Subgroups — #38735014

Order 24896.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₈₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#27159455	C₂	1	1	yes	maximal, characteristic, complemented
3	#27159407	C₂	1	1	yes	maximal, characteristic
4	#20261976	—	2	1	no	—
5	#20261969	—	2	1	no	—
6	#20261967	—	2	1	no	—
7	#20261953	—	2	1	no	—
8	D₃₁₁₂	C₄	1	1	yes	characteristic
9	C₈×D₃₈₉	C₂²	1	1	yes	characteristic
10	Q₁₆×C₃₈₉	C₄	1	1	yes	characteristic
11	#15691012	—	4	1	no	—
12	D₁₅₅₆	—	2	1	no	—
13	D₁₅₅₆	—	4	1	no	—
14	C₄×D₃₈₉	—	4	1	no	—
15	C₄×D₃₈₉	D₄	1	1	yes	characteristic
16	#15691005	D₄	1	1	yes	characteristic
17	Q₈×C₃₈₉	—	2	1	no	—
18	C₈×C₃₈₉	C₂×C₄	1	1	yes	characteristic
19	C₂×D₃₈₉	—	4	1	no	—
20	C₂×D₃₈₉	SD₁₆	1	1	yes	characteristic
21	C₄×C₃₈₉	—	4	1	no	—
22	C₄×C₃₈₉	C₂²⋊C₄	1	1	yes	characteristic
23	Dic₃₈₉	D₈	1	1	yes	characteristic
24	C₂×C₃₈₉	#102	1	1	yes	characteristic
25	D₃₈₉	—	2	1	no	—
26	D₃₈₉	—	8	1	no	—
27	C₃₈₉	#359	1	1	yes	characteristic, complemented, Sylow
28	#359	—	389	1	no	maximal, Sylow
29	#135	—	389	1	no	—
30	C₂×C₁₆	—	389	1	no	—
31	#108	—	389	1	no	—
32	#41	—	778	1	no	—
33	Q₁₆	#13095555	1	1	yes	characteristic
34	SD₁₆	—	778	1	no	—
35	D₈	—	389	1	no	—
36	M₁₆	—	778	1	no	—
37	C₂×C₈	—	389	1	no	—
38	C₁₆	—	778	1	no	—
39	Q₈	—	2	1	no	—
40	D₄	—	778	1	no	—
41	D₄	—	1556	1	no	—
42	C₂×C₄	—	1556	1	no	—
43	C₂×C₄	—	389	1	no	—
44	C₈	—	1556	1	no	—
45	C₈	—	389	1	no	—
46	C₈	C₂×#13095555	1	1	yes	characteristic
47	C₂²	—	1556	1	no	—
48	C₂²	—	389	1	no	—
49	C₄	—	4	1	no	—
50	C₄	—	389	1	no	—
51	C₄	C₂²⋊#13095555	1	1	yes	characteristic
52	C₂	—	778	1	no	—
53	C₂	—	3112	1	no	—
54	C₂	#27159446	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27159446
commutator	C₈×C₃₈₉	C₂×C₄
Frattini	C₈	C₂×#13095555
Fitting	Q₁₆×C₃₈₉	C₄
socle	C₂×C₃₈₉	#102
prime radical	#27159407	C₂
cosocle	C₈×D₃₈₉	C₂²
hypercenter	Q₁₆	#13095555
hypocenter	C₃₈₉	#359
LCS	G ▷ C₈×C₃₈₉ ▷ C₄×C₃₈₉ ▷ C₂×C₃₈₉ ▷ C₃₈₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. D₃₈₉⋊C₁₆	C₂	semidirect
2. #27159455	C₂	semidirect
27. C₃₈₉	#359	semidirect

Maximal subgroups

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

subgroup	index
D₃₈₉⋊C₁₆	2
#27159455	2
#27159407	2
#359	389