Subgroups — #14669167

Order 2816.

310 conjugacy classes of subgroups.

The subgroup lattice has 180 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	#13070400	C₂	1	1	yes	maximal, characteristic
3	#13068495	C₂	1	2	yes	maximal
4	#13066712	C₂	1	2	yes	maximal
5	C₂×C₁₁×#346	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×#66883	C₂²	1	2	yes	—
10	#10622719	C₂²	1	2	yes	—
11	#10622714	—	2	2	no	—
12	C₁₁×#346	C₄	1	4	yes	complemented
13	#10622161	—	2	2	no	—
14	#10622144	C₄	1	4	yes	complemented
15	#10622143	C₄	1	2	yes	complemented
16	#10622142	C₄	1	2	yes	complemented
17	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
19	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
20	#66979	—	2	2	no	—
21	C₂×#4318	—	2	2	no	—
22	C₂×C₁₁×C₁₆	—	2	1	no	—
23	C₂×C₁₁×C₁₆	—	2	1	no	—
24	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
25	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
26	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
27	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
28	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
29	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
30	C₄×C₈×C₁₁	Q₈	1	2	yes	—
31	#66883	—	2	2	no	—
32	#66883	C₂×C₄	1	4	yes	—
33	#66882	C₂×C₄	1	4	yes	—
34	#66881	—	2	2	no	—
35	#66879	—	4	2	no	—
36	C₈×Dic₁₁	—	4	2	no	—
37	#12671	—	11	1	no	maximal, Sylow
38	C₂²×C₄×C₁₁	—	2	1	no	—
39	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
40	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
41	C₂×C₈×C₁₁	D₈	1	2	yes	—
42	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
43	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
48	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
49	C₄²×C₁₁	—	2	1	no	—
50	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
51	C₂²⋊Dic₁₁	—	4	2	no	—
52	C₄⋊Dic₁₁	—	2	4	no	—
53	C₄×Dic₁₁	—	4	2	no	—
54	#4318	—	2	4	no	—
55	#4318	—	4	2	no	—
56	C₂×C₁₁⋊C₈	—	4	2	no	—
57	C₁₁×C₁₆	—	2	2	no	—
58	C₁₁×C₁₆	C₄²	1	2	yes	—
59	C₁₁×C₁₆	C₄²	1	2	yes	—
60	C₂×#368	—	11	1	no	—
61	#2158	—	11	1	no	—
62	C₂×#346	D₁₁	1	1	yes	characteristic
63	#1772	—	11	2	no	—
64	#1382	—	11	2	no	—
65	C₂³×C₁₁	#135	1	1	yes	characteristic
66	C₂×C₄×C₁₁	—	2	2	no	—
67	C₂×C₄×C₁₁	—	4	2	no	—
68	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
70	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
71	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
72	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
73	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
74	C₂×Dic₁₁	—	4	4	no	—
75	C₈×C₁₁	#107	1	4	yes	—
76	C₈×C₁₁	C₂×C₄²	1	1	yes	characteristic
77	C₈×C₁₁	#117	1	1	yes	characteristic
78	C₈×C₁₁	C₄×Q₈	1	1	yes	characteristic
79	C₈×C₁₁	C₄×Q₈	1	1	yes	characteristic
80	C₁₁⋊C₈	—	4	4	no	—
81	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
82	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
83	C₂×#108	—	11	2	no	—
84	#427	—	11	2	no	—
85	#405	—	22	2	no	—
86	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
87	#368	—	11	4	no	—
88	#367	—	11	2	no	—
89	#366	—	11	2	no	—
90	#346	Dic₁₁	1	4	yes	complemented
91	#339	—	22	2	no	—
92	C₂²×C₁₁	—	2	2	no	—
93	C₂²×C₁₁	#427	1	1	yes	characteristic
94	C₂²×C₁₁	C₄×D₈	1	1	yes	characteristic
95	C₂²×C₁₁	C₄×Q₁₆	1	1	yes	characteristic
96	C₄×C₁₁	—	4	2	no	—
97	C₄×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
98	C₄×C₁₁	C₂×#107	1	1	yes	characteristic
99	C₄×C₁₁	C₄×D₈	1	1	yes	characteristic
