Subgroups — C₂×#20266018 #27186325

Order 12928.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#11717581	C₂	1	2	yes	maximal
2	#20266018	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×#11717581	C₄	1	4	yes	—
5	C₄×#11717581	C₄	1	4	yes	—
6	C₄×#11717581	C₂²	1	4	yes	—
7	C₂²×#11717579	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
9	C₈×Dic₁₀₁	C₄	1	2	yes	—
10	C₈×Dic₁₀₁	C₂²	1	2	yes	—
11	C₂²×C₈×C₁₀₁	C₄	1	1	yes	characteristic
12	C₂×#11717581	—	2	8	no	—
13	C₂×#11717581	C₂×C₄	1	8	yes	—
14	C₂²×Dic₁₀₁	C₂×C₄	1	2	yes	—
15	C₂×#11717579	C₈	1	4	yes	complemented
16	C₂×#11717579	C₂×C₄	1	2	yes	—
17	C₄×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₁₀₁	C₂×C₄	1	2	yes	—
19	C₄×Dic₁₀₁	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₀₁	C₈	1	4	yes	complemented
22	C₂×C₈×C₁₀₁	C₂×C₄	1	2	yes	—
23	C₂³×C₁₀₁	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₁₀₁	C₄²	1	1	yes	characteristic
25	C₂×C₄×C₁₀₁	C₂×C₈	1	2	yes	—
26	C₂×C₄×C₁₀₁	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₁₀₁	C₄²	1	2	yes	—
29	C₂×Dic₁₀₁	M₁₆	1	8	yes	—
30	C₂×Dic₁₀₁	C₂²×C₄	1	2	yes	—
31	#11717581	—	2	8	no	—
32	C₈×C₁₀₁	C₂×C₈	1	4	yes	complemented
33	#11717579	C₂×C₈	1	4	yes	complemented
34	C₂²×C₁₀₁	C₄×C₈	1	2	yes	—
35	C₂²×C₁₀₁	#97	1	4	yes	—
36	C₂²×C₁₀₁	C₂×C₄²	1	1	yes	characteristic
37	C₄×C₁₀₁	C₄×C₈	1	2	yes	—
38	C₄×C₁₀₁	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₁₀₁	C₂²×C₈	1	1	yes	characteristic
40	Dic₁₀₁	#97	1	4	yes	—
41	Dic₁₀₁	C₂×M₁₆	1	4	yes	—
42	C₂×C₁₀₁	#322	1	4	yes	complemented
43	C₂×C₁₀₁	C₂×C₄×C₈	1	1	yes	characteristic
44	C₂×C₁₀₁	C₂×#97	1	2	yes	—
45	C₂×#322	—	101	1	no	maximal, Sylow
46	C₁₀₁	C₂×#322	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₄×C₈	—	101	2	no	—
48	C₂×C₄×C₈	—	101	1	no	—
49	#322	—	101	4	no	—
50	C₂²×C₈	—	101	1	no	—
51	C₂²×C₈	—	101	4	no	—
52	C₂²×C₈	#87938	1	1	yes	characteristic
53	C₂×C₄²	—	101	1	no	—
54	C₄×C₈	—	101	4	no	—
55	C₄×C₈	—	101	4	no	—
56	C₄×C₈	—	101	2	no	—
57	C₄×C₈	—	101	2	no	—
58	C₂²×C₄	—	101	2	no	—
59	C₂²×C₄	C₂×#87938	1	1	yes	characteristic
60	C₂×C₈	—	101	4	no	—
61	C₂×C₈	—	101	2	no	—
62	C₂×C₈	—	101	8	no	—
63	C₂×C₈	—	202	8	no	—
64	C₂×C₈	#11717581	1	4	yes	complemented
65	C₂×C₈	C₂×#87938	1	2	yes	—
66	C₄²	—	101	2	no	—
67	C₄²	—	101	1	no	—
68	C₄²	—	101	1	no	—
69	C₂³	C₄×#87938	1	1	yes	characteristic
70	C₂×C₄	—	101	8	no	—
71	C₂×C₄	—	101	2	no	—
72	C₂×C₄	—	101	2	no	—
73	C₂×C₄	C₄×#87938	1	1	yes	characteristic
74	C₂×C₄	C₂×#11717581	1	2	yes	—
75	C₂×C₄	D₁₀₁⋊C₈	1	2	yes	—
76	C₂×C₄	C₂²×#87938	1	1	yes	characteristic
77	C₈	—	101	4	no	—
78	C₈	—	202	8	no	—
79	C₈	C₂×#11717581	1	4	yes	complemented
80	C₂²	C₄×#11717581	1	2	yes	—
81	C₂²	#15692309	1	4	yes	—
82	C₂²	C₂×C₄×#87938	1	1	yes	characteristic
83	C₄	—	101	4	no	—
84	C₄	—	101	4	no	—
85	C₄	C₄×#11717581	1	2	yes	—
86	C₄	C₂²×#11717581	1	1	yes	characteristic
87	C₄	C₂×D₁₀₁⋊C₈	1	1	yes	characteristic
88	C₂	#20266018	1	4	yes	direct product factor
89	C₂	C₂×C₄×#11717581	1	1	yes	characteristic
90	C₂	C₂×#15692309	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×#87938
commutator	C₂×C₁₀₁	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#87938
Fitting	C₂²×C₈×C₁₀₁	C₄
socle, prime radical	C₂³×C₁₀₁	C₄²
cosocle	C₄×Dic₁₀₁	C₂³
hypercenter	C₂²×C₈	#87938
hypocenter	C₁₀₁	C₂×#322
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #20266018	C₂	direct (N × H)
15. C₂×#11717579	C₈	semidirect
21. C₂×C₈×C₁₀₁	C₈	semidirect
32. C₈×C₁₀₁	C₂×C₈	semidirect
33. #11717579	C₂×C₈	semidirect
42. C₂×C₁₀₁	#322	semidirect
46. C₁₀₁	C₂×#322	semidirect
64. C₂×C₈	#11717581	semidirect
79. C₈	C₂×#11717581	semidirect
88. C₂	#20266018	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#11717581	2
#20266018	2
C₂×C₈×Dic₁₀₁	2
C₂×#322	101

Subgroups — C2×#20266018 #27186325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20266018 #27186325