no—
887#117—92no—
888#117—92no—
889#117—91no—
890C2×C4⋊C4—31no—
891C2×C4⋊C4—92no—
892C2×C42—91no—
893C2×C42—92no—
894C23×C3—31no—
895C22×D3C23×D311yescharacteristic
896C3×Q8—34no—
897C3×Q8—122no—
898C3×Q8—122no—
899C3×Q8—121no—
900C3×Q8—122no—
901C2×C3×C4—21no—
902C2×C3×C4—21no—
903C2×C3×C4—22no—
904C2×C3×C4—22no—
905C2×C3×C4—21no—
906C2×C3×C4—31no—
907C2×C3×C4—32no—
908C2×C3×C4—34no—
909C2×C3×C4—31no—
910C2×C3×C4—31no—
911C2×C3×C4—32no—
912C2×C3×C4—31no—
913C2×C3×C4—32no—
914C2×C3×C4—31no—
915C2×C3×C4—32no—
916C2×C3×C4—31no—
917C2×C3×C4—31no—
918C2×C3×C4—122no—
919C2×C3×C4C23×D311yescharacteristic
920C2×C3×C4C23×D311yescharacteristic
921C2×C3×C4C23×D312yes—
922C2×C3×C4C23×D312yes—
923C2×C3×C4C23×D312yes—
924C2×C3×C4C23×D312yes—
925C2×C3×C4C23×D311yescharacteristic
926C2×C3×C4C23×D311yescharacteristic
927C2×C3×C4C23×D311yescharacteristic
928C2×C3×C4C23×D311yescharacteristic
929C2×Dic3—32no—
930C2×Dic3—32no—
931C2×Dic3—31no—
932C2×Dic3—31no—
933C2×Dic3—38no—
934C2×Dic3—31no—
935C2×Dic3—32no—
936C2×Dic3—31no—
937C2×Dic3—32no—
938C2×Dic3—31no—
939C2×Dic3—31no—
940C2×Dic3—31no—
941C2×Dic3—31no—
942C2×Dic3—62no—
943C2×Dic3—61no—
944C2×Dic3—61no—
945C2×Dic3—61no—
946C2×Dic3—62no—
947C2×Dic3—61no—
948C2×Dic3—62no—
949C2×Dic3—121no—
950C2×Dic3C23×D311yescharacteristic
951C2×Dic3C23×D311yescharacteristic
952C2×Dic3C23×D312yes—
953C2×Dic3C23×D312yes—
954C2×Dic3C23×D311yescharacteristic
955C2×Dic3C23×D311yescharacteristic
956C2×Dic3C23×D312yes—
957C2×Dic3C23×D311yescharacteristic
958C2×Dic3C23×D311yescharacteristic
959C2×Dic3C23×D311yescharacteristic
960C2×Dic3C23×D312yes—
961C4×D3—38no—
962C4×D3—42no—
963C4×D3—62no—
964C4×D3—121no—
965C4×D3D3×Q814yes—
966Dic6—34no—
967Dic6—34no—
968Dic6—38no—
969Dic6—38no—
970Dic6—42no—
971Dic6—41no—
972Dic6—42no—
973Dic6—42no—
974Dic6—64no—
975Dic6—62no—
976Dic6—62no—
977Dic6—62no—
978Dic6—64no—
979Dic6—64no—
980Dic6—62no—
981Dic6—122no—
982Dic6—124no—
983Dic6—122no—
984Dic6—122no—
985Dic6—121no—
986Dic6—121no—
987Dic6—122no—
988Dic6—122no—
989Dic6D3×Q814yes—
990C2×C32C23×Q811yescharacteristic
991C2×C32C2×2−1+411yescharacteristic
992C2×C32#58511yescharacteristic
993C3×D3—22no—
994C2×Q8—31no—
995C2×Q8—32no—
996C2×Q8—31no—
997C2×Q8—32no—
998C2×Q8—32no—
999C2×Q8—92no—
1000C2×Q8—91no—
1001C2×Q8—92no—
1002C2×Q8—91no—
1003C2×Q8—92no—
1004C2×Q8—98no—
1005C2×Q8—91no—
1006C2×Q8—92no—
1007C2×Q8—91no—
1008C22×C4—31no—
1009C22×C4—32no—
1010C22×C4—92no—
1011C22×C4—91no—
1012C22×C4—91no—
1013C4⋊C4—32no—
1014C4⋊C4—31no—
