Subgroups — #342×C₄₈₇ #44528524

Order 31168.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊C₄×C₄₈₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊C₄×C₄₈₇	C₂	1	2	yes	maximal
3	C₂⁴×C₄₈₇	C₂²	1	1	yes	characteristic
4	C₂²×C₄×C₄₈₇	—	2	2	no	—
5	C₂²×C₄×C₄₈₇	C₄	1	2	yes	complemented
6	C₂²⋊C₄×C₄₈₇	—	2	2	no	—
7	C₂²⋊C₄×C₄₈₇	—	2	2	no	—
8	C₂²⋊C₄×C₄₈₇	C₄	1	4	yes	complemented
9	C₂³×C₄₈₇	—	4	2	no	—
10	C₂³×C₄₈₇	C₂×C₄	1	1	yes	characteristic
11	C₂³×C₄₈₇	C₂×C₄	1	2	yes	—
12	C₂³×C₄₈₇	D₄	1	2	yes	—
13	C₂³×C₄₈₇	D₄	1	1	yes	characteristic
14	C₂³×C₄₈₇	Q₈	1	1	yes	characteristic
15	C₂×C₄×C₄₈₇	—	2	4	no	—
16	C₂×C₄×C₄₈₇	—	2	2	no	—
17	C₂×C₄×C₄₈₇	—	4	4	no	—
18	C₂×C₄×C₄₈₇	—	4	2	no	—
19	C₂²×C₄₈₇	—	2	2	no	—
20	C₂²×C₄₈₇	—	2	4	no	—
21	C₂²×C₄₈₇	—	4	2	no	—
22	C₂²×C₄₈₇	—	4	1	no	—
23	C₂²×C₄₈₇	—	4	1	no	—
24	C₂²×C₄₈₇	C₄²	1	1	yes	characteristic
25	C₂²×C₄₈₇	C₂²⋊C₄	1	2	yes	—
26	C₂²×C₄₈₇	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₄₈₇	C₄⋊C₄	1	1	yes	characteristic
28	C₂²×C₄₈₇	C₄⋊C₄	1	2	yes	—
29	C₄×C₄₈₇	—	4	4	no	—
30	C₄×C₄₈₇	—	4	2	no	—
31	C₂×C₄₈₇	—	2	2	no	—
32	C₂×C₄₈₇	—	2	1	no	—
33	C₂×C₄₈₇	—	2	1	no	—
34	C₂×C₄₈₇	—	2	2	no	—
35	C₂×C₄₈₇	#95	1	1	yes	characteristic
36	C₂×C₄₈₇	#99	1	2	yes	—
37	C₄₈₇	#342	1	1	yes	characteristic, direct product factor, Sylow
38	#342	C₄₈₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂×C₂²⋊C₄	C₂×C₄₈₇	1	1	yes	characteristic
40	C₂×C₂²⋊C₄	C₂×C₄₈₇	1	2	yes	—
41	C₂⁴	C₂²×C₄₈₇	1	1	yes	characteristic
42	C₂²×C₄	—	2	2	no	—
43	C₂²×C₄	C₄×C₄₈₇	1	2	yes	complemented
44	C₂²⋊C₄	—	2	2	no	—
45	C₂²⋊C₄	—	2	2	no	—
46	C₂²⋊C₄	C₄×C₄₈₇	1	4	yes	complemented
47	C₂³	—	4	2	no	—
48	C₂³	C₂×C₄×C₄₈₇	1	1	yes	characteristic
49	C₂³	C₂×C₄×C₄₈₇	1	2	yes	—
50	C₂³	D₄×C₄₈₇	1	2	yes	—
51	C₂³	D₄×C₄₈₇	1	1	yes	characteristic
52	C₂³	Q₈×C₄₈₇	1	1	yes	characteristic
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	2	4	no	—
55	C₂×C₄	—	4	4	no	—
56	C₂×C₄	—	4	2	no	—
57	C₂²	—	2	2	no	—
58	C₂²	—	2	4	no	—
59	C₂²	—	4	2	no	—
60	C₂²	—	4	1	no	—
61	C₂²	—	4	1	no	—
62	C₂²	C₄²×C₄₈₇	1	1	yes	characteristic
63	C₂²	C₂²⋊C₄×C₄₈₇	1	2	yes	—
64	C₂²	C₂²⋊C₄×C₄₈₇	1	1	yes	characteristic
65	C₂²	C₄⋊C₄×C₄₈₇	1	1	yes	characteristic
66	C₂²	C₄⋊C₄×C₄₈₇	1	2	yes	—
67	C₄	—	4	4	no	—
68	C₄	—	4	2	no	—
69	C₂	—	2	2	no	—
70	C₂	—	2	1	no	—
71	C₂	—	2	1	no	—
72	C₂	—	2	2	no	—
73	C₂	#95×C₄₈₇	1	1	yes	characteristic
74	C₂	#99×C₄₈₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₈₇	C₂²⋊C₄
commutator	C₂²	C₄²×C₄₈₇
Frattini, cosocle	C₂⁴	C₂²×C₄₈₇
prime radical	C₂⁴×C₄₈₇	C₂²
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₈₇ ◁ C₂⁴×C₄₈₇ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₂²×C₄×C₄₈₇	C₄	semidirect
8. C₂²⋊C₄×C₄₈₇	C₄	semidirect
37. C₄₈₇	#342	direct (N × H)
38. #342	C₄₈₇	direct (N × H)
43. C₂²×C₄	C₄×C₄₈₇	semidirect
46. C₂²⋊C₄	C₄×C₄₈₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂²⋊C₄×C₄₈₇	2
#342	487

Subgroups — #342×C487 #44528524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #342×C₄₈₇ #44528524