Finite Group Databasebeta

← #11909878

Subgroups — #11909878

Order 1152.

2124 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#634C211yesmaximal, characteristic, complemented
2C3×#5541C211yesmaximal, characteristic, complemented
3C3×#5538C211yesmaximal, characteristic
4#10595202C212yesmaximal
5#10595120C212yesmaximal, complemented
6#10594915C211yesmaximal, characteristic, complemented
7#10594915C211yesmaximal, characteristic, complemented
8#10594849C211yesmaximal, characteristic, complemented
9#10594840C211yesmaximal, characteristic, complemented
10#10594828C211yesmaximal, characteristic, complemented
11#10594824C211yesmaximal, characteristic, complemented
12C2×#63844C211yesmaximal, characteristic, complemented
13#10594808C211yesmaximal, characteristic, complemented
14#10594479C212yesmaximal, complemented
15#10594315C212yesmaximal, complemented
16#10594158C212yesmaximal, complemented
17#10594147C212yesmaximal, complemented
18#10594031C212yesmaximal, complemented
19#10594029C212yesmaximal, complemented
20#10593885C211yesmaximal, characteristic, complemented
21#10593881C211yesmaximal, characteristic, complemented
22#10593860C211yesmaximal, characteristic, complemented
23#10593852C211yesmaximal, characteristic, complemented
24#86842—31nomaximal
25#86129—31nomaximal
26C22×#634C2211yescharacteristic
27C22×#634C2211yescharacteristic
28C2×D3×Dic6C2211yescharacteristic
29C32×C4×D4C2211yescharacteristic
30D4×C3⋊Dic3C2212yes—
31#64133C2211yescharacteristic
32#64133C2211yescharacteristic
33#64097C2212yes—
34#64087C2212yes—
35#64087C2212yes—
36#64078C2211yescharacteristic
37C4×#634C2211yescharacteristic
38C3×#939C2211yescharacteristic
39C3×#935C2211yescharacteristic
40C3×#935C2212yes—
41C3×C4×#67C2211yescharacteristic
42C3×C4×#67C2211yescharacteristic
43C3×#926C2211yescharacteristic
44C3×#926C2211yescharacteristic
45C2×C3×C4⋊Dic3C2211yescharacteristic
46C3×#924C2211yescharacteristic
47C3×#924C2211yescharacteristic
48C2×C3×C4×Dic3C2211yescharacteristic
49C3×#898C2211yescharacteristic
50C3×#889C2211yescharacteristic
51C3×#889C2212yes—
52C3×#886C2211yescharacteristic
53C3×#885C2211yescharacteristic
54C3×#879C2211yescharacteristic
55C3×#879C2212yes—
56C3×#878C2211yescharacteristic
57C3×#877C2212yes—
58C3×#872C2211yescharacteristic
59C3×#870C2211yescharacteristic
60C3×C4×Dic6C2211yescharacteristic
61C3×C4×Dic6C2211yescharacteristic
62#63982C2212yes—
63#63982C2212yes—
64#67⋊Dic3C2212yes—
65#67⋊Dic3C2212yes—
66C2×#3724C2212yes—
67#63964C2212yes—
68#63961C2212yes—
69#63959C2212yes—
70#63957C2212yes—
71#63957C2212yes—
72#63956C2212yes—
73#63956C2212yes—
74#63956C2212yes—
75#63955C2212yes—
76#63955C2212yes—
77C2×Dic32C2212yes—
78#63918C2211yescharacteristic
79#63896C2212yes—
80#63896C2212yes—
81#63878C2212yes—
82#63877C2212yes—
83#63870C2212yes—
84#63869C2211yescharacteristic
85#63869C2212yes—
86#63867C2212yes—
87#63866C2211yescharacteristic
88#63866C2211yescharacteristic
89#63861C2212yes—
90#63861C2212yes—
91#63859C2212yes—
92#63858C2212yes—
93#63857C2211yescharacteristic
94#63857C2211yescharacteristic
95#63847C2212yes—
96#63847C2212yes—
97#63847C2212yes—
98#63846C2212yes—
99#63845C2212yes—
100#63845C2212yes—
101#63845C2212yes—
102#63845C2212yes—
103#63844C2211yescharacteristic
104#63844C2212yes—
105#63844C2211yescharacteristic
106#63844C2211yescharacteristic
107#63844C2211yescharacteristic
108#63844C2212yes—
109#63844C2212yes—
110#63844C2211yescharacteristic
111#63844C2211yescharacteristic
112#63844C2211yescharacteristic
