Subgroups — Dic₁₁×#368 #14669187

Order 2816.

314 conjugacy classes of subgroups.

The subgroup lattice has 178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622144	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	#108×Dic₁₁	C₂	1	2	yes	maximal
4	#13066709	C₂	1	2	yes	maximal
5	C₂×C₁₁×#368	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₁₁×#108	C₂²	1	2	yes	—
8	M₁₆×Dic₁₁	—	2	2	no	—
9	C₂×#66883	C₂²	1	2	yes	—
10	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
11	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
12	C₁₁×#368	C₄	1	4	yes	complemented
13	#10622196	—	2	2	no	—
14	#10622144	C₄	1	4	yes	complemented
15	C₁₆×Dic₁₁	C₄	1	4	yes	—
16	C₂×C₁₁×M₁₆	—	2	2	no	—
17	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
18	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
19	C₂×#4318	—	2	2	no	—
20	C₂²×C₁₁⋊C₈	D₄	1	1	yes	characteristic
21	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
22	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
23	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
24	C₁₁×#108	—	2	2	no	—
25	C₁₁×#108	C₂×C₄	1	4	yes	—
26	#66883	—	2	2	no	—
27	#66883	C₂×C₄	1	4	yes	—
28	#66879	—	4	2	no	—
29	C₈×Dic₁₁	—	4	2	no	—
30	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
31	C₈×Dic₁₁	Q₈	1	2	yes	—
32	C₂×C₁₁⋊C₁₆	—	2	1	no	—
33	C₂×C₁₁⋊C₁₆	—	2	1	no	—
34	C₂×C₁₁⋊C₁₆	C₂×C₄	1	2	yes	—
35	C₄×#368	—	11	1	no	maximal, Sylow
36	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
37	C₂²×Dic₁₁	Q₁₆	1	2	yes	—
38	C₁₁×M₁₆	—	2	4	no	—
39	C₁₁×M₁₆	—	4	2	no	—
40	C₂×C₈×C₁₁	—	4	2	no	—
41	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
46	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
47	C₄×Dic₁₁	C₄⋊C₄	1	2	yes	—
48	C₄×Dic₁₁	D₈	1	1	yes	characteristic
49	C₄×Dic₁₁	D₈	1	1	yes	characteristic
50	#4318	—	2	4	no	—
51	#4318	—	4	2	no	—
52	C₂×C₁₁⋊C₈	—	2	1	no	—
53	C₂×C₁₁⋊C₈	—	2	1	no	—
54	C₂×C₁₁⋊C₈	—	4	2	no	—
55	C₂×C₁₁⋊C₈	C₄⋊C₄	1	2	yes	—
56	C₁₁×C₁₆	C₄²	1	4	yes	—
57	C₁₁⋊C₁₆	—	2	2	no	—
58	C₂×#368	—	11	1	no	—
59	C₂×#368	D₁₁	1	1	yes	characteristic
60	C₂×C₄×C₁₆	—	11	1	no	—
61	C₄×#108	—	11	2	no	—
62	#1381	—	11	2	no	—
63	C₂³×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
64	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
66	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
67	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
68	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
69	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
70	C₂×Dic₁₁	—	2	4	no	—
71	C₂×Dic₁₁	#107	1	2	yes	—
72	C₂×Dic₁₁	#107	1	2	yes	—
73	C₈×C₁₁	—	4	4	no	—
74	C₈×C₁₁	C₂×C₄²	1	1	yes	characteristic
75	C₈×C₁₁	#117	1	1	yes	characteristic
76	C₈×C₁₁	C₄×Q₈	1	1	yes	characteristic
77	C₈×C₁₁	C₄×Q₈	1	1	yes	characteristic
78	C₁₁⋊C₈	—	2	2	no	—
79	C₁₁⋊C₈	—	4	4	no	—
80	C₂²×C₁₆	—	11	1	no	—
81	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
82	C₂×#108	—	11	2	no	—
83	C₂×#108	C₂×D₁₁	1	2	yes	—
84	C₄×M₁₆	—	22	2	no	—
85	C₂×C₄×C₈	—	11	1	no	—
86	#368	—	11	4	no	—
87	#368	Dic₁₁	1	4	yes	direct product factor
88	C₄×C₁₆	—	11	4	no	—
89	#341	—	22	2	no	—
90	C₂²×C₁₁	—	2	2	no	—
91	C₂²×C₁₁	C₂×#107	1	1	yes	characteristic
92	C₂²×C₁₁	C₄×Q₁₆	1	1	yes	characteristic
93	C₂²×C₁₁	C₄×Q₁₆	1	1	yes	characteristic
94	C₄×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
95	C₄×C₁₁	#427	1	1	yes	characteristic
96	C₄×C₁₁	C₄×D₈	1	1	yes	characteristic
