Subgroups — #38734161

Order 24896.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27159341	C₂	1	1	yes	maximal, characteristic
2	#27159313	C₂	1	2	yes	maximal, complemented
3	#27159296	C₂	1	2	yes	maximal
4	C₄×#15691005	C₂	1	1	yes	maximal, characteristic, complemented
5	#97×C₃₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₃₈₉	C₂²	1	1	yes	characteristic
7	C₂×#15691005	C₂²	1	2	yes	—
8	#20261945	C₄	1	2	yes	—
9	#20261943	C₄	1	2	yes	—
10	C₄×Dic₃₈₉	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₃₈₉	C₂²	1	2	yes	—
12	C₄²×C₃₈₉	C₂²	1	1	yes	characteristic
13	C₂²×D₃₈₉	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₃₈₉	C₂×C₄	1	2	yes	—
15	C₂×Dic₃₈₉	C₂×C₄	1	1	yes	characteristic
16	C₄×D₃₈₉	—	2	2	no	—
17	#15691005	—	2	2	no	—
18	C₂×C₄×C₃₈₉	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₃₈₉	C₂³	1	1	yes	characteristic
20	C₈×C₃₈₉	—	2	2	no	—
21	C₂²×C₃₈₉	C₂²×C₄	1	1	yes	characteristic
22	C₂×D₃₈₉	—	2	1	no	—
23	C₂×D₃₈₉	—	2	2	no	—
24	C₄×C₃₈₉	—	2	2	no	—
25	C₄×C₃₈₉	#41	1	2	yes	—
26	Dic₃₈₉	—	2	1	no	—
27	Dic₃₈₉	—	2	2	no	—
28	C₂×C₃₈₉	#117	1	1	yes	characteristic
29	C₂×C₃₈₉	#131	1	2	yes	—
30	D₃₈₉	—	4	1	no	—
31	C₃₈₉	#433	1	1	yes	characteristic, complemented, Sylow
32	#433	—	389	1	no	maximal, Sylow
33	#117	—	389	1	no	—
34	C₄⋊C₈	—	389	2	no	—
35	C₂²⋊C₈	—	389	2	no	—
36	#97	D₃₈₉	1	1	yes	characteristic, complemented
37	C₄×C₈	—	389	1	no	—
38	C₂²×C₄	—	389	1	no	—
39	C₂×C₈	—	389	2	no	—
40	C₂×C₈	C₂×D₃₈₉	1	2	yes	—
41	C₄⋊C₄	—	389	2	no	—
42	C₂²⋊C₄	—	389	2	no	—
43	C₄²	—	389	1	no	—
44	C₄²	C₂×D₃₈₉	1	1	yes	characteristic
45	C₂³	—	389	1	no	—
46	C₂×C₄	—	778	2	no	—
47	C₂×C₄	—	389	2	no	—
48	C₂×C₄	—	389	1	no	—
49	C₂×C₄	C₄×D₃₈₉	1	2	yes	—
50	C₂×C₄	C₂²×D₃₈₉	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₈	—	778	2	no	—
53	C₂²	—	778	1	no	—
54	C₂²	—	778	2	no	—
55	C₂²	C₂×C₄×D₃₈₉	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	778	1	no	—
58	C₄	—	778	2	no	—
59	C₄	#20261966	1	2	yes	—
60	C₂	—	1556	1	no	—
61	C₂	#27159341	1	1	yes	characteristic
62	C₂	#27159392	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃₈₉
commutator, socle	C₂²×C₃₈₉	C₂²×C₄
Fitting	#97×C₃₈₉	C₂
prime radical	C₂²×D₃₈₉	C₂×C₄
cosocle	C₂×C₄×C₃₈₉	C₂³
hypercenter	#97	D₃₈₉
hypocenter	C₃₈₉	#433
LCS	G ▷ C₂²×C₃₈₉ ▷ C₃₈₉
UCS	C₁ ◁ C₂×C₄ ◁ #97

Complements

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

N	H ≅ G/N	type
2. #27159313	C₂	semidirect
4. C₄×#15691005	C₂	semidirect
5. #97×C₃₈₉	C₂	semidirect
31. C₃₈₉	#433	semidirect
36. #97	D₃₈₉	semidirect

Maximal subgroups

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

subgroup	index
#27159341	2
#27159313	2
#27159296	2
C₄×#15691005	2
#97×C₃₈₉	2
#433	389