Subgroups — Q₈×C₁₁×#101 #14599709

Order 2816.

970 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₁₁	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₁×M₁₆	C₂	1	2	yes	maximal
3	C₁₁×#1997	C₂	1	6	yes	maximal
4	C₁₁×#1801	C₂	1	3	yes	maximal
5	C₄×C₁₁×#101	C₂	1	3	yes	maximal
6	Q₈²×C₁₁	—	2	2	no	—
7	Q₈²×C₁₁	—	2	6	no	—
8	C₂×C₁₁×C₄⋊Q₈	C₄	1	6	yes	—
9	C₂×C₁₁×C₄⋊Q₈	C₂²	1	3	yes	—
10	C₂×C₄×Q₈×C₁₁	C₄	1	2	yes	—
11	C₂×C₄×Q₈×C₁₁	C₂²	1	3	yes	—
12	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₁₁×#446	—	2	6	no	—
14	C₈×Q₈×C₁₁	—	2	2	no	—
15	C₁₁×#423	C₂²	1	6	yes	—
16	C₂×C₁₁×#101	C₂²	1	3	yes	—
17	C₂×C₁₁×#101	C₂²	1	1	yes	characteristic
18	C₄×C₁₁×M₁₆	C₂²	1	6	yes	—
19	C₁₁×#343	C₂²	1	6	yes	—
20	C₁₁×#343	C₂²	1	6	yes	—
21	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×Q₈×C₁₁	C₂×C₄	1	6	yes	—
23	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
24	C₂×C₁₁×M₁₆	C₂³	1	6	yes	—
25	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
26	C₁₁×C₄⋊Q₈	—	2	12	no	—
27	C₁₁×C₄⋊Q₈	—	2	12	no	—
28	C₁₁×C₄⋊Q₈	—	2	6	no	—
29	C₁₁×C₄⋊Q₈	—	2	6	no	—
30	C₄×Q₈×C₁₁	—	2	6	no	—
31	C₄×Q₈×C₁₁	—	2	2	no	—
32	C₄×Q₈×C₁₁	—	2	6	no	—
33	C₄×Q₈×C₁₁	—	2	6	no	—
34	C₄×Q₈×C₁₁	D₄	1	2	yes	—
35	C₄×Q₈×C₁₁	D₄	1	6	yes	—
36	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	6	yes	—
37	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	6	yes	—
38	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	3	yes	—
39	C₂×C₁₁×C₄⋊C₄	C₂³	1	3	yes	—
40	C₂×C₄²×C₁₁	C₂×C₄	1	6	yes	—
41	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
42	C₁₁×C₄⋊C₈	—	2	6	no	—
43	C₁₁×C₄⋊C₈	—	2	6	no	—
44	C₁₁×#101	—	2	6	no	—
45	C₁₁×#101	Q₈	1	4	yes	direct product factor
46	C₁₁×#97	—	2	6	no	—
47	C₄×C₈×C₁₁	—	2	6	no	—
48	Q₈×#101	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂×Q₈×C₁₁	—	2	4	no	—
50	C₂×Q₈×C₁₁	—	2	12	no	—
51	C₂×Q₈×C₁₁	—	2	2	no	—
52	C₂×Q₈×C₁₁	—	2	2	no	—
53	C₂×Q₈×C₁₁	—	8	6	no	—
54	C₂×Q₈×C₁₁	C₂²⋊C₄	1	3	yes	—
55	C₂×Q₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×Q₈×C₁₁	C₂×Q₈	1	2	yes	—
57	C₂×Q₈×C₁₁	#41	1	2	yes	—
58	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
59	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
60	C₂²×C₄×C₁₁	C₂²×C₄	1	6	yes	—
61	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
62	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
63	C₁₁×M₁₆	—	2	6	no	—
64	C₁₁×M₁₆	—	2	2	no	—
65	C₁₁×M₁₆	—	2	6	no	—
66	C₁₁×M₁₆	C₂×Q₈	1	4	yes	—
67	C₂×C₈×C₁₁	—	2	2	no	—
68	C₂×C₈×C₁₁	—	2	6	no	—
69	C₁₁×C₄⋊C₄	—	2	12	no	—
70	C₁₁×C₄⋊C₄	—	2	6	no	—
71	C₁₁×C₄⋊C₄	—	2	6	no	—
72	C₁₁×C₄⋊C₄	—	2	6	no	—
73	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	6	yes	—
74	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	6	yes	—
75	C₄²×C₁₁	—	2	6	no	—
76	C₄²×C₁₁	—	2	6	no	—
77	C₄²×C₁₁	C₂×D₄	1	6	yes	—
78	C₄²×C₁₁	C₂×D₄	1	6	yes	—
79	C₂×Q₈²	C₂×C₁₁	1	1	yes	characteristic
80	Q₈×M₁₆	C₂×C₁₁	1	2	yes	—
81	#1997	C₂×C₁₁	1	6	yes	—
82	#1801	C₂×C₁₁	1	3	yes	—
