Subgroups — C₂³×C₁₁×#101 #14637265

Order 2816.

4990 conjugacy classes of subgroups.

The subgroup lattice has 172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₁₁×M₁₆	C₂	1	2	yes	maximal
3	C₂²×C₁₁×#101	C₂	1	28	yes	maximal, direct product factor
4	C₂³×Q₈×C₁₁	—	2	14	no	—
5	C₂³×Q₈×C₁₁	—	2	2	no	—
6	C₂³×Q₈×C₁₁	C₄	1	14	yes	—
7	C₂³×Q₈×C₁₁	C₂²	1	14	yes	—
8	C₂⁴×C₄×C₁₁	C₄	1	2	yes	—
9	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
10	C₂²×C₁₁×M₁₆	—	2	14	no	—
11	C₂²×C₁₁×M₁₆	C₂²	1	28	yes	—
12	C₂³×C₈×C₁₁	—	2	2	no	—
13	C₂×C₁₁×#101	C₂²	1	112	yes	direct product factor
14	C₂⁵×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×Q₈×C₁₁	—	2	84	no	—
16	C₂²×Q₈×C₁₁	—	2	28	no	—
17	C₂²×Q₈×C₁₁	—	2	28	no	—
18	C₂²×Q₈×C₁₁	—	2	84	no	—
19	C₂²×Q₈×C₁₁	C₂×C₄	1	84	yes	—
20	C₂²×Q₈×C₁₁	C₂³	1	28	yes	—
21	C₂³×C₄×C₁₁	—	2	14	no	—
22	C₂³×C₄×C₁₁	—	2	2	no	—
23	C₂³×C₄×C₁₁	C₂×C₄	1	28	yes	—
24	C₂³×C₄×C₁₁	C₂×C₄	1	7	yes	—
25	C₂³×C₄×C₁₁	D₄	1	14	yes	—
26	C₂³×C₄×C₁₁	D₄	1	2	yes	—
27	C₂³×C₄×C₁₁	C₂³	1	7	yes	—
28	C₂×C₁₁×M₁₆	—	2	84	no	—
29	C₂×C₁₁×M₁₆	C₂³	1	56	yes	—
30	C₂²×C₈×C₁₁	—	2	28	no	—
31	C₁₁×#101	C₂³	1	64	yes	direct product factor
32	C₂³×#101	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂⁴×C₁₁	—	2	8	no	—
34	C₂⁴×C₁₁	C₂²⋊C₄	1	7	yes	—
35	C₂⁴×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
36	C₂⁴×C₁₁	C₂²×C₄	1	7	yes	—
37	C₂×Q₈×C₁₁	—	2	168	no	—
38	C₂×Q₈×C₁₁	—	2	168	no	—
39	C₂×Q₈×C₁₁	—	2	56	no	—
40	C₂×Q₈×C₁₁	—	2	56	no	—
41	C₂×Q₈×C₁₁	C₂²×C₄	1	56	yes	—
42	C₂×Q₈×C₁₁	C₂⁴	1	8	yes	—
43	C₂²×C₄×C₁₁	—	2	84	no	—
44	C₂²×C₄×C₁₁	—	2	28	no	—
45	C₂²×C₄×C₁₁	C₂²⋊C₄	1	42	yes	—
46	C₂²×C₄×C₁₁	C₂²⋊C₄	1	14	yes	—
47	C₂²×C₄×C₁₁	C₂²×C₄	1	56	yes	—
48	C₂²×C₄×C₁₁	C₂²×C₄	1	21	yes	—
49	C₂²×C₄×C₁₁	C₂×D₄	1	14	yes	—
50	C₂²×C₄×C₁₁	C₂×D₄	1	42	yes	—
51	C₂²×C₄×C₁₁	C₂⁴	1	7	yes	—
52	C₁₁×M₁₆	—	2	56	no	—
53	C₁₁×M₁₆	C₂⁴	1	16	yes	—
54	C₂×C₈×C₁₁	—	2	56	no	—
55	C₂⁴×Q₈	C₂×C₁₁	1	1	yes	characteristic
56	C₂³×M₁₆	C₂×C₁₁	1	2	yes	—
57	C₂²×#101	C₂×C₁₁	1	28	yes	direct product factor
58	C₂³×C₁₁	—	2	28	no	—
59	C₂³×C₁₁	—	2	28	no	—
60	C₂³×C₁₁	#101	1	8	yes	direct product factor
61	C₂³×C₁₁	C₂×C₂²⋊C₄	1	21	yes	—
62	C₂³×C₁₁	C₂×C₂²⋊C₄	1	7	yes	—
63	C₂³×C₁₁	C₂³×C₄	1	7	yes	—
