Subgroups — C₁₁×#33393 #14610586

Order 2816.

1102 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#578	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#3407	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2916	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2148	C₂	1	6	yes	maximal, complemented
5	C₂×C₁₁×#362	C₂	1	6	yes	maximal, complemented
6	C₂×C₁₁×2₋¹⁺⁴	—	2	1	no	—
7	C₁₁×#578	—	2	4	no	—
8	C₁₁×#578	C₄	1	8	yes	—
9	C₂×C₁₁×#137	—	2	3	no	—
10	C₂×C₁₁×#135	C₂²	1	3	yes	—
11	C₂²×C₁₁×Q₁₆	C₂²	1	3	yes	—
12	C₁₁×#568	—	2	1	no	—
13	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
14	C₁₁×#504	—	2	4	no	—
15	C₂×C₁₁×M₃₂	C₂²	1	6	yes	—
16	C₁₁×#430	—	2	3	no	—
17	C₂×C₁₁×#108	C₂²	1	6	yes	—
18	C₁₁×#362	C₂²	1	12	yes	—
19	C₁₁×#361	C₂²	1	4	yes	—
20	C₁₁×2₋¹⁺⁴	—	2	8	no	—
21	C₁₁×2₋¹⁺⁴	—	4	4	no	—
22	C₂×C₁₁×#41	—	2	3	no	—
23	C₂×C₁₁×#41	—	4	3	no	—
24	C₂×C₁₁×#41	D₄	1	1	yes	characteristic
25	C₂²×Q₈×C₁₁	—	2	3	no	—
26	C₂²×Q₈×C₁₁	—	4	1	no	—
27	C₁₁×#137	—	2	24	no	—
28	C₁₁×#135	—	2	6	no	—
29	C₁₁×#135	C₂×C₄	1	12	yes	—
30	C₂×C₁₁×Q₁₆	—	2	3	no	—
31	C₂×C₁₁×Q₁₆	—	2	6	no	—
32	C₂×C₁₁×Q₁₆	C₂×C₄	1	12	yes	—
33	C₂×C₁₁×Q₁₆	C₂³	1	3	yes	—
34	C₂×C₁₁×SD₁₆	—	2	3	no	—
35	C₂×C₁₁×D₈	C₂³	1	1	yes	characteristic
36	C₁₁×#131	—	4	4	no	—
37	C₁₁×#131	C₂×C₄	1	4	yes	—
38	C₁₁×#131	D₄	1	4	yes	—
39	C₂×C₁₁×M₁₆	—	2	6	no	—
40	C₂×C₁₁×M₁₆	D₄	1	3	yes	—
41	C₂²×C₈×C₁₁	C₂³	1	3	yes	—
42	C₁₁×M₃₂	—	2	6	no	—
43	C₁₁×M₃₂	C₂³	1	4	yes	—
44	C₂×C₁₁×C₁₆	—	2	6	no	—
45	C₁₁×#108	—	2	6	no	—
46	C₁₁×#108	C₂³	1	4	yes	—
47	#33393	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₁₁×#41	—	2	12	no	—
49	C₁₁×#41	—	4	24	no	—
50	C₁₁×#41	—	4	6	no	—
51	C₁₁×#41	C₂²⋊C₄	1	4	yes	—
52	C₁₁×#41	D₈	1	4	yes	—
53	C₂×Q₈×C₁₁	—	2	12	no	—
54	C₂×Q₈×C₁₁	—	2	3	no	—
55	C₂×Q₈×C₁₁	—	4	8	no	—
56	C₂×Q₈×C₁₁	—	4	6	no	—
57	C₂×Q₈×C₁₁	—	4	3	no	—
58	C₂×Q₈×C₁₁	SD₁₆	1	1	yes	characteristic
59	C₂×D₄×C₁₁	—	2	1	no	—
60	C₂×D₄×C₁₁	—	4	3	no	—
61	C₂×D₄×C₁₁	SD₁₆	1	3	yes	—
62	C₂²×C₄×C₁₁	—	4	3	no	—
63	C₂²×C₄×C₁₁	—	4	3	no	—
64	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
65	C₁₁×Q₁₆	—	2	12	no	—
66	C₁₁×Q₁₆	—	2	3	no	—
67	C₁₁×Q₁₆	C₂²×C₄	1	6	yes	—
68	C₁₁×SD₁₆	—	2	12	no	—
69	C₁₁×D₈	—	2	1	no	—
70	C₁₁×D₈	C₂²×C₄	1	2	yes	—
71	C₁₁×M₁₆	—	2	4	no	—
72	C₁₁×M₁₆	—	4	6	no	—
73	C₁₁×M₁₆	C₂²⋊C₄	1	12	yes	—
74	C₂×C₈×C₁₁	—	4	6	no	—
75	C₂×C₈×C₁₁	C₂²×C₄	1	6	yes	—
76	C₂×C₈×C₁₁	C₂×D₄	1	6	yes	—
77	C₂×C₈×C₁₁	C₂×D₄	1	3	yes	—
78	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
79	C₁₁×C₁₆	—	2	4	no	—
80	C₂×#578	C₂×C₁₁	1	1	yes	characteristic
