Finite Group Databasebeta

← #11906023

Subgroups — #11906023

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×#64315C212yesmaximal, complemented
2#10596198C211yesmaximal, characteristic, complemented
3C3×#5726C211yesmaximal, characteristic, complemented
4C3×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
5#10595397C212yesmaximal, complemented
6#10595361C212yesmaximal, complemented
7#10595358C212yesmaximal, complemented
8#10594513C214yesmaximal, complemented
9#10594512C212yesmaximal, complemented
10#10594370C212yesmaximal, complemented
11#10594369C212yesmaximal, complemented
12#10594366C214yesmaximal, complemented
13D3×#888C212yesmaximal, complemented
14#10593968C211yesmaximal, characteristic, complemented
15#10593904C211yesmaximal, characteristic, complemented
16#10593896C211yesmaximal, characteristic, complemented
17C4×#3795C211yesmaximal, characteristic, complemented
18#86679—31nomaximal
19#86214—31nomaximal
20C2×Q8×C3⋊D3C2212yes—
21C2×C3×#239C2212yes—
22C2×C3×D3×Q8C2212yes—
23#64315—216no—
24C2×#3798C2212yes—
25C2×#3798C2214yes—
26C2×#3796C2212yes—
27C2×#3796C2214yes—
28C2×#3795C2214yes—
29C2×#3795C2211yescharacteristic
30C2×D3×Dic6C2212yes—
31C2×D3×Dic6C2214yes—
32C32×C4⋊Q8C2211yescharacteristic
33#64155C2212yes—
34#64105C2214yes—
35#64102C2212yes—
36#64097C2212yes—
37C4×C4⋊(C3⋊D3)C2211yescharacteristic
38C4×#634C2211yescharacteristic
39C3×#946C2212yes—
40C3×#944C2212yes—
41C3×#895C2212yes—
42C3×#894C2214yes—
43C3×D3×C4⋊C4C2212yes—
44C3×D3×C4⋊C4C2212yes—
45C3×D3×C4⋊C4C2212yes—
46C3×#888C2212yes—
47C3×#888C2212yes—
48C3×C4×D12C2211yescharacteristic
49C3×C4×D12C2211yescharacteristic
50C3×C42×D3C2211yescharacteristic
51C3×#869C2211yescharacteristic
52#63919C2212yes—
53#63918C2211yescharacteristic
54#63911C2211yescharacteristic
55#63909C2212yes—
56#63909C2211yescharacteristic
57#63908C2211yescharacteristic
58#63907C2214yes—
59#63906C2212yes—
60#63905C2214yes—
61C4×#626C2212yes—
62C4×#625C2212yes—
63#63899C2214yes—
64#63898C2212yes—
65#63896C2214yes—
66Dic3×D12C2211yescharacteristic
67#63890C2214yes—
68D3×C4⋊Dic3C2212yes—
69#63886C2214yes—
70#63884C2214yes—
71#63881C2214yes—
72#63879C2212yes—
73#63877C2212yes—
74D3×Dic3⋊C4C2214yes—
75C4×D3×Dic3C2212yes—
76#63871C2212yes—
77#63865C2214yes—
78#63856C2212yes—
79#63852C2212yes—
80#63850C2214yes—
81#63850C2214yes—
82#63844C2211yescharacteristic
83#63841C2211yescharacteristic
84#63840C2214yes—
85#63839C2214yes—
86C2×#1010—32no—
87C2×#1007—32no—
88C3×#547—31no—
89C2×C3×C4⋊Q8—31no—
90#5824—32no—
91#5816—32no—
92#5727—31no—
