Finite Group Databasebeta

← #11906021

Subgroups — #11906021

Order 1152.

3098 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64316C212yesmaximal, complemented
2#10596197C211yesmaximal, characteristic, complemented
3C3×#5727C211yesmaximal, characteristic, complemented
4C3×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
5#10595403C212yesmaximal, complemented
6#10595397C212yesmaximal, complemented
7#10595341C212yesmaximal, complemented
8#10594518C212yesmaximal, complemented
9#10594517C212yesmaximal, complemented
10#10594516C214yesmaximal, complemented
11#10594515C212yesmaximal, complemented
12#10594374C212yesmaximal, complemented
13#10594328C214yesmaximal, complemented
14#10593968C211yesmaximal, characteristic, complemented
15C4×#3799C211yesmaximal, characteristic, complemented
16#10593903C211yesmaximal, characteristic, complemented
17#10593869C211yesmaximal, characteristic, complemented
18#86746—31nomaximal
19#86214—31nomaximal
20C2×#3832C2212yes—
21C2×C3×D3×Q8C2212yes—
22C2×C3×D3×Q8C2212yes—
23#64316—216no—
24C2×#3799C2212yes—
25C2×#3799C2214yes—
26C2×#3799C2214yes—
27C2×#3799C2211yescharacteristic
28C2×#3798C2212yes—
29C2×#3798C2214yes—
30C2×#3797C2214yes—
31C2×#3797C2212yes—
32C32×C4⋊Q8C2211yescharacteristic
33#64155C2212yes—
34#64104C2212yes—
35#64103C2214yes—
36C4⋊C4×C3⋊D3C2212yes—
37C4×C4⋊(C3⋊D3)C2211yescharacteristic
38C4×C4⋊(C3⋊D3)C2211yescharacteristic
39C3×#946C2212yes—
40C3×#944C2212yes—
41C3×#896C2214yes—
42C3×#893C2212yes—
43C3×D3×C4⋊C4C2212yes—
44C3×D3×C4⋊C4C2212yes—
45C3×#888C2212yes—
46C3×#888C2212yes—
47C3×#888C2212yes—
48C3×C4×D12C2211yescharacteristic
49C3×C42×D3C2211yescharacteristic
50C3×#869C2211yescharacteristic
51C3×C4×Dic6C2211yescharacteristic
52#63918C2211yescharacteristic
53#63918C2212yes—
54#63916C2212yes—
55#63911C2211yescharacteristic
56#63910C2214yes—
57#63909C2211yescharacteristic
58#63908C2211yescharacteristic
59#63907C2214yes—
60#63906C2212yes—
61#63905C2214yes—
62#63904C2214yes—
63#63904C2212yes—
64C4×#626C2212yes—
65C4×#626C2212yes—
66#63900C2212yes—
67#63897C2214yes—
68#63895C2214yes—
69#63894C2211yescharacteristic
70#63894C2212yes—
71#63888C2214yes—
72#63883C2214yes—
73C4×#624C2212yes—
74#63871C2212yes—
75#63856C2212yes—
76#63854C2214yes—
77#63853C2214yes—
78#63852C2212yes—
79#63851C2214yes—
80#63850C2214yes—
81Dic3×Dic6C2211yescharacteristic
82#63841C2211yescharacteristic
83#63839C2214yes—
84#63839C2214yes—
85#63836C2212yes—
86C2×#1007—32no—
87C2×#1007—32no—
88C3×D4×Q8—31no—
89C2×C3×C4⋊Q8—31no—
90#5816—32no—
