Subgroups — #28378009

Order 13952.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295923	C₂	1	1	yes	maximal, characteristic
2	#20295895	C₂	1	1	yes	maximal, characteristic
3	#20295285	C₂	1	1	yes	maximal, characteristic
4	D₁₀₉⋊M₁₆	—	2	1	no	—
5	#16812773	—	2	1	no	—
6	C₂×Dic₄₃₆	C₄	1	1	yes	characteristic
7	C₂×#13182012	C₂²	1	1	yes	characteristic
8	#16812679	—	2	1	no	—
9	#16812622	—	2	1	no	—
10	#106×C₁₀₉	C₄	1	1	yes	characteristic
11	#13182039	—	4	1	no	—
12	#13182038	—	4	1	no	—
13	D₁₀₉⋊C₈	—	2	2	no	—
14	#13182032	—	4	1	no	—
15	C₂×Dic₂₁₈	—	2	1	no	—
16	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
17	Dic₄₃₆	—	4	1	no	—
18	#13182012	—	4	1	no	—
19	C₂×#11724784	D₄	1	1	yes	characteristic
20	C₄⋊Dic₁₀₉	—	4	1	no	—
21	#13182006	—	4	1	no	—
22	C₂×C₈×C₁₀₉	C₂×C₄	1	1	yes	characteristic
23	C₄⋊C₄×C₁₀₉	—	2	1	no	—
24	C₂²×D₁₀₉	SD₁₆	1	1	yes	characteristic
25	C₂×C₄×C₁₀₉	—	4	1	no	—
26	C₂×C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₁₀₉	—	4	1	no	—
28	C₂×Dic₁₀₉	D₈	1	1	yes	characteristic
29	C₄×D₁₀₉	—	2	1	no	—
30	C₄×D₁₀₉	—	2	1	no	—
31	Dic₂₁₈	—	4	1	no	—
32	Dic₂₁₈	—	4	1	no	—
33	#11724786	—	4	2	no	—
34	C₈×C₁₀₉	—	2	1	no	—
35	#11724784	—	2	1	no	—
36	C₂²×C₁₀₉	#102	1	1	yes	characteristic
37	C₂×D₁₀₉	—	2	1	no	—
38	C₂×D₁₀₉	—	4	1	no	—
39	C₄×C₁₀₉	—	8	1	no	—
40	C₄×C₁₀₉	#99	1	1	yes	characteristic
41	C₄×C₁₀₉	#104	1	1	yes	characteristic
42	Dic₁₀₉	—	2	1	no	—
43	Dic₁₀₉	—	8	1	no	—
44	C₂×C₁₀₉	—	2	1	no	—
45	C₂×C₁₀₉	#327	1	1	yes	characteristic
46	D₁₀₉	—	4	1	no	—
47	#1342	—	109	1	no	maximal, Sylow
48	C₁₀₉	#1342	1	1	yes	characteristic, complemented, Sylow
49	#470	—	109	1	no	—
50	#349	—	109	1	no	—
51	#338	—	109	1	no	—
52	C₂×Q₁₆	—	109	1	no	—
53	C₂×M₁₆	—	109	1	no	—
54	C₂×M₁₆	—	218	1	no	—
55	C₂²⋊Q₈	—	218	1	no	—
56	M₃₂	—	218	1	no	—
57	#106	#89137	1	1	yes	characteristic
58	#103	—	218	1	no	—
59	C₂×Q₈	—	218	1	no	—
60	C₂²×C₄	—	109	1	no	—
61	Q₁₆	—	436	1	no	—
62	M₁₆	—	436	1	no	—
63	M₁₆	—	436	1	no	—
64	M₁₆	—	436	1	no	—
65	C₂×C₈	—	109	1	no	—
66	C₂×C₈	—	218	2	no	—
67	C₂×C₈	C₂×#89137	1	1	yes	characteristic
68	C₄⋊C₄	—	2	1	no	—
69	C₄⋊C₄	—	436	1	no	—
70	C₂²⋊C₄	—	436	1	no	—
71	C₁₆	—	436	1	no	—
72	C₂³	—	109	1	no	—
73	Q₈	—	436	1	no	—
74	Q₈	—	436	1	no	—
75	C₂×C₄	—	4	1	no	—
76	C₂×C₄	—	109	1	no	—
77	C₂×C₄	—	436	1	no	—
78	C₂×C₄	—	218	1	no	—
79	C₂×C₄	—	218	1	no	—
80	C₂×C₄	C₂²⋊#89137	1	1	yes	characteristic
81	C₈	—	2	1	no	—
82	C₈	—	436	2	no	—
83	C₈	—	218	1	no	—
84	C₂²	—	436	1	no	—
85	C₂²	—	218	1	no	—
86	C₂²	#16812761	1	1	yes	characteristic
87	C₄	—	8	1	no	—
88	C₄	—	872	1	no	—
89	C₄	—	218	1	no	—
90	C₄	#16812758	1	1	yes	characteristic
91	C₄	#16812764	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	436	1	no	—
94	C₂	#20295878	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20295878
commutator	C₂×C₈×C₁₀₉	C₂×C₄
Frattini	C₂×C₈	C₂×#89137
Fitting	#106×C₁₀₉	C₄
socle	C₂×C₁₀₉	#327
prime radical	C₂²×D₁₀₉	SD₁₆
cosocle	C₂×#13182012	C₂²
hypercenter	#106	#89137
hypocenter	C₁₀₉	#1342
LCS	G ▷ C₂×C₈×C₁₀₉ ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #106

Complements

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

N	H ≅ G/N	type
48. C₁₀₉	#1342	semidirect

Maximal subgroups

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

subgroup	index
#20295923	2
#20295895	2
#20295285	2
#1342	109