Subgroups — #38734945

Order 24896.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#15691012	C₂	1	2	yes	maximal
2	C₂×#20261945	C₂	1	1	yes	maximal, characteristic
3	C₂×#15691012	—	2	2	no	—
4	C₂²×Dic₃₈₉	C₄	1	1	yes	characteristic
5	C₂²×Dic₃₈₉	C₂²	1	1	yes	characteristic
6	#20261945	—	2	2	no	—
7	C₂²×C₄×C₃₈₉	C₄	1	1	yes	characteristic
8	#15691012	—	4	2	no	—
9	C₂×Dic₃₈₉	—	2	1	no	—
10	C₂×Dic₃₈₉	—	2	1	no	—
11	C₂×Dic₃₈₉	—	4	1	no	—
12	C₂×Dic₃₈₉	C₈	1	2	yes	complemented
13	C₂×Dic₃₈₉	D₄	1	2	yes	—
14	C₂³×C₃₈₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₃₈₉	—	2	1	no	—
16	C₂×C₄×C₃₈₉	—	4	1	no	—
17	C₂²×C₃₈₉	—	2	1	no	—
18	C₂²×C₃₈₉	—	2	1	no	—
19	C₂²×C₃₈₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₂²×C₃₈₉	C₂×C₈	1	1	yes	characteristic
21	C₂²×C₃₈₉	M₁₆	1	1	yes	characteristic
22	C₄×C₃₈₉	—	4	1	no	—
23	Dic₃₈₉	—	2	2	no	—
24	Dic₃₈₉	—	2	2	no	—
25	C₂×C₃₈₉	—	2	1	no	—
26	C₂×C₃₈₉	—	2	1	no	—
27	C₂×C₃₈₉	C₂²⋊C₈	1	1	yes	characteristic
28	C₂×C₃₈₉	#99	1	1	yes	characteristic
29	C₂×C₃₈₉	#101	1	1	yes	characteristic
30	C₃₈₉	#324	1	1	yes	characteristic, complemented, Sylow
31	#324	—	389	1	no	maximal, Sylow
32	C₂×C₄⋊C₄	—	389	1	no	—
33	C₂²⋊C₈	—	389	2	no	—
34	C₂²×C₄	—	389	1	no	—
35	C₂²×C₄	—	389	1	no	—
36	C₂²×C₄	#13095555	1	1	yes	characteristic
37	C₂×C₈	—	778	2	no	—
38	C₄⋊C₄	—	778	2	no	—
39	C₂³	C₂×#13095555	1	1	yes	characteristic
40	C₂×C₄	—	2	1	no	—
41	C₂×C₄	—	4	1	no	—
42	C₂×C₄	—	778	1	no	—
43	C₂×C₄	—	778	1	no	—
44	C₂×C₄	—	1556	1	no	—
45	C₂×C₄	—	389	2	no	—
46	C₂×C₄	—	389	2	no	—
47	C₈	—	1556	2	no	—
48	C₂²	—	2	1	no	—
49	C₂²	—	2	1	no	—
50	C₂²	C₂²⋊#13095555	1	1	yes	characteristic
51	C₂²	D₃₈₉⋊C₈	1	1	yes	characteristic
52	C₂²	#20261976	1	1	yes	characteristic
53	C₄	—	4	1	no	—
54	C₄	—	778	2	no	—
55	C₄	—	778	2	no	—
56	C₂	—	2	1	no	—
57	C₂	—	2	1	no	—
58	C₂	#27159441	1	1	yes	characteristic
59	C₂	#27159442	1	1	yes	characteristic
60	C₂	#27159445	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#13095555
commutator	C₂²×C₃₈₉	C₂×C₈
Frattini	C₂³	C₂×#13095555
Fitting	C₂²×C₄×C₃₈₉	C₄
socle	C₂²×C₃₈₉	C₂²⋊C₄
prime radical	C₂³×C₃₈₉	C₂×C₄
cosocle	C₂²×Dic₃₈₉	C₂²
hypercenter	C₂²×C₄	#13095555
hypocenter	C₃₈₉	#324
LCS	G ▷ C₂²×C₃₈₉ ▷ C₂×C₃₈₉ ▷ C₃₈₉
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
12. C₂×Dic₃₈₉	C₈	semidirect
30. C₃₈₉	#324	semidirect

Maximal subgroups

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

subgroup	index
C₂²⋊#15691012	2
C₂×#20261945	2
#324	389