Subgroups — C₂²×C₁₁×#487 #14637796

Order 2816.

2398 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	C₂²×C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#487	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₁₁×#103	C₂	1	4	yes	maximal
5	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
6	C₂³×Q₈×C₁₁	—	2	1	no	—
7	C₂³×Q₈×C₁₁	C₂²	1	2	yes	—
8	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
9	C₂×C₁₁×C₄⋊Q₈	—	2	6	no	—
10	C₂×C₁₁×C₄⋊Q₈	—	2	6	no	—
11	C₂×C₁₁×C₄⋊Q₈	C₂²	1	12	yes	—
12	C₂×C₁₁×C₄⋊Q₈	C₂²	1	12	yes	—
13	C₂²×C₁₁×C₄⋊C₄	—	2	1	no	—
14	C₂²×C₁₁×C₄⋊C₄	—	2	1	no	—
15	C₂²×C₁₁×C₄⋊C₄	—	2	1	no	—
16	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#487	C₂²	1	64	yes	direct product factor
19	C₂×C₁₁×#103	C₂²	1	48	yes	—
20	C₂×C₄×C₈×C₁₁	C₂²	1	12	yes	—
21	C₂²×Q₈×C₁₁	—	2	6	no	—
22	C₂²×Q₈×C₁₁	—	2	12	no	—
23	C₂²×Q₈×C₁₁	—	2	16	no	—
24	C₂²×Q₈×C₁₁	—	4	8	no	—
25	C₂²×Q₈×C₁₁	C₂³	1	12	yes	—
26	C₂³×C₄×C₁₁	—	2	2	no	—
27	C₂³×C₄×C₁₁	—	2	2	no	—
28	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
31	C₂²×C₈×C₁₁	—	2	8	no	—
32	C₂²×C₈×C₁₁	C₂³	1	12	yes	—
33	C₁₁×C₄⋊Q₈	—	2	24	no	—
34	C₁₁×C₄⋊Q₈	—	2	24	no	—
35	C₁₁×C₄⋊Q₈	C₂³	1	16	yes	—
36	C₁₁×C₄⋊Q₈	C₂³	1	16	yes	—
37	C₂×C₁₁×C₄⋊C₄	—	2	12	no	—
38	C₂×C₁₁×C₄⋊C₄	—	2	12	no	—
39	C₂×C₁₁×C₄⋊C₄	—	2	12	no	—
40	C₂×C₁₁×C₄⋊C₄	—	2	6	no	—
41	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
42	C₂×C₄²×C₁₁	D₄	1	6	yes	—
43	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
44	C₁₁×#103	C₂³	1	64	yes	—
45	C₄×C₈×C₁₁	C₂³	1	16	yes	—
46	C₂²×#487	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
48	C₂×Q₈×C₁₁	—	2	12	no	—
49	C₂×Q₈×C₁₁	—	2	16	no	—
50	C₂×Q₈×C₁₁	—	2	48	no	—
51	C₂×Q₈×C₁₁	—	4	24	no	—
52	C₂×Q₈×C₁₁	—	4	48	no	—
53	C₂×Q₈×C₁₁	C₂⁴	1	8	yes	—
54	C₂²×C₄×C₁₁	—	2	12	no	—
55	C₂²×C₄×C₁₁	—	2	12	no	—
56	C₂²×C₄×C₁₁	—	4	8	no	—
57	C₂²×C₄×C₁₁	—	4	8	no	—
58	C₂²×C₄×C₁₁	SD₁₆	1	8	yes	—
59	C₂²×C₄×C₁₁	Q₁₆	1	8	yes	—
60	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
61	C₂²×C₄×C₁₁	C₂×D₄	1	6	yes	—
62	C₂²×C₄×C₁₁	C₂×D₄	1	6	yes	—
63	C₂²×C₄×C₁₁	#41	1	8	yes	—
64	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
65	C₂×C₈×C₁₁	—	2	24	no	—
66	C₂×C₈×C₁₁	C₂⁴	1	8	yes	—
67	C₁₁×C₄⋊C₄	—	2	16	no	—
68	C₁₁×C₄⋊C₄	—	2	16	no	—
69	C₁₁×C₄⋊C₄	—	2	16	no	—
70	C₁₁×C₄⋊C₄	—	2	12	no	—
71	C₁₁×C₄⋊C₄	C₂⁴	1	8	yes	—
72	C₄²×C₁₁	C₂×D₄	1	12	yes	—
73	C₄²×C₁₁	C₂⁴	1	4	yes	—
74	C₂²×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic
75	C₂²×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic
76	C₂×#487	C₂×C₁₁	1	24	yes	direct product factor
77	C₂²×#103	C₂×C₁₁	1	4	yes	—
78	C₂²×C₄×C₈	C₂×C₁₁	1	1	yes	characteristic
