Subgroups — #38735149

Order 24896.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#15691012	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#15691012	C₂	1	2	yes	maximal
3	#27159439	C₂	1	2	yes	maximal
4	C₄×#15691012	C₂	1	1	yes	maximal, characteristic
5	#27159349	C₂	1	1	yes	maximal, characteristic
6	C₂×#15691012	C₂²	1	1	yes	characteristic
7	C₂×#15691012	C₂²	1	2	yes	—
8	C₂×#15691012	C₂²	1	1	yes	characteristic
9	C₂×Dic₇₇₈	C₄	1	1	yes	characteristic
10	#20261945	C₄	1	2	yes	—
11	C₄×Dic₃₈₉	C₂²	1	1	yes	characteristic
12	C₄×Dic₃₈₉	C₂²	1	2	yes	—
13	C₄⋊C₄×C₃₈₉	C₄	1	1	yes	characteristic
14	#15691012	—	2	1	no	—
15	#15691012	—	2	2	no	—
16	#15691012	Q₈	1	2	yes	complemented
17	Dic₇₇₈	—	2	2	no	—
18	C₂×Dic₃₈₉	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₃₈₉	C₂×C₄	1	2	yes	—
20	C₂×Dic₃₈₉	C₂³	1	1	yes	characteristic
21	C₂×C₄×C₃₈₉	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₃₈₉	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₃₈₉	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₃₈₉	—	2	2	no	—
25	C₄×C₃₈₉	M₁₆	1	2	yes	—
26	Dic₃₈₉	—	2	2	no	—
27	Dic₃₈₉	—	2	1	no	—
28	Dic₃₈₉	C₂×Q₈	1	1	yes	characteristic
29	Dic₃₈₉	#41	1	1	yes	characteristic
30	C₂×C₃₈₉	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₃₈₉	C₂×M₁₆	1	1	yes	characteristic
32	C₂×C₃₈₉	#131	1	1	yes	characteristic
33	C₃₈₉	#446	1	1	yes	characteristic, complemented, Sylow
34	#446	—	389	1	no	maximal, Sylow
35	C₄×Q₈	—	389	1	no	—
36	C₄⋊C₈	—	389	1	no	—
37	C₄⋊C₈	—	389	2	no	—
38	#97	—	389	2	no	—
39	C₄×C₈	—	389	1	no	—
40	C₂×Q₈	—	389	1	no	—
41	C₂×C₈	—	389	1	no	—
42	C₂×C₈	—	389	2	no	—
43	C₂×C₈	—	389	1	no	—
44	C₄⋊C₄	—	389	2	no	—
45	C₄⋊C₄	#13095555	1	1	yes	characteristic
46	C₄²	—	389	1	no	—
47	C₄²	—	389	2	no	—
48	Q₈	—	778	2	no	—
49	C₂×C₄	—	389	1	no	—
50	C₂×C₄	—	389	2	no	—
51	C₂×C₄	—	389	1	no	—
52	C₂×C₄	C₂×#13095555	1	2	yes	—
53	C₂×C₄	C₂×#13095555	1	1	yes	characteristic
54	C₈	—	778	1	no	—
55	C₈	—	778	2	no	—
56	C₈	—	389	2	no	—
57	C₂²	C₂²×#13095555	1	1	yes	characteristic
58	C₄	—	2	2	no	—
59	C₄	—	778	2	no	—
60	C₄	—	778	1	no	—
61	C₄	—	389	1	no	—
62	C₄	—	389	1	no	—
63	C₄	#20261976	1	2	yes	—
64	C₂	Q₈×#13095555	1	1	yes	characteristic
65	C₂	C₂×#20261976	1	1	yes	characteristic
66	C₂	#27159471	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#13095555
commutator, socle, prime radical	C₂²×C₃₈₉	C₂²×C₄
Fitting	C₄⋊C₄×C₃₈₉	C₄
cosocle	C₂×Dic₃₈₉	C₂³
hypercenter	C₄⋊C₄	#13095555
hypocenter	C₃₈₉	#446
LCS	G ▷ C₂²×C₃₈₉ ▷ C₃₈₉
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
16. #15691012	Q₈	semidirect
33. C₃₈₉	#446	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#15691012	2
#27159439	2
C₄×#15691012	2
#27159349	2
#446	389