Subgroups — D₁₁×#2868 #14959868

Order 2816.

3774 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₁×C₄⋊Q₈	C₂	1	6	yes	maximal
2	#13077014	C₂	1	1	yes	maximal, characteristic, complemented
3	#13077013	C₂	1	8	yes	maximal, complemented
4	#13077012	C₂	1	6	yes	maximal, complemented
5	D₁₁×#384	C₂	1	8	yes	maximal
6	C₄³×D₁₁	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#2868	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Q₈×D₁₁	C₂²	1	4	yes	—
9	C₂×C₁₁×C₄⋊Q₈	C₂²	1	6	yes	—
10	C₂×#66997	C₂²	1	12	yes	—
11	D₁₁×C₄⋊Q₈	—	2	48	no	—
12	C₂×C₄⋊C₄×D₁₁	C₂²	1	24	yes	—
13	C₂×#66941	C₂²	1	24	yes	—
14	C₂×C₄²×D₁₁	C₂²	1	3	yes	—
15	C₂×C₄²×D₁₁	C₂²	1	4	yes	—
16	C₂×#66922	C₂²	1	6	yes	—
17	C₁₁×#384	C₂²	1	8	yes	—
18	C₄³×C₁₁	C₂²	1	1	yes	characteristic
19	#10622589	C₂²	1	48	yes	—
20	#10622548	C₂²	1	8	yes	—
21	C₄²×Dic₁₁	C₂²	1	3	yes	—
22	C₄²×Dic₁₁	C₂²	1	4	yes	—
23	C₂²×Q₈×C₁₁	C₂³	1	4	yes	—
24	C₂×Q₈×D₁₁	—	2	48	no	—
25	C₂²×C₄×D₁₁	C₂³	1	8	yes	—
26	C₂²×C₄×D₁₁	C₂³	1	1	yes	characteristic
27	C₂²×C₄×D₁₁	C₂³	1	6	yes	—
28	C₂²×Dic₂₂	C₂³	1	4	yes	—
29	C₂²×Dic₂₂	C₂³	1	8	yes	—
30	C₁₁×C₄⋊Q₈	—	2	24	no	—
31	C₂×C₁₁×C₄⋊C₄	C₂³	1	24	yes	—
32	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
33	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
34	#66997	—	2	48	no	—
35	C₂×C₄⋊Dic₁₁	C₂³	1	24	yes	—
36	C₂×Dic₁₁⋊C₄	C₂³	1	48	yes	—
37	C₂×C₄×Dic₁₁	C₂³	1	6	yes	—
38	C₂×C₄×Dic₁₁	C₂³	1	3	yes	—
39	C₂×C₄×Dic₁₁	C₂³	1	12	yes	—
40	C₄⋊C₄×D₁₁	—	2	96	no	—
41	#66941	—	2	96	no	—
42	C₄²×D₁₁	D₄	1	24	yes	—
43	C₄²×D₁₁	Q₈	1	32	yes	complemented
44	#66922	—	2	24	no	—
45	C₂×#2868	—	11	1	no	maximal, Sylow
46	C₂³×D₁₁	C₂⁴	1	1	yes	characteristic
47	C₂×Q₈×C₁₁	—	2	24	no	—
48	C₂²×C₄×C₁₁	C₂⁴	1	8	yes	—
49	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
51	C₂²×Dic₁₁	C₂⁴	1	8	yes	—
52	C₂²×Dic₁₁	C₂⁴	1	1	yes	characteristic
53	C₂²×Dic₁₁	C₂⁴	1	6	yes	—
54	Q₈×D₁₁	—	4	64	no	—
55	C₂×C₄×D₁₁	—	2	48	no	—
56	C₂×C₄×D₁₁	C₂×D₄	1	12	yes	—
57	C₂×C₄×D₁₁	C₂×D₄	1	24	yes	—
58	C₂×C₄×D₁₁	C₂×Q₈	1	48	yes	—
59	C₂×Dic₂₂	—	2	48	no	—
60	C₂×Dic₂₂	—	2	24	no	—
61	C₁₁×C₄⋊C₄	—	2	48	no	—
62	C₄²×C₁₁	C₂×D₄	1	12	yes	—
63	C₄²×C₁₁	C₂×Q₈	1	16	yes	complemented
64	C₄⋊Dic₁₁	—	2	48	no	—
65	Dic₁₁⋊C₄	—	2	96	no	—
66	C₄×Dic₁₁	C₂×D₄	1	24	yes	—
67	C₄×Dic₁₁	C₂×D₄	1	12	yes	—
