Subgroups — C₂×#13070758 #14908396

Order 2816.

574 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622295	C₂	1	1	yes	maximal, characteristic
2	#13070758	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10622128	C₂	1	2	yes	maximal
4	C₂×C₄⋊(C₁₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
5	C₂×#10622202	C₂	1	2	yes	maximal
6	C₂×C₄×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₁₁	—	2	1	no	—
9	C₂×#66922	—	2	1	no	—
10	C₄×C₁₁×Q₁₆	—	2	2	no	—
11	C₄×C₁₁×Q₁₆	C₂²	1	4	yes	—
12	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#103	—	2	1	no	—
14	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×#66882	—	2	1	no	—
16	C₂×#66882	C₂²	1	2	yes	—
17	C₂²×C₁₁⋊C₁₆	C₂²	1	2	yes	—
18	#10622295	—	2	2	no	—
19	#10622295	C₂²	1	4	yes	—
20	#10622202	C₂²	1	8	yes	—
21	#10622128	C₂²	1	8	yes	—
22	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	4	yes	—
23	C₂²×Q₈×C₁₁	—	2	1	no	—
24	C₂²×Dic₂₂	—	4	1	no	—
25	C₂×C₁₁×Q₁₆	—	2	1	no	—
26	C₂×C₁₁×Q₁₆	—	2	2	no	—
27	C₂×C₁₁×Q₁₆	Q₈	1	4	yes	complemented
28	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
29	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
31	C₄×Q₈×C₁₁	—	2	4	no	—
32	C₄×Q₈×C₁₁	—	4	2	no	—
33	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
34	C₂×C₁₁×C₄⋊C₄	—	4	1	no	—
35	C₂×C₄²×C₁₁	—	4	1	no	—
36	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
37	C₂×C₄⋊Dic₁₁	—	2	2	no	—
38	C₂×C₄⋊Dic₁₁	—	4	1	no	—
39	#66922	—	2	4	no	—
40	#66922	—	4	2	no	—
41	C₁₁×#107	—	2	1	no	—
42	C₁₁×#107	C₂³	1	2	yes	—
43	C₁₁×#103	—	2	4	no	—
44	C₄×C₈×C₁₁	D₄	1	2	yes	—
45	C₄×C₈×C₁₁	C₂³	1	2	yes	—
46	#66882	—	2	2	no	—
47	#66882	—	2	4	no	—
48	#66882	C₂³	1	4	yes	—
49	C₂×C₁₁⋊C₁₆	—	2	4	no	—
50	C₂×C₁₁⋊C₁₆	C₂³	1	4	yes	—
51	C₂×#2225	—	11	1	no	maximal, Sylow
52	C₂×Q₈×C₁₁	—	2	4	no	—
53	C₂×Q₈×C₁₁	—	2	2	no	—
54	C₂×Q₈×C₁₁	—	4	1	no	—
55	C₂×Q₈×C₁₁	—	4	2	no	—
56	C₂²×C₄×C₁₁	—	4	1	no	—
57	C₂²×C₄×C₁₁	—	4	1	no	—
58	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
59	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
60	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
61	C₂²×Dic₁₁	—	4	2	no	—
62	C₂×Dic₂₂	—	4	4	no	—
63	C₂×Dic₂₂	—	8	4	no	—
64	C₁₁×Q₁₆	—	2	4	no	—
65	C₁₁×Q₁₆	—	2	2	no	—
66	C₁₁×Q₁₆	C₂×Q₈	1	4	yes	complemented
67	C₂×C₈×C₁₁	—	2	2	no	—
68	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
69	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
70	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
71	C₂×C₈×C₁₁	#41	1	2	yes	—
72	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
73	C₁₁×C₄⋊C₄	—	2	2	no	—
74	C₁₁×C₄⋊C₄	—	4	1	no	—
75	C₁₁×C₄⋊C₄	—	4	4	no	—
76	C₄²×C₁₁	—	4	4	no	—
77	C₄²×C₁₁	D₈	1	2	yes	—
78	C₄²×C₁₁	C₂×D₄	1	2	yes	—
79	C₄⋊Dic₁₁	—	2	4	no	—
80	C₄⋊Dic₁₁	—	4	4	no	—
81	C₄⋊Dic₁₁	—	4	2	no	—
82	C₁₁⋊C₁₆	—	2	4	no	—
83	C₂×#500	—	11	1	no	—
84	C₂×C₄×Q₁₆	D₁₁	1	1	yes	characteristic
