Subgroups — #14640337

Order 2816.

344 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068362	C₂	1	1	yes	maximal, characteristic
2	C₄×#66867	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1831	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×C₄⋊C₈	C₄	1	2	yes	—
5	C₄³×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×#66867	—	2	1	no	—
7	C₂×#66867	C₄	1	2	yes	—
8	C₂×C₄×C₁₁⋊C₈	—	2	1	no	—
9	C₂×C₄×C₁₁⋊C₈	—	2	1	no	—
10	C₁₁×#336	—	2	1	no	—
11	C₁₁×#336	—	2	1	no	—
12	#10622162	—	2	1	no	—
13	#10622162	C₄	1	2	yes	—
14	C₂²×C₈×C₁₁	—	2	2	no	—
15	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
22	C₂²×C₁₁⋊C₈	—	2	2	no	—
23	C₂²×C₁₁⋊C₈	—	2	2	no	—
24	C₁₁×C₄⋊C₈	—	4	2	no	—
25	#66867	—	2	4	no	—
26	#66867	—	2	2	no	—
27	#66867	C₈	1	4	yes	complemented
28	C₄×C₁₁⋊C₈	—	2	4	no	—
29	C₄×C₁₁⋊C₈	—	2	4	no	—
30	#7030	—	11	1	no	maximal, Sylow
31	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
32	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₁	—	4	2	no	—
39	C₂×C₈×C₁₁	—	4	2	no	—
40	C₂×C₈×C₁₁	—	4	2	no	—
41	C₄²×C₁₁	—	2	1	no	—
42	C₄²×C₁₁	—	2	1	no	—
43	C₄²×C₁₁	—	2	2	no	—
44	C₄²×C₁₁	—	2	2	no	—
45	C₄²×C₁₁	—	2	2	no	—
46	C₄²×C₁₁	—	2	2	no	—
47	C₄²×C₁₁	—	4	1	no	—
48	C₄²×C₁₁	C₂×C₈	1	2	yes	—
49	C₄²×C₁₁	M₁₆	1	2	yes	—
50	C₂×C₁₁⋊C₈	—	2	4	no	—
51	C₂×C₁₁⋊C₈	—	2	4	no	—
52	C₂×C₁₁⋊C₈	—	2	4	no	—
53	C₂×C₁₁⋊C₈	—	2	4	no	—
54	C₂×C₁₁⋊C₈	—	4	2	no	—
55	C₂×C₁₁⋊C₈	—	4	2	no	—
56	#1831	D₁₁	1	1	yes	characteristic
57	#1744	—	11	1	no	—
58	C₄×#97	—	11	1	no	—
59	C₂³×C₁₁	#95	1	1	yes	characteristic
60	C₂×C₄×C₁₁	—	2	1	no	—
61	C₂×C₄×C₁₁	—	2	1	no	—
62	C₂×C₄×C₁₁	—	2	1	no	—
63	C₂×C₄×C₁₁	—	2	1	no	—
64	C₂×C₄×C₁₁	—	2	1	no	—
65	C₂×C₄×C₁₁	—	2	1	no	—
66	C₂×C₄×C₁₁	—	2	1	no	—
67	C₂×C₄×C₁₁	—	2	1	no	—
68	C₂×C₄×C₁₁	—	2	1	no	—
69	C₂×C₄×C₁₁	—	2	1	no	—
70	C₂×C₄×C₁₁	—	2	1	no	—
71	C₂×C₄×C₁₁	—	2	1	no	—
72	C₂×C₄×C₁₁	—	2	1	no	—
73	C₂×C₄×C₁₁	C₄×C₈	1	1	yes	characteristic
74	C₂×C₄×C₁₁	#97	1	1	yes	characteristic
75	C₂×C₄×C₁₁	C₂²⋊C₈	1	2	yes	—
76	C₂×C₄×C₁₁	#100	1	1	yes	characteristic
77	C₂×C₄×C₁₁	#101	1	1	yes	characteristic
78	C₂×C₄×C₁₁	#104	1	2	yes	—
79	C₂×C₄×C₁₁	#104	1	2	yes	—
80	C₂×C₄×C₁₁	#104	1	2	yes	—
81	C₂×C₄×C₁₁	C₄⋊C₈	1	2	yes	—
82	C₂×C₄×C₁₁	#108	1	2	yes	—
83	C₈×C₁₁	—	8	2	no	—
84	C₁₁⋊C₈	—	2	8	no	—
85	C₁₁⋊C₈	—	4	4	no	—
86	C₂×C₄⋊C₈	Dic₁₁	1	2	yes	—
87	C₂×#97	—	11	2	no	—
88	C₂×#97	—	22	1	no	—
89	C₂×C₄×C₈	—	22	1	no	—
90	C₂×C₄×C₈	—	22	1	no	—
91	C₄³	C₂×D₁₁	1	1	yes	characteristic
92	#336	—	2	1	no	—
93	#336	—	2	1	no	—
94	#336	—	11	2	no	—
95	#336	—	22	1	no	—
96	C₂²×C₁₁	#336	1	1	yes	characteristic
97	C₂²×C₁₁	#339	1	1	yes	characteristic
98	C₂²×C₁₁	#339	1	1	yes	characteristic
99	C₂²×C₁₁	#339	1	1	yes	characteristic
100	C₂²×C₁₁	#341	1	1	yes	characteristic
101	C₂²×C₁₁	#343	1	1	yes	characteristic
102	C₂²×C₁₁	#344	1	1	yes	characteristic
103	C₄×C₁₁	—	2	1	no	—
104	C₄×C₁₁	—	2	1	no	—
105	C₄×C₁₁	—	2	2	no	—
106	C₄×C₁₁	—	2	2	no	—
107	C₄×C₁₁	—	2	2	no	—
108	C₄×C₁₁	—	2	2	no	—
109	C₄×C₁₁	—	4	1	no	—
110	C₄×C₁₁	#329	1	2	yes	—
111	C₄×C₁₁	#330	1	2	yes	—
112	C₂²×C₈	—	2	2	no	—
113	C₂²×C₈	—	22	2	no	—
114	C₂²×C₈	—	22	2	no	—
115	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
116	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
117	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
118	C₂×C₄²	D₄₄	1	1	yes	characteristic
119	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
