Subgroups — C₁₁×#3338 #13066176

Order 1408.

356 conjugacy classes of subgroups.

The subgroup lattice has 168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#554	C₂	1	2	yes	maximal
2	C₁₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#484	C₂	1	4	yes	maximal, complemented
4	C₁₁×#477	C₂	1	2	yes	maximal, complemented
5	C₁₁×#467	C₂	1	2	yes	maximal, complemented
6	C₄×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₁×#107	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₁	C₂²	1	2	yes	—
11	C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
12	C₁₁×#125	—	2	2	no	—
13	C₁₁×C₂²⋊Q₈	—	2	4	no	—
14	C₁₁×C₂²⋊Q₈	C₂²	1	4	yes	—
15	C₄×Q₈×C₁₁	C₂²	1	2	yes	—
16	C₄×D₄×C₁₁	—	2	2	no	—
17	C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
19	C₁₁×#107	C₂²	1	2	yes	—
20	C₁₁×#107	C₂²	1	2	yes	—
21	C₁₁×#107	C₂²	1	1	yes	characteristic
22	C₁₁×#107	C₂²	1	4	yes	—
23	C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₁₁×#103	C₂²	1	2	yes	—
25	C₁₁×#103	C₂²	1	4	yes	—
26	C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
28	C₂×Q₈×C₁₁	—	2	2	no	—
29	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
30	C₂×D₄×C₁₁	D₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₁	—	2	4	no	—
32	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
33	C₁₁×Q₁₆	—	2	2	no	—
34	C₂×C₈×C₁₁	—	2	4	no	—
35	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
36	C₂×C₈×C₁₁	C₂³	1	2	yes	—
37	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
38	C₁₁×C₄⋊C₄	—	2	4	no	—
39	C₁₁×C₄⋊C₄	—	2	2	no	—
40	C₁₁×C₄⋊C₄	—	2	2	no	—
41	C₁₁×C₄⋊C₄	—	2	4	no	—
42	C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
43	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
44	C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
45	C₁₁×C₂²⋊C₄	—	2	4	no	—
46	C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
47	C₄²×C₁₁	—	2	2	no	—
48	C₄²×C₁₁	C₂³	1	1	yes	characteristic
49	#3338	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂³×C₁₁	C₂×D₄	1	2	yes	—
51	Q₈×C₁₁	—	2	2	no	—
52	Q₈×C₁₁	—	2	2	no	—
53	Q₈×C₁₁	—	8	2	no	—
54	D₄×C₁₁	Q₁₆	1	4	yes	complemented
55	C₂×C₄×C₁₁	—	2	2	no	—
56	C₂×C₄×C₁₁	—	2	2	no	—
57	C₂×C₄×C₁₁	—	2	2	no	—
58	C₂×C₄×C₁₁	—	2	2	no	—
59	C₂×C₄×C₁₁	—	2	4	no	—
60	C₂×C₄×C₁₁	—	8	4	no	—
61	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
63	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
65	C₈×C₁₁	—	2	2	no	—
66	C₈×C₁₁	—	2	1	no	—
67	C₈×C₁₁	#41	1	2	yes	—
68	#554	C₂×C₁₁	1	2	yes	—
69	#500	C₂×C₁₁	1	1	yes	characteristic, complemented
70	#484	C₂×C₁₁	1	4	yes	complemented
71	#477	C₂×C₁₁	1	2	yes	complemented
72	#467	C₂×C₁₁	1	2	yes	complemented
73	C₄×Q₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
74	C₈×D₄	C₂×C₁₁	1	1	yes	characteristic
75	C₂×#107	C₂×C₁₁	1	2	yes	complemented
76	C₂²×C₁₁	—	2	2	no	—
77	C₂²×C₁₁	—	2	2	no	—
78	C₂²×C₁₁	C₂×Q₁₆	1	4	yes	—
79	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
80	C₄×C₁₁	—	2	2	no	—
81	C₄×C₁₁	—	2	1	no	—
82	C₄×C₁₁	—	4	2	no	—
83	C₄×C₁₁	—	4	2	no	—
84	C₄×C₁₁	—	4	4	no	—
85	C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
86	C₄×C₁₁	C₂×#41	1	1	yes	characteristic
87	C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
88	C₂×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
89	C₂²×C₈	C₂²×C₁₁	1	2	yes	—
90	C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
91	#125	—	2	2	no	—
92	C₂²⋊Q₈	—	2	4	no	—
93	C₂²⋊Q₈	C₂²×C₁₁	1	4	yes	—
94	C₄×Q₈	C₂²×C₁₁	1	2	yes	—
