Subgroups — #27193131

Order 13184.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20268049	C₂	1	1	yes	maximal, characteristic
2	#20267573	C₂	1	1	yes	maximal, characteristic
3	H(3,ℤ/4)×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₁₂	C₄	1	1	yes	characteristic, complemented
5	#15693000	—	2	1	no	—
6	#15692961	—	2	1	no	—
7	#15692953	C₄	1	1	yes	characteristic, complemented
8	#15692946	—	2	1	no	—
9	C₂×M₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
10	#117×C₁₀₃	—	2	1	no	—
11	C₂×Dic₂₀₆	—	2	1	no	—
12	Dic₄₁₂	—	4	1	no	—
13	C₄⋊Dic₁₀₃	—	2	1	no	—
14	Dic₁₀₃⋊C₄	—	4	1	no	—
15	C₂²⋊Dic₁₀₃	—	4	1	no	—
16	C₁₀₃⋊C₁₆	—	4	1	no	—
17	C₂²×C₄×C₁₀₃	D₄	1	1	yes	characteristic
18	M₁₆×C₁₀₃	—	4	1	no	—
19	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₁₀₃	D₄	1	1	yes	characteristic
21	C₄⋊C₄×C₁₀₃	—	4	1	no	—
22	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
23	C₄²×C₁₀₃	—	2	2	no	—
24	C₂³×C₁₀₃	D₈	1	1	yes	characteristic
25	C₂×C₄×C₁₀₃	—	2	1	no	—
26	C₂×C₄×C₁₀₃	—	2	1	no	—
27	C₂×C₄×C₁₀₃	—	4	2	no	—
28	C₂×C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₀₃	SD₁₆	1	1	yes	characteristic
30	C₂×Dic₁₀₃	—	4	1	no	—
31	C₂×Dic₁₀₃	—	4	1	no	—
32	Dic₂₀₆	—	4	1	no	—
33	Dic₂₀₆	—	4	1	no	—
34	C₈×C₁₀₃	—	2	1	no	—
35	C₈×C₁₀₃	—	2	1	no	—
36	C₂²×C₁₀₃	—	2	1	no	—
37	C₂²×C₁₀₃	—	4	1	no	—
38	C₂²×C₁₀₃	#102	1	1	yes	characteristic
39	C₄×C₁₀₃	—	2	1	no	—
40	C₄×C₁₀₃	—	8	2	no	—
41	C₄×C₁₀₃	#99	1	1	yes	characteristic
42	C₄×C₁₀₃	#104	1	1	yes	characteristic
43	Dic₁₀₃	—	8	1	no	—
44	Dic₁₀₃	—	8	1	no	—
45	C₂×C₁₀₃	—	2	1	no	—
46	C₂×C₁₀₃	—	4	1	no	—
47	C₂×C₁₀₃	#327	1	1	yes	characteristic
48	#1340	—	103	1	no	maximal, Sylow
49	C₁₀₃	#1340	1	1	yes	characteristic, complemented, Sylow
50	#470	—	103	1	no	—
51	#349	—	103	1	no	—
52	H(3,ℤ/4)	D₁₀₃	1	1	yes	characteristic
53	C₂×Q₁₆	—	103	1	no	—
54	C₂×M₁₆	C₂×D₁₀₃	1	1	yes	characteristic
55	C₂²⋊Q₈	—	206	1	no	—
56	#117	—	2	1	no	—
57	M₃₂	—	206	1	no	—
58	#106	—	103	1	no	—
59	#103	—	206	1	no	—
60	C₂×Q₈	—	206	1	no	—
61	C₂²×C₄	C₂²⋊D₁₀₃	1	1	yes	characteristic
62	Q₁₆	—	412	1	no	—
63	M₁₆	—	4	1	no	—
64	C₂×C₈	C₄×D₁₀₃	1	1	yes	characteristic
65	C₂×C₈	D₄₁₂	1	1	yes	characteristic
66	C₄⋊C₄	—	4	1	no	—
67	C₄⋊C₄	—	412	1	no	—
68	C₄⋊C₄	—	206	1	no	—
69	C₂²⋊C₄	—	4	1	no	—
70	C₂²⋊C₄	—	412	1	no	—
71	C₄²	—	2	2	no	—
72	C₁₆	—	412	1	no	—
73	C₂³	#13110090	1	1	yes	characteristic
74	Q₈	—	412	1	no	—
75	Q₈	—	412	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	4	2	no	—
79	C₂×C₄	—	412	1	no	—
80	C₂×C₄	—	412	1	no	—
81	C₂×C₄	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
82	C₂×C₄	#13110092	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	2	1	no	—
85	C₂²	—	2	1	no	—
86	C₂²	—	4	1	no	—
87	C₂²	#15692941	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	8	2	no	—
90	C₄	—	824	1	no	—
91	C₄	—	824	1	no	—
92	C₄	#15692935	1	1	yes	characteristic
93	C₄	#15692949	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	4	1	no	—
96	C₂	#20267524	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20267524
commutator	C₂×C₈×C₁₀₃	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₁₀₃
Fitting	H(3,ℤ/4)×C₁₀₃	C₂
socle	C₂×C₁₀₃	#327
prime radical	C₂³×C₁₀₃	D₈
cosocle	C₂×M₁₆×C₁₀₃	C₂²
hypercenter	H(3,ℤ/4)	D₁₀₃
hypocenter	C₁₀₃	#1340
LCS	G ▷ C₂×C₈×C₁₀₃ ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ H(3,ℤ/4)

Complements

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

N	H ≅ G/N	type
4. C₂×Dic₄₁₂	C₄	semidirect
7. #15692953	C₄	semidirect
49. C₁₀₃	#1340	semidirect

Maximal subgroups

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

subgroup	index
#20268049	2
#20267573	2
H(3,ℤ/4)×C₁₀₃	2
#1340	103