91Q8×#67—32no—
92#5727—32no—
93#5727—31no—
94#5727D311yescharacteristic, complemented
95#5726—31no—
96#5726—31no—
97#5726—32no—
98#5726—32no—
99#5726—31no—
100#5726—61no—
101#5725—32no—
102#5724—34no—
103D3×C4⋊Q8—32no—
104D3×C4⋊Q8—32no—
105D3×C4⋊Q8D311yescharacteristic, complemented
106#5631—32no—
107#5631—34no—
108#5628—32no—
109#5628—34no—
110Q8×D12—31no—
111C4×#239—31no—
112#5551—32no—
113#5551—31no—
114#5548—32no—
115#5548—31no—
116#5507—34no—
117#5507—32no—
118#5507—32no—
119#5477—31no—
120C4×#235—31no—
121C2×C32×Q8C2312yes—
122#3832—28no—
123C2×C4⋊(C3⋊D3)C2314yes—
124C2×C4⋊(C3⋊D3)C2311yescharacteristic
125C2×C4⋊(C3⋊D3)C2311yescharacteristic
126C2×C4×C3⋊D3C2312yes—
127C2×C4×C3⋊D3C2314yes—
128C2×C4×C3⋊D3C2312yes—
129C3×D3×Q8—28no—
130C3×D3×Q8—28no—
131C2×C3×D12C2311yescharacteristic
132C2×C3×C4×D3C2314yes—
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×C4×D3C2314yes—
136C2×C3×C4×D3C2312yes—
137C2×C3×C4×D3C2311yescharacteristic
138C2×C3×Dic6C2314yes—
139C2×C3×Dic6C2314yes—
140C2×C3×Dic6C2312yes—
141C2×C3×Dic6C2311yescharacteristic
142C2×#627C2312yes—
143C2×#627C2314yes—
144C2×#626C2312yes—
145C2×#626C2312yes—
146C2×#626C2314yes—
147C2×#626C2312yes—
148C2×#626C2312yes—
149C2×#625C2312yes—
150C2×#624C2314yes—
151C2×#624C2314yes—
152C2×#624C2312yes—
153C2×#624C2312yes—
154#3799—28no—
155#3799—216no—
156#3799—216no—
157#3799D418yescomplemented
158#3798—28no—
159#3798—216no—
160#3797—28no—
161#3797—216no—
162C32×C4⋊C4C2312yes—
163C32×C4⋊C4C2312yes—
164C32×C42C2311yescharacteristic
165#3752C2312yes—
166#3752C2312yes—
167#3752C2314yes—
168C4⋊(C3⋊Dic3)C2311yescharacteristic
169C4⋊(C3⋊Dic3)C2311yescharacteristic
170#3750C2314yes—
171C3×(C2×D3)⋊C4C2314yes—
172C3×(C2×D3)⋊C4C2312yes—
173C3×C4⋊Dic3C2311yescharacteristic
174C3×C4⋊Dic3C2312yes—
175C3×C4⋊Dic3C2312yes—
176C3×C4⋊Dic3C2311yescharacteristic
177C3×Dic3⋊C4C2314yes—
178C3×Dic3⋊C4C2314yes—
179C3×Dic3⋊C4C2314yes—
180C3×Dic3⋊C4C2312yes—
181C3×C4×Dic3C2311yescharacteristic
182C3×C4×Dic3C2311yescharacteristic
183C3×C4×Dic3C2312yes—
184C3×C4×Dic3C2311yescharacteristic
185#3724C2314yes—
186Dic3⋊Dic3C2312yes—
187Dic3⋊Dic3C2312yes—
188Dic3⋊Dic3C2314yes—
189#3722C2312yes—
190#3722C2314yes—
191#3722C2312yes—
192(C2×D3)⋊Dic3C2312yes—
193(C2×D3)⋊Dic3C2312yes—
194(C2×D3)⋊Dic3C2314yes—
195Dic32C2312yes—
196Dic32C2312yes—
197#3499—91noSylow
198C22×C3×Q8—32no—
199C22×C3×Q8—32no—
200#1007—616no—
201#1007—616no—
202C2×#239—32no—
203C2×#239—32no—
204C2×#239—31no—
205C2×#239—34no—
206C2×#239—32no—
207C2×#239—34no—
208C2×#239—62no—
