Subgroups — #27193194

Order 13184.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20268171	C₂	1	1	yes	maximal, characteristic
2	#20267544	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₁₂	—	2	1	no	—
5	C₂×Dic₄₁₂	C₄	1	2	yes	—
6	#15693021	—	2	1	no	—
7	C₄⋊(C₁₀₃⋊C₈)	—	2	1	no	—
8	C₂×C₁₆×C₁₀₃	—	2	1	no	—
9	C₄×C₈×C₁₀₃	C₂²	1	1	yes	characteristic
10	C₂×Dic₂₀₆	—	2	2	no	—
11	Dic₄₁₂	—	4	2	no	—
12	Dic₄₁₂	—	4	1	no	—
13	Dic₄₁₂	—	4	1	no	—
14	C₂×C₁₀₃⋊C₈	—	4	1	no	—
15	C₄⋊Dic₁₀₃	—	4	1	no	—
16	C₄⋊Dic₁₀₃	—	4	1	no	—
17	C₂×C₈×C₁₀₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₀₃	D₄	1	1	yes	characteristic
19	C₄²×C₁₀₃	D₄	1	1	yes	characteristic
20	C₁₆×C₁₀₃	—	4	1	no	—
21	C₂×C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₁₀₃	D₈	1	1	yes	characteristic
23	C₂×C₄×C₁₀₃	SD₁₆	1	1	yes	characteristic
24	C₂×Dic₁₀₃	—	4	2	no	—
25	Dic₂₀₆	—	4	2	no	—
26	Dic₂₀₆	—	4	2	no	—
27	C₈×C₁₀₃	—	2	1	no	—
28	C₈×C₁₀₃	D₈	1	1	yes	characteristic
29	C₈×C₁₀₃	SD₁₆	1	1	yes	characteristic
30	C₁₀₃⋊C₈	—	8	1	no	—
31	C₂²×C₁₀₃	#102	1	1	yes	characteristic
32	C₄×C₁₀₃	—	2	1	no	—
33	C₄×C₁₀₃	#100	1	1	yes	characteristic
34	C₄×C₁₀₃	#102	1	1	yes	characteristic
35	C₄×C₁₀₃	SD₃₂	1	1	yes	characteristic
36	C₄×C₁₀₃	Q₃₂	1	1	yes	characteristic
37	Dic₁₀₃	—	8	2	no	—
38	C₂×C₁₀₃	#331	1	1	yes	characteristic
39	C₂×C₁₀₃	#358	1	1	yes	characteristic
40	C₂×C₁₀₃	#362	1	1	yes	characteristic
41	#1362	—	103	1	no	maximal, Sylow
42	C₁₀₃	#1362	1	1	yes	characteristic, complemented, Sylow
43	#494	—	103	1	no	—
44	C₄⋊C₁₆	D₁₀₃	1	1	yes	characteristic
45	#335	—	103	1	no	—
46	C₂×Q₁₆	—	103	2	no	—
47	C₂×Q₁₆	—	206	1	no	—
48	C₄⋊Q₈	—	206	1	no	—
49	C₂×C₁₆	—	2	1	no	—
50	C₄⋊C₈	—	206	1	no	—
51	C₄×C₈	C₂×D₁₀₃	1	1	yes	characteristic
52	C₂×Q₈	—	206	2	no	—
53	Q₁₆	—	412	2	no	—
54	Q₁₆	—	412	1	no	—
55	Q₁₆	—	412	1	no	—
56	C₂×C₈	—	412	1	no	—
57	C₂×C₈	C₄×D₁₀₃	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₁₀₃	1	1	yes	characteristic
59	C₄⋊C₄	—	412	1	no	—
60	C₄⋊C₄	—	412	1	no	—
61	C₄²	D₄₁₂	1	1	yes	characteristic
62	C₁₆	—	4	1	no	—
63	Q₈	—	412	2	no	—
64	Q₈	—	412	2	no	—
65	C₂×C₄	—	412	2	no	—
66	C₂×C₄	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
67	C₂×C₄	D₈₂₄	1	1	yes	characteristic
68	C₂×C₄	#13110094	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	824	1	no	—
71	C₈	#13110090	1	1	yes	characteristic
72	C₈	#13110092	1	1	yes	characteristic
73	C₂²	#15692943	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	824	2	no	—
76	C₄	#15692937	1	1	yes	characteristic
77	C₄	#15692941	1	1	yes	characteristic
78	C₄	#15692966	1	1	yes	characteristic
79	C₄	Dic₈₂₄	1	1	yes	characteristic
80	C₂	#20267534	1	1	yes	characteristic
81	C₂	#20267596	1	1	yes	characteristic
82	C₂	#20267608	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15692943
commutator	C₂×C₈×C₁₀₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₁₀₃
Fitting	C₄⋊C₁₆×C₁₀₃	C₂
socle, prime radical	C₂²×C₁₀₃	#102
cosocle	C₄×C₈×C₁₀₃	C₂²
hypercenter	C₄⋊C₁₆	D₁₀₃
hypocenter	C₁₀₃	#1362
LCS	G ▷ C₂×C₈×C₁₀₃ ▷ C₂×C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
42. C₁₀₃	#1362	semidirect

Maximal subgroups

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

subgroup	index
#20268171	2
#20267544	2
C₄⋊C₁₆×C₁₀₃	2
#1362	103