Subgroups — #14907273

Order 2816.

490 conjugacy classes of subgroups.

The subgroup lattice has 186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077550	C₂	1	1	yes	maximal, characteristic
2	#13070522	C₂	1	8	yes	maximal, complemented
3	#13070374	C₂	1	2	yes	maximal
4	#13070372	C₂	1	1	yes	maximal, characteristic
5	#13070212	C₂	1	2	yes	maximal
6	C₂×C₁₁×#346	C₂	1	1	yes	maximal, characteristic
7	#10623001	C₄	1	1	yes	characteristic
8	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
9	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	#10622715	C₄	1	2	yes	—
12	#10622714	C₂²	1	2	yes	—
13	C₂×#66876	C₂²	1	2	yes	—
14	#10622537	C₄	1	1	yes	characteristic
15	#10622292	C₄	1	4	yes	—
16	C₈×Dic₂₂	C₂²	1	4	yes	—
17	C₁₁×#346	C₂²	1	4	yes	—
18	#10622140	C₂²	1	4	yes	—
19	Dic₁₁⋊C₁₆	C₂²	1	8	yes	—
20	C₁₆×Dic₁₁	C₂²	1	4	yes	—
21	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	4	yes	—
22	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
24	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
25	#66979	C₂×C₄	1	2	yes	—
26	#66977	C₈	1	4	yes	—
27	C₂×#4318	C₂×C₄	1	2	yes	—
28	#66923	C₈	1	2	yes	—
29	#66922	C₈	1	2	yes	—
30	C₄×Dic₂₂	C₂×C₄	1	4	yes	—
31	C₂×C₁₁×C₁₆	—	2	2	no	—
32	C₂×C₁₁×C₁₆	Q₈	1	4	yes	complemented
33	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
34	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
35	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
36	C₄×C₈×C₁₁	C₂³	1	2	yes	—
37	#66879	C₂×C₄	1	4	yes	—
38	Dic₁₁⋊C₈	C₂×C₄	1	8	yes	—
39	C₈×Dic₁₁	C₂³	1	4	yes	—
40	#66876	—	2	4	no	—
41	C₂×C₁₁⋊C₁₆	C₂³	1	4	yes	—
42	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
43	#33475	—	11	1	no	maximal, Sylow
44	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
45	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
46	C₂×Dic₂₂	C₂×C₈	1	4	yes	—
47	C₂×C₈×C₁₁	—	2	2	no	—
48	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
49	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
51	C₂×C₈×C₁₁	#41	1	2	yes	—
52	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
53	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
54	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
55	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
56	C₂²⋊Dic₁₁	C₂×C₈	1	4	yes	—
57	C₄⋊Dic₁₁	C₂×C₈	1	4	yes	—
58	C₄⋊Dic₁₁	C₂×C₈	1	4	yes	—
59	Dic₁₁⋊C₄	C₂×C₈	1	8	yes	—
60	C₄×Dic₁₁	C₂²×C₄	1	4	yes	—
61	#4318	—	2	4	no	—
62	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
63	C₁₁×C₁₆	—	2	2	no	—
64	C₁₁×C₁₆	C₂×Q₈	1	4	yes	—
65	C₁₁⋊C₁₆	—	2	4	no	—
66	#2960	—	11	1	no	—
67	#2183	—	11	8	no	—
68	#2151	—	11	2	no	—
69	#2150	—	11	1	no	—
70	#2108	—	11	2	no	—
71	C₂×#346	D₁₁	1	1	yes	characteristic
72	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
73	C₂×C₄×C₁₁	—	4	2	no	—
74	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
75	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
76	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
77	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
78	C₂×C₄×C₁₁	#131	1	2	yes	—
79	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
80	C₂×Dic₁₁	C₂²×C₈	1	8	yes	—
81	Dic₂₂	—	4	4	no	—
82	C₈×C₁₁	—	2	2	no	—
83	C₈×C₁₁	C₄×Q₈	1	2	yes	—
84	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
85	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
86	C₁₁⋊C₈	—	2	4	no	—
87	#533	—	11	1	no	—
88	C₂×M₃₂	—	11	2	no	—
89	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
90	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
91	#446	—	11	4	no	—
92	C₈×Q₈	—	11	4	no	—
93	#424	—	11	2	no	—
94	#423	—	11	1	no	—
95	#405	—	11	2	no	—