83	C₄×#101	C₂×C₁₁	1	3	yes	—
84	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
85	Q₈×C₁₁	—	2	4	no	—
86	Q₈×C₁₁	—	2	4	no	—
87	Q₈×C₁₁	—	2	6	no	—
88	Q₈×C₁₁	—	8	12	no	—
89	Q₈×C₁₁	#101	1	4	yes	direct product factor
90	C₂×C₄×C₁₁	—	2	2	no	—
91	C₂×C₄×C₁₁	—	2	2	no	—
92	C₂×C₄×C₁₁	—	2	6	no	—
93	C₂×C₄×C₁₁	—	2	6	no	—
94	C₂×C₄×C₁₁	—	4	3	no	—
95	C₂×C₄×C₁₁	—	4	6	no	—
96	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	3	yes	—
97	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	6	yes	—
98	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	3	yes	—
99	C₂×C₄×C₁₁	C₄×Q₈	1	4	yes	—
100	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
101	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
102	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
103	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
104	C₈×C₁₁	—	2	4	no	—
105	C₈×C₁₁	—	4	6	no	—
106	Q₈²	—	2	2	no	—
107	Q₈²	—	2	6	no	—
108	C₂×C₄⋊Q₈	C₄×C₁₁	1	6	yes	—
109	C₂×C₄⋊Q₈	C₂²×C₁₁	1	3	yes	—
110	C₂×C₄×Q₈	C₄×C₁₁	1	2	yes	—
111	C₂×C₄×Q₈	C₂²×C₁₁	1	3	yes	—
112	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
113	#446	—	2	6	no	—
114	C₈×Q₈	—	2	2	no	—
115	#423	C₂²×C₁₁	1	6	yes	—
116	C₂×#101	C₂²×C₁₁	1	3	yes	—
117	C₂×#101	C₂²×C₁₁	1	1	yes	characteristic
118	C₄×M₁₆	C₂²×C₁₁	1	6	yes	—
119	#343	C₂²×C₁₁	1	6	yes	—
120	#343	C₂²×C₁₁	1	6	yes	—
121	C₂²×C₁₁	—	2	1	no	—
122	C₂²×C₁₁	—	2	1	no	—
123	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
125	C₂²×C₁₁	#519	1	1	yes	characteristic
126	C₄×C₁₁	—	2	4	no	—
127	C₄×C₁₁	—	2	3	no	—
128	C₄×C₁₁	—	2	6	no	—
129	C₄×C₁₁	—	4	6	no	—
130	C₄×C₁₁	C₂×#101	1	6	yes	—
131	C₄×C₁₁	#548	1	2	yes	—
132	C₄×C₁₁	D₄×Q₈	1	2	yes	—
133	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
134	C₂²×Q₈	C₂×C₄×C₁₁	1	6	yes	—
135	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
136	C₂×M₁₆	C₂³×C₁₁	1	6	yes	—
137	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
138	C₄⋊Q₈	—	2	12	no	—
139	C₄⋊Q₈	—	2	12	no	—
140	C₄⋊Q₈	—	2	6	no	—
141	C₄⋊Q₈	—	2	6	no	—
142	C₄×Q₈	—	2	6	no	—
143	C₄×Q₈	—	2	2	no	—
144	C₄×Q₈	—	2	6	no	—
145	C₄×Q₈	—	2	6	no	—
146	C₄×Q₈	D₄×C₁₁	1	2	yes	—
147	C₄×Q₈	D₄×C₁₁	1	6	yes	—
148	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	6	yes	—
149	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	6	yes	—
150	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	3	yes	—
151	C₂×C₄⋊C₄	C₂³×C₁₁	1	3	yes	—
152	C₂×C₄²	C₂×C₄×C₁₁	1	6	yes	—
153	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
154	C₄⋊C₈	—	2	6	no	—
155	C₄⋊C₈	—	2	6	no	—
156	#101	—	2	6	no	—
157	#101	Q₈×C₁₁	1	4	yes	direct product factor
158	#97	—	2	6	no	—
159	C₄×C₈	—	2	6	no	—
160	C₂×C₁₁	—	2	1	no	—
161	C₂×C₁₁	—	2	1	no	—
162	C₂×C₁₁	Q₈×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₁₁	C₂²×#101	1	1	yes	characteristic
164	C₂×C₁₁	#2888	1	1	yes	characteristic
165	C₂×Q₈	—	2	4	no	—
166	C₂×Q₈	—	2	12	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	2	no	—
