Finite Group Databasebeta

← #11906026

Subgroups — #11906026

Order 1152.

3092 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64298C212yesmaximal, complemented
2D4×#634C211yesmaximal, characteristic, complemented
3C3×#5551C211yesmaximal, characteristic, complemented
4C3×#5548C211yesmaximal, characteristic, complemented
5#10595134C212yesmaximal, complemented
6#10595133C212yesmaximal, complemented
7#10594915C212yesmaximal, complemented
8#10594887C212yesmaximal, complemented
9#10594884C212yesmaximal, complemented
10#10594370C212yesmaximal, complemented
11D3×#888C212yesmaximal, complemented
12#10594062C214yesmaximal, complemented
13#10594057C214yesmaximal, complemented
14#10593904C211yesmaximal, characteristic, complemented
15#10593895C211yesmaximal, characteristic, complemented
16D3×#869C211yesmaximal, characteristic, complemented
17C4×#3795C211yesmaximal, characteristic, complemented
18#86679—31nomaximal
19#86243—31nomaximal
20C22×#634C2212yes—
21C2×C3×#235C2212yes—
22C2×C3×#235C2212yes—
23C2×#3805C2214yes—
24C2×#3805C2214yes—
25#64298—216no—
26C2×#3795C2214yes—
27C2×#3795C2212yes—
28C2×#3795C2211yescharacteristic
29C2×D3×Dic6C2214yes—
30C2×D3×Dic6C2212yes—
31C2×D3×Dic6C2212yes—
32C32×C4×D4C2211yescharacteristic
33D4×C3⋊Dic3C2212yes—
34#64133C2212yes—
35#64097C2212yes—
36#64087C2214yes—
37#64078C2211yescharacteristic
38C4×#634C2211yescharacteristic
39C3×#940C2211yescharacteristic
40C3×#938C2212yes—
41C3×#938C2211yescharacteristic
42C3×C4×#67C2212yes—
43C3×#924C2212yes—
44C3×#895C2211yescharacteristic
45C3×D3×C4⋊C4C2212yes—
46C3×#888C2211yescharacteristic
47C3×#885C2212yes—
48C3×#884C2212yes—
49C3×#883C2214yes—
50C3×C4×D12C2211yescharacteristic
51C3×C4×D12C2211yescharacteristic
52C3×C42×D3C2211yescharacteristic
53C3×#869C2211yescharacteristic
54#63982C2214yes—
55#67⋊Dic3C2214yes—
56#63970C2214yes—
57#63969C2214yes—
58#63969C2214yes—
59#63959C2214yes—
60#63919C2212yes—
61#63918C2212yes—
62#63918C2212yes—
63#63908C2212yes—
64#63905C2214yes—
65C4×#625C2212yes—
66#63899C2214yes—
67#63898C2212yes—
68#63896C2214yes—
69Dic3×D12C2211yescharacteristic
70#63891C2214yes—
71D3×C4⋊Dic3C2212yes—
72D3×C4⋊Dic3C2212yes—
73D3×C4⋊Dic3C2212yes—
74#63884C2214yes—
75#63879C2212yes—
76#63877C2212yes—
77D3×Dic3⋊C4C2214yes—
78C4×D3×Dic3C2212yes—
79#63866C2212yes—
80#63857C2212yes—
81#63856C2212yes—
82#63844C2211yescharacteristic
83#63841C2211yescharacteristic
84#63840C2214yes—
85#63839C2214yes—
86C2×#1010—32no—
87C2×#1010—32no—
88C3×#547—31no—
89C3×#532—31no—
90#5825—32no—
91#5824—32no—
92#5727—31no—
93D3×C4⋊Q8—32no—
94D3×C4⋊Q8—31no—
95#5716—32no—
96#5675—34no—
97#5655—34no—
