Subgroups — Q₈×C₁₁×#100 #14599707

Order 2816.

1198 conjugacy classes of subgroups.

The subgroup lattice has 264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₁×M₁₆	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1997	C₂	1	6	yes	maximal, complemented
4	C₁₁×#1800	C₂	1	3	yes	maximal
5	C₄×C₁₁×#100	C₂	1	3	yes	maximal
6	C₂³×Q₈×C₁₁	C₄	1	2	yes	—
7	D₄×Q₈×C₁₁	—	2	2	no	—
8	D₄×Q₈×C₁₁	—	2	6	no	—
9	C₂×C₁₁×C₄⋊Q₈	C₂²	1	3	yes	—
10	C₂×C₁₁×C₂²⋊Q₈	C₄	1	6	yes	—
11	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₁	C₂²	1	3	yes	—
13	C₁₁×#446	—	2	6	no	—
14	C₈×Q₈×C₁₁	—	2	2	no	—
15	C₁₁×#423	C₂²	1	6	yes	—
16	C₂×C₁₁×#100	C₂²	1	3	yes	—
17	C₂×C₁₁×#100	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	—	2	6	no	—
22	C₂²×Q₈×C₁₁	—	2	2	no	—
23	C₂²×Q₈×C₁₁	—	4	8	no	—
24	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₂²×Q₈×C₁₁	C₂×C₄	1	6	yes	—
26	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
27	C₂³×C₄×C₁₁	C₂×C₄	1	6	yes	—
28	C₂×C₁₁×M₁₆	C₂³	1	6	yes	—
29	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
30	C₁₁×C₄⋊Q₈	—	2	6	no	—
31	C₁₁×C₄⋊Q₈	—	2	6	no	—
32	C₁₁×C₂²⋊Q₈	—	2	12	no	—
33	C₁₁×C₂²⋊Q₈	—	2	12	no	—
34	C₄×Q₈×C₁₁	D₄	1	2	yes	—
35	C₄×Q₈×C₁₁	D₄	1	6	yes	—
36	C₄×D₄×C₁₁	—	2	6	no	—
37	C₄×D₄×C₁₁	—	2	6	no	—
38	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	6	yes	—
39	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	3	yes	—
40	C₂×C₁₁×C₄⋊C₄	C₂³	1	3	yes	—
41	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	6	yes	—
42	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
43	C₁₁×C₄⋊C₈	—	2	6	no	—
44	C₁₁×C₄⋊C₈	—	2	6	no	—
45	C₁₁×#100	—	2	6	no	—
46	C₁₁×#100	Q₈	1	4	yes	direct product factor
47	C₁₁×#97	—	2	6	no	—
48	C₄×C₈×C₁₁	—	2	6	no	—
49	Q₈×#100	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
51	C₂×Q₈×C₁₁	—	2	4	no	—
52	C₂×Q₈×C₁₁	—	2	6	no	—
53	C₂×Q₈×C₁₁	—	2	6	no	—
54	C₂×Q₈×C₁₁	—	4	12	no	—
55	C₂×Q₈×C₁₁	—	4	24	no	—
56	C₂×Q₈×C₁₁	—	4	8	no	—
57	C₂×Q₈×C₁₁	C₂²⋊C₄	1	3	yes	—
58	C₂×Q₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×D₄×C₁₁	—	2	2	no	—
60	C₂×D₄×C₁₁	—	2	2	no	—
61	C₂×D₄×C₁₁	C₂×Q₈	1	2	yes	—
62	C₂×D₄×C₁₁	#41	1	2	yes	—
63	C₂²×C₄×C₁₁	—	2	6	no	—
64	C₂²×C₄×C₁₁	—	2	6	no	—
65	C₂²×C₄×C₁₁	—	4	12	no	—
66	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
67	C₂²×C₄×C₁₁	C₂²×C₄	1	6	yes	—
68	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
69	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
70	C₁₁×M₁₆	—	2	6	no	—
71	C₁₁×M₁₆	—	2	2	no	—
72	C₁₁×M₁₆	—	2	6	no	—
73	C₁₁×M₁₆	C₂×Q₈	1	4	yes	complemented
74	C₂×C₈×C₁₁	—	2	2	no	—
75	C₂×C₈×C₁₁	—	2	6	no	—
76	C₁₁×C₄⋊C₄	—	2	12	no	—
77	C₁₁×C₄⋊C₄	—	2	6	no	—
78	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	6	yes	—
79	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	6	yes	—
80	C₁₁×C₂²⋊C₄	—	2	12	no	—
81	C₄²×C₁₁	C₂×D₄	1	6	yes	—
82	C₄²×C₁₁	C₂×D₄	1	6	yes	—
83	C₂×D₄×Q₈	C₂×C₁₁	1	1	yes	characteristic
84	Q₈×M₁₆	C₂×C₁₁	1	2	yes	complemented
85	#1997	C₂×C₁₁	1	6	yes	complemented
86	#1800	C₂×C₁₁	1	3	yes	—
87	C₄×#100	C₂×C₁₁	1	3	yes	—
88	C₂³×C₁₁	—	2	2	no	—
89	C₂³×C₁₁	—	2	2	no	—
90	C₂³×C₁₁	—	4	2	no	—
91	C₂³×C₁₁	—	4	2	no	—
92	C₂³×C₁₁	C₄×Q₈	1	4	yes	—
93	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
