Subgroups — #14669099

Order 2816.

334 conjugacy classes of subgroups.

The subgroup lattice has 182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070372	C₂	1	2	yes	maximal
2	C₂×#10622104	C₂	1	2	yes	maximal
3	#13066696	C₂	1	2	yes	maximal
4	C₁₁×#1726	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×#97	C₄	1	1	yes	characteristic
6	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
7	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₁₁×#376	C₄	1	1	yes	characteristic
12	C₂×#66876	C₂²	1	4	yes	—
13	#10622104	—	2	4	no	—
14	C₄⋊(C₁₁⋊C₁₆)	C₄	1	8	yes	complemented
15	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
19	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₁₁×#97	—	2	2	no	—
23	C₁₁×#97	—	2	2	no	—
24	C₁₁×#97	D₄	1	2	yes	—
25	C₁₁×#97	Q₈	1	2	yes	—
26	C₄×C₈×C₁₁	—	2	2	no	—
27	C₄×C₈×C₁₁	—	2	2	no	—
28	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
29	C₁₁×#95	—	2	2	no	—
30	#66876	—	2	4	no	—
31	#66876	—	2	4	no	—
32	C₂×C₁₁⋊C₁₆	C₂×C₄	1	8	yes	—
33	#12657	—	11	1	no	maximal, Sylow
34	C₂²×C₄×C₁₁	—	2	1	no	—
35	C₂²×C₄×C₁₁	—	2	1	no	—
36	C₂²×C₄×C₁₁	M₁₆	1	2	yes	—
37	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₁	—	2	1	no	—
39	C₂×C₈×C₁₁	—	2	1	no	—
40	C₂×C₈×C₁₁	—	2	1	no	—
41	C₂×C₈×C₁₁	—	2	1	no	—
42	C₂×C₈×C₁₁	—	2	1	no	—
43	C₂×C₈×C₁₁	—	2	1	no	—
44	C₂×C₈×C₁₁	C₄²	1	2	yes	—
45	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
46	C₂×C₈×C₁₁	M₁₆	1	2	yes	—
47	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
48	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
49	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₈×C₁₁	#41	1	2	yes	—
51	C₄²×C₁₁	—	2	1	no	—
52	C₄²×C₁₁	—	2	1	no	—
53	C₄²×C₁₁	C₄²	1	2	yes	—
54	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
55	C₄²×C₁₁	M₁₆	1	2	yes	—
56	C₄²×C₁₁	M₁₆	1	2	yes	—
57	C₁₁⋊C₁₆	—	2	8	no	—
58	#2150	—	11	2	no	—
59	C₂×#347	—	11	2	no	—
60	#1726	D₁₁	1	1	yes	characteristic
61	#1375	—	11	2	no	—
62	C₂³×C₁₁	C₂×M₁₆	1	1	yes	characteristic
63	C₂×C₄×C₁₁	—	2	2	no	—
64	C₂×C₄×C₁₁	—	2	2	no	—
65	C₂×C₄×C₁₁	—	4	2	no	—
66	C₂×C₄×C₁₁	—	4	2	no	—
67	C₂×C₄×C₁₁	—	4	2	no	—
68	C₂×C₄×C₁₁	#97	1	4	yes	—
69	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
70	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
72	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
73	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
74	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
75	C₈×C₁₁	—	2	2	no	—
76	C₈×C₁₁	—	2	2	no	—
77	C₈×C₁₁	—	2	2	no	—
78	C₈×C₁₁	C₄×D₄	1	2	yes	—
79	C₈×C₁₁	C₄×Q₈	1	2	yes	—
80	C₂×M₃₂	—	11	4	no	—
81	C₂×#97	Dic₁₁	1	1	yes	characteristic
82	C₂×#97	C₂×D₁₁	1	1	yes	characteristic
83	C₂×#97	C₂×D₁₁	1	1	yes	characteristic
84	C₂×C₄×C₈	Dic₁₁	1	1	yes	characteristic
85	C₂×C₄×C₈	Dic₁₁	1	1	yes	characteristic
86	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
87	#376	Dic₁₁	1	1	yes	characteristic
88	C₄⋊C₁₆	—	11	8	no	—
89	#347	—	22	4	no	—
90	C₂²×C₁₁	—	2	2	no	—
91	C₂²×C₁₁	C₂×#97	1	1	yes	characteristic
92	C₂²×C₁₁	#423	1	1	yes	characteristic
93	C₂²×C₁₁	#432	1	1	yes	characteristic
94	C₄×C₁₁	—	2	4	no	—
95	C₄×C₁₁	—	4	2	no	—
96	C₄×C₁₁	—	4	2	no	—
97	C₄×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
98	C₄×C₁₁	C₄×M₁₆	1	1	yes	characteristic
99	C₄×C₁₁	#423	1	1	yes	characteristic
100	C₄×C₁₁	#432	1	1	yes	characteristic
