Subgroups — #14907135

Order 2816.

718 conjugacy classes of subgroups.

The subgroup lattice has 218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077468	C₂	1	2	yes	maximal, complemented
2	#13070492	C₂	1	4	yes	maximal, complemented
3	D₁₆×Dic₁₁	C₂	1	4	yes	maximal, complemented
4	#13070400	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070332	C₂	1	2	yes	maximal, complemented
6	#13070212	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₁×D₁₆	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
9	#10623329	—	2	2	no	—
10	C₂×C₁₁×D₁₆	C₄	1	8	yes	complemented
11	C₂×C₁₁×D₁₆	C₂²	1	2	yes	—
12	C₂×C₁₁×D₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
14	#10622828	—	2	2	no	—
15	#10622765	—	2	4	no	—
16	D₈×Dic₁₁	C₂²	1	8	yes	complemented
17	#10622719	C₂²	1	2	yes	—
18	#10622714	C₂²	1	1	yes	characteristic
19	C₂×#66876	C₂²	1	1	yes	characteristic
20	#10622200	C₂²	1	8	yes	complemented
21	#10622143	C₂²	1	2	yes	complemented
22	#10622142	C₂²	1	2	yes	complemented
23	#10622140	C₂²	1	2	yes	complemented
24	C₁₆×Dic₁₁	C₂²	1	2	yes	complemented
25	C₂²×D₄×C₁₁	—	2	2	no	—
26	C₂×C₁₁×D₈	—	2	2	no	—
27	C₂×C₁₁×D₈	—	2	4	no	—
28	C₂×C₁₁×D₈	C₂×C₄	1	8	yes	complemented
29	C₂×C₁₁×D₈	C₂³	1	4	yes	—
30	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
31	C₂×C₂²⋊Dic₁₁	—	4	4	no	—
32	D₄×Dic₁₁	—	2	8	no	—
33	D₄×Dic₁₁	—	4	4	no	—
34	#66979	—	2	2	no	—
35	#66979	D₄	1	1	yes	characteristic
36	C₂×#4318	D₄	1	1	yes	characteristic
37	C₁₁×D₁₆	C₂×C₄	1	8	yes	complemented
38	C₁₁×D₁₆	C₂×C₄	1	8	yes	complemented
39	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	complemented
40	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
41	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
42	#66896	—	2	8	no	—
43	#66882	C₂³	1	4	yes	—
44	#66881	—	2	2	no	—
45	#66879	D₄	1	2	yes	—
46	C₈×Dic₁₁	C₂³	1	2	yes	—
47	#66876	—	2	2	no	—
48	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
49	#33456	—	11	1	no	maximal, Sylow
50	C₂⁴×C₁₁	—	4	2	no	—
51	C₂×D₄×C₁₁	—	2	8	no	—
52	C₂×D₄×C₁₁	—	2	4	no	—
53	C₂×D₄×C₁₁	—	4	2	no	—
54	C₂×D₄×C₁₁	—	4	4	no	—
55	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
56	C₂²×Dic₁₁	—	4	8	no	—
57	C₁₁×D₈	—	2	8	no	—
58	C₁₁×D₈	—	2	4	no	—
59	C₁₁×D₈	C₂²×C₄	1	8	yes	—
60	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
61	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₁₁	#41	1	2	yes	—
63	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
64	C₂²⋊Dic₁₁	—	4	8	no	—
65	C₂²⋊Dic₁₁	—	4	2	no	—
66	C₂²⋊Dic₁₁	D₈	1	2	yes	—
67	C₄⋊Dic₁₁	—	2	4	no	—
68	C₄⋊Dic₁₁	D₈	1	2	yes	—
69	C₄×Dic₁₁	—	4	2	no	—
70	C₄×Dic₁₁	C₂×D₄	1	2	yes	—
71	#4318	—	2	2	no	—
72	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
73	C₁₁×C₁₆	C₂²×C₄	1	2	yes	—
74	C₁₁×C₁₆	C₂²×C₄	1	2	yes	—
75	C₁₁⋊C₁₆	—	2	2	no	—
76	C₂²×D₁₆	D₁₁	1	1	yes	characteristic
77	#2948	—	11	2	no	—
78	#2177	—	11	4	no	—
79	C₄×D₁₆	—	11	4	no	—
80	#2158	—	11	1	no	—
81	#2140	—	11	2	no	—
82	#2108	—	11	1	no	—
83	C₂³×C₁₁	—	4	4	no	—
84	C₂³×C₁₁	—	4	8	no	—
85	C₂³×C₁₁	—	16	4	no	—
86	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
87	D₄×C₁₁	—	2	8	no	—
88	D₄×C₁₁	—	4	4	no	—
89	D₄×C₁₁	—	4	8	no	—
90	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
91	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
92	C₂×C₄×C₁₁	#135	1	2	yes	—
93	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
94	C₂×Dic₁₁	—	4	4	no	—
95	C₂×Dic₁₁	—	16	8	no	—
96	C₂×Dic₁₁	C₂×D₈	1	4	yes	—
97	C₈×C₁₁	C₄×D₄	1	2	yes	—
98	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
99	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
100	C₁₁⋊C₈	—	2	2	no	—
101	C₂²×D₈	C₂×D₁₁	1	2	yes	—
102	#518	—	22	2	no	—
103	C₂×D₁₆	Dic₁₁	1	8	yes	complemented
