Subgroups — C₂×#20296084 #28379996

Order 13952.

368 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20296084	C₂	1	8	yes	maximal, direct product factor
2	C₂×#16812773	C₂	1	3	yes	maximal, complemented
3	C₂²×#13182032	C₂	1	3	yes	maximal, complemented
4	C₂×#16812706	C₂	1	1	yes	maximal, characteristic
5	#16812773	C₂²	1	12	yes	complemented
6	C₂×#13182032	C₂²	1	1	yes	characteristic
7	C₂×#13182032	C₂²	1	3	yes	—
8	C₂×#13182032	C₂²	1	12	yes	complemented
9	#16812706	C₄	1	4	yes	—
10	#16812706	C₂²	1	4	yes	—
11	C₂×#13182013	C₄	1	3	yes	—
12	C₂²×#11724784	C₂²	1	3	yes	—
13	C₂×#41×C₁₀₉	C₄	1	1	yes	characteristic
14	#13182032	C₂³	1	2	yes	—
15	#13182032	C₂³	1	6	yes	—
16	#13182013	C₂×C₄	1	12	yes	—
17	C₂×#11724784	C₂×C₄	1	3	yes	—
18	C₂×#11724784	C₂×C₄	1	6	yes	—
19	C₂×#11724784	C₂³	1	1	yes	characteristic
20	C₂×#11724784	C₂³	1	6	yes	—
21	#41×C₁₀₉	C₈	1	4	yes	—
22	#41×C₁₀₉	C₂×C₄	1	4	yes	—
23	C₂×Q₈×C₁₀₉	C₈	1	1	yes	characteristic
24	C₂×D₄×C₁₀₉	C₈	1	3	yes	—
25	C₂²×C₄×C₁₀₉	C₂×C₄	1	3	yes	—
26	C₂³×C₁₀₉	C₂×C₈	1	3	yes	—
27	Q₈×C₁₀₉	C₂×C₈	1	4	yes	—
28	D₄×C₁₀₉	C₂×C₈	1	12	yes	—
29	C₂×C₄×C₁₀₉	C₂×C₈	1	3	yes	—
30	C₂×C₄×C₁₀₉	C₂×C₈	1	6	yes	—
31	C₂×C₄×C₁₀₉	C₂²×C₄	1	6	yes	—
32	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
33	#11724784	C₂²×C₄	1	1	yes	characteristic
34	#11724784	C₂²×C₄	1	6	yes	—
35	#11724784	C₂⁴	1	1	yes	characteristic
36	C₂²×C₁₀₉	—	2	6	no	—
37	C₂²×C₁₀₉	C₂²×C₈	1	6	yes	—
38	C₂²×C₁₀₉	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₁₀₉	C₂²×C₈	1	1	yes	characteristic
40	C₄×C₁₀₉	C₂²×C₈	1	6	yes	—
41	C₄×C₁₀₉	C₂³×C₄	1	1	yes	characteristic
42	C₂×C₁₀₉	—	2	6	no	—
43	C₂×C₁₀₉	#504	1	2	yes	complemented
44	C₂×C₁₀₉	C₂³×C₈	1	1	yes	characteristic
45	C₂×#504	—	109	1	no	maximal, Sylow
46	C₁₀₉	C₂×#504	1	1	yes	characteristic, complemented, Sylow
47	C₂×#131	—	109	1	no	—
48	#504	—	109	8	no	—
49	C₂×M₃₂	—	109	3	no	—
50	C₂²×C₁₆	—	109	3	no	—
51	C₂×#41	#89137	1	1	yes	characteristic
52	#131	—	109	4	no	—
53	#131	—	109	4	no	—
54	C₂×M₁₆	—	109	3	no	—
55	C₂²×C₈	—	109	3	no	—
56	M₃₂	—	109	12	no	—
57	C₂×C₁₆	—	109	1	no	—
58	C₂×C₁₆	—	109	3	no	—
59	C₂×C₁₆	—	109	12	no	—
60	#41	#11724786	1	4	yes	—
61	#41	C₂×#89137	1	4	yes	—
62	C₂×Q₈	#11724786	1	1	yes	characteristic
63	C₂×D₄	#11724786	1	3	yes	—
64	C₂²×C₄	C₂×#89137	1	3	yes	—
65	M₁₆	—	109	12	no	—
66	C₂×C₈	—	109	6	no	—
67	C₂×C₈	—	109	6	no	—
68	C₂×C₈	—	109	3	no	—
69	C₂×C₈	—	109	1	no	—
70	C₁₆	—	109	2	no	—
71	C₁₆	—	109	6	no	—
72	C₂³	C₂×#11724786	1	3	yes	—
73	Q₈	C₂×#11724786	1	4	yes	—
74	D₄	C₂×#11724786	1	12	yes	—
75	C₂×C₄	C₂×#11724786	1	3	yes	—
76	C₂×C₄	C₂×#11724786	1	6	yes	—
77	C₂×C₄	C₂²×#89137	1	6	yes	—
78	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
79	C₈	—	109	1	no	—
80	C₈	—	109	1	no	—
81	C₈	—	109	6	no	—
82	C₂²	—	2	6	no	—
83	C₂²	C₂²×#11724786	1	6	yes	—
84	C₂²	C₂²×#11724786	1	1	yes	characteristic
85	C₄	C₂²×#11724786	1	1	yes	characteristic
86	C₄	C₂²×#11724786	1	6	yes	—
87	C₄	C₂³×#89137	1	1	yes	characteristic
88	C₂	—	2	6	no	—
89	C₂	#20296084	1	2	yes	direct product factor
90	C₂	C₂³×#11724786	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#89137
commutator	C₂×C₁₀₉	C₂³×C₈
Frattini	C₄	C₂³×#89137
Fitting, prime radical	C₂×#41×C₁₀₉	C₄
socle	C₂²×C₁₀₉	C₂²×C₈
cosocle	#11724784	C₂⁴
hypercenter	C₂×#41	#89137
hypocenter	C₁₀₉	C₂×#504
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. #20296084	C₂	direct (N × H)
2. C₂×#16812773	C₂	semidirect
3. C₂²×#13182032	C₂	semidirect
5. #16812773	C₂²	semidirect
8. C₂×#13182032	C₂²	semidirect
43. C₂×C₁₀₉	#504	semidirect
46. C₁₀₉	C₂×#504	semidirect
89. C₂	#20296084	direct (N × H)

Maximal subgroups

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

subgroup	index
#20296084	2
C₂×#16812773	2
C₂²×#13182032	2
C₂×#16812706	2
C₂×#504	109

Subgroups — C2×#20296084 #28379996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20296084 #28379996