97	C₄×C₁₁	C₄×D₈	1	1	yes	characteristic
98	Dic₁₁	—	2	2	no	—
99	Dic₁₁	#368	1	4	yes	direct product factor
100	C₂×M₁₆	—	2	2	no	—
101	C₂×M₁₆	—	22	2	no	—
102	C₂²×C₈	—	11	1	no	—
103	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
104	C₂×C₄²	—	11	1	no	—
105	C₂×C₁₆	—	11	2	no	—
106	C₂×C₁₆	—	22	1	no	—
107	C₂×C₁₆	—	22	1	no	—
108	C₂×C₁₆	C₄×D₁₁	1	2	yes	—
109	C₂×C₁₆	C₄×D₁₁	1	2	yes	—
110	C₂×C₁₆	C₂×Dic₁₁	1	2	yes	—
111	#108	—	2	2	no	—
112	#108	—	11	4	no	—
113	#108	—	22	2	no	—
114	#108	C₂×Dic₁₁	1	4	yes	—
115	#97	—	44	2	no	—
116	C₄×C₈	—	11	2	no	—
117	C₄×C₈	—	11	2	no	—
118	C₄×C₈	—	44	2	no	—
119	C₂×C₁₁	—	2	1	no	—
120	C₂×C₁₁	—	2	1	no	—
121	C₂×C₁₁	C₄×#107	1	1	yes	characteristic
122	C₂×C₁₁	C₂×#368	1	2	yes	—
123	C₂²×C₄	—	11	2	no	—
124	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
125	M₁₆	—	2	4	no	—
126	M₁₆	—	4	2	no	—
127	M₁₆	—	22	4	no	—
128	M₁₆	—	44	2	no	—
129	C₂×C₈	—	4	2	no	—
130	C₂×C₈	—	11	2	no	—
131	C₂×C₈	—	22	1	no	—
132	C₂×C₈	—	22	1	no	—
133	C₂×C₈	—	44	2	no	—
134	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
135	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
136	C₂×C₈	#4341	1	1	yes	characteristic
137	C₂×C₈	Q₈×D₁₁	1	1	yes	characteristic
138	C₂×C₈	#4343	1	1	yes	characteristic
139	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
140	C₄²	—	11	2	no	—
141	C₄²	—	11	1	no	—
142	C₄²	—	11	1	no	—
143	C₁₆	—	22	2	no	—
144	C₁₆	C₄×Dic₁₁	1	4	yes	—
145	C₁₁	C₄×#368	1	1	yes	characteristic, complemented, Sylow
146	C₂³	Q₁₆×D₁₁	1	1	yes	characteristic
147	C₂×C₄	—	11	2	no	—
148	C₂×C₄	—	11	2	no	—
149	C₂×C₄	—	22	4	no	—
150	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
151	C₂×C₄	#66946	1	1	yes	characteristic
152	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
153	C₂×C₄	#66965	1	1	yes	characteristic
154	C₂×C₄	#66972	1	1	yes	characteristic
155	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
156	C₈	—	4	4	no	—
157	C₈	—	22	2	no	—
158	C₈	—	44	4	no	—
159	C₈	#66940	1	1	yes	characteristic
160	C₈	#66945	1	1	yes	characteristic
161	C₈	C₂×C₄×Dic₁₁	1	1	yes	characteristic
162	C₈	Q₈×Dic₁₁	1	1	yes	characteristic
163	C₂²	—	2	2	no	—
164	C₂²	#10622486	1	1	yes	characteristic
165	C₂²	D₁₁×#107	1	1	yes	characteristic
166	C₂²	Q₁₆×Dic₁₁	1	1	yes	characteristic
167	C₄	—	11	4	no	—
168	C₄	—	22	2	no	—
169	C₄	#10622485	1	1	yes	characteristic
170	C₄	#10622493	1	1	yes	characteristic
171	C₄	C₄⋊C₄×Dic₁₁	1	1	yes	characteristic
172	C₄	D₈×Dic₁₁	1	1	yes	characteristic
173	C₂	—	2	1	no	—
174	C₂	—	2	1	no	—
175	C₂	#107×Dic₁₁	1	1	yes	characteristic
176	C₂	D₁₁×#368	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₈×D₁₁
commutator	C₈×C₁₁	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₂×C₁₁×#368	C₂
socle	C₂²×C₁₁	C₂×#107
prime radical	C₂³×C₁₁	C₂×Q₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₂×#368	D₁₁
hypocenter	C₁₁	C₄×#368
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

Complements

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

N	H ≅ G/N	type
12. C₁₁×#368	C₄	semidirect
14. #10622144	C₄	semidirect
87. #368	Dic₁₁	direct (N × H)
99. Dic₁₁	#368	direct (N × H)
145. C₁₁	C₄×#368	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622144	2
C₂×C₁₆×Dic₁₁	2
#108×Dic₁₁	2
#13066709	2
C₂×C₁₁×#368	2
C₄×#368	11

Subgroups — Dic11×#368 #14669187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₁×#368 #14669187