Subgroups — C₄×#10622099 #14668595

Order 2816.

510 conjugacy classes of subgroups.

The subgroup lattice has 128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622099	C₂	1	4	yes	maximal
2	C₂×C₄×C₁₁⋊C₁₆	C₂	1	2	yes	maximal
3	C₄²×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₁	C₄	1	2	yes	—
5	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₄³×C₁₁	C₄	1	1	yes	characteristic
9	C₂²×C₁₁⋊C₁₆	C₂²	1	4	yes	—
10	#10622099	C₄	1	16	yes	direct product factor
11	C₄×C₁₁⋊C₁₆	C₄	1	8	yes	complemented
12	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
13	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
15	C₂×C₄²×C₁₁	C₈	1	4	yes	—
16	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₁₁	C₈	1	8	yes	—
19	C₄×C₈×C₁₁	C₈	1	4	yes	—
20	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
21	C₄×C₈×C₁₁	C₂×C₄	1	8	yes	—
22	C₂×C₁₁⋊C₁₆	C₂×C₄	1	8	yes	—
23	C₂×C₁₁⋊C₁₆	C₂×C₄	1	16	yes	—
24	C₄×#346	—	11	1	no	maximal, Sylow
25	C₂²×C₄×C₁₁	C₂×C₈	1	4	yes	—
26	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
27	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₈×C₁₁	C₄²	1	2	yes	—
29	C₂×C₈×C₁₁	C₄²	1	4	yes	—
30	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
31	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
32	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
33	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
34	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
35	C₄²×C₁₁	—	2	8	no	—
36	C₄²×C₁₁	C₄²	1	4	yes	—
37	C₄²×C₁₁	C₄²	1	2	yes	—
38	C₄²×C₁₁	C₂×C₈	1	4	yes	—
39	C₄²×C₁₁	C₂×C₈	1	2	yes	—
40	C₁₁⋊C₁₆	C₄²	1	16	yes	complemented
41	C₂×#346	—	11	4	no	—
42	C₂×C₄×C₁₆	—	11	2	no	—
43	C₄²×C₈	D₁₁	1	1	yes	characteristic
44	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
45	C₂×C₄×C₁₁	—	2	8	no	—
46	C₂×C₄×C₁₁	C₄×C₈	1	8	yes	—
47	C₂×C₄×C₁₁	C₄×C₈	1	4	yes	—
48	C₂×C₄×C₁₁	M₃₂	1	8	yes	—
49	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
50	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
51	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
53	C₈×C₁₁	C₄×C₈	1	4	yes	—
54	C₈×C₁₁	C₄×C₈	1	8	yes	—
55	C₈×C₁₁	C₂×C₄²	1	4	yes	—
56	C₂²×C₁₆	—	11	4	no	—
57	C₂×C₄×C₈	Dic₁₁	1	2	yes	—
58	C₂×C₄×C₈	Dic₁₁	1	1	yes	characteristic
59	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
60	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
61	C₄³	Dic₁₁	1	1	yes	characteristic
62	#346	—	11	16	no	—
63	C₄×C₁₆	—	11	8	no	—
64	C₂²×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
65	C₂²×C₁₁	C₂×C₄×C₈	1	2	yes	—
66	C₂²×C₁₁	C₂×M₃₂	1	4	yes	—
67	C₄×C₁₁	—	2	8	no	—
68	C₄×C₁₁	#346	1	8	yes	complemented
69	C₄×C₁₁	C₄³	1	1	yes	characteristic
70	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
71	C₄×C₁₁	C₂×C₄×C₈	1	2	yes	—