104	C₂×D₁₆	C₂×D₁₁	1	2	yes	—
105	C₂×D₁₆	C₂×D₁₁	1	2	yes	—
106	C₂×M₃₂	—	11	1	no	—
107	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
108	#442	—	22	4	no	—
109	C₄×D₈	—	11	8	no	—
110	#427	—	11	2	no	—
111	#418	—	22	2	no	—
112	#405	—	11	1	no	—
113	#367	—	11	2	no	—
114	#366	—	11	2	no	—
115	#357	—	11	8	no	—
116	#346	—	11	2	no	—
117	C₄×C₁₆	—	11	2	no	—
118	C₂²×C₁₁	—	2	2	no	—
119	C₂²×C₁₁	—	4	8	no	—
120	C₂²×C₁₁	—	8	8	no	—
121	C₂²×C₁₁	—	16	8	no	—
122	C₂²×C₁₁	C₄×D₈	1	2	yes	—
123	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
124	C₄×C₁₁	C₄×D₈	1	2	yes	—
125	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
126	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
127	Dic₁₁	—	2	4	no	—
128	Dic₁₁	—	8	4	no	—
129	C₂²×D₄	—	2	2	no	—
130	C₂×D₈	—	2	2	no	—
131	C₂×D₈	—	2	4	no	—
132	C₂×D₈	C₂×Dic₁₁	1	8	yes	complemented
133	C₂×D₈	C₂²×D₁₁	1	4	yes	—
134	C₂×M₁₆	—	11	1	no	—
135	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
136	C₄×D₄	—	22	8	no	—
137	C₄×D₄	—	44	4	no	—
138	#117	—	11	1	no	—
139	#117	—	22	2	no	—
140	C₂×C₂²⋊C₄	—	44	4	no	—
141	D₁₆	C₂×Dic₁₁	1	8	yes	complemented
142	D₁₆	C₂×Dic₁₁	1	8	yes	complemented
143	M₃₂	—	22	2	no	—
144	C₂×C₁₆	—	11	2	no	—
145	C₂×C₁₆	C₂×Dic₁₁	1	4	yes	complemented
146	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
147	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
148	#107	—	11	4	no	—
149	#106	—	22	2	no	—
150	#102	—	22	8	no	—
151	#97	—	11	2	no	—
152	C₄×C₈	—	11	2	no	—
153	C₂×C₁₁	—	2	2	no	—
154	C₂×C₁₁	—	8	8	no	—
155	C₂×C₁₁	C₂×C₄×D₈	1	1	yes	characteristic
156	C₂×C₁₁	#3415	1	2	yes	—
157	C₂⁴	—	4	2	no	—
158	C₂×D₄	—	2	8	no	—
159	C₂×D₄	—	2	4	no	—
160	C₂×D₄	—	4	2	no	—
161	C₂×D₄	—	4	4	no	—
162	C₂²×C₄	—	44	8	no	—
163	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
164	D₈	—	2	8	no	—
165	D₈	—	2	4	no	—
166	D₈	C₂²×Dic₁₁	1	8	yes	—
167	M₁₆	—	22	2	no	—
168	C₂×C₈	—	11	2	no	—
169	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
170	C₂×C₈	#4341	1	2	yes	—
171	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
172	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
173	C₄⋊C₄	—	11	2	no	—
174	C₄⋊C₄	—	22	4	no	—
175	C₂²⋊C₄	—	11	2	no	—
176	C₂²⋊C₄	—	44	8	no	—
177	C₂²⋊C₄	—	44	2	no	—
178	C₄²	—	11	2	no	—
179	C₄²	—	44	2	no	—
180	C₁₆	—	22	2	no	—
181	C₁₆	C₂²×Dic₁₁	1	2	yes	—
182	C₁₆	C₂²×Dic₁₁	1	2	yes	—
183	C₁₁	#33456	1	1	yes	characteristic, complemented, Sylow
184	C₂³	—	4	4	no	—
185	C₂³	—	4	8	no	—
186	C₂³	—	16	4	no	—
187	C₂³	D₈×D₁₁	1	1	yes	characteristic
188	D₄	—	2	8	no	—
189	D₄	—	4	8	no	—
190	D₄	—	4	4	no	—
191	C₂×C₄	—	11	4	no	—
192	C₂×C₄	—	44	4	no	—
193	C₂×C₄	—	176	8	no	—
194	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
195	C₂×C₄	#66965	1	2	yes	—
196	C₂×C₄	D₄×Dic₁₁	1	2	yes	—
197	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
198	C₈	—	22	2	no	—
199	C₈	D₄×Dic₁₁	1	2	yes	—
200	C₈	C₂×#4341	1	1	yes	characteristic
201	C₈	C₂³×Dic₁₁	1	1	yes	characteristic
202	C₂²	—	2	2	no	—
203	C₂²	—	4	8	no	—
204	C₂²	—	8	8	no	—
205	C₂²	—	16	8	no	—
206	C₂²	D₈×Dic₁₁	1	2	yes	—
207	C₂²	C₂×D₈×D₁₁	1	1	yes	characteristic
208	C₄	—	22	4	no	—
209	C₄	—	88	4	no	—
210	C₄	D₈×Dic₁₁	1	2	yes	—
211	C₄	C₂×#66965	1	1	yes	characteristic
212	C₄	C₂×D₄×Dic₁₁	1	1	yes	characteristic
213	C₂	—	2	2	no	—
214	C₂	—	8	8	no	—
215	C₂	C₂×D₈×Dic₁₁	1	1	yes	characteristic
216	C₂	#13081753	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₁
commutator	C₈×C₁₁	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₁
Fitting, prime radical	C₂²×C₁₁×D₁₆	C₂
socle	C₂²×C₁₁	C₂²×D₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	C₂²×D₁₆	D₁₁
hypocenter	C₁₁	#33456
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×D₁₆

