Subgroups — C₂×#20299720 #28407826

Order 14464.

368 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299720	C₂	1	8	yes	maximal, direct product factor
2	C₂×#16813719	C₂	1	3	yes	maximal, complemented
3	C₂×#16813717	C₂	1	3	yes	maximal, complemented
4	C₂×#16813710	C₂	1	1	yes	maximal, characteristic
5	#16813719	C₂²	1	12	yes	complemented
6	#16813717	C₂²	1	12	yes	complemented
7	C₂×#14268659	C₂²	1	1	yes	characteristic
8	C₂×#14268659	C₂²	1	3	yes	—
9	#16813710	C₄	1	4	yes	—
10	#16813710	C₂²	1	4	yes	—
11	C₂×#14268657	C₄	1	3	yes	—
12	C₂×#14268655	C₂²	1	3	yes	—
13	C₂×#14268648	C₄	1	1	yes	characteristic
14	#14268659	C₂³	1	2	yes	—
15	#14268659	C₂³	1	6	yes	—
16	#14268657	C₂×C₄	1	12	yes	—
17	#14268655	C₂×C₄	1	6	yes	—
18	#14268655	C₂³	1	6	yes	—
19	C₂×#11744753	C₂×C₄	1	3	yes	—
20	C₂×#11744753	C₂³	1	1	yes	characteristic
21	#14268648	C₈	1	4	yes	—
22	#14268648	C₂×C₄	1	4	yes	—
23	C₂×D₄₅₂	C₈	1	3	yes	—
24	C₂×C₄×D₁₁₃	C₂×C₄	1	3	yes	—
25	C₂×Q₈×C₁₁₃	C₈	1	1	yes	characteristic
26	C₂²×D₁₁₃	C₂×C₈	1	3	yes	—
27	Q₈×C₁₁₃	C₂×C₈	1	4	yes	—
28	C₂×C₄×C₁₁₃	C₂×C₈	1	3	yes	—
29	C₂×Dic₁₁₃	C₂²×C₄	1	1	yes	characteristic
30	D₄₅₂	C₂×C₈	1	12	yes	—
31	C₄×D₁₁₃	C₂×C₈	1	6	yes	—
32	C₄×D₁₁₃	C₂²×C₄	1	6	yes	—
33	#11744753	C₂²×C₄	1	6	yes	—
34	#11744753	C₂²×C₄	1	1	yes	characteristic
35	#11744753	C₂⁴	1	1	yes	characteristic
36	C₂²×C₁₁₃	C₂²×C₈	1	1	yes	characteristic
37	C₂×D₁₁₃	—	2	6	no	—
38	C₂×D₁₁₃	C₂²×C₈	1	6	yes	—
39	C₄×C₁₁₃	C₂²×C₈	1	6	yes	—
40	Dic₁₁₃	C₂²×C₈	1	1	yes	characteristic
41	Dic₁₁₃	C₂³×C₄	1	1	yes	characteristic
42	C₂×C₁₁₃	#504	1	2	yes	complemented
43	C₂×C₁₁₃	C₂³×C₈	1	1	yes	characteristic
44	D₁₁₃	—	2	6	no	—
45	C₂×#504	—	113	1	no	maximal, Sylow
46	C₁₁₃	C₂×#504	1	1	yes	characteristic, complemented, Sylow
47	C₂×#131	—	113	1	no	—
48	#504	—	113	8	no	—
49	C₂×M₃₂	—	113	3	no	—
50	C₂²×C₁₆	—	113	3	no	—
51	C₂×#41	—	113	1	no	—
52	#131	—	113	4	no	—
53	#131	—	113	4	no	—
54	C₂×M₁₆	—	113	3	no	—
55	C₂²×C₈	—	113	3	no	—
56	M₃₂	—	113	12	no	—
57	C₂×C₁₆	—	113	1	no	—
58	C₂×C₁₆	—	113	3	no	—
59	C₂×C₁₆	—	113	12	no	—
60	#41	—	113	4	no	—
61	#41	—	113	4	no	—
62	C₂×Q₈	#11744762	1	1	yes	characteristic
63	C₂×D₄	—	113	3	no	—
64	C₂²×C₄	—	113	3	no	—
65	M₁₆	—	113	12	no	—
66	C₂×C₈	—	113	1	no	—
67	C₂×C₈	—	113	6	no	—
68	C₂×C₈	—	113	3	no	—
69	C₂×C₈	—	113	6	no	—
70	C₁₆	—	113	2	no	—
71	C₁₆	—	113	6	no	—
72	C₂³	—	113	3	no	—
73	Q₈	C₂×#11744762	1	4	yes	—
74	D₄	—	113	12	no	—
75	C₂×C₄	—	113	1	no	—
76	C₂×C₄	—	113	6	no	—
77	C₂×C₄	—	113	6	no	—
78	C₂×C₄	C₂×#11744762	1	3	yes	—
79	C₈	—	113	1	no	—
80	C₈	—	113	1	no	—
81	C₈	—	113	6	no	—
82	C₂²	—	113	6	no	—
83	C₂²	—	226	6	no	—
84	C₂²	C₂²×#11744762	1	1	yes	characteristic
85	C₄	—	113	1	no	—
86	C₄	—	113	1	no	—
87	C₄	C₂²×#11744762	1	6	yes	—
88	C₂	—	226	6	no	—
89	C₂	#20299720	1	2	yes	direct product factor
90	C₂	C₂³×#11744762	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#11744762
commutator	C₂×C₁₁₃	C₂³×C₈
Frattini	C₂	C₂³×#11744762
Fitting	C₂×Q₈×C₁₁₃	C₈
socle	C₂²×C₁₁₃	C₂²×C₈
prime radical	C₂×#14268648	C₄
cosocle	#11744753	C₂⁴
hypercenter	C₂×Q₈	#11744762
hypocenter	C₁₁₃	C₂×#504
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. #20299720	C₂	direct (N × H)
2. C₂×#16813719	C₂	semidirect
3. C₂×#16813717	C₂	semidirect
5. #16813719	C₂²	semidirect
6. #16813717	C₂²	semidirect
42. C₂×C₁₁₃	#504	semidirect
46. C₁₁₃	C₂×#504	semidirect
89. C₂	#20299720	direct (N × H)

Maximal subgroups

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

subgroup	index
#20299720	2
C₂×#16813719	2
C₂×#16813717	2
C₂×#16813710	2
C₂×#504	113

Subgroups — C2×#20299720 #28407826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20299720 #28407826