98#5648—34no—
99#5632—32no—
100#5628—32no—
101#5611—32no—
102#5611—32no—
103#5611—32no—
104#5611—34no—
105#5596—32no—
106#5555—31no—
107#5551—32no—
108#5551—31no—
109#5551D311yescharacteristic, complemented
110#5548D311yescharacteristic, complemented
111D4×Dic6—31no—
112D4×Dic6—31no—
113D4×Dic6—32no—
114D4×Dic6—31no—
115D4×Dic6—61no—
116C4×#237—31no—
117#5507—32no—
118C2×#888—32no—
119C4×#235—31no—
120C2×#869—31no—
121C2×C32×D4C2311yescharacteristic
122C22×C32×C4C2312yes—
123C22×C3⋊Dic3C2314yes—
124C2×#634—28no—
125C2×#634C2312yes—
126C2×#634C2314yes—
127C2×#634C2311yescharacteristic
128C2×C3×#67C2314yes—
129C2×C3×#67C2312yes—
130C2×C3×#67C2312yes—
131C2×C3×#67C2312yes—
132C3×#235—28no—
133C3×#235—28no—
134C2×C3×D12C2312yes—
135C2×C3×D12C2311yescharacteristic
136C2×C3×D12C2311yescharacteristic
137C2×C3×C4×D3C2314yes—
138C2×C3×C4×D3C2311yescharacteristic
139C2×C3×C4×D3C2312yes—
140C2×C3×C4×D3C2311yescharacteristic
141C2×C3×C4×D3C2312yes—
142C2×C3×C4×D3C2311yescharacteristic
143C2×C3×Dic6C2312yes—
144C2×C3×Dic6C2312yes—
145C2×#627C2314yes—
146C2×#627C2314yes—
147C2×#625C2314yes—
148C2×#625C2312yes—
149#3805—216no—
150#3805—216no—
151C2×D3×Dic3C2314yes—
152C2×D3×Dic3C2314yes—
153C2×D3×Dic3C2314yes—
154C2×D3×Dic3C2312yes—
155C2×D3×Dic3C2312yes—
156#3795—28no—
157#3795—216no—
158#3795D418yescomplemented
159D3×Dic6—28no—
160D3×Dic6—28no—
161D3×Dic6—216no—
162C32×C4⋊C4C2311yescharacteristic
163C32×C22⋊C4C2312yes—
164C32×C42C2311yescharacteristic
165#3757C2314yes—
166C4⋊(C3⋊Dic3)C2311yescharacteristic
167C4⋊(C3⋊Dic3)C2312yes—
168C4⋊(C3⋊Dic3)C2312yes—
169#3750C2312yes—
170#3750C2314yes—
171C4×C3⋊Dic3C2312yes—
172C3×#217C2314yes—
173C3×#217C2312yes—
174C3×(C2×D3)⋊C4C2312yes—
175C3×(C2×D3)⋊C4C2312yes—
176C3×(C2×D3)⋊C4C2312yes—
177C3×C4⋊Dic3C2312yes—
178C3×C4⋊Dic3C2311yescharacteristic
179C3×C4⋊Dic3C2312yes—
180C3×C4⋊Dic3C2311yescharacteristic
181C3×Dic3⋊C4C2314yes—
182C3×Dic3⋊C4C2312yes—
183C3×C4×Dic3C2311yescharacteristic
184C3×C4×Dic3C2311yescharacteristic
185C3×C4×Dic3C2311yescharacteristic
186#3724C2314yes—
187#3724C2312yes—
188Dic3⋊Dic3C2314yes—
189Dic3⋊Dic3C2314yes—
190Dic3⋊Dic3C2314yes—
191(C2×D3)⋊Dic3C2312yes—
192(C2×D3)⋊Dic3C2314yes—
193(C2×D3)⋊Dic3C2314yes—
194(C2×D3)⋊Dic3C2312yes—
195Dic32C2312yes—
196Dic32C2312yes—
197#3499—91noSylow
198C2×C3×#41—32no—
199C2×C3×#41—32no—
200#1010—616no—
201#1010—616no—
202C2×D3×Q8—32no—
203C2×D3×Q8—34no—
204C2×D3×Q8—32no—
205C2×#237—34no—
206C2×#237—34no—
207C2×#237—34no—
208C2×#237—34no—
209C2×#237—31no—
210C2×#237—32no—
211C2×#237—34no—
212C2×#235—31no—
213C2×#235—34no—
214C2×#235—32no—
215C2×#235C2×D312yes—
216C2×#235C2×D312yes—
