Subgroups — C₂×#27131264 #37565277

Order 24256.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₃₇₉	C₂	1	1	yes	maximal, characteristic
3	#27131264	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊C₄×C₃₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₃₇₉	—	2	1	no	—
6	C₂×C₃₇₉⋊C₈	C₄	1	4	yes	complemented
7	C₂×C₃₇₉⋊C₈	C₂²	1	2	yes	—
8	C₄⋊Dic₃₇₉	—	2	1	no	—
9	C₄⋊Dic₃₇₉	C₂²	1	2	yes	—
10	C₂²×C₄×C₃₇₉	—	2	1	no	—
11	C₂²×C₄×C₃₇₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₃₇₉	—	2	1	no	—
13	C₄⋊C₄×C₃₇₉	C₂²	1	2	yes	—
14	C₂×Dic₃₇₉	—	2	2	no	—
15	C₂×Dic₃₇₉	—	4	2	no	—
16	C₃₇₉⋊C₈	C₂×C₄	1	4	yes	complemented
17	C₂³×C₃₇₉	D₄	1	1	yes	characteristic
18	C₂×C₄×C₃₇₉	—	2	2	no	—
19	C₂×C₄×C₃₇₉	—	4	2	no	—
20	C₂×C₄×C₃₇₉	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₃₇₉	D₄	1	1	yes	characteristic
22	C₂×C₄×C₃₇₉	Q₈	1	2	yes	—
23	C₂×C₄×C₃₇₉	C₂³	1	1	yes	characteristic
24	C₂²×C₃₇₉	C₄⋊C₄	1	2	yes	—
25	C₂²×C₃₇₉	D₈	1	2	yes	—
26	C₂²×C₃₇₉	Q₁₆	1	2	yes	—
27	C₂²×C₃₇₉	C₂×D₄	1	1	yes	characteristic
28	C₄×C₃₇₉	—	4	2	no	—
29	C₄×C₃₇₉	C₄⋊C₄	1	2	yes	—
30	C₄×C₃₇₉	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₃₇₉	C₂×Q₈	1	1	yes	characteristic
32	Dic₃₇₉	—	4	2	no	—
33	C₂×C₃₇₉	#107	1	4	yes	complemented
34	C₂×C₃₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₃₇₉	C₂×D₈	1	1	yes	characteristic
36	C₂×C₃₇₉	C₂×Q₁₆	1	1	yes	characteristic
37	C₃₇₉	C₂×#107	1	1	yes	characteristic, complemented, Sylow
38	C₂×#107	—	379	1	no	maximal, Sylow
39	C₂²×C₈	—	379	1	no	—
40	C₂×C₄⋊C₄	—	379	1	no	—
41	C₂×C₄⋊C₄	D₃₇₉	1	1	yes	characteristic
42	#107	—	379	4	no	—
43	C₂²×C₄	—	2	1	no	—
44	C₂²×C₄	—	758	1	no	—
45	C₂²×C₄	C₂×D₃₇₉	1	1	yes	characteristic
46	C₂×C₈	—	379	4	no	—
47	C₂×C₈	—	379	2	no	—
48	C₄⋊C₄	—	2	1	no	—
49	C₄⋊C₄	—	379	2	no	—
50	C₄⋊C₄	—	758	1	no	—
51	C₄⋊C₄	C₂×D₃₇₉	1	2	yes	—
52	C₂³	C₂²⋊D₃₇₉	1	1	yes	characteristic
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	4	2	no	—
55	C₂×C₄	—	1516	2	no	—
56	C₂×C₄	—	758	2	no	—
57	C₂×C₄	C₄×D₃₇₉	1	2	yes	—
58	C₂×C₄	C₂²⋊D₃₇₉	1	1	yes	characteristic
59	C₂×C₄	Dic₇₅₈	1	2	yes	—
60	C₂×C₄	C₂²×D₃₇₉	1	1	yes	characteristic
61	C₈	—	379	4	no	—
62	C₂²	Dic₃₇₉⋊C₄	1	2	yes	—
63	C₂²	#20258591	1	2	yes	—
64	C₂²	#20258596	1	2	yes	—
65	C₂²	C₂×C₂²⋊D₃₇₉	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	—	1516	2	no	—
68	C₄	Dic₃₇₉⋊C₄	1	2	yes	—
69	C₄	C₂×C₄×D₃₇₉	1	1	yes	characteristic
70	C₄	C₂×Dic₇₅₈	1	1	yes	characteristic
71	C₂	#27131264	1	4	yes	direct product factor
72	C₂	C₂×Dic₃₇₉⋊C₄	1	1	yes	characteristic
73	C₂	C₂×#20258591	1	1	yes	characteristic
74	C₂	C₂×#20258596	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₃₇₉
commutator	C₄×C₃₇₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₇₉
Fitting	C₂×C₄⋊C₄×C₃₇₉	C₂
socle, prime radical	C₂³×C₃₇₉	D₄
cosocle	C₂×C₄×C₃₇₉	C₂³
hypercenter	C₂×C₄⋊C₄	D₃₇₉
hypocenter	C₃₇₉	C₂×#107
LCS	G ▷ C₄×C₃₇₉ ▷ C₂×C₃₇₉ ▷ C₃₇₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #27131264	C₂	direct (N × H)
6. C₂×C₃₇₉⋊C₈	C₄	semidirect
16. C₃₇₉⋊C₈	C₂×C₄	semidirect
33. C₂×C₃₇₉	#107	semidirect
37. C₃₇₉	C₂×#107	semidirect
71. C₂	#27131264	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₇₉⋊C₈	2
C₂×C₄⋊Dic₃₇₉	2
#27131264	2
C₂×C₄⋊C₄×C₃₇₉	2
C₂×#107	379

Subgroups — C2×#27131264 #37565277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27131264 #37565277