Subgroups — C₂²×#10622549 #14912048

Order 2816.

4286 conjugacy classes of subgroups.

The subgroup lattice has 174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊Dic₁₁	C₂	1	2	yes	maximal
2	C₂×#10622549	C₂	1	24	yes	maximal, direct product factor
3	C₂²×C₁₁⋊#95	C₂	1	4	yes	maximal
4	C₂³×C₄²×C₁₁	C₂	1	1	yes	maximal, characteristic
5	C₂⁴×C₄×C₁₁	C₂²	1	2	yes	—
6	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
7	C₂⁴×Dic₁₁	C₂²	1	4	yes	—
8	C₂²×C₄²×C₁₁	C₄	1	16	yes	complemented
9	C₂²×C₄²×C₁₁	C₂²	1	12	yes	—
10	C₂²×C₄⋊Dic₁₁	—	2	16	no	—
11	C₂²×C₄⋊Dic₁₁	C₂²	1	24	yes	—
12	C₂×C₁₁⋊#95	C₂²	1	48	yes	—
13	#10622549	C₂²	1	64	yes	direct product factor
14	C₂⁵×C₁₁	C₂³	1	1	yes	characteristic
15	C₂³×C₄×C₁₁	—	2	16	no	—
16	C₂³×C₄×C₁₁	C₂×C₄	1	16	yes	—
17	C₂³×C₄×C₁₁	C₂×C₄	1	8	yes	—
18	C₂³×C₄×C₁₁	D₄	1	8	yes	—
19	C₂³×C₄×C₁₁	Q₈	1	8	yes	—
20	C₂³×C₄×C₁₁	C₂³	1	12	yes	—
21	C₂³×C₄×C₁₁	C₂³	1	6	yes	—
22	C₂³×Dic₁₁	—	2	16	no	—
23	C₂³×Dic₁₁	—	2	32	no	—
24	C₂³×Dic₁₁	C₂³	1	24	yes	—
25	C₂×C₄²×C₁₁	C₂×C₄	1	96	yes	complemented
26	C₂×C₄²×C₁₁	C₂³	1	16	yes	—
27	C₂×C₄⋊Dic₁₁	—	2	96	no	—
28	C₂×C₄⋊Dic₁₁	C₂³	1	32	yes	—
29	C₁₁⋊#95	C₂³	1	64	yes	—
30	C₂²×#382	—	11	1	no	maximal, Sylow
31	C₂⁴×C₁₁	C₂²×C₄	1	4	yes	—
32	C₂⁴×C₁₁	C₂×D₄	1	4	yes	—
33	C₂⁴×C₁₁	C₂×Q₈	1	4	yes	—
34	C₂⁴×C₁₁	#41	1	16	yes	—
35	C₂⁴×C₁₁	C₂⁴	1	3	yes	—
36	C₂²×C₄×C₁₁	—	2	64	no	—
37	C₂²×C₄×C₁₁	—	2	48	no	—
38	C₂²×C₄×C₁₁	C₄⋊C₄	1	64	yes	—
39	C₂²×C₄×C₁₁	C₂²×C₄	1	48	yes	—
40	C₂²×C₄×C₁₁	C₂²×C₄	1	24	yes	—
41	C₂²×C₄×C₁₁	C₂×D₄	1	24	yes	—
42	C₂²×C₄×C₁₁	C₂×Q₈	1	24	yes	—
43	C₂²×C₄×C₁₁	C₂⁴	1	8	yes	—
44	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
45	C₂²×Dic₁₁	—	2	48	no	—
46	C₂²×Dic₁₁	—	2	96	no	—
47	C₂²×Dic₁₁	—	4	64	no	—
48	C₂²×Dic₁₁	C₂⁴	1	16	yes	—
49	C₄²×C₁₁	C₂²×C₄	1	64	yes	complemented
50	C₄⋊Dic₁₁	—	2	64	no	—
51	C₂³×C₄⋊C₄	—	11	2	no	—
52	C₂³×C₄²	D₁₁	1	1	yes	characteristic
53	C₂×#382	—	11	24	no	—
54	C₂²×#95	—	11	4	no	—
55	C₂³×C₁₁	C₂×C₄⋊C₄	1	16	yes	—
56	C₂³×C₁₁	#117	1	32	yes	—
57	C₂³×C₁₁	#124	1	32	yes	—
58	C₂³×C₁₁	#125	1	32	yes	—
59	C₂³×C₁₁	C₂³×C₄	1	6	yes	—
60	C₂³×C₁₁	C₂²×D₄	1	6	yes	—
61	C₂³×C₁₁	C₂²×Q₈	1	6	yes	—
62	C₂³×C₁₁	C₂×#41	1	24	yes	—
63	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
64	C₂×C₄×C₁₁	—	2	96	no	—
65	C₂×C₄×C₁₁	—	2	16	no	—
66	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	96	yes	—
67	C₂×C₄×C₁₁	C₂³×C₄	1	16	yes	—
68	C₂×C₄×C₁₁	C₂³×C₄	1	8	yes	—
69	C₂×C₄×C₁₁	C₂²×D₄	1	8	yes	—
70	C₂×C₄×C₁₁	C₂²×Q₈	1	8	yes	—
71	C₂×Dic₁₁	—	2	16	no	—
72	C₂×Dic₁₁	—	2	32	no	—
73	C₂×Dic₁₁	—	4	96	no	—
74	C₂⁴×C₄	—	11	4	no	—
75	C₂⁴×C₄	C₂×D₁₁	1	2	yes	—
76	C₂⁴×C₄	C₂×D₁₁	1	1	yes	characteristic
77	C₂²×C₄⋊C₄	—	11	24	no	—
78	C₂²×C₄⋊C₄	—	22	16	no	—
79	C₂²×C₄²	Dic₁₁	1	16	yes	complemented
80	C₂²×C₄²	C₂×D₁₁	1	12	yes	—
81	#382	—	11	64	no	—
82	C₂×#95	—	11	48	no	—
83	C₂²×C₁₁	#382	1	64	yes	complemented