113#63844C2212yes—
114Dic3×Dic6C2211yescharacteristic
115Dic3×Dic6C2212yes—
116#63841C2211yescharacteristic
117#63840C2212yes—
118#63840C2212yes—
119#63839C2212yes—
120#63838C2212yes—
121#63838C2212yes—
122#63837C2212yes—
123#63837C2212yes—
124#63837C2212yes—
125C3×#552—31no—
126C3×#529—31no—
127#5702—32no—
128#5701—32no—
129#5701—32no—
130#5701—32no—
131#5698—31no—
132#5696—32no—
133#5685—32no—
134#5685—32no—
135#5685—31no—
136#5671—32no—
137#5650—32no—
138#5650—32no—
139#5650—32no—
140#5649—32no—
141#5632—31no—
142#5632—31no—
143#5625—31no—
144#5622—31no—
145#5622—32no—
146#5600—32no—
147#5572—31no—
148#5570—31no—
149#5567—31no—
150#5567—31no—
151#5542—31no—
152#5541—31no—
153#5541D311yescharacteristic, complemented
154#5538D311yescharacteristic
155D4×Dic6—31no—
156D4×Dic6—31no—
157D4×Dic6—31no—
158D4×Dic6—31no—
159D4×Dic6—61no—
160#5533—31no—
161#5531—32no—
162#5518—31no—
163#5518—31no—
164#5517—32no—
165#5516—31no—
166#5516—31no—
167#5516—31no—
168#5513—31no—
169C2×#887—31no—
170#5470—31no—
171C2×C4×Dic6—31no—
172C2×C32×D4C2311yescharacteristic
173C22×C32×C4C2311yescharacteristic
174C22×C32×C4C2311yescharacteristic
175C22×C3⋊Dic3C2312yes—
176C22×C3⋊Dic3C2312yes—
177C2×#634—24no—
178C2×#634—24no—
179C2×#634C2311yescharacteristic
180C2×#634C2311yescharacteristic
181C2×#634C2312yes—
182C2×#634C2312yes—
183C2×#634C2311yescharacteristic
184C2×C3×#67C2311yescharacteristic
185C2×C3×#67C2311yescharacteristic
186C22×C3×Dic3C2312yes—
187C22×C3×Dic3C2311yescharacteristic
188C22×C3×Dic3C2311yescharacteristic
189C2×C3×C4×D3C2311yescharacteristic
190C2×C3×Dic6C2311yescharacteristic
191C2×C3×Dic6C2311yescharacteristic
192C2×#627C2312yes—
193C2×#627C2312yes—
194C2×D3×Dic3C2312yes—
195D3×Dic6—24no—
196C32×C4⋊C4C2311yescharacteristic
197C32×C22⋊C4C2311yescharacteristic
198C32×C22⋊C4C2311yescharacteristic
199C32×C42C2311yescharacteristic
200#3757C2312yes—
201#3757C2312yes—
202C4⋊(C3⋊Dic3)C2311yescharacteristic
203C4⋊(C3⋊Dic3)C2312yes—
204C4⋊(C3⋊Dic3)C2312yes—
205#3750C2312yes—
206#3750C2312yes—
207#3750C2312yes—
208C4×C3⋊Dic3C2312yes—
209C3×#217C2312yes—
210C3×#217C2311yescharacteristic
211C3×#217C2312yes—
212C3×#217C2312yes—
213C3×#217C2311yescharacteristic
214C3×#217C2311yescharacteristic
215C3×#217C2311yescharacteristic
216C3×(C2×D3)⋊C4C2311yescharacteristic
217C3×(C2×D3)⋊C4C2311yescharacteristic
218C3×(C2×D3)⋊C4C2311yescharacteristic
219C3×(C2×D3)⋊C4C2311yescharacteristic
220C3×C4⋊Dic3C2311yescharacteristic
221C3×C4⋊Dic3C2311yescharacteristic
222C3×C4⋊Dic3C2312yes—
223C3×C4⋊Dic3C2311yescharacteristic
224C3×C4⋊Dic3C2311yescharacteristic
225C3×C4⋊Dic3C2311yescharacteristic
226C3×C4⋊Dic3C2311yescharacteristic
227C3×Dic3⋊C4C2312yes—
228C3×Dic3⋊C4C2312yes—
229C3×Dic3⋊C4C2311yescharacteristic
230C3×Dic3⋊C4C2311yescharacteristic
231C3×Dic3⋊C4C2312yes—
232C3×Dic3⋊C4C2311yescharacteristic
233C3×Dic3⋊C4C2311yescharacteristic
234C3×Dic3⋊C4C2312yes—
235C3×Dic3⋊C4C2312yes—
236C3×Dic3⋊C4C2311yescharacteristic
237C3×Dic3⋊C4C2311yescharacteristic
238C3×C4×Dic3C2312yes—
239C3×C4×Dic3C2312yes—
240C3×C4×Dic3C2311yescharacteristic
241C3×C4×Dic3C2311yescharacteristic
242C3×C4×Dic3C2311yescharacteristic
243C3×C4×Dic3C2311yescharacteristic
244C3×C4×Dic3C2311yescharacteristic
245#3724C2312yes—
246#3724C2312yes—
247#3724C2312yes—
248#3724C2312yes—
249#3724C2312yes—
250#3724C2312yes—
251#3724C2312yes—
252#3724C2312yes—
253Dic3⋊Dic3C2312yes—
254Dic3⋊Dic3C2312yes—
255Dic3⋊Dic3C2312yes—
256Dic3⋊Dic3C2312yes—
257Dic3⋊Dic3C2312yes—