93#5727—31no—
94#5727—32no—
95#5727—31no—
96#5727—61no—
97#5726—32no—
98#5726—31no—
99#5726D311yescharacteristic, complemented
100#5725—32no—
101#5724—34no—
102D3×C4⋊Q8—32no—
103D3×C4⋊Q8D311yescharacteristic, complemented
104#5655—34no—
105#5648—34no—
106#5632—32no—
107#5628—32no—
108#5611—32no—
109#5596—32no—
110#5555—31no—
111#5548—31no—
112D4×Dic6—31no—
113C4×#237—31no—
114#5507—32no—
115#5507—34no—
116#5507—32no—
117#5507—32no—
118C2×#888—32no—
119#5477—31no—
120C4×#235—31no—
121C2×C32×Q8C2312yes—
122Q8×C3⋊D3—28no—
123C2×C4⋊(C3⋊D3)C2311yescharacteristic
124C2×C4×C3⋊D3C2312yes—
125C2×C4×C3⋊D3C2314yes—
126C2×#634C2314yes—
127C2×#634C2311yescharacteristic
128C3×#239—28no—
129C3×D3×Q8—28no—
130C2×C3×D12C2314yes—
131C2×C3×D12C2311yescharacteristic
132C2×C3×D12C2311yescharacteristic
133C2×C3×C4×D3C2314yes—
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×C4×D3C2311yescharacteristic
136C2×C3×C4×D3C2314yes—
137C2×C3×C4×D3C2312yes—
138C2×C3×C4×D3C2312yes—
139C2×C3×C4×D3C2311yescharacteristic
140C2×C3×Dic6C2314yes—
141C2×C3×Dic6C2312yes—
142C2×#627C2312yes—
143C2×#627C2314yes—
144C2×#626C2314yes—
145C2×#626C2312yes—
146C2×#626C2312yes—
147C2×#626C2312yes—
148C2×#625C2312yes—
149C2×#625C2312yes—
150C2×D3×Dic3C2314yes—
151C2×D3×Dic3C2314yes—
152C2×D3×Dic3C2312yes—
153C2×D3×Dic3C2312yes—
154#3798—28no—
155#3798—216no—
156#3796—28no—
157#3796—216no—
158#3795—216no—
159#3795D418yescomplemented
160D3×Dic6—28no—
161D3×Dic6—216no—
162C32×C4⋊C4C2312yes—
163C32×C4⋊C4C2312yes—
164C32×C42C2311yescharacteristic
165#3752C2312yes—
166#3752C2314yes—
167C4⋊(C3⋊Dic3)C2311yescharacteristic
168C4⋊(C3⋊Dic3)C2311yescharacteristic
169#3750C2312yes—
170#3750C2314yes—
171C4×C3⋊Dic3C2312yes—
172C3×(C2×D3)⋊C4C2312yes—
173C3×(C2×D3)⋊C4C2312yes—
174C3×(C2×D3)⋊C4C2314yes—
175C3×C4⋊Dic3C2312yes—
176C3×C4⋊Dic3C2312yes—
177C3×C4⋊Dic3C2311yescharacteristic
178C3×C4⋊Dic3C2311yescharacteristic
179C3×Dic3⋊C4C2314yes—
180C3×Dic3⋊C4C2314yes—
181C3×Dic3⋊C4C2314yes—
182C3×C4×Dic3C2311yescharacteristic
183C3×C4×Dic3C2311yescharacteristic
184C3×C4×Dic3C2311yescharacteristic
185#3724C2314yes—
186#3724C2312yes—
187Dic3⋊Dic3C2314yes—
188Dic3⋊Dic3C2312yes—
189#3722C2312yes—
190#3722C2314yes—
191(C2×D3)⋊Dic3C2312yes—
192(C2×D3)⋊Dic3C2312yes—
193(C2×D3)⋊Dic3C2312yes—
194(C2×D3)⋊Dic3C2314yes—
195Dic32C2312yes—
196Dic32C2312yes—
197#3499—91noSylow
198C2×C3×#41—32no—
199C22×C3×Q8—32no—
200#1010—616no—
201#1007—616no—
202C2×#239—34no—
203C2×#239—32no—
204C2×#239C2×D312yes—
205C2×D3×Q8—32no—
206C2×D3×Q8—32no—
207C2×D3×Q8—34no—
