Subgroups — C₂²×#15692955 #27203719

Order 13184.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Dic₁₀₃	C₂	1	2	yes	maximal
2	C₂×#15692955	C₂	1	12	yes	maximal, direct product factor
3	C₂³×C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₁₀₃	—	2	2	no	—
5	C₂×C₄⋊Dic₁₀₃	—	2	6	no	—
6	C₂×C₄⋊Dic₁₀₃	C₂²	1	12	yes	—
7	#15692955	C₂²	1	16	yes	direct product factor
8	C₂³×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₀₃	C₄	1	8	yes	complemented
10	C₂²×C₈×C₁₀₃	C₂²	1	6	yes	—
11	C₂²×Dic₁₀₃	—	2	12	no	—
12	C₂²×Dic₁₀₃	—	4	8	no	—
13	C₄⋊Dic₁₀₃	—	2	12	no	—
14	C₄⋊Dic₁₀₃	C₂³	1	8	yes	—
15	C₂⁴×C₁₀₃	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₁₀₃	C₂×C₄	1	4	yes	—
17	C₂²×C₄×C₁₀₃	D₄	1	3	yes	—
18	C₂²×C₄×C₁₀₃	Q₈	1	4	yes	—
19	C₂²×C₄×C₁₀₃	C₂³	1	3	yes	—
20	C₂×C₈×C₁₀₃	C₂×C₄	1	24	yes	complemented
21	C₂×C₈×C₁₀₃	C₂³	1	4	yes	—
22	C₂³×C₁₀₃	C₄⋊C₄	1	4	yes	—
23	C₂³×C₁₀₃	D₈	1	4	yes	—
24	C₂³×C₁₀₃	Q₁₆	1	4	yes	—
25	C₂³×C₁₀₃	C₂×D₄	1	3	yes	—
26	C₂×C₄×C₁₀₃	C₄⋊C₄	1	12	yes	—
27	C₂×C₄×C₁₀₃	C₂²×C₄	1	6	yes	—
28	C₂×C₄×C₁₀₃	C₂×D₄	1	3	yes	—
29	C₂×C₄×C₁₀₃	C₂×Q₈	1	6	yes	—
30	C₂×C₄×C₁₀₃	C₂⁴	1	1	yes	characteristic
31	C₂×Dic₁₀₃	—	2	8	no	—
32	C₂×Dic₁₀₃	—	4	24	no	—
33	C₈×C₁₀₃	C₂²×C₄	1	8	yes	complemented
34	C₂²×C₁₀₃	#107	1	16	yes	complemented
35	C₂²×C₁₀₃	C₂×C₄⋊C₄	1	6	yes	—
36	C₂²×C₁₀₃	C₂×D₈	1	6	yes	—
37	C₂²×C₁₀₃	C₂×Q₁₆	1	6	yes	—
38	C₂²×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
39	C₄×C₁₀₃	C₂×C₄⋊C₄	1	6	yes	—
40	C₄×C₁₀₃	C₂³×C₄	1	1	yes	characteristic
41	C₄×C₁₀₃	C₂²×Q₈	1	1	yes	characteristic
42	Dic₁₀₃	—	4	8	no	—
43	C₂×C₁₀₃	C₂×#107	1	12	yes	complemented
44	C₂×C₁₀₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
45	C₂×C₁₀₃	C₂²×D₈	1	1	yes	characteristic
46	C₂×C₁₀₃	C₂²×Q₁₆	1	1	yes	characteristic
47	C₂²×#107	—	103	1	no	maximal, Sylow
48	C₁₀₃	C₂²×#107	1	1	yes	characteristic, complemented, Sylow
49	C₂³×C₈	D₁₀₃	1	1	yes	characteristic
50	C₂²×C₄⋊C₄	—	103	2	no	—
51	C₂×#107	—	103	12	no	—
52	C₂³×C₄	—	206	2	no	—
53	C₂³×C₄	C₂×D₁₀₃	1	1	yes	characteristic
54	C₂²×C₈	Dic₁₀₃	1	8	yes	complemented
55	C₂²×C₈	C₂×D₁₀₃	1	6	yes	—
56	C₂×C₄⋊C₄	—	103	12	no	—