209C2×D3×Q8—34no—
210C2×D3×Q8—34no—
211C2×D3×Q8—32no—
212C2×D3×Q8—32no—
213C2×D3×Q8C2×D312yes—
214C2×D3×Q8C2×D312yes—
215C2×#235—32no—
216C2×#235—34no—
217C2×#235—32no—
218C2×#235—34no—
219C2×#235—31no—
220C2×#235—34no—
221C2×#235—34no—
222C2×#235—32no—
223C3×C4⋊Q8—21no—
224C3×C4⋊Q8—32no—
225C3×C4⋊Q8—32no—
226C3×C4⋊Q8—32no—
227C3×C4⋊Q8—32no—
228C3×C4⋊Q8—31no—
229C3×C4⋊Q8C2×D311yescharacteristic
230C3×C4⋊Q8C2×D311yescharacteristic
231C3×C22⋊Q8—32no—
232C3×C22⋊Q8—34no—
233C3×C4×Q8—31no—
234C3×C4×D4—32no—
235C3×C4×D4—31no—
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—34no—
245#946—62no—
246#946C2×D312yes—
247Q8×Dic3—31no—
248#944—34no—
249#944—34no—
250#944C2×D312yes—
251#940—31no—
252#938—31no—
253#938—32no—
254#930—31no—
255#930—32no—
256#930—31no—
257#929—34no—
258#929—34no—
259C4×#67—32no—
260C4×#67—34no—
261C4×#67—32no—
262C4×#67—32no—
263#926—31no—
264#924—32no—
265#924—34no—
266#897—32no—
267#897—34no—
268#896—34no—
269#896—34no—
270#896—34no—
271#896C2×D314yes—
272#895—32no—
273#895—31no—
274#895—32no—
275#895—32no—
276#895—34no—
277#895—62no—
278#894—34no—
279#894—34no—
280#894—34no—
281#894—34no—
282#894—34no—
283#894—34no—
284#894—34no—
285#894—64no—
286#893—34no—
287#893—32no—
288#893—32no—
289#893—31no—
290#893C2×D312yes—
291#892—31no—
292#892—32no—
293D3×C4⋊C4—32no—
294D3×C4⋊C4—32no—
295D3×C4⋊C4—32no—
296D3×C4⋊C4—32no—
297D3×C4⋊C4—34no—
298D3×C4⋊C4—34no—
299D3×C4⋊C4—62no—
300D3×C4⋊C4C2×D312yes—
301D3×C4⋊C4C2×D312yes—
302#888—34no—
303#888—34no—
304#888—31no—
305#888—32no—
306#888C2×D312yes—
307#888C2×D312yes—
308#888C2×D312yes—
309#885—34no—
310#885—32no—
311#884—32no—
312#884—34no—
313#883—34no—
314#883—34no—
315#883—34no—
316#875—32no—
317#874—31no—
318C4×D12—32no—
319C4×D12—32no—
320C4×D12—31no—
321C4×D12—31no—
322C4×D12—31no—
323C4×D12—31no—
324C4×D12—31no—
325C4×D12—32no—
326C4×D12—61no—
327C4×D12—61no—
328C4×D12C2×D311yescharacteristic
329#872—32no—
330C42×D3—32no—
331C42×D3—32no—
332C42×D3C2×D311yescharacteristic
333#869—31no—
334#869—32no—
335#869C2×D311yescharacteristic
336C4×Dic6—31no—
337C4×Dic6C2×D311yescharacteristic
338C22×C3⋊D3C2412yes—
339C22×C3⋊D3C2412yes—
340C22×C3×D3C2412yes—
341C22×C3×D3C2411yescharacteristic
342C32×Q8—24no—
343C2×C32×C4C2411yescharacteristic
344C2×C32×C4C2414yes—
345C2×C32×C4C2411yescharacteristic
346C2×C32×C4C2411yescharacteristic
347C2×C3⋊Dic3C2412yes—
348C2×C3⋊Dic3C2412yes—
349C4⋊(C3⋊D3)—28no—
350C4⋊(C3⋊D3)—22no—
351C4⋊(C3⋊D3)C2×D414yes—
352C4×C3⋊D3—28no—
353C4×C3⋊D3—24no—
354C4×C3⋊D3—24no—
