Subgroups — #14640641

Order 2816.

218 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070372	C₂	1	1	yes	maximal, characteristic
2	#13066899	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₁×C₁₆	—	2	1	no	—
5	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×#66876	—	2	1	no	—
7	#10622538	C₄	1	1	yes	characteristic
8	#10622538	C₄	1	1	yes	characteristic
9	C₁₁×C₄⋊C₁₆	—	2	1	no	—
10	C₁₁×C₄⋊C₁₆	C₄	1	2	yes	—
11	C₄⋊(C₁₁⋊C₁₆)	—	2	1	no	—
12	C₄⋊(C₁₁⋊C₁₆)	C₄	1	2	yes	—
13	#10622093	—	2	1	no	—
14	C₈×C₁₁⋊C₈	—	2	1	no	—
15	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₁	Q₈	1	1	yes	characteristic
17	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₁×C₁₆	—	2	2	no	—
19	C₂×C₁₁×C₁₆	—	4	1	no	—
20	C₂×C₁₁×C₁₆	—	4	1	no	—
21	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
24	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
25	C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
26	C₂²⋊(C₁₁⋊C₈)	C₈	1	2	yes	—
27	#66876	—	4	1	no	—
28	#66876	—	4	1	no	—
29	C₂×C₁₁⋊C₁₆	—	2	2	no	—
30	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
31	C₄⋊(C₁₁⋊C₈)	C₈	1	2	yes	—
32	C₄×C₁₁⋊C₈	—	2	1	no	—
33	C₄×C₁₁⋊C₈	—	2	1	no	—
34	#7153	—	11	1	no	maximal, Sylow
35	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
37	C₂²×C₄×C₁₁	M₁₆	1	1	yes	characteristic
38	C₂×C₈×C₁₁	—	2	1	no	—
39	C₂×C₈×C₁₁	—	2	1	no	—
40	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
45	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
46	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
47	C₂×C₈×C₁₁	Q₁₆	1	1	yes	characteristic
48	C₄²×C₁₁	C₄²	1	1	yes	characteristic
49	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
50	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
51	C₄²×C₁₁	M₁₆	1	1	yes	characteristic
52	C₂×C₁₁⋊C₈	—	2	2	no	—
53	C₂×C₁₁⋊C₈	—	2	2	no	—
54	C₁₁×C₁₆	—	4	2	no	—
55	C₁₁⋊C₁₆	—	4	2	no	—
56	#2150	—	11	1	no	—
57	C₂×C₄⋊C₁₆	D₁₁	1	1	yes	characteristic
58	#1450	—	11	1	no	—
59	C₂³×C₁₁	C₄⋊C₈	1	1	yes	characteristic
60	C₂×C₄×C₁₁	—	2	2	no	—
61	C₂×C₄×C₁₁	—	4	1	no	—
62	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
63	C₂×C₄×C₁₁	C₄×C₈	1	1	yes	characteristic
64	C₂×C₄×C₁₁	#97	1	1	yes	characteristic
65	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
66	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
67	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
68	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
69	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
70	C₂×C₄×C₁₁	#108	1	1	yes	characteristic
71	C₂×C₄×C₁₁	#108	1	1	yes	characteristic
72	C₈×C₁₁	—	2	1	no	—
73	C₈×C₁₁	—	2	1	no	—
74	C₈×C₁₁	#102	1	1	yes	characteristic
75	C₈×C₁₁	#102	1	1	yes	characteristic
76	C₈×C₁₁	#103	1	1	yes	characteristic
77	C₈×C₁₁	#103	1	1	yes	characteristic
78	C₁₁⋊C₈	—	4	2	no	—
79	C₁₁⋊C₈	—	4	2	no	—
80	C₂×M₃₂	—	22	1	no	—
81	C₂²×C₁₆	—	2	1	no	—
82	#431	—	11	1	no	—
83	#431	—	11	1	no	—
84	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
85	C₄⋊C₁₆	—	2	1	no	—
86	C₄⋊C₁₆	—	11	2	no	—
87	C₄⋊C₁₆	—	22	1	no	—
88	C₄⋊C₁₆	Dic₁₁	1	2	yes	—
89	#322	—	22	1	no	—
90	C₈²	—	22	1	no	—
91	C₂²×C₁₁	—	2	1	no	—
92	C₂²×C₁₁	—	2	1	no	—
93	C₂²×C₁₁	#334	1	1	yes	characteristic
94	C₂²×C₁₁	#335	1	1	yes	characteristic
95	C₂²×C₁₁	#336	1	1	yes	characteristic
96	C₄×C₁₁	—	2	1	no	—
97	C₄×C₁₁	—	2	1	no	—
98	C₄×C₁₁	—	2	1	no	—
99	C₄×C₁₁	#334	1	1	yes	characteristic
100	C₄×C₁₁	#335	1	1	yes	characteristic
101	C₄×C₁₁	#340	1	1	yes	characteristic
102	C₄×C₁₁	#341	1	1	yes	characteristic
103	C₄×C₁₁	#350	1	2	yes	—
104	C₂²×C₈	Dic₂₂	1	1	yes	characteristic
105	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