101	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
102	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
103	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
104	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
105	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
106	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
107	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
108	M₃₂	—	22	4	no	—
109	M₃₂	—	22	4	no	—
110	C₂×C₁₆	—	11	8	no	—
111	#97	—	2	2	no	—
112	#97	—	2	2	no	—
113	#97	Dic₂₂	1	2	yes	—
114	#97	D₄₄	1	2	yes	—
115	C₄×C₈	—	2	2	no	—
116	C₄×C₈	—	2	2	no	—
117	C₄×C₈	C₄×D₁₁	1	4	yes	—
118	#95	—	2	2	no	—
119	C₂×C₁₁	—	2	1	no	—
120	C₂×C₁₁	—	2	1	no	—
121	C₂×C₁₁	#1767	1	1	yes	characteristic
122	C₂×C₁₁	#2110	1	2	yes	—
123	C₂²×C₄	—	2	1	no	—
124	C₂²×C₄	—	2	1	no	—
125	C₂²×C₄	#4318	1	2	yes	—
126	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
127	C₂×C₈	—	2	1	no	—
128	C₂×C₈	—	2	1	no	—
129	C₂×C₈	—	2	1	no	—
130	C₂×C₈	—	2	1	no	—
131	C₂×C₈	—	2	1	no	—
132	C₂×C₈	—	2	1	no	—
133	C₂×C₈	#4318	1	2	yes	—
134	C₂×C₈	C₄×Dic₁₁	1	2	yes	—
135	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
136	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
137	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
138	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
139	C₂×C₈	#4339	1	2	yes	—
140	C₄²	—	2	1	no	—
141	C₄²	—	2	1	no	—
142	C₄²	#4318	1	2	yes	—
143	C₄²	#4318	1	2	yes	—
144	C₄²	C₄×Dic₁₁	1	2	yes	—
145	C₄²	C₄⋊Dic₁₁	1	2	yes	—
146	C₁₆	—	22	8	no	—
147	C₁₁	#12657	1	1	yes	characteristic, complemented, Sylow
148	C₂³	C₂×#4318	1	1	yes	characteristic
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	4	2	no	—
152	C₂×C₄	—	4	2	no	—
153	C₂×C₄	—	4	2	no	—
154	C₂×C₄	#66867	1	4	yes	—
155	C₂×C₄	C₂×#4318	1	1	yes	characteristic
156	C₂×C₄	C₂×#4318	1	1	yes	characteristic
157	C₂×C₄	C₂×#4318	1	1	yes	characteristic
158	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
159	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
160	C₂×C₄	#66979	1	1	yes	characteristic
161	C₈	—	2	2	no	—
162	C₈	—	2	2	no	—
163	C₈	—	2	2	no	—
164	C₈	C₄×Dic₂₂	1	2	yes	—
165	C₈	C₄×D₄₄	1	2	yes	—
166	C₂²	—	2	2	no	—
167	C₂²	C₂×#66867	1	1	yes	characteristic
168	C₂²	#10622537	1	1	yes	characteristic
169	C₂²	#10622539	1	1	yes	characteristic
170	C₄	—	2	4	no	—
171	C₄	—	4	2	no	—
172	C₄	—	4	2	no	—
173	C₄	C₄×#4318	1	1	yes	characteristic
174	C₄	#10622537	1	1	yes	characteristic
175	C₄	#10622539	1	1	yes	characteristic
176	C₄	C₄×C₄⋊Dic₁₁	1	1	yes	characteristic
177	C₂	—	2	1	no	—
178	C₂	—	2	1	no	—
179	C₂	#13068469	1	1	yes	characteristic
180	C₂	#13070221	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×Dic₁₁
commutator	C₂×C₄×C₁₁	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1726	C₂
socle	C₂²×C₁₁	C₂×#97
prime radical	C₂³×C₁₁	C₂×M₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1726	D₁₁
hypocenter	C₁₁	#12657
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ #1726

Complements

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

N	H ≅ G/N	type
14. C₄⋊(C₁₁⋊C₁₆)	C₄	semidirect
147. C₁₁	#12657	semidirect

Maximal subgroups

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

subgroup	index
#13070372	2
C₂×#10622104	2
#13066696	2
C₁₁×#1726	2
#12657	11