355C2×C3×Dic3C2412yes—
356C2×C3×Dic3C2411yescharacteristic
357C2×C3×Dic3C2414yes—
358C2×C3×Dic3C2412yes—
359C2×C3×Dic3C2411yescharacteristic
360C2×C3×Dic3C2412yes—
361C2×C3×Dic3C2411yescharacteristic
362C3×D12—22no—
363C3×C4×D3—28no—
364C3×C4×D3—24no—
365C3×C4×D3—22no—
366C3×C4×D3—28no—
367C3×C4×D3—22no—
368C3×C4×D3C2×D414yes—
369C3×Dic6—24no—
370C3×Dic6—28no—
371C3×Dic6—28no—
372C3×Dic6C2×D414yes—
373#627—28no—
374#627—24no—
375#626—28no—
376#626—24no—
377#626—24no—
378#626—24no—
379#626C2×D418yes—
380#625—24no—
381#624—28no—
382#624—28no—
383#624—24no—
384#624C2×D418yes—
385C2×2−1+4—92no—
386D4×Q8—31no—
387D4×Q8—91no—
388D4×Q8—92no—
389#547—92no—
390#547—94no—
391#547—92no—
392#547—91no—
393#547—92no—
394#547—91no—
395#536—94no—
396#536—92no—
397#532—91no—
398#532—92no—
399C2×C4⋊Q8—31no—
400C2×C4⋊Q8—92no—
401C4×#41—91no—
402C2×C3×Q8—22no—
403C2×C3×Q8—31no—
404C2×C3×Q8—34no—
405C2×C3×Q8—34no—
406C2×C3×Q8—32no—
407C2×C3×Q8—68no—
408C2×C3×Q8—68no—
409C2×C3×Q8C22×D312yes—
410C2×C3×Q8C22×D312yes—
411C2×C3×D4—31no—
412C22×C3×C4—31no—
413C22×C3×C4—34no—
414C22×C3×C4—32no—
415C22×C3×C4—31no—
416C22×C3×C4—31no—
417C22×C3×C4—34no—
418C2×#67—32no—
419C2×#67—32no—
420C2×#67—32no—
421C2×#67—34no—
422C2×#67—32no—
423C2×#67—32no—
424C2×#67—32no—
425#239—38no—
426#239—616no—
427#239—616no—
428#239—68no—
429#239—68no—
430#239—68no—
431#239—128no—
432D3×Q8—28no—
433D3×Q8—28no—
434D3×Q8—616no—
435D3×Q8—616no—
436D3×Q8—68no—
437D3×Q8—68no—
438#235—38no—
439#235—616no—
440#235—68no—
441#235—616no—
442#235—616no—
443#235—616no—
444#235—68no—
445#235—68no—
446C2×D12—32no—
447C2×D12—31no—
448C2×D12—31no—
449C2×D12—32no—
450C2×D12—32no—
451C2×D12—32no—
452C2×D12—34no—
453C2×D12—31no—
454C2×D12—31no—
455C2×D12—34no—
456C2×D12—34no—
457C2×D12—61no—
458C2×D12—61no—
459C2×D12—64no—
460C2×D12C22×D311yescharacteristic
461C2×C4×D3—32no—
462C2×C4×D3—32no—
463C2×C4×D3—32no—
464C2×C4×D3—32no—
465C2×C4×D3—32no—
466C2×C4×D3—32no—
467C2×C4×D3—34no—
468C2×C4×D3—34no—
469C2×C4×D3—32no—
470C2×C4×D3—32no—
471C2×C4×D3—34no—
472C2×C4×D3—34no—
473C2×C4×D3—34no—
474C2×C4×D3—34no—
475C2×C4×D3—62no—
476C2×C4×D3—62no—
477C2×C4×D3—64no—
478C2×C4×D3C22×D311yescharacteristic
479C2×C4×D3C22×D311yescharacteristic
480C2×C4×D3C22×D312yes—
481C2×C4×D3C22×D314yes—
482C2×C4×D3C22×D314yes—
483C2×C4×D3C22×D311yescharacteristic
484C2×Dic6—32no—
485C2×Dic6—34no—
486C2×Dic6—32no—
487C2×Dic6—34no—
488C2×Dic6C22×D312yes—
489C2×Dic6C22×D314yes—
490C2×Dic6C22×D314yes—
491C2×Dic6C22×D311yescharacteristic
492C3×C4⋊C4—22no—
493C3×C4⋊C4—22no—
