Subgroups — #14647532

Order 2816.

362 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068732	C₂	1	2	yes	maximal
2	#13068361	C₂	1	1	yes	maximal, characteristic
3	C₂×#10622096	C₂	1	1	yes	maximal, characteristic
4	C₂×#10622118	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	C₄²×Dic₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
10	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
11	C₁₁×#335	—	2	2	no	—
12	#10622188	—	2	4	no	—
13	#10622188	C₄	1	2	yes	—
14	#10622188	C₄	1	2	yes	—
15	#10622118	—	2	4	no	—
16	#10622096	—	2	2	no	—
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	2	yes	—
22	C₂×C₄×Dic₁₁	D₄	1	2	yes	—
23	C₂×C₄×Dic₁₁	Q₈	1	2	yes	—
24	C₂²×C₁₁⋊C₈	—	2	2	no	—
25	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
26	C₁₁×C₄⋊C₈	—	2	2	no	—
27	C₁₁×C₄⋊C₈	—	2	2	no	—
28	C₄×C₈×C₁₁	D₄	1	2	yes	—
29	C₄×C₈×C₁₁	Q₈	1	2	yes	—
30	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
31	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
32	C₄×C₁₁⋊C₈	D₄	1	2	yes	—
33	C₄×C₁₁⋊C₈	Q₈	1	2	yes	—
34	#8811	—	11	1	no	maximal, Sylow
35	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
38	C₂²×Dic₁₁	C₄⋊C₄	1	4	yes	—
39	C₂×C₈×C₁₁	—	2	2	no	—
40	C₂×C₈×C₁₁	—	2	2	no	—
41	C₂×C₈×C₁₁	—	4	2	no	—
42	C₂×C₈×C₁₁	—	4	4	no	—
43	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
44	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
45	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
46	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
47	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
48	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
49	C₄×Dic₁₁	—	2	2	no	—
50	C₄×Dic₁₁	—	2	2	no	—
51	C₄×Dic₁₁	—	2	2	no	—
52	C₄×Dic₁₁	—	2	2	no	—
53	C₄×Dic₁₁	—	4	2	no	—
54	C₂×C₁₁⋊C₈	—	2	2	no	—
55	C₂×C₁₁⋊C₈	—	2	2	no	—
56	C₂×C₁₁⋊C₈	—	4	2	no	—
57	C₂×C₁₁⋊C₈	—	4	4	no	—
58	C₂×C₁₁⋊C₈	C₄⋊C₄	1	4	yes	—
59	#1831	—	11	2	no	—
60	#1744	—	11	1	no	—
61	C₂×#335	—	11	1	no	—
62	C₂×#335	D₁₁	1	1	yes	characteristic
63	C₂×#334	—	11	2	no	—
64	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₁	—	2	2	no	—
66	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
69	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
70	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
71	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
72	C₂×C₄×C₁₁	#131	1	2	yes	—
73	C₂×C₄×C₁₁	#131	1	2	yes	—
74	C₂×C₄×C₁₁	#135	1	2	yes	—
75	C₂×C₄×C₁₁	#135	1	2	yes	—
76	C₂×Dic₁₁	—	2	4	no	—
77	C₂×Dic₁₁	—	2	4	no	—
78	C₂×Dic₁₁	—	2	4	no	—
79	C₈×C₁₁	—	2	2	no	—
80	C₈×C₁₁	—	2	2	no	—
81	C₈×C₁₁	—	8	2	no	—
82	C₁₁⋊C₈	—	2	4	no	—
83	C₁₁⋊C₈	—	8	2	no	—
84	C₂×C₄⋊C₈	—	11	2	no	—
85	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
86	C₂×C₄×C₈	—	11	1	no	—
87	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
88	C₄³	—	11	1	no	—
89	#336	—	11	2	no	—
90	#336	—	11	2	no	—
91	#336	—	22	4	no	—
92	#335	—	2	2	no	—
93	#335	—	22	2	no	—
94	#334	—	22	4	no	—
95	C₂²×C₁₁	#384	1	1	yes	characteristic
96	C₂²×C₁₁	#424	1	2	yes	—
97	C₂²×C₁₁	#427	1	2	yes	—
98	C₂²×C₁₁	#430	1	2	yes	—
99	C₄×C₁₁	—	2	1	no	—
100	C₄×C₁₁	—	2	1	no	—
101	C₄×C₁₁	#424	1	1	yes	characteristic
102	C₄×C₁₁	#424	1	2	yes	—
103	C₄×C₁₁	#424	1	1	yes	characteristic
104	C₄×C₁₁	#495	1	1	yes	characteristic
105	C₄×C₁₁	#495	1	1	yes	characteristic