94	Q₈×C₁₁	—	2	6	no	—
95	Q₈×C₁₁	—	4	12	no	—
96	Q₈×C₁₁	—	4	12	no	—
97	Q₈×C₁₁	#100	1	4	yes	direct product factor
98	D₄×C₁₁	—	2	4	no	—
99	D₄×C₁₁	—	2	4	no	—
100	C₂×C₄×C₁₁	—	2	6	no	—
101	C₂×C₄×C₁₁	—	2	6	no	—
102	C₂×C₄×C₁₁	—	4	3	no	—
103	C₂×C₄×C₁₁	—	4	12	no	—
104	C₂×C₄×C₁₁	—	4	12	no	—
105	C₂×C₄×C₁₁	—	4	6	no	—
106	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	6	yes	—
107	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	3	yes	—
108	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	3	yes	—
109	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
110	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
111	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
112	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
113	C₈×C₁₁	—	2	4	no	—
114	C₈×C₁₁	—	4	6	no	—
115	C₂³×Q₈	C₄×C₁₁	1	2	yes	—
116	D₄×Q₈	—	2	2	no	—
117	D₄×Q₈	—	2	6	no	—
118	C₂×C₄⋊Q₈	C₂²×C₁₁	1	3	yes	—
119	C₂×C₂²⋊Q₈	C₄×C₁₁	1	6	yes	—
120	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
121	C₂×C₄×D₄	C₂²×C₁₁	1	3	yes	—
122	#446	—	2	6	no	—
123	C₈×Q₈	—	2	2	no	—
124	#423	C₂²×C₁₁	1	6	yes	—
125	C₂×#100	C₂²×C₁₁	1	3	yes	—
126	C₂×#100	C₂²×C₁₁	1	1	yes	characteristic
127	C₄×M₁₆	C₂²×C₁₁	1	6	yes	—
128	#343	C₂²×C₁₁	1	6	yes	—
129	#343	C₂²×C₁₁	1	6	yes	—
130	C₂²×C₁₁	—	2	1	no	—
131	C₂²×C₁₁	—	2	1	no	—
132	C₂²×C₁₁	—	2	4	no	—
133	C₂²×C₁₁	—	4	4	no	—
134	C₂²×C₁₁	—	4	4	no	—
135	C₂²×C₁₁	—	4	2	no	—
136	C₂²×C₁₁	—	4	2	no	—
137	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
139	C₂²×C₁₁	#519	1	1	yes	characteristic
140	C₄×C₁₁	—	2	3	no	—
141	C₄×C₁₁	—	2	6	no	—
142	C₄×C₁₁	—	4	6	no	—
143	C₄×C₁₁	C₂×#100	1	6	yes	—
144	C₄×C₁₁	#548	1	2	yes	—
145	C₄×C₁₁	D₄×Q₈	1	2	yes	—
146	C₂²×Q₈	—	2	6	no	—
147	C₂²×Q₈	—	2	2	no	—
148	C₂²×Q₈	—	4	8	no	—
149	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
150	C₂²×Q₈	C₂×C₄×C₁₁	1	6	yes	—
151	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
152	C₂³×C₄	C₂×C₄×C₁₁	1	6	yes	—
153	C₂×M₁₆	C₂³×C₁₁	1	6	yes	—
154	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
155	C₄⋊Q₈	—	2	6	no	—
156	C₄⋊Q₈	—	2	6	no	—
157	C₂²⋊Q₈	—	2	12	no	—
158	C₂²⋊Q₈	—	2	12	no	—
159	C₄×Q₈	D₄×C₁₁	1	2	yes	—
160	C₄×Q₈	D₄×C₁₁	1	6	yes	—
161	C₄×D₄	—	2	6	no	—
162	C₄×D₄	—	2	6	no	—
163	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	6	yes	—
164	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	3	yes	—
165	C₂×C₄⋊C₄	C₂³×C₁₁	1	3	yes	—
166	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	6	yes	—
167	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
168	C₄⋊C₈	—	2	6	no	—
169	C₄⋊C₈	—	2	6	no	—
170	#100	—	2	6	no	—
171	#100	Q₈×C₁₁	1	4	yes	direct product factor
172	#97	—	2	6	no	—
173	C₄×C₈	—	2	6	no	—
174	C₂×C₁₁	—	2	1	no	—
175	C₂×C₁₁	—	2	1	no	—
176	C₂×C₁₁	—	4	4	no	—
177	C₂×C₁₁	Q₈×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₁₁	C₂²×#100	1	1	yes	characteristic
179	C₂×C₁₁	#2889	1	1	yes	characteristic
180	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
181	C₂×Q₈	—	2	4	no	—
182	C₂×Q₈	—	2	6	no	—
183	C₂×Q₈	—	2	6	no	—
184	C₂×Q₈	—	4	12	no	—
185	C₂×Q₈	—	4	24	no	—
186	C₂×Q₈	—	4	8	no	—
187	C₂×Q₈	C₁₁×C₂²⋊C₄	1	3	yes	—
188	C₂×Q₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