258Dic3⋊Dic3C2312yes—
259Dic3⋊Dic3C2312yes—
260Dic3⋊Dic3C2312yes—
261Dic3⋊Dic3C2312yes—
262(C2×D3)⋊Dic3C2312yes—
263(C2×D3)⋊Dic3C2312yes—
264(C2×D3)⋊Dic3C2312yes—
265Dic32C2312yes—
266Dic32C2312yes—
267Dic32C2312yes—
268Dic32C2312yes—
269Dic32C2312yes—
270Dic32C2312yes—
271Dic32C2312yes—
272Dic32C2312yes—
273Dic32C2312yes—
274#3523—91noSylow
275C2×D3×Q8—31no—
276C22×Dic6—31no—
277C22×Dic6—31no—
278C22×Dic6—31no—
279C22×Dic6—31no—
280C22×Dic6—31no—
281C22×Dic6—61no—
282C22×Dic6—61no—
283C3×#126—31no—
284C3×#126—31no—
285C3×#126—32no—
286C3×#125—31no—
287C3×#125—32no—
288C3×#125—31no—
289C3×#124—31no—
290C3×#123—32no—
291C3×#123—31no—
292C3×#123—31no—
293C3×C22⋊Q8—31no—
294C3×C22⋊Q8—31no—
295C3×C22⋊Q8—31no—
296C3×#121—31no—
297C3×C4×Q8—31no—
298C3×C4×Q8—31no—
299C3×C4×D4—21no—
300C3×C4×D4—31no—
301C3×C4×D4—31no—
302C3×C4×D4C2×D311yescharacteristic
303C3×C4×D4C2×D311yescharacteristic
304C3×#117—31no—
305C3×#117—31no—
306C3×#117—32no—
307C3×#117—31no—
308C2×C3×C4⋊C4—31no—
309C2×C3×C42—31no—
310Q8×Dic3—32no—
311Q8×Dic3—31no—
312#944—32no—
313#944—31no—
314#944—31no—
315#939C2×D311yescharacteristic
316#936—32no—
317#935—32no—
318#935C2×D311yescharacteristic
319#935C2×D312yes—
320D4×Dic3—32no—
321D4×Dic3—32no—
322D4×Dic3—32no—
323D4×Dic3—32no—
324D4×Dic3—62no—
325#929—32no—
326C4×#67C2×D311yescharacteristic
327C4×#67C2×D311yescharacteristic
328#926—32no—
329#926—32no—
330#926—31no—
331#926C2×D311yescharacteristic
332#926C2×D311yescharacteristic
333C2×C4⋊Dic3C2×D311yescharacteristic
334#924—31no—
335#924—31no—
336#924—31no—
337#924—31no—
338#924—32no—
339#924—31no—
340#924—31no—
341#924—61no—
342#924—61no—
343#924C2×D311yescharacteristic
344#924C2×D311yescharacteristic
345C2×Dic3⋊C4—32no—
346C2×Dic3⋊C4—32no—
347C2×C4×Dic3—32no—
348C2×C4×Dic3—32no—
349C2×C4×Dic3C2×D311yescharacteristic
350#898—32no—
351#898—32no—
352#898—32no—
353#898C2×D311yescharacteristic
354#897—31no—
355#897—31no—
356#896—32no—
357#896—32no—
358#892—31no—
359#892—32no—
360#890—32no—
361#890—32no—
362#890—32no—
363#890—32no—
364#890—32no—
365#890—32no—
366#890—31no—
367#889—32no—
368#889—32no—
369#889—32no—
370#889—32no—
371#889—32no—
372#889—32no—
373#889—32no—
374#889—32no—
375#889—32no—
376#889—32no—
377#889—32no—
378#889—32no—
379#889—32no—
380#889—32no—
381#889C2×D311yescharacteristic
382#889C2×D312yes—
383#888—32no—
384#888—32no—
385#888—32no—
386#888—32no—
387#888—32no—
388#888—32no—
389#888—32no—
390#888—31no—
391#888—62no—
392#887—32no—
393#887—32no—
394#887—32no—
395#887—32no—
396#887—31no—
397#887—31no—
398#887—32no—
399#887—32no—
400#887—32no—
401#887—32no—
402#887—32no—
403#887—31no—
404#887—31no—
405#887—32no—
406#887—32no—
407#887—31no—
408#887—31no—
409#887—31no—
410#886C2×D311yescharacteristic
411#885—32no—
412#885C2×D311yescharacteristic
413#67⋊C4—32no—
414#67⋊C4—32no—
415#879—32no—
416#879—32no—
417#879—32no—
418#879—32no—
419#879—32no—
420#879—32no—
421#879—32no—
422#879—32no—
423#879—32no—
424#879—32no—
425#879C2×D312yes—
426#879C2×D311yescharacteristic
427#878—32no—
428#878—32no—
429#878—32no—
430#878—32no—
431#878—32no—
432#878—32no—
433#878—32no—
434#878—32no—
435#878—32no—
436#878—32no—
437#878—32no—
438#878—62no—
439#878—62no—
440#878C2×D311yescharacteristic
441#877—32no—
442#877—32no—
443#877—32no—
444#877—32no—
445#877—32no—
446#877—32no—
447#877—32no—
448#877—32no—
449#877C2×D312yes—
450#876—32no—
451#872—32no—
452#872C2×D311yescharacteristic
453#870—32no—
454#870—31no—
455#870—32no—
456#870C2×D311yescharacteristic