217C22×Dic6—32no—
218C22×Dic6—32no—
219C22×Dic6—34no—
220C22×Dic6—32no—
221C22×Dic6—32no—
222C22×Dic6—62no—
223C3×C4⋊Q8—31no—
224C3×C4⋊Q8—31no—
225C3×#127—31no—
226C3×#124—32no—
227C3×#123—34no—
228C3×C22⋊Q8—32no—
229C3×#121—32no—
230C3×#121—31no—
231C3×#121—31no—
232C3×#121—32no—
233C3×C4×D4—21no—
234C3×C4×D4—32no—
235C3×C4×D4—31no—
236C3×C4×D4—31no—
237C3×C4×D4C2×D311yescharacteristic
238C3×C4×D4C2×D311yescharacteristic
239C2×C3×C4⋊C4—32no—
240C2×C3×C42—31no—
241#946—32no—
242#944—34no—
243#944—32no—
244#940C2×D311yescharacteristic
245#939—34no—
246#938—34no—
247#938—32no—
248#938C2×D312yes—
249#938C2×D311yescharacteristic
250#936—34no—
251#935—34no—
252#935—34no—
253#935—34no—
254D4×Dic3—32no—
255D4×Dic3—32no—
256D4×Dic3—34no—
257D4×Dic3—32no—
258D4×Dic3—31no—
259D4×Dic3—62no—
260#930—32no—
261#929—34no—
262C4×#67—32no—
263C4×#67—32no—
264C4×#67—32no—
265C4×#67C2×D312yes—
266#926—31no—
267C2×C4⋊Dic3—32no—
268C2×C4⋊Dic3—32no—
269C2×C4⋊Dic3—32no—
270#924—32no—
271#924—32no—
272#924—32no—
273#924—32no—
274#924—62no—
275#924C2×D312yes—
276C2×Dic3⋊C4—34no—
277C2×C4×Dic3—32no—
278#897—32no—
279#896—34no—
280#896—34no—
281#895C2×D311yescharacteristic
282#894—34no—
283#893—32no—
284#892—31no—
285D3×C4⋊C4—32no—
286D3×C4⋊C4—32no—
287D3×C4⋊C4—34no—
288D3×C4⋊C4—32no—
289D3×C4⋊C4C2×D312yes—
290#888—34no—
291#888—32no—
292#888—32no—
293#888—32no—
294#888—32no—
295#888—34no—
296#888—34no—
297#888—32no—
298#888—32no—
299#888—62no—
300#888C2×D311yescharacteristic
301#887—31no—
302#886—34no—
303#885—34no—
304#885C2×D312yes—
305#884C2×D312yes—
306#883—34no—
307#883—34no—
308#883—34no—
309#883—34no—
310#883C2×D314yes—
311#67⋊C4—34no—
312#67⋊C4—32no—
313#878—34no—
314#878—34no—
315#878—34no—
316#878—34no—
317#878—34no—
318#878—34no—
319#878—64no—
320#877—32no—
321C4×D12—31no—
322C4×D12C2×D311yescharacteristic
323C4×D12C2×D311yescharacteristic
324#872—32no—
325C42×D3—32no—
326C42×D3C2×D311yescharacteristic
327#869—32no—
328#869—31no—
329#869—31no—
330#869—32no—
331#869—32no—
332#869—61no—
333#869C2×D311yescharacteristic
334C4×Dic6—31no—
335C4×Dic6—31no—
336C4×Dic6—31no—
337C4×Dic6—61no—
338C23×C32C2412yes—
339C22×C3×D3C2412yes—
340C22×C3×D3C2411yescharacteristic
341C22×C3×D3C2412yes—
342C32×D4—22no—
343C2×C32×C4—24no—
344C2×C32×C4C2411yescharacteristic
345C2×C32×C4C2412yes—
346C2×C32×C4C2411yescharacteristic
347C2×C32×C4C2411yescharacteristic
348C2×C3⋊Dic3—28no—
349C2×C3⋊Dic3C2412yes—
350C2×C3⋊Dic3C2414yes—
351C2×C3⋊Dic3C2412yes—
352#634—24no—
353#634—28no—
354#634C2×D414yes—
355C3×#67—24no—
356C3×#67—28no—
357C3×#67—24no—
358C3×#67—24no—
359C2×C3×Dic3C2412yes—
