Subgroups — C₂²×#10622092 #14719342

Order 2816.

1182 conjugacy classes of subgroups.

The subgroup lattice has 182 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×#10622092	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₈×C₁₁	C₄	1	2	yes	—
6	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
7	C₂³×C₁₁⋊C₈	C₄	1	2	yes	—
8	C₂³×C₁₁⋊C₈	C₄	1	2	yes	—
9	C₂×C₄×C₈×C₁₁	C₄	1	6	yes	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	6	yes	—
11	C₂×C₄×C₁₁⋊C₈	C₄	1	6	yes	—
12	C₂×C₄×C₁₁⋊C₈	C₄	1	6	yes	—
13	C₂×C₄×C₁₁⋊C₈	C₂²	1	6	yes	—
14	C₂×C₄×C₁₁⋊C₈	C₂²	1	6	yes	—
15	#10622092	C₂²	1	16	yes	direct product factor
16	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₁	—	2	8	no	—
20	C₂²×C₈×C₁₁	C₂×C₄	1	12	yes	—
21	C₂×C₄²×C₁₁	C₂×C₄	1	3	yes	—
22	C₂×C₄²×C₁₁	C₂×C₄	1	3	yes	—
23	C₂×C₄²×C₁₁	C₂×C₄	1	3	yes	—
24	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
25	C₂²×C₁₁⋊C₈	—	2	8	no	—
26	C₂²×C₁₁⋊C₈	C₈	1	16	yes	complemented
27	C₂²×C₁₁⋊C₈	C₂×C₄	1	12	yes	—
28	C₂²×C₁₁⋊C₈	C₂×C₄	1	12	yes	—
29	C₄×C₈×C₁₁	C₂×C₄	1	12	yes	—
30	C₄×C₈×C₁₁	C₂³	1	4	yes	—
31	C₄×C₁₁⋊C₈	C₂×C₄	1	12	yes	—
32	C₄×C₁₁⋊C₈	C₂×C₄	1	12	yes	—
33	C₄×C₁₁⋊C₈	C₂³	1	4	yes	—
34	C₄×C₁₁⋊C₈	C₂³	1	4	yes	—
35	C₂²×#322	—	11	1	no	maximal, Sylow
36	C₂⁴×C₁₁	C₄²	1	1	yes	characteristic
37	C₂²×C₄×C₁₁	C₄²	1	3	yes	—
38	C₂²×C₄×C₁₁	C₄²	1	3	yes	—
39	C₂²×C₄×C₁₁	C₄²	1	3	yes	—
40	C₂²×C₄×C₁₁	C₂×C₈	1	8	yes	—
41	C₂²×C₄×C₁₁	M₁₆	1	8	yes	—
42	C₂²×C₄×C₁₁	M₁₆	1	8	yes	—
43	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
44	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
45	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
46	C₂×C₈×C₁₁	—	2	24	no	—
47	C₂×C₈×C₁₁	C₂²×C₄	1	8	yes	—
48	C₄²×C₁₁	C₄²	1	6	yes	—
49	C₄²×C₁₁	C₂²×C₄	1	3	yes	—
50	C₄²×C₁₁	C₂²×C₄	1	3	yes	—
51	C₄²×C₁₁	C₂²×C₄	1	3	yes	—
52	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
53	C₂×C₁₁⋊C₈	—	2	24	no	—
54	C₂×C₁₁⋊C₈	C₂×C₈	1	48	yes	complemented
55	C₂×C₁₁⋊C₈	C₂²×C₄	1	8	yes	—
56	C₂×C₁₁⋊C₈	C₂²×C₄	1	8	yes	—
57	C₂²×C₄×C₈	—	11	1	no	—
58	C₂²×C₄×C₈	—	11	1	no	—
59	C₂²×C₄×C₈	D₁₁	1	1	yes	characteristic
60	C₂×#322	—	11	12	no	—
61	C₂³×C₁₁	C₄×C₈	1	4	yes	—
62	C₂³×C₁₁	#97	1	4	yes	—
63	C₂³×C₁₁	#97	1	4	yes	—
64	C₂³×C₁₁	C₂×C₄²	1	3	yes	—
65	C₂×C₄×C₁₁	C₄×C₈	1	12	yes	—
66	C₂×C₄×C₁₁	#97	1	12	yes	—
