Subgroups — #462×C₂₇₇ #31799596

Order 17728.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×C₂₇₇	C₂	1	2	yes	maximal
2	C₄⋊Q₈×C₂₇₇	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₈×C₂₇₇	C₂	1	1	yes	maximal, characteristic
4	C₄⋊C₈×C₂₇₇	C₂	1	1	yes	maximal, characteristic
5	#103×C₂₇₇	C₂	1	2	yes	maximal
6	C₂×Q₈×C₂₇₇	C₂²	1	2	yes	—
7	C₂×Q₈×C₂₇₇	C₂²	1	1	yes	characteristic
8	Q₁₆×C₂₇₇	—	2	4	no	—
9	C₂×C₈×C₂₇₇	C₂²	1	2	yes	—
10	C₄⋊C₄×C₂₇₇	—	2	1	no	—
11	C₄⋊C₄×C₂₇₇	—	2	1	no	—
12	C₄⋊C₄×C₂₇₇	—	2	1	no	—
13	C₄⋊C₄×C₂₇₇	C₂²	1	1	yes	characteristic
14	C₄²×C₂₇₇	—	2	1	no	—
15	C₄²×C₂₇₇	C₂²	1	1	yes	characteristic
16	Q₈×C₂₇₇	—	2	1	no	—
17	Q₈×C₂₇₇	—	2	2	no	—
18	Q₈×C₂₇₇	—	2	2	no	—
19	Q₈×C₂₇₇	D₄	1	2	yes	—
20	C₂×C₄×C₂₇₇	—	2	1	no	—
21	C₂×C₄×C₂₇₇	—	2	1	no	—
22	C₂×C₄×C₂₇₇	—	2	2	no	—
23	C₂×C₄×C₂₇₇	D₄	1	1	yes	characteristic
24	C₂×C₄×C₂₇₇	D₄	1	1	yes	characteristic
25	C₂×C₄×C₂₇₇	C₂³	1	1	yes	characteristic
26	C₈×C₂₇₇	—	2	2	no	—
27	C₂²×C₂₇₇	C₂×D₄	1	1	yes	characteristic
28	C₄×C₂₇₇	—	2	2	no	—
29	C₄×C₂₇₇	—	2	1	no	—
30	C₄×C₂₇₇	—	4	2	no	—
31	C₄×C₂₇₇	—	4	1	no	—
32	C₄×C₂₇₇	Q₁₆	1	2	yes	complemented
33	C₄×C₂₇₇	C₂×D₄	1	1	yes	characteristic
34	C₄×C₂₇₇	#41	1	1	yes	characteristic
35	C₂×C₂₇₇	#121	1	1	yes	characteristic
36	C₂×C₂₇₇	C₂×Q₁₆	1	1	yes	characteristic
37	C₂×C₂₇₇	#137	1	1	yes	characteristic
38	C₂₇₇	#462	1	1	yes	characteristic, direct product factor, Sylow
39	#462	C₂₇₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂×Q₁₆	C₂×C₂₇₇	1	2	yes	—
41	C₄⋊Q₈	C₂×C₂₇₇	1	1	yes	characteristic
42	C₄×Q₈	C₂×C₂₇₇	1	1	yes	characteristic
43	C₄⋊C₈	C₂×C₂₇₇	1	1	yes	characteristic
44	#103	C₂×C₂₇₇	1	2	yes	—
45	C₂×Q₈	C₂²×C₂₇₇	1	2	yes	—
46	C₂×Q₈	C₂²×C₂₇₇	1	1	yes	characteristic
47	Q₁₆	—	2	4	no	—
48	C₂×C₈	C₂²×C₂₇₇	1	2	yes	—
49	C₄⋊C₄	—	2	1	no	—
50	C₄⋊C₄	—	2	1	no	—
51	C₄⋊C₄	—	2	1	no	—
52	C₄⋊C₄	C₂²×C₂₇₇	1	1	yes	characteristic
53	C₄²	—	2	1	no	—
54	C₄²	C₂²×C₂₇₇	1	1	yes	characteristic
55	Q₈	—	2	1	no	—
56	Q₈	—	2	2	no	—
57	Q₈	—	2	2	no	—
58	Q₈	D₄×C₂₇₇	1	2	yes	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	D₄×C₂₇₇	1	1	yes	characteristic
63	C₂×C₄	D₄×C₂₇₇	1	1	yes	characteristic
64	C₂×C₄	C₂³×C₂₇₇	1	1	yes	characteristic
65	C₈	—	2	2	no	—
66	C₂²	C₂×D₄×C₂₇₇	1	1	yes	characteristic
67	C₄	—	2	2	no	—
68	C₄	—	2	1	no	—
69	C₄	—	4	2	no	—
70	C₄	—	4	1	no	—
71	C₄	Q₁₆×C₂₇₇	1	2	yes	complemented
72	C₄	C₂×D₄×C₂₇₇	1	1	yes	characteristic
73	C₄	#41×C₂₇₇	1	1	yes	characteristic
74	C₂	#121×C₂₇₇	1	1	yes	characteristic
75	C₂	C₂×Q₁₆×C₂₇₇	1	1	yes	characteristic
76	C₂	#137×C₂₇₇	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₇₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₂₇₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₇₇ ◁ C₄²×C₂₇₇ ◁ G

Complements

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

N	H ≅ G/N	type
32. C₄×C₂₇₇	Q₁₆	semidirect
38. C₂₇₇	#462	direct (N × H)
39. #462	C₂₇₇	direct (N × H)
71. C₄	Q₁₆×C₂₇₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×C₂₇₇	2
C₄⋊Q₈×C₂₇₇	2
C₄×Q₈×C₂₇₇	2
C₄⋊C₈×C₂₇₇	2
#103×C₂₇₇	2
#462	277

Subgroups — #462×C277 #31799596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #462×C₂₇₇ #31799596