Subgroups — #14640708

Order 2816.

274 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622099	C₂	1	1	yes	maximal, characteristic
2	C₄×#66882	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#334	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
5	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×#66882	C₄	1	2	yes	—
7	C₂²×C₁₁⋊C₁₆	—	2	1	no	—
8	C₄×C₄⋊Dic₁₁	—	2	1	no	—
9	C₁₁×#334	—	2	1	no	—
10	C₁₁×#334	C₄	1	2	yes	complemented
11	#10622189	—	2	1	no	—
12	#10622099	—	2	1	no	—
13	#10622099	C₄	1	2	yes	complemented
14	C₂²×C₈×C₁₁	—	4	1	no	—
15	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
18	C₂×C₄⋊Dic₁₁	—	2	2	no	—
19	C₂×C₄×Dic₁₁	—	4	1	no	—
20	C₁₁×C₄⋊C₈	—	2	2	no	—
21	C₁₁×C₄⋊C₈	—	4	1	no	—
22	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
25	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
26	C₁₁⋊#95	—	4	1	no	—
27	#66882	—	2	2	no	—
28	#66882	C₈	1	4	yes	complemented
29	C₂×C₁₁⋊C₁₆	—	2	4	no	—
30	C₂×C₁₁⋊C₁₆	—	2	2	no	—
31	#7178	—	11	1	no	maximal, Sylow
32	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
34	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
35	C₂²×Dic₁₁	—	4	2	no	—
36	C₂×C₈×C₁₁	—	2	2	no	—
37	C₂×C₈×C₁₁	—	4	2	no	—
38	C₂×C₈×C₁₁	—	8	2	no	—
39	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
40	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
44	C₂×C₈×C₁₁	M₁₆	1	2	yes	—
45	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
46	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
47	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
48	C₄²×C₁₁	Q₁₆	1	1	yes	characteristic
49	C₄⋊Dic₁₁	—	2	4	no	—
50	C₄⋊Dic₁₁	—	4	2	no	—
51	C₄×Dic₁₁	—	8	2	no	—
52	C₁₁⋊C₁₆	—	2	4	no	—
53	C₂×#346	—	11	1	no	—
54	C₄×#107	—	11	1	no	—
55	C₂×#334	D₁₁	1	1	yes	characteristic
56	C₂³×C₁₁	#102	1	1	yes	characteristic
57	C₂×C₄×C₁₁	—	2	2	no	—
58	C₂×C₄×C₁₁	—	2	1	no	—
59	C₂×C₄×C₁₁	—	2	1	no	—
60	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
61	C₂×C₄×C₁₁	C₂²⋊C₈	1	2	yes	—
62	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
63	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
64	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
65	C₂×C₄×C₁₁	#104	1	2	yes	—
66	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
67	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
68	C₂×Dic₁₁	—	4	4	no	—
69	C₂×Dic₁₁	—	8	2	no	—
70	C₂×Dic₁₁	—	8	2	no	—
71	C₈×C₁₁	—	2	1	no	—
72	C₈×C₁₁	—	2	1	no	—
73	C₈×C₁₁	—	8	2	no	—
74	C₈×C₁₁	C₄×C₈	1	1	yes	characteristic
75	C₈×C₁₁	#97	1	1	yes	characteristic
76	C₈×C₁₁	C₄⋊C₈	1	2	yes	—
77	C₂²×C₁₆	—	22	1	no	—
78	C₂×#107	—	11	2	no	—
79	C₂×C₄⋊C₈	—	2	1	no	—
80	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
81	C₄×C₄⋊C₄	—	22	1	no	—
82	#346	—	11	2	no	—
83	#346	—	22	1	no	—
84	#340	—	22	1	no	—
85	#334	—	2	1	no	—
86	#334	Dic₁₁	1	2	yes	complemented
87	C₂²×C₁₁	D₄⋊C₈	1	2	yes	—
88	C₂²×C₁₁	#340	1	1	yes	characteristic
89	C₂²×C₁₁	#360	1	2	yes	—
90	C₂²×C₁₁	#361	1	1	yes	characteristic
91	C₂²×C₁₁	#362	1	1	yes	characteristic
92	C₄×C₁₁	—	2	1	no	—
93	C₄×C₁₁	—	2	1	no	—
94	C₄×C₁₁	—	2	1	no	—
95	C₄×C₁₁	—	2	1	no	—
96	C₄×C₁₁	Q₈⋊C₈	1	2	yes	—
97	C₄×C₁₁	#336	1	1	yes	characteristic
98	C₄×C₁₁	#339	1	1	yes	characteristic
99	Dic₁₁	—	8	4	no	—
100	C₂²×C₈	—	4	1	no	—
101	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