494C3×C4⋊C4—31no—
495C3×C4⋊C4—34no—
496C3×C4⋊C4—32no—
497C3×C4⋊C4—34no—
498C3×C4⋊C4—32no—
499C3×C4⋊C4—31no—
500C3×C4⋊C4—34no—
501C3×C4⋊C4—32no—
502C3×C4⋊C4C22×D312yes—
503C3×C4⋊C4C22×D312yes—
504C3×C4⋊C4C22×D312yes—
505C3×C4⋊C4C22×D312yes—
506C3×C22⋊C4—34no—
507C3×C22⋊C4—32no—
508C3×C42—21no—
509C3×C42—31no—
510C3×C42—31no—
511C3×C42—32no—
512C3×C42—31no—
513C3×C42C22×D311yescharacteristic
514C3×C42C22×D311yescharacteristic
515#217—34no—
516#217—32no—
517#217—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—32no—
524(C2×D3)⋊C4—32no—
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—32no—
528(C2×D3)⋊C4—32no—
529(C2×D3)⋊C4—32no—
530(C2×D3)⋊C4—34no—
531(C2×D3)⋊C4—32no—
532(C2×D3)⋊C4—34no—
533(C2×D3)⋊C4—62no—
534(C2×D3)⋊C4—62no—
535(C2×D3)⋊C4—64no—
536(C2×D3)⋊C4C22×D312yes—
537(C2×D3)⋊C4C22×D314yes—
538C4⋊Dic3—31no—
539C4⋊Dic3—31no—
540C4⋊Dic3—31no—
541C4⋊Dic3—31no—
542C4⋊Dic3—32no—
543C4⋊Dic3—34no—
544C4⋊Dic3—32no—
545C4⋊Dic3—61no—
546C4⋊Dic3—61no—
547C4⋊Dic3C22×D311yescharacteristic
548C4⋊Dic3C22×D312yes—
549C4⋊Dic3C22×D311yescharacteristic
550C4⋊Dic3C22×D312yes—
551Dic3⋊C4—34no—
552Dic3⋊C4—34no—
553Dic3⋊C4—32no—
554Dic3⋊C4—34no—
555Dic3⋊C4—32no—
556Dic3⋊C4—34no—
557Dic3⋊C4—34no—
558Dic3⋊C4—64no—
559Dic3⋊C4C22×D312yes—
560Dic3⋊C4C22×D314yes—
561Dic3⋊C4C22×D314yes—
562Dic3⋊C4C22×D314yes—
563C4×Dic3—32no—
564C4×Dic3—32no—
565C4×Dic3—32no—
566C4×Dic3—32no—
567C4×Dic3C22×D312yes—
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—22no—
577C2×C3⋊D3C22×D414yes—
578C2×C3×D3—21no—
579C2×C3×D3—21no—
580C2×C3×D3—22no—
581C2×C3×D3—22no—
582C2×C3×D3—22no—
583C2×C3×D3C22×D412yes—
584C32×C4—24no—
585C32×C4—21no—
586C32×C4C22×D412yes—
587C32×C42−1+412yescomplemented
588C3⋊Dic3—22no—
589C3⋊Dic3—22no—
590C3×Dic3—22no—
591C3×Dic3—24no—
592C3×Dic3—22no—
593C3×Dic3—21no—
594C3×Dic3C22×D414yes—
595C3×Dic3C22×D412yes—
596C3×Dic32−1+412yescomplemented
5972−1+4—1816no—
598C2×#41—92no—
599C2×#41—94no—
600C2×#41—91no—
601C2×#41—94no—
602C2×#41—94no—
603C2×#41—92no—
604C2×#41—92no—
605C22×Q8—32no—
606C22×Q8—32no—
607C22×Q8—94no—
608C22×Q8—92no—
609C4⋊Q8—32no—
610C4⋊Q8—32no—
611C4⋊Q8—32no—
612C4⋊Q8—32no—
613C4⋊Q8—31no—
614C4⋊Q8—91no—
615C4⋊Q8—92no—
616C4⋊Q8—94no—
617C4⋊Q8—94no—
618C4⋊Q8D3211yescharacteristic
619#127—91no—
620#124—92no—
621#124—94no—
622#123—94no—
623#123—94no—
624#123—94no—
625#123—94no—
626#123—94no—
627#123—94no—
628C22⋊Q8—32no—
629C22⋊Q8—34no—
630C22⋊Q8—94no—
631C22⋊Q8—94no—
632C22⋊Q8—94no—
633C22⋊Q8—92no—
634C22⋊Q8—92no—
635C22⋊Q8—92no—
636#121—94no—