79	C₂³×C₁₁	#124	1	4	yes	—
80	C₂³×C₁₁	C₂×SD₁₆	1	4	yes	—
81	C₂³×C₁₁	C₂×Q₁₆	1	4	yes	—
82	C₂³×C₁₁	C₂²×D₄	1	3	yes	—
83	Q₈×C₁₁	—	2	16	no	—
84	Q₈×C₁₁	—	4	24	no	—
85	Q₈×C₁₁	—	4	32	no	—
86	C₂×C₄×C₁₁	—	2	8	no	—
87	C₂×C₄×C₁₁	—	2	8	no	—
88	C₂×C₄×C₁₁	—	4	24	no	—
89	C₂×C₄×C₁₁	—	4	24	no	—
90	C₂×C₄×C₁₁	#124	1	12	yes	—
91	C₂×C₄×C₁₁	C₂×SD₁₆	1	24	yes	—
92	C₂×C₄×C₁₁	C₂×Q₁₆	1	24	yes	—
93	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
94	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
95	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
96	C₂×C₄×C₁₁	C₂×#41	1	12	yes	—
97	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
98	C₈×C₁₁	—	2	8	no	—
99	C₂³×Q₈	—	2	1	no	—
100	C₂³×Q₈	C₂²×C₁₁	1	2	yes	—
101	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
102	C₂×C₄⋊Q₈	—	2	6	no	—
103	C₂×C₄⋊Q₈	—	2	6	no	—
104	C₂×C₄⋊Q₈	C₂²×C₁₁	1	12	yes	—
105	C₂×C₄⋊Q₈	C₂²×C₁₁	1	12	yes	—
106	C₂²×C₄⋊C₄	—	2	1	no	—
107	C₂²×C₄⋊C₄	—	2	1	no	—
108	C₂²×C₄⋊C₄	—	2	1	no	—
109	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
110	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
111	#487	C₂²×C₁₁	1	64	yes	direct product factor
112	C₂×#103	C₂²×C₁₁	1	48	yes	—
113	C₂×C₄×C₈	C₂²×C₁₁	1	12	yes	—
114	C₂²×C₁₁	#487	1	16	yes	direct product factor
115	C₂²×C₁₁	C₂×#124	1	6	yes	—
116	C₂²×C₁₁	C₂²×SD₁₆	1	6	yes	—
117	C₂²×C₁₁	C₂²×Q₁₆	1	6	yes	—
118	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
119	C₄×C₁₁	—	4	8	no	—
120	C₄×C₁₁	—	4	8	no	—
121	C₄×C₁₁	C₂×#124	1	6	yes	—
122	C₄×C₁₁	C₂²×SD₁₆	1	8	yes	—
123	C₄×C₁₁	C₂²×Q₁₆	1	8	yes	—
124	C₄×C₁₁	C₂²×#41	1	2	yes	—
125	C₂²×Q₈	—	2	6	no	—
126	C₂²×Q₈	—	2	12	no	—
127	C₂²×Q₈	—	2	16	no	—
128	C₂²×Q₈	—	4	8	no	—
129	C₂²×Q₈	C₂³×C₁₁	1	12	yes	—
130	C₂³×C₄	—	2	2	no	—
131	C₂³×C₄	—	2	2	no	—
132	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
133	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
134	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
135	C₂²×C₈	—	2	8	no	—
136	C₂²×C₈	C₂³×C₁₁	1	12	yes	—
137	C₄⋊Q₈	—	2	24	no	—
138	C₄⋊Q₈	—	2	24	no	—
139	C₄⋊Q₈	C₂³×C₁₁	1	16	yes	—
140	C₄⋊Q₈	C₂³×C₁₁	1	16	yes	—
141	C₂×C₄⋊C₄	—	2	12	no	—
142	C₂×C₄⋊C₄	—	2	12	no	—
143	C₂×C₄⋊C₄	—	2	12	no	—
144	C₂×C₄⋊C₄	—	2	6	no	—
145	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
146	C₂×C₄²	D₄×C₁₁	1	6	yes	—
147	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
148	#103	C₂³×C₁₁	1	64	yes	—
149	C₄×C₈	C₂³×C₁₁	1	16	yes	—
150	C₂×C₁₁	C₂×#487	1	12	yes	direct product factor
151	C₂×C₁₁	C₂²×#124	1	1	yes	characteristic
152	C₂×C₁₁	C₂³×SD₁₆	1	1	yes	characteristic
153	C₂×C₁₁	C₂³×Q₁₆	1	1	yes	characteristic
154	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