67	C₂×C₄×C₁₁	#97	1	12	yes	—
68	C₂×C₄×C₁₁	C₂×C₄²	1	3	yes	—
69	C₂×C₄×C₁₁	C₂×C₄²	1	3	yes	—
70	C₂×C₄×C₁₁	C₂×C₄²	1	3	yes	—
71	C₂×C₄×C₁₁	C₂²×C₈	1	12	yes	—
72	C₂×C₄×C₁₁	C₂×M₁₆	1	12	yes	—
73	C₂×C₄×C₁₁	C₂×M₁₆	1	12	yes	—
74	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
76	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
77	C₈×C₁₁	—	2	8	no	—
78	C₁₁⋊C₈	—	2	8	no	—
79	C₁₁⋊C₈	C₂²×C₈	1	16	yes	complemented
80	C₂³×C₈	—	11	2	no	—
81	C₂³×C₈	—	11	2	no	—
82	C₂³×C₈	Dic₁₁	1	2	yes	—
83	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
84	C₂×C₄×C₈	—	11	6	no	—
85	C₂×C₄×C₈	—	11	6	no	—
86	C₂×C₄×C₈	—	11	6	no	—
87	C₂×C₄×C₈	—	11	6	no	—
88	C₂×C₄×C₈	Dic₁₁	1	6	yes	—
89	C₂×C₄×C₈	C₂×D₁₁	1	6	yes	—
90	#322	—	11	16	no	—
91	C₂²×C₁₁	#322	1	16	yes	complemented
92	C₂²×C₁₁	C₂×C₄×C₈	1	6	yes	—
93	C₂²×C₁₁	C₂×#97	1	6	yes	—
94	C₂²×C₁₁	C₂×#97	1	6	yes	—
95	C₂²×C₁₁	C₂²×C₄²	1	1	yes	characteristic
96	C₄×C₁₁	C₂×C₄×C₈	1	6	yes	—
97	C₄×C₁₁	C₂×#97	1	6	yes	—
98	C₄×C₁₁	C₂×#97	1	6	yes	—
99	C₄×C₁₁	C₂³×C₈	1	2	yes	—
100	C₄×C₁₁	C₂²×M₁₆	1	2	yes	—
101	C₄×C₁₁	C₂²×M₁₆	1	2	yes	—
102	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
103	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
104	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
105	C₂²×C₈	—	2	8	no	—
106	C₂²×C₈	—	11	16	no	—
107	C₂²×C₈	—	11	12	no	—
108	C₂²×C₈	—	11	12	no	—
109	C₂²×C₈	—	22	8	no	—
110	C₂²×C₈	C₂×Dic₁₁	1	12	yes	—
111	C₂×C₄²	C₄×D₁₁	1	3	yes	—
112	C₂×C₄²	C₄×D₁₁	1	3	yes	—
113	C₂×C₄²	C₂×Dic₁₁	1	3	yes	—
114	C₂×C₄²	C₂²×D₁₁	1	3	yes	—
115	C₄×C₈	—	11	12	no	—
116	C₄×C₈	—	11	12	no	—
117	C₄×C₈	—	11	4	no	—
118	C₄×C₈	—	11	4	no	—
119	C₄×C₈	C₂×Dic₁₁	1	12	yes	—
120	C₄×C₈	C₂²×D₁₁	1	4	yes	—
121	C₂×C₁₁	C₂×#322	1	12	yes	complemented
122	C₂×C₁₁	C₂²×C₄×C₈	1	1	yes	characteristic
123	C₂×C₁₁	C₂²×#97	1	1	yes	characteristic
124	C₂×C₁₁	C₂²×#97	1	1	yes	characteristic
125	C₂⁴	C₄×Dic₁₁	1	1	yes	characteristic
126	C₂²×C₄	C₈×D₁₁	1	8	yes	—
127	C₂²×C₄	#4313	1	8	yes	—
128	C₂²×C₄	#4318	1	8	yes	—
129	C₂²×C₄	C₄×Dic₁₁	1	3	yes	—
130	C₂²×C₄	C₄×Dic₁₁	1	3	yes	—
131	C₂²×C₄	C₄×Dic₁₁	1	3	yes	—
132	C₂²×C₄	C₂×C₄×D₁₁	1	3	yes	—
133	C₂²×C₄	C₂×C₄×D₁₁	1	3	yes	—
134	C₂²×C₄	C₂²×Dic₁₁	1	3	yes	—
135	C₂×C₈	—	2	24	no	—
136	C₂×C₈	—	11	48	no	—
137	C₂×C₈	—	11	8	no	—
138	C₂×C₈	—	11	8	no	—