84	C₂²×C₁₁	C₂²×C₄⋊C₄	1	12	yes	—
85	C₂²×C₁₁	C₂×#117	1	24	yes	—
86	C₂²×C₁₁	C₂×#124	1	24	yes	—
87	C₂²×C₁₁	C₂×#125	1	24	yes	—
88	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
89	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
90	C₂²×C₁₁	C₂³×Q₈	1	1	yes	characteristic
91	C₂²×C₁₁	C₂²×#41	1	4	yes	—
92	C₄×C₁₁	—	2	16	no	—
93	C₄×C₁₁	C₂²×C₄⋊C₄	1	16	yes	—
94	Dic₁₁	—	4	16	no	—
95	C₂⁵	C₂²×D₁₁	1	1	yes	characteristic
96	C₂³×C₄	—	2	16	no	—
97	C₂³×C₄	—	11	24	no	—
98	C₂³×C₄	—	22	16	no	—
99	C₂³×C₄	—	22	32	no	—
100	C₂³×C₄	Dic₂₂	1	8	yes	—
101	C₂³×C₄	D₄₄	1	8	yes	—
102	C₂³×C₄	C₂×Dic₁₁	1	16	yes	—
103	C₂³×C₄	C₂×Dic₁₁	1	8	yes	—
104	C₂³×C₄	C₂²×D₁₁	1	12	yes	—
105	C₂³×C₄	C₂²×D₁₁	1	6	yes	—
106	C₂×C₄⋊C₄	—	11	32	no	—
107	C₂×C₄⋊C₄	—	22	96	no	—
108	C₂×C₄²	C₂×Dic₁₁	1	96	yes	complemented
109	C₂×C₄²	C₂²×D₁₁	1	16	yes	—
110	#95	—	11	64	no	—
111	C₂×C₁₁	C₂×#382	1	24	yes	complemented
112	C₂×C₁₁	C₂³×C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₁₁	C₂²×#117	1	2	yes	—
114	C₂×C₁₁	C₂²×#124	1	2	yes	—
115	C₂×C₁₁	C₂²×#125	1	2	yes	—
116	C₂⁴	C₂×Dic₂₂	1	4	yes	—
117	C₂⁴	C₂×D₄₄	1	4	yes	—
118	C₂⁴	#4339	1	16	yes	—
119	C₂⁴	C₂²×Dic₁₁	1	4	yes	—
120	C₂⁴	C₂³×D₁₁	1	3	yes	—
121	C₂²×C₄	—	2	64	no	—
122	C₂²×C₄	—	2	48	no	—
123	C₂²×C₄	—	11	16	no	—
124	C₂²×C₄	—	22	48	no	—
125	C₂²×C₄	—	22	96	no	—
126	C₂²×C₄	—	44	64	no	—
127	C₂²×C₄	C₄⋊Dic₁₁	1	64	yes	—
128	C₂²×C₄	C₂×Dic₂₂	1	24	yes	—
129	C₂²×C₄	C₂×D₄₄	1	24	yes	—
130	C₂²×C₄	C₂²×Dic₁₁	1	48	yes	—
131	C₂²×C₄	C₂²×Dic₁₁	1	24	yes	—
132	C₂²×C₄	C₂³×D₁₁	1	8	yes	—
133	C₂²×C₄	C₂³×D₁₁	1	4	yes	—
134	C₄⋊C₄	—	22	64	no	—
135	C₄²	C₂²×Dic₁₁	1	64	yes	complemented
136	C₁₁	C₂²×#382	1	1	yes	characteristic, complemented, Sylow
137	C₂³	#66923	1	32	yes	—
138	C₂³	#66928	1	32	yes	—
139	C₂³	C₂×C₄⋊Dic₁₁	1	16	yes	—
140	C₂³	#66979	1	32	yes	—
141	C₂³	C₂²×Dic₂₂	1	6	yes	—
142	C₂³	C₂²×D₄₄	1	6	yes	—
143	C₂³	C₂×#4339	1	24	yes	—
144	C₂³	C₂³×Dic₁₁	1	6	yes	—
145	C₂³	C₂⁴×D₁₁	1	1	yes	characteristic
146	C₂×C₄	—	2	96	no	—
147	C₂×C₄	—	2	16	no	—
148	C₂×C₄	—	22	16	no	—
149	C₂×C₄	—	22	32	no	—
150	C₂×C₄	—	44	96	no	—
151	C₂×C₄	C₂×C₄⋊Dic₁₁	1	96	yes	—
152	C₂×C₄	C₂²×Dic₂₂	1	8	yes	—
153	C₂×C₄	C₂²×D₄₄	1	8	yes	—
154	C₂×C₄	C₂³×Dic₁₁	1	16	yes	—
155	C₂×C₄	C₂³×Dic₁₁	1	8	yes	—
156	C₂²	#10622549	1	64	yes	direct product factor
157	C₂²	C₂×#66923	1	24	yes	—
158	C₂²	C₂×#66928	1	24	yes	—
159	C₂²	C₂²×C₄⋊Dic₁₁	1	12	yes	—
160	C₂²	C₂×#66979	1	24	yes	—
161	C₂²	C₂³×Dic₂₂	1	1	yes	characteristic
162	C₂²	C₂³×D₄₄	1	1	yes	characteristic
163	C₂²	C₂²×#4339	1	4	yes	—
164	C₂²	C₂⁴×Dic₁₁	1	1	yes	characteristic
165	C₄	—	2	16	no	—
166	C₄	—	44	16	no	—
167	C₄	C₂²×C₄⋊Dic₁₁	1	16	yes	—
168	C₂	C₂×#10622549	1	24	yes	direct product factor
169	C₂	C₂³×C₄⋊Dic₁₁	1	1	yes	characteristic
170	C₂	C₂²×#66979	1	2	yes	—
171	C₂	C₂²×#66928	1	2	yes	—
172	C₂	C₂²×#66923	1	2	yes	—

