Subgroups — C₄×#15692165 #27170816

Order 12928.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15692165	C₂	1	4	yes	maximal
2	C₂×C₄×#11717579	C₂	1	1	yes	maximal, characteristic
3	C₄²×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11717579	C₂²	1	2	yes	—
6	C₂×C₄×Dic₁₀₁	C₄	1	4	yes	—
7	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	—
8	#15692165	C₄	1	16	yes	direct product factor
9	C₄×#11717579	C₄	1	4	yes	complemented
10	C₂²×C₈×C₁₀₁	C₂²	1	2	yes	—
11	C₂×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₁₀₁	C₄	1	4	yes	complemented
13	C₂²×Dic₁₀₁	C₂×C₄	1	4	yes	—
14	C₂×#11717579	C₂×C₄	1	4	yes	—
15	C₂×#11717579	C₂×C₄	1	8	yes	—
16	C₄×Dic₁₀₁	—	2	8	no	—
17	C₄×Dic₁₀₁	C₂×C₄	1	8	yes	—
18	C₂²×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
19	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
20	C₂×C₈×C₁₀₁	C₂×C₄	1	8	yes	—
21	C₂×C₈×C₁₀₁	C₂×C₄	1	4	yes	—
22	C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
23	C₄²×C₁₀₁	C₂×C₄	1	2	yes	—
24	C₂³×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₀₁	C₄²	1	4	yes	—
26	C₂×C₄×C₁₀₁	M₁₆	1	8	yes	—
27	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₀₁	C₂²×C₄	1	4	yes	—
29	C₂×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₁₀₁	—	2	8	no	—
31	C₂×Dic₁₀₁	C₄²	1	8	yes	—
32	C₈×C₁₀₁	C₄²	1	8	yes	complemented
33	#11717579	C₄²	1	8	yes	complemented
34	C₂²×C₁₀₁	C₂×C₄²	1	2	yes	—
35	C₂²×C₁₀₁	C₂×C₄²	1	1	yes	characteristic
36	C₂²×C₁₀₁	C₂×M₁₆	1	4	yes	—
37	C₄×C₁₀₁	#97	1	8	yes	complemented
38	C₄×C₁₀₁	C₂×C₄²	1	2	yes	—
39	C₄×C₁₀₁	C₂×C₄²	1	2	yes	—
40	Dic₁₀₁	—	2	8	no	—
41	C₂×C₁₀₁	C₄³	1	1	yes	characteristic
42	C₂×C₁₀₁	C₂×#97	1	2	yes	—
43	C₂×C₁₀₁	C₄×M₁₆	1	4	yes	—
44	C₄×#97	—	101	1	no	maximal, Sylow
45	C₁₀₁	C₄×#97	1	1	yes	characteristic, complemented, Sylow
46	C₂×#97	—	101	4	no	—
47	C₂×C₄×C₈	—	101	1	no	—
48	C₂×C₄×C₈	D₁₀₁	1	1	yes	characteristic
49	C₄³	—	101	1	no	—
50	C₂²×C₈	—	101	2	no	—
51	C₂²×C₈	C₂×D₁₀₁	1	2	yes	—
52	C₂×C₄²	—	101	2	no	—
53	C₂×C₄²	—	101	4	no	—
54	C₂×C₄²	C₂×D₁₀₁	1	1	yes	characteristic
55	#97	—	101	16	no	—
56	C₄×C₈	—	101	4	no	—
57	C₄×C₈	Dic₁₀₁	1	4	yes	complemented
58	C₂²×C₄	—	101	4	no	—
59	C₂²×C₄	C₄×D₁₀₁	1	2	yes	—
60	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
61	C₂×C₈	—	101	4	no	—
62	C₂×C₈	—	101	8	no	—
63	C₂×C₈	C₄×D₁₀₁	1	8	yes	—
64	C₂×C₈	C₂×Dic₁₀₁	1	4	yes	—
65	C₄²	—	101	8	no	—
66	C₄²	—	202	8	no	—
67	C₄²	C₄×D₁₀₁	1	2	yes	—
68	C₄²	C₂×Dic₁₀₁	1	2	yes	—
69	C₂³	C₂×C₄×D₁₀₁	1	1	yes	characteristic
70	C₂×C₄	—	101	8	no	—
71	C₂×C₄	—	202	8	no	—
72	C₂×C₄	C₄×Dic₁₀₁	1	4	yes	—
73	C₂×C₄	#13108057	1	8	yes	—
74	C₂×C₄	C₂×C₄×D₁₀₁	1	1	yes	characteristic
75	C₂×C₄	C₂×C₄×D₁₀₁	1	4	yes	—
76	C₂×C₄	C₂²×Dic₁₀₁	1	1	yes	characteristic
77	C₈	—	101	8	no	—
78	C₈	C₄×Dic₁₀₁	1	8	yes	complemented
79	C₂²	C₄²×D₁₀₁	1	2	yes	—
80	C₂²	C₂×C₄×Dic₁₀₁	1	1	yes	characteristic
81	C₂²	C₂×#13108057	1	4	yes	—
82	C₄	—	202	8	no	—
83	C₄	#15692165	1	8	yes	direct product factor
84	C₄	C₄²×D₁₀₁	1	2	yes	—
85	C₄	C₂×C₄×Dic₁₀₁	1	2	yes	—
86	C₂	C₄²×Dic₁₀₁	1	1	yes	characteristic
87	C₂	C₂×#15692165	1	2	yes	—
88	C₂	C₄×#13108057	1	4	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂×D₁₀₁
commutator	C₂×C₁₀₁	C₄³
Frattini	C₂²×C₄	C₂²×D₁₀₁
Fitting	C₂×C₄×C₈×C₁₀₁	C₂
socle, prime radical	C₂³×C₁₀₁	C₂²×C₄
cosocle	C₂²×C₄×C₁₀₁	C₂³
hypercenter	C₂×C₄×C₈	D₁₀₁
hypocenter	C₁₀₁	C₄×#97
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
8. #15692165	C₄	direct (N × H)
9. C₄×#11717579	C₄	semidirect
12. C₄×C₈×C₁₀₁	C₄	semidirect
32. C₈×C₁₀₁	C₄²	semidirect
33. #11717579	C₄²	semidirect
37. C₄×C₁₀₁	#97	semidirect
45. C₁₀₁	C₄×#97	semidirect
57. C₄×C₈	Dic₁₀₁	semidirect
78. C₈	C₄×Dic₁₀₁	semidirect
83. C₄	#15692165	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15692165	2
C₂×C₄×#11717579	2
C₄²×Dic₁₀₁	2
C₂×C₄×C₈×C₁₀₁	2
C₄×#97	101

Subgroups — C4×#15692165 #27170816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15692165 #27170816