68	C₄×Dic₁₁	C₂×Q₈	1	48	yes	complemented
69	C₂²×C₄⋊Q₈	—	11	6	no	—
70	#2868	—	11	8	no	—
71	#2868	—	11	1	no	—
72	#2868	—	11	6	no	—
73	#2868	D₁₁	1	1	yes	characteristic, direct product factor
74	C₂×#384	—	11	8	no	—
75	C₂×C₄³	—	11	1	no	—
76	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
77	C₂²×D₁₁	C₂²×D₄	1	6	yes	—
78	C₂²×D₁₁	C₂²×Q₈	1	8	yes	—
79	Q₈×C₁₁	—	4	16	no	—
80	C₂×C₄×C₁₁	—	2	24	no	—
81	C₂×C₄×C₁₁	C₂²×D₄	1	6	yes	—
82	C₂×C₄×C₁₁	C₂²×D₄	1	12	yes	—
83	C₂×C₄×C₁₁	C₂²×Q₈	1	24	yes	—
84	C₂×Dic₁₁	—	2	24	no	—
85	C₂×Dic₁₁	C₂²×D₄	1	6	yes	—
86	C₂×Dic₁₁	C₂²×D₄	1	12	yes	—
87	C₂×Dic₁₁	C₂²×Q₈	1	24	yes	—
88	C₄×D₁₁	—	4	32	no	—
89	C₄×D₁₁	#127	1	16	yes	—
90	C₄×D₁₁	C₄⋊Q₈	1	96	yes	complemented
91	Dic₂₂	—	4	16	no	—
92	Dic₂₂	—	4	32	no	—
93	C₂³×Q₈	—	11	4	no	—
94	C₂×C₄⋊Q₈	—	11	12	no	—
95	C₂×C₄⋊Q₈	—	11	24	no	—
96	C₂×C₄⋊Q₈	—	11	6	no	—
97	C₂×C₄⋊Q₈	—	22	48	no	—
98	C₂×C₄⋊Q₈	C₂×D₁₁	1	6	yes	—
99	C₂²×C₄⋊C₄	—	11	24	no	—
100	C₂²×C₄²	—	11	3	no	—
101	C₂²×C₄²	—	11	4	no	—
102	#384	—	11	48	no	—
103	#384	—	11	8	no	—
104	#384	C₂×D₁₁	1	8	yes	—
105	C₄³	—	11	4	no	—
106	C₄³	—	11	3	no	—
107	C₄³	C₂×D₁₁	1	1	yes	characteristic
108	C₂²×C₁₁	C₂³×D₄	1	3	yes	—
109	C₂²×C₁₁	C₂³×Q₈	1	4	yes	—
110	C₂×D₁₁	C₂×#127	1	4	yes	—
111	C₂×D₁₁	C₂×C₄⋊Q₈	1	24	yes	—
112	C₄×C₁₁	—	4	8	no	—
113	C₄×C₁₁	C₂×#127	1	4	yes	—
114	C₄×C₁₁	C₂×C₄⋊Q₈	1	24	yes	complemented
115	Dic₁₁	—	4	8	no	—
116	Dic₁₁	C₂×#127	1	4	yes	—
117	Dic₁₁	C₂×C₄⋊Q₈	1	24	yes	complemented
118	C₂²×Q₈	—	11	8	no	—
119	C₂²×Q₈	—	11	4	no	—
120	C₂²×Q₈	—	22	48	no	—
121	C₂²×Q₈	C₂²×D₁₁	1	4	yes	—
122	C₂³×C₄	—	11	6	no	—
123	C₂³×C₄	—	11	1	no	—
124	C₂³×C₄	—	11	8	no	—
125	C₄⋊Q₈	—	2	24	no	—
126	C₄⋊Q₈	—	22	96	no	—
127	C₄⋊Q₈	—	22	48	no	—
128	C₄⋊Q₈	—	22	24	no	—
129	C₂×C₄⋊C₄	—	11	48	no	—
130	C₂×C₄⋊C₄	—	11	24	no	—
131	C₂×C₄⋊C₄	—	22	96	no	—
132	C₂×C₄⋊C₄	C₂²×D₁₁	1	24	yes	—
133	C₂×C₄²	—	11	3	no	—
134	C₂×C₄²	—	11	6	no	—
135	C₂×C₄²	—	11	12	no	—
136	C₂×C₄²	—	11	24	no	—
137	C₂×C₄²	—	11	32	no	—
138	C₂×C₄²	C₂²×D₁₁	1	3	yes	—
139	C₂×C₄²	C₂²×D₁₁	1	4	yes	—
140	C₂×C₁₁	C₂²×#127	1	1	yes	characteristic
141	C₂×C₁₁	C₂²×C₄⋊Q₈	1	6	yes	—
142	D₁₁	#2868	1	8	yes	direct product factor
143	C₂⁴	—	11	1	no	—
144	C₂×Q₈	—	2	24	no	—
145	C₂×Q₈	—	22	48	no	—
146	C₂×Q₈	—	22	24	no	—
147	C₂×Q₈	—	44	64	no	—
148	C₂²×C₄	—	11	6	no	—
149	C₂²×C₄	—	11	1	no	—