Complements

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

N	H ≅ G/N	type
1. #13077468	C₂	semidirect
2. #13070492	C₂	semidirect
3. D₁₆×Dic₁₁	C₂	semidirect
4. #13070400	C₂	semidirect
5. #13070332	C₂	semidirect
6. #13070212	C₂	semidirect
10. C₂×C₁₁×D₁₆	C₄	semidirect
16. D₈×Dic₁₁	C₂²	semidirect
20. #10622200	C₂²	semidirect
21. #10622143	C₂²	semidirect
22. #10622142	C₂²	semidirect
23. #10622140	C₂²	semidirect
24. C₁₆×Dic₁₁	C₂²	semidirect
28. C₂×C₁₁×D₈	C₂×C₄	semidirect
37. C₁₁×D₁₆	C₂×C₄	semidirect
38. C₁₁×D₁₆	C₂×C₄	semidirect
39. C₂×C₁₁×C₁₆	C₂×C₄	semidirect
103. C₂×D₁₆	Dic₁₁	semidirect
132. C₂×D₈	C₂×Dic₁₁	semidirect
141. D₁₆	C₂×Dic₁₁	semidirect
142. D₁₆	C₂×Dic₁₁	semidirect
145. C₂×C₁₆	C₂×Dic₁₁	semidirect
183. C₁₁	#33456	semidirect

Maximal subgroups

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

subgroup	index
#13077468	2
#13070492	2
D₁₆×Dic₁₁	2
#13070400	2
#13070332	2
#13070212	2
C₂²×C₁₁×D₁₆	2
#33456	11