457#869—31no—
458#869—31no—
459#869—31no—
460#869—31no—
461#869—31no—
462#869—61no—
463C4×Dic6—32no—
464C4×Dic6—31no—
465C4×Dic6—31no—
466C4×Dic6—31no—
467C4×Dic6—32no—
468C4×Dic6—32no—
469C4×Dic6—32no—
470C4×Dic6—32no—
471C4×Dic6—31no—
472C4×Dic6—31no—
473C4×Dic6—31no—
474C4×Dic6—31no—
475C4×Dic6—31no—
476C4×Dic6—31no—
477C4×Dic6—31no—
478C4×Dic6—32no—
479C4×Dic6—32no—
480C4×Dic6—32no—
481C4×Dic6—61no—
482C4×Dic6C2×D311yescharacteristic
483C4×Dic6C2×D311yescharacteristic
484C23×C32C2411yescharacteristic
485C23×C32C2411yescharacteristic
486C22×C3×D3C2411yescharacteristic
487C32×D4—22no—
488C2×C32×C4—22no—
489C2×C32×C4—22no—
490C2×C32×C4C2411yescharacteristic
491C2×C32×C4C2411yescharacteristic
492C2×C32×C4C2411yescharacteristic
493C2×C32×C4C2411yescharacteristic
494C2×C32×C4C2411yescharacteristic
495C2×C3⋊Dic3—24no—
496C2×C3⋊Dic3—24no—
497C2×C3⋊Dic3C2412yes—
498C2×C3⋊Dic3C2412yes—
499C2×C3⋊Dic3C2412yes—
500C2×C3⋊Dic3C2412yes—
501#634—22no—
502#634—22no—
503#634—24no—
504#634—24no—
505#634#4114yes—
506C3×#67—22no—
507C3×#67—22no—
508C2×C3×Dic3—24no—
509C2×C3×Dic3—22no—
510C2×C3×Dic3—22no—
511C2×C3×Dic3C2412yes—
512C2×C3×Dic3C2411yescharacteristic
513C2×C3×Dic3C2411yescharacteristic
514C2×C3×Dic3C2412yes—
515C2×C3×Dic3C2412yes—
516C2×C3×Dic3C2411yescharacteristic
517C2×C3×Dic3C2411yescharacteristic
518C2×C3×Dic3C2411yescharacteristic
519C2×C3×Dic3C2412yes—
520C2×C3×Dic3C2411yescharacteristic
521C2×C3×Dic3C2411yescharacteristic
522C3×C4×D3—22no—
523C3×Dic6—22no—
524C3×Dic6—22no—
525#627—24no—
526#627—24no—
527D3×Dic3—24no—
528#557—91no—
529#557—91no—
530#557—92no—
531#556—91no—
532#556—92no—
533#552—31no—
534#552—91no—
535#552—92no—
536#552—92no—
537D4×Q8—91no—
538D4×Q8—91no—
539D4×Q8—91no—
540#541—91no—
541#541—91no—
542#541—92no—
543#541—92no—
544#533—91no—
545#533—92no—
546#529—31no—
547#529—92no—
548#519—91no—
549#519—91no—
550C2×C4×Q8—91no—
551C2×C3×Q8—31no—
552C2×C3×Q8—31no—
553C2×C3×D4—21no—
554C2×C3×D4—31no—
555C2×C3×D4—31no—
556C2×C3×D4C22×D311yescharacteristic
557C2×C3×D4C22×D311yescharacteristic
558C22×C3×C4—21no—
559C22×C3×C4—21no—
560C22×C3×C4—31no—
561C22×C3×C4—32no—
562C22×C3×C4—31no—
563C22×C3×C4—31no—
564C22×C3×C4C22×D311yescharacteristic
565C22×C3×C4C22×D311yescharacteristic
566C22×C3×C4C22×D311yescharacteristic
567C22×C3×C4C22×D311yescharacteristic
568C2×#67C22×D311yescharacteristic
569C2×#67C22×D311yescharacteristic
570C22×Dic3—32no—
571C22×Dic3—32no—
572C22×Dic3—32no—
573C22×Dic3—32no—
574C22×Dic3—32no—
575C22×Dic3—62no—
576C22×Dic3—62no—
577C22×Dic3C22×D311yescharacteristic
578C22×Dic3C22×D312yes—
579C22×Dic3C22×D311yescharacteristic
580D3×Q8—64no—
581C2×C4×D3—32no—
582C2×C4×D3C22×D311yescharacteristic
583C2×Dic6—31no—
584C2×Dic6—31no—
585C2×Dic6—31no—
586C2×Dic6—31no—
587C2×Dic6—32no—
588C2×Dic6—32no—
589C2×Dic6—31no—
590C2×Dic6—31no—
591C2×Dic6—32no—
592C2×Dic6—32no—
593C2×Dic6—32no—
594C2×Dic6—32no—
595C2×Dic6—32no—
596C2×Dic6—32no—
597C2×Dic6—61no—
598C2×Dic6—61no—
599C2×Dic6—61no—
600C2×Dic6—62no—
601C2×Dic6—62no—
602C2×Dic6—64no—
603C2×Dic6—64no—
604C2×Dic6—64no—
605C2×Dic6—64no—
606C2×Dic6—64no—
607C2×Dic6—124no—
608C2×Dic6—124no—
609C2×Dic6C22×D311yescharacteristic
610C2×Dic6C22×D311yescharacteristic
611C3×C4⋊C4—21no—
612C3×C4⋊C4—31no—
613C3×C4⋊C4—31no—
614C3×C4⋊C4—31no—
615C3×C4⋊C4—31no—
616C3×C4⋊C4—31no—
617C3×C4⋊C4—31no—
618C3×C4⋊C4—31no—
619C3×C4⋊C4—32no—
620C3×C4⋊C4—31no—
621C3×C4⋊C4—31no—
622C3×C4⋊C4—32no—
623C3×C4⋊C4—32no—
624C3×C4⋊C4—32no—
625C3×C4⋊C4—31no—