72	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
73	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
74	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
75	C₂×C₄²	C₁₁⋊C₈	1	4	yes	—
76	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
77	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
78	C₂×C₁₆	—	11	8	no	—
79	C₂×C₁₆	—	11	16	no	—
80	C₄×C₈	C₁₁⋊C₈	1	8	yes	—
81	C₄×C₈	C₁₁⋊C₈	1	4	yes	—
82	C₄×C₈	C₄×D₁₁	1	4	yes	—
83	C₄×C₈	C₄×D₁₁	1	8	yes	—
84	C₂×C₁₁	C₄²×C₈	1	1	yes	characteristic
85	C₂×C₁₁	C₂×#346	1	2	yes	—
86	C₂×C₁₁	C₄×M₃₂	1	4	yes	—
87	C₂²×C₄	C₂×C₁₁⋊C₈	1	4	yes	—
88	C₂²×C₄	C₂×C₁₁⋊C₈	1	2	yes	—
89	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
90	C₂×C₈	C₂×C₁₁⋊C₈	1	4	yes	—
91	C₂×C₈	C₂×C₁₁⋊C₈	1	4	yes	—
92	C₂×C₈	C₂×C₁₁⋊C₈	1	4	yes	—
93	C₂×C₈	C₄×Dic₁₁	1	2	yes	—
94	C₂×C₈	C₄×Dic₁₁	1	4	yes	—
95	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
96	C₂×C₈	C₂×C₄×D₁₁	1	4	yes	—
97	C₄²	—	2	8	no	—
98	C₄²	C₂×C₁₁⋊C₈	1	4	yes	—
99	C₄²	C₂×C₁₁⋊C₈	1	2	yes	—
100	C₄²	C₄×Dic₁₁	1	4	yes	—
101	C₄²	C₄×Dic₁₁	1	2	yes	—
102	C₁₆	—	11	16	no	—
103	C₁₁	C₄×#346	1	1	yes	characteristic, complemented, Sylow
104	C₂³	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
105	C₂×C₄	—	2	8	no	—
106	C₂×C₄	C₄×C₁₁⋊C₈	1	8	yes	—
107	C₂×C₄	C₄×C₁₁⋊C₈	1	4	yes	—
108	C₂×C₄	#66876	1	8	yes	—
109	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
110	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
111	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
112	C₂×C₄	C₂×C₄×Dic₁₁	1	2	yes	—
113	C₈	C₄×C₁₁⋊C₈	1	8	yes	—
114	C₈	C₄×C₁₁⋊C₈	1	4	yes	—
115	C₈	C₄²×D₁₁	1	4	yes	—
116	C₂²	C₂×C₄×C₁₁⋊C₈	1	1	yes	characteristic
117	C₂²	C₂×C₄×C₁₁⋊C₈	1	2	yes	—
118	C₂²	C₂×#66876	1	4	yes	—
119	C₄	—	2	8	no	—
120	C₄	#10622099	1	8	yes	direct product factor
121	C₄	C₂×C₄×C₁₁⋊C₈	1	2	yes	—
122	C₄	C₂×C₄×C₁₁⋊C₈	1	1	yes	characteristic
123	C₄	C₄²×Dic₁₁	1	1	yes	characteristic
124	C₂	C₄²×C₁₁⋊C₈	1	1	yes	characteristic
125	C₂	C₂×#10622099	1	2	yes	—
126	C₂	C₄×#66876	1	4	yes	—

	subgroup	G/H
center	C₂×C₄×C₈	C₂×D₁₁
commutator	C₂×C₁₁	C₄²×C₈
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₄²×C₈×C₁₁	C₂
socle, prime radical	C₂³×C₁₁	C₂²×C₈
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₄²×C₈	D₁₁
hypocenter	C₁₁	C₄×#346
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄×C₈ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
10. #10622099	C₄	direct (N × H)
11. C₄×C₁₁⋊C₁₆	C₄	semidirect
40. C₁₁⋊C₁₆	C₄²	semidirect
68. C₄×C₁₁	#346	semidirect
103. C₁₁	C₄×#346	semidirect
120. C₄	#10622099	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×#10622099	2
C₂×C₄×C₁₁⋊C₁₆	2
C₄²×C₈×C₁₁	2
C₄×#346	11

Subgroups — C4×#10622099 #14668595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#10622099 #14668595