208C2×D3×Q8—32no—
209C2×D3×Q8—62no—
210C2×D3×Q8C2×D312yes—
211C2×#237—31no—
212C2×#237—34no—
213C2×#237—34no—
214C2×#237—32no—
215C2×#235—31no—
216C2×#235—34no—
217C2×#235—34no—
218C2×#235—32no—
219C2×#235—34no—
220C2×#235—32no—
221C22×Dic6—32no—
222C22×Dic6—34no—
223C3×C4⋊Q8—21no—
224C3×C4⋊Q8—32no—
225C3×C4⋊Q8—32no—
226C3×C4⋊Q8—32no—
227C3×C4⋊Q8—31no—
228C3×C4⋊Q8C2×D311yescharacteristic
229C3×C4⋊Q8C2×D311yescharacteristic
230C3×#123—34no—
231C3×C22⋊Q8—32no—
232C3×#121—32no—
233C3×C4×D4—31no—
234C3×C4×D4—31no—
235C2×C3×C4⋊C4—32no—
236C2×C3×C4⋊C4—32no—
237C2×C3×C4⋊C4—32no—
238C2×C3×C42—31no—
239#947—34no—
240#946—32no—
241#946—32no—
242#946—32no—
243#946—32no—
244#946—62no—
245#946C2×D312yes—
246#944—34no—
247#944C2×D312yes—
248#940—31no—
249#939—34no—
250#938—31no—
251#935—34no—
252D4×Dic3—32no—
253D4×Dic3—31no—
254#930—31no—
255#930—32no—
256#930—31no—
257#930—32no—
258#929—34no—
259#929—34no—
260#929—34no—
261C4×#67—32no—
262C4×#67—32no—
263C4×#67—32no—
264C4×#67—32no—
265#926—31no—
266C2×C4⋊Dic3—32no—
267#924—32no—
268C2×Dic3⋊C4—34no—
269C2×C4×Dic3—32no—
270#897—32no—
271#896—34no—
272#896—34no—
273#896—34no—
274#896—34no—
275#896—34no—
276#896—34no—
277#896—64no—
278#895—34no—
279#895—32no—
280#895—31no—
281#895C2×D312yes—
282#894—34no—
283#894—34no—
284#894—34no—
285#894—34no—
286#894C2×D314yes—
287#893—32no—
288#893—32no—
289#893—32no—
290#893—34no—
291#893—62no—
292#892—31no—
293D3×C4⋊C4—34no—
294D3×C4⋊C4—32no—
295D3×C4⋊C4C2×D312yes—
296D3×C4⋊C4C2×D312yes—
297D3×C4⋊C4C2×D312yes—
298#888—34no—
299#888—32no—
300#888—32no—
301#888—32no—
302#888—32no—
303#888—34no—
304#888—34no—
305#888—31no—
306#888—62no—
307#888C2×D312yes—
308#888C2×D312yes—
309#887—31no—
310#886—34no—
311#885—34no—
312#885—32no—
313#884—32no—
314#883—34no—
315#67⋊C4—32no—
316#67⋊C4—34no—
317#878—34no—
318#878—34no—
319#877—32no—
320#875—32no—
321#874—31no—
322C4×D12—31no—
323C4×D12—32no—
324C4×D12—31no—
325C4×D12—31no—
326C4×D12—61no—
327C4×D12C2×D311yescharacteristic
328C4×D12C2×D311yescharacteristic
329#872—32no—
330C42×D3—32no—
331C42×D3C2×D311yescharacteristic
332#869—31no—
333#869C2×D311yescharacteristic
334C4×Dic6—31no—
335C4×Dic6—31no—
336C4×Dic6—31no—
337C4×Dic6—61no—
338C22×C3⋊D3C2412yes—
339C22×C3×D3C2412yes—
340C22×C3×D3C2411yescharacteristic
341C22×C3×D3C2412yes—
342C32×Q8—24no—
343C2×C32×C4C2411yescharacteristic
344C2×C32×C4C2414yes—
345C2×C32×C4C2411yescharacteristic
346C2×C32×C4C2411yescharacteristic
347C2×C3⋊Dic3C2412yes—
348C2×C3⋊Dic3C2412yes—
349C2×C3⋊Dic3C2412yes—
350C4⋊(C3⋊D3)—22no—
351C4×C3⋊D3—24no—