626C3×C4⋊C4—32no—
627C3×C4⋊C4—32no—
628C3×C4⋊C4—31no—
629C3×C4⋊C4—31no—
630C3×C4⋊C4C22×D311yescharacteristic
631C3×C4⋊C4C22×D311yescharacteristic
632C3×C22⋊C4—21no—
633C3×C22⋊C4—21no—
634C3×C22⋊C4—31no—
635C3×C22⋊C4—31no—
636C3×C22⋊C4—31no—
637C3×C22⋊C4—32no—
638C3×C22⋊C4—32no—
639C3×C22⋊C4—31no—
640C3×C22⋊C4—32no—
641C3×C22⋊C4—31no—
642C3×C22⋊C4—31no—
643C3×C22⋊C4—31no—
644C3×C22⋊C4—31no—
645C3×C22⋊C4C22×D311yescharacteristic
646C3×C22⋊C4C22×D311yescharacteristic
647C3×C22⋊C4C22×D311yescharacteristic
648C3×C22⋊C4C22×D311yescharacteristic
649C3×C42—21no—
650C3×C42—31no—
651C3×C42—31no—
652C3×C42—32no—
653C3×C42—31no—
654C3×C42—31no—
655C3×C42—31no—
656C3×C42—32no—
657C3×C42C22×D311yescharacteristic
658C3×C42C22×D311yescharacteristic
659#217—32no—
660#217—32no—
661#217—32no—
662#217—32no—
663#217—32no—
664#217—32no—
665#217—32no—
666#217—62no—
667#217—62no—
668#217C22×D311yescharacteristic
669#217C22×D311yescharacteristic
670#217C22×D312yes—
671#217C22×D312yes—
672#217C22×D311yescharacteristic
673#217C22×D311yescharacteristic
674#217C22×D312yes—
675(C2×D3)⋊C4—32no—
676(C2×D3)⋊C4—32no—
677(C2×D3)⋊C4—32no—
678(C2×D3)⋊C4C22×D311yescharacteristic
679(C2×D3)⋊C4C22×D311yescharacteristic
680(C2×D3)⋊C4C22×D311yescharacteristic
681(C2×D3)⋊C4C22×D311yescharacteristic
682C4⋊Dic3—31no—
683C4⋊Dic3—32no—
684C4⋊Dic3—31no—
685C4⋊Dic3—32no—
686C4⋊Dic3—32no—
687C4⋊Dic3—32no—
688C4⋊Dic3—32no—
689C4⋊Dic3—32no—
690C4⋊Dic3—32no—
691C4⋊Dic3—32no—
692C4⋊Dic3—32no—
693C4⋊Dic3—32no—
694C4⋊Dic3—32no—
695C4⋊Dic3—32no—
696C4⋊Dic3—32no—
697C4⋊Dic3—61no—
698C4⋊Dic3—62no—
699C4⋊Dic3—62no—
700C4⋊Dic3C22×D311yescharacteristic
701C4⋊Dic3C22×D311yescharacteristic
702C4⋊Dic3C22×D311yescharacteristic
703C4⋊Dic3C22×D311yescharacteristic
704C4⋊Dic3C22×D312yes—
705C4⋊Dic3C22×D311yescharacteristic
706C4⋊Dic3C22×D311yescharacteristic
707Dic3⋊C4—32no—
708Dic3⋊C4—32no—
709Dic3⋊C4—32no—
710Dic3⋊C4—32no—
711Dic3⋊C4—32no—
712Dic3⋊C4—32no—
713Dic3⋊C4—32no—
714Dic3⋊C4—32no—
715Dic3⋊C4—32no—
716Dic3⋊C4—32no—
717Dic3⋊C4—32no—
718Dic3⋊C4—32no—
719Dic3⋊C4—32no—
720Dic3⋊C4—32no—
721Dic3⋊C4—32no—
722Dic3⋊C4—32no—
723Dic3⋊C4—32no—
724Dic3⋊C4—32no—
725Dic3⋊C4—32no—
726Dic3⋊C4—32no—
727Dic3⋊C4—32no—
728Dic3⋊C4—32no—
729Dic3⋊C4—32no—
730Dic3⋊C4—32no—
731Dic3⋊C4—32no—
732Dic3⋊C4—32no—
733Dic3⋊C4—32no—
734Dic3⋊C4—32no—
735Dic3⋊C4—32no—
736Dic3⋊C4—32no—
737Dic3⋊C4—32no—
738Dic3⋊C4—62no—
739Dic3⋊C4—62no—
740Dic3⋊C4—62no—
741Dic3⋊C4C22×D311yescharacteristic
742Dic3⋊C4C22×D311yescharacteristic
743Dic3⋊C4C22×D312yes—
744Dic3⋊C4C22×D312yes—
745Dic3⋊C4C22×D311yescharacteristic
746Dic3⋊C4C22×D311yescharacteristic
747Dic3⋊C4C22×D312yes—
748Dic3⋊C4C22×D312yes—
749Dic3⋊C4C22×D311yescharacteristic
750Dic3⋊C4C22×D312yes—
751Dic3⋊C4C22×D311yescharacteristic
752C4×Dic3—32no—
753C4×Dic3—32no—
754C4×Dic3—32no—
755C4×Dic3—32no—
756C4×Dic3—32no—
757C4×Dic3—32no—
758C4×Dic3—32no—
759C4×Dic3—32no—
760C4×Dic3—32no—
761C4×Dic3—32no—
762C4×Dic3—32no—
763C4×Dic3—32no—
764C4×Dic3—32no—
765C4×Dic3—32no—
766C4×Dic3—32no—
767C4×Dic3—32no—
768C4×Dic3—32no—
769C4×Dic3—32no—
770C4×Dic3—32no—
771C4×Dic3—32no—
772C4×Dic3—62no—
773C4×Dic3C22×D312yes—
774C4×Dic3C22×D311yescharacteristic
775C4×Dic3C22×D311yescharacteristic
776C4×Dic3C22×D311yescharacteristic
777C4×Dic3C22×D312yes—
778C4×Dic3C22×D311yescharacteristic
779C4×Dic3C22×D311yescharacteristic
780C22×C32—21no—
781C22×C32—21no—
782C22×C32—21no—
783C22×C32—21no—
784C22×C32—21no—
785C22×C322−1+412yes—
786C22×C32C2511yescharacteristic
787C2×C3×D3—21no—