	subgroup	G/H
center	C₂⁵	C₂²×D₁₁
commutator	C₂²×C₁₁	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₁₁
Fitting	C₂³×C₄²×C₁₁	C₂
socle, prime radical	C₂⁵×C₁₁	C₂³
cosocle	C₂³×C₁₁	C₂⁵
hypercenter	C₂³×C₄²	D₁₁
hypocenter	C₁₁	C₂²×#382
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂⁵ ◁ C₂³×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×#10622549	C₂	direct (N × H)
8. C₂²×C₄²×C₁₁	C₄	semidirect
13. #10622549	C₂²	direct (N × H)
25. C₂×C₄²×C₁₁	C₂×C₄	semidirect
49. C₄²×C₁₁	C₂²×C₄	semidirect
79. C₂²×C₄²	Dic₁₁	semidirect
83. C₂²×C₁₁	#382	semidirect
108. C₂×C₄²	C₂×Dic₁₁	semidirect
111. C₂×C₁₁	C₂×#382	semidirect
135. C₄²	C₂²×Dic₁₁	semidirect
136. C₁₁	C₂²×#382	semidirect
156. C₂²	#10622549	direct (N × H)
168. C₂	C₂×#10622549	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊Dic₁₁	2
C₂×#10622549	2
C₂²×C₁₁⋊#95	2
C₂³×C₄²×C₁₁	2
C₂²×#382	11

Subgroups — C22×#10622549 #14912048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#10622549 #14912048