360C2×C3×Dic3C2411yescharacteristic
361C2×C3×Dic3C2414yes—
362C2×C3×Dic3C2412yes—
363C2×C3×Dic3C2411yescharacteristic
364C2×C3×Dic3C2411yescharacteristic
365C3×D12—24no—
366C3×D12—22no—
367C3×D12C2×D414yes—
368C3×C4×D3—28no—
369C3×C4×D3—24no—
370C3×C4×D3—24no—
371C3×C4×D3—22no—
372C3×C4×D3—22no—
373C3×C4×D3C2×D414yes—
374C3×Dic6—24no—
375C3×Dic6—24no—
376#627—28no—
377#627—28no—
378#625—28no—
379#625C2×D418yes—
380D3×Dic3—28no—
381D3×Dic3—28no—
382D3×Dic3—28no—
383D3×Dic3—24no—
384D3×Dic3C2×D418yes—
385C2×2−1+4—92no—
386D4×Q8—92no—
387D4×Q8—91no—
388D4×Q8—91no—
389#547—31no—
390#547—92no—
391#547—91no—
392#547—92no—
393#547—92no—
394#547—94no—
395#536—92no—
396#536—94no—
397#532—31no—
398#532—92no—
399C2×C4⋊Q8—91no—
400C2×C4⋊Q8—92no—
401C4×#41—91no—
402C3×#41—68no—
403C3×#41—68no—
404C2×C3×Q8—32no—
405C2×C3×Q8—32no—
406C2×C3×D4—21no—
407C2×C3×D4—32no—
408C2×C3×D4—32no—
409C2×C3×D4—34no—
410C2×C3×D4—32no—
411C2×C3×D4—31no—
412C2×C3×D4—31no—
413C2×C3×D4—32no—
414C2×C3×D4C22×D311yescharacteristic
415C2×C3×D4C22×D311yescharacteristic
416C22×C3×C4—22no—
417C22×C3×C4—31no—
418C22×C3×C4—32no—
419C22×C3×C4—34no—
420C22×C3×C4—32no—
421C22×C3×C4—31no—
422C22×C3×C4—31no—
423C22×C3×C4C22×D312yes—
424C22×C3×C4C22×D312yes—
425C2×#67—32no—
426C2×#67—32no—
427C2×#67—34no—
428C2×#67—34no—
429C2×#67C22×D312yes—
430C2×#67C22×D312yes—
431C2×#67C22×D314yes—
432C2×#67C22×D312yes—
433C22×Dic3—32no—
434C22×Dic3—34no—
435C22×Dic3—34no—
436C22×Dic3—34no—
437C22×Dic3—32no—
438C22×Dic3—34no—
439C22×Dic3—34no—
440C22×Dic3—64no—
441D3×Q8—68no—
442D3×Q8—616no—
443D3×Q8—68no—
444#237—38no—
445#237—616no—
446#237—68no—
447#237—616no—
448#237—616no—
449#237—616no—
450#237—616no—
451#235—28no—
452#235—28no—
453#235—38no—
454#235—616no—
455#235—68no—
456C2×D12C22×D311yescharacteristic
457C2×D12C22×D312yes—
458C2×D12C22×D311yescharacteristic
459C2×C4×D3—32no—
460C2×C4×D3—32no—
461C2×C4×D3—34no—
462C2×C4×D3—34no—
463C2×C4×D3—34no—
464C2×C4×D3C22×D312yes—
465C2×C4×D3C22×D311yescharacteristic
466C2×C4×D3C22×D311yescharacteristic
467C2×C4×D3C22×D312yes—
468C2×C4×D3C22×D314yes—
469C2×C4×D3C22×D311yescharacteristic
470C2×Dic6—31no—
471C2×Dic6—31no—
472C2×Dic6—32no—
473C2×Dic6—32no—
474C2×Dic6—34no—
475C2×Dic6—34no—
476C2×Dic6—34no—
477C2×Dic6—34no—
478C2×Dic6—34no—
479C2×Dic6—34no—
480C2×Dic6—61no—
481C2×Dic6—62no—
482C2×Dic6—64no—
483C2×Dic6—68no—
484C2×Dic6—616no—
485C2×Dic6—68no—
486C2×Dic6—68no—
487C2×Dic6—68no—
488C2×Dic6—128no—
489C2×Dic6C22×D312yes—
490C2×Dic6C22×D312yes—
491C3×C4⋊C4—21no—
492C3×C4⋊C4—31no—
493C3×C4⋊C4—32no—
494C3×C4⋊C4—31no—
495C3×C4⋊C4—32no—
496C3×C4⋊C4—34no—
497C3×C4⋊C4—32no—