788C2×C3×D3—21no—
789C2×C3×D3—21no—
790C32×C4—21no—
791C32×C4—21no—
792C32×C4—21no—
793C32×C4—21no—
794C32×C4C2×#4112yes—
795C3⋊Dic3—22no—
796C3⋊Dic3—22no—
797C3⋊Dic3—22no—
798C3⋊Dic3C2×#4114yes—
799C3×Dic3—22no—
800C3×Dic3—21no—
801C3×Dic3—22no—
802C3×Dic3—21no—
803C3×Dic3—22no—
804C3×Dic3—21no—
805C3×Dic3—22no—
806C3×Dic3—21no—
807C3×Dic3—21no—
808C3×Dic3—21no—
809C3×Dic32−1+412yes—
810C22×Q8—91no—
811C22×Q8—91no—
812C22×Q8—91no—
813C4⋊Q8—91no—
814C4⋊Q8—91no—
815C4⋊Q8—91no—
816C4⋊Q8—92no—
817C4⋊Q8—92no—
818C4⋊Q8—92no—
819C4⋊Q8—92no—
820C4⋊Q8—91no—
821#126—31no—
822#126—31no—
823#126—32no—
824#126—92no—
825#126—92no—
826#126—92no—
827#126—92no—
828#126—92no—
829#126—92no—
830#126—92no—
831#125—31no—
832#125—32no—
833#125—31no—
834#125—92no—
835#125—92no—
836#125—91no—
837#125—92no—
838#125—92no—
839#125—92no—
840#125—92no—
841#125—92no—
842#125—92no—
843#125—92no—
844#125—92no—
845#125—92no—
846#124—31no—
847#124—92no—
848#123—31no—
849#123—32no—
850#123—31no—
851#123—92no—
852C22⋊Q8—31no—
853C22⋊Q8—31no—
854C22⋊Q8—31no—
855C22⋊Q8—92no—
856C22⋊Q8—92no—
857C22⋊Q8—92no—
858C22⋊Q8—92no—
859C22⋊Q8—92no—
860C22⋊Q8—91no—
861C22⋊Q8—91no—
862C22⋊Q8—91no—
863C22⋊Q8—91no—
864C22⋊Q8—92no—
865C22⋊Q8—92no—
866#121—31no—
867C4×Q8—31no—
868C4×Q8—31no—
869C4×Q8—91no—
870C4×Q8—91no—
871C4×Q8—92no—
872C4×Q8—91no—
873C4×Q8—91no—
874C4×Q8—92no—
875C4×Q8—91no—
876C4×Q8—92no—
877C4×Q8—92no—
878C4×Q8—91no—
879C4×Q8—92no—
880C4×Q8—91no—
881C4×Q8—92no—
882C4×Q8—92no—
883C4×Q8—91no—
884C4×Q8—92no—
885C4×Q8—92no—
886C4×Q8—92no—
887C4×Q8—91no—
888C4×D4—31no—
889C4×D4—31no—
890C4×D4—92no—
891C4×D4—92no—
892C4×D4—92no—
893C4×D4D3211yescharacteristic
894#117—31no—
895#117—31no—
896#117—32no—
897#117—31no—
898#117—92no—
899#117—92no—
900#117—92no—
901#117—92no—
902#117—92no—
903#117—92no—
904#117—91no—
905C2×C4⋊C4—31no—
906C2×C4⋊C4—92no—
907C2×C42—31no—
908C2×C42—92no—
909C23×C3—21no—
910C23×C3—21no—
911C23×C3—31no—
912C23×C3C23×D311yescharacteristic
913C23×C3C23×D311yescharacteristic
914C23×C3C23×D311yescharacteristic
915C23×C3C23×D311yescharacteristic
916C22×D3C23×D311yescharacteristic
917C3×Q8—62no—
918C3×Q8—62no—
919C3×D4—24no—
920C3×D4—22no—
921C3×D4—22no—
922C3×D4—62no—
923C3×D4—62no—
924C2×C3×C4—22no—
925C2×C3×C4—22no—
926C2×C3×C4—22no—
927C2×C3×C4—22no—
928C2×C3×C4—21no—
929C2×C3×C4—21no—
930C2×C3×C4—21no—
931C2×C3×C4—21no—
932C2×C3×C4—21no—
933C2×C3×C4—31no—
934C2×C3×C4—31no—
935C2×C3×C4—31no—
936C2×C3×C4—32no—
937C2×C3×C4—31no—
938C2×C3×C4—31no—
939C2×C3×C4—31no—
940C2×C3×C4—32no—
941C2×C3×C4—32no—
942C2×C3×C4—32no—
943C2×C3×C4—31no—
944C2×C3×C4—42no—
945C2×C3×C4—42no—
946C2×C3×C4—62no—
947C2×C3×C4—62no—
948C2×C3×C4—64no—
949C2×C3×C4—62no—
950C2×C3×C4C23×D311yescharacteristic
951C2×C3×C4C23×D311yescharacteristic
952C2×C3×C4C23×D311yescharacteristic
953C2×C3×C4C23×D311yescharacteristic
954C2×C3×C4C23×D311yescharacteristic
955C2×C3×C4C23×D311yescharacteristic
956C2×C3×C4C23×D311yescharacteristic
957C2×C3×C4C23×D311yescharacteristic
958C2×C3×C4C23×D311yescharacteristic
959C2×C3×C4C23×D311yescharacteristic
960#67—22no—
961#67—22no—
962C2×Dic3—24no—
963C2×Dic3—22no—
964C2×Dic3—22no—
965C2×Dic3—32no—
966C2×Dic3—32no—
967C2×Dic3—32no—
968C2×Dic3—32no—
969C2×Dic3—32no—
970C2×Dic3—32no—
971C2×Dic3—32no—
972C2×Dic3—32no—
973C2×Dic3—62no—
974C2×Dic3—62no—
975C2×Dic3—62no—
976C2×Dic3—62no—
977C2×Dic3—64no—
978C2×Dic3—64no—
979C2×Dic3—64no—
980C2×Dic3—64no—
981C2×Dic3—64no—
982C2×Dic3—124no—
983C2×Dic3—124no—
984C2×Dic3C23×D311yescharacteristic
