Subgroups — C₂²×#10622117 #14722741

Order 2816.

942 conjugacy classes of subgroups.

The subgroup lattice has 206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₁₁⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#10622117	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₈×C₁₁	—	2	1	no	—
6	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
7	C₂³×C₁₁⋊C₈	—	2	1	no	—
8	C₂³×C₁₁⋊C₈	C₄	1	1	yes	characteristic
9	C₂³×C₁₁⋊C₈	C₄	1	1	yes	characteristic
10	C₂×C₁₁×C₄⋊C₈	—	2	3	no	—
11	C₂×C₁₁×C₄⋊C₈	C₂²	1	6	yes	—
12	C₂×C₄⋊(C₁₁⋊C₈)	—	2	3	no	—
13	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	6	yes	—
14	C₂×C₄×C₁₁⋊C₈	C₄	1	6	yes	—
15	C₂×C₄×C₁₁⋊C₈	C₂²	1	6	yes	—
16	#10622117	C₂²	1	16	yes	direct product factor
17	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
19	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
20	C₂²×C₈×C₁₁	—	2	6	no	—
21	C₂²×C₈×C₁₁	—	4	4	no	—
22	C₂×C₄²×C₁₁	C₂×C₄	1	3	yes	—
23	C₂×C₄²×C₁₁	D₄	1	3	yes	—
24	C₂×C₄²×C₁₁	Q₈	1	3	yes	—
25	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
26	C₂²×C₁₁⋊C₈	—	2	4	no	—
27	C₂²×C₁₁⋊C₈	—	2	6	no	—
28	C₂²×C₁₁⋊C₈	—	4	4	no	—
29	C₂²×C₁₁⋊C₈	C₈	1	8	yes	complemented
30	C₂²×C₁₁⋊C₈	C₂×C₄	1	6	yes	—
31	C₂²×C₁₁⋊C₈	C₂×C₄	1	6	yes	—
32	C₁₁×C₄⋊C₈	—	2	6	no	—
33	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
34	C₄⋊(C₁₁⋊C₈)	—	2	6	no	—
35	C₄⋊(C₁₁⋊C₈)	C₂³	1	4	yes	—
36	C₄×C₁₁⋊C₈	C₂×C₄	1	12	yes	—
37	C₄×C₁₁⋊C₈	C₂³	1	4	yes	—
38	C₂²×#335	—	11	1	no	maximal, Sylow
39	C₂⁴×C₁₁	C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₁	—	2	4	no	—
41	C₂²×C₄×C₁₁	C₄⋊C₄	1	3	yes	—
42	C₂²×C₄×C₁₁	C₄⋊C₄	1	3	yes	—
43	C₂²×C₄×C₁₁	C₄⋊C₄	1	3	yes	—
44	C₂²×C₄×C₁₁	C₂×C₈	1	4	yes	—
45	C₂²×C₄×C₁₁	M₁₆	1	4	yes	—
46	C₂²×C₄×C₁₁	D₈	1	4	yes	—
47	C₂²×C₄×C₁₁	Q₁₆	1	4	yes	—
48	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
49	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
50	C₂²×C₄×C₁₁	C₂×Q₈	1	3	yes	—
51	C₂×C₈×C₁₁	—	2	4	no	—
52	C₂×C₈×C₁₁	—	4	12	no	—
53	C₄²×C₁₁	C₄⋊C₄	1	6	yes	—
54	C₄²×C₁₁	C₂²×C₄	1	3	yes	—
55	C₄²×C₁₁	C₂×D₄	1	3	yes	—
56	C₄²×C₁₁	C₂×Q₈	1	3	yes	—
57	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
58	C₂×C₁₁⋊C₈	—	2	12	no	—
59	C₂×C₁₁⋊C₈	—	2	4	no	—
60	C₂×C₁₁⋊C₈	—	4	12	no	—
61	C₂×C₁₁⋊C₈	C₂×C₈	1	24	yes	complemented
62	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
63	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
64	C₂²×C₄⋊C₈	—	11	1	no	—
65	C₂²×C₄⋊C₈	D₁₁	1	1	yes	characteristic
66	C₂²×C₄×C₈	—	11	1	no	—
67	C₂×#335	—	11	12	no	—
68	C₂³×C₁₁	C₄⋊C₈	1	4	yes	—
69	C₂³×C₁₁	#107	1	4	yes	—
70	C₂³×C₁₁	#108	1	4	yes	—
71	C₂³×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