102	C₂²×C₈	D₄₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄	—	22	2	no	—
104	C₂×C₄²	—	44	1	no	—
105	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
106	C₂×C₁₆	—	22	4	no	—
107	C₂×C₁₆	—	22	2	no	—
108	#107	—	11	4	no	—
109	#107	—	22	2	no	—
110	C₄⋊C₈	—	2	2	no	—
111	C₄⋊C₈	—	4	1	no	—
112	C₄×C₈	Dic₂₂	1	1	yes	characteristic
113	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
114	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
115	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
116	#95	—	44	1	no	—
117	C₂×C₁₁	#1279	1	1	yes	characteristic
118	C₂×C₁₁	#1333	1	2	yes	—
119	C₂×C₁₁	#1334	1	2	yes	—
120	C₂×C₁₁	#1386	1	1	yes	characteristic
121	C₂×C₁₁	#1387	1	1	yes	characteristic
122	C₂²×C₄	—	44	2	no	—
123	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
124	C₂²×C₄	#4323	1	1	yes	characteristic
125	C₂²×C₄	#4325	1	1	yes	characteristic
126	C₂×C₈	—	2	2	no	—
127	C₂×C₈	—	4	2	no	—
128	C₂×C₈	—	8	2	no	—
129	C₂×C₈	C₈×D₁₁	1	2	yes	—
130	C₂×C₈	#4313	1	2	yes	—
131	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
132	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
133	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
134	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
135	C₄⋊C₄	—	22	4	no	—
136	C₄⋊C₄	—	44	2	no	—
137	C₄²	—	88	2	no	—
138	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
139	C₄²	#4324	1	1	yes	characteristic
140	C₄²	#4326	1	1	yes	characteristic
141	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
142	C₁₆	—	22	4	no	—
143	C₁₁	#7178	1	1	yes	characteristic, complemented, Sylow
144	C₂³	#66873	1	1	yes	characteristic
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	1	no	—
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	44	4	no	—
149	C₂×C₄	—	88	2	no	—
150	C₂×C₄	—	88	2	no	—
151	C₂×C₄	#66871	1	1	yes	characteristic
152	C₂×C₄	#66872	1	1	yes	characteristic
153	C₂×C₄	#66874	1	1	yes	characteristic
154	C₂×C₄	(C₂×D₁₁)⋊C₈	1	2	yes	—
155	C₂×C₄	#66889	1	2	yes	—
156	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
157	C₂×C₄	#66896	1	1	yes	characteristic
158	C₂×C₄	#66899	1	1	yes	characteristic
159	C₈	—	2	1	no	—
160	C₈	—	2	1	no	—
161	C₈	—	8	2	no	—
162	C₈	C₈×Dic₁₁	1	1	yes	characteristic
163	C₈	Dic₁₁⋊C₈	1	2	yes	—
164	C₈	#66879	1	1	yes	characteristic
165	C₂²	#10622121	1	2	yes	—
166	C₂²	#10622126	1	2	yes	—
167	C₂²	#10622133	1	1	yes	characteristic
168	C₂²	#10622134	1	1	yes	characteristic
169	C₂²	#10622167	1	1	yes	characteristic
170	C₄	—	2	1	no	—
171	C₄	—	2	1	no	—
172	C₄	—	2	1	no	—
173	C₄	—	2	1	no	—
174	C₄	—	88	4	no	—
175	C₄	#10622122	1	2	yes	—
176	C₄	#10622188	1	1	yes	characteristic
177	C₄	#10622193	1	1	yes	characteristic
178	C₂	#13066455	1	1	yes	characteristic
179	C₂	#13066582	1	2	yes	—
180	C₂	#13066585	1	2	yes	—
181	C₂	#13066723	1	1	yes	characteristic
182	C₂	#13066726	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#66873
commutator	C₈×C₁₁	C₄×C₈
Frattini	C₂×C₄×C₈	C₂×D₁₁
Fitting	C₂×C₁₁×#334	C₂
socle, prime radical	C₂³×C₁₁	#102
cosocle	C₂×C₄×C₈×C₁₁	C₂²
hypercenter	C₂×#334	D₁₁
hypocenter	C₁₁	#7178
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
10. C₁₁×#334	C₄	semidirect
13. #10622099	C₄	semidirect
28. #66882	C₈	semidirect
86. #334	Dic₁₁	semidirect
143. C₁₁	#7178	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622099	2
C₄×#66882	2
C₂×C₁₁×#334	2
#7178	11