352C4×C3⋊D3—28no—
353#634—28no—
354#634C2×D414yes—
355C2×C3×Dic3C2412yes—
356C2×C3×Dic3C2411yescharacteristic
357C2×C3×Dic3C2414yes—
358C2×C3×Dic3C2412yes—
359C2×C3×Dic3C2411yescharacteristic
360C2×C3×Dic3C2411yescharacteristic
361C3×D12—28no—
362C3×D12—22no—
363C3×D12C2×D414yes—
364C3×C4×D3—28no—
365C3×C4×D3—28no—
366C3×C4×D3—24no—
367C3×C4×D3—22no—
368C3×C4×D3—24no—
369C3×C4×D3—22no—
370C3×C4×D3C2×D414yes—
371C3×Dic6—24no—
372C3×Dic6—28no—
373#627—28no—
374#627—24no—
375#626—28no—
376#626—24no—
377#626—24no—
378#626—24no—
379#625—24no—
380#625C2×D418yes—
381D3×Dic3—28no—
382D3×Dic3—28no—
383D3×Dic3—24no—
384D3×Dic3C2×D418yes—
385C2×2−1+4—92no—
386D4×Q8—91no—
387D4×Q8—92no—
388D4×Q8—91no—
389#547—31no—
390#547—92no—
391#547—92no—
392#547—94no—
393#547—91no—
394#547—92no—
395#536—92no—
396#536—94no—
397#532—91no—
398#532—92no—
399C2×C4⋊Q8—31no—
400C2×C4⋊Q8—92no—
401C4×#41—91no—
402C3×#41—68no—
403C2×C3×Q8—22no—
404C2×C3×Q8—34no—
405C2×C3×Q8—32no—
406C2×C3×Q8—68no—
407C2×C3×Q8C22×D312yes—
408C2×C3×Q8C22×D312yes—
409C2×C3×D4—31no—
410C2×C3×D4—31no—
411C2×C3×D4—34no—
412C22×C3×C4—31no—
413C22×C3×C4—32no—
414C22×C3×C4—34no—
415C22×C3×C4—32no—
416C22×C3×C4—31no—
417C22×C3×C4—31no—
418C22×C3×C4—34no—
419C2×#67—32no—
420C2×#67—32no—
421C2×#67—32no—
422C2×#67—32no—
423C2×#67—32no—
424C2×#67—32no—
425C2×#67—34no—
426C2×#67—32no—
427C22×Dic3—32no—
428C22×Dic3—34no—
429C22×Dic3—32no—
430C22×Dic3—34no—
431#239—28no—
432#239—616no—
433#239—68no—
434D3×Q8—28no—
435D3×Q8—68no—
436D3×Q8—68no—
437D3×Q8—68no—
438D3×Q8—616no—
439D3×Q8—128no—
440#237—38no—
441#237—616no—
442#237—68no—
443#237—616no—
444#235—38no—
445#235—616no—
446#235—616no—
447#235—68no—
448#235—616no—
449#235—68no—
450C2×D12—32no—
451C2×D12—32no—
452C2×D12—32no—
453C2×D12—34no—
454C2×D12—31no—
455C2×D12—31no—
456C2×D12—61no—
457C2×D12C22×D311yescharacteristic
458C2×D12C22×D314yes—
459C2×D12C22×D311yescharacteristic
460C2×C4×D3—32no—
461C2×C4×D3—32no—
462C2×C4×D3—34no—
463C2×C4×D3—34no—
464C2×C4×D3—32no—
465C2×C4×D3—32no—
466C2×C4×D3—34no—
467C2×C4×D3—34no—
468C2×C4×D3—62no—
469C2×C4×D3—64no—
470C2×C4×D3C22×D312yes—
471C2×C4×D3C22×D311yescharacteristic
472C2×C4×D3C22×D311yescharacteristic
473C2×C4×D3C22×D312yes—
474C2×C4×D3C22×D314yes—
475C2×C4×D3C22×D314yes—
476C2×C4×D3C22×D311yescharacteristic
477C2×Dic6—31no—
478C2×Dic6—31no—
479C2×Dic6—34no—
480C2×Dic6—34no—
481C2×Dic6—32no—
482C2×Dic6—34no—
483C2×Dic6—32no—
484C2×Dic6—34no—
485C2×Dic6—61no—
486C2×Dic6—64no—
487C2×Dic6—68no—
488C2×Dic6—616no—
489C2×Dic6C22×D312yes—