64	Q₈×C₁₁	—	2	112	no	—
65	Q₈×C₁₁	—	2	16	no	—
66	C₂×C₄×C₁₁	—	2	56	no	—
67	C₂×C₄×C₁₁	—	2	56	no	—
68	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	42	yes	—
69	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	42	yes	—
70	C₂×C₄×C₁₁	C₂³×C₄	1	16	yes	—
71	C₂×C₄×C₁₁	C₂³×C₄	1	7	yes	—
72	C₂×C₄×C₁₁	C₂²×D₄	1	14	yes	—
73	C₂×C₄×C₁₁	C₂²×D₄	1	14	yes	—
74	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
75	C₈×C₁₁	—	2	16	no	—
76	C₂³×Q₈	—	2	2	no	—
77	C₂³×Q₈	—	2	14	no	—
78	C₂³×Q₈	C₄×C₁₁	1	14	yes	—
79	C₂³×Q₈	C₂²×C₁₁	1	14	yes	—
80	C₂⁴×C₄	C₄×C₁₁	1	2	yes	—
81	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
82	C₂²×M₁₆	—	2	14	no	—
83	C₂²×M₁₆	C₂²×C₁₁	1	28	yes	—
84	C₂³×C₈	—	2	2	no	—
85	C₂×#101	C₂²×C₁₁	1	112	yes	direct product factor
86	C₂²×C₁₁	—	2	42	no	—
87	C₂²×C₁₁	—	2	14	no	—
88	C₂²×C₁₁	C₂×#101	1	28	yes	direct product factor
89	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	7	yes	—
90	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	7	yes	—
91	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
92	C₄×C₁₁	—	2	16	no	—
93	C₄×C₁₁	C₂²×C₂²⋊C₄	1	14	yes	—
94	C₄×C₁₁	C₂³×D₄	1	2	yes	—
95	C₂⁵	C₂×C₄×C₁₁	1	1	yes	characteristic
96	C₂²×Q₈	—	2	84	no	—
97	C₂²×Q₈	—	2	28	no	—
98	C₂²×Q₈	—	2	28	no	—
99	C₂²×Q₈	—	2	84	no	—
100	C₂²×Q₈	C₂×C₄×C₁₁	1	84	yes	—
101	C₂²×Q₈	C₂³×C₁₁	1	28	yes	—
102	C₂³×C₄	—	2	14	no	—
103	C₂³×C₄	—	2	2	no	—
104	C₂³×C₄	C₂×C₄×C₁₁	1	28	yes	—
105	C₂³×C₄	C₂×C₄×C₁₁	1	7	yes	—
106	C₂³×C₄	D₄×C₁₁	1	2	yes	—
107	C₂³×C₄	D₄×C₁₁	1	14	yes	—
108	C₂³×C₄	C₂³×C₁₁	1	7	yes	—
109	C₂×M₁₆	—	2	84	no	—
110	C₂×M₁₆	C₂³×C₁₁	1	56	yes	—
111	C₂²×C₈	—	2	28	no	—
112	#101	C₂³×C₁₁	1	64	yes	direct product factor
113	C₂×C₁₁	—	2	7	no	—
114	C₂×C₁₁	—	2	1	no	—
115	C₂×C₁₁	C₂²×#101	1	14	yes	direct product factor
116	C₂×C₁₁	C₂³×C₂²⋊C₄	1	1	yes	characteristic
117	C₂⁴	—	2	8	no	—
118	C₂⁴	C₁₁×C₂²⋊C₄	1	7	yes	—
119	C₂⁴	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
120	C₂⁴	C₂²×C₄×C₁₁	1	7	yes	—
121	C₂×Q₈	—	2	168	no	—
122	C₂×Q₈	—	2	168	no	—
123	C₂×Q₈	—	2	56	no	—
124	C₂×Q₈	—	2	56	no	—
125	C₂×Q₈	C₂²×C₄×C₁₁	1	56	yes	—
126	C₂×Q₈	C₂⁴×C₁₁	1	8	yes	—
127	C₂²×C₄	—	2	84	no	—
128	C₂²×C₄	—	2	28	no	—
129	C₂²×C₄	C₁₁×C₂²⋊C₄	1	42	yes	—