81	#3407	C₂×C₁₁	1	1	yes	characteristic, complemented
82	#2916	C₂×C₁₁	1	1	yes	characteristic, complemented
83	#2148	C₂×C₁₁	1	6	yes	complemented
84	C₂×#362	C₂×C₁₁	1	6	yes	complemented
85	C₂³×C₁₁	—	4	1	no	—
86	C₂³×C₁₁	C₂×SD₁₆	1	3	yes	—
87	Q₈×C₁₁	—	2	6	no	—
88	Q₈×C₁₁	—	4	3	no	—
89	Q₈×C₁₁	—	4	12	no	—
90	Q₈×C₁₁	#102	1	4	yes	—
91	D₄×C₁₁	—	2	2	no	—
92	D₄×C₁₁	—	4	12	no	—
93	D₄×C₁₁	—	4	1	no	—
94	D₄×C₁₁	#102	1	12	yes	—
95	C₂×C₄×C₁₁	—	4	3	no	—
96	C₂×C₄×C₁₁	—	4	12	no	—
97	C₂×C₄×C₁₁	—	4	12	no	—
98	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	6	yes	—
99	C₂×C₄×C₁₁	C₂×D₈	1	6	yes	—
100	C₂×C₄×C₁₁	C₂×SD₁₆	1	3	yes	—
101	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
102	C₈×C₁₁	—	4	4	no	—
103	C₈×C₁₁	C₂×C₂²⋊C₄	1	6	yes	—
104	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
105	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
106	C₂×2₋¹⁺⁴	—	2	1	no	—
107	#578	—	2	4	no	—
108	#578	C₄×C₁₁	1	8	yes	—
109	C₂×#137	—	2	3	no	—
110	C₂×#135	C₂²×C₁₁	1	3	yes	—
111	C₂²×Q₁₆	C₂²×C₁₁	1	3	yes	—
112	#568	—	2	1	no	—
113	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
114	#504	—	2	4	no	—
115	C₂×M₃₂	C₂²×C₁₁	1	6	yes	—
116	#430	—	2	3	no	—
117	C₂×#108	C₂²×C₁₁	1	6	yes	—
118	#362	C₂²×C₁₁	1	12	yes	—
119	#361	C₂²×C₁₁	1	4	yes	—
120	C₂²×C₁₁	—	4	3	no	—
121	C₂²×C₁₁	—	4	2	no	—
122	C₂²×C₁₁	—	8	2	no	—
123	C₂²×C₁₁	C₂×#102	1	6	yes	—
124	C₂²×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
125	C₄×C₁₁	—	4	6	no	—
126	C₄×C₁₁	C₂×#102	1	6	yes	—
127	C₄×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
128	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
129	2₋¹⁺⁴	—	2	8	no	—
130	2₋¹⁺⁴	—	4	4	no	—
131	C₂×#41	—	2	3	no	—
132	C₂×#41	—	4	3	no	—
133	C₂×#41	D₄×C₁₁	1	1	yes	characteristic
134	C₂²×Q₈	—	2	3	no	—
135	C₂²×Q₈	—	4	1	no	—
136	#137	—	2	24	no	—
137	#135	—	2	6	no	—
138	#135	C₂×C₄×C₁₁	1	12	yes	—
139	C₂×Q₁₆	—	2	3	no	—
140	C₂×Q₁₆	—	2	6	no	—
141	C₂×Q₁₆	C₂×C₄×C₁₁	1	12	yes	—
142	C₂×Q₁₆	C₂³×C₁₁	1	3	yes	—
143	C₂×SD₁₆	—	2	3	no	—
144	C₂×D₈	C₂³×C₁₁	1	1	yes	characteristic
145	#131	—	4	4	no	—
146	#131	C₂×C₄×C₁₁	1	4	yes	—
147	#131	D₄×C₁₁	1	4	yes	—
148	C₂×M₁₆	—	2	6	no	—
149	C₂×M₁₆	D₄×C₁₁	1	3	yes	—
150	C₂²×C₈	C₂³×C₁₁	1	3	yes	—
151	M₃₂	—	2	6	no	—
152	M₃₂	C₂³×C₁₁	1	4	yes	—
153	C₂×C₁₆	—	2	6	no	—
154	#108	—	2	6	no	—
155	#108	C₂³×C₁₁	1	4	yes	—
156	C₂×C₁₁	—	2	1	no	—
157	C₂×C₁₁	—	2	6	no	—
158	C₂×C₁₁	—	8	2	no	—
159	C₂×C₁₁	C₂²×#102	1	1	yes	characteristic
160	#41	—	2	12	no	—
161	#41	—	4	24	no	—
162	#41	—	4	6	no	—
163	#41	C₁₁×C₂²⋊C₄	1	4	yes	—
164	#41	C₁₁×D₈	1	4	yes	—
165	C₂×Q₈	—	2	12	no	—
166	C₂×Q₈	—	2	3	no	—