490C2×Dic6C22×D314yes—
491C3×C4⋊C4—22no—
492C3×C4⋊C4—22no—
493C3×C4⋊C4—31no—
494C3×C4⋊C4—31no—
495C3×C4⋊C4—34no—
496C3×C4⋊C4—34no—
497C3×C4⋊C4—32no—
498C3×C4⋊C4—34no—
499C3×C4⋊C4—32no—
500C3×C4⋊C4C22×D312yes—
501C3×C4⋊C4C22×D312yes—
502C3×C4⋊C4C22×D312yes—
503C3×C4⋊C4C22×D312yes—
504C3×C22⋊C4—32no—
505C3×C22⋊C4—32no—
506C3×C22⋊C4—34no—
507C3×C42—21no—
508C3×C42—31no—
509C3×C42—31no—
510C3×C42—31no—
511C3×C42C22×D311yescharacteristic
512C3×C42C22×D311yescharacteristic
513#217—32no—
514#217—32no—
515#217—34no—
516#217—32no—
517(C2×D3)⋊C4—32no—
518(C2×D3)⋊C4—32no—
519(C2×D3)⋊C4—32no—
520(C2×D3)⋊C4—34no—
521(C2×D3)⋊C4—32no—
522(C2×D3)⋊C4—32no—
523(C2×D3)⋊C4—34no—
524(C2×D3)⋊C4—34no—
525(C2×D3)⋊C4—32no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—32no—
528(C2×D3)⋊C4—34no—
529(C2×D3)⋊C4—62no—
530(C2×D3)⋊C4—64no—
531(C2×D3)⋊C4C22×D312yes—
532(C2×D3)⋊C4C22×D312yes—
533(C2×D3)⋊C4C22×D314yes—
534C4⋊Dic3—31no—
535C4⋊Dic3—31no—
536C4⋊Dic3—31no—
537C4⋊Dic3—31no—
538C4⋊Dic3—32no—
539C4⋊Dic3—34no—
540C4⋊Dic3—61no—
541C4⋊Dic3—61no—
542C4⋊Dic3C22×D311yescharacteristic
543C4⋊Dic3C22×D311yescharacteristic
544C4⋊Dic3C22×D312yes—
545C4⋊Dic3C22×D312yes—
546Dic3⋊C4—32no—
547Dic3⋊C4—32no—
548Dic3⋊C4—34no—
549Dic3⋊C4—34no—
550Dic3⋊C4—32no—
551Dic3⋊C4—32no—
552Dic3⋊C4—34no—
553Dic3⋊C4—32no—
554Dic3⋊C4—34no—
555Dic3⋊C4—34no—
556Dic3⋊C4—62no—
557Dic3⋊C4—64no—
558Dic3⋊C4C22×D314yes—
559Dic3⋊C4C22×D314yes—
560Dic3⋊C4C22×D314yes—
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×C32C2511yescharacteristic
572C2×C3⋊D3—22no—
573C2×C3⋊D3—22no—
574C2×C3⋊D3—22no—
575C2×C3×D3—22no—
576C2×C3×D3—21no—
577C2×C3×D3—21no—
578C2×C3×D3—22no—
579C2×C3×D3—22no—
580C2×C3×D3—22no—
581C2×C3×D3—22no—
582C2×C3×D3C22×D414yes—
583C2×C3×D3C22×D412yes—
584C32×C4—24no—
585C32×C4—21no—
586C32×C4C22×D412yes—
587C32×C42−1+412yescomplemented
588C3⋊Dic3—22no—
589C3⋊Dic3—22no—
590C3⋊Dic3C22×D414yes—
591C3×Dic3—24no—
592C3×Dic3—22no—
593C3×Dic3—21no—
594C3×Dic3—22no—
595C3×Dic3C22×D412yes—
596C3×Dic32−1+412yescomplemented
5972−1+4—1816no—
598C2×#41—32no—
599C2×#41—92no—
600C2×#41—94no—
601C2×#41—91no—
602C2×#41—94no—
603C2×#41—94no—
604C2×#41—92no—
605C22×Q8—32no—
606C22×Q8—94no—
607C22×Q8—92no—
608C22×Q8—92no—
609C4⋊Q8—32no—
610C4⋊Q8—32no—
611C4⋊Q8—32no—
612C4⋊Q8—31no—
613C4⋊Q8—91no—
614C4⋊Q8—94no—
615C4⋊Q8—92no—
616C4⋊Q8—94no—
617C4⋊Q8—92no—
618C4⋊Q8D3211yescharacteristic
619#127—91no—
620#124—92no—
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—32no—
637#121—92no—
638#121—91no—
639#121—92no—
640#121—94no—
641#121—91no—
