Subgroups — C₁₁×#59924 #14637117

Order 2816.

1772 conjugacy classes of subgroups.

The subgroup lattice has 164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2811	C₂	1	4	yes	maximal
2	C₁₁×#2567	C₂	1	12	yes	maximal
3	C₁₁×#2551	C₂	1	6	yes	maximal
4	C₁₁×#2369	C₂	1	6	yes	maximal
5	C₄×C₁₁×C₄⋊Q₈	C₂	1	3	yes	maximal
6	C₂×C₁₁×C₄⋊Q₈	C₂²	1	12	yes	—
7	C₂×C₁₁×C₄⋊Q₈	C₂²	1	3	yes	—
8	C₂×C₄×Q₈×C₁₁	C₂²	1	6	yes	—
9	C₁₁×#395	C₂²	1	24	yes	—
10	C₁₁×#395	C₂²	1	8	yes	—
11	C₁₁×#391	C₂²	1	6	yes	—
12	C₁₁×#391	C₂²	1	24	yes	—
13	C₁₁×#389	C₂²	1	24	yes	—
14	C₁₁×#389	C₂²	1	12	yes	—
15	C₁₁×#384	C₂²	1	3	yes	—
16	C₁₁×#384	C₂²	1	8	yes	—
17	C₄×C₁₁×C₄⋊C₄	C₂²	1	12	yes	—
18	C₄×C₁₁×C₄⋊C₄	C₂²	1	12	yes	—
19	C₄³×C₁₁	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₁₁	C₂³	1	8	yes	—
21	C₂²×Q₈×C₁₁	C₂³	1	6	yes	—
22	C₁₁×C₄⋊Q₈	—	4	24	no	—
23	C₁₁×C₄⋊Q₈	Q₈	1	24	yes	complemented
24	C₄×Q₈×C₁₁	—	4	12	no	—
25	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
26	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
27	C₂×C₁₁×C₄⋊C₄	C₂³	1	6	yes	—
28	C₂×C₁₁×C₄⋊C₄	C₂³	1	24	yes	—
29	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
30	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
31	C₂×C₄²×C₁₁	C₂³	1	12	yes	—
32	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
33	C₂×C₄²×C₁₁	C₂³	1	8	yes	—
34	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
35	C₁₁×#95	C₂³	1	24	yes	—
36	C₁₁×#95	C₂³	1	24	yes	—
37	#59924	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂×Q₈×C₁₁	—	4	6	no	—
39	C₂×Q₈×C₁₁	—	4	6	no	—
40	C₂×Q₈×C₁₁	—	4	24	no	—
41	C₂×Q₈×C₁₁	C₂×Q₈	1	24	yes	—
42	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
43	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
44	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
45	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
46	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
47	C₁₁×C₄⋊C₄	—	2	24	no	—
48	C₁₁×C₄⋊C₄	—	4	12	no	—
49	C₁₁×C₄⋊C₄	—	4	6	no	—
50	C₁₁×C₄⋊C₄	—	4	24	no	—
51	C₁₁×C₄⋊C₄	C₂×Q₈	1	48	yes	—
52	C₄²×C₁₁	—	2	6	no	—
53	C₄²×C₁₁	—	2	24	no	—
54	C₄²×C₁₁	—	4	8	no	—
55	C₄²×C₁₁	—	4	1	no	—
56	C₄²×C₁₁	C₂×Q₈	1	12	yes	—
57	#2811	C₂×C₁₁	1	4	yes	—
58	#2567	C₂×C₁₁	1	12	yes	—
59	#2551	C₂×C₁₁	1	6	yes	—
60	#2369	C₂×C₁₁	1	6	yes	—
61	C₄×C₄⋊Q₈	C₂×C₁₁	1	3	yes	—
62	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
63	Q₈×C₁₁	—	4	24	no	—
64	Q₈×C₁₁	—	8	16	no	—
65	C₂×C₄×C₁₁	—	2	12	no	—
66	C₂×C₄×C₁₁	—	2	3	no	—
67	C₂×C₄×C₁₁	—	2	12	no	—
68	C₂×C₄×C₁₁	—	2	3	no	—
69	C₂×C₄×C₁₁	—	2	3	no	—
70	C₂×C₄×C₁₁	—	2	12	no	—
71	C₂×C₄×C₁₁	—	2	24	no	—
72	C₂×C₄×C₁₁	C₂²×Q₈	1	6	yes	—
73	C₂×C₄×C₁₁	C₂²×Q₈	1	24	yes	—
74	C₂×C₄×C₁₁	C₂²×Q₈	1	12	yes	—
75	C₂×C₄×C₁₁	H(5,𝔽₂)	1	6	yes	—
76	C₂×C₄⋊Q₈	C₂²×C₁₁	1	12	yes	—
77	C₂×C₄⋊Q₈	C₂²×C₁₁	1	3	yes	—
78	C₂×C₄×Q₈	C₂²×C₁₁	1	6	yes	—
79	#395	C₂²×C₁₁	1	8	yes	—
80	#395	C₂²×C₁₁	1	24	yes	—
81	#391	C₂²×C₁₁	1	6	yes	—
82	#391	C₂²×C₁₁	1	24	yes	—
83	#389	C₂²×C₁₁	1	12	yes	—
84	#389	C₂²×C₁₁	1	24	yes	—
