Subgroups — C₂×#27159455 #38735113

Order 24896.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20261976	C₂	1	2	yes	maximal
2	#27159455	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×D₃₈₉	C₂	1	1	yes	maximal, characteristic
4	#20261976	—	2	2	no	—
5	#20261976	C₂²	1	4	yes	—
6	C₂×#15691012	—	2	2	no	—
7	C₂×C₄×D₃₈₉	C₂²	1	1	yes	characteristic
8	C₂×#15691005	C₄	1	1	yes	characteristic
9	C₈×D₃₈₉	C₄	1	2	yes	—
10	C₈×D₃₈₉	C₂²	1	2	yes	—
11	C₂×C₈×C₃₈₉	C₄	1	1	yes	characteristic
12	#15691012	—	2	4	no	—
13	C₂²×D₃₈₉	Q₈	1	1	yes	characteristic
14	C₂×Dic₃₈₉	D₄	1	1	yes	characteristic
15	C₄×D₃₈₉	C₂×C₄	1	1	yes	characteristic
16	C₄×D₃₈₉	D₄	1	1	yes	characteristic
17	C₄×D₃₈₉	Q₈	1	1	yes	characteristic
18	C₄×D₃₈₉	C₂³	1	1	yes	characteristic
19	#15691005	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₃₈₉	C₂×C₄	1	1	yes	characteristic
21	C₈×C₃₈₉	C₂×C₄	1	2	yes	—
22	C₂²×C₃₈₉	C₄⋊C₄	1	1	yes	characteristic
23	C₂×D₃₈₉	—	2	2	no	—
24	C₂×D₃₈₉	C₄⋊C₄	1	1	yes	characteristic
25	C₂×D₃₈₉	C₂×Q₈	1	1	yes	characteristic
26	C₄×C₃₈₉	C₄⋊C₄	1	1	yes	characteristic
27	C₄×C₃₈₉	C₂²×C₄	1	1	yes	characteristic
28	Dic₃₈₉	C₄⋊C₄	1	1	yes	characteristic
29	Dic₃₈₉	C₂×D₄	1	1	yes	characteristic
30	C₂×C₃₈₉	#108	1	2	yes	complemented
31	C₂×C₃₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
32	D₃₈₉	—	2	1	no	—
33	D₃₈₉	—	2	1	no	—
34	C₃₈₉	C₂×#108	1	1	yes	characteristic, complemented, Sylow
35	C₂×#108	—	389	1	no	maximal, Sylow
36	C₂×M₁₆	—	389	2	no	—
37	C₂²×C₈	—	389	1	no	—
38	#108	—	389	4	no	—
39	C₂²×C₄	—	389	1	no	—
40	M₁₆	—	778	2	no	—
41	M₁₆	—	389	4	no	—
42	C₂×C₈	—	778	2	no	—
43	C₂×C₈	—	389	1	no	—
44	C₂×C₈	—	389	2	no	—
45	C₂×C₈	—	389	2	no	—
46	C₂×C₈	#13095555	1	1	yes	characteristic
47	C₂³	—	389	1	no	—
48	C₂×C₄	—	389	1	no	—
49	C₂×C₄	—	389	1	no	—
50	C₂×C₄	—	389	1	no	—
51	C₂×C₄	—	389	1	no	—
52	C₂×C₄	—	389	1	no	—
53	C₂×C₄	C₂×#13095555	1	1	yes	characteristic
54	C₈	—	778	4	no	—
55	C₈	—	389	2	no	—
56	C₈	C₂×#13095555	1	2	yes	—
57	C₂²	—	778	2	no	—
58	C₂²	—	389	1	no	—
59	C₂²	—	389	1	no	—
60	C₂²	C₄⋊#13095555	1	1	yes	characteristic
61	C₄	—	389	1	no	—
62	C₄	—	389	1	no	—
63	C₄	C₄⋊#13095555	1	1	yes	characteristic
64	C₄	C₂²×#13095555	1	1	yes	characteristic
65	C₂	—	778	1	no	—
66	C₂	—	778	1	no	—
67	C₂	#27159455	1	2	yes	direct product factor
68	C₂	C₂×C₄⋊#13095555	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#13095555
commutator	C₄×C₃₈₉	C₂²×C₄
Frattini	C₄	C₂²×#13095555
Fitting	C₂×C₈×C₃₈₉	C₄
socle	C₂²×C₃₈₉	C₄⋊C₄
prime radical	C₂²×D₃₈₉	Q₈
cosocle	C₄×D₃₈₉	C₂³
hypercenter	C₂×C₈	#13095555
hypocenter	C₃₈₉	C₂×#108
LCS	G ▷ C₄×C₃₈₉ ▷ C₂×C₃₈₉ ▷ C₃₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #27159455	C₂	direct (N × H)
30. C₂×C₃₈₉	#108	semidirect
34. C₃₈₉	C₂×#108	semidirect
67. C₂	#27159455	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#20261976	2
#27159455	2
C₂×C₈×D₃₈₉	2
C₂×#108	389

Subgroups — C2×#27159455 #38735113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27159455 #38735113