57	C₂×C₄⋊C₄	—	206	6	no	—
58	#107	—	103	16	no	—
59	C₂⁴	D₄₁₂	1	1	yes	characteristic
60	C₂²×C₄	—	412	8	no	—
61	C₂²×C₄	—	206	12	no	—
62	C₂²×C₄	Dic₂₀₆	1	4	yes	—
63	C₂²×C₄	D₄₁₂	1	3	yes	—
64	C₂²×C₄	C₂×Dic₁₀₃	1	4	yes	—
65	C₂²×C₄	C₂²×D₁₀₃	1	3	yes	—
66	C₂×C₈	C₂×Dic₁₀₃	1	24	yes	complemented
67	C₂×C₈	C₂²×D₁₀₃	1	4	yes	—
68	C₄⋊C₄	—	103	8	no	—
69	C₄⋊C₄	—	206	12	no	—
70	C₂³	C₄⋊Dic₁₀₃	1	4	yes	—
71	C₂³	D₈₂₄	1	4	yes	—
72	C₂³	Dic₄₁₂	1	4	yes	—
73	C₂³	C₂×D₄₁₂	1	3	yes	—
74	C₂×C₄	—	412	24	no	—
75	C₂×C₄	—	206	8	no	—
76	C₂×C₄	C₄⋊Dic₁₀₃	1	12	yes	—
77	C₂×C₄	C₂²×Dic₁₀₃	1	6	yes	—
78	C₂×C₄	C₂×D₄₁₂	1	3	yes	—
79	C₂×C₄	C₂×Dic₂₀₆	1	6	yes	—
80	C₂×C₄	C₂³×D₁₀₃	1	1	yes	characteristic
81	C₈	C₂²×Dic₁₀₃	1	8	yes	complemented
82	C₂²	#15692955	1	16	yes	direct product factor
83	C₂²	C₂×C₄⋊Dic₁₀₃	1	6	yes	—
84	C₂²	C₂×D₈₂₄	1	6	yes	—
85	C₂²	C₂×Dic₄₁₂	1	6	yes	—
86	C₂²	C₂²×D₄₁₂	1	1	yes	characteristic
87	C₄	—	412	8	no	—
88	C₄	C₂×C₄⋊Dic₁₀₃	1	6	yes	—
89	C₄	C₂³×Dic₁₀₃	1	1	yes	characteristic
90	C₄	C₂²×Dic₂₀₆	1	1	yes	characteristic
91	C₂	C₂×#15692955	1	12	yes	direct product factor
92	C₂	C₂²×C₄⋊Dic₁₀₃	1	1	yes	characteristic
93	C₂	C₂²×D₈₂₄	1	1	yes	characteristic
94	C₂	C₂²×Dic₄₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄₁₂
commutator	C₄×C₁₀₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₀₃
Fitting	C₂³×C₈×C₁₀₃	C₂
socle, prime radical	C₂⁴×C₁₀₃	D₄
cosocle	C₂×C₄×C₁₀₃	C₂⁴
hypercenter	C₂³×C₈	D₁₀₃
hypocenter	C₁₀₃	C₂²×#107
LCS	G ▷ C₄×C₁₀₃ ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#15692955	C₂	direct (N × H)
7. #15692955	C₂²	direct (N × H)
9. C₂²×C₈×C₁₀₃	C₄	semidirect
20. C₂×C₈×C₁₀₃	C₂×C₄	semidirect
33. C₈×C₁₀₃	C₂²×C₄	semidirect
34. C₂²×C₁₀₃	#107	semidirect
43. C₂×C₁₀₃	C₂×#107	semidirect
48. C₁₀₃	C₂²×#107	semidirect
54. C₂²×C₈	Dic₁₀₃	semidirect
66. C₂×C₈	C₂×Dic₁₀₃	semidirect
81. C₈	C₂²×Dic₁₀₃	semidirect
82. C₂²	#15692955	direct (N × H)
91. C₂	C₂×#15692955	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Dic₁₀₃	2
C₂×#15692955	2
C₂³×C₈×C₁₀₃	2
C₂²×#107	103

Subgroups — C22×#15692955 #27203719

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15692955 #27203719