Subgroups — C₂×#16813540 #20298577

Order 7232.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₂₂₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#14268631	C₂	1	1	yes	maximal, characteristic
3	#16813540	C₂	1	4	yes	maximal, direct product factor
4	C₂×M₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₂₆	—	2	1	no	—
6	C₂×Dic₂₂₆	—	2	1	no	—
7	C₂×Dic₂₂₆	—	2	1	no	—
8	C₂×Dic₂₂₆	—	2	1	no	—
9	C₂×Dic₂₂₆	C₄	1	2	yes	—
10	C₂×Dic₂₂₆	C₂²	1	2	yes	—
11	C₂²×Dic₁₁₃	C₄	1	2	yes	—
12	#14268631	—	2	1	no	—
13	#14268631	C₂²	1	2	yes	—
14	C₂×#11744751	—	2	1	no	—
15	C₂²×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
16	M₁₆×C₁₁₃	—	2	1	no	—
17	M₁₆×C₁₁₃	C₂²	1	2	yes	—
18	C₂×C₈×C₁₁₃	—	2	1	no	—
19	C₂³×C₁₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
22	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
23	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
24	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
25	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
26	C₂×Dic₁₁₃	—	2	2	no	—
27	C₂×Dic₁₁₃	—	2	2	no	—
28	C₂×Dic₁₁₃	C₂×C₄	1	4	yes	—
29	Dic₂₂₆	—	2	2	no	—
30	Dic₂₂₆	—	2	2	no	—
31	Dic₂₂₆	—	2	2	no	—
32	Dic₂₂₆	—	2	2	no	—
33	C₈×C₁₁₃	—	2	2	no	—
34	#11744751	—	2	2	no	—
35	C₂²×C₁₁₃	—	2	2	no	—
36	C₂²×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
37	C₂²×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
38	C₂²×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
39	C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
40	C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
41	C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
42	C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
43	Dic₁₁₃	—	2	4	no	—
44	C₂×C₁₁₃	—	2	1	no	—
45	C₂×C₁₁₃	—	2	1	no	—
46	C₂×C₁₁₃	#101	1	2	yes	complemented
47	C₂×C₁₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
48	C₁₁₃	C₂×#101	1	1	yes	characteristic, complemented, Sylow
49	C₂×#101	—	113	1	no	maximal, Sylow
50	C₂²×Q₈	—	113	1	no	—
51	C₂×M₁₆	—	113	1	no	—
52	C₂×M₁₆	D₁₁₃	1	1	yes	characteristic
53	#101	—	113	4	no	—
54	C₂×Q₈	—	113	2	no	—
55	C₂×Q₈	—	113	2	no	—
56	C₂×Q₈	—	226	1	no	—
57	C₂×Q₈	—	226	1	no	—
58	C₂×Q₈	—	226	1	no	—
59	C₂×Q₈	—	226	1	no	—
60	C₂²×C₄	—	113	2	no	—
61	C₂²×C₄	C₂×D₁₁₃	1	1	yes	characteristic
62	M₁₆	—	2	1	no	—
63	M₁₆	—	113	2	no	—
64	M₁₆	—	226	1	no	—
65	M₁₆	C₂×D₁₁₃	1	2	yes	—
66	C₂×C₈	—	2	1	no	—
67	C₂×C₈	—	226	1	no	—
68	C₂³	C₄×D₁₁₃	1	1	yes	characteristic
69	Q₈	—	226	2	no	—
70	Q₈	—	226	2	no	—
71	Q₈	—	226	2	no	—
72	Q₈	—	226	2	no	—
73	C₂×C₄	—	113	4	no	—
74	C₂×C₄	—	226	2	no	—
75	C₂×C₄	—	226	2	no	—
76	C₂×C₄	C₄×D₁₁₃	1	1	yes	characteristic
77	C₂×C₄	D₄₅₂	1	1	yes	characteristic
78	C₂×C₄	D₄₅₂	1	1	yes	characteristic
79	C₂×C₄	C₂²⋊D₁₁₃	1	1	yes	characteristic
80	C₂×C₄	C₂²⋊D₁₁₃	1	1	yes	characteristic
81	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
82	C₈	—	2	2	no	—
83	C₈	—	226	2	no	—
84	C₂²	—	2	2	no	—
85	C₂²	#14268624	1	1	yes	characteristic
86	C₂²	#14268624	1	1	yes	characteristic
87	C₂²	C₂×C₄×D₁₁₃	1	1	yes	characteristic
88	C₄	—	226	4	no	—
89	C₄	#14268624	1	1	yes	characteristic
90	C₄	#14268624	1	1	yes	characteristic
91	C₄	C₂×C₂²⋊D₁₁₃	1	1	yes	characteristic
92	C₄	C₂×D₄₅₂	1	1	yes	characteristic
93	C₂	—	2	1	no	—
94	C₂	—	2	1	no	—
95	C₂	#16813540	1	2	yes	direct product factor
96	C₂	C₂×#14268624	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14268624
commutator	C₂²×C₁₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₁₃
Fitting	C₂×M₁₆×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₂²⋊C₄
hypercenter	C₂×M₁₆	D₁₁₃
hypocenter	C₁₁₃	C₂×#101
LCS	G ▷ C₂²×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. #16813540	C₂	direct (N × H)
46. C₂×C₁₁₃	#101	semidirect
48. C₁₁₃	C₂×#101	semidirect
95. C₂	#16813540	direct (N × H)

Subgroups — C2×#16813540 #20298577

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16813540 #20298577