120	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
121	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
122	C₄⋊C₈	—	4	2	no	—
123	#97	—	11	4	no	—
124	#97	—	22	4	no	—
125	#97	—	22	2	no	—
126	C₄×C₈	—	22	4	no	—
127	C₄×C₈	—	22	4	no	—
128	C₂×C₁₁	#1276	1	1	yes	characteristic
129	C₂×C₁₁	#1278	1	1	yes	characteristic
130	C₂×C₁₁	#1283	1	1	yes	characteristic
131	C₂×C₁₁	#1295	1	1	yes	characteristic
132	C₂×C₁₁	#1299	1	1	yes	characteristic
133	C₂×C₁₁	#1300	1	1	yes	characteristic
134	C₂×C₁₁	#1302	1	1	yes	characteristic
135	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
136	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
137	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
138	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
139	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
140	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
141	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
142	C₂×C₈	—	4	2	no	—
143	C₂×C₈	—	4	2	no	—
144	C₂×C₈	—	4	2	no	—
145	C₂×C₈	—	22	4	no	—
146	C₂×C₈	—	22	4	no	—
147	C₂×C₈	—	22	4	no	—
148	C₂×C₈	—	22	4	no	—
149	C₂×C₈	—	44	2	no	—
150	C₂×C₈	—	44	2	no	—
151	C₄²	—	2	2	no	—
152	C₄²	—	2	2	no	—
153	C₄²	—	2	1	no	—
154	C₄²	—	2	1	no	—
155	C₄²	—	2	2	no	—
156	C₄²	—	2	2	no	—
157	C₄²	—	4	1	no	—
158	C₄²	C₈×D₁₁	1	2	yes	—
159	C₄²	#4313	1	2	yes	—
160	C₁₁	#7030	1	1	yes	characteristic, complemented, Sylow
161	C₂³	C₁₁⋊#95	1	1	yes	characteristic
162	C₂×C₄	—	2	1	no	—
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	1	no	—
166	C₂×C₄	—	2	1	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	1	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	2	1	no	—
174	C₂×C₄	—	2	1	no	—
175	C₂×C₄	C₈×Dic₁₁	1	1	yes	characteristic
176	C₂×C₄	Dic₁₁⋊C₈	1	2	yes	—
177	C₂×C₄	#66879	1	1	yes	characteristic
178	C₂×C₄	(C₂×D₁₁)⋊C₈	1	2	yes	—
179	C₂×C₄	#66886	1	2	yes	—
180	C₂×C₄	#66889	1	2	yes	—
181	C₂×C₄	#66897	1	1	yes	characteristic
182	C₂×C₄	#66900	1	1	yes	characteristic
183	C₂×C₄	#66901	1	2	yes	—
184	C₂×C₄	#66901	1	2	yes	—
185	C₈	—	8	2	no	—
186	C₈	—	22	8	no	—
187	C₈	—	44	4	no	—
188	C₂²	#10622168	1	1	yes	characteristic
189	C₂²	#10622170	1	1	yes	characteristic
190	C₂²	#10622170	1	1	yes	characteristic
191	C₂²	#10622188	1	1	yes	characteristic
192	C₂²	#10622193	1	1	yes	characteristic
193	C₂²	#10622194	1	1	yes	characteristic
194	C₂²	#10622196	1	1	yes	characteristic
195	C₄	—	2	2	no	—
196	C₄	—	2	2	no	—
197	C₄	—	2	2	no	—
198	C₄	—	2	2	no	—
199	C₄	—	2	1	no	—
200	C₄	—	2	1	no	—
201	C₄	—	4	1	no	—
202	C₄	#10622178	1	2	yes	—
203	C₄	#10622181	1	2	yes	—
204	C₂	#13066448	1	1	yes	characteristic
205	C₂	#13066452	1	1	yes	characteristic
206	C₂	#13066466	1	1	yes	characteristic
207	C₂	#13066497	1	1	yes	characteristic
208	C₂	#13066505	1	1	yes	characteristic
209	C₂	#13066508	1	1	yes	characteristic
210	C₂	#13066514	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₁₁
commutator	C₂×C₄×C₁₁	C₄×C₈
Frattini	C₄³	C₂×D₁₁
Fitting	C₁₁×#1831	C₂
socle, prime radical	C₂³×C₁₁	#95
cosocle	C₄³×C₁₁	C₂²
hypercenter	#1831	D₁₁
hypocenter	C₁₁	#7030
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1831

Complements

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

N	H ≅ G/N	type
27. #66867	C₈	semidirect
160. C₁₁	#7030	semidirect

Maximal subgroups

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

subgroup	index
#13068362	2
C₄×#66867	2
C₁₁×#1831	2
#7030	11