642C4×Q8—91no—
643C4×Q8—91no—
644C4×D4—31no—
645C4×D4—31no—
646C4×D4—92no—
647C4×D4—91no—
648C4×D4—94no—
649C4×D4—92no—
650C4×D4—92no—
651C4×D4—92no—
652C4×D4—92no—
653C4×D4—91no—
654#117—92no—
655#117—91no—
656C2×C4⋊C4—32no—
657C2×C4⋊C4—32no—
658C2×C4⋊C4—32no—
659C2×C4⋊C4—94no—
660C2×C4⋊C4—92no—
661C2×C42—31no—
662C2×C42—92no—
663C23×C3—31no—
664C23×C3—32no—
665C23×C3—32no—
666C22×D3—32no—
667C22×D3—32no—
668C22×D3—62no—
669C22×D3C23×D312yes—
670C22×D3C23×D311yescharacteristic
671C22×D3C23×D312yes—
672C3×Q8—24no—
673C3×Q8—24no—
674C3×Q8—44no—
675C3×Q8—68no—
676C3×Q8—64no—
677C3×D4—34no—
678C3×D4—68no—
679C3×D4—62no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—24no—
684C2×C3×C4—31no—
685C2×C3×C4—31no—
686C2×C3×C4—34no—
687C2×C3×C4—32no—
688C2×C3×C4—32no—
689C2×C3×C4—31no—
690C2×C3×C4—34no—
691C2×C3×C4—62no—
692C2×C3×C4—68no—
693C2×C3×C4—68no—
694C2×C3×C4—64no—
695C2×C3×C4—64no—
696C2×C3×C4—62no—
697C2×C3×C4C23×D311yescharacteristic
698C2×C3×C4C23×D311yescharacteristic
699C2×C3×C4C23×D314yes—
700C2×C3×C4C23×D314yes—
701C2×C3×C4C23×D311yescharacteristic
702C2×C3×C4C23×D311yescharacteristic
703C2×C3×C4C23×D311yescharacteristic
704C2×C3×C4C23×D311yescharacteristic
705#67—38no—
706#67—38no—
707#67—64no—
708#67—68no—
709#67—64no—
710#67—64no—
711#67—64no—
712#67—64no—
713C2×Dic3—32no—
714C2×Dic3—32no—
715C2×Dic3—38no—
716C2×Dic3—32no—
717C2×Dic3—32no—
718C2×Dic3—32no—
719C2×Dic3—32no—
720C2×Dic3—62no—
721C2×Dic3—62no—
722C2×Dic3—62no—
723C2×Dic3—68no—
724C2×Dic3—68no—
725C2×Dic3—64no—
726C2×Dic3C23×D312yes—
727C2×Dic3C23×D311yescharacteristic
728C2×Dic3C23×D312yes—
729C2×Dic3C23×D314yes—
730C2×Dic3C23×D311yescharacteristic
731C2×Dic3C23×D311yescharacteristic
732D12—28no—
733D12—22no—
734D12—64no—
735D12—64no—
736D12—64no—
737D12—64no—
738D12—68no—
739D12—62no—
740D12—62no—
741D12D3×D414yes—
742C4×D3—28no—
743C4×D3—28no—
744C4×D3—24no—
745C4×D3—22no—
746C4×D3—24no—
747C4×D3—22no—
748C4×D3—38no—
749C4×D3—68no—
750C4×D3—68no—
751C4×D3—68no—
752C4×D3—64no—
753C4×D3—68no—
754C4×D3—64no—
755C4×D3—64no—
756C4×D3—128no—
757C4×D3—124no—
758C4×D3D3×D414yes—
759Dic6—24no—
760Dic6—28no—
761Dic6—34no—
762Dic6—34no—
763Dic6—64no—
764Dic6—68no—
765Dic6—68no—
766Dic6—64no—
767Dic6—68no—
768Dic6—68no—
769Dic6—64no—
770Dic6—128no—
771C2×C32C23×D411yescharacteristic
772C2×C32C2×2−1+411yescharacteristic
773C2×C32C2×2−1+411yescharacteristic
774C3⋊D3—42no—
775C3×D3—24no—
776C3×D3—22no—
777C3×D3—42no—
778#41—68no—
779#41—98no—
780#41—188no—
781#41—1816no—
782#41—1816no—
783#41—1816no—
784#41—188no—
