Subgroups — #14909279

Order 2816.

474 conjugacy classes of subgroups.

The subgroup lattice has 220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13079152	C₂	1	2	yes	maximal
2	#13070900	C₂	1	4	yes	maximal, complemented
3	#13070893	C₂	1	2	yes	maximal, complemented
4	#13070890	C₂	1	2	yes	maximal, complemented
5	#13070402	C₂	1	2	yes	maximal
6	#13070400	C₂	1	1	yes	maximal, characteristic
7	#13070212	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₁×#366	C₂	1	1	yes	maximal, characteristic
9	#10623031	—	2	2	no	—
10	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×#107	C₂²	1	2	yes	—
12	#10622719	C₂²	1	2	yes	—
13	#10622714	C₂²	1	1	yes	characteristic
14	C₂×#66876	C₂²	1	1	yes	characteristic
15	#10622577	—	2	2	no	—
16	#10622491	C₂²	1	4	yes	—
17	#10622489	—	2	4	no	—
18	#10622487	C₂²	1	4	yes	—
19	C₁₁×#366	C₂²	1	2	yes	—
20	C₁₁×#366	C₂²	1	2	yes	—
21	#10622143	C₂²	1	2	yes	—
22	#10622142	C₂²	1	1	yes	characteristic
23	#10622142	C₂²	1	1	yes	characteristic
24	#10622140	C₂²	1	2	yes	—
25	C₁₆×Dic₁₁	C₂²	1	2	yes	—
26	#10622128	C₂²	1	4	yes	—
27	#10622127	C₂²	1	4	yes	—
28	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
29	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
30	#66979	—	2	2	no	—
31	#66979	D₄	1	1	yes	characteristic
32	#66977	—	4	4	no	—
33	C₂×#4318	D₄	1	1	yes	characteristic
34	#66943	—	2	4	no	—
35	#66943	—	4	2	no	—
36	#66941	—	2	4	no	—
37	#66941	—	4	2	no	—
38	C₂×C₁₁×C₁₆	Q₈	1	4	yes	complemented
39	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
40	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
41	C₁₁×#107	—	2	2	no	—
42	C₁₁×#107	C₂³	1	4	yes	—
43	#66882	C₂³	1	2	yes	—
44	#66882	C₂³	1	2	yes	—
45	#66881	—	2	2	no	—
46	#66879	D₄	1	2	yes	—
47	C₈×Dic₁₁	C₂³	1	2	yes	—
48	#66876	Q₈	1	4	yes	complemented
49	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
50	#66872	—	2	4	no	—
51	#66871	—	2	4	no	—
52	#33729	—	11	1	no	maximal, Sylow
53	C₂²×C₄×C₁₁	—	4	2	no	—
54	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
55	C₂×Dic₂₂	—	4	4	no	—
56	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
58	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
59	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
60	C₁₁×C₄⋊C₄	—	2	4	no	—
61	C₁₁×C₄⋊C₄	—	4	2	no	—
62	C₂²⋊Dic₁₁	—	4	2	no	—
63	C₂²⋊Dic₁₁	D₈	1	2	yes	—
64	C₄⋊Dic₁₁	—	2	2	no	—
65	C₄⋊Dic₁₁	—	2	2	no	—
66	C₄⋊Dic₁₁	—	4	4	no	—
67	C₄⋊Dic₁₁	D₈	1	1	yes	characteristic
68	C₄⋊Dic₁₁	D₈	1	1	yes	characteristic
69	Dic₁₁⋊C₄	—	4	4	no	—
70	Dic₁₁⋊C₄	—	4	4	no	—
71	C₄×Dic₁₁	—	4	2	no	—
72	C₄×Dic₁₁	C₂×D₄	1	2	yes	—
73	#4318	Q₁₆	1	4	yes	—
74	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
75	C₁₁×C₁₆	C₂×Q₈	1	2	yes	—
76	C₁₁×C₁₆	C₂×Q₈	1	2	yes	—
77	C₁₁⋊C₁₆	C₂×Q₈	1	4	yes	—
78	#3164	—	11	2	no	—
79	#2255	—	11	4	no	—
80	#2253	—	11	2	no	—
81	#2252	—	11	2	no	—
82	#2159	—	11	2	no	—
83	#2158	—	11	1	no	—
84	C₂×#366	D₁₁	1	1	yes	characteristic
85	#2108	—	11	1	no	—
86	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
87	C₂×C₄×C₁₁	—	4	4	no	—
88	C₂×C₄×C₁₁	—	16	2	no	—
89	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
90	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
91	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
92	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
93	C₂×Dic₁₁	—	4	2	no	—
94	C₂×Dic₁₁	—	4	2	no	—
95	C₂×Dic₁₁	C₂×D₈	1	2	yes	—
96	C₂×Dic₁₁	C₂×D₈	1	2	yes	—
97	Dic₂₂	—	16	4	no	—
98	C₈×C₁₁	C₄⋊Q₈	1	2	yes	—
99	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
100	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
101	C₁₁⋊C₈	C₂×Q₁₆	1	4	yes	—
102	#544	—	22	2	no	—
103	C₂×M₃₂	—	11	1	no	—
104	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
105	#501	—	22	4	no	—
106	#500	—	11	4	no	—
107	#499	—	11	4	no	—
108	#428	—	22	2	no	—
109	#427	—	11	2	no	—
110	C₂×#107	C₂×D₁₁	1	2	yes	—
111	#405	—	11	1	no	—
112	#367	—	11	2	no	—
