Subgroups — #14645025

Order 2816.

430 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#66881	C₂	1	1	yes	maximal, characteristic
2	#13068481	C₂	1	2	yes	maximal
3	C₂×#10622093	C₂	1	1	yes	maximal, characteristic
4	#13066455	C₂	1	2	yes	maximal
5	C₂×C₁₁×#335	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×#66881	C₄	1	2	yes	—
9	C₂×C₈×Dic₁₁	—	2	2	no	—
10	C₄×C₄⋊Dic₁₁	C₂²	1	2	yes	—
11	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
13	C₁₁×#335	C₄	1	4	yes	complemented
14	#10622189	C₄	1	2	yes	—
15	#10622188	—	2	2	no	—
16	#10622093	C₄	1	4	yes	complemented
17	C₂²×C₈×C₁₁	—	2	2	no	—
18	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₁	C₂×C₄	1	4	yes	—
22	C₂×C₄×Dic₁₁	—	2	2	no	—
23	C₂²×C₁₁⋊C₈	—	2	1	no	—
24	C₂²×C₁₁⋊C₈	D₄	1	2	yes	—
25	C₁₁×C₄⋊C₈	—	2	2	no	—
26	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
27	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
28	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
29	C₁₁⋊#95	—	2	2	no	—
30	#66881	C₈	1	8	yes	complemented
31	C₈×Dic₁₁	—	4	4	no	—
32	C₄×C₁₁⋊C₈	—	2	1	no	—
33	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
34	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
35	C₄×C₁₁⋊C₈	Q₈	1	2	yes	—
36	#8285	—	11	1	no	maximal, Sylow
37	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
40	C₂²×Dic₁₁	—	2	4	no	—
41	C₂×C₈×C₁₁	—	2	4	no	—
42	C₂×C₈×C₁₁	—	2	2	no	—
43	C₂×C₈×C₁₁	—	4	2	no	—
44	C₂×C₈×C₁₁	—	4	2	no	—
45	C₂×C₈×C₁₁	C₄²	1	2	yes	—
46	C₂×C₈×C₁₁	C₄²	1	2	yes	—
47	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
48	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
49	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
50	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
51	C₄²×C₁₁	#41	1	1	yes	characteristic
52	C₄⋊Dic₁₁	—	2	4	no	—
53	C₄⋊Dic₁₁	C₂×C₈	1	8	yes	—
54	C₄×Dic₁₁	—	4	2	no	—
55	C₄×Dic₁₁	—	4	2	no	—
56	C₂×C₁₁⋊C₈	—	2	2	no	—
57	C₂×C₁₁⋊C₈	—	2	2	no	—
58	C₂×C₁₁⋊C₈	—	2	2	no	—
59	C₂×C₁₁⋊C₈	—	4	2	no	—
60	C₂×C₁₁⋊C₈	C₄⋊C₄	1	4	yes	—
61	C₄×#106	—	11	1	no	—
62	C₈×C₄⋊C₄	—	11	2	no	—
63	C₂×#335	D₁₁	1	1	yes	characteristic
64	C₂×#322	—	11	1	no	—
65	#1279	—	11	2	no	—
66	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
67	C₂×C₄×C₁₁	—	2	2	no	—
68	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
69	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
71	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
72	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
73	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
74	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
75	C₂×C₄×C₁₁	#131	1	2	yes	—
76	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
77	C₂×C₄×C₁₁	#137	1	2	yes	—
78	C₂×Dic₁₁	—	2	8	no	—
79	C₂×Dic₁₁	—	4	4	no	—
80	C₂×Dic₁₁	—	4	4	no	—
81	C₈×C₁₁	—	2	2	no	—
82	C₈×C₁₁	—	4	4	no	—
83	C₈×C₁₁	C₄×C₈	1	4	yes	complemented
84	C₁₁⋊C₈	—	2	4	no	—
85	C₁₁⋊C₈	—	4	2	no	—
86	C₂×#106	—	11	2	no	—
87	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
88	C₂×C₄×C₈	—	11	1	no	—
89	C₂×C₄×C₈	—	11	1	no	—
90	C₂×C₄×C₈	—	22	2	no	—
91	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
92	C₄×C₄⋊C₄	—	11	2	no	—
93	#340	—	11	2	no	—
94	#336	—	22	2	no	—
95	#335	Dic₁₁	1	4	yes	complemented
96	#322	—	11	4	no	—
97	C₂²×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
98	C₂²×C₁₁	C₈×D₄	1	2	yes	—
99	C₂²×C₁₁	#440	1	2	yes	—
100	C₂²×C₁₁	#444	1	2	yes	—
101	C₄×C₁₁	—	2	1	no	—
102	C₄×C₁₁	—	2	1	no	—
103	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
104	C₄×C₁₁	#405	1	1	yes	characteristic
105	C₄×C₁₁	#428	1	2	yes	—
106	C₄×C₁₁	#441	1	1	yes	characteristic
