Subgroups — #42122721

Order 27712.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28357281	C₂	1	2	yes	maximal
2	#28357218	C₂	1	1	yes	maximal, characteristic
3	#20294106	—	2	2	no	—
4	C₂×Dic₈₆₆	C₂²	1	1	yes	characteristic
5	#20294076	—	2	2	no	—
6	C₄×Dic₄₃₃	C₄	1	1	yes	characteristic
7	C₂×Q₈×C₄₃₃	C₄	1	1	yes	characteristic
8	#16812365	—	4	2	no	—
9	Dic₈₆₆	—	4	1	no	—
10	C₂×Dic₄₃₃	—	2	1	no	—
11	C₂×Dic₄₃₃	D₄	1	2	yes	—
12	Q₈×C₄₃₃	—	4	1	no	—
13	C₂×C₄×C₄₃₃	—	2	1	no	—
14	C₂×C₄×C₄₃₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄₃₃	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₄₃₃	—	2	1	no	—
17	C₄×C₄₃₃	—	4	1	no	—
18	Dic₄₃₃	—	2	2	no	—
19	Dic₄₃₃	—	2	2	no	—
20	C₂×C₄₃₃	—	2	1	no	—
21	C₂×C₄₃₃	#99	1	1	yes	characteristic
22	C₄₃₃	#356	1	1	yes	characteristic, complemented, Sylow
23	#356	—	433	1	no	maximal, Sylow
24	C₄⋊Q₈	—	433	1	no	—
25	#101	—	433	2	no	—
26	C₂×Q₈	—	433	1	no	—
27	C₂×Q₈	#13181884	1	1	yes	characteristic
28	M₁₆	—	866	2	no	—
29	C₄⋊C₄	—	866	2	no	—
30	C₄²	—	433	1	no	—
31	Q₈	—	4	1	no	—
32	Q₈	—	1732	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	866	1	no	—
35	C₂×C₄	—	433	2	no	—
36	C₂×C₄	C₂×#13181884	1	1	yes	characteristic
37	C₈	—	1732	2	no	—
38	C₂²	C₂²⋊#13181884	1	1	yes	characteristic
39	C₄	—	2	1	no	—
40	C₄	—	4	1	no	—
41	C₄	—	866	2	no	—
42	C₄	—	866	2	no	—
43	C₂	—	2	1	no	—
44	C₂	#28357278	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. C₄₃₃	#356	semidirect

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