106	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
107	M₃₂	—	44	1	no	—
108	M₃₂	—	44	1	no	—
109	C₂×C₁₆	—	2	2	no	—
110	C₂×C₁₆	—	4	1	no	—
111	C₂×C₁₆	—	4	1	no	—
112	C₂×C₁₆	—	22	2	no	—
113	C₄⋊C₈	—	11	2	no	—
114	C₄⋊C₈	—	22	1	no	—
115	C₂²⋊C₈	—	11	2	no	—
116	C₂²⋊C₈	—	22	1	no	—
117	C₄×C₈	—	22	1	no	—
118	C₄×C₈	—	22	1	no	—
119	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
120	C₄×C₈	D₄₄	1	1	yes	characteristic
121	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
122	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
123	C₂×C₁₁	—	2	1	no	—
124	C₂×C₁₁	—	2	1	no	—
125	C₂×C₁₁	#1277	1	1	yes	characteristic
126	C₂×C₁₁	#1378	1	1	yes	characteristic
127	C₂×C₁₁	#1379	1	1	yes	characteristic
128	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
129	C₂²×C₄	#4313	1	1	yes	characteristic
130	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
131	C₂×C₈	—	2	1	no	—
132	C₂×C₈	—	2	1	no	—
133	C₂×C₈	—	22	2	no	—
134	C₂×C₈	—	22	2	no	—
135	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
136	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
137	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
138	C₂×C₈	#4323	1	1	yes	characteristic
139	C₂×C₈	#4324	1	1	yes	characteristic
140	C₂×C₈	#4325	1	1	yes	characteristic
141	C₂×C₈	#4326	1	1	yes	characteristic
142	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
143	C₄²	C₈×D₁₁	1	1	yes	characteristic
144	C₄²	#4313	1	1	yes	characteristic
145	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
146	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
147	C₁₆	—	4	2	no	—
148	C₁₆	—	44	2	no	—
149	C₁₁	#7153	1	1	yes	characteristic, complemented, Sylow
150	C₂³	Dic₁₁⋊C₈	1	1	yes	characteristic
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	4	1	no	—
153	C₂×C₄	#66871	1	1	yes	characteristic
154	C₂×C₄	#66872	1	1	yes	characteristic
155	C₂×C₄	C₈×Dic₁₁	1	1	yes	characteristic
156	C₂×C₄	Dic₁₁⋊C₈	1	1	yes	characteristic
157	C₂×C₄	#66879	1	1	yes	characteristic
158	C₂×C₄	(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
159	C₂×C₄	(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
160	C₂×C₄	#66886	1	1	yes	characteristic
161	C₂×C₄	#66886	1	1	yes	characteristic
162	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
163	C₈	—	2	1	no	—
164	C₈	—	2	1	no	—
165	C₈	—	44	2	no	—
166	C₈	—	44	2	no	—
167	C₈	#66873	1	1	yes	characteristic
168	C₈	#66874	1	1	yes	characteristic
169	C₈	#66896	1	1	yes	characteristic
170	C₈	#66899	1	1	yes	characteristic
171	C₂²	—	2	1	no	—
172	C₂²	—	2	1	no	—
173	C₂²	#10622117	1	1	yes	characteristic
174	C₂²	#10622118	1	1	yes	characteristic
175	C₂²	#10622188	1	1	yes	characteristic
176	C₄	—	2	1	no	—
177	C₄	—	2	1	no	—
178	C₄	—	2	1	no	—
179	C₄	#10622117	1	1	yes	characteristic
180	C₄	#10622118	1	1	yes	characteristic
181	C₄	#10622146	1	2	yes	—
182	C₄	#10622167	1	1	yes	characteristic
183	C₄	#10622196	1	1	yes	characteristic
184	C₂	—	2	1	no	—
185	C₂	—	2	1	no	—
186	C₂	#13066450	1	1	yes	characteristic
187	C₂	#13066703	1	1	yes	characteristic
188	C₂	#13066704	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	(C₂×D₁₁)⋊C₄
commutator	C₂×C₄×C₁₁	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₁
Fitting	C₂×C₁₁×C₄⋊C₁₆	C₂
socle	C₂²×C₁₁	#336
prime radical	C₂³×C₁₁	C₄⋊C₈
cosocle	C₂×C₄×C₈×C₁₁	C₂²
hypercenter	C₂×C₄⋊C₁₆	D₁₁
hypocenter	C₁₁	#7153
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
149. C₁₁	#7153	semidirect

Maximal subgroups

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

subgroup	index
#13070372	2
#13066899	2
C₂×C₁₁×C₄⋊C₁₆	2
#7153	11