637#121—92no—
638#121—91no—
639#121—92no—
640#121—91no—
641#121—92no—
642C4×Q8—31no—
643C4×Q8—91no—
644C4×D4—32no—
645C4×D4—31no—
646C4×D4—91no—
647C4×D4—92no—
648C4×D4—92no—
649C4×D4—92no—
650C4×D4—92no—
651C4×D4—94no—
652C4×D4—91no—
653C4×D4—91no—
654#117—92no—
655#117—91no—
656C2×C4⋊C4—32no—
657C2×C4⋊C4—32no—
658C2×C4⋊C4—94no—
659C2×C4⋊C4—92no—
660C2×C4⋊C4—92no—
661C2×C42—31no—
662C2×C42—92no—
663C23×C3—31no—
664C23×C3—32no—
665C22×D3—32no—
666C22×D3—32no—
667C22×D3—32no—
668C22×D3—32no—
669C22×D3—62no—
670C22×D3—62no—
671C22×D3C23×D312yes—
672C22×D3C23×D311yescharacteristic
673C3×Q8—24no—
674C3×Q8—24no—
675C3×Q8—34no—
676C3×Q8—44no—
677C3×Q8—68no—
678C3×Q8—68no—
679C3×Q8—64no—
680C3×D4—62no—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—24no—
684C2×C3×C4—21no—
685C2×C3×C4—31no—
686C2×C3×C4—31no—
687C2×C3×C4—32no—
688C2×C3×C4—34no—
689C2×C3×C4—32no—
690C2×C3×C4—32no—
691C2×C3×C4—31no—
692C2×C3×C4—34no—
693C2×C3×C4—68no—
694C2×C3×C4—62no—
695C2×C3×C4—68no—
696C2×C3×C4—64no—
697C2×C3×C4—62no—
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
705C2×C3×C4C23×D311yescharacteristic
706#67—38no—
707#67—68no—
708#67—64no—
709#67—64no—
710#67—64no—
711#67—64no—
712#67—64no—
713C2×Dic3—32no—
714C2×Dic3—32no—
715C2×Dic3—32no—
716C2×Dic3—32no—
717C2×Dic3—62no—
718C2×Dic3—62no—
719C2×Dic3C23×D312yes—
720C2×Dic3C23×D311yescharacteristic
721C2×Dic3C23×D312yes—
722C2×Dic3C23×D314yes—
723C2×Dic3C23×D311yescharacteristic
724C2×Dic3C23×D312yes—
725C2×Dic3C23×D311yescharacteristic
726D12—22no—
727D12—38no—
728D12—34no—
729D12—34no—
730D12—64no—
731D12—68no—
732D12—68no—
733D12—64no—
734D12—64no—
735D12—68no—
736D12—64no—
737D12—62no—
738D12—62no—
739D12—122no—
740D12—128no—
741C4×D3—28no—
742C4×D3—24no—
743C4×D3—22no—
744C4×D3—28no—
745C4×D3—22no—
746C4×D3—38no—
747C4×D3—38no—
748C4×D3—64no—
749C4×D3—68no—
750C4×D3—68no—
751C4×D3—68no—
752C4×D3—68no—
753C4×D3—68no—
754C4×D3—64no—
755C4×D3—64no—
756C4×D3—64no—
757C4×D3—64no—
758C4×D3—68no—
759C4×D3—64no—
760C4×D3—124no—
761C4×D3—124no—
762C4×D3—128no—
763C4×D3D3×D414yes—
764Dic6—24no—
765Dic6—28no—
766Dic6—28no—
767Dic6—64no—
768Dic6—68no—
769Dic6—64no—
770Dic6—68no—
771Dic6D3×D414yes—
772C2×C32C23×D411yescharacteristic
773C2×C32C2×2−1+411yescharacteristic
774C2×C32C2×2−1+411yescharacteristic
775C3⋊D3—24no—
776C3⋊D3—42no—
777C3×D3—22no—
778C3×D3—42no—
779#41—98no—
780#41—188no—
781#41—1816no—
782#41—1816no—
783#41—1816no—
784#41—188no—
785#41—188no—
786C2×Q8—31no—
787C2×Q8—34no—
788C2×Q8—32no—
789C2×Q8—34no—
790C2×Q8—68no—