96	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
97	C₄⋊C₁₆	—	11	8	no	—
98	C₄⋊C₁₆	—	11	4	no	—
99	#346	—	11	4	no	—
100	#346	C₂×D₁₁	1	4	yes	—
101	C₄×C₁₆	—	11	4	no	—
102	C₂²×C₁₁	—	2	2	no	—
103	C₂²×C₁₁	C₈×Q₈	1	2	yes	—
104	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
105	C₄×C₁₁	—	2	2	no	—
106	C₄×C₁₁	—	2	2	no	—
107	C₄×C₁₁	C₈×Q₈	1	2	yes	—
108	C₄×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
109	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
110	Dic₁₁	—	2	8	no	—
111	C₂×M₁₆	—	11	2	no	—
112	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
113	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
114	C₄⋊Q₈	—	11	2	no	—
115	#125	—	11	2	no	—
116	C₂²⋊Q₈	—	11	4	no	—
117	C₄×Q₈	—	11	4	no	—
118	#117	—	11	2	no	—
119	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
120	M₃₂	—	22	4	no	—
121	C₂×C₁₆	—	2	2	no	—
122	C₂×C₁₆	—	11	4	no	—
123	C₂×C₁₆	Dic₂₂	1	4	yes	complemented
124	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
125	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
126	C₄⋊C₈	—	11	8	no	—
127	C₄⋊C₈	—	11	4	no	—
128	#97	—	11	4	no	—
129	C₄×C₈	—	11	4	no	—
130	C₄×C₈	C₄×D₁₁	1	2	yes	—
131	C₄×C₈	C₂²×D₁₁	1	2	yes	—
132	C₂×C₁₁	—	2	2	no	—
133	C₂×C₁₁	C₂×C₈×Q₈	1	1	yes	characteristic
134	C₂×C₁₁	#3407	1	2	yes	—
135	C₂×Q₈	—	11	4	no	—
136	C₂²×C₄	C₈×D₁₁	1	2	yes	—
137	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
138	M₁₆	—	22	4	no	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	11	4	no	—
141	C₂×C₈	C₂×Dic₂₂	1	2	yes	—
142	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
143	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
144	C₂×C₈	#4339	1	2	yes	—
145	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
146	C₄⋊C₄	—	11	4	no	—
147	C₄⋊C₄	—	11	8	no	—
148	C₄⋊C₄	—	11	4	no	—
149	C₂²⋊C₄	—	11	4	no	—
150	C₄²	—	11	4	no	—
151	C₄²	C₈×D₁₁	1	1	yes	characteristic
152	C₄²	C₈×D₁₁	1	1	yes	characteristic
153	C₄²	C₂×C₄×D₁₁	1	2	yes	—
154	C₁₆	—	2	2	no	—
155	C₁₆	—	22	4	no	—
156	C₁₆	C₂×Dic₂₂	1	4	yes	—
157	C₁₁	#33475	1	1	yes	characteristic, complemented, Sylow
158	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
159	Q₈	—	44	4	no	—
160	C₂×C₄	—	4	2	no	—
161	C₂×C₄	—	11	8	no	—
162	C₂×C₄	C₄×Dic₂₂	1	2	yes	—
163	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
164	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
165	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
166	C₂×C₄	#66954	1	2	yes	—
167	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
168	C₈	—	2	2	no	—
169	C₈	—	22	4	no	—
170	C₈	C₄×Dic₂₂	1	2	yes	—
171	C₈	C₂²×Dic₂₂	1	1	yes	characteristic
172	C₈	C₂×#4339	1	1	yes	characteristic
173	C₂²	—	2	2	no	—
174	C₂²	C₈×Dic₂₂	1	2	yes	—
175	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
176	C₄	—	2	2	no	—
177	C₄	—	2	2	no	—
178	C₄	—	22	8	no	—
179	C₄	C₈×Dic₂₂	1	2	yes	—
180	C₄	C₂×C₄×Dic₂₂	1	1	yes	characteristic
181	C₄	C₂×#66954	1	1	yes	characteristic
182	C₂	—	2	2	no	—
183	C₂	C₂×C₈×Dic₂₂	1	1	yes	characteristic
184	C₂	#13081718	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₂×C₁₁×#346	C₂
prime radical	C₂³×C₁₁	C₂²×C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	C₂×#346	D₁₁
hypocenter	C₁₁	#33475
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#346

Complements

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

N	H ≅ G/N	type
2. #13070522	C₂	semidirect
32. C₂×C₁₁×C₁₆	Q₈	semidirect
123. C₂×C₁₆	Dic₂₂	semidirect
157. C₁₁	#33475	semidirect

Maximal subgroups

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

subgroup	index
#13077550	2
#13070522	2
#13070374	2
#13070372	2
#13070212	2
C₂×C₁₁×#346	2
#33475	11