106	C₄×C₁₁	#499	1	2	yes	—
107	Dic₁₁	—	4	4	no	—
108	C₂²×C₈	—	2	2	no	—
109	C₂²×C₈	—	11	2	no	—
110	C₂²×C₈	—	22	2	no	—
111	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
112	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
113	C₂×C₄²	—	11	2	no	—
114	C₂×C₄²	—	11	2	no	—
115	C₂×C₄²	—	11	2	no	—
116	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
117	C₄⋊C₈	—	2	2	no	—
118	C₄⋊C₈	—	2	2	no	—
119	C₄⋊C₈	—	22	2	no	—
120	C₄⋊C₈	—	22	2	no	—
121	C₄×C₈	—	11	2	no	—
122	C₄×C₈	—	11	2	no	—
123	C₄×C₈	Dic₂₂	1	2	yes	—
124	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
125	C₂×C₁₁	#1572	1	4	yes	—
126	C₂×C₁₁	#1843	1	1	yes	characteristic
127	C₂×C₁₁	#1846	1	1	yes	characteristic
128	C₂×C₁₁	#1849	1	1	yes	characteristic
129	C₂²×C₄	—	11	4	no	—
130	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
131	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
132	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
133	C₂×C₈	—	2	2	no	—
134	C₂×C₈	—	2	2	no	—
135	C₂×C₈	—	4	4	no	—
136	C₂×C₈	—	4	2	no	—
137	C₂×C₈	—	11	4	no	—
138	C₂×C₈	—	22	2	no	—
139	C₂×C₈	—	22	2	no	—
140	C₂×C₈	—	44	4	no	—
141	C₂×C₈	—	44	2	no	—
142	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
143	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
144	C₄²	—	22	2	no	—
145	C₄²	—	22	2	no	—
146	C₄²	—	22	2	no	—
147	C₄²	—	22	2	no	—
148	C₄²	—	44	2	no	—
149	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
150	C₄²	D₄×D₁₁	1	1	yes	characteristic
151	C₄²	Q₈×D₁₁	1	1	yes	characteristic
152	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
153	C₁₁	#8811	1	1	yes	characteristic, complemented, Sylow
154	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	22	4	no	—
157	C₂×C₄	—	22	4	no	—
158	C₂×C₄	—	22	4	no	—
159	C₂×C₄	#66941	1	1	yes	characteristic
160	C₂×C₄	#66941	1	1	yes	characteristic
161	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
162	C₂×C₄	#66954	1	2	yes	—
163	C₂×C₄	#66960	1	2	yes	—
164	C₂×C₄	#66965	1	2	yes	—
165	C₂×C₄	#66972	1	2	yes	—
166	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
167	C₂×C₄	#66993	1	1	yes	characteristic
168	C₂×C₄	#66997	1	1	yes	characteristic
169	C₈	—	2	2	no	—
170	C₈	—	2	2	no	—
171	C₈	—	8	2	no	—
172	C₈	—	22	4	no	—
173	C₈	—	88	2	no	—
174	C₂²	#10622452	1	2	yes	—
175	C₂²	#10622493	1	2	yes	—
176	C₂²	#10622506	1	2	yes	—
177	C₂²	#10622589	1	1	yes	characteristic
178	C₄	—	2	1	no	—
179	C₄	—	2	1	no	—
180	C₄	—	44	4	no	—
181	C₄	#10622452	1	2	yes	—
182	C₄	#10622491	1	2	yes	—
183	C₄	#10622715	1	1	yes	characteristic
184	C₄	#10622732	1	1	yes	characteristic
185	C₄	#10622768	1	1	yes	characteristic
186	C₄	#10622804	1	1	yes	characteristic
187	C₂	#13067395	1	4	yes	—
188	C₂	#13068769	1	1	yes	characteristic
189	C₂	#13068779	1	1	yes	characteristic
190	C₂	#13068789	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₁
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₁₁×#335	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×#335	D₁₁
hypocenter	C₁₁	#8811
LCS	G ▷ C₂²×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
153. C₁₁	#8811	semidirect

Maximal subgroups

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

subgroup	index
#13068732	2
#13068361	2
C₂×#10622096	2
C₂×#10622118	2
C₂×C₁₁×#335	2
#8811	11