Subgroups — C₂×#20299692 #28407729

Order 14464.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14268659	C₂	1	2	yes	maximal
2	#20299692	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×#11744753	C₂	1	1	yes	maximal, characteristic
4	C₂×#14268659	C₄	1	8	yes	complemented
5	C₂×#14268659	C₂²	1	4	yes	—
6	C₂²×#11744753	C₄	1	1	yes	characteristic
7	C₂²×#11744753	C₂²	1	1	yes	characteristic
8	C₄×#11744753	C₄	1	2	yes	—
9	C₄×#11744753	C₂²	1	2	yes	—
10	C₂×C₄×Dic₁₁₃	C₄	1	1	yes	characteristic
11	#14268659	C₂×C₄	1	8	yes	complemented
12	C₂×#11744753	C₈	1	4	yes	—
13	C₂×#11744753	C₂×C₄	1	1	yes	characteristic
14	C₂×#11744753	C₂×C₄	1	4	yes	—
15	C₂×#11744753	C₂×C₄	1	2	yes	—
16	C₂×#11744753	C₂³	1	1	yes	characteristic
17	C₂²×Dic₁₁₃	C₈	1	1	yes	characteristic
18	C₂²×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₁₁₃	C₈	1	2	yes	—
20	C₄×Dic₁₁₃	C₂×C₄	1	2	yes	—
21	C₂²×C₄×C₁₁₃	C₈	1	1	yes	characteristic
22	C₂³×C₁₁₃	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₁₁₃	—	2	2	no	—
24	C₂×C₄×C₁₁₃	C₂×C₈	1	2	yes	—
25	C₂×Dic₁₁₃	—	2	2	no	—
26	C₂×Dic₁₁₃	C₄²	1	2	yes	—
27	C₂×Dic₁₁₃	C₂×C₈	1	2	yes	—
28	C₂×Dic₁₁₃	C₂×C₈	1	1	yes	characteristic
29	C₂×Dic₁₁₃	C₂×C₈	1	2	yes	—
30	C₂×Dic₁₁₃	C₂²×C₄	1	1	yes	characteristic
31	#11744753	C₄²	1	2	yes	—
32	#11744753	C₂×C₈	1	4	yes	—
33	#11744753	C₂²×C₄	1	2	yes	—
34	C₂²×C₁₁₃	C₄×C₈	1	2	yes	—
35	C₂²×C₁₁₃	M₃₂	1	2	yes	—
36	C₂²×C₁₁₃	M₃₂	1	2	yes	—
37	C₂²×C₁₁₃	C₂²×C₈	1	1	yes	characteristic
38	C₄×C₁₁₃	—	2	2	no	—
39	Dic₁₁₃	—	2	2	no	—
40	Dic₁₁₃	C₄×C₈	1	2	yes	—
41	Dic₁₁₃	C₂×C₄²	1	1	yes	characteristic
42	Dic₁₁₃	C₂²×C₈	1	1	yes	characteristic
43	C₂×C₁₁₃	#346	1	4	yes	complemented
44	C₂×C₁₁₃	C₂×C₄×C₈	1	1	yes	characteristic
45	C₂×C₁₁₃	C₂×M₃₂	1	1	yes	characteristic
46	C₂×C₁₁₃	C₂×M₃₂	1	1	yes	characteristic
47	C₂×#346	—	113	1	no	maximal, Sylow
48	C₁₁₃	C₂×#346	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₁₆	—	113	2	no	—
50	C₂×C₄×C₈	—	113	1	no	—
51	#346	—	113	4	no	—
52	C₂²×C₈	—	113	1	no	—
53	C₂²×C₈	—	113	1	no	—
54	C₂×C₄²	—	113	1	no	—
55	C₂×C₁₆	—	113	4	no	—
56	C₂×C₁₆	—	113	8	no	—
57	C₄×C₈	—	113	2	no	—
58	C₄×C₈	—	113	2	no	—
59	C₂²×C₄	—	113	1	no	—
60	C₂²×C₄	—	113	1	no	—
61	C₂²×C₄	#11744762	1	1	yes	characteristic
62	C₂×C₈	—	113	1	no	—
63	C₂×C₈	—	113	1	no	—
64	C₂×C₈	—	113	2	no	—
65	C₂×C₈	—	113	4	no	—
66	C₂×C₈	—	113	4	no	—
67	C₄²	—	113	2	no	—
68	C₄²	—	113	2	no	—
69	C₁₆	—	113	8	no	—
70	C₂³	C₂×#11744762	1	1	yes	characteristic
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	113	2	no	—
73	C₂×C₄	—	113	2	no	—
74	C₂×C₄	—	113	1	no	—
75	C₂×C₄	—	113	1	no	—
76	C₂×C₄	—	113	2	no	—
77	C₂×C₄	—	226	2	no	—
78	C₂×C₄	C₂×#11744762	1	2	yes	—
79	C₈	—	113	2	no	—
80	C₈	—	113	2	no	—
81	C₈	—	113	4	no	—
82	C₂²	C₄×#11744762	1	2	yes	—
83	C₂²	#16813718	1	2	yes	—
84	C₂²	#16813719	1	2	yes	—
85	C₂²	C₂²×#11744762	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	113	1	no	—
88	C₄	—	113	1	no	—
89	C₄	—	113	2	no	—
90	C₄	—	226	2	no	—
91	C₂	#20299692	1	4	yes	direct product factor
92	C₂	C₂×C₄×#11744762	1	1	yes	characteristic
93	C₂	C₂×#16813718	1	1	yes	characteristic
94	C₂	C₂×#16813719	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#11744762
commutator	C₂×C₁₁₃	C₂×C₄×C₈
Frattini	C₂²	C₂²×#11744762
Fitting	C₂²×C₄×C₁₁₃	C₈
socle, prime radical	C₂³×C₁₁₃	C₂×C₈
cosocle	C₂×#11744753	C₂³
hypercenter	C₂²×C₄	#11744762
hypocenter	C₁₁₃	C₂×#346
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. #20299692	C₂	direct (N × H)
4. C₂×#14268659	C₄	semidirect
11. #14268659	C₂×C₄	semidirect
43. C₂×C₁₁₃	#346	semidirect
48. C₁₁₃	C₂×#346	semidirect
91. C₂	#20299692	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×#14268659	2
#20299692	2
C₂×C₄×#11744753	2
C₂×#346	113

Subgroups — C2×#20299692 #28407729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20299692 #28407729