791C2×Q8—68no—
792C2×Q8—94no—
793C2×Q8—92no—
794C2×Q8—1816no—
795C2×Q8—188no—
796C2×Q8C2×D3212yes—
797C2×D4—31no—
798C2×D4—92no—
799C2×D4—92no—
800C2×D4—92no—
801C2×D4—94no—
802C2×D4—92no—
803C2×D4—92no—
804C2×D4—91no—
805C2×D4—91no—
806C2×D4—94no—
807C22×C4—31no—
808C22×C4—31no—
809C22×C4—31no—
810C22×C4—34no—
811C22×C4—34no—
812C22×C4—32no—
813C22×C4—92no—
814C22×C4—92no—
815C22×C4—94no—
816C22×C4—94no—
817C22×C4—92no—
818C22×C4—94no—
819C22×C4—92no—
820C4⋊C4—34no—
821C4⋊C4—32no—
822C4⋊C4—34no—
823C4⋊C4—32no—
824C4⋊C4—31no—
825C4⋊C4—34no—
826C4⋊C4—32no—
827C4⋊C4—31no—
828C4⋊C4—92no—
829C4⋊C4—94no—
830C4⋊C4—94no—
831C4⋊C4—92no—
832C4⋊C4—91no—
833C4⋊C4—94no—
834C4⋊C4—91no—
835C4⋊C4C2×D3212yes—
836C4⋊C4C2×D3212yes—
837C22⋊C4—34no—
838C22⋊C4—32no—
839C22⋊C4—92no—
840C22⋊C4—92no—
841C22⋊C4—94no—
842C22⋊C4—92no—
843C22⋊C4—92no—
844C22⋊C4—94no—
845C22⋊C4—92no—
846C22⋊C4—94no—
847C22⋊C4—92no—
848C42—31no—
849C42—31no—
850C42—31no—
851C42—32no—
852C42—92no—
853C42—92no—
854C42C2×D3211yescharacteristic
855C22×C3—21no—
856C22×C3—32no—
857C22×C3—61no—
858C22×C3—61no—
859C22×C3—62no—
860C22×C3—62no—
861C22×C3—62no—
862C22×C3C24×D311yescharacteristic
863C22×C3C24×D311yescharacteristic
864C2×D3—21no—
865C2×D3—21no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—22no—
869C2×D3—34no—
870C2×D3—34no—
871C2×D3—64no—
872C2×D3—62no—
873C2×D3—62no—
874C2×D3—62no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—62no—
879C2×D3—62no—
880C2×D3—62no—
881C2×D3—62no—
882C2×D3—122no—
883C2×D3—122no—
884C2×D3—122no—
885C2×D3—122no—
886C2×D3—122no—
887C2×D3C2×D3×D412yes—
888C3×C4—24no—
889C3×C4—24no—
890C3×C4—21no—
891C3×C4—21no—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—32no—
895C3×C4—34no—
896C3×C4—32no—
897C3×C4—44no—
898C3×C4—41no—
899C3×C4—62no—
900C3×C4—64no—
901C3×C4—62no—
902C3×C4—61no—
903C3×C4C2×D3×D412yes—
904C3×C4C2×D3×D412yes—
905C3×C4#100712yescomplemented
906C3×C4#100712yescomplemented
907Dic3—24no—
908Dic3—22no—
909Dic3—21no—
910Dic3—22no—
911Dic3—62no—
912Dic3—62no—
913Dic3—62no—
914Dic3—62no—
915Dic3—122no—
916Dic3—122no—
917Dic3C2×D3×D412yes—
918Dic3C2×D3×D414yes—
919Dic3#100712yescomplemented
920C32#349911yescharacteristic, complemented, Sylow
921C23—31no—
922C23—32no—
923C23—92no—
924C23—92no—
925Q8—24no—
926Q8—34no—
927Q8—68no—
928Q8—68no—
929Q8—64no—
930Q8—184no—
931Q8—188no—
932D4—62no—
933D4—98no—
934D4—94no—
935D4—188no—
936D4—184no—
937D4—184no—
938D4—184no—
939D4—188no—
940D4—184no—
941D4—182no—
942C2×C4—31no—
943C2×C4—31no—
944C2×C4—32no—