139	C₂×C₈	—	22	24	no	—
140	C₂×C₈	C₂²×Dic₁₁	1	8	yes	—
141	C₄²	C₄×Dic₁₁	1	6	yes	—
142	C₄²	C₂×C₄×D₁₁	1	3	yes	—
143	C₄²	C₂×C₄×D₁₁	1	3	yes	—
144	C₄²	C₂²×Dic₁₁	1	3	yes	—
145	C₄²	C₂³×D₁₁	1	1	yes	characteristic
146	C₁₁	C₂²×#322	1	1	yes	characteristic, complemented, Sylow
147	C₂³	#66867	1	4	yes	—
148	C₂³	C₈×Dic₁₁	1	4	yes	—
149	C₂³	#66879	1	4	yes	—
150	C₂³	C₂×C₄×Dic₁₁	1	3	yes	—
151	C₂×C₄	#66867	1	12	yes	—
152	C₂×C₄	C₈×Dic₁₁	1	12	yes	—
153	C₂×C₄	#66879	1	12	yes	—
154	C₂×C₄	C₂×C₈×D₁₁	1	12	yes	—
155	C₂×C₄	C₂×#4313	1	12	yes	—
156	C₂×C₄	C₂×#4318	1	12	yes	—
157	C₂×C₄	C₂×C₄×Dic₁₁	1	3	yes	—
158	C₂×C₄	C₂×C₄×Dic₁₁	1	3	yes	—
159	C₂×C₄	C₂×C₄×Dic₁₁	1	3	yes	—
160	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
161	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
162	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
163	C₈	—	2	8	no	—
164	C₈	—	11	16	no	—
165	C₈	—	22	8	no	—
166	C₂²	#10622092	1	16	yes	direct product factor
167	C₂²	C₂×#66867	1	6	yes	—
168	C₂²	C₂×C₈×Dic₁₁	1	6	yes	—
169	C₂²	C₂×#66879	1	6	yes	—
170	C₂²	C₂²×C₄×Dic₁₁	1	1	yes	characteristic
171	C₄	C₂×#66867	1	6	yes	—
172	C₄	C₂×C₈×Dic₁₁	1	6	yes	—
173	C₄	C₂×#66879	1	6	yes	—
174	C₄	C₂²×C₈×D₁₁	1	2	yes	—
175	C₄	C₂²×#4313	1	2	yes	—
176	C₄	C₂²×#4318	1	2	yes	—
177	C₂	C₂×#10622092	1	12	yes	direct product factor
178	C₂	C₂²×C₈×Dic₁₁	1	1	yes	characteristic
179	C₂	C₂²×#66879	1	1	yes	characteristic
180	C₂	C₂²×#66867	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄²	C₂×D₁₁
commutator	C₂×C₁₁	C₂²×C₄×C₈
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂²×C₄×C₈×C₁₁	C₂
socle, prime radical	C₂⁴×C₁₁	C₄²
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂²×C₄×C₈	D₁₁
hypocenter	C₁₁	C₂²×#322
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×#10622092	C₂	direct (N × H)
15. #10622092	C₂²	direct (N × H)
26. C₂²×C₁₁⋊C₈	C₈	semidirect
54. C₂×C₁₁⋊C₈	C₂×C₈	semidirect
79. C₁₁⋊C₈	C₂²×C₈	semidirect
91. C₂²×C₁₁	#322	semidirect
121. C₂×C₁₁	C₂×#322	semidirect
146. C₁₁	C₂²×#322	semidirect
166. C₂²	#10622092	direct (N × H)
177. C₂	C₂×#10622092	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
C₂×#10622092	2
C₂²×C₄×C₈×C₁₁	2
C₂²×#322	11

Subgroups — C22×#10622092 #14719342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#10622092 #14719342