Subgroups — #28378966

Order 13952.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812766	C₂	1	3	yes	maximal
2	C₂×C₄⋊#11724786	C₂	1	3	yes	maximal
3	#20294871	C₂	1	1	yes	maximal, characteristic
4	C₂²×#11724786	C₂²	1	3	yes	—
5	C₂²×#11724786	C₂²	1	1	yes	characteristic
6	#16812766	—	2	6	no	—
7	C₄⋊#11724786	—	2	6	no	—
8	C₂×C₄×Dic₁₀₉	C₂²	1	3	yes	—
9	#16812606	C₄	1	3	yes	—
10	#95×C₁₀₉	C₄	1	1	yes	characteristic
11	C₂×#11724786	—	2	6	no	—
12	C₂×#11724786	—	2	3	no	—
13	C₂×#11724786	—	2	3	no	—
14	C₂²×Dic₁₀₉	C₂×C₄	1	3	yes	—
15	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
16	C₄×Dic₁₀₉	D₄	1	6	yes	—
17	C₄×Dic₁₀₉	Q₈	1	6	yes	—
18	C₂²×C₄×C₁₀₉	C₂×C₄	1	3	yes	—
19	C₂³×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
20	C₂×C₄×C₁₀₉	—	2	6	no	—
21	C₂×C₄×C₁₀₉	C₄⋊C₄	1	6	yes	—
22	C₂×Dic₁₀₉	—	2	3	no	—
23	C₂×Dic₁₀₉	—	2	3	no	—
24	C₂×Dic₁₀₉	C₄⋊C₄	1	6	yes	—
25	C₂×Dic₁₀₉	C₂×D₄	1	3	yes	—
26	C₂×Dic₁₀₉	C₂×Q₈	1	3	yes	—
27	#11724786	—	4	3	no	—
28	#11724786	—	4	1	no	—
29	C₂²×C₁₀₉	C₂×C₄⋊C₄	1	3	yes	—
30	C₂²×C₁₀₉	#131	1	3	yes	—
31	C₂²×C₁₀₉	#131	1	1	yes	characteristic
32	C₄×C₁₀₉	—	2	6	no	—
33	Dic₁₀₉	—	2	6	no	—
34	Dic₁₀₉	#127	1	1	yes	characteristic
35	Dic₁₀₉	C₄⋊Q₈	1	3	yes	—
36	C₂×C₁₀₉	#384	1	1	yes	characteristic
37	C₂×C₁₀₉	#424	1	3	yes	—
38	C₂×C₁₀₉	#424	1	3	yes	—
39	#1843	—	109	1	no	maximal, Sylow
40	C₁₀₉	#1843	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₄⋊C₈	—	109	3	no	—
42	C₂×C₄⋊C₈	—	109	3	no	—
43	#376	—	109	1	no	—
44	C₂²×C₈	—	109	3	no	—
45	C₂²×C₈	—	109	1	no	—
46	C₂×C₄²	—	109	3	no	—
47	C₄⋊C₈	—	218	6	no	—
48	C₄⋊C₈	—	218	6	no	—
49	#95	—	109	3	no	—
50	#95	#89137	1	1	yes	characteristic
51	C₂²×C₄	—	109	1	no	—
52	C₂²×C₄	—	109	3	no	—
53	C₂²×C₄	C₂×#89137	1	3	yes	—
54	C₂×C₈	—	218	6	no	—
55	C₂×C₈	—	218	3	no	—
56	C₂×C₈	—	218	3	no	—
57	C₄²	—	109	6	no	—
58	C₄²	—	109	6	no	—
59	C₂³	C₂²×#89137	1	1	yes	characteristic
60	C₂×C₄	—	2	6	no	—
61	C₂×C₄	—	109	3	no	—
62	C₂×C₄	—	109	3	no	—
63	C₂×C₄	—	109	6	no	—
64	C₂×C₄	—	218	3	no	—
65	C₂×C₄	—	218	3	no	—
66	C₂×C₄	C₄⋊#89137	1	6	yes	—
67	C₈	—	436	3	no	—
68	C₈	—	436	1	no	—
69	C₂²	C₂×C₄⋊#89137	1	3	yes	—
70	C₂²	#16812786	1	3	yes	—
71	C₂²	#16812787	1	1	yes	characteristic
72	C₄	—	2	6	no	—
73	C₄	—	109	1	no	—
74	C₄	—	109	3	no	—
75	C₄	—	218	6	no	—
76	C₂	#20295972	1	1	yes	characteristic
77	C₂	#20296032	1	3	yes	—
78	C₂	#20296033	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#89137
commutator, socle, prime radical	C₂³×C₁₀₉	C₂²×C₄
Fitting	#95×C₁₀₉	C₄
cosocle	C₂²×Dic₁₀₉	C₂³
hypercenter	#95	#89137
hypocenter	C₁₀₉	#1843
LCS	G ▷ C₂³×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
40. C₁₀₉	#1843	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16812766	2
C₂×C₄⋊#11724786	2
#20294871	2
#1843	109