Subgroups — C₂×#20295915 #28379234

Order 13952.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13182032	C₂	1	2	yes	maximal
2	#20295915	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#13182032	C₄	1	8	yes	complemented
5	C₂×#13182032	C₂²	1	4	yes	—
6	C₂²×#11724784	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₁₀₉	C₄	1	1	yes	characteristic
8	C₈×Dic₁₀₉	C₄	1	2	yes	—
9	C₈×Dic₁₀₉	C₂²	1	2	yes	—
10	C₂²×C₈×C₁₀₉	C₄	1	1	yes	characteristic
11	#13182032	C₂×C₄	1	8	yes	complemented
12	C₂²×Dic₁₀₉	C₈	1	2	yes	—
13	C₂×#11724784	C₂×C₄	1	1	yes	characteristic
14	C₂×#11724784	C₂×C₄	1	4	yes	—
15	C₂×#11724784	C₂³	1	1	yes	characteristic
16	C₄×Dic₁₀₉	C₈	1	2	yes	—
17	C₄×Dic₁₀₉	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₀₉	C₈	1	4	yes	—
20	C₂×C₈×C₁₀₉	C₂×C₄	1	2	yes	—
21	C₂³×C₁₀₉	C₂×C₈	1	1	yes	characteristic
22	C₂×C₄×C₁₀₉	C₄²	1	2	yes	—
23	C₂×C₄×C₁₀₉	C₂×C₈	1	2	yes	—
24	C₂×C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
25	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
26	C₂×Dic₁₀₉	—	2	4	no	—
27	C₂×Dic₁₀₉	C₂×C₈	1	4	yes	—
28	C₈×C₁₀₉	C₂×C₈	1	4	yes	—
29	#11724784	C₄²	1	2	yes	—
30	#11724784	C₂²×C₄	1	2	yes	—
31	C₂²×C₁₀₉	C₄×C₈	1	2	yes	—
32	C₂²×C₁₀₉	M₃₂	1	4	yes	—
33	C₂²×C₁₀₉	C₂²×C₈	1	1	yes	characteristic
34	C₄×C₁₀₉	C₄×C₈	1	2	yes	—
35	C₄×C₁₀₉	C₂×C₄²	1	1	yes	characteristic
36	C₄×C₁₀₉	C₂²×C₈	1	1	yes	characteristic
37	Dic₁₀₉	—	2	4	no	—
38	C₂×C₁₀₉	#346	1	4	yes	complemented
39	C₂×C₁₀₉	C₂×C₄×C₈	1	1	yes	characteristic
40	C₂×C₁₀₉	C₂×M₃₂	1	2	yes	—
41	C₂×#346	—	109	1	no	maximal, Sylow
42	C₁₀₉	C₂×#346	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₁₆	—	109	2	no	—
44	C₂×C₄×C₈	—	109	1	no	—
45	#346	—	109	4	no	—
46	C₂²×C₈	—	109	1	no	—
47	C₂²×C₈	#89137	1	1	yes	characteristic
48	C₂×C₄²	—	109	1	no	—
49	C₂×C₁₆	—	109	4	no	—
50	C₂×C₁₆	—	109	8	no	—
51	C₄×C₈	—	109	2	no	—
52	C₄×C₈	—	109	2	no	—
53	C₂²×C₄	—	109	2	no	—
54	C₂²×C₄	C₂×#89137	1	1	yes	characteristic
55	C₂×C₈	—	109	4	no	—
56	C₂×C₈	—	109	1	no	—
57	C₂×C₈	—	109	1	no	—
58	C₂×C₈	#11724786	1	4	yes	—
59	C₂×C₈	C₂×#89137	1	2	yes	—
60	C₄²	—	109	2	no	—
61	C₄²	—	109	2	no	—
62	C₁₆	—	109	8	no	—
63	C₂³	D₁₀₉⋊C₈	1	1	yes	characteristic
64	C₂×C₄	—	109	4	no	—
65	C₂×C₄	—	218	4	no	—
66	C₂×C₄	C₄×#89137	1	2	yes	—
67	C₂×C₄	C₂×#11724786	1	2	yes	—
68	C₂×C₄	D₁₀₉⋊C₈	1	1	yes	characteristic
69	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
70	C₈	—	109	2	no	—
71	C₈	—	109	2	no	—
72	C₈	C₂×#11724786	1	4	yes	—
73	C₂²	C₄×#11724786	1	2	yes	—
74	C₂²	#16812774	1	4	yes	—
75	C₂²	C₂×D₁₀₉⋊C₈	1	1	yes	characteristic
76	C₄	—	218	4	no	—
77	C₄	C₄×#11724786	1	2	yes	—
78	C₄	C₂×C₄×#89137	1	1	yes	characteristic
79	C₄	C₂²×#11724786	1	1	yes	characteristic
80	C₂	#20295915	1	4	yes	direct product factor
81	C₂	C₂×C₄×#11724786	1	1	yes	characteristic
82	C₂	C₂×#16812774	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×#89137
commutator	C₂×C₁₀₉	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#89137
Fitting	C₂²×C₈×C₁₀₉	C₄
socle, prime radical	C₂³×C₁₀₉	C₂×C₈
cosocle	C₂×#11724784	C₂³
hypercenter	C₂²×C₈	#89137
hypocenter	C₁₀₉	C₂×#346
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #20295915	C₂	direct (N × H)
4. C₂×#13182032	C₄	semidirect
11. #13182032	C₂×C₄	semidirect
38. C₂×C₁₀₉	#346	semidirect
42. C₁₀₉	C₂×#346	semidirect
80. C₂	#20295915	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×#13182032	2
#20295915	2
C₂×C₈×Dic₁₀₉	2
C₂×#346	109

Subgroups — C2×#20295915 #28379234

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20295915 #28379234