Subgroups — C₂×#13066527 #14644155

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622539	C₂	1	2	yes	maximal
2	#13066527	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₁×#423	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₁×M₁₆	C₄	1	2	yes	—
5	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
6	C₁₁×#423	—	2	2	no	—
7	C₁₁×#423	C₄	1	2	yes	—
8	C₁₁×#423	C₂²	1	2	yes	—
9	C₂×C₁₁×C₄⋊C₈	—	2	2	no	—
10	C₂×C₂²⋊(C₁₁⋊C₈)	C₄	1	4	yes	—
11	#10622539	—	2	2	no	—
12	#10622539	—	2	2	no	—
13	#10622539	C₄	1	4	yes	—
14	#10622539	C₂²	1	4	yes	—
15	C₂×C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
16	C₂×#66867	—	2	2	no	—
17	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
18	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₁×M₁₆	—	2	2	no	—
20	C₂×C₁₁×M₁₆	—	4	4	no	—
21	C₂×C₁₁×M₁₆	C₂×C₄	1	4	yes	—
22	C₂²×C₈×C₁₁	—	2	2	no	—
23	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₁	D₄	1	2	yes	—
28	C₂×C₄²×C₁₁	D₄	1	2	yes	—
29	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
30	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
32	C₂²×C₁₁⋊C₈	—	2	4	no	—
33	C₁₁×C₄⋊C₈	—	2	4	no	—
34	C₁₁×C₄⋊C₈	—	2	4	no	—
35	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
36	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	8	yes	—
37	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
38	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
39	#66867	—	2	4	no	—
40	#66867	—	2	4	no	—
41	C₂×#1307	—	11	1	no	maximal, Sylow
42	C₂⁴×C₁₁	C₄²	1	1	yes	characteristic
43	C₂²×C₄×C₁₁	—	2	2	no	—
44	C₂²×C₄×C₁₁	—	2	2	no	—
45	C₂²×C₄×C₁₁	—	4	4	no	—
46	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	C₄²	1	2	yes	—
48	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
51	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
56	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
58	C₁₁×M₁₆	—	4	4	no	—
59	C₁₁×M₁₆	—	4	4	no	—
60	C₂×C₈×C₁₁	—	2	4	no	—
61	C₂×C₈×C₁₁	—	4	4	no	—
62	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
63	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
64	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
65	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
66	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
67	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
68	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
69	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₁	C₂×D₄	1	2	yes	—
71	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
72	C₂×C₁₁⋊C₈	—	2	8	no	—
73	C₂×C₁₁⋊C₈	—	4	8	no	—
74	C₂×#432	—	11	2	no	—
75	C₂×#423	D₁₁	1	1	yes	characteristic
76	#1307	—	11	4	no	—
77	C₂³×C₁₁	—	2	2	no	—
78	C₂³×C₁₁	—	2	4	no	—
79	C₂³×C₁₁	#95	1	1	yes	characteristic
80	C₂³×C₁₁	#95	1	1	yes	characteristic
81	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
82	C₂×C₄×C₁₁	—	2	2	no	—
83	C₂×C₄×C₁₁	—	2	4	no	—
84	C₂×C₄×C₁₁	—	2	4	no	—
85	C₂×C₄×C₁₁	—	2	2	no	—
86	C₂×C₄×C₁₁	—	2	2	no	—
87	C₂×C₄×C₁₁	—	2	1	no	—
88	C₂×C₄×C₁₁	—	2	1	no	—
89	C₂×C₄×C₁₁	—	2	1	no	—
90	C₂×C₄×C₁₁	—	2	1	no	—
91	C₂×C₄×C₁₁	—	4	2	no	—
92	C₂×C₄×C₁₁	—	4	2	no	—
93	C₂×C₄×C₁₁	—	4	2	no	—
94	C₂×C₄×C₁₁	—	4	2	no	—
95	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
96	C₂×C₄×C₁₁	#95	1	2	yes	—
97	C₂×C₄×C₁₁	#95	1	2	yes	—
98	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
99	C₂×C₄×C₁₁	#100	1	2	yes	—
100	C₂×C₄×C₁₁	#101	1	2	yes	—
101	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
102	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
104	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
105	C₈×C₁₁	—	4	4	no	—
106	C₁₁⋊C₈	—	4	8	no	—
107	C₂²×M₁₆	Dic₁₁	1	2	yes	—
108	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
109	#432	—	11	4	no	—
110	#432	—	11	4	no	—
111	#432	—	22	2	no	—
112	#432	—	22	2	no	—
113	#423	—	2	2	no	—
114	#423	Dic₁₁	1	2	yes	—
115	#423	C₂×D₁₁	1	2	yes	—
116	C₂×C₄⋊C₈	—	2	2	no	—
117	C₂×C₄⋊C₈	—	22	2	no	—
118	C₂×C₂²⋊C₈	—	11	4	no	—
119	C₂×#97	—	22	2	no	—
120	C₂²×C₁₁	—	2	1	no	—
121	C₂²×C₁₁	—	2	1	no	—
122	C₂²×C₁₁	—	2	2	no	—
123	C₂²×C₁₁	—	2	2	no	—
124	C₂²×C₁₁	—	4	4	no	—
125	C₂²×C₁₁	#343	1	2	yes	—
126	C₂²×C₁₁	#344	1	4	yes	—
127	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
128	C₄×C₁₁	—	2	1	no	—
129	C₄×C₁₁	—	2	1	no	—
130	C₄×C₁₁	—	2	2	no	—
131	C₄×C₁₁	—	2	2	no	—
132	C₄×C₁₁	—	2	2	no	—
133	C₄×C₁₁	—	2	2	no	—
134	C₄×C₁₁	#343	1	2	yes	—
135	C₄×C₁₁	C₂×#100	1	1	yes	characteristic
136	C₄×C₁₁	C₂×#101	1	1	yes	characteristic
137	C₂³×C₄	C₄×D₁₁	1	2	yes	—
