Subgroups — C₂×#100×C₃₁₁ #34091237

Order 19904.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×C₃₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×C₃₁₁	C₂	1	2	yes	maximal, complemented
3	#100×C₃₁₁	C₂	1	4	yes	maximal, direct product factor
4	C₂⁴×C₃₁₁	C₄	1	2	yes	—
5	C₂×D₄×C₃₁₁	—	2	2	no	—
6	C₂×D₄×C₃₁₁	—	2	2	no	—
7	C₂×D₄×C₃₁₁	C₄	1	2	yes	—
8	C₂×D₄×C₃₁₁	C₂²	1	2	yes	—
9	C₂²×C₄×C₃₁₁	C₂²	1	1	yes	characteristic
10	M₁₆×C₃₁₁	—	2	2	no	—
11	M₁₆×C₃₁₁	C₂²	1	4	yes	complemented
12	C₂×C₈×C₃₁₁	—	2	2	no	—
13	C₂³×C₃₁₁	—	2	2	no	—
14	C₂³×C₃₁₁	—	2	2	no	—
15	C₂³×C₃₁₁	—	4	4	no	—
16	C₂³×C₃₁₁	C₂×C₄	1	1	yes	characteristic
17	C₂³×C₃₁₁	C₂×C₄	1	4	yes	—
18	D₄×C₃₁₁	—	2	4	no	—
19	D₄×C₃₁₁	—	2	4	no	—
20	C₂×C₄×C₃₁₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₃₁₁	D₄	1	2	yes	—
22	C₂×C₄×C₃₁₁	D₄	1	2	yes	—
23	C₂×C₄×C₃₁₁	C₂³	1	1	yes	characteristic
24	C₈×C₃₁₁	—	2	4	no	—
25	C₂²×C₃₁₁	—	2	2	no	—
26	C₂²×C₃₁₁	—	2	4	no	—
27	C₂²×C₃₁₁	—	4	4	no	—
28	C₂²×C₃₁₁	—	4	4	no	—
29	C₂²×C₃₁₁	—	4	4	no	—
30	C₂²×C₃₁₁	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₃₁₁	C₂²⋊C₄	1	1	yes	characteristic
32	C₂²×C₃₁₁	C₂²×C₄	1	1	yes	characteristic
33	C₄×C₃₁₁	C₂²⋊C₄	1	2	yes	—
34	C₄×C₃₁₁	C₂×D₄	1	2	yes	—
35	C₂×C₃₁₁	—	2	1	no	—
36	C₂×C₃₁₁	—	2	1	no	—
37	C₂×C₃₁₁	—	4	4	no	—
38	C₂×C₃₁₁	#100	1	2	yes	direct product factor
39	C₂×C₃₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₃₁₁	C₂×#100	1	1	yes	characteristic, direct product factor, Sylow
41	C₂×#100	C₃₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×D₄	C₂×C₃₁₁	1	1	yes	characteristic
43	C₂×M₁₆	C₂×C₃₁₁	1	2	yes	complemented
44	#100	C₂×C₃₁₁	1	4	yes	direct product factor
45	C₂⁴	C₄×C₃₁₁	1	2	yes	—
46	C₂×D₄	—	2	2	no	—
47	C₂×D₄	—	2	2	no	—
48	C₂×D₄	C₄×C₃₁₁	1	2	yes	—
49	C₂×D₄	C₂²×C₃₁₁	1	2	yes	—
50	C₂²×C₄	C₂²×C₃₁₁	1	1	yes	characteristic
51	M₁₆	—	2	2	no	—
52	M₁₆	C₂²×C₃₁₁	1	4	yes	complemented
53	C₂×C₈	—	2	2	no	—
54	C₂³	—	2	2	no	—
55	C₂³	—	2	2	no	—
56	C₂³	—	4	4	no	—
57	C₂³	C₂×C₄×C₃₁₁	1	1	yes	characteristic
58	C₂³	C₂×C₄×C₃₁₁	1	4	yes	—
59	D₄	—	2	4	no	—
60	D₄	—	2	4	no	—
61	C₂×C₄	C₂×C₄×C₃₁₁	1	1	yes	characteristic
62	C₂×C₄	D₄×C₃₁₁	1	2	yes	—
63	C₂×C₄	D₄×C₃₁₁	1	2	yes	—
64	C₂×C₄	C₂³×C₃₁₁	1	1	yes	characteristic
65	C₈	—	2	4	no	—
66	C₂²	—	2	2	no	—
67	C₂²	—	2	4	no	—
68	C₂²	—	4	4	no	—
69	C₂²	—	4	4	no	—
70	C₂²	—	4	4	no	—
71	C₂²	C₂²⋊C₄×C₃₁₁	1	1	yes	characteristic
72	C₂²	C₂²⋊C₄×C₃₁₁	1	1	yes	characteristic
73	C₂²	C₂²×C₄×C₃₁₁	1	1	yes	characteristic
74	C₄	C₂²⋊C₄×C₃₁₁	1	2	yes	—
75	C₄	C₂×D₄×C₃₁₁	1	2	yes	—
76	C₂	—	2	1	no	—
77	C₂	—	2	1	no	—
78	C₂	—	4	4	no	—
79	C₂	#100×C₃₁₁	1	2	yes	direct product factor
80	C₂	C₂×C₂²⋊C₄×C₃₁₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁₁	C₂²⋊C₄
commutator	C₂²	C₂²×C₄×C₃₁₁
Frattini, cosocle	C₂×C₄	C₂³×C₃₁₁
prime radical	C₂²×D₄×C₃₁₁	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁₁ ◁ C₂²×C₄×C₃₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×M₁₆×C₃₁₁	C₂	semidirect
3. #100×C₃₁₁	C₂	direct (N × H)
11. M₁₆×C₃₁₁	C₂²	semidirect
38. C₂×C₃₁₁	#100	direct (N × H)
40. C₃₁₁	C₂×#100	direct (N × H)
41. C₂×#100	C₃₁₁	direct (N × H)
43. C₂×M₁₆	C₂×C₃₁₁	semidirect
44. #100	C₂×C₃₁₁	direct (N × H)
52. M₁₆	C₂²×C₃₁₁	semidirect
79. C₂	#100×C₃₁₁	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×D₄×C₃₁₁	2
C₂×M₁₆×C₃₁₁	2
#100×C₃₁₁	2
C₂×#100	311

Subgroups — C2×#100×C311 #34091237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#100×C₃₁₁ #34091237