Subgroups — #28377993

Order 13952.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295915	C₂	1	1	yes	maximal, characteristic
2	#20295887	C₂	1	1	yes	maximal, characteristic
3	#20295120	C₂	1	1	yes	maximal, characteristic
4	C₂×#13182032	—	2	1	no	—
5	C₄⋊#11724786	—	2	1	no	—
6	C₂×Dic₄₃₆	C₄	1	1	yes	characteristic
7	#16812664	—	2	1	no	—
8	#16812622	—	2	1	no	—
9	C₈×Dic₁₀₉	C₂²	1	1	yes	characteristic
10	#107×C₁₀₉	C₄	1	1	yes	characteristic
11	C₂×#11724786	—	4	1	no	—
12	#13182032	—	2	2	no	—
13	C₂×Dic₂₁₈	—	2	1	no	—
14	Dic₄₃₆	—	2	1	no	—
15	Dic₄₃₆	C₈	1	2	yes	complemented
16	C₂×#11724784	D₄	1	1	yes	characteristic
17	#13182008	—	4	1	no	—
18	C₄×Dic₁₀₉	—	4	1	no	—
19	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
21	C₄⋊C₄×C₁₀₉	—	2	1	no	—
22	C₂×C₄×C₁₀₉	—	4	1	no	—
23	C₂×C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×Dic₁₀₉	—	4	1	no	—
25	C₂×Dic₁₀₉	D₈	1	1	yes	characteristic
26	C₂×Dic₁₀₉	SD₁₆	1	1	yes	characteristic
27	Dic₂₁₈	—	2	2	no	—
28	Dic₂₁₈	—	4	1	no	—
29	#11724786	—	8	1	no	—
30	C₈×C₁₀₉	C₂×C₈	1	1	yes	characteristic
31	C₈×C₁₀₉	M₁₆	1	1	yes	characteristic
32	#11724784	—	2	1	no	—
33	C₂²×C₁₀₉	#102	1	1	yes	characteristic
34	C₄×C₁₀₉	—	8	1	no	—
35	C₄×C₁₀₉	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₁₀₉	#104	1	1	yes	characteristic
37	Dic₁₀₉	—	2	1	no	—
38	Dic₁₀₉	—	2	1	no	—
39	Dic₁₀₉	—	4	2	no	—
40	C₂×C₁₀₉	D₄⋊C₈	1	1	yes	characteristic
41	C₂×C₁₀₉	#360	1	1	yes	characteristic
42	C₂×C₁₀₉	#362	1	1	yes	characteristic
43	#1334	—	109	1	no	maximal, Sylow
44	C₁₀₉	#1334	1	1	yes	characteristic, complemented, Sylow
45	C₄×Q₁₆	—	109	1	no	—
46	#346	—	109	1	no	—
47	#334	—	109	1	no	—
48	C₂×Q₁₆	—	109	1	no	—
49	C₄×Q₈	—	218	1	no	—
50	C₂×C₁₆	—	218	1	no	—
51	#107	#89137	1	1	yes	characteristic
52	C₄⋊C₈	—	218	1	no	—
53	#103	—	218	1	no	—
54	C₄×C₈	—	109	1	no	—
55	C₂×Q₈	—	218	1	no	—
56	Q₁₆	—	109	2	no	—
57	Q₁₆	—	218	1	no	—
58	C₂×C₈	—	109	1	no	—
59	C₂×C₈	—	436	1	no	—
60	C₂×C₈	C₂×#89137	1	1	yes	characteristic
61	C₄⋊C₄	—	2	1	no	—
62	C₄⋊C₄	—	436	1	no	—
63	C₄²	—	109	1	no	—
64	C₄²	—	436	1	no	—
65	C₁₆	—	218	2	no	—
66	Q₈	—	436	1	no	—
67	Q₈	—	218	2	no	—
68	C₂×C₄	—	4	1	no	—
69	C₂×C₄	—	109	1	no	—
70	C₂×C₄	—	109	1	no	—
71	C₂×C₄	—	436	1	no	—
72	C₂×C₄	C₂²⋊#89137	1	1	yes	characteristic
73	C₈	—	872	1	no	—
74	C₈	—	218	1	no	—
75	C₈	D₁₀₉⋊C₈	1	1	yes	characteristic
76	C₈	#13182039	1	1	yes	characteristic
77	C₂²	#16812761	1	1	yes	characteristic
78	C₄	—	8	1	no	—
79	C₄	—	436	2	no	—
80	C₄	—	218	1	no	—
81	C₄	—	218	1	no	—
82	C₄	#16812756	1	1	yes	characteristic
83	C₄	#16812764	1	1	yes	characteristic
84	C₂	#20295874	1	1	yes	characteristic
85	C₂	#20295942	1	1	yes	characteristic
86	C₂	#20295945	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16812761
commutator	C₈×C₁₀₉	C₂×C₈
Frattini	C₂×C₈	C₂×#89137
Fitting	#107×C₁₀₉	C₄
socle, prime radical	C₂²×C₁₀₉	#102
cosocle	C₈×Dic₁₀₉	C₂²
hypercenter	#107	#89137
hypocenter	C₁₀₉	#1334
LCS	G ▷ C₈×C₁₀₉ ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
15. Dic₄₃₆	C₈	semidirect
44. C₁₀₉	#1334	semidirect

Maximal subgroups

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

subgroup	index
#20295915	2
#20295887	2
#20295120	2
#1334	109