Subgroups — C₂²⋊#19153866 #37548834

Order 23168.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19153866	C₂	1	2	yes	maximal, complemented
2	C₂²×#15668424	C₂	1	1	yes	maximal, characteristic
3	#19153866	—	2	2	no	—
4	C₂×#15668424	—	2	2	no	—
5	C₂×#15668424	C₄	1	1	yes	characteristic
6	C₂×#15668424	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₈₁	C₄	1	1	yes	characteristic
8	#15668424	—	2	1	no	—
9	#15668424	D₄	1	2	yes	—
10	C₂²×C₄×C₁₈₁	C₈	1	1	yes	characteristic
11	C₂×C₈×C₁₈₁	—	2	1	no	—
12	C₂×C₈×C₁₈₁	—	2	1	no	—
13	C₂×C₈×C₁₈₁	C₈	1	1	yes	characteristic
14	C₂×C₈×C₁₈₁	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₁₈₁	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₁₈₁	—	2	1	no	—
17	C₂×C₄×C₁₈₁	—	2	1	no	—
18	C₂×C₄×C₁₈₁	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₁₈₁	C₂×C₈	1	1	yes	characteristic
20	C₈×C₁₈₁	—	2	1	no	—
21	C₈×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₁₈₁	M₁₆	1	1	yes	characteristic
23	C₂²×C₁₈₁	—	2	1	no	—
24	C₂²×C₁₈₁	—	2	1	no	—
25	C₂²×C₁₈₁	C₃₂	1	2	yes	complemented
26	C₂²×C₁₈₁	C₂×C₁₆	1	1	yes	characteristic
27	C₄×C₁₈₁	—	2	1	no	—
28	C₄×C₁₈₁	C₂²⋊C₈	1	1	yes	characteristic
29	C₄×C₁₈₁	M₃₂	1	1	yes	characteristic
30	C₂×C₁₈₁	—	2	2	no	—
31	C₂×C₁₈₁	C₂²⋊C₁₆	1	1	yes	characteristic
32	C₂×C₁₈₁	C₂×C₃₂	1	1	yes	characteristic
33	C₂×C₁₈₁	M₆₄	1	1	yes	characteristic
34	C₁₈₁	C₂²⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
35	C₂²⋊C₃₂	—	181	1	no	maximal, Sylow
36	C₂²×C₁₆	—	181	1	no	—
37	C₂×C₃₂	—	181	2	no	—
38	C₂²×C₈	#10624382	1	1	yes	characteristic
39	C₂×C₁₆	—	362	2	no	—
40	C₂×C₁₆	—	181	1	no	—
41	C₂×C₁₆	—	181	1	no	—
42	C₃₂	—	362	2	no	—
43	C₂²×C₄	#13089685	1	1	yes	characteristic
44	C₂×C₈	—	2	1	no	—
45	C₂×C₈	—	2	1	no	—
46	C₂×C₈	#13089685	1	1	yes	characteristic
47	C₂×C₈	C₂×#10624382	1	1	yes	characteristic
48	C₁₆	—	362	1	no	—
49	C₁₆	—	181	2	no	—
50	C₂³	#15668452	1	1	yes	characteristic
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	#15668452	1	1	yes	characteristic
54	C₂×C₄	C₂×#13089685	1	1	yes	characteristic
55	C₈	—	2	1	no	—
56	C₈	C₂²⋊#10624382	1	1	yes	characteristic
57	C₈	#15668458	1	1	yes	characteristic
58	C₂²	—	2	1	no	—
59	C₂²	—	2	1	no	—
60	C₂²	#19153866	1	2	yes	complemented
61	C₂²	C₂×#15668452	1	1	yes	characteristic
62	C₄	—	2	1	no	—
63	C₄	C₂²⋊#13089685	1	1	yes	characteristic
64	C₄	#19153890	1	1	yes	characteristic
65	C₂	—	2	2	no	—
66	C₂	C₂²⋊#15668452	1	1	yes	characteristic
67	C₂	C₂×#19153866	1	1	yes	characteristic
68	C₂	#26042211	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×#10624382
commutator	C₂×C₁₈₁	C₂×C₃₂
Fitting	C₂²×C₈×C₁₈₁	C₄
socle	C₂²×C₁₈₁	C₂×C₁₆
prime radical	C₂³×C₁₈₁	C₁₆
cosocle	C₂×#15668424	C₂²
hypercenter	C₂²×C₈	#10624382
hypocenter	C₁₈₁	C₂²⋊C₃₂
LCS	G ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#19153866	C₂	semidirect
25. C₂²×C₁₈₁	C₃₂	semidirect
34. C₁₈₁	C₂²⋊C₃₂	semidirect
60. C₂²	#19153866	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19153866	2
C₂²×#15668424	2
C₂²⋊C₃₂	181

Subgroups — C22⋊#19153866 #37548834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#19153866 #37548834