85	#2225	—	11	8	no	—
86	C₂×#367	—	11	2	no	—
87	C₂×C₄⋊C₁₆	—	11	1	no	—
88	C₂×#358	—	11	2	no	—
89	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
90	Q₈×C₁₁	—	2	4	no	—
91	Q₈×C₁₁	—	4	2	no	—
92	Q₈×C₁₁	—	4	4	no	—
93	C₂×C₄×C₁₁	—	2	2	no	—
94	C₂×C₄×C₁₁	—	4	2	no	—
95	C₂×C₄×C₁₁	—	4	4	no	—
96	C₂×C₄×C₁₁	—	4	2	no	—
97	C₂×C₄×C₁₁	—	8	2	no	—
98	C₂×C₄×C₁₁	SD₃₂	1	4	yes	—
99	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
100	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
101	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
102	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
103	C₂×C₄×C₁₁	#137	1	2	yes	—
104	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
105	C₂×Dic₁₁	—	4	4	no	—
106	C₂×Dic₁₁	—	8	4	no	—
107	Dic₂₂	—	8	8	no	—
108	C₈×C₁₁	—	2	2	no	—
109	C₈×C₁₁	C₂²⋊Q₈	1	2	yes	—
110	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
111	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
112	C₂²×Q₁₆	C₂×D₁₁	1	1	yes	characteristic
113	C₂×C₄⋊Q₈	—	22	1	no	—
114	C₂×C₄×Q₈	—	2	1	no	—
115	C₂²×C₁₆	—	11	2	no	—
116	#500	—	11	4	no	—
117	#500	—	22	2	no	—
118	C₄×Q₁₆	—	2	2	no	—
119	C₄×Q₁₆	C₂×D₁₁	1	4	yes	—
120	C₂×#107	—	11	2	no	—
121	C₂×#107	—	22	1	no	—
122	C₂×#107	C₂×D₁₁	1	1	yes	characteristic
123	C₂×#103	—	2	1	no	—
124	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
125	#367	—	11	8	no	—
126	C₄⋊C₁₆	—	11	4	no	—
127	#358	—	11	8	no	—
128	C₂²×C₁₁	#474	1	2	yes	—
129	C₂²×C₁₁	C₂×SD₃₂	1	2	yes	—
130	C₂²×C₁₁	#510	1	2	yes	—
131	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
132	C₄×C₁₁	—	2	2	no	—
133	C₄×C₁₁	—	4	4	no	—
134	C₄×C₁₁	—	8	2	no	—
135	C₄×C₁₁	#474	1	2	yes	—
136	C₄×C₁₁	C₂×SD₃₂	1	4	yes	—
137	C₄×C₁₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
138	C₄×C₁₁	C₂×#137	1	1	yes	characteristic
139	Dic₁₁	—	8	4	no	—
140	C₂²×Q₈	—	2	1	no	—
141	C₂²×Q₈	—	44	1	no	—
142	C₂×Q₁₆	—	2	2	no	—
143	C₂×Q₁₆	—	2	1	no	—
144	C₂×Q₁₆	Dic₂₂	1	4	yes	complemented
145	C₂×Q₁₆	C₂²×D₁₁	1	2	yes	—
146	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
147	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
148	C₄⋊Q₈	—	22	4	no	—
149	C₄⋊Q₈	—	44	2	no	—
150	C₄×Q₈	—	2	4	no	—
151	C₄×Q₈	—	4	2	no	—
152	C₂×C₄⋊C₄	—	2	1	no	—
153	C₂×C₄⋊C₄	—	4	1	no	—
154	C₂×C₄⋊C₄	—	22	2	no	—
155	C₂×C₄⋊C₄	—	44	1	no	—
156	C₂×C₄²	—	4	1	no	—
157	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
158	C₂×C₁₆	—	11	4	no	—
159	C₂×C₁₆	—	22	4	no	—
160	#107	—	2	1	no	—
161	#107	—	11	4	no	—
162	#107	—	22	2	no	—
163	#107	—	22	4	no	—
164	#107	C₂²×D₁₁	1	2	yes	—
165	#103	—	2	4	no	—
166	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
167	C₄×C₈	C₂²×D₁₁	1	2	yes	—
168	C₂×C₁₁	#2225	1	4	yes	complemented
169	C₂×C₁₁	C₂×#474	1	1	yes	characteristic
170	C₂×C₁₁	C₂²×SD₃₂	1	1	yes	characteristic
171	C₂×C₁₁	C₂×#510	1	1	yes	characteristic