107	C₄×C₁₁	#442	1	1	yes	characteristic
108	C₄×C₁₁	C₈×Q₈	1	2	yes	—
109	Dic₁₁	—	4	8	no	—
110	C₂²×C₈	—	2	2	no	—
111	C₂²×C₈	—	11	2	no	—
112	C₂²×C₈	—	22	1	no	—
113	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
114	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
115	C₂×C₄⋊C₄	—	11	4	no	—
116	C₂×C₄²	—	22	2	no	—
117	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
118	#106	—	11	8	no	—
119	C₄⋊C₈	—	2	2	no	—
120	C₄⋊C₈	C₂×Dic₁₁	1	4	yes	—
121	C₄×C₈	—	11	2	no	—
122	C₄×C₈	—	11	2	no	—
123	C₄×C₈	—	11	2	no	—
124	C₄×C₈	—	22	1	no	—
125	C₄×C₈	—	44	4	no	—
126	C₄×C₈	C₄×D₁₁	1	2	yes	—
127	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
128	#95	—	22	2	no	—
129	C₂×C₁₁	SD₁₆⋊C₈	1	4	yes	—
130	C₂×C₁₁	C₈×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₁₁	#1773	1	1	yes	characteristic
132	C₂×C₁₁	#1776	1	1	yes	characteristic
133	C₂²×C₄	—	22	4	no	—
134	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
135	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
136	C₂²×C₄	#4343	1	1	yes	characteristic
137	C₂×C₈	—	2	2	no	—
138	C₂×C₈	—	2	4	no	—
139	C₂×C₈	—	4	2	no	—
140	C₂×C₈	—	4	2	no	—
141	C₂×C₈	—	11	4	no	—
142	C₂×C₈	—	22	2	no	—
143	C₂×C₈	—	22	2	no	—
144	C₂×C₈	—	22	2	no	—
145	C₂×C₈	—	44	2	no	—
146	C₂×C₈	C₈×D₁₁	1	4	yes	—
147	C₂×C₈	C₄×Dic₁₁	1	2	yes	—
148	C₂×C₈	C₄×Dic₁₁	1	2	yes	—
149	C₄⋊C₄	—	11	8	no	—
150	C₄⋊C₄	—	22	4	no	—
151	C₄²	—	44	2	no	—
152	C₄²	—	44	2	no	—
153	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
154	C₄²	#4341	1	1	yes	characteristic
155	C₄²	Q₈×D₁₁	1	1	yes	characteristic
156	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
157	C₁₁	#8285	1	1	yes	characteristic, complemented, Sylow
158	C₂³	#66946	1	1	yes	characteristic
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	22	8	no	—
161	C₂×C₄	—	44	4	no	—
162	C₂×C₄	—	44	4	no	—
163	C₂×C₄	#66940	1	1	yes	characteristic
164	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
165	C₂×C₄	#66945	1	1	yes	characteristic
166	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
167	C₂×C₄	#66960	1	2	yes	—
168	C₂×C₄	#66964	1	2	yes	—
169	C₂×C₄	#66971	1	2	yes	—
170	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
171	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
172	C₂×C₄	Q₈×Dic₁₁	1	1	yes	characteristic
173	C₈	—	2	2	no	—
174	C₈	—	4	4	no	—
175	C₈	—	22	4	no	—
176	C₈	—	44	2	no	—
177	C₈	C₈×Dic₁₁	1	4	yes	complemented
178	C₂²	#10622447	1	2	yes	—
179	C₂²	#10622502	1	2	yes	—
180	C₂²	#10622507	1	2	yes	—
181	C₂²	C₄⋊C₄×Dic₁₁	1	1	yes	characteristic
182	C₄	—	2	1	no	—
183	C₄	—	2	1	no	—
184	C₄	—	44	8	no	—
185	C₄	#10622443	1	2	yes	—
186	C₄	#10622494	1	2	yes	—
187	C₄	C₂×C₈×Dic₁₁	1	1	yes	characteristic
188	C₄	#10622735	1	1	yes	characteristic
189	C₄	#10622765	1	1	yes	characteristic
190	C₄	#10622797	1	1	yes	characteristic
191	C₂	#13067427	1	4	yes	—
192	C₂	#13068481	1	1	yes	characteristic
193	C₂	#13068503	1	1	yes	characteristic
194	C₂	#13068515	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₁
commutator	C₄×C₁₁	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₁₁×#335	C₂
socle, prime radical	C₂³×C₁₁	C₄×D₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×#335	D₁₁
hypocenter	C₁₁	#8285
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
13. C₁₁×#335	C₄	semidirect
16. #10622093	C₄	semidirect
30. #66881	C₈	semidirect
83. C₈×C₁₁	C₄×C₈	semidirect
95. #335	Dic₁₁	semidirect
157. C₁₁	#8285	semidirect
177. C₈	C₈×Dic₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₄×#66881	2
#13068481	2
C₂×#10622093	2
#13066455	2
C₂×C₁₁×#335	2
#8285	11