Subgroups — #28360973

Order 13952.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295052	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊#13182004	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊C₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#13182013	C₄	1	1	yes	characteristic
5	#16812658	C₄	1	1	yes	characteristic
6	C₂×#13182004	—	2	1	no	—
7	#16812628	—	2	1	no	—
8	#16812628	—	2	1	no	—
9	C₂²×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₁₀₉	—	2	1	no	—
11	#13182013	—	4	1	no	—
12	C₂×#11724784	—	2	1	no	—
13	C₄⋊Dic₁₀₉	C₈	1	1	yes	characteristic
14	C₄⋊Dic₁₀₉	C₈	1	1	yes	characteristic
15	C₂²⋊Dic₁₀₉	—	2	1	no	—
16	C₄×Dic₁₀₉	—	2	1	no	—
17	#13182004	—	4	1	no	—
18	C₂²×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₀₉	—	4	1	no	—
20	C₂×C₈×C₁₀₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₀₉	D₄	1	1	yes	characteristic
22	C₁₆×C₁₀₉	—	4	1	no	—
23	C₂³×C₁₀₉	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₁₀₉	—	2	1	no	—
25	C₂×C₄×C₁₀₉	—	2	1	no	—
26	C₂×C₄×C₁₀₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₀₉	C₂×C₈	1	1	yes	characteristic
28	C₂×Dic₁₀₉	—	2	1	no	—
29	C₂×Dic₁₀₉	—	2	1	no	—
30	C₈×C₁₀₉	—	2	1	no	—
31	C₈×C₁₀₉	—	2	1	no	—
32	#11724784	—	4	1	no	—
33	C₂²×C₁₀₉	—	2	1	no	—
34	C₂²×C₁₀₉	—	2	1	no	—
35	C₂²×C₁₀₉	—	2	1	no	—
36	C₂²×C₁₀₉	C₂²⋊C₈	1	1	yes	characteristic
37	C₄×C₁₀₉	—	2	1	no	—
38	C₄×C₁₀₉	#99	1	1	yes	characteristic
39	C₄×C₁₀₉	#101	1	1	yes	characteristic
40	Dic₁₀₉	—	4	1	no	—
41	Dic₁₀₉	—	4	1	no	—
42	C₂×C₁₀₉	—	4	1	no	—
43	C₂×C₁₀₉	#324	1	1	yes	characteristic
44	C₂×C₁₀₉	#350	1	1	yes	characteristic
45	C₂×C₁₀₉	#350	1	1	yes	characteristic
46	#1323	—	109	1	no	maximal, Sylow
47	C₁₀₉	#1323	1	1	yes	characteristic, complemented, Sylow
48	#424	—	109	1	no	—
49	C₂²⋊C₁₆	—	109	1	no	—
50	C₂²⋊C₁₆	D₁₀₉	1	1	yes	characteristic
51	C₂×M₁₆	—	109	1	no	—
52	C₂²×C₈	C₂×D₁₀₉	1	1	yes	characteristic
53	#117	—	109	1	no	—
54	C₂×C₁₆	—	2	1	no	—
55	C₂×C₁₆	—	218	1	no	—
56	C₄⋊C₈	—	218	1	no	—
57	C₄⋊C₈	—	218	1	no	—
58	C₂²×C₄	C₄×D₁₀₉	1	1	yes	characteristic
59	M₁₆	—	436	1	no	—
60	C₂×C₈	—	4	1	no	—
61	C₂×C₈	—	218	1	no	—
62	C₂×C₈	D₄₃₆	1	1	yes	characteristic
63	C₂×C₈	C₂²⋊D₁₀₉	1	1	yes	characteristic
64	C₄⋊C₄	—	109	1	no	—
65	C₄⋊C₄	—	109	1	no	—
66	C₂²⋊C₄	—	218	1	no	—
67	C₄²	—	218	1	no	—
68	C₁₆	—	4	1	no	—
69	C₁₆	—	436	1	no	—
70	C₂³	#13182012	1	1	yes	characteristic
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	218	1	no	—
74	C₂×C₄	—	218	1	no	—
75	C₂×C₄	#13182006	1	1	yes	characteristic
76	C₂×C₄	C₈×D₁₀₉	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	2	1	no	—
79	C₈	—	436	1	no	—
80	C₂²	—	2	1	no	—
81	C₂²	—	2	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	#16812611	1	1	yes	characteristic
84	C₄	—	2	1	no	—
85	C₄	—	436	1	no	—
86	C₄	—	436	1	no	—
87	C₄	#16812613	1	1	yes	characteristic
88	C₄	#16812617	1	1	yes	characteristic
89	C₂	—	4	1	no	—
90	C₂	#20294751	1	1	yes	characteristic
91	C₂	#20294809	1	1	yes	characteristic
92	C₂	#20294811	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13182006
commutator	C₂×C₄×C₁₀₉	C₂×C₈
Frattini	C₂²×C₈	C₂×D₁₀₉
Fitting	C₂²⋊C₁₆×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²⋊C₈
prime radical	C₂³×C₁₀₉	M₁₆
cosocle	C₂²×C₈×C₁₀₉	C₂²
hypercenter	C₂²⋊C₁₆	D₁₀₉
hypocenter	C₁₀₉	#1323
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
47. C₁₀₉	#1323	semidirect

Maximal subgroups

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

subgroup	index
#20295052	2
C₂²⋊#13182004	2
C₂²⋊C₁₆×C₁₀₉	2
#1323	109