85	#384	C₂²×C₁₁	1	3	yes	—
86	#384	C₂²×C₁₁	1	8	yes	—
87	C₄×C₄⋊C₄	C₂²×C₁₁	1	12	yes	—
88	C₄×C₄⋊C₄	C₂²×C₁₁	1	12	yes	—
89	C₄³	C₂²×C₁₁	1	1	yes	characteristic
90	C₂²×C₁₁	C₂³×Q₈	1	3	yes	—
91	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	3	yes	—
92	C₂²×C₁₁	#585	1	1	yes	characteristic
93	C₄×C₁₁	—	2	24	no	—
94	C₄×C₁₁	—	2	6	no	—
95	C₄×C₁₁	—	4	1	no	—
96	C₄×C₁₁	—	4	12	no	—
97	C₄×C₁₁	Q₈²	1	12	yes	—
98	C₂²×Q₈	C₂³×C₁₁	1	8	yes	—
99	C₂²×Q₈	C₂³×C₁₁	1	6	yes	—
100	C₄⋊Q₈	—	4	24	no	—
101	C₄⋊Q₈	Q₈×C₁₁	1	24	yes	complemented
102	C₄×Q₈	—	4	12	no	—
103	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
104	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
105	C₂×C₄⋊C₄	C₂³×C₁₁	1	6	yes	—
106	C₂×C₄⋊C₄	C₂³×C₁₁	1	24	yes	—
107	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
108	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
109	C₂×C₄²	C₂³×C₁₁	1	12	yes	—
110	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
111	C₂×C₄²	C₂³×C₁₁	1	8	yes	—
112	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
113	#95	C₂³×C₁₁	1	24	yes	—
114	#95	C₂³×C₁₁	1	24	yes	—
115	C₂×C₁₁	C₂×Q₈²	1	3	yes	—
116	C₂×C₁₁	#3501	1	3	yes	—
117	C₂×C₁₁	#3549	1	1	yes	characteristic
118	C₂×Q₈	—	4	6	no	—
119	C₂×Q₈	—	4	6	no	—
120	C₂×Q₈	—	4	24	no	—
121	C₂×Q₈	C₂×Q₈×C₁₁	1	24	yes	—
122	C₂²×C₄	C₂⁴×C₁₁	1	12	yes	—
123	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
124	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
125	C₂²×C₄	C₂⁴×C₁₁	1	12	yes	—
126	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
127	C₄⋊C₄	—	2	24	no	—
128	C₄⋊C₄	—	4	12	no	—
129	C₄⋊C₄	—	4	6	no	—
130	C₄⋊C₄	—	4	24	no	—
131	C₄⋊C₄	C₂×Q₈×C₁₁	1	48	yes	—
132	C₄²	—	2	6	no	—
133	C₄²	—	2	24	no	—
134	C₄²	—	4	8	no	—
135	C₄²	—	4	1	no	—
136	C₄²	C₂×Q₈×C₁₁	1	12	yes	—
137	C₁₁	#59924	1	1	yes	characteristic, direct product factor, Sylow
138	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
139	Q₈	—	4	24	no	—
140	Q₈	—	8	16	no	—
141	C₂×C₄	—	2	12	no	—
142	C₂×C₄	—	2	3	no	—
143	C₂×C₄	—	2	12	no	—
144	C₂×C₄	—	2	3	no	—
145	C₂×C₄	—	2	3	no	—
146	C₂×C₄	—	2	12	no	—
147	C₂×C₄	—	2	24	no	—
148	C₂×C₄	C₂²×Q₈×C₁₁	1	6	yes	—
149	C₂×C₄	C₂²×Q₈×C₁₁	1	24	yes	—
150	C₂×C₄	C₂²×Q₈×C₁₁	1	12	yes	—
151	C₂×C₄	C₁₁×H(5,𝔽₂)	1	6	yes	—
152	C₂²	C₂³×Q₈×C₁₁	1	3	yes	—
153	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	3	yes	—
154	C₂²	C₁₁×#585	1	1	yes	characteristic
155	C₄	—	2	6	no	—
156	C₄	—	2	24	no	—
157	C₄	—	4	12	no	—
158	C₄	—	4	1	no	—
159	C₄	Q₈²×C₁₁	1	12	yes	—
160	C₂	C₂×Q₈²×C₁₁	1	3	yes	—
161	C₂	C₁₁×#3501	1	3	yes	—
162	C₂	C₁₁×#3549	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
23. C₁₁×C₄⋊Q₈	Q₈	semidirect
37. #59924	C₁₁	direct (N × H)
101. C₄⋊Q₈	Q₈×C₁₁	semidirect
137. C₁₁	#59924	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#2811	2
C₁₁×#2567	2
C₁₁×#2551	2
C₁₁×#2369	2
C₄×C₁₁×C₄⋊Q₈	2
#59924	11

Subgroups — C11×#59924 #14637117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#59924 #14637117