Subgroups — #37565441

Order 24256.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20258594	C₂	1	2	yes	maximal, complemented
2	C₄×Dic₇₅₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₃₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	#27131252	C₂	1	2	yes	maximal, complemented
5	#127×C₃₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₇₅₈	C₂²	1	1	yes	characteristic
7	#20258594	—	2	4	no	—
8	C₂×C₃₇₉⋊C₈	C₂²	1	2	yes	—
9	C₄⋊Dic₃₇₉	C₂²	1	1	yes	characteristic
10	Dic₃₇₉⋊C₄	—	2	1	no	—
11	C₄×Dic₃₇₉	—	2	1	no	—
12	C₂×D₄×C₃₇₉	—	2	1	no	—
13	C₂×D₄×C₃₇₉	—	2	1	no	—
14	C₂×D₄×C₃₇₉	C₂²	1	2	yes	—
15	C₄²×C₃₇₉	C₂²	1	1	yes	characteristic
16	Dic₇₅₈	—	2	1	no	—
17	Dic₇₅₈	D₄	1	2	yes	complemented
18	C₂×Dic₃₇₉	—	2	1	no	—
19	C₂×Dic₃₇₉	—	2	1	no	—
20	C₃₇₉⋊C₈	—	2	2	no	—
21	C₂³×C₃₇₉	—	2	2	no	—
22	D₄×C₃₇₉	—	2	2	no	—
23	D₄×C₃₇₉	—	2	2	no	—
24	D₄×C₃₇₉	—	4	2	no	—
25	D₄×C₃₇₉	—	4	2	no	—
26	C₂×C₄×C₃₇₉	D₄	1	1	yes	characteristic
27	C₂×C₄×C₃₇₉	D₄	1	1	yes	characteristic
28	C₂×C₄×C₃₇₉	C₂³	1	1	yes	characteristic
29	C₂²×C₃₇₉	—	4	2	no	—
30	C₂²×C₃₇₉	—	4	2	no	—
31	C₂²×C₃₇₉	—	4	2	no	—
32	C₂²×C₃₇₉	C₂×D₄	1	1	yes	characteristic
33	C₄×C₃₇₉	—	2	1	no	—
34	C₄×C₃₇₉	SD₁₆	1	2	yes	complemented
35	C₄×C₃₇₉	C₂×D₄	1	1	yes	characteristic
36	C₄×C₃₇₉	#41	1	1	yes	characteristic
37	Dic₃₇₉	—	2	2	no	—
38	Dic₃₇₉	—	4	1	no	—
39	C₂×C₃₇₉	—	8	2	no	—
40	C₂×C₃₇₉	#121	1	1	yes	characteristic
41	C₂×C₃₇₉	C₂×SD₁₆	1	1	yes	characteristic
42	C₂×C₃₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
43	C₃₇₉	#460	1	1	yes	characteristic, complemented, Sylow
44	#460	—	379	1	no	maximal, Sylow
45	C₂×SD₁₆	—	379	2	no	—
46	#127	D₃₇₉	1	1	yes	characteristic
47	C₄×Q₈	—	379	1	no	—
48	C₄⋊C₈	—	379	1	no	—
49	#102	—	379	2	no	—
50	C₂×Q₈	—	379	1	no	—
51	C₂×D₄	—	2	1	no	—
52	C₂×D₄	—	2	1	no	—
53	C₂×D₄	C₂×D₃₇₉	1	2	yes	—
54	SD₁₆	—	758	4	no	—
55	C₂×C₈	—	379	2	no	—
56	C₄⋊C₄	—	379	1	no	—
57	C₄⋊C₄	—	758	1	no	—
58	C₄²	—	758	1	no	—
59	C₄²	C₂×D₃₇₉	1	1	yes	characteristic
60	C₂³	—	2	2	no	—
61	Q₈	—	379	2	no	—
62	Q₈	—	758	1	no	—
63	D₄	—	2	2	no	—
64	D₄	—	2	2	no	—
65	D₄	—	4	2	no	—
66	D₄	—	4	2	no	—
67	C₂×C₄	—	758	1	no	—
68	C₂×C₄	—	758	1	no	—
69	C₂×C₄	C₂²⋊D₃₇₉	1	1	yes	characteristic
70	C₂×C₄	C₂²⋊D₃₇₉	1	1	yes	characteristic
71	C₂×C₄	C₂²×D₃₇₉	1	1	yes	characteristic
72	C₈	—	758	2	no	—
73	C₂²	—	4	2	no	—
74	C₂²	—	4	2	no	—
75	C₂²	—	4	2	no	—
76	C₂²	C₂×C₂²⋊D₃₇₉	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	1516	1	no	—
79	C₄	—	758	2	no	—
80	C₄	#20258594	1	2	yes	complemented
81	C₄	D₄×D₃₇₉	1	1	yes	characteristic
82	C₄	#20258605	1	1	yes	characteristic
83	C₂	—	8	2	no	—
84	C₂	#27131302	1	1	yes	characteristic
85	C₂	C₂×#20258594	1	1	yes	characteristic
86	C₂	#27131357	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₃₇₉
commutator, cosocle	C₂×C₄×C₃₇₉	C₂³
Frattini	C₂×C₄	C₂²×D₃₇₉
Fitting, prime radical	#127×C₃₇₉	C₂
socle	C₂²×C₃₇₉	C₂×D₄
hypercenter	#127	D₃₇₉
hypocenter	C₃₇₉	#460
LCS	G ▷ C₂×C₄×C₃₇₉ ▷ C₂×C₃₇₉ ▷ C₃₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×#20258594	C₂	semidirect
2. C₄×Dic₇₅₈	C₂	semidirect
3. C₄⋊(C₃₇₉⋊C₈)	C₂	semidirect
4. #27131252	C₂	semidirect
17. Dic₇₅₈	D₄	semidirect
34. C₄×C₃₇₉	SD₁₆	semidirect
43. C₃₇₉	#460	semidirect
80. C₄	#20258594	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20258594	2
C₄×Dic₇₅₈	2
C₄⋊(C₃₇₉⋊C₈)	2
#27131252	2
#127×C₃₇₉	2
#460	379