Subgroups — #38734142

Order 24896.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20261950	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₃₈₉	C₂	1	1	yes	maximal, characteristic
3	#27159317	C₂	1	2	yes	maximal, complemented
4	#27159315	C₂	1	2	yes	maximal, complemented
5	#117×C₃₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₈₉	—	2	1	no	—
7	#20261950	C₄	1	4	yes	complemented
8	C₂×#15691005	C₂²	1	2	yes	—
9	C₄⋊Dic₃₈₉	—	2	1	no	—
10	C₄⋊Dic₃₈₉	C₂²	1	2	yes	—
11	C₂²×C₄×C₃₈₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₃₈₉	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₃₈₉	C₂²	1	1	yes	characteristic
14	C₂²⋊C₄×C₃₈₉	—	2	1	no	—
15	C₄²×C₃₈₉	—	2	1	no	—
16	C₂×Dic₃₈₉	—	2	2	no	—
17	C₂×Dic₃₈₉	—	4	2	no	—
18	#15691005	C₂×C₄	1	4	yes	complemented
19	C₂³×C₃₈₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₃₈₉	—	2	1	no	—
21	C₂×C₄×C₃₈₉	—	2	1	no	—
22	C₂×C₄×C₃₈₉	C₂×C₄	1	2	yes	—
23	C₂×C₄×C₃₈₉	D₄	1	1	yes	characteristic
24	C₂×C₄×C₃₈₉	Q₈	1	2	yes	—
25	C₂×C₄×C₃₈₉	C₂³	1	1	yes	characteristic
26	C₂²×C₃₈₉	—	2	1	no	—
27	C₂²×C₃₈₉	—	2	1	no	—
28	C₂²×C₃₈₉	C₄⋊C₄	1	2	yes	—
29	C₂²×C₃₈₉	C₂×D₄	1	1	yes	characteristic
30	C₄×C₃₈₉	—	4	1	no	—
31	C₄×C₃₈₉	—	4	1	no	—
32	C₄×C₃₈₉	C₄⋊C₄	1	2	yes	—
33	C₄×C₃₈₉	C₂²×C₄	1	1	yes	characteristic
34	C₄×C₃₈₉	C₂×Q₈	1	1	yes	characteristic
35	Dic₃₈₉	—	4	2	no	—
36	C₂×C₃₈₉	—	2	2	no	—
37	C₂×C₃₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₃₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
39	C₂×C₃₈₉	#137	1	1	yes	characteristic
40	C₃₈₉	#428	1	1	yes	characteristic, complemented, Sylow
41	#428	—	389	1	no	maximal, Sylow
42	C₂×M₁₆	—	389	1	no	—
43	#117	D₃₈₉	1	1	yes	characteristic
44	C₂×C₄⋊C₄	—	389	1	no	—
45	#107	—	389	2	no	—
46	#106	—	389	2	no	—
47	C₂²×C₄	—	778	1	no	—
48	C₂²×C₄	C₂×D₃₈₉	1	1	yes	characteristic
49	M₁₆	—	389	4	no	—
50	C₂×C₈	—	389	2	no	—
51	C₄⋊C₄	—	778	1	no	—
52	C₄⋊C₄	—	389	2	no	—
53	C₄⋊C₄	C₂×D₃₈₉	1	1	yes	characteristic
54	C₄⋊C₄	C₂×D₃₈₉	1	1	yes	characteristic
55	C₂²⋊C₄	—	2	1	no	—
56	C₄²	—	2	1	no	—
57	C₂³	C₂²⋊D₃₈₉	1	1	yes	characteristic
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	778	2	no	—
61	C₂×C₄	—	1556	2	no	—
62	C₂×C₄	C₄×D₃₈₉	1	2	yes	—
63	C₂×C₄	C₂²⋊D₃₈₉	1	1	yes	characteristic
64	C₂×C₄	Dic₇₇₈	1	2	yes	—
65	C₂×C₄	C₂²×D₃₈₉	1	1	yes	characteristic
66	C₈	—	389	4	no	—
67	C₂²	—	2	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	#20261945	1	2	yes	—
70	C₂²	C₂×C₂²⋊D₃₈₉	1	1	yes	characteristic
71	C₄	—	4	1	no	—
72	C₄	—	4	1	no	—
73	C₄	—	1556	2	no	—
74	C₄	#20261945	1	2	yes	—
75	C₄	C₂×C₄×D₃₈₉	1	1	yes	characteristic
76	C₄	C₂×Dic₇₇₈	1	1	yes	characteristic
77	C₂	—	2	2	no	—
78	C₂	C₂×#20261945	1	1	yes	characteristic
79	C₂	#27159409	1	1	yes	characteristic
80	C₂	#27159414	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₈₉
commutator	C₄×C₃₈₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₈₉
Fitting	#117×C₃₈₉	C₂
socle	C₂²×C₃₈₉	C₂×D₄
prime radical	C₂³×C₃₈₉	D₄
cosocle	C₂×C₄×C₃₈₉	C₂³
hypercenter	#117	D₃₈₉
hypocenter	C₃₈₉	#428
LCS	G ▷ C₄×C₃₈₉ ▷ C₂×C₃₈₉ ▷ C₃₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. #27159317	C₂	semidirect
4. #27159315	C₂	semidirect
7. #20261950	C₄	semidirect
18. #15691005	C₂×C₄	semidirect
40. C₃₈₉	#428	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20261950	2
C₂×C₄⋊Dic₃₈₉	2
#27159317	2
#27159315	2
#117×C₃₈₉	2
#428	389