167	C₂×Q₈	—	4	8	no	—
168	C₂×Q₈	—	4	6	no	—
169	C₂×Q₈	—	4	3	no	—
170	C₂×Q₈	C₁₁×SD₁₆	1	1	yes	characteristic
171	C₂×D₄	—	2	1	no	—
172	C₂×D₄	—	4	3	no	—
173	C₂×D₄	C₁₁×SD₁₆	1	3	yes	—
174	C₂²×C₄	—	4	3	no	—
175	C₂²×C₄	—	4	3	no	—
176	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
177	Q₁₆	—	2	12	no	—
178	Q₁₆	—	2	3	no	—
179	Q₁₆	C₂²×C₄×C₁₁	1	6	yes	—
180	SD₁₆	—	2	12	no	—
181	D₈	—	2	1	no	—
182	D₈	C₂²×C₄×C₁₁	1	2	yes	—
183	M₁₆	—	2	4	no	—
184	M₁₆	—	4	6	no	—
185	M₁₆	C₁₁×C₂²⋊C₄	1	12	yes	—
186	C₂×C₈	—	4	6	no	—
187	C₂×C₈	C₂²×C₄×C₁₁	1	6	yes	—
188	C₂×C₈	C₂×D₄×C₁₁	1	3	yes	—
189	C₂×C₈	C₂×D₄×C₁₁	1	6	yes	—
190	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
191	C₁₆	—	2	4	no	—
192	C₁₁	#33393	1	1	yes	characteristic, direct product factor, Sylow
193	C₂³	—	4	1	no	—
194	C₂³	C₂×C₁₁×SD₁₆	1	3	yes	—
195	Q₈	—	2	6	no	—
196	Q₈	—	4	12	no	—
197	Q₈	—	4	3	no	—
198	Q₈	C₁₁×#102	1	4	yes	—
199	D₄	—	2	2	no	—
200	D₄	—	4	12	no	—
201	D₄	—	4	1	no	—
202	D₄	C₁₁×#102	1	12	yes	—
203	C₂×C₄	—	4	12	no	—
204	C₂×C₄	—	4	3	no	—
205	C₂×C₄	—	4	12	no	—
206	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	6	yes	—
207	C₂×C₄	C₂×C₁₁×D₈	1	6	yes	—
208	C₂×C₄	C₂×C₁₁×SD₁₆	1	3	yes	—
209	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
210	C₈	—	4	4	no	—
211	C₈	C₂×C₁₁×C₂²⋊C₄	1	6	yes	—
212	C₈	C₂³×C₄×C₁₁	1	1	yes	characteristic
213	C₈	C₂²×D₄×C₁₁	1	1	yes	characteristic
214	C₂²	—	4	3	no	—
215	C₂²	—	4	2	no	—
216	C₂²	—	8	2	no	—
217	C₂²	C₂×C₁₁×#102	1	6	yes	—
218	C₂²	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
219	C₄	—	4	6	no	—
220	C₄	C₂×C₁₁×#102	1	6	yes	—
221	C₄	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
222	C₄	C₂²×C₁₁×D₈	1	1	yes	characteristic
223	C₂	—	2	1	no	—
224	C₂	—	2	6	no	—
225	C₂	—	8	2	no	—
226	C₂	C₂²×C₁₁×#102	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	C₂²×#102
commutator	C₈	C₂³×C₄×C₁₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#578	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₁₁×#41 ◁ C₂×C₁₁×#131 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#3407	C₂	semidirect
3. C₁₁×#2916	C₂	semidirect
4. C₁₁×#2148	C₂	semidirect
5. C₂×C₁₁×#362	C₂	semidirect
47. #33393	C₁₁	direct (N × H)
81. #3407	C₂×C₁₁	semidirect
82. #2916	C₂×C₁₁	semidirect
83. #2148	C₂×C₁₁	semidirect
84. C₂×#362	C₂×C₁₁	semidirect
192. C₁₁	#33393	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×C₁₁×#578	2
C₁₁×#3407	2
C₁₁×#2916	2
C₁₁×#2148	2
C₂×C₁₁×#362	2
#33393	11

Subgroups — C11×#33393 #14610586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33393 #14610586