130	C₂²×C₄	C₁₁×C₂²⋊C₄	1	14	yes	—
131	C₂²×C₄	C₂²×C₄×C₁₁	1	56	yes	—
132	C₂²×C₄	C₂²×C₄×C₁₁	1	21	yes	—
133	C₂²×C₄	C₂×D₄×C₁₁	1	14	yes	—
134	C₂²×C₄	C₂×D₄×C₁₁	1	42	yes	—
135	C₂²×C₄	C₂⁴×C₁₁	1	7	yes	—
136	M₁₆	—	2	56	no	—
137	M₁₆	C₂⁴×C₁₁	1	16	yes	—
138	C₂×C₈	—	2	56	no	—
139	C₁₁	C₂³×#101	1	1	yes	characteristic, direct product factor, Sylow
140	C₂³	—	2	28	no	—
141	C₂³	—	2	28	no	—
142	C₂³	C₁₁×#101	1	8	yes	direct product factor
143	C₂³	C₂×C₁₁×C₂²⋊C₄	1	21	yes	—
144	C₂³	C₂×C₁₁×C₂²⋊C₄	1	7	yes	—
145	C₂³	C₂³×C₄×C₁₁	1	7	yes	—
146	Q₈	—	2	112	no	—
147	Q₈	—	2	16	no	—
148	C₂×C₄	—	2	56	no	—
149	C₂×C₄	—	2	56	no	—
150	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	42	yes	—
151	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	42	yes	—
152	C₂×C₄	C₂³×C₄×C₁₁	1	16	yes	—
153	C₂×C₄	C₂³×C₄×C₁₁	1	7	yes	—
154	C₂×C₄	C₂²×D₄×C₁₁	1	14	yes	—
155	C₂×C₄	C₂²×D₄×C₁₁	1	14	yes	—
156	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
157	C₈	—	2	16	no	—
158	C₂²	—	2	42	no	—
159	C₂²	—	2	14	no	—
160	C₂²	C₂×C₁₁×#101	1	28	yes	direct product factor
161	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	7	yes	—
162	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	7	yes	—
163	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
164	C₄	—	2	16	no	—
165	C₄	C₂²×C₁₁×C₂²⋊C₄	1	14	yes	—
166	C₄	C₂³×D₄×C₁₁	1	2	yes	—
167	C₂	—	2	7	no	—
168	C₂	—	2	1	no	—
169	C₂	C₂²×C₁₁×#101	1	14	yes	direct product factor
170	C₂	C₂³×C₁₁×C₂²⋊C₄	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂²×C₁₁×#101	C₂	direct (N × H)
13. C₂×C₁₁×#101	C₂²	direct (N × H)
31. C₁₁×#101	C₂³	direct (N × H)
32. C₂³×#101	C₁₁	direct (N × H)
57. C₂²×#101	C₂×C₁₁	direct (N × H)
60. C₂³×C₁₁	#101	direct (N × H)
85. C₂×#101	C₂²×C₁₁	direct (N × H)
88. C₂²×C₁₁	C₂×#101	direct (N × H)
112. #101	C₂³×C₁₁	direct (N × H)
115. C₂×C₁₁	C₂²×#101	direct (N × H)
139. C₁₁	C₂³×#101	direct (N × H)
142. C₂³	C₁₁×#101	direct (N × H)
160. C₂²	C₂×C₁₁×#101	direct (N × H)
169. C₂	C₂²×C₁₁×#101	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×Q₈×C₁₁	2
C₂³×C₁₁×M₁₆	2
C₂²×C₁₁×#101	2
C₂³×#101	11

Subgroups — C23×C11×#101 #14637265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₁₁×#101 #14637265