1015C4⋊C4—32no—
1016C4⋊C4—31no—
1017C4⋊C4—31no—
1018C4⋊C4—31no—
1019C4⋊C4—32no—
1020C4⋊C4—32no—
1021C4⋊C4—31no—
1022C4⋊C4—31no—
1023C4⋊C4—32no—
1024C4⋊C4—31no—
1025C4⋊C4—31no—
1026C4⋊C4—32no—
1027C4⋊C4—32no—
1028C4⋊C4—32no—
1029C4⋊C4—32no—
1030C4⋊C4—32no—
1031C4⋊C4—32no—
1032C4⋊C4—92no—
1033C4⋊C4—92no—
1034C4⋊C4—92no—
1035C4⋊C4—91no—
1036C4⋊C4—92no—
1037C4⋊C4—92no—
1038C4⋊C4—92no—
1039C4⋊C4—91no—
1040C4⋊C4—91no—
1041C4⋊C4—91no—
1042C4⋊C4—92no—
1043C4⋊C4—91no—
1044C4⋊C4—92no—
1045C4⋊C4—91no—
1046C4⋊C4—92no—
1047C4⋊C4—92no—
1048C4⋊C4—92no—
1049C4⋊C4—92no—
1050C4⋊C4—91no—
1051C4⋊C4—91no—
1052C4⋊C4—92no—
1053C4⋊C4—92no—
1054C4⋊C4—92no—
1055C4⋊C4—91no—
1056C4⋊C4—91no—
1057C4⋊C4—92no—
1058C4⋊C4—92no—
1059C4⋊C4—92no—
1060C4⋊C4—91no—
1061C4⋊C4—91no—
1062C4⋊C4C2×D3211yescharacteristic
1063C4⋊C4C2×D3211yescharacteristic
1064C4⋊C4C2×D3212yes—
1065C4⋊C4C2×D3212yes—
1066C22⋊C4—31no—
1067C22⋊C4—32no—
1068C22⋊C4—31no—
1069C22⋊C4—91no—
1070C22⋊C4—91no—
1071C22⋊C4—92no—
1072C42—32no—
1073C42—31no—
1074C42—32no—
1075C42—31no—
1076C42—32no—
1077C42—32no—
1078C42—31no—
1079C42—91no—
1080C42—92no—
1081C42—92no—
1082C42—91no—
1083C42—92no—
1084C42—92no—
1085C42—92no—
1086C42—92no—
1087C42—92no—
1088C42—92no—
1089C42—91no—
1090C42—92no—
1091C42—92no—
1092C42—91no—
1093C42C2×D3211yescharacteristic
1094C22×C3—21no—
1095C22×C3—32no—
1096C22×C3—61no—
1097C22×C3—61no—
1098C22×C3C24×D311yescharacteristic
1099C22×C3C24×D311yescharacteristic
1100C2×D3—21no—
1101C2×D3—21no—
1102C2×D3C2×D3×Q812yes—
1103C3×C4—22no—
1104C3×C4—21no—
1105C3×C4—21no—
1106C3×C4—22no—
1107C3×C4—22no—
1108C3×C4—21no—
1109C3×C4—22no—
1110C3×C4—21no—
1111C3×C4—22no—
1112C3×C4—32no—
1113C3×C4—34no—
1114C3×C4—42no—
1115C3×C4—41no—
1116C3×C4—42no—
1117C3×C4—41no—
1118C3×C4—62no—
1119C3×C4—62no—
1120C3×C4—61no—
1121C3×C4—62no—
1122C3×C4—61no—
1123C3×C4—61no—
1124C3×C4—61no—
1125C3×C4—61no—
1126C3×C4—61no—
1127C3×C4C2×D3×Q812yes—
1128C3×C4C2×D3×Q812yes—
1129Dic3—21no—
1130Dic3—22no—
1131Dic3—21no—
1132Dic3—21no—
1133Dic3—22no—
1134Dic3—22no—
1135Dic3—21no—
1136Dic3—21no—
1137Dic3—21no—
1138Dic3—34no—
1139Dic3—34no—
1140Dic3—32no—
1141Dic3—32no—
1142Dic3—64no—
1143Dic3—62no—
1144Dic3—61no—
1145Dic3—61no—
1146Dic3—61no—
1147Dic3—61no—
1148Dic3—61no—
1149Dic3—62no—
1150Dic3—61no—
1151Dic3—62no—
1152Dic3—121no—
1153Dic3—122no—
1154Dic3—121no—
1155Dic3—121no—
1156Dic3C2×D3×Q812yes—
1157Dic3C2×D3×Q814yes—
1158C32#350211yescharacteristic, complemented, Sylow
1159C23—31no—
1160Q8—34no—
1161Q8—98no—