785C2×Q8—32no—
786C2×Q8—34no—
787C2×Q8—68no—
788C2×Q8—94no—
789C2×Q8—92no—
790C2×Q8—91no—
791C2×Q8—94no—
792C2×Q8—1816no—
793C2×Q8—188no—
794C2×Q8—188no—
795C2×Q8C2×D3212yes—
796C2×D4—31no—
797C2×D4—31no—
798C2×D4—34no—
799C2×D4—92no—
800C2×D4—92no—
801C2×D4—94no—
802C2×D4—92no—
803C2×D4—92no—
804C2×D4—92no—
805C2×D4—91no—
806C22×C4—31no—
807C22×C4—31no—
808C22×C4—31no—
809C22×C4—32no—
810C22×C4—34no—
811C22×C4—34no—
812C22×C4—32no—
813C22×C4—92no—
814C22×C4—92no—
815C22×C4—94no—
816C22×C4—94no—
817C22×C4—94no—
818C22×C4—92no—
819C4⋊C4—31no—
820C4⋊C4—34no—
821C4⋊C4—32no—
822C4⋊C4—34no—
823C4⋊C4—34no—
824C4⋊C4—32no—
825C4⋊C4—31no—
826C4⋊C4—92no—
827C4⋊C4—94no—
828C4⋊C4—94no—
829C4⋊C4—92no—
830C4⋊C4—91no—
831C4⋊C4—94no—
832C4⋊C4—92no—
833C4⋊C4—91no—
834C4⋊C4C2×D3212yes—
835C4⋊C4C2×D3212yes—
836C22⋊C4—32no—
837C22⋊C4—32no—
838C22⋊C4—34no—
839C22⋊C4—92no—
840C22⋊C4—94no—
841C22⋊C4—92no—
842C22⋊C4—92no—
843C22⋊C4—92no—
844C22⋊C4—94no—
845C22⋊C4—94no—
846C22⋊C4—92no—
847C42—31no—
848C42—31no—
849C42—31no—
850C42—92no—
851C42—92no—
852C42—92no—
853C42C2×D3211yescharacteristic
854C22×C3—21no—
855C22×C3—34no—
856C22×C3—32no—
857C22×C3—62no—
858C22×C3—62no—
859C22×C3—61no—
860C22×C3—61no—
861C22×C3—62no—
862C22×C3—62no—
863C22×C3—62no—
864C22×C3C24×D311yescharacteristic
865C22×C3C24×D311yescharacteristic
866C2×D3—21no—
867C2×D3—21no—
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—64no—
874C2×D3—62no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—122no—
881C2×D3—122no—
882C2×D3C2×D3×D412yes—
883C2×D3C2×D3×D414yes—
884C3×C4—24no—
885C3×C4—24no—
886C3×C4—21no—
887C3×C4—21no—
888C3×C4—22no—
889C3×C4—22no—
890C3×C4—32no—
891C3×C4—32no—
892C3×C4—44no—
893C3×C4—41no—
894C3×C4—62no—
895C3×C4—64no—
896C3×C4—62no—
897C3×C4—61no—
898C3×C4C2×D3×D412yes—
899C3×C4C2×D3×D412yes—
900C3×C4#100712yescomplemented
901C3×C4#101012yescomplemented
902Dic3—24no—
903Dic3—22no—
904Dic3—21no—
905Dic3—22no—
906Dic3—34no—
907Dic3—34no—
908Dic3—64no—
909Dic3—62no—
910Dic3—62no—
911Dic3—62no—
912Dic3—62no—
913Dic3—122no—
914Dic3—122no—
915Dic3C2×D3×D412yes—
916Dic3#100712yescomplemented
917C32#349911yescharacteristic, complemented, Sylow
918C23—32no—
919C23—31no—
920C23—32no—
921C23—92no—
922Q8—24no—
923Q8—68no—
924Q8—64no—
925Q8—94no—
926Q8—188no—
927Q8—184no—
928Q8—188no—
929D4—34no—
930D4—68no—
931D4—62no—
932D4—98no—
933D4—184no—
934D4—184no—
935D4—184no—
936D4—188no—
937D4—184no—
938D4—182no—
939C2×C4—31no—
940C2×C4—31no—
941C2×C4—34no—
942C2×C4—31no—
943C2×C4—32no—
944C2×C4—32no—
945C2×C4—34no—