498C3×C4⋊C4C22×D311yescharacteristic
499C3×C4⋊C4C22×D311yescharacteristic
500C3×C22⋊C4—22no—
501C3×C22⋊C4—32no—
502C3×C22⋊C4—34no—
503C3×C22⋊C4—32no—
504C3×C22⋊C4—32no—
505C3×C22⋊C4—32no—
506C3×C22⋊C4C22×D312yes—
507C3×C22⋊C4C22×D312yes—
508C3×C42—21no—
509C3×C42—31no—
510C3×C42—31no—
511C3×C42—31no—
512C3×C42C22×D311yescharacteristic
513C3×C42C22×D311yescharacteristic
514#217—34no—
515#217—34no—
516#217—32no—
517#217—34no—
518#217—34no—
519#217—32no—
520#217—64no—
521#217C22×D312yes—
522#217C22×D314yes—
523(C2×D3)⋊C4—32no—
524(C2×D3)⋊C4—32no—
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4C22×D312yes—
528(C2×D3)⋊C4C22×D312yes—
529(C2×D3)⋊C4C22×D312yes—
530C4⋊Dic3—31no—
531C4⋊Dic3—31no—
532C4⋊Dic3—32no—
533C4⋊Dic3—32no—
534C4⋊Dic3—32no—
535C4⋊Dic3—32no—
536C4⋊Dic3—34no—
537C4⋊Dic3—34no—
538C4⋊Dic3—34no—
539C4⋊Dic3—61no—
540C4⋊Dic3—62no—
541C4⋊Dic3—62no—
542C4⋊Dic3C22×D311yescharacteristic
543C4⋊Dic3C22×D312yes—
544C4⋊Dic3C22×D312yes—
545C4⋊Dic3C22×D311yescharacteristic
546Dic3⋊C4—32no—
547Dic3⋊C4—32no—
548Dic3⋊C4—34no—
549Dic3⋊C4—34no—
550Dic3⋊C4—32no—
551Dic3⋊C4—32no—
552Dic3⋊C4—34no—
553Dic3⋊C4—34no—
554Dic3⋊C4—34no—
555Dic3⋊C4—34no—
556Dic3⋊C4—34no—
557Dic3⋊C4—62no—
558Dic3⋊C4—64no—
559Dic3⋊C4C22×D314yes—
560Dic3⋊C4C22×D312yes—
561C4×Dic3—32no—
562C4×Dic3—32no—
563C4×Dic3—32no—
564C4×Dic3—32no—
565C4×Dic3—32no—
566C4×Dic3—32no—
567C4×Dic3—62no—
568C4×Dic3C22×D311yescharacteristic
569C4×Dic3C22×D311yescharacteristic
570C4×Dic3C22×D311yescharacteristic
571C22×C32—22no—
572C22×C32—22no—
573C22×C32—22no—
574C22×C32C2511yescharacteristic
575C2×C3×D3—22no—
576C2×C3×D3—21no—
577C2×C3×D3—22no—
578C2×C3×D3—21no—
579C2×C3×D3—22no—
580C2×C3×D3—22no—
581C2×C3×D3—22no—
582C2×C3×D3C22×D412yes—
583C2×C3×D3C22×D414yes—
584C32×C4—22no—
585C32×C4—21no—
586C32×C4C22×D412yes—
587C32×C42−1+412yescomplemented
588C3⋊Dic3—24no—
589C3⋊Dic3—22no—
590C3⋊Dic3C22×D414yes—
591C3×Dic3—22no—
592C3×Dic3—24no—
593C3×Dic3—22no—
594C3×Dic3—21no—
595C3×Dic3C22×D412yes—
596C3×Dic32−1+412yescomplemented
5972−1+4—1816no—
598C2×#41—32no—
599C2×#41—32no—
600C2×#41—91no—
601C2×#41—94no—
602C2×#41—92no—
603C2×#41—94no—
604C2×#41—94no—
605C22×Q8—92no—
606C22×Q8—94no—
607C22×Q8—92no—
608C22×Q8—92no—
609C4⋊Q8—31no—
610C4⋊Q8—31no—
611C4⋊Q8—92no—
612C4⋊Q8—92no—
613C4⋊Q8—92no—
614C4⋊Q8—94no—
615C4⋊Q8—92no—
616C4⋊Q8—94no—
617C4⋊Q8—92no—
618C4⋊Q8—91no—
619#127—31no—
620#124—32no—
621#124—94no—
622#123—34no—
623#123—94no—
624#123—94no—
625#123—94no—
626#123—94no—
627#123—94no—
628C22⋊Q8—32no—
629C22⋊Q8—94no—
630C22⋊Q8—94no—
631C22⋊Q8—94no—
632C22⋊Q8—92no—
633C22⋊Q8—92no—
634C22⋊Q8—92no—
635C22⋊Q8—94no—