113	#367	—	11	4	no	—
114	#366	—	11	1	no	—
115	#366	—	11	1	no	—
116	#366	—	11	4	no	—
117	#366	C₂×D₁₁	1	2	yes	—
118	#366	C₂×D₁₁	1	2	yes	—
119	#346	—	11	2	no	—
120	C₄×C₁₆	—	11	2	no	—
121	C₂²×C₁₁	—	2	1	no	—
122	C₂²×C₁₁	—	2	1	no	—
123	C₂²×C₁₁	#500	1	2	yes	—
124	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
125	C₄×C₁₁	—	8	4	no	—
126	C₄×C₁₁	#500	1	2	yes	—
127	C₄×C₁₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
128	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
129	Dic₁₁	—	2	2	no	—
130	Dic₁₁	—	2	2	no	—
131	Dic₁₁	—	8	2	no	—
132	Dic₁₁	—	8	2	no	—
133	C₂×M₁₆	—	11	1	no	—
134	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
135	C₄⋊Q₈	—	22	4	no	—
136	C₄⋊Q₈	—	44	2	no	—
137	#125	—	22	4	no	—
138	#125	—	44	2	no	—
139	C₂²⋊Q₈	—	44	4	no	—
140	#117	—	11	1	no	—
141	#117	—	22	2	no	—
142	C₂×C₄⋊C₄	—	2	2	no	—
143	M₃₂	—	11	4	no	—
144	C₂×C₁₆	—	11	2	no	—
145	C₂×C₁₆	Dic₂₂	1	4	yes	complemented
146	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
147	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
148	#107	—	2	2	no	—
149	#107	—	11	2	no	—
150	#107	—	11	2	no	—
151	#107	—	22	4	no	—
152	#107	C₂²×D₁₁	1	4	yes	—
153	#106	—	22	4	no	—
154	#106	—	22	2	no	—
155	#97	—	11	2	no	—
156	C₄×C₈	—	11	2	no	—
157	C₂×C₁₁	—	2	2	no	—
158	C₂×C₁₁	C₂×#500	1	1	yes	characteristic
159	C₂×C₁₁	#3415	1	1	yes	characteristic
160	C₂×C₁₁	#3417	1	1	yes	characteristic
161	C₂×Q₈	—	44	4	no	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
164	M₁₆	—	11	4	no	—
165	C₂×C₈	—	11	2	no	—
166	C₂×C₈	C₂×Dic₂₂	1	2	yes	—
167	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
168	C₂×C₈	Q₈×D₁₁	1	2	yes	—
169	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
170	C₄⋊C₄	—	2	4	no	—
171	C₄⋊C₄	—	4	2	no	—
172	C₄⋊C₄	—	11	1	no	—
173	C₄⋊C₄	—	11	1	no	—
174	C₄⋊C₄	—	22	2	no	—
175	C₄⋊C₄	—	22	2	no	—
176	C₄⋊C₄	—	44	4	no	—
177	C₄⋊C₄	—	44	4	no	—
178	C₄⋊C₄	—	44	4	no	—
179	C₂²⋊C₄	—	11	2	no	—
180	C₂²⋊C₄	—	44	2	no	—
181	C₄²	—	11	2	no	—
182	C₄²	—	44	2	no	—
183	C₁₆	—	11	4	no	—
184	C₁₆	C₂×Dic₂₂	1	2	yes	—
185	C₁₆	C₂×Dic₂₂	1	2	yes	—
186	C₁₁	#33729	1	1	yes	characteristic, complemented, Sylow
187	C₂³	D₈×D₁₁	1	1	yes	characteristic
188	Q₈	—	176	4	no	—
189	C₂×C₄	—	4	4	no	—
190	C₂×C₄	—	11	2	no	—
191	C₂×C₄	—	11	2	no	—
192	C₂×C₄	—	16	2	no	—
193	C₂×C₄	—	44	2	no	—
194	C₂×C₄	—	44	2	no	—
195	C₂×C₄	#66941	1	2	yes	—
196	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
197	C₂×C₄	Q₁₆×D₁₁	1	2	yes	—
198	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
199	C₈	—	11	4	no	—
200	C₈	#66941	1	2	yes	—
201	C₈	C₂²×Dic₂₂	1	1	yes	characteristic
202	C₈	C₂×Q₈×D₁₁	1	1	yes	characteristic
203	C₂²	—	2	1	no	—
204	C₂²	—	2	1	no	—
205	C₂²	#10622487	1	2	yes	—
206	C₂²	C₂×D₈×D₁₁	1	1	yes	characteristic
207	C₄	—	8	4	no	—
208	C₄	—	22	2	no	—
209	C₄	—	22	2	no	—
210	C₄	—	88	2	no	—
211	C₄	—	88	2	no	—
212	C₄	#10622487	1	2	yes	—
213	C₄	C₂×#66941	1	1	yes	characteristic
214	C₄	C₂×Q₁₆×D₁₁	1	1	yes	characteristic
215	C₂	—	2	2	no	—
216	C₂	C₂×#10622487	1	1	yes	characteristic
217	C₂	#13081753	1	1	yes	characteristic
218	C₂	#13081765	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₁
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₂×C₁₁×#366	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	C₂³×C₁₁	C₂×D₈
hypercenter	C₂×#366	D₁₁
hypocenter	C₁₁	#33729
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

Complements

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

N	H ≅ G/N	type
2. #13070900	C₂	semidirect
3. #13070893	C₂	semidirect
4. #13070890	C₂	semidirect
38. C₂×C₁₁×C₁₆	Q₈	semidirect
48. #66876	Q₈	semidirect
145. C₂×C₁₆	Dic₂₂	semidirect
186. C₁₁	#33729	semidirect

Maximal subgroups

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

subgroup	index
#13079152	2
#13070900	2
#13070893	2
#13070890	2
#13070402	2
#13070400	2
#13070212	2
C₂×C₁₁×#366	2
#33729	11