Subgroups — #14662781

Order 2816.

282 conjugacy classes of subgroups.

The subgroup lattice has 136 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	1	yes	maximal, characteristic
2	#13066899	C₂	1	1	yes	maximal, characteristic
3	#13066536	C₂	1	4	yes	maximal, complemented
4	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×M₃₂	C₄	1	2	yes	—
6	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂²×C₁₁⋊C₁₆	C₄	1	2	yes	—
8	#10622538	C₄	1	2	yes	—
9	C₁₁×#346	C₂²	1	2	yes	—
10	C₄×C₁₁×C₁₆	C₄	1	2	yes	—
11	#10622099	C₄	1	2	yes	—
12	#10622099	C₂²	1	2	yes	—
13	#10622093	C₂²	1	2	yes	—
14	C₈×C₁₁⋊C₈	C₄	1	2	yes	—
15	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₁₁×M₃₂	C₈	1	8	yes	complemented
19	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
20	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
24	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
25	C₂×C₁₁⋊C₁₆	—	2	4	no	—
26	C₂×C₁₁⋊C₁₆	C₂×C₄	1	4	yes	—
27	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
28	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
29	#11406	—	11	1	no	maximal, Sylow
30	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
31	C₂²×C₄×C₁₁	M₁₆	1	2	yes	—
32	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
33	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
34	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
35	C₂×C₈×C₁₁	M₁₆	1	4	yes	—
36	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
38	C₄²×C₁₁	C₄²	1	1	yes	characteristic
39	C₄²×C₁₁	M₁₆	1	2	yes	—
40	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₁₁⋊C₈	—	2	4	no	—
42	C₁₁×C₁₆	C₂×C₈	1	8	yes	—
43	C₁₁⋊C₁₆	—	2	4	no	—
44	C₄×M₃₂	D₁₁	1	1	yes	characteristic
45	C₂×#346	—	11	1	no	—
46	#1450	—	11	1	no	—
47	#1313	—	11	4	no	—
48	C₂³×C₁₁	#97	1	1	yes	characteristic
49	C₂×C₄×C₁₁	—	4	2	no	—
50	C₂×C₄×C₁₁	C₄×C₈	1	2	yes	—
51	C₂×C₄×C₁₁	#97	1	2	yes	—
52	C₂×C₄×C₁₁	#97	1	1	yes	characteristic
53	C₂×C₄×C₁₁	#97	1	2	yes	—
54	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
55	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
56	C₈×C₁₁	C₄×C₈	1	2	yes	—
57	C₈×C₁₁	#97	1	2	yes	—
58	C₈×C₁₁	C₂²×C₈	1	2	yes	—
59	C₈×C₁₁	C₂×M₁₆	1	2	yes	—
60	C₁₁⋊C₈	—	4	4	no	—
61	C₂×M₃₂	Dic₁₁	1	2	yes	—
62	C₂²×C₁₆	—	11	2	no	—
63	#431	—	11	2	no	—
64	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
65	#346	—	11	2	no	—
66	#346	—	11	2	no	—
67	#346	C₂×D₁₁	1	2	yes	—
68	C₄×C₁₆	Dic₁₁	1	2	yes	—
69	#322	—	11	2	no	—
70	C₈²	—	11	2	no	—
71	C₂²×C₁₁	—	2	2	no	—
72	C₂²×C₁₁	#322	1	2	yes	—
73	C₂²×C₁₁	C₂×#97	1	1	yes	characteristic
74	C₄×C₁₁	—	2	2	no	—
75	C₄×C₁₁	—	2	2	no	—
76	C₄×C₁₁	#322	1	2	yes	—
77	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
78	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
79	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
80	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
81	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
82	M₃₂	C₁₁⋊C₈	1	8	yes	complemented
83	C₂×C₁₆	—	11	4	no	—
84	C₂×C₁₆	—	22	4	no	—
85	C₂×C₁₆	C₂×Dic₁₁	1	4	yes	—
86	C₄⋊C₈	—	22	2	no	—
87	C₂²⋊C₈	—	22	2	no	—
88	C₄×C₈	—	11	4	no	—
89	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
90	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
91	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
92	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
93	C₂×C₁₁	—	2	2	no	—
94	C₂×C₁₁	C₂×#322	1	1	yes	characteristic
95	C₂×C₁₁	#2110	1	2	yes	—
96	C₂²×C₄	#4313	1	2	yes	—
97	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
98	C₂×C₈	—	22	4	no	—
99	C₂×C₈	#4313	1	4	yes	—
100	C₂×C₈	C₂×C₁₁⋊C₈	1	4	yes	—
101	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
102	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
103	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
104	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
105	C₄²	#4313	1	2	yes	—
106	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
107	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
108	C₁₆	—	22	4	no	—
109	C₁₆	C₂×C₁₁⋊C₈	1	8	yes	—
110	C₁₁	#11406	1	1	yes	characteristic, complemented, Sylow
111	C₂³	#66879	1	1	yes	characteristic
112	C₂×C₄	—	4	2	no	—
113	C₂×C₄	C₄×C₁₁⋊C₈	1	2	yes	—
114	C₂×C₄	#66879	1	2	yes	—
115	C₂×C₄	#66879	1	1	yes	characteristic
116	C₂×C₄	#66879	1	2	yes	—
117	C₂×C₄	C₂×#4313	1	2	yes	—
118	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
119	C₈	—	44	4	no	—
120	C₈	C₄×C₁₁⋊C₈	1	2	yes	—
121	C₈	#66879	1	2	yes	—
122	C₈	C₂×#4313	1	2	yes	—
123	C₈	C₂²×C₁₁⋊C₈	1	2	yes	—
124	C₂²	—	2	2	no	—
125	C₂²	#10622093	1	2	yes	—
126	C₂²	C₂×#66879	1	1	yes	characteristic
127	C₄	—	2	2	no	—
128	C₄	—	2	2	no	—
129	C₄	#10622093	1	2	yes	—
130	C₄	C₂×C₄×C₁₁⋊C₈	1	1	yes	characteristic
131	C₄	C₂×#66879	1	1	yes	characteristic
132	C₂	—	2	2	no	—
133	C₂	C₂×#10622093	1	1	yes	characteristic
134	C₂	#13070220	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₄×Dic₁₁
commutator	C₄×C₁₁	C₂×C₄×C₈
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₄×C₁₁×M₃₂	C₂
socle	C₂²×C₁₁	C₂×#97
prime radical	C₂³×C₁₁	#97
cosocle	C₄×C₈×C₁₁	C₂³
hypercenter	C₄×M₃₂	D₁₁
hypocenter	C₁₁	#11406
LCS	G ▷ C₄×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
3. #13066536	C₂	semidirect
18. C₁₁×M₃₂	C₈	semidirect
82. M₃₂	C₁₁⋊C₈	semidirect
110. C₁₁	#11406	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622099	2
#13066899	2
#13066536	2
C₄×C₁₁×M₃₂	2
#11406	11