946C2×C4—62no—
947C2×C4—68no—
948C2×C4—68no—
949C2×C4—64no—
950C2×C4—62no—
951C2×C4—64no—
952C2×C4—98no—
953C2×C4—92no—
954C2×C4—92no—
955C2×C4—92no—
956C2×C4—188no—
957C2×C4—184no—
958C2×C4—188no—
959C2×C4—188no—
960C2×C4—184no—
961C2×C4C22×D3211yescharacteristic
962C2×C4C22×D3214yes—
963C2×C4C22×D3211yescharacteristic
964C2×C4C22×D3211yescharacteristic
965C2×C3—21no—
966C2×C3—21no—
967C2×C3—21no—
968C2×C3—62no—
969C2×C3—64no—
970C2×C3—122no—
971C2×C3C22×D3×D411yescharacteristic
972C2×C3C22×D3×D411yescharacteristic
973C2×C3C2×#100711yescharacteristic
974C2×C3C2×#100711yescharacteristic
975C2×C3C2×#101011yescharacteristic
976C2×C3D3×2−1+411yescharacteristic
977D3—24no—
978D3—22no—
979D3—42no—
980D3—124no—
981D3—122no—
982D3—122no—
983C22—32no—
984C22—34no—
985C22—62no—
986C22—61no—
987C22—61no—
988C22—62no—
989C22—62no—
990C22—62no—
991C22—62no—
992C22—182no—
993C22—182no—
994C22—182no—
995C22C23×D3211yescharacteristic
996C4—24no—
997C4—21no—
998C4—32no—
999C4—32no—
1000C4—62no—
1001C4—64no—
1002C4—61no—
1003C4—62no—
1004C4—94no—
1005C4—182no—
1006C4—182no—
1007C4D32×D412yes—
1008C4#6431512yescomplemented
1009C3—21no—
1010C3#8621411yescharacteristic, complemented
1011C3#8667911yescharacteristic, complemented
1012C2—62no—
1013C2—64no—
1014C2—122no—
1015C2—362no—
1016C2C2×D32×D411yescharacteristic
1017C2C2×#6431511yescharacteristic
1018C2D3×#100711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
hypercenterC4⋊Q8D32
hypocenterC32#3499
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#64315C2semidirect
2. #10596198C2semidirect
3. C3×#5726C2semidirect
4. C3×D3×C4⋊Q8C2semidirect
5. #10595397C2semidirect
6. #10595361C2semidirect
7. #10595358C2semidirect
8. #10594513C2semidirect
9. #10594512C2semidirect
10. #10594370C2semidirect
11. #10594369C2semidirect
12. #10594366C2semidirect
13. D3×#888C2semidirect
14. #10593968C2semidirect
15. #10593904C2semidirect
16. #10593896C2semidirect
17. C4×#3795C2semidirect
99. #5726D3semidirect
103. D3×C4⋊Q8D3semidirect
159. #3795D4semidirect
587. C32×C42−1+4semidirect
596. C3×Dic32−1+4semidirect
900. C3×C4#1007semidirect
901. C3×C4#1010semidirect
916. Dic3#1007semidirect
917. C32#3499semidirect
1008. C4#64315semidirect
1010. C3#86214semidirect
1011. C3#86679semidirect

Maximal subgroups

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

subgroupindex
C2×#643152
#105961982
C3×#57262
C3×D3×C4⋊Q82
#105953972
#105953612
#105953582
#105945132
#105945122
#105943702
#105943692
#105943662
D3×#8882
#105939682
#105939042
#105938962
C4×#37952
#866793
#862143