Subgroups — #27193302

Order 13184.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20268181	C₂	1	1	yes	maximal, characteristic
2	#20267586	C₂	1	1	yes	maximal, characteristic, complemented
3	#355×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13110092	—	2	1	no	—
5	C₂×#13110090	—	2	1	no	—
6	#15693018	C₄	1	1	yes	characteristic, complemented
7	#15692936	—	2	1	no	—
8	#15692932	C₄	1	1	yes	characteristic, complemented
9	#124×C₁₀₃	C₂²	1	1	yes	characteristic
10	#101×C₁₀₃	—	2	1	no	—
11	C₂×D₄₁₂	—	2	1	no	—
12	C₂×D₄₁₂	—	4	1	no	—
13	#13110092	—	4	2	no	—
14	#13110090	—	4	2	no	—
15	C₂×C₁₀₃⋊C₈	—	2	1	no	—
16	C₂²⋊Dic₁₀₃	—	4	1	no	—
17	C₂×Q₈×C₁₀₃	D₄	1	1	yes	characteristic
18	C₂×D₄×C₁₀₃	D₄	1	1	yes	characteristic
19	M₁₆×C₁₀₃	—	4	1	no	—
20	C₂²⋊C₄×C₁₀₃	—	4	1	no	—
21	C₄²×C₁₀₃	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₁₀₃	—	2	1	no	—
23	C₂²×D₁₀₃	—	4	1	no	—
24	Q₈×C₁₀₃	—	4	1	no	—
25	D₄×C₁₀₃	—	4	1	no	—
26	C₂×C₄×C₁₀₃	—	2	1	no	—
27	C₂×C₄×C₁₀₃	—	2	1	no	—
28	C₂×C₄×C₁₀₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₁₀₃	—	8	1	no	—
30	D₄₁₂	—	4	1	no	—
31	D₄₁₂	—	4	1	no	—
32	D₄₁₂	—	8	2	no	—
33	C₈×C₁₀₃	—	8	1	no	—
34	C₁₀₃⋊C₈	—	2	2	no	—
35	C₂²×C₁₀₃	—	4	1	no	—
36	C₂²×C₁₀₃	—	8	1	no	—
37	C₂²×C₁₀₃	#99	1	1	yes	characteristic
38	C₂×D₁₀₃	—	8	2	no	—
39	C₂×D₁₀₃	—	8	1	no	—
40	C₄×C₁₀₃	—	2	1	no	—
41	C₄×C₁₀₃	—	4	1	no	—
42	C₄×C₁₀₃	—	4	1	no	—
43	Dic₁₀₃	—	16	1	no	—
44	C₂×C₁₀₃	—	2	1	no	—
45	C₂×C₁₀₃	—	8	1	no	—
46	C₂×C₁₀₃	#353	1	1	yes	characteristic
47	D₁₀₃	—	16	1	no	—
48	#1406	—	103	1	no	maximal, Sylow
49	C₁₀₃	#1406	1	1	yes	characteristic, complemented, Sylow
50	#496	—	103	1	no	—
51	#355	D₁₀₃	1	1	yes	characteristic, complemented
52	#354	—	103	1	no	—
53	C₂×SD₁₆	—	206	1	no	—
54	C₂×D₈	—	206	1	no	—
55	#127	—	103	1	no	—
56	#124	C₂×D₁₀₃	1	1	yes	characteristic
57	#101	—	2	1	no	—
58	#99	—	206	1	no	—
59	#97	—	103	1	no	—
60	C₂×Q₈	C₂²⋊D₁₀₃	1	1	yes	characteristic
61	C₂×D₄	—	412	1	no	—
62	C₂×D₄	—	206	1	no	—
63	C₂×D₄	D₄₁₂	1	1	yes	characteristic
64	SD₁₆	—	412	2	no	—
65	D₈	—	412	2	no	—
66	M₁₆	—	4	1	no	—
67	C₂×C₈	—	206	1	no	—
68	C₂²⋊C₄	—	4	1	no	—
69	C₂²⋊C₄	—	412	1	no	—
70	C₄²	C₄×D₁₀₃	1	1	yes	characteristic
71	C₂³	—	2	1	no	—
72	C₂³	—	412	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	824	2	no	—
76	D₄	—	412	1	no	—
77	D₄	—	412	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	824	1	no	—
81	C₂×C₄	(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
82	C₈	—	8	1	no	—
83	C₈	—	206	2	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	824	2	no	—
87	C₂²	—	824	1	no	—
88	C₂²	#15692935	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	4	1	no	—
92	C₄	—	1648	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	8	1	no	—
95	C₂	—	1648	1	no	—
96	C₂	#20267583	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20267583
commutator	C₄²×C₁₀₃	C₂×C₄
Frattini	#124	C₂×D₁₀₃
Fitting	#355×C₁₀₃	C₂
socle	C₂×C₁₀₃	#353
prime radical	#20268181	C₂
cosocle	#124×C₁₀₃	C₂²
hypercenter	#355	D₁₀₃
hypocenter	C₁₀₃	#1406
LCS	G ▷ C₄²×C₁₀₃ ▷ C₂×C₄×C₁₀₃ ▷ C₂²×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #355

Complements

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

N	H ≅ G/N	type
2. #20267586	C₂	semidirect
3. #355×C₁₀₃	C₂	semidirect
6. #15693018	C₄	semidirect
8. #15692932	C₄	semidirect
49. C₁₀₃	#1406	semidirect
51. #355	D₁₀₃	semidirect

Maximal subgroups

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

subgroup	index
#20268181	2
#20267586	2
#355×C₁₀₃	2
#1406	103