72	C₂×C₄×C₁₁	—	2	6	no	—
73	C₂×C₄×C₁₁	—	2	6	no	—
74	C₂×C₄×C₁₁	C₄⋊C₈	1	12	yes	—
75	C₂×C₄×C₁₁	#107	1	12	yes	—
76	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
77	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
78	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
79	C₂×C₄×C₁₁	C₂²×C₈	1	6	yes	—
80	C₂×C₄×C₁₁	C₂×M₁₆	1	6	yes	—
81	C₂×C₄×C₁₁	C₂×D₈	1	6	yes	—
82	C₂×C₄×C₁₁	C₂×Q₁₆	1	6	yes	—
83	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
85	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
86	C₈×C₁₁	—	4	4	no	—
87	C₁₁⋊C₈	—	2	4	no	—
88	C₁₁⋊C₈	—	4	4	no	—
89	C₁₁⋊C₈	C₂²×C₈	1	8	yes	complemented
90	C₂³×C₈	—	2	1	no	—
91	C₂³×C₈	—	11	1	no	—
92	C₂³×C₈	—	11	1	no	—
93	C₂³×C₈	—	22	1	no	—
94	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
95	C₂×C₄⋊C₈	—	2	3	no	—
96	C₂×C₄⋊C₈	—	11	6	no	—
97	C₂×C₄⋊C₈	—	22	3	no	—
98	C₂×C₄⋊C₈	C₂×D₁₁	1	6	yes	—
99	C₂×C₄×C₈	—	11	6	no	—
100	C₂×C₄×C₈	—	11	6	no	—
101	#335	—	11	16	no	—
102	C₂²×C₁₁	#335	1	16	yes	complemented
103	C₂²×C₁₁	C₂×C₄⋊C₈	1	6	yes	—
104	C₂²×C₁₁	C₂×#107	1	6	yes	—
105	C₂²×C₁₁	C₂×#108	1	6	yes	—
106	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
107	C₄×C₁₁	—	2	3	no	—
108	C₄×C₁₁	—	2	1	no	—
109	C₄×C₁₁	C₂×C₄⋊C₈	1	6	yes	—
110	C₄×C₁₁	C₂×#107	1	6	yes	—
111	C₄×C₁₁	C₂³×C₈	1	1	yes	characteristic
112	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
113	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
114	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
115	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
116	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
117	C₂³×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
118	C₂²×C₈	—	2	6	no	—
119	C₂²×C₈	—	4	4	no	—
120	C₂²×C₈	—	11	8	no	—
121	C₂²×C₈	—	11	6	no	—
122	C₂²×C₈	—	11	6	no	—
123	C₂²×C₈	—	22	4	no	—
124	C₂²×C₈	—	22	6	no	—
125	C₂²×C₈	—	44	4	no	—
126	C₂×C₄²	Dic₂₂	1	3	yes	—
127	C₂×C₄²	C₄×D₁₁	1	3	yes	—
128	C₂×C₄²	C₂²⋊D₁₁	1	3	yes	—
129	C₂×C₄²	C₂²×D₁₁	1	3	yes	—
130	C₄⋊C₈	—	2	6	no	—
131	C₄⋊C₈	—	11	4	no	—
132	C₄⋊C₈	—	22	6	no	—
133	C₄⋊C₈	C₂²×D₁₁	1	4	yes	—
134	C₄×C₈	—	11	12	no	—
135	C₄×C₈	—	11	4	no	—
136	C₂×C₁₁	C₂×#335	1	12	yes	complemented
137	C₂×C₁₁	C₂²×C₄⋊C₈	1	1	yes	characteristic
138	C₂×C₁₁	C₂²×#107	1	1	yes	characteristic
139	C₂×C₁₁	C₂²×#108	1	1	yes	characteristic
140	C₂⁴	Dic₁₁⋊C₄	1	1	yes	characteristic
141	C₂²×C₄	—	2	4	no	—
142	C₂²×C₄	C₈×D₁₁	1	4	yes	—
143	C₂²×C₄	#4313	1	4	yes	—
144	C₂²×C₄	Dic₁₁⋊C₄	1	3	yes	—
145	C₂²×C₄	Dic₁₁⋊C₄	1	3	yes	—
146	C₂²×C₄	Dic₁₁⋊C₄	1	3	yes	—
147	C₂²×C₄	#4323	1	4	yes	—
148	C₂²×C₄	#4326	1	4	yes	—
149	C₂²×C₄	C₂×Dic₂₂	1	3	yes	—
