Subgroups — #36378629

Order 22592.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#15667732	C₂	1	1	yes	maximal, characteristic
2	C₄×#15667732	C₂	1	1	yes	maximal, characteristic
3	C₈×Dic₃₅₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#15667732	C₄	1	2	yes	—
5	C₂×#15667732	C₄	1	2	yes	—
6	C₂×#15667725	C₄	1	1	yes	characteristic
7	C₄×Dic₃₅₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₃₅₃	C₄	1	1	yes	characteristic
9	#15667732	—	2	2	no	—
10	#15667732	C₈	1	4	yes	complemented
11	C₂×Dic₃₅₃	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₃₅₃	C₂×C₄	1	1	yes	characteristic
13	#15667725	—	2	1	no	—
14	C₂×C₄×C₃₅₃	C₂×C₄	1	1	yes	characteristic
15	C₈×C₃₅₃	—	2	1	no	—
16	C₂²×C₃₅₃	C₄²	1	1	yes	characteristic
17	C₄×C₃₅₃	M₁₆	1	1	yes	characteristic
18	C₄×C₃₅₃	M₁₆	1	1	yes	characteristic
19	Dic₃₅₃	C₂×C₈	1	2	yes	—
20	Dic₃₅₃	M₁₆	1	2	yes	—
21	C₂×C₃₅₃	C₄×C₈	1	1	yes	characteristic
22	C₂×C₃₅₃	#97	1	1	yes	characteristic
23	C₂×C₃₅₃	#97	1	1	yes	characteristic
24	C₃₅₃	#322	1	1	yes	characteristic, complemented, Sylow
25	#322	—	353	1	no	maximal, Sylow
26	C₄×C₈	—	353	1	no	—
27	C₄×C₈	—	353	1	no	—
28	C₄×C₈	—	353	1	no	—
29	C₂×C₈	—	353	2	no	—
30	C₂×C₈	—	353	2	no	—
31	C₂×C₈	—	353	1	no	—
32	C₂×C₈	#13083443	1	1	yes	characteristic
33	C₄²	—	353	1	no	—
34	C₂×C₄	—	353	1	no	—
35	C₂×C₄	—	353	1	no	—
36	C₂×C₄	C₂×#13083443	1	1	yes	characteristic
37	C₈	—	2	1	no	—
38	C₈	—	353	4	no	—
39	C₈	—	706	2	no	—
40	C₈	—	706	1	no	—
41	C₂²	C₄×#13083443	1	1	yes	characteristic
42	C₄	—	353	2	no	—
43	C₄	—	353	2	no	—
44	C₄	#19150746	1	1	yes	characteristic
45	C₄	#19150747	1	1	yes	characteristic
46	C₂	C₈×#13083443	1	1	yes	characteristic
47	C₂	#26015046	1	1	yes	characteristic
48	C₂	#26015047	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#13083443
commutator	C₂×C₃₅₃	C₄×C₈
Fitting	C₂×C₈×C₃₅₃	C₄
socle, prime radical	C₂²×C₃₅₃	C₄²
cosocle	C₄×Dic₃₅₃	C₂²
hypercenter	C₂×C₈	#13083443
hypocenter	C₃₅₃	#322
LCS	G ▷ C₂×C₃₅₃ ▷ C₃₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
10. #15667732	C₈	semidirect
24. C₃₅₃	#322	semidirect

Maximal subgroups

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

subgroup	index
C₄×#15667732	2
C₈×Dic₃₅₃	2
#322	353