138	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
139	C₂×M₁₆	—	2	2	no	—
140	C₂×M₁₆	—	4	4	no	—
141	C₂×M₁₆	C₂×Dic₁₁	1	4	yes	—
142	C₂²×C₈	—	2	2	no	—
143	C₂²×C₈	—	22	4	no	—
144	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
145	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
146	C₂×C₄²	C₄×D₁₁	1	2	yes	—
147	C₂×C₄²	D₄₄	1	1	yes	characteristic
148	C₂×C₄²	D₄₄	1	1	yes	characteristic
149	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
150	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
151	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
152	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
153	C₄⋊C₈	—	2	4	no	—
154	C₄⋊C₈	—	2	4	no	—
155	C₄⋊C₈	—	22	4	no	—
156	C₄⋊C₈	—	22	4	no	—
157	C₂²⋊C₈	—	11	8	no	—
158	C₂²⋊C₈	—	22	4	no	—
159	#97	—	22	4	no	—
160	#97	—	22	4	no	—
161	C₂×C₁₁	—	4	1	no	—
162	C₂×C₁₁	—	4	1	no	—
163	C₂×C₁₁	#1307	1	4	yes	complemented
164	C₂×C₁₁	C₂×#343	1	1	yes	characteristic
165	C₂×C₁₁	C₂×#344	1	2	yes	—
166	C₂⁴	C₄×Dic₁₁	1	1	yes	characteristic
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	—	2	2	no	—
169	C₂²×C₄	—	4	4	no	—
170	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
171	C₂²×C₄	C₄×Dic₁₁	1	2	yes	—
172	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
173	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
174	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
175	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
176	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
177	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
178	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
179	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
180	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
181	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
182	M₁₆	—	4	4	no	—
183	M₁₆	—	4	4	no	—
184	C₂×C₈	—	2	4	no	—
185	C₂×C₈	—	4	4	no	—
186	C₂×C₈	—	22	8	no	—
187	C₂×C₈	—	44	8	no	—
188	C₄²	Dic₁₁⋊C₄	1	2	yes	—
189	C₄²	Dic₁₁⋊C₄	1	2	yes	—
190	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
191	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
192	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
193	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
194	C₄²	C₂²⋊Dic₁₁	1	2	yes	—
195	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
196	C₄²	C₂×D₄₄	1	1	yes	characteristic
197	C₄²	C₂×C₂²⋊D₁₁	1	2	yes	—
198	C₁₁	C₂×#1307	1	1	yes	characteristic, complemented, Sylow
199	C₂³	—	2	2	no	—
200	C₂³	—	2	4	no	—
201	C₂³	C₁₁⋊#95	1	1	yes	characteristic
202	C₂³	C₁₁⋊#95	1	1	yes	characteristic
203	C₂³	C₂×C₄×Dic₁₁	1	1	yes	characteristic
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	4	no	—
206	C₂×C₄	—	2	4	no	—
207	C₂×C₄	—	2	1	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
218	C₂×C₄	C₁₁⋊#95	1	2	yes	—
219	C₂×C₄	C₁₁⋊#95	1	2	yes	—
220	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
221	C₂×C₄	#66897	1	2	yes	—
222	C₂×C₄	#66900	1	2	yes	—
223	C₂×C₄	C₂×Dic₁₁⋊C₄	1	2	yes	—
224	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
225	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	2	yes	—
226	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
227	C₈	—	4	4	no	—
228	C₈	—	44	8	no	—
229	C₂²	—	2	1	no	—
230	C₂²	—	2	1	no	—
231	C₂²	—	2	2	no	—
232	C₂²	—	2	2	no	—
233	C₂²	—	4	4	no	—
234	C₂²	#10622168	1	2	yes	—
235	C₂²	#10622197	1	4	yes	—
236	C₂²	C₂×C₁₁⋊#95	1	1	yes	characteristic
237	C₄	—	2	1	no	—
238	C₄	—	2	1	no	—
239	C₄	—	2	2	no	—
240	C₄	—	2	2	no	—
241	C₄	—	2	2	no	—
242	C₄	—	2	2	no	—
243	C₄	#10622168	1	2	yes	—
244	C₄	C₂×#66897	1	1	yes	characteristic
245	C₄	C₂×#66900	1	1	yes	characteristic
246	C₂	—	4	1	no	—
247	C₂	—	4	1	no	—
248	C₂	#13066527	1	4	yes	direct product factor
249	C₂	C₂×#10622168	1	1	yes	characteristic
250	C₂	C₂×#10622197	1	2	yes	—

	subgroup	G/H
center	C₂³	C₁₁⋊#95
commutator	C₂³×C₁₁	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₁₁×#423	C₂
socle	C₂³×C₁₁	#95
prime radical	C₂⁴×C₁₁	C₄²
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×#423	D₁₁
hypocenter	C₁₁	C₂×#1307
LCS	G ▷ C₂³×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
2. #13066527	C₂	direct (N × H)
163. C₂×C₁₁	#1307	semidirect
198. C₁₁	C₂×#1307	semidirect
248. C₂	#13066527	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#10622539	2
#13066527	2
C₂×C₁₁×#423	2
C₂×#1307	11

Subgroups — C2×#13066527 #14644155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066527 #14644155