636#121—31no—
637#121—32no—
638#121—31no—
639#121—32no—
640#121—92no—
641#121—94no—
642C4×Q8—91no—
643C4×Q8—91no—
644C4×D4—32no—
645C4×D4—31no—
646C4×D4—31no—
647C4×D4—91no—
648C4×D4—92no—
649C4×D4—94no—
650C4×D4—92no—
651C4×D4—92no—
652C4×D4—92no—
653C4×D4D3211yescharacteristic
654#117—92no—
655#117—91no—
656C2×C4⋊C4—32no—
657C2×C4⋊C4—94no—
658C2×C4⋊C4—92no—
659C2×C4⋊C4—92no—
660C2×C4⋊C4—92no—
661C2×C42—31no—
662C2×C42—92no—
663C23×C3—22no—
664C23×C3—31no—
665C23×C3—32no—
666C23×C3—32no—
667C23×C3C23×D312yes—
668C23×C3C23×D312yes—
669C22×D3C23×D312yes—
670C22×D3C23×D311yescharacteristic
671C22×D3C23×D312yes—
672C3×Q8—64no—
673C3×Q8—64no—
674C3×D4—24no—
675C3×D4—22no—
676C3×D4—22no—
677C3×D4—34no—
678C3×D4—64no—
679C3×D4—64no—
680C3×D4—64no—
681C3×D4—68no—
682C3×D4—64no—
683C3×D4—62no—
684C2×C3×C4—24no—
685C2×C3×C4—24no—
686C2×C3×C4—21no—
687C2×C3×C4—21no—
688C2×C3×C4—21no—
689C2×C3×C4—22no—
690C2×C3×C4—31no—
691C2×C3×C4—31no—
692C2×C3×C4—34no—
693C2×C3×C4—32no—
694C2×C3×C4—32no—
695C2×C3×C4—34no—
696C2×C3×C4—31no—
697C2×C3×C4—44no—
698C2×C3×C4—62no—
699C2×C3×C4—68no—
700C2×C3×C4—64no—
701C2×C3×C4—62no—
702C2×C3×C4—64no—
703C2×C3×C4C23×D311yescharacteristic
704C2×C3×C4C23×D312yes—
705C2×C3×C4C23×D312yes—
706C2×C3×C4C23×D311yescharacteristic
707C2×C3×C4C23×D311yescharacteristic
708C2×C3×C4C23×D311yescharacteristic
709C2×C3×C4C23×D311yescharacteristic
710C2×C3×C4C23×D311yescharacteristic
711#67—28no—
712#67—24no—
713#67—24no—
714#67—24no—
715#67—38no—
716#67—38no—
717#67—68no—
718#67—68no—
719C2×Dic3—32no—
720C2×Dic3—32no—
721C2×Dic3—38no—
722C2×Dic3—32no—
723C2×Dic3—32no—
724C2×Dic3—34no—
725C2×Dic3—34no—
726C2×Dic3—62no—
727C2×Dic3—62no—
728C2×Dic3—64no—
729C2×Dic3—68no—
730C2×Dic3—68no—
731C2×Dic3—68no—
732C2×Dic3—68no—
733C2×Dic3—68no—
734C2×Dic3—64no—
735C2×Dic3—128no—
736C2×Dic3C23×D312yes—
737C2×Dic3C23×D311yescharacteristic
738C2×Dic3C23×D312yes—
739C2×Dic3C23×D314yes—
740C2×Dic3C23×D311yescharacteristic
741C2×Dic3C23×D311yescharacteristic
742D12—24no—
743D12—22no—
744D12D3×D414yes—
745C4×D3—28no—
746C4×D3—24no—
747C4×D3—24no—
748C4×D3—22no—
749C4×D3—22no—
750C4×D3—38no—
751C4×D3—68no—
752C4×D3—64no—
753C4×D3—68no—
754C4×D3—68no—
755C4×D3D3×D414yes—
756Dic6—24no—
757Dic6—24no—
758Dic6—34no—
759Dic6—34no—
760Dic6—64no—
761Dic6—68no—
762Dic6—68no—
763Dic6—68no—
764Dic6—68no—
765Dic6—68no—
766Dic6—64no—
767Dic6—64no—
768Dic6—68no—
769Dic6—128no—
770Dic6—124no—
771C2×C32—42no—
772C2×C32C23×D411yescharacteristic
773C2×C32C2×2−1+411yescharacteristic
774C2×C32C2×2−1+411yescharacteristic
775C3×D3—24no—
776C3×D3—22no—
777C3×D3—42no—
778#41—68no—
779#41—68no—