150	C₂²×C₄	C₂×C₄×D₁₁	1	3	yes	—
151	C₂²×C₄	C₂×C₂²⋊D₁₁	1	3	yes	—
152	C₂×C₈	—	2	4	no	—
153	C₂×C₈	—	4	12	no	—
154	C₂×C₈	—	11	24	no	—
155	C₂×C₈	—	11	4	no	—
156	C₂×C₈	—	11	4	no	—
157	C₂×C₈	—	22	12	no	—
158	C₂×C₈	—	22	4	no	—
159	C₂×C₈	—	44	12	no	—
160	C₄²	Dic₁₁⋊C₄	1	6	yes	—
161	C₄²	C₂×Dic₂₂	1	3	yes	—
162	C₄²	C₂×C₄×D₁₁	1	3	yes	—
163	C₄²	C₂×C₂²⋊D₁₁	1	3	yes	—
164	C₄²	C₂³×D₁₁	1	1	yes	characteristic
165	C₁₁	C₂²×#335	1	1	yes	characteristic, complemented, Sylow
166	C₂³	#66871	1	4	yes	—
167	C₂³	Dic₁₁⋊C₈	1	4	yes	—
168	C₂³	#66886	1	4	yes	—
169	C₂³	C₂×Dic₁₁⋊C₄	1	3	yes	—
170	C₂×C₄	—	2	6	no	—
171	C₂×C₄	—	2	6	no	—
172	C₂×C₄	#66871	1	12	yes	—
173	C₂×C₄	Dic₁₁⋊C₈	1	12	yes	—
174	C₂×C₄	C₂×C₈×D₁₁	1	6	yes	—
175	C₂×C₄	C₂×#4313	1	6	yes	—
176	C₂×C₄	C₂×Dic₁₁⋊C₄	1	3	yes	—
177	C₂×C₄	C₂×Dic₁₁⋊C₄	1	3	yes	—
178	C₂×C₄	C₂×Dic₁₁⋊C₄	1	3	yes	—
179	C₂×C₄	C₂×#4323	1	6	yes	—
180	C₂×C₄	C₂×#4326	1	6	yes	—
181	C₂×C₄	C₂²×Dic₂₂	1	1	yes	characteristic
182	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
183	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
184	C₈	—	4	4	no	—
185	C₈	—	11	8	no	—
186	C₈	—	22	4	no	—
187	C₈	—	44	4	no	—
188	C₂²	#10622117	1	16	yes	direct product factor
189	C₂²	C₂×#66871	1	6	yes	—
190	C₂²	C₂×Dic₁₁⋊C₈	1	6	yes	—
191	C₂²	C₂×#66886	1	6	yes	—
192	C₂²	C₂²×Dic₁₁⋊C₄	1	1	yes	characteristic
193	C₄	—	2	3	no	—
194	C₄	—	2	1	no	—
195	C₄	C₂×#66871	1	6	yes	—
196	C₄	C₂×Dic₁₁⋊C₈	1	6	yes	—
197	C₄	C₂²×C₈×D₁₁	1	1	yes	characteristic
198	C₄	C₂²×#4313	1	1	yes	characteristic
199	C₄	C₂²×#4323	1	1	yes	characteristic
200	C₄	C₂²×#4326	1	1	yes	characteristic
201	C₂	C₂×#10622117	1	12	yes	direct product factor
202	C₂	C₂²×Dic₁₁⋊C₈	1	1	yes	characteristic
203	C₂	C₂²×#66871	1	1	yes	characteristic
204	C₂	C₂²×#66886	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂³×C₈
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂²×C₁₁×C₄⋊C₈	C₂
socle, prime radical	C₂⁴×C₁₁	C₄⋊C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂²×C₄⋊C₈	D₁₁
hypocenter	C₁₁	C₂²×#335
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. C₂×#10622117	C₂	direct (N × H)
16. #10622117	C₂²	direct (N × H)
29. C₂²×C₁₁⋊C₈	C₈	semidirect
61. C₂×C₁₁⋊C₈	C₂×C₈	semidirect
89. C₁₁⋊C₈	C₂²×C₈	semidirect
102. C₂²×C₁₁	#335	semidirect
136. C₂×C₁₁	C₂×#335	semidirect
165. C₁₁	C₂²×#335	semidirect
188. C₂²	#10622117	direct (N × H)
201. C₂	C₂×#10622117	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×C₄⋊(C₁₁⋊C₈)	2
C₂²×C₄×C₁₁⋊C₈	2
C₂×#10622117	2
C₂²×C₁₁×C₄⋊C₈	2
C₂²×#335	11

Subgroups — C22×#10622117 #14722741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#10622117 #14722741