155	C₂×Q₈	—	2	12	no	—
156	C₂×Q₈	—	2	16	no	—
157	C₂×Q₈	—	2	48	no	—
158	C₂×Q₈	—	4	24	no	—
159	C₂×Q₈	—	4	48	no	—
160	C₂×Q₈	C₂⁴×C₁₁	1	8	yes	—
161	C₂²×C₄	—	2	12	no	—
162	C₂²×C₄	—	2	12	no	—
163	C₂²×C₄	—	4	8	no	—
164	C₂²×C₄	—	4	8	no	—
165	C₂²×C₄	C₁₁×SD₁₆	1	8	yes	—
166	C₂²×C₄	C₁₁×Q₁₆	1	8	yes	—
167	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
168	C₂²×C₄	C₂×D₄×C₁₁	1	6	yes	—
169	C₂²×C₄	C₂×D₄×C₁₁	1	6	yes	—
170	C₂²×C₄	C₁₁×#41	1	8	yes	—
171	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
172	C₂×C₈	—	2	24	no	—
173	C₂×C₈	C₂⁴×C₁₁	1	8	yes	—
174	C₄⋊C₄	—	2	16	no	—
175	C₄⋊C₄	—	2	16	no	—
176	C₄⋊C₄	—	2	16	no	—
177	C₄⋊C₄	—	2	12	no	—
178	C₄⋊C₄	C₂⁴×C₁₁	1	8	yes	—
179	C₄²	C₂×D₄×C₁₁	1	12	yes	—
180	C₄²	C₂⁴×C₁₁	1	4	yes	—
181	C₁₁	C₂²×#487	1	1	yes	characteristic, direct product factor, Sylow
182	C₂³	C₁₁×#124	1	4	yes	—
183	C₂³	C₂×C₁₁×SD₁₆	1	4	yes	—
184	C₂³	C₂×C₁₁×Q₁₆	1	4	yes	—
185	C₂³	C₂²×D₄×C₁₁	1	3	yes	—
186	Q₈	—	2	16	no	—
187	Q₈	—	4	24	no	—
188	Q₈	—	4	32	no	—
189	C₂×C₄	—	2	8	no	—
190	C₂×C₄	—	2	8	no	—
191	C₂×C₄	—	4	24	no	—
192	C₂×C₄	—	4	24	no	—
193	C₂×C₄	C₁₁×#124	1	12	yes	—
194	C₂×C₄	C₂×C₁₁×SD₁₆	1	24	yes	—
195	C₂×C₄	C₂×C₁₁×Q₁₆	1	24	yes	—
196	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
197	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
198	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
199	C₂×C₄	C₂×C₁₁×#41	1	12	yes	—
200	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
201	C₈	—	2	8	no	—
202	C₂²	C₁₁×#487	1	16	yes	direct product factor
203	C₂²	C₂×C₁₁×#124	1	6	yes	—
204	C₂²	C₂²×C₁₁×SD₁₆	1	6	yes	—
205	C₂²	C₂²×C₁₁×Q₁₆	1	6	yes	—
206	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
207	C₄	—	4	8	no	—
208	C₄	—	4	8	no	—
209	C₄	C₂×C₁₁×#124	1	6	yes	—
210	C₄	C₂²×C₁₁×SD₁₆	1	8	yes	—
211	C₄	C₂²×C₁₁×Q₁₆	1	8	yes	—
212	C₄	C₂²×C₁₁×#41	1	2	yes	—
213	C₂	C₂×C₁₁×#487	1	12	yes	direct product factor
214	C₂	C₂²×C₁₁×#124	1	1	yes	characteristic
215	C₂	C₂³×C₁₁×SD₁₆	1	1	yes	characteristic
216	C₂	C₂³×C₁₁×Q₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₁×#487	C₂	direct (N × H)
18. C₁₁×#487	C₂²	direct (N × H)
46. C₂²×#487	C₁₁	direct (N × H)
76. C₂×#487	C₂×C₁₁	direct (N × H)
111. #487	C₂²×C₁₁	direct (N × H)
114. C₂²×C₁₁	#487	direct (N × H)
150. C₂×C₁₁	C₂×#487	direct (N × H)
181. C₁₁	C₂²×#487	direct (N × H)
202. C₂²	C₁₁×#487	direct (N × H)
213. C₂	C₂×C₁₁×#487	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×C₄⋊Q₈	2
C₂×C₁₁×#487	2
C₂²×C₁₁×#103	2
C₂²×C₄×C₈×C₁₁	2
C₂²×#487	11

Subgroups — C22×C11×#487 #14637796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×#487 #14637796