945C2×C4—34no—
946C2×C4—31no—
947C2×C4—32no—
948C2×C4—32no—
949C2×C4—34no—
950C2×C4—68no—
951C2×C4—62no—
952C2×C4—68no—
953C2×C4—64no—
954C2×C4—62no—
955C2×C4—98no—
956C2×C4—92no—
957C2×C4—92no—
958C2×C4—188no—
959C2×C4—188no—
960C2×C4—184no—
961C2×C4—188no—
962C2×C4—184no—
963C2×C4—184no—
964C2×C4C22×D3211yescharacteristic
965C2×C4C22×D3214yes—
966C2×C4C22×D3211yescharacteristic
967C2×C4C22×D3211yescharacteristic
968C2×C3—21no—
969C2×C3—21no—
970C2×C3—21no—
971C2×C3—62no—
972C2×C3—122no—
973C2×C3C22×D3×D411yescharacteristic
974C2×C3C22×D3×D411yescharacteristic
975C2×C3C2×#100711yescharacteristic
976C2×C3C2×#100711yescharacteristic
977C2×C3C2×#100711yescharacteristic
978C2×C3D3×2−1+411yescharacteristic
979D3—22no—
980D3—42no—
981D3—64no—
982D3—64no—
983D3—124no—
984D3—122no—
985D3—122no—
986D3—242no—
987C22—32no—
988C22—61no—
989C22—61no—
990C22—62no—
991C22—62no—
992C22—62no—
993C22—94no—
994C22—182no—
995C22—182no—
996C22—182no—
997C22—182no—
998C22—182no—
999C22C23×D3211yescharacteristic
1000C4—24no—
1001C4—21no—
1002C4—32no—
1003C4—34no—
1004C4—32no—
1005C4—62no—
1006C4—64no—
1007C4—61no—
1008C4—62no—
1009C4—182no—
1010C4—182no—
1011C4D32×D412yes—
1012C4#6431612yescomplemented
1013C3—21no—
1014C3#8621411yescharacteristic, complemented
1015C3#8674611yescharacteristic, complemented
1016C2—62no—
1017C2—122no—
1018C2—184no—
1019C2—362no—
1020C2C2×D32×D411yescharacteristic
1021C2C2×#6431611yescharacteristic
1022C2D3×#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×#64316C2semidirect
2. #10596197C2semidirect
3. C3×#5727C2semidirect
4. C3×D3×C4⋊Q8C2semidirect
5. #10595403C2semidirect
6. #10595397C2semidirect
7. #10595341C2semidirect
8. #10594518C2semidirect
9. #10594517C2semidirect
10. #10594516C2semidirect
11. #10594515C2semidirect
12. #10594374C2semidirect
13. #10594328C2semidirect
14. #10593968C2semidirect
15. C4×#3799C2semidirect
16. #10593903C2semidirect
17. #10593869C2semidirect
94. #5727D3semidirect
105. D3×C4⋊Q8D3semidirect
157. #3799D4semidirect
587. C32×C42−1+4semidirect
596. C3×Dic32−1+4semidirect
905. C3×C4#1007semidirect
906. C3×C4#1007semidirect
919. Dic3#1007semidirect
920. C32#3499semidirect
1012. C4#64316semidirect
1014. C3#86214semidirect
1015. C3#86746semidirect

Maximal subgroups

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

subgroupindex
C2×#643162
#105961972
C3×#57272
C3×D3×C4⋊Q82
#105954032
#105953972
#105953412
#105945182
#105945172
#105945162
#105945152
#105943742
#105943282
#105939682
C4×#37992
#105939032
#105938692
#867463
#862143