985C2×Dic3C23×D312yes—
986C2×Dic3C23×D311yescharacteristic
987C2×Dic3C23×D311yescharacteristic
988C2×Dic3C23×D311yescharacteristic
989C2×Dic3C23×D312yes—
990C2×Dic3C23×D312yes—
991C2×Dic3C23×D311yescharacteristic
992C2×Dic3C23×D312yes—
993C2×Dic3C23×D311yescharacteristic
994C2×Dic3C23×D311yescharacteristic
995C4×D3—22no—
996C4×D3—64no—
997Dic6—22no—
998Dic6—22no—
999Dic6—34no—
1000Dic6—34no—
1001Dic6—64no—
1002Dic6—64no—
1003Dic6—64no—
1004Dic6—64no—
1005Dic6—64no—
1006Dic6—64no—
1007Dic6—64no—
1008Dic6—64no—
1009Dic6—62no—
1010Dic6—62no—
1011Dic6—62no—
1012Dic6—62no—
1013Dic6—64no—
1014Dic6—124no—
1015Dic6—124no—
1016Dic6—122no—
1017Dic6—122no—
1018C2×C32—22no—
1019C2×C32—41no—
1020C2×C32C22×#4111yescharacteristic
1021C2×C32C2×2−1+411yescharacteristic
1022C2×C32C2×2−1+411yescharacteristic
1023C3×D3—41no—
1024C2×Q8—31no—
1025C2×Q8—31no—
1026C2×Q8—92no—
1027C2×Q8—92no—
1028C2×Q8—91no—
1029C2×Q8—92no—
1030C2×Q8—92no—
1031C2×Q8—91no—
1032C2×Q8—91no—
1033C2×Q8—184no—
1034C2×Q8—184no—
1035C2×Q8—184no—
1036C2×D4—31no—
1037C2×D4—31no—
1038C2×D4C2×D3211yescharacteristic
1039C22×C4—31no—
1040C22×C4—31no—
1041C22×C4—32no—
1042C22×C4—31no—
1043C22×C4—92no—
1044C22×C4—92no—
1045C22×C4—92no—
1046C22×C4C2×D3211yescharacteristic
1047C22×C4C2×D3211yescharacteristic
1048C4⋊C4—31no—
1049C4⋊C4—31no—
1050C4⋊C4—32no—
1051C4⋊C4—31no—
1052C4⋊C4—31no—
1053C4⋊C4—31no—
1054C4⋊C4—31no—
1055C4⋊C4—31no—
1056C4⋊C4—32no—
1057C4⋊C4—32no—
1058C4⋊C4—32no—
1059C4⋊C4—31no—
1060C4⋊C4—31no—
1061C4⋊C4—31no—
1062C4⋊C4—31no—
1063C4⋊C4—31no—
1064C4⋊C4—32no—
1065C4⋊C4—32no—
1066C4⋊C4—92no—
1067C4⋊C4—92no—
1068C4⋊C4—92no—
1069C4⋊C4—92no—
1070C4⋊C4—92no—
1071C4⋊C4—92no—
1072C4⋊C4—92no—
1073C4⋊C4—92no—
1074C4⋊C4—92no—
1075C4⋊C4—92no—
1076C4⋊C4—92no—
1077C4⋊C4—92no—
1078C4⋊C4—92no—
1079C4⋊C4—92no—
1080C4⋊C4—92no—
1081C4⋊C4—92no—
1082C4⋊C4—92no—
1083C4⋊C4—92no—
1084C4⋊C4—91no—
1085C4⋊C4—92no—
1086C4⋊C4—92no—
1087C4⋊C4—92no—
1088C4⋊C4—92no—
1089C4⋊C4C2×D3211yescharacteristic
1090C22⋊C4—31no—
1091C22⋊C4—31no—
1092C22⋊C4—32no—
1093C22⋊C4—32no—
1094C22⋊C4—31no—
1095C22⋊C4—31no—
1096C22⋊C4—32no—
1097C22⋊C4—31no—
1098C22⋊C4—31no—
1099C22⋊C4—31no—
1100C22⋊C4—31no—
1101C22⋊C4—92no—
1102C22⋊C4—92no—
1103C22⋊C4—92no—
1104C22⋊C4—92no—
1105C22⋊C4—92no—
1106C22⋊C4C2×D3211yescharacteristic
1107C22⋊C4C2×D3211yescharacteristic
1108C42—31no—
1109C42—31no—
1110C42—31no—
1111C42—31no—
1112C42—32no—
1113C42—32no—
1114C42—31no—
1115C42—92no—
1116C42—92no—
1117C42—92no—
1118C42—92no—
1119C42—92no—
1120C42—92no—
1121C42—92no—
1122C42—92no—
1123C42—92no—
1124C42—92no—
1125C42C2×D3211yescharacteristic
1126C22×C3—21no—
1127C22×C3—21no—
1128C22×C3—21no—
1129C22×C3—21no—
1130C22×C3—22no—
1131C22×C3—21no—
1132C22×C3—21no—
1133C22×C3—21no—
1134C22×C3—21no—
1135C22×C3—21no—
1136C22×C3—21no—
1137C22×C3—22no—
1138C22×C3—21no—
1139C22×C3—41no—
1140C22×C3—41no—
1141C22×C3—41no—
1142C22×C3—41no—
1143C22×C3—61no—
1144C22×C3—61no—
1145C22×C3—61no—
1146C22×C3#101012yes—
1147C22×C3#101012yes—
1148C22×C3C24×D311yescharacteristic
1149C22×C3C24×D311yescharacteristic
1150C2×D3—21no—
1151C2×D3—21no—
1152C2×D3—21no—
1153C3×C4—22no—
1154C3×C4—21no—
1155C3×C4—21no—
1156C3×C4—21no—
1157C3×C4—21no—
1158C3×C4—21no—
1159C3×C4—21no—
1160C3×C4—21no—
1161C3×C4—21no—
1162C3×C4—22no—
1163C3×C4—32no—
1164C3×C4—41no—
1165C3×C4—41no—
1166C3×C4—41no—
1167C3×C4—61no—
1168C3×C4—62no—
1169C3×C4—62no—
1170C3×C4—61no—
1171C3×C4—61no—
1172C3×C4—62no—
1173C3×C4—62no—
1174C3×C4—61no—
1175C3×C4—61no—