169	C₂×Q₈	—	8	6	no	—
170	C₂×Q₈	C₁₁×C₂²⋊C₄	1	3	yes	—
171	C₂×Q₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×Q₈	C₂×Q₈×C₁₁	1	2	yes	—
173	C₂×Q₈	C₁₁×#41	1	2	yes	—
174	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
175	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
176	C₂²×C₄	C₂²×C₄×C₁₁	1	6	yes	—
177	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
178	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
179	M₁₆	—	2	2	no	—
180	M₁₆	—	2	6	no	—
181	M₁₆	—	2	6	no	—
182	M₁₆	C₂×Q₈×C₁₁	1	4	yes	—
183	C₂×C₈	—	2	2	no	—
184	C₂×C₈	—	2	6	no	—
185	C₄⋊C₄	—	2	12	no	—
186	C₄⋊C₄	—	2	6	no	—
187	C₄⋊C₄	—	2	6	no	—
188	C₄⋊C₄	—	2	6	no	—
189	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	6	yes	—
190	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	6	yes	—
191	C₄²	—	2	6	no	—
192	C₄²	—	2	6	no	—
193	C₄²	C₂×D₄×C₁₁	1	6	yes	—
194	C₄²	C₂×D₄×C₁₁	1	6	yes	—
195	C₁₁	Q₈×#101	1	1	yes	characteristic, direct product factor, Sylow
196	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
197	Q₈	—	2	4	no	—
198	Q₈	—	2	4	no	—
199	Q₈	—	2	6	no	—
200	Q₈	—	8	12	no	—
201	Q₈	C₁₁×#101	1	4	yes	direct product factor
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	6	no	—
205	C₂×C₄	—	2	6	no	—
206	C₂×C₄	—	4	3	no	—
207	C₂×C₄	—	4	6	no	—
208	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	3	yes	—
209	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	6	yes	—
210	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	3	yes	—
211	C₂×C₄	C₄×Q₈×C₁₁	1	4	yes	—
212	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
213	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
214	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
215	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
216	C₈	—	2	4	no	—
217	C₈	—	4	6	no	—
218	C₂²	—	2	1	no	—
219	C₂²	—	2	1	no	—
220	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
221	C₂²	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
222	C₂²	C₁₁×#519	1	1	yes	characteristic
223	C₄	—	2	4	no	—
224	C₄	—	2	3	no	—
225	C₄	—	2	6	no	—
226	C₄	—	4	6	no	—
227	C₄	C₂×C₁₁×#101	1	6	yes	—
228	C₄	C₁₁×#548	1	2	yes	—
229	C₄	D₄×Q₈×C₁₁	1	2	yes	—
230	C₂	—	2	1	no	—
231	C₂	—	2	1	no	—
232	C₂	Q₈×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
233	C₂	C₂²×C₁₁×#101	1	1	yes	characteristic
234	C₂	C₁₁×#2888	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂³×C₁₁	C₂³×C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄×Q₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
45. C₁₁×#101	Q₈	direct (N × H)
48. Q₈×#101	C₁₁	direct (N × H)
89. Q₈×C₁₁	#101	direct (N × H)
157. #101	Q₈×C₁₁	direct (N × H)
195. C₁₁	Q₈×#101	direct (N × H)
201. Q₈	C₁₁×#101	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₈²×C₁₁	2
Q₈×C₁₁×M₁₆	2
C₁₁×#1997	2
C₁₁×#1801	2
C₄×C₁₁×#101	2
Q₈×#101	11

Subgroups — Q8×C11×#101 #14599709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₁₁×#101 #14599709