189	C₂×D₄	—	2	2	no	—
190	C₂×D₄	—	2	2	no	—
191	C₂×D₄	C₂×Q₈×C₁₁	1	2	yes	—
192	C₂×D₄	C₁₁×#41	1	2	yes	—
193	C₂²×C₄	—	2	6	no	—
194	C₂²×C₄	—	2	6	no	—
195	C₂²×C₄	—	4	12	no	—
196	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
197	C₂²×C₄	C₂²×C₄×C₁₁	1	6	yes	—
198	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
199	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
200	M₁₆	—	2	2	no	—
201	M₁₆	—	2	6	no	—
202	M₁₆	—	2	6	no	—
203	M₁₆	C₂×Q₈×C₁₁	1	4	yes	complemented
204	C₂×C₈	—	2	2	no	—
205	C₂×C₈	—	2	6	no	—
206	C₄⋊C₄	—	2	12	no	—
207	C₄⋊C₄	—	2	6	no	—
208	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	6	yes	—
209	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	6	yes	—
210	C₂²⋊C₄	—	2	12	no	—
211	C₄²	C₂×D₄×C₁₁	1	6	yes	—
212	C₄²	C₂×D₄×C₁₁	1	6	yes	—
213	C₁₁	Q₈×#100	1	1	yes	characteristic, direct product factor, Sylow
214	C₂³	—	2	2	no	—
215	C₂³	—	2	2	no	—
216	C₂³	—	4	2	no	—
217	C₂³	—	4	2	no	—
218	C₂³	C₄×Q₈×C₁₁	1	4	yes	—
219	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
220	Q₈	—	2	6	no	—
221	Q₈	—	4	12	no	—
222	Q₈	—	4	12	no	—
223	Q₈	C₁₁×#100	1	4	yes	direct product factor
224	D₄	—	2	4	no	—
225	D₄	—	2	4	no	—
226	C₂×C₄	—	2	6	no	—
227	C₂×C₄	—	2	6	no	—
228	C₂×C₄	—	4	3	no	—
229	C₂×C₄	—	4	12	no	—
230	C₂×C₄	—	4	12	no	—
231	C₂×C₄	—	4	6	no	—
232	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	6	yes	—
233	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	3	yes	—
234	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	3	yes	—
235	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
236	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
237	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
238	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
239	C₈	—	2	4	no	—
240	C₈	—	4	6	no	—
241	C₂²	—	2	1	no	—
242	C₂²	—	2	1	no	—
243	C₂²	—	2	4	no	—
244	C₂²	—	4	4	no	—
245	C₂²	—	4	4	no	—
246	C₂²	—	4	2	no	—
247	C₂²	—	4	2	no	—
248	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
249	C₂²	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
250	C₂²	C₁₁×#519	1	1	yes	characteristic
251	C₄	—	2	3	no	—
252	C₄	—	2	6	no	—
253	C₄	—	4	6	no	—
254	C₄	C₂×C₁₁×#100	1	6	yes	—
255	C₄	C₁₁×#548	1	2	yes	—
256	C₄	D₄×Q₈×C₁₁	1	2	yes	—
257	C₂	—	2	1	no	—
258	C₂	—	2	1	no	—
259	C₂	—	4	4	no	—
260	C₂	Q₈×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
261	C₂	C₂²×C₁₁×#100	1	1	yes	characteristic
262	C₂	C₁₁×#2889	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	C₂²×D₄×C₁₁	C₂³
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
2. Q₈×C₁₁×M₁₆	C₂	semidirect
3. C₁₁×#1997	C₂	semidirect
46. C₁₁×#100	Q₈	direct (N × H)
49. Q₈×#100	C₁₁	direct (N × H)
73. C₁₁×M₁₆	C₂×Q₈	semidirect
84. Q₈×M₁₆	C₂×C₁₁	semidirect
85. #1997	C₂×C₁₁	semidirect
97. Q₈×C₁₁	#100	direct (N × H)
171. #100	Q₈×C₁₁	direct (N × H)
203. M₁₆	C₂×Q₈×C₁₁	semidirect
213. C₁₁	Q₈×#100	direct (N × H)
223. Q₈	C₁₁×#100	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×D₄×Q₈×C₁₁	2
Q₈×C₁₁×M₁₆	2
C₁₁×#1997	2
C₁₁×#1800	2
C₄×C₁₁×#100	2
Q₈×#100	11

Subgroups — Q8×C11×#100 #14599707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₁₁×#100 #14599707