1176C3×C4—61no—
1177C3×C4D3×#4112yes—
1178C3×C4D3×#4112yes—
1179Dic3—22no—
1180Dic3—21no—
1181Dic3—21no—
1182Dic3—22no—
1183Dic3—22no—
1184Dic3—21no—
1185Dic3—21no—
1186Dic3—21no—
1187Dic3—21no—
1188Dic3—22no—
1189Dic3—34no—
1190Dic3—34no—
1191Dic3—64no—
1192Dic3—62no—
1193Dic3—62no—
1194Dic3—62no—
1195Dic3—62no—
1196Dic3—62no—
1197Dic3—62no—
1198Dic3—122no—
1199Dic3—122no—
1200Dic3—122no—
1201Dic3#101012yes—
1202C32#352311yescharacteristic, complemented, Sylow
1203C23—31no—
1204C23C22×D3211yescharacteristic
1205C23C22×D3211yescharacteristic
1206Q8—62no—
1207Q8—62no—
1208Q8—94no—
1209Q8—184no—
1210Q8—184no—
1211Q8—184no—
1212Q8—184no—
1213Q8—182no—
1214Q8—182no—
1215D4—22no—
1216D4—62no—
1217D4—62no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—31no—
1221C2×C4—31no—
1222C2×C4—31no—
1223C2×C4—32no—
1224C2×C4—31no—
1225C2×C4—31no—
1226C2×C4—32no—
1227C2×C4—31no—
1228C2×C4—32no—
1229C2×C4—31no—
1230C2×C4—32no—
1231C2×C4—62no—
1232C2×C4—62no—
1233C2×C4—64no—
1234C2×C4—62no—
1235C2×C4—92no—
1236C2×C4—92no—
1237C2×C4—92no—
1238C2×C4—92no—
1239C2×C4—184no—
1240C2×C4—184no—
1241C2×C4—184no—
1242C2×C4C22×D3211yescharacteristic
1243C2×C4C22×D3211yescharacteristic
1244C2×C4C22×D3211yescharacteristic
1245C2×C4C22×D3211yescharacteristic
1246C2×C4C22×D3211yescharacteristic
1247C2×C3—22no—
1248C2×C3—22no—
1249C2×C3—21no—
1250C2×C3—21no—
1251C2×C3—21no—
1252C2×C3—42no—
1253C2×C3—42no—
1254C2×C3—41no—
1255C2×C3—41no—
1256C2×C3—121no—
1257C2×C3C2×D3×#4111yescharacteristic
1258C2×C3C2×D3×#4111yescharacteristic
1259C2×C3C2×#101011yescharacteristic
1260C2×C3C2×#101011yescharacteristic
1261C2×C3C2×#101011yescharacteristic
1262C2×C3D3×2−1+411yescharacteristic
1263D3—41no—
1264C22—21no—
1265C22—21no—
1266C22—21no—
1267C22—21no—
1268C22—21no—
1269C22—61no—
1270C22—61no—
1271C22—61no—
1272C22#6429812yes—
1273C22C23×D3211yescharacteristic
1274C4—21no—
1275C4—21no—
1276C4—21no—
1277C4—21no—
1278C4—32no—
1279C4—61no—
1280C4—62no—
1281C4—61no—
1282C4—62no—
1283C4—61no—
1284C4—61no—
1285C4—62no—
1286C4—61no—
1287C4—61no—
1288C4—62no—
1289C4—94no—
1290C4—182no—
1291C4—182no—
1292C4—182no—
1293C4#6431212yes—
1294C3—21no—
1295C3#8612911yescharacteristic, complemented
1296C3#8684211yescharacteristic, complemented
1297C2—22no—
1298C2—41no—
1299C2—121no—
1300C2C2×#6429811yescharacteristic
1301C2C2×#6431211yescharacteristic
1302C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
prime radicalC3×#939C22
hypercenterC4×D4D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D4×#634C2semidirect
2. C3×#5541C2semidirect
5. #10595120C2semidirect
6. #10594915C2semidirect
7. #10594915C2semidirect
8. #10594849C2semidirect
9. #10594840C2semidirect
10. #10594828C2semidirect
11. #10594824C2semidirect
12. C2×#63844C2semidirect
13. #10594808C2semidirect
14. #10594479C2semidirect
15. #10594315C2semidirect
16. #10594158C2semidirect
17. #10594147C2semidirect
18. #10594031C2semidirect
19. #10594029C2semidirect
20. #10593885C2semidirect
21. #10593881C2semidirect
22. #10593860C2semidirect
23. #10593852C2semidirect
153. #5541D3semidirect
1202. C32#3523semidirect
1295. C3#86129semidirect
1296. C3#86842semidirect

Maximal subgroups

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

subgroupindex
D4×#6342
C3×#55412
C3×#55382
#105952022
#105951202
#105949152
#105948492
#105948402
#105948282
#105948242
C2×#638442
#105948082
#105944792
#105943152
#105941582
#105941472
#105940312
#105940292
#105938852
#105938812
#105938602
#105938522
#868423
#861293