95	C₄×D₄	—	2	2	no	—
96	C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
97	C₂×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
98	#107	C₂²×C₁₁	1	1	yes	characteristic
99	#107	C₂²×C₁₁	1	2	yes	—
100	#107	C₂²×C₁₁	1	4	yes	—
101	#107	C₂²×C₁₁	1	2	yes	—
102	C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
103	#103	C₂²×C₁₁	1	2	yes	—
104	#103	C₂²×C₁₁	1	4	yes	—
105	C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
106	C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
107	C₂×C₁₁	—	2	4	no	—
108	C₂×C₁₁	#547	1	1	yes	characteristic
109	C₂×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
110	C₂×C₁₁	#576	1	1	yes	characteristic
111	C₂×Q₈	—	2	2	no	—
112	C₂×Q₈	C₂³×C₁₁	1	2	yes	—
113	C₂×D₄	D₄×C₁₁	1	1	yes	characteristic
114	C₂²×C₄	—	2	4	no	—
115	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
116	Q₁₆	—	2	2	no	—
117	C₂×C₈	—	2	4	no	—
118	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
119	C₂×C₈	C₂³×C₁₁	1	2	yes	—
120	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
121	C₄⋊C₄	—	2	4	no	—
122	C₄⋊C₄	—	2	2	no	—
123	C₄⋊C₄	—	2	2	no	—
124	C₄⋊C₄	—	2	4	no	—
125	C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
126	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
127	C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
128	C₂²⋊C₄	—	2	4	no	—
129	C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
130	C₄²	—	2	2	no	—
131	C₄²	C₂³×C₁₁	1	1	yes	characteristic
132	C₁₁	#3338	1	1	yes	characteristic, direct product factor, Sylow
133	C₂³	C₂×D₄×C₁₁	1	2	yes	—
134	Q₈	—	2	2	no	—
135	Q₈	—	2	2	no	—
136	Q₈	—	8	2	no	—
137	D₄	C₁₁×Q₁₆	1	4	yes	complemented
138	C₂×C₄	—	2	2	no	—
139	C₂×C₄	—	2	2	no	—
140	C₂×C₄	—	2	2	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	4	no	—
143	C₂×C₄	—	8	4	no	—
144	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
145	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
146	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
147	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
148	C₈	—	2	2	no	—
149	C₈	—	2	1	no	—
150	C₈	C₁₁×#41	1	2	yes	—
151	C₂²	—	2	2	no	—
152	C₂²	—	2	2	no	—
153	C₂²	C₂×C₁₁×Q₁₆	1	4	yes	—
154	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
155	C₄	—	2	2	no	—
156	C₄	—	2	1	no	—
157	C₄	—	4	2	no	—
158	C₄	—	4	2	no	—
159	C₄	—	4	4	no	—
160	C₄	C₂×C₁₁×Q₁₆	1	2	yes	—
161	C₄	C₂×C₁₁×#41	1	1	yes	characteristic
162	C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
163	C₂	—	2	4	no	—
164	C₂	C₁₁×#547	1	1	yes	characteristic
165	C₂	C₂²×C₁₁×Q₁₆	1	1	yes	characteristic
166	C₂	C₁₁×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₁
prime radical	C₂×D₄×C₁₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄×D₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#500	C₂	semidirect
3. C₁₁×#484	C₂	semidirect
4. C₁₁×#477	C₂	semidirect
5. C₁₁×#467	C₂	semidirect
6. C₄×C₁₁×Q₁₆	C₂	semidirect
8. C₂×C₁₁×#107	C₂	semidirect
49. #3338	C₁₁	direct (N × H)
54. D₄×C₁₁	Q₁₆	semidirect
69. #500	C₂×C₁₁	semidirect
70. #484	C₂×C₁₁	semidirect
71. #477	C₂×C₁₁	semidirect
72. #467	C₂×C₁₁	semidirect
73. C₄×Q₁₆	C₂×C₁₁	semidirect
75. C₂×#107	C₂×C₁₁	semidirect
132. C₁₁	#3338	direct (N × H)
137. D₄	C₁₁×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#554	2
C₁₁×#500	2
C₁₁×#484	2
C₁₁×#477	2
C₁₁×#467	2
C₄×C₁₁×Q₁₆	2
C₈×D₄×C₁₁	2
C₂×C₁₁×#107	2
#3338	11

Subgroups — C11×#3338 #13066176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#3338 #13066176