780#41—98no—
781#41—188no—
782#41—1816no—
783#41—1816no—
784#41—1816no—
785C2×Q8—32no—
786C2×Q8—32no—
787C2×Q8—94no—
788C2×Q8—94no—
789C2×Q8—91no—
790C2×Q8—94no—
791C2×Q8—92no—
792C2×Q8—188no—
793C2×Q8—188no—
794C2×Q8—1816no—
795C2×Q8—188no—
796C2×D4—32no—
797C2×D4—32no—
798C2×D4—34no—
799C2×D4—32no—
800C2×D4—31no—
801C2×D4—31no—
802C2×D4—32no—
803C2×D4—92no—
804C2×D4—94no—
805C2×D4C2×D3211yescharacteristic
806C22×C4—31no—
807C22×C4—31no—
808C22×C4—31no—
809C22×C4—32no—
810C22×C4—34no—
811C22×C4—32no—
812C22×C4—92no—
813C22×C4—92no—
814C22×C4—94no—
815C22×C4—94no—
816C22×C4—94no—
817C22×C4—94no—
818C22×C4C2×D3212yes—
819C4⋊C4—32no—
820C4⋊C4—34no—
821C4⋊C4—32no—
822C4⋊C4—31no—
823C4⋊C4—32no—
824C4⋊C4—31no—
825C4⋊C4—94no—
826C4⋊C4—94no—
827C4⋊C4—94no—
828C4⋊C4—94no—
829C4⋊C4—92no—
830C4⋊C4—92no—
831C4⋊C4—94no—
832C4⋊C4—92no—
833C4⋊C4—92no—
834C4⋊C4—91no—
835C4⋊C4C2×D3211yescharacteristic
836C22⋊C4—32no—
837C22⋊C4—34no—
838C22⋊C4—32no—
839C22⋊C4—32no—
840C22⋊C4—32no—
841C22⋊C4—92no—
842C22⋊C4—92no—
843C22⋊C4—94no—
844C22⋊C4—94no—
845C22⋊C4—94no—
846C22⋊C4C2×D3212yes—
847C42—31no—
848C42—31no—
849C42—31no—
850C42—92no—
851C42—92no—
852C42—92no—
853C42C2×D3211yescharacteristic
854C22×C3—24no—
855C22×C3—22no—
856C22×C3—22no—
857C22×C3—22no—
858C22×C3—22no—
859C22×C3—22no—
860C22×C3—22no—
861C22×C3—21no—
862C22×C3—34no—
863C22×C3—32no—
864C22×C3—42no—
865C22×C3—42no—
866C22×C3—62no—
867C22×C3—61no—
868C22×C3—62no—
869C22×C3—61no—
870C22×C3—62no—
871C22×C3—62no—
872C22×C3—62no—
873C22×C3C24×D311yescharacteristic
874C22×C3C24×D311yescharacteristic
875C2×D3—22no—
876C2×D3—21no—
877C2×D3—21no—
878C2×D3—22no—
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3C2×D3×D414yes—
883C2×D3C2×D3×D412yes—
884C3×C4—22no—
885C3×C4—22no—
886C3×C4—21no—
887C3×C4—21no—
888C3×C4—22no—
889C3×C4—22no—
890C3×C4—32no—
891C3×C4—32no—
892C3×C4—42no—
893C3×C4—41no—
894C3×C4—62no—
895C3×C4—64no—
896C3×C4—61no—
897C3×C4—62no—
898C3×C4C2×D3×D412yes—
899C3×C4C2×D3×D412yes—
900C3×C4#101012yescomplemented
901C3×C4#101012yescomplemented
902Dic3—24no—
903Dic3—22no—
904Dic3—22no—
905Dic3—21no—
906Dic3—34no—
907Dic3—34no—
908Dic3—64no—
909Dic3—64no—
910Dic3—64no—
911Dic3—62no—
912Dic3—62no—
913Dic3—124no—
914Dic3—122no—
915Dic3C2×D3×D412yes—
916Dic3#101012yescomplemented
917C32#349911yescharacteristic, complemented, Sylow
918C23—32no—
919C23—31no—
920C23—32no—
921C23C22×D3212yes—
922Q8—64no—
923Q8—64no—
924Q8—94no—
925Q8—188no—
926Q8—188no—
927Q8—188no—
928Q8—184no—
929D4—22no—
930D4—34no—
931D4—64no—
932D4—64no—
933D4—64no—
934D4—64no—
935D4—68no—
936D4—62no—
937D4—98no—
938D4—188no—
939C2×C4—24no—
