Subgroups — #1842×C₁₇₉ #37505064

Order 22912.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₈×C₁₇₉	C₂	1	6	yes	maximal
2	C₄³×C₁₇₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₁₇₉	C₂²	1	4	yes	—
4	C₂×C₄²×C₁₇₉	C₄	1	3	yes	—
5	C₂×C₄²×C₁₇₉	C₄	1	1	yes	characteristic
6	C₂×C₄²×C₁₇₉	C₂²	1	3	yes	—
7	C₄⋊C₈×C₁₇₉	—	2	12	no	—
8	C₂²×C₄×C₁₇₉	C₂×C₄	1	3	yes	—
9	C₂²×C₄×C₁₇₉	C₂×C₄	1	3	yes	—
10	C₂²×C₄×C₁₇₉	C₂³	1	1	yes	characteristic
11	C₂×C₈×C₁₇₉	—	2	12	no	—
12	C₄²×C₁₇₉	—	2	6	no	—
13	C₄²×C₁₇₉	C₈	1	4	yes	complemented
14	C₄²×C₁₇₉	D₄	1	6	yes	—
15	C₄²×C₁₇₉	Q₈	1	6	yes	—
16	C₂³×C₁₇₉	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₇₉	—	2	6	no	—
18	C₂×C₄×C₁₇₉	C₄⋊C₄	1	6	yes	—
19	C₂×C₄×C₁₇₉	C₄⋊C₄	1	6	yes	—
20	C₂×C₄×C₁₇₉	C₂×C₈	1	6	yes	—
21	C₂×C₄×C₁₇₉	M₁₆	1	6	yes	—
22	C₂×C₄×C₁₇₉	C₂×D₄	1	3	yes	—
23	C₂×C₄×C₁₇₉	C₂×Q₈	1	3	yes	—
24	C₈×C₁₇₉	—	4	4	no	—
25	C₂²×C₁₇₉	C₂×C₄⋊C₄	1	3	yes	—
26	C₂²×C₁₇₉	C₂²×C₈	1	1	yes	characteristic
27	C₂²×C₁₇₉	C₂×M₁₆	1	3	yes	—
28	C₄×C₁₇₉	—	2	6	no	—
29	C₄×C₁₇₉	C₄⋊C₈	1	12	yes	complemented
30	C₄×C₁₇₉	#127	1	1	yes	characteristic
31	C₄×C₁₇₉	C₄⋊Q₈	1	3	yes	—
32	C₂×C₁₇₉	#384	1	1	yes	characteristic
33	C₂×C₁₇₉	C₂×C₄⋊C₈	1	3	yes	—
34	C₂×C₁₇₉	#423	1	3	yes	—
35	C₁₇₉	#1842	1	1	yes	characteristic, direct product factor, Sylow
36	#1842	C₁₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×C₄⋊C₈	C₂×C₁₇₉	1	6	yes	—
38	C₄³	C₂×C₁₇₉	1	1	yes	characteristic
39	C₂²×C₈	C₂²×C₁₇₉	1	4	yes	—
40	C₂×C₄²	C₄×C₁₇₉	1	3	yes	—
41	C₂×C₄²	C₄×C₁₇₉	1	1	yes	characteristic
42	C₂×C₄²	C₂²×C₁₇₉	1	3	yes	—
43	C₄⋊C₈	—	2	12	no	—
44	C₂²×C₄	C₂×C₄×C₁₇₉	1	3	yes	—
45	C₂²×C₄	C₂×C₄×C₁₇₉	1	3	yes	—
46	C₂²×C₄	C₂³×C₁₇₉	1	1	yes	characteristic
47	C₂×C₈	—	2	12	no	—
48	C₄²	—	2	6	no	—
49	C₄²	C₈×C₁₇₉	1	4	yes	complemented
50	C₄²	D₄×C₁₇₉	1	6	yes	—
51	C₄²	Q₈×C₁₇₉	1	6	yes	—
52	C₂³	C₂²×C₄×C₁₇₉	1	1	yes	characteristic
53	C₂×C₄	—	2	6	no	—
54	C₂×C₄	C₄⋊C₄×C₁₇₉	1	6	yes	—
55	C₂×C₄	C₄⋊C₄×C₁₇₉	1	6	yes	—
56	C₂×C₄	C₂×C₈×C₁₇₉	1	6	yes	—
57	C₂×C₄	M₁₆×C₁₇₉	1	6	yes	—
58	C₂×C₄	C₂×D₄×C₁₇₉	1	3	yes	—
59	C₂×C₄	C₂×Q₈×C₁₇₉	1	3	yes	—
60	C₈	—	4	4	no	—
61	C₂²	C₂×C₄⋊C₄×C₁₇₉	1	3	yes	—
62	C₂²	C₂²×C₈×C₁₇₉	1	1	yes	characteristic
63	C₂²	C₂×M₁₆×C₁₇₉	1	3	yes	—
64	C₄	—	2	6	no	—
65	C₄	C₄⋊C₈×C₁₇₉	1	12	yes	complemented
66	C₄	#127×C₁₇₉	1	1	yes	characteristic
67	C₄	C₄⋊Q₈×C₁₇₉	1	3	yes	—
68	C₂	#384×C₁₇₉	1	1	yes	characteristic
69	C₂	C₂×C₄⋊C₈×C₁₇₉	1	3	yes	—
70	C₂	#423×C₁₇₉	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₇₉	C₂³
commutator	C₂²	C₂²×C₈×C₁₇₉
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇₉
socle, prime radical	C₂³×C₁₇₉	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇₉ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₄²×C₁₇₉	C₈	semidirect
29. C₄×C₁₇₉	C₄⋊C₈	semidirect
35. C₁₇₉	#1842	direct (N × H)
36. #1842	C₁₇₉	direct (N × H)
49. C₄²	C₈×C₁₇₉	semidirect
65. C₄	C₄⋊C₈×C₁₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₈×C₁₇₉	2
C₄³×C₁₇₉	2
#1842	179

Subgroups — #1842×C179 #37505064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1842×C₁₇₉ #37505064