150	C₂²×C₄	—	11	24	no	—
151	C₂²×C₄	—	11	12	no	—
152	C₂²×C₄	—	11	48	no	—
153	C₂²×C₄	—	11	8	no	—
154	C₂²×C₄	—	22	48	no	—
155	C₂²×C₄	C₂³×D₁₁	1	8	yes	—
156	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
157	C₂²×C₄	C₂³×D₁₁	1	6	yes	—
158	C₄⋊C₄	—	2	48	no	—
159	C₄⋊C₄	—	22	96	no	—
160	C₄⋊C₄	—	22	48	no	—
161	C₄²	—	11	12	no	—
162	C₄²	—	11	24	no	—
163	C₄²	—	11	48	no	—
164	C₄²	D₄×D₁₁	1	12	yes	—
165	C₄²	Q₈×D₁₁	1	16	yes	complemented
166	C₁₁	C₂×#2868	1	1	yes	characteristic, complemented, Sylow
167	C₂³	—	11	6	no	—
168	C₂³	—	11	8	no	—
169	C₂³	C₂⁴×D₁₁	1	1	yes	characteristic
170	Q₈	—	4	16	no	—
171	Q₈	—	44	32	no	—
172	Q₈	—	44	16	no	—
173	C₂×C₄	—	2	24	no	—
174	C₂×C₄	—	11	12	no	—
175	C₂×C₄	—	11	6	no	—
176	C₂×C₄	—	11	24	no	—
177	C₂×C₄	—	11	16	no	—
178	C₂×C₄	—	11	96	no	—
179	C₂×C₄	—	22	24	no	—
180	C₂×C₄	—	44	32	no	—
181	C₂×C₄	C₂×D₄×D₁₁	1	6	yes	—
182	C₂×C₄	C₂×D₄×D₁₁	1	12	yes	—
183	C₂×C₄	C₂×Q₈×D₁₁	1	24	yes	—
184	C₂²	—	11	4	no	—
185	C₂²	—	11	24	no	—
186	C₂²	C₂²×D₄×D₁₁	1	3	yes	—
187	C₂²	C₂²×Q₈×D₁₁	1	4	yes	—
188	C₄	—	4	8	no	—
189	C₄	—	11	4	no	—
190	C₄	—	11	24	no	—
191	C₄	—	44	8	no	—
192	C₄	D₁₁×#127	1	4	yes	—
193	C₄	D₁₁×C₄⋊Q₈	1	24	yes	complemented
194	C₂	—	11	8	no	—
195	C₂	C₂×D₁₁×#127	1	1	yes	characteristic
196	C₂	C₂×D₁₁×C₄⋊Q₈	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₁₁
commutator, socle, cosocle	C₂³×C₁₁	C₂⁵
Fitting	C₁₁×#2868	C₂
prime radical	C₂³×D₁₁	C₂⁴
hypercenter	#2868	D₁₁
hypocenter	C₁₁	C₂×#2868
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ #2868

Complements

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

N	H ≅ G/N	type
2. #13077014	C₂	semidirect
3. #13077013	C₂	semidirect
4. #13077012	C₂	semidirect
7. C₁₁×#2868	C₂	semidirect
43. C₄²×D₁₁	Q₈	semidirect
63. C₄²×C₁₁	C₂×Q₈	semidirect
68. C₄×Dic₁₁	C₂×Q₈	semidirect
73. #2868	D₁₁	direct (N × H)
90. C₄×D₁₁	C₄⋊Q₈	semidirect
114. C₄×C₁₁	C₂×C₄⋊Q₈	semidirect
117. Dic₁₁	C₂×C₄⋊Q₈	semidirect
142. D₁₁	#2868	direct (N × H)
165. C₄²	Q₈×D₁₁	semidirect
166. C₁₁	C₂×#2868	semidirect
193. C₄	D₁₁×C₄⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₁×C₄⋊Q₈	2
#13077014	2
#13077013	2
#13077012	2
D₁₁×#384	2
C₄³×D₁₁	2
C₁₁×#2868	2
C₂×#2868	11

Subgroups — D11×#2868 #14959868

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×#2868 #14959868