Subgroups — #27193283

Order 13184.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15692960	C₂	1	1	yes	maximal, characteristic
2	#20267625	C₂	1	1	yes	maximal, characteristic, complemented
3	M₆₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₁₀₃	C₄	1	1	yes	characteristic
5	#15692960	—	2	1	no	—
6	#15692960	—	2	1	no	—
7	C₂×C₁₀₃⋊C₁₆	C₄	1	1	yes	characteristic
8	C₁₀₃⋊C₃₂	—	2	1	no	—
9	C₂×C₁₆×C₁₀₃	C₂²	1	1	yes	characteristic
10	C₃₂×C₁₀₃	—	2	1	no	—
11	C₂×C₄×D₁₀₃	C₈	1	1	yes	characteristic
12	C₂×C₁₀₃⋊C₈	C₈	1	1	yes	characteristic
13	C₈×D₁₀₃	—	2	1	no	—
14	C₈×D₁₀₃	—	2	1	no	—
15	C₁₀₃⋊C₁₆	—	2	1	no	—
16	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
17	C₁₆×C₁₀₃	D₄	1	1	yes	characteristic
18	C₁₆×C₁₀₃	D₄	1	1	yes	characteristic
19	C₂²×D₁₀₃	C₁₆	1	1	yes	characteristic
20	C₂×C₄×C₁₀₃	C₂×C₈	1	1	yes	characteristic
21	C₂×Dic₁₀₃	C₁₆	1	1	yes	characteristic
22	C₄×D₁₀₃	—	2	1	no	—
23	C₄×D₁₀₃	—	2	1	no	—
24	C₈×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₁₀₃	M₁₆	1	1	yes	characteristic
26	C₁₀₃⋊C₈	—	2	1	no	—
27	C₂²×C₁₀₃	C₂×C₁₆	1	1	yes	characteristic
28	C₂×D₁₀₃	—	2	1	no	—
29	C₂×D₁₀₃	—	4	1	no	—
30	C₄×C₁₀₃	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₁₀₃	M₃₂	1	1	yes	characteristic
32	Dic₁₀₃	—	2	1	no	—
33	C₂×C₁₀₃	—	2	1	no	—
34	C₂×C₁₀₃	C₂²⋊C₁₆	1	1	yes	characteristic
35	D₁₀₃	—	4	1	no	—
36	#1400	—	103	1	no	maximal, Sylow
37	C₁₀₃	#1400	1	1	yes	characteristic, complemented, Sylow
38	C₂×M₃₂	—	103	1	no	—
39	M₆₄	—	103	1	no	—
40	M₆₄	D₁₀₃	1	1	yes	characteristic, complemented
41	C₂²×C₈	—	103	1	no	—
42	M₃₂	—	206	1	no	—
43	M₃₂	—	206	1	no	—
44	C₂×C₁₆	—	103	1	no	—
45	C₂×C₁₆	C₂×D₁₀₃	1	1	yes	characteristic
46	C₃₂	—	2	1	no	—
47	C₃₂	—	206	1	no	—
48	C₂²×C₄	—	103	1	no	—
49	C₂×C₈	—	103	1	no	—
50	C₂×C₈	—	206	1	no	—
51	C₂×C₈	—	206	1	no	—
52	C₂×C₈	C₄×D₁₀₃	1	1	yes	characteristic
53	C₁₆	—	206	1	no	—
54	C₁₆	D₄₁₂	1	1	yes	characteristic
55	C₁₆	C₂²⋊D₁₀₃	1	1	yes	characteristic
56	C₂³	—	103	1	no	—
57	C₂×C₄	—	103	1	no	—
58	C₂×C₄	—	206	1	no	—
59	C₂×C₄	—	206	1	no	—
60	C₂×C₄	C₈×D₁₀₃	1	1	yes	characteristic
61	C₈	—	206	1	no	—
62	C₈	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
63	C₈	#13110088	1	1	yes	characteristic
64	C₂²	—	412	1	no	—
65	C₂²	—	206	1	no	—
66	C₂²	C₁₆×D₁₀₃	1	1	yes	characteristic
67	C₄	—	206	1	no	—
68	C₄	(C₂×D₁₀₃)⋊C₈	1	1	yes	characteristic
69	C₄	#15692960	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	412	1	no	—
72	C₂	(C₂×D₁₀₃)⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₈	(C₂×D₁₀₃)⋊C₄
commutator	C₂²×C₁₀₃	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₁₀₃
Fitting	M₆₄×C₁₀₃	C₂
socle	C₂×C₁₀₃	C₂²⋊C₁₆
prime radical	C₂²×D₁₀₃	C₁₆
cosocle	C₂×C₁₆×C₁₀₃	C₂²
hypercenter	M₆₄	D₁₀₃
hypocenter	C₁₀₃	#1400
LCS	G ▷ C₂²×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. #20267625	C₂	semidirect
3. M₆₄×C₁₀₃	C₂	semidirect
37. C₁₀₃	#1400	semidirect
40. M₆₄	D₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15692960	2
#20267625	2
M₆₄×C₁₀₃	2
#1400	103