100	C₄×C₁₁	C₄×Q₁₆	1	1	yes	characteristic
101	Dic₁₁	—	8	4	no	—
102	C₂×M₁₆	—	22	2	no	—
103	C₂²×C₈	D₄₄	1	1	yes	characteristic
104	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
105	#117	—	22	2	no	—
106	C₂×C₄²	D₄₄	1	1	yes	characteristic
107	C₂×C₁₆	—	2	1	no	—
108	C₂×C₁₆	—	2	1	no	—
109	C₂×C₁₆	C₄×D₁₁	1	1	yes	characteristic
110	C₂×C₁₆	C₄×D₁₁	1	1	yes	characteristic
111	C₂×C₁₆	C₄×D₁₁	1	2	yes	—
112	C₂×C₁₆	C₂×Dic₁₁	1	2	yes	—
113	C₂×C₁₆	C₂×Dic₁₁	1	2	yes	—
114	#108	—	11	4	no	—
115	#108	—	22	2	no	—
116	#107	—	11	4	no	—
117	#106	—	22	2	no	—
118	#97	—	44	2	no	—
119	C₄×C₈	—	44	2	no	—
120	C₄×C₈	Dic₂₂	1	2	yes	—
121	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
122	C₂×C₁₁	—	2	1	no	—
123	C₂×C₁₁	—	2	1	no	—
124	C₂×C₁₁	C₄×#107	1	1	yes	characteristic
125	C₂×C₁₁	#2179	1	2	yes	—
126	C₂²×C₄	—	2	1	no	—
127	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
128	M₁₆	—	22	4	no	—
129	M₁₆	—	44	2	no	—
130	C₂×C₈	—	44	2	no	—
131	C₂×C₈	D₈₈	1	2	yes	—
132	C₂×C₈	Dic₄₄	1	2	yes	—
133	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
134	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
135	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
136	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
137	C₂×C₈	#4339	1	1	yes	characteristic
138	C₂×C₈	#4339	1	1	yes	characteristic
139	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
140	C₄⋊C₄	—	22	4	no	—
141	C₂²⋊C₄	—	44	2	no	—
142	C₄²	—	2	1	no	—
143	C₄²	—	44	2	no	—
144	C₄²	C₄⋊Dic₁₁	1	2	yes	—
145	C₁₆	—	2	2	no	—
146	C₁₆	C₄×Dic₁₁	1	2	yes	—
147	C₁₆	C₄×Dic₁₁	1	2	yes	—
148	C₁₁	#12671	1	1	yes	characteristic, complemented, Sylow
149	C₂³	#66957	1	1	yes	characteristic
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	4	2	no	—
152	C₂×C₄	—	44	4	no	—
153	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
154	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
155	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
156	C₂×C₄	#66957	1	1	yes	characteristic
157	C₂×C₄	C₂×Dic₄₄	1	1	yes	characteristic
158	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
159	C₈	—	44	4	no	—
160	C₈	#66882	1	4	yes	—
161	C₈	C₄×Dic₂₂	1	1	yes	characteristic
162	C₈	C₄×Dic₂₂	1	1	yes	characteristic
163	C₈	C₂×C₄×Dic₁₁	1	1	yes	characteristic
164	C₈	#66979	1	1	yes	characteristic
165	C₂²	—	2	2	no	—
166	C₂²	C₄×D₈₈	1	1	yes	characteristic
167	C₂²	C₄×Dic₄₄	1	1	yes	characteristic
168	C₂²	#10622719	1	1	yes	characteristic
169	C₄	—	4	2	no	—
170	C₄	—	88	4	no	—
171	C₄	C₄×D₈₈	1	1	yes	characteristic
172	C₄	C₄×Dic₄₄	1	1	yes	characteristic
173	C₄	C₄×C₄⋊Dic₁₁	1	1	yes	characteristic
174	C₄	C₂×#66882	1	1	yes	characteristic
175	C₂	—	2	1	no	—
176	C₂	—	2	1	no	—
177	C₂	C₄×#66882	1	1	yes	characteristic
178	C₂	#13070503	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₈₈
commutator	C₈×C₁₁	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₂×C₁₁×#346	C₂
socle	C₂²×C₁₁	C₄×D₈
prime radical	C₂³×C₁₁	#135
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₂×#346	D₁₁
hypocenter	C₁₁	#12671
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#346

Complements

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

N	H ≅ G/N	type
12. C₁₁×#346	C₄	semidirect
14. #10622144	C₄	semidirect
15. #10622143	C₄	semidirect
16. #10622142	C₄	semidirect
90. #346	Dic₁₁	semidirect
148. C₁₁	#12671	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
#13070400	2
#13068495	2
#13066712	2
C₂×C₁₁×#346	2
#12671	11