940C2×C4—31no—
941C2×C4—31no—
942C2×C4—34no—
943C2×C4—31no—
944C2×C4—32no—
945C2×C4—32no—
946C2×C4—34no—
947C2×C4—62no—
948C2×C4—68no—
949C2×C4—62no—
950C2×C4—64no—
951C2×C4—64no—
952C2×C4—98no—
953C2×C4—92no—
954C2×C4—92no—
955C2×C4—94no—
956C2×C4—184no—
957C2×C4—188no—
958C2×C4—188no—
959C2×C4—188no—
960C2×C4—188no—
961C2×C4C22×D3211yescharacteristic
962C2×C4C22×D3212yes—
963C2×C4C22×D3211yescharacteristic
964C2×C4C22×D3211yescharacteristic
965C2×C3—21no—
966C2×C3—21no—
967C2×C3—21no—
968C2×C3—44no—
969C2×C3—42no—
970C2×C3—42no—
971C2×C3—62no—
972C2×C3—64no—
973C2×C3—122no—
974C2×C3C22×D3×D411yescharacteristic
975C2×C3C22×D3×D411yescharacteristic
976C2×C3C2×#101011yescharacteristic
977C2×C3C2×#101011yescharacteristic
978C2×C3C2×#101011yescharacteristic
979C2×C3D3×2−1+411yescharacteristic
980D3—24no—
981D3—22no—
982D3—42no—
983C22—22no—
984C22—22no—
985C22—22no—
986C22—32no—
987C22—34no—
988C22—62no—
989C22—61no—
990C22—61no—
991C22—62no—
992C22—62no—
993C22—62no—
994C22—62no—
995C22C23×D3211yescharacteristic
996C4—22no—
997C4—21no—
998C4—32no—
999C4—32no—
1000C4—61no—
1001C4—62no—
1002C4—62no—
1003C4—64no—
1004C4—94no—
1005C4—184no—
1006C4—182no—
1007C4#6429812yescomplemented
1008C4D32×D412yes—
1009C3—21no—
1010C3#8624311yescharacteristic, complemented
1011C3#8667911yescharacteristic, complemented
1012C2—42no—
1013C2—62no—
1014C2—64no—
1015C2—122no—
1016C2C2×#6429811yescharacteristic
1017C2C2×D32×D411yescharacteristic
1018C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×D4C22
hypercenterC4×D4D32
hypocenterC32#3499
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64298C2semidirect
2. D4×#634C2semidirect
3. C3×#5551C2semidirect
4. C3×#5548C2semidirect
5. #10595134C2semidirect
6. #10595133C2semidirect
7. #10594915C2semidirect
8. #10594887C2semidirect
9. #10594884C2semidirect
10. #10594370C2semidirect
11. D3×#888C2semidirect
12. #10594062C2semidirect
13. #10594057C2semidirect
14. #10593904C2semidirect
15. #10593895C2semidirect
16. D3×#869C2semidirect
17. C4×#3795C2semidirect
109. #5551D3semidirect
110. #5548D3semidirect
158. #3795D4semidirect
587. C32×C42−1+4semidirect
596. C3×Dic32−1+4semidirect
900. C3×C4#1010semidirect
901. C3×C4#1010semidirect
916. Dic3#1010semidirect
917. C32#3499semidirect
1007. C4#64298semidirect
1010. C3#86243semidirect
1011. C3#86679semidirect

Maximal subgroups

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

subgroupindex
C2×#642982
D4×#6342
C3×#55512
C3×#55482
#105951342
#105951332
#105949152
#105948872
#105948842
#105943702
D3×#8882
#105940622
#105940572
#105939042
#105938952
D3×#8692
C4×#37952
#866793
#862433