Subgroups — C₂×#106×C₃₇₉ #37564801

Order 24256.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₃₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×C₃₇₉	C₂	1	2	yes	maximal
3	#106×C₃₇₉	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄×C₃₇₉	—	2	2	no	—
5	C₂²×C₄×C₃₇₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₃₇₉	C₄	1	4	yes	complemented
7	C₂×C₈×C₃₇₉	C₂²	1	2	yes	—
8	C₄⋊C₄×C₃₇₉	—	2	2	no	—
9	C₄⋊C₄×C₃₇₉	C₂²	1	4	yes	—
10	C₂³×C₃₇₉	D₄	1	1	yes	characteristic
11	C₂×C₄×C₃₇₉	—	2	4	no	—
12	C₂×C₄×C₃₇₉	—	4	4	no	—
13	C₂×C₄×C₃₇₉	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₃₇₉	D₄	1	1	yes	characteristic
15	C₂×C₄×C₃₇₉	Q₈	1	2	yes	—
16	C₂×C₄×C₃₇₉	C₂³	1	1	yes	characteristic
17	C₈×C₃₇₉	C₂×C₄	1	4	yes	complemented
18	C₂²×C₃₇₉	C₄⋊C₄	1	2	yes	—
19	C₂²×C₃₇₉	SD₁₆	1	4	yes	—
20	C₂²×C₃₇₉	C₂×D₄	1	1	yes	characteristic
21	C₄×C₃₇₉	—	4	4	no	—
22	C₄×C₃₇₉	C₄⋊C₄	1	2	yes	—
23	C₄×C₃₇₉	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₃₇₉	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₃₇₉	#106	1	4	yes	direct product factor
26	C₂×C₃₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂×C₃₇₉	C₂×SD₁₆	1	2	yes	—
28	C₃₇₉	C₂×#106	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×#106	C₃₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂²×C₈	C₂×C₃₇₉	1	1	yes	characteristic
31	C₂×C₄⋊C₄	C₂×C₃₇₉	1	2	yes	—
32	#106	C₂×C₃₇₉	1	4	yes	direct product factor
33	C₂²×C₄	—	2	2	no	—
34	C₂²×C₄	C₂²×C₃₇₉	1	1	yes	characteristic
35	C₂×C₈	C₄×C₃₇₉	1	4	yes	complemented
36	C₂×C₈	C₂²×C₃₇₉	1	2	yes	—
37	C₄⋊C₄	—	2	2	no	—
38	C₄⋊C₄	C₂²×C₃₇₉	1	4	yes	—
39	C₂³	D₄×C₃₇₉	1	1	yes	characteristic
40	C₂×C₄	—	2	4	no	—
41	C₂×C₄	—	4	4	no	—
42	C₂×C₄	C₂×C₄×C₃₇₉	1	2	yes	—
43	C₂×C₄	D₄×C₃₇₉	1	1	yes	characteristic
44	C₂×C₄	Q₈×C₃₇₉	1	2	yes	—
45	C₂×C₄	C₂³×C₃₇₉	1	1	yes	characteristic
46	C₈	C₂×C₄×C₃₇₉	1	4	yes	complemented
47	C₂²	C₄⋊C₄×C₃₇₉	1	2	yes	—
48	C₂²	SD₁₆×C₃₇₉	1	4	yes	—
49	C₂²	C₂×D₄×C₃₇₉	1	1	yes	characteristic
50	C₄	—	4	4	no	—
51	C₄	C₄⋊C₄×C₃₇₉	1	2	yes	—
52	C₄	C₂²×C₄×C₃₇₉	1	1	yes	characteristic
53	C₄	C₂×Q₈×C₃₇₉	1	1	yes	characteristic
54	C₂	#106×C₃₇₉	1	4	yes	direct product factor
55	C₂	C₂×C₄⋊C₄×C₃₇₉	1	1	yes	characteristic
56	C₂	C₂×SD₁₆×C₃₇₉	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃₇₉	D₄
commutator	C₄	C₂²×C₄×C₃₇₉
Frattini, cosocle	C₂×C₄	C₂³×C₃₇₉
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₇₉ ◁ C₂²×C₄×C₃₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. #106×C₃₇₉	C₂	direct (N × H)
6. C₂×C₈×C₃₇₉	C₄	semidirect
17. C₈×C₃₇₉	C₂×C₄	semidirect
25. C₂×C₃₇₉	#106	direct (N × H)
28. C₃₇₉	C₂×#106	direct (N × H)
29. C₂×#106	C₃₇₉	direct (N × H)
32. #106	C₂×C₃₇₉	direct (N × H)
35. C₂×C₈	C₄×C₃₇₉	semidirect
46. C₈	C₂×C₄×C₃₇₉	semidirect
54. C₂	#106×C₃₇₉	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×C₈×C₃₇₉	2
C₂×C₄⋊C₄×C₃₇₉	2
#106×C₃₇₉	2
C₂×#106	379

Subgroups — C2×#106×C379 #37564801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#106×C₃₇₉ #37564801