Subgroups — #27186177

Order 12928.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15692329	C₂	1	2	yes	maximal
2	C₂×C₈×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
3	#15692329	—	2	2	no	—
4	#15692329	C₄	1	4	yes	complemented
5	C₂×#13108077	—	2	2	no	—
6	C₂²×#11717579	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₁₀₁	C₄	1	1	yes	characteristic
8	C₈×Dic₁₀₁	—	2	2	no	—
9	C₂²×C₈×C₁₀₁	C₄	1	1	yes	characteristic
10	#13108077	—	2	4	no	—
11	C₂²×Dic₁₀₁	—	2	1	no	—
12	C₂×#11717579	C₂×C₄	1	2	yes	—
13	C₂×#11717579	D₄	1	1	yes	characteristic
14	C₂×#11717579	D₄	1	2	yes	—
15	C₂×#11717579	Q₈	1	1	yes	characteristic
16	C₄×Dic₁₀₁	—	2	1	no	—
17	C₄×Dic₁₀₁	C₈	1	2	yes	—
18	C₂²×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₀₁	—	2	1	no	—
20	C₂×C₈×C₁₀₁	—	2	1	no	—
21	C₂×C₈×C₁₀₁	C₈	1	2	yes	—
22	C₂³×C₁₀₁	M₁₆	1	1	yes	characteristic
23	C₂×C₄×C₁₀₁	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₀₁	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₁₀₁	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₁₀₁	M₁₆	1	1	yes	characteristic
29	C₂×Dic₁₀₁	—	2	4	no	—
30	C₂×Dic₁₀₁	—	2	2	no	—
31	C₈×C₁₀₁	—	2	2	no	—
32	#11717579	C₂²⋊C₄	1	2	yes	—
33	#11717579	C₄⋊C₄	1	2	yes	—
34	C₂²×C₁₀₁	—	2	2	no	—
35	C₂²×C₁₀₁	#97	1	1	yes	characteristic
36	C₂²×C₁₀₁	C₂²⋊C₈	1	1	yes	characteristic
37	C₂²×C₁₀₁	C₄⋊C₈	1	1	yes	characteristic
38	C₄×C₁₀₁	#95	1	1	yes	characteristic
39	C₄×C₁₀₁	C₄×C₈	1	1	yes	characteristic
40	C₄×C₁₀₁	C₂²⋊C₈	1	1	yes	characteristic
41	C₄×C₁₀₁	C₄⋊C₈	1	1	yes	characteristic
42	Dic₁₀₁	—	2	4	no	—
43	C₂×C₁₀₁	—	2	1	no	—
44	C₂×C₁₀₁	—	2	1	no	—
45	C₂×C₁₀₁	#336	1	1	yes	characteristic
46	C₂×C₁₀₁	#364	1	2	yes	—
47	#1376	—	101	1	no	maximal, Sylow
48	C₁₀₁	#1376	1	1	yes	characteristic, complemented, Sylow
49	C₂×M₃₂	—	101	2	no	—
50	C₂×C₄×C₈	—	101	1	no	—
51	C₂²×C₈	—	101	1	no	—
52	C₂²×C₈	#87938	1	1	yes	characteristic
53	C₂×C₄²	—	101	1	no	—
54	M₃₂	—	101	4	no	—
55	M₃₂	—	202	2	no	—
56	C₂×C₁₆	—	202	2	no	—
57	C₄×C₈	—	202	2	no	—
58	C₂²×C₄	—	202	1	no	—
59	C₂²×C₄	C₂×#87938	1	1	yes	characteristic
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	—	101	2	no	—
63	C₂×C₈	—	101	2	no	—
64	C₂×C₈	—	101	1	no	—
65	C₂×C₈	—	101	1	no	—
66	C₂×C₈	#11717581	1	2	yes	—
67	C₄²	—	101	2	no	—
68	C₄²	—	202	1	no	—
69	C₁₆	—	202	4	no	—
70	C₂³	#13108084	1	1	yes	characteristic
71	C₂×C₄	—	202	4	no	—
72	C₂×C₄	—	202	2	no	—
73	C₂×C₄	C₄×#87938	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊#87938	1	1	yes	characteristic
75	C₂×C₄	C₄⋊#87938	1	1	yes	characteristic
76	C₂×C₄	C₂×#11717581	1	1	yes	characteristic
77	C₂×C₄	D₁₀₁⋊C₈	1	1	yes	characteristic
78	C₂×C₄	#13108083	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	—	101	2	no	—
81	C₈	—	101	2	no	—
82	C₂²	—	2	2	no	—
83	C₂²	#15692310	1	1	yes	characteristic
84	C₂²	#15692312	1	1	yes	characteristic
85	C₂²	C₄⋊#11717581	1	1	yes	characteristic
86	C₄	—	202	4	no	—
87	C₄	(C₂×#87938)⋊C₄	1	1	yes	characteristic
88	C₄	C₄×#11717581	1	1	yes	characteristic
89	C₄	C₂²⋊#11717581	1	1	yes	characteristic
90	C₄	#15692322	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#20266043	1	1	yes	characteristic
94	C₂	#20266099	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄⋊#87938
commutator	C₄×C₁₀₁	C₄×C₈
Frattini	C₂²×C₄	C₂×#87938
Fitting	C₂²×C₈×C₁₀₁	C₄
socle	C₂²×C₁₀₁	C₄⋊C₈
prime radical	C₂³×C₁₀₁	M₁₆
cosocle	C₂²×#11717579	C₂²
hypercenter	C₂²×C₈	#87938
hypocenter	C₁₀₁	#1376
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #15692329	C₄	semidirect
48. C₁₀₁	#1376	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15692329	2
C₂×C₈×Dic₁₀₁	2
#1376	101