Subgroups — #37565608

Order 24256.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27131323	C₂	1	1	yes	maximal, characteristic, complemented
2	#27131252	C₂	1	4	yes	maximal, complemented
3	#27131242	C₂	1	1	yes	maximal, characteristic, complemented
4	#127×C₃₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃₇₉⋊C₈	C₂²	1	2	yes	—
6	C₄⋊Dic₃₇₉	C₂²	1	2	yes	—
7	Dic₃₇₉⋊C₄	—	2	2	no	—
8	C₂×D₄×C₃₇₉	—	2	2	no	—
9	C₂×D₄×C₃₇₉	C₂²	1	2	yes	—
10	C₄²×C₃₇₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₃₇₉	—	2	2	no	—
12	C₃₇₉⋊C₈	—	2	2	no	—
13	C₂³×C₃₇₉	—	2	2	no	—
14	D₄×C₃₇₉	—	2	4	no	—
15	D₄×C₃₇₉	—	4	4	no	—
16	C₂×C₄×C₃₇₉	D₄	1	2	yes	—
17	C₂×C₄×C₃₇₉	C₂³	1	1	yes	characteristic
18	C₂²×C₃₇₉	—	4	2	no	—
19	C₂²×C₃₇₉	—	4	4	no	—
20	C₂²×C₃₇₉	C₂×D₄	1	1	yes	characteristic
21	C₄×C₃₇₉	—	2	2	no	—
22	C₄×C₃₇₉	#41	1	2	yes	—
23	Dic₃₇₉	—	4	2	no	—
24	C₂×C₃₇₉	—	8	2	no	—
25	C₂×C₃₇₉	#124	1	1	yes	characteristic
26	C₂×C₃₇₉	AGL(1,ℤ/8)	1	2	yes	—
27	C₃₇₉	#490	1	1	yes	characteristic, complemented, Sylow
28	#490	—	379	1	no	maximal, Sylow
29	#127	D₃₇₉	1	1	yes	characteristic
30	#125	—	379	1	no	—
31	#102	—	379	4	no	—
32	#97	—	379	1	no	—
33	C₂×D₄	—	2	2	no	—
34	C₂×D₄	C₂×D₃₇₉	1	2	yes	—
35	C₂×C₈	—	379	2	no	—
36	C₄⋊C₄	—	379	2	no	—
37	C₄⋊C₄	—	758	2	no	—
38	C₄²	C₂×D₃₇₉	1	1	yes	characteristic
39	C₂³	—	2	2	no	—
40	D₄	—	2	4	no	—
41	D₄	—	4	4	no	—
42	C₂×C₄	—	758	2	no	—
43	C₂×C₄	C₂²⋊D₃₇₉	1	2	yes	—
44	C₂×C₄	C₂²×D₃₇₉	1	1	yes	characteristic
45	C₈	—	758	2	no	—
46	C₂²	—	4	2	no	—
47	C₂²	—	4	4	no	—
48	C₂²	C₂×C₂²⋊D₃₇₉	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	1516	2	no	—
51	C₄	#20258605	1	2	yes	—
52	C₂	—	8	2	no	—
53	C₂	#27131318	1	1	yes	characteristic
54	C₂	#27131357	1	2	yes	—

	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	#490
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. #27131323	C₂	semidirect
2. #27131252	C₂	semidirect
3. #27131242	C₂	semidirect
27. C₃₇₉	#490	semidirect

Maximal subgroups

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

subgroup	index
#27131323	2
#27131252	2
#27131242	2
#127×C₃₇₉	2
#490	379