172	C₂×Q₈	—	2	4	no	—
173	C₂×Q₈	—	2	2	no	—
174	C₂×Q₈	—	4	1	no	—
175	C₂×Q₈	—	4	2	no	—
176	C₂×Q₈	—	44	4	no	—
177	C₂×Q₈	—	88	4	no	—
178	C₂²×C₄	—	4	1	no	—
179	C₂²×C₄	—	4	1	no	—
180	C₂²×C₄	—	44	2	no	—
181	C₂²×C₄	#4323	1	1	yes	characteristic
182	C₂²×C₄	#4323	1	1	yes	characteristic
183	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
184	Q₁₆	—	2	4	no	—
185	Q₁₆	—	2	2	no	—
186	Q₁₆	C₂×Dic₂₂	1	4	yes	complemented
187	C₂×C₈	—	2	2	no	—
188	C₂×C₈	C₂×Dic₂₂	1	2	yes	—
189	C₂×C₈	#4339	1	2	yes	—
190	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
191	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
192	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
193	C₄⋊C₄	—	2	2	no	—
194	C₄⋊C₄	—	4	1	no	—
195	C₄⋊C₄	—	4	4	no	—
196	C₄⋊C₄	—	22	4	no	—
197	C₄⋊C₄	—	44	2	no	—
198	C₄⋊C₄	—	44	4	no	—
199	C₄²	—	4	4	no	—
200	C₄²	#4323	1	2	yes	—
201	C₄²	C₂×C₂²⋊D₁₁	1	2	yes	—
202	C₁₆	—	22	4	no	—
203	C₁₁	C₂×#2225	1	1	yes	characteristic, complemented, Sylow
204	C₂³	C₂×#4323	1	1	yes	characteristic
205	Q₈	—	2	4	no	—
206	Q₈	—	4	2	no	—
207	Q₈	—	4	4	no	—
208	Q₈	—	88	8	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	8	2	no	—
214	C₂×C₄	—	44	4	no	—
215	C₂×C₄	—	88	4	no	—
216	C₂×C₄	#66892	1	4	yes	—
217	C₂×C₄	#66977	1	2	yes	—
218	C₂×C₄	C₂×#4323	1	2	yes	—
219	C₂×C₄	C₂×#4323	1	2	yes	—
220	C₂×C₄	C₂×#4323	1	1	yes	characteristic
221	C₂×C₄	#67004	1	2	yes	—
222	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
223	C₈	—	2	2	no	—
224	C₈	#66977	1	2	yes	—
225	C₈	C₂²×Dic₂₂	1	1	yes	characteristic
226	C₈	C₂×#4339	1	1	yes	characteristic
227	C₂²	#10622620	1	2	yes	—
228	C₂²	C₂×#66892	1	2	yes	—
229	C₂²	#10622808	1	2	yes	—
230	C₂²	C₂²×#4323	1	1	yes	characteristic
231	C₄	—	2	2	no	—
232	C₄	—	4	4	no	—
233	C₄	—	8	2	no	—
234	C₄	—	88	4	no	—
235	C₄	#10622620	1	2	yes	—
236	C₄	C₂×#66892	1	4	yes	—
237	C₄	C₂×#66977	1	1	yes	characteristic
238	C₄	C₂×#67004	1	1	yes	characteristic
239	C₂	#13070758	1	4	yes	direct product factor
240	C₂	C₂×#10622620	1	1	yes	characteristic
241	C₂	C₂²×#66892	1	1	yes	characteristic
242	C₂	C₂×#10622808	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#4323
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₂×C₄×C₁₁×Q₁₆	C₂
socle, prime radical	C₂³×C₁₁	C₂×D₈
hypercenter	C₂×C₄×Q₁₆	D₁₁
hypocenter	C₁₁	C₂×#2225
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #13070758	C₂	direct (N × H)
27. C₂×C₁₁×Q₁₆	Q₈	semidirect
66. C₁₁×Q₁₆	C₂×Q₈	semidirect
144. C₂×Q₁₆	Dic₂₂	semidirect
168. C₂×C₁₁	#2225	semidirect
186. Q₁₆	C₂×Dic₂₂	semidirect
203. C₁₁	C₂×#2225	semidirect
239. C₂	#13070758	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×#10622295	2
#13070758	2
C₂×#10622128	2
C₂×C₄⋊(C₁₁⋊C₁₆)	2
C₂×#10622202	2
C₂×C₄×C₁₁×Q₁₆	2
C₂×#2225	11

Subgroups — C2×#13070758 #14908396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13070758 #14908396