Subgroups — #38734388

Order 24896.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27159383	C₂	1	1	yes	maximal, characteristic, complemented
2	#27159346	C₂	1	1	yes	maximal, characteristic
3	#27159315	C₂	1	1	yes	maximal, characteristic, complemented
4	#27159313	C₂	1	1	yes	maximal, characteristic, complemented
5	#27159306	C₂	1	1	yes	maximal, characteristic
6	#27159304	C₂	1	1	yes	maximal, characteristic
7	#106×C₃₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₇₇₈	—	2	1	no	—
9	C₂×D₁₅₅₆	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₃₈₉	—	2	1	no	—
11	C₂×#15691005	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₃₈₉	C₂²	1	1	yes	characteristic
13	#20261945	—	2	1	no	—
14	#20261943	—	2	1	no	—
15	C₄×Dic₃₈₉	C₂²	1	1	yes	characteristic
16	C₂×C₈×C₃₈₉	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₃₈₉	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₃₈₉	C₂²	1	1	yes	characteristic
19	C₂²×D₃₈₉	—	2	1	no	—
20	Dic₇₇₈	—	4	2	no	—
21	D₁₅₅₆	—	2	1	no	—
22	D₁₅₅₆	Q₈	1	2	yes	complemented
23	C₂×Dic₃₈₉	—	2	1	no	—
24	C₂×Dic₃₈₉	D₄	1	1	yes	characteristic
25	C₂×Dic₃₈₉	D₄	1	1	yes	characteristic
26	C₄×D₃₈₉	—	4	2	no	—
27	#15691005	—	2	1	no	—
28	C₂×C₄×C₃₈₉	—	2	1	no	—
29	C₂×C₄×C₃₈₉	—	2	1	no	—
30	C₂×C₄×C₃₈₉	C₂³	1	1	yes	characteristic
31	C₈×C₃₈₉	—	2	1	no	—
32	C₂²×C₃₈₉	C₂×D₄	1	1	yes	characteristic
33	C₂×D₃₈₉	—	2	2	no	—
34	C₂×D₃₈₉	—	4	1	no	—
35	C₂×D₃₈₉	—	4	1	no	—
36	C₄×C₃₈₉	—	4	1	no	—
37	C₄×C₃₈₉	—	4	1	no	—
38	C₄×C₃₈₉	C₂×Q₈	1	1	yes	characteristic
39	C₄×C₃₈₉	#41	1	1	yes	characteristic
40	Dic₃₈₉	—	2	1	no	—
41	Dic₃₈₉	—	4	1	no	—
42	Dic₃₈₉	SD₁₆	1	2	yes	—
43	C₂×C₃₈₉	C₂²⋊Q₈	1	1	yes	characteristic
44	C₂×C₃₈₉	C₂×SD₁₆	1	1	yes	characteristic
45	C₂×C₃₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
46	D₃₈₉	—	4	2	no	—
47	C₃₈₉	#476	1	1	yes	characteristic, complemented, Sylow
48	#476	—	389	1	no	maximal, Sylow
49	C₄⋊Q₈	—	389	1	no	—
50	C₄×D₄	—	389	1	no	—
51	#106	—	389	1	no	—
52	#106	D₃₈₉	1	1	yes	characteristic, complemented
53	C₄⋊C₈	—	389	1	no	—
54	#102	—	389	1	no	—
55	#102	—	389	1	no	—
56	C₂×Q₈	—	778	1	no	—
57	C₂×D₄	—	389	1	no	—
58	C₂²×C₄	—	778	1	no	—
59	C₂×C₈	—	389	1	no	—
60	C₂×C₈	C₂×D₃₈₉	1	1	yes	characteristic
61	C₄⋊C₄	—	778	1	no	—
62	C₄⋊C₄	—	389	1	no	—
63	C₄⋊C₄	C₂×D₃₈₉	1	1	yes	characteristic
64	C₄⋊C₄	C₂×D₃₈₉	1	1	yes	characteristic
65	C₂²⋊C₄	—	778	1	no	—
66	C₄²	—	389	1	no	—
67	C₂³	—	778	1	no	—
68	Q₈	—	1556	2	no	—
69	D₄	—	778	1	no	—
70	D₄	—	389	2	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	778	1	no	—
74	C₂×C₄	—	1556	2	no	—
75	C₂×C₄	—	389	1	no	—
76	C₂×C₄	—	389	1	no	—
77	C₂×C₄	C₂²×D₃₈₉	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	778	1	no	—
80	C₂²	—	778	2	no	—
81	C₂²	—	1556	1	no	—
82	C₂²	—	1556	1	no	—
83	C₂²	D₄×D₃₈₉	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	778	1	no	—
87	C₄	—	1556	1	no	—
88	C₄	—	389	2	no	—
89	C₄	Q₈×D₃₈₉	1	1	yes	characteristic
90	C₄	#20261966	1	1	yes	characteristic
91	C₂	—	1556	2	no	—
92	C₂	#27159362	1	1	yes	characteristic
93	C₂	SD₁₆×D₃₈₉	1	1	yes	characteristic
94	C₂	#27159411	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₃₈₉
commutator, cosocle	C₂×C₄×C₃₈₉	C₂³
Frattini	C₂×C₄	C₂²×D₃₈₉
Fitting	#106×C₃₈₉	C₂
socle	C₂²×C₃₈₉	C₂×D₄
prime radical	C₂×D₁₅₅₆	C₂²
hypercenter	#106	D₃₈₉
hypocenter	C₃₈₉	#476
LCS	G ▷ C₂×C₄×C₃₈₉ ▷ C₂×C₃₈₉ ▷ C₃₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
1. #27159383	C₂	semidirect
3. #27159315	C₂	semidirect
4. #27159313	C₂	semidirect
7. #106×C₃₈₉	C₂	semidirect
22. D₁₅₅₆	Q₈	semidirect
47. C₃₈₉	#476	semidirect
52. #106	D₃₈₉	semidirect

Maximal subgroups

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

subgroup	index
#27159383	2
#27159346	2
#27159315	2
#27159313	2
#27159306	2
#27159304	2
#106×C₃₈₉	2
#476	389