1162Q8—94no—
1163Q8—122no—
1164Q8—122no—
1165Q8—122no—
1166Q8—121no—
1167Q8—184no—
1168Q8—182no—
1169Q8—182no—
1170Q8—362no—
1171Q8—361no—
1172Q8—362no—
1173C2×C4—32no—
1174C2×C4—31no—
1175C2×C4—34no—
1176C2×C4—31no—
1177C2×C4—31no—
1178C2×C4—31no—
1179C2×C4—31no—
1180C2×C4—32no—
1181C2×C4—31no—
1182C2×C4—32no—
1183C2×C4—31no—
1184C2×C4—32no—
1185C2×C4—98no—
1186C2×C4—92no—
1187C2×C4—91no—
1188C2×C4—91no—
1189C2×C4—92no—
1190C2×C4—91no—
1191C2×C4—91no—
1192C2×C4—122no—
1193C2×C4—182no—
1194C2×C4—361no—
1195C2×C4C22×D3212yes—
1196C2×C4C22×D3211yescharacteristic
1197C2×C4C22×D3212yes—
1198C2×C4C22×D3211yescharacteristic
1199C2×C4C22×D3211yescharacteristic
1200C2×C3—21no—
1201C2×C3—21no—
1202C2×C3—21no—
1203C2×C3—62no—
1204C2×C3C22×D3×Q811yescharacteristic
1205C2×C3C22×D3×Q811yescharacteristic
1206C2×C3#596411yescharacteristic
1207C2×C3#596611yescharacteristic
1208C2×C3D3×2−1+411yescharacteristic
1209C2×C3D3×2−1+411yescharacteristic
1210D3—22no—
1211C22—32no—
1212C22—61no—
1213C22—61no—
1214C22C23×D3211yescharacteristic
1215C4—22no—
1216C4—21no—
1217C4—22no—
1218C4—21no—
1219C4—32no—
1220C4—34no—
1221C4—61no—
1222C4—61no—
1223C4—61no—
1224C4—62no—
1225C4—61no—
1226C4—61no—
1227C4—61no—
1228C4—62no—
1229C4—62no—
1230C4—94no—
1231C4—92no—
1232C4—181no—
1233C4—182no—
1234C4—181no—
1235C4—181no—
1236C4D32×Q812yes—
1237C3—21no—
1238C3#8658511yescharacteristic, complemented
1239C3#8703211yescharacteristic, complemented
1240C2—62no—
1241C2C2×D32×Q811yescharacteristic
1242C2#1059669411yescharacteristic
1243C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#125C22
prime radicalC22×C3×D3C24
hypercenter#125D32
hypocenterC32#3502
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #10596156C2semidirect
3. C3×#5685C2semidirect
4. #10594596C2semidirect
13. #10594324C2semidirect
14. #10594322C2semidirect
15. #10594317C2semidirect
16. #10594315C2semidirect
17. #10594314C2semidirect
18. #10594313C2semidirect
19. #10594313C2semidirect
22. #10593864C2semidirect
23. #10593856C2semidirect
151. #5685D3semidirect
190. D3×Dic6Q8semidirect
1158. C32#3502semidirect
1238. C3#86585semidirect
1239. C3#87032semidirect

Maximal subgroups

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

subgroupindex
#105961562
C3×#56892
C3×#56852
#105945962
#105944772
#105943912
#105943892
#105943882
#105943852
#105943572
D3×#8872
#105943422
#105943242
#105943222
#105943172
#105943152
#105943142
#105943132
#105939262
#105938852
#105938642
#105938562
#870323
#865853