Subgroups — #28378047

Order 13952.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295947	C₂	1	1	yes	maximal, characteristic
2	#20295890	C₂	1	1	yes	maximal, characteristic
3	#20295404	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	C₂×#13182019	—	2	1	no	—
8	#16812697	—	2	1	no	—
9	C₈×Dic₁₀₉	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₁₀₉	C₄	1	1	yes	characteristic
11	C₂×#11724786	—	4	1	no	—
12	#13182032	—	4	1	no	—
13	C₂×Dic₂₁₈	—	2	1	no	—
14	Dic₄₃₆	—	4	1	no	—
15	#13182019	—	4	1	no	—
16	#13182019	—	4	1	no	—
17	C₂×#11724784	D₄	1	1	yes	characteristic
18	#13182008	—	4	1	no	—
19	#13182008	—	4	1	no	—
20	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
21	C₂×Q₈×C₁₀₉	—	2	1	no	—
22	Q₁₆×C₁₀₉	—	4	1	no	—
23	C₂×C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
24	Q₈×C₁₀₉	—	4	1	no	—
25	Q₈×C₁₀₉	—	4	1	no	—
26	C₂×C₄×C₁₀₉	—	4	1	no	—
27	C₂×C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×Dic₁₀₉	—	4	1	no	—
29	C₂×Dic₁₀₉	D₈	1	1	yes	characteristic
30	C₂×Dic₁₀₉	SD₁₆	1	1	yes	characteristic
31	Dic₂₁₈	—	4	1	no	—
32	Dic₂₁₈	—	4	1	no	—
33	#11724786	—	8	1	no	—
34	C₈×C₁₀₉	—	2	1	no	—
35	#11724784	D₈	1	1	yes	characteristic
36	#11724784	SD₁₆	1	1	yes	characteristic
37	C₂²×C₁₀₉	#102	1	1	yes	characteristic
38	C₄×C₁₀₉	—	8	1	no	—
39	C₄×C₁₀₉	#100	1	1	yes	characteristic
40	C₄×C₁₀₉	#102	1	1	yes	characteristic
41	Dic₁₀₉	—	2	1	no	—
42	Dic₁₀₉	—	8	1	no	—
43	Dic₁₀₉	SD₃₂	1	1	yes	characteristic
44	Dic₁₀₉	Q₃₂	1	1	yes	characteristic
45	C₂×C₁₀₉	#331	1	1	yes	characteristic
46	C₂×C₁₀₉	#358	1	1	yes	characteristic
47	C₂×C₁₀₉	#362	1	1	yes	characteristic
48	#1362	—	109	1	no	maximal, Sylow
49	C₁₀₉	#1362	1	1	yes	characteristic, complemented, Sylow
50	#494	—	109	1	no	—
51	C₄⋊C₁₆	—	109	1	no	—
52	#335	—	109	1	no	—
53	C₂×Q₁₆	—	109	1	no	—
54	C₂×Q₁₆	—	218	1	no	—
55	C₂×Q₁₆	#89137	1	1	yes	characteristic
56	C₄⋊Q₈	—	218	1	no	—
57	C₂×C₁₆	—	218	1	no	—
58	C₄⋊C₈	—	218	1	no	—
59	C₄×C₈	—	109	1	no	—
60	C₂×Q₈	—	2	1	no	—
61	C₂×Q₈	—	218	1	no	—
62	Q₁₆	—	4	1	no	—
63	Q₁₆	—	436	1	no	—
64	Q₁₆	—	436	1	no	—
65	Q₁₆	—	436	1	no	—
66	C₂×C₈	—	109	1	no	—
67	C₂×C₈	—	436	1	no	—
68	C₂×C₈	C₂×#89137	1	1	yes	characteristic
69	C₄⋊C₄	—	436	1	no	—
70	C₄⋊C₄	—	436	1	no	—
71	C₄²	—	109	1	no	—
72	C₁₆	—	436	1	no	—
73	Q₈	—	4	1	no	—
74	Q₈	—	4	1	no	—
75	Q₈	—	436	1	no	—
76	Q₈	—	436	1	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	—	109	1	no	—
79	C₂×C₄	—	109	1	no	—
80	C₂×C₄	—	436	1	no	—
81	C₂×C₄	C₂²⋊#89137	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	872	1	no	—
84	C₈	—	109	1	no	—
85	C₈	—	109	1	no	—
86	C₂²	#16812761	1	1	yes	characteristic
87	C₄	—	8	1	no	—
88	C₄	—	872	1	no	—
89	C₄	—	109	1	no	—
90	C₄	—	109	1	no	—
91	C₄	—	218	1	no	—
92	C₄	#16812759	1	1	yes	characteristic
93	C₄	#16812761	1	1	yes	characteristic
94	C₂	#20295884	1	1	yes	characteristic
95	C₂	#20295939	1	1	yes	characteristic
96	C₂	#20295945	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16812761
commutator	C₂×C₈×C₁₀₉	C₂×C₄
Frattini	C₂×C₈	C₂×#89137
Fitting	C₂×Q₁₆×C₁₀₉	C₄
socle, prime radical	C₂²×C₁₀₉	#102
cosocle	C₈×Dic₁₀₉	C₂²
hypercenter	C₂×Q₁₆	#89137
hypocenter	C₁₀₉	#1362
LCS	G ▷ C₂×C₈×C₁₀₉ ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
49. C₁₀₉	#1362	semidirect

Maximal subgroups

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

subgroup	index
#20295947	2
#20295890	2
#20295404	2
#1362	109