Subgroups — #14670190

Order 2816.

382 conjugacy classes of subgroups.

The subgroup lattice has 148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622101	C₂	1	4	yes	maximal
2	#13070372	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	C₂×#66876	C₂²	1	4	yes	—
10	#10622101	—	2	8	no	—
11	C₄⋊(C₁₁⋊C₁₆)	—	2	4	no	—
12	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
14	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
15	C₂×C₄²×C₁₁	—	2	2	no	—
16	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₁₁	—	2	4	no	—
19	C₄×C₈×C₁₁	C₈	1	2	yes	—
20	C₄×C₈×C₁₁	C₈	1	2	yes	—
21	C₄×C₈×C₁₁	D₄	1	2	yes	—
22	C₄×C₈×C₁₁	D₄	1	4	yes	—
23	C₄×C₈×C₁₁	Q₈	1	4	yes	—
24	C₄×C₈×C₁₁	Q₈	1	2	yes	—
25	#66876	—	2	8	no	—
26	C₂×C₁₁⋊C₁₆	—	2	4	no	—
27	#12900	—	11	1	no	maximal, Sylow
28	C₂²×C₄×C₁₁	—	2	2	no	—
29	C₂²×C₄×C₁₁	M₁₆	1	2	yes	—
30	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₁	—	2	2	no	—
32	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
33	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
34	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
35	C₂×C₈×C₁₁	M₁₆	1	4	yes	—
36	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
37	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
38	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
39	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
40	C₄²×C₁₁	—	2	8	no	—
41	C₄²×C₁₁	—	2	2	no	—
42	C₄²×C₁₁	C₄⋊C₄	1	4	yes	—
43	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
44	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
45	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
46	C₁₁⋊C₁₆	—	4	4	no	—
47	C₂×#364	—	11	4	no	—
48	#2150	—	11	2	no	—
49	C₄²×C₈	D₁₁	1	1	yes	characteristic
50	C₂³×C₁₁	C₂×M₁₆	1	1	yes	characteristic
51	C₂×C₄×C₁₁	—	2	8	no	—
52	C₂×C₄×C₁₁	—	2	4	no	—
53	C₂×C₄×C₁₁	—	2	4	no	—
54	C₂×C₄×C₁₁	C₄⋊C₈	1	2	yes	—
55	C₂×C₄×C₁₁	C₄⋊C₈	1	2	yes	—
56	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
57	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
59	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
60	C₈×C₁₁	—	2	2	no	—
61	C₈×C₁₁	C₄⋊C₈	1	8	yes	—
62	C₈×C₁₁	#127	1	1	yes	characteristic
63	C₈×C₁₁	C₄⋊Q₈	1	2	yes	—
64	C₈×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
65	C₂×M₃₂	—	11	4	no	—
66	C₂×C₄×C₈	Dic₁₁	1	2	yes	—
67	C₂×C₄×C₈	Dic₁₁	1	1	yes	characteristic
68	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
69	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
70	C₄³	Dic₁₁	1	1	yes	characteristic
71	#364	—	22	8	no	—
72	C₄⋊C₁₆	—	22	4	no	—
73	C₂²×C₁₁	—	2	2	no	—
74	C₂²×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
75	C₂²×C₁₁	#423	1	2	yes	—
76	C₄×C₁₁	—	2	8	no	—
77	C₄×C₁₁	—	2	2	no	—
78	C₄×C₁₁	#364	1	4	yes	complemented
79	C₄×C₁₁	#384	1	1	yes	characteristic
80	C₄×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
81	C₄×C₁₁	#423	1	1	yes	characteristic
82	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
83	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
84	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
85	C₂×C₄²	—	2	2	no	—
86	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
87	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
88	M₃₂	—	22	8	no	—
89	C₂×C₁₆	—	22	4	no	—
90	C₄×C₈	—	2	4	no	—
91	C₄×C₈	C₁₁⋊C₈	1	2	yes	—
92	C₄×C₈	C₁₁⋊C₈	1	2	yes	—
93	C₄×C₈	Dic₂₂	1	4	yes	—
94	C₄×C₈	Dic₂₂	1	2	yes	—
95	C₄×C₈	D₄₄	1	4	yes	—
96	C₄×C₈	D₄₄	1	2	yes	—
97	C₂×C₁₁	—	2	2	no	—
98	C₂×C₁₁	#1842	1	1	yes	characteristic
99	C₂×C₁₁	C₂×#364	1	2	yes	—
100	C₂²×C₄	—	2	2	no	—
101	C₂²×C₄	#4318	1	2	yes	—
102	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
103	C₂×C₈	—	2	2	no	—
104	C₂×C₈	C₂×C₁₁⋊C₈	1	4	yes	—
105	C₂×C₈	#4318	1	4	yes	—
106	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
107	C₂×C₈	C₄⋊Dic₁₁	1	4	yes	—
108	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
109	C₂×C₈	C₂×Dic₂₂	1	2	yes	—
110	C₂×C₈	C₂×D₄₄	1	2	yes	—
111	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
112	C₄²	—	2	8	no	—
113	C₄²	—	2	2	no	—
114	C₄²	C₂×C₁₁⋊C₈	1	1	yes	characteristic
115	C₄²	C₂×C₁₁⋊C₈	1	1	yes	characteristic
116	C₄²	C₄⋊Dic₁₁	1	4	yes	—
117	C₄²	C₄⋊Dic₁₁	1	2	yes	—
118	C₁₆	—	44	4	no	—
119	C₁₁	#12900	1	1	yes	characteristic, complemented, Sylow
120	C₂³	C₂×#4318	1	1	yes	characteristic
121	C₂×C₄	—	2	8	no	—
122	C₂×C₄	—	2	4	no	—
123	C₂×C₄	—	2	4	no	—
124	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	2	yes	—
125	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	2	yes	—
126	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
127	C₂×C₄	C₂×#4318	1	2	yes	—
128	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
129	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
130	C₈	—	2	2	no	—
131	C₈	C₄⋊(C₁₁⋊C₈)	1	8	yes	—
132	C₈	#66922	1	2	yes	—
133	C₈	#66922	1	1	yes	characteristic
134	C₈	#66927	1	1	yes	characteristic
135	C₂²	—	2	2	no	—
136	C₂²	C₂×C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
137	C₂²	#10622537	1	2	yes	—
138	C₄	—	2	8	no	—
139	C₄	—	2	2	no	—
140	C₄	#10622101	1	4	yes	complemented
141	C₄	C₂×C₄⋊(C₁₁⋊C₈)	1	2	yes	—
142	C₄	#10622537	1	1	yes	characteristic
143	C₄	#10622548	1	1	yes	characteristic
144	C₂	—	2	2	no	—
145	C₂	#13068768	1	1	yes	characteristic
146	C₂	C₂×#10622101	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₂×D₄₄
commutator	C₂×C₄×C₁₁	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₄²×C₈×C₁₁	C₂
socle	C₂²×C₁₁	C₂×C₄⋊C₈
prime radical	C₂³×C₁₁	C₂×M₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₄²×C₈	D₁₁
hypocenter	C₁₁	#12900
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
78. C₄×C₁₁	#364	semidirect
119. C₁₁	#12900	semidirect
140. C₄	#10622101	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622101	2
#13070372	2
C₄²×C₈×C₁₁	2
#12900	11