Subgroups — C₂×#13068135 #14736402

Order 2816.

682 conjugacy classes of subgroups.

The subgroup lattice has 280 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	C₂×#10622462	C₂	1	2	yes	maximal
3	C₂×#10622292	C₂	1	1	yes	maximal, characteristic
4	#13068135	C₂	1	8	yes	maximal, direct product factor
5	C₂×#10622120	C₂	1	2	yes	maximal
6	C₂×C₁₁×#334	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₄₄	—	2	2	no	—
8	C₂×#66922	C₂²	1	2	yes	—
9	C₂×C₄×Dic₂₂	C₂²	1	1	yes	characteristic
10	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₂×#66882	—	2	1	no	—
13	C₂×#66882	—	2	1	no	—
14	C₂×#66880	—	2	2	no	—
15	C₂×#66879	—	2	1	no	—
16	C₂×Dic₁₁⋊C₈	—	2	1	no	—
17	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
18	#10622462	—	2	4	no	—
19	#10622462	C₂²	1	8	yes	—
20	#10622295	—	2	2	no	—
21	#10622295	C₂²	1	4	yes	—
22	#10622292	—	2	2	no	—
23	#10622292	C₂²	1	4	yes	—
24	C₁₁×#334	C₂²	1	4	yes	—
25	#10622120	C₂²	1	8	yes	—
26	C₂²×Dic₂₂	—	2	2	no	—
27	C₂²×Dic₂₂	D₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₁	—	2	2	no	—
29	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
32	C₂×C₄⋊Dic₁₁	—	2	2	no	—
33	C₂×C₄⋊Dic₁₁	—	2	2	no	—
34	C₂×C₄⋊Dic₁₁	D₄	1	1	yes	characteristic
35	C₂×Dic₁₁⋊C₄	—	2	1	no	—
36	C₂×C₄×Dic₁₁	—	2	1	no	—
37	C₂²×C₁₁⋊C₈	—	2	1	no	—
38	C₂×Dic₄₄	—	2	8	no	—
39	C₂×Dic₄₄	—	4	8	no	—
40	#66922	—	2	2	no	—
41	#66922	—	2	2	no	—
42	#66922	—	2	2	no	—
43	#66922	C₂³	1	4	yes	—
44	C₄×Dic₂₂	—	2	1	no	—
45	C₄×Dic₂₂	—	2	1	no	—
46	C₄×Dic₂₂	D₄	1	2	yes	—
47	C₄×Dic₂₂	C₂³	1	2	yes	—
48	C₁₁×C₄⋊C₈	—	2	2	no	—
49	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
50	C₄×C₈×C₁₁	D₄	1	2	yes	—
51	C₄×C₈×C₁₁	C₂³	1	2	yes	—
52	#66882	—	2	4	no	—
53	#66882	—	2	4	no	—
54	#66880	—	2	8	no	—
55	#66879	—	2	4	no	—
56	Dic₁₁⋊C₈	—	2	4	no	—
57	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
58	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
59	C₂×#1694	—	11	1	no	maximal, Sylow
60	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
63	C₂²×Dic₁₁	—	2	1	no	—
64	C₂²×Dic₁₁	—	2	1	no	—
65	C₂²×Dic₁₁	—	4	2	no	—
66	C₂×Dic₂₂	—	2	1	no	—
67	C₂×Dic₂₂	—	2	4	no	—
68	C₂×Dic₂₂	—	2	4	no	—
69	C₂×Dic₂₂	—	4	2	no	—
70	C₂×Dic₂₂	—	4	4	no	—
71	C₂×Dic₂₂	—	4	4	no	—
72	C₂×Dic₂₂	C₂×D₄	1	2	yes	—
73	C₂×C₈×C₁₁	—	2	2	no	—
74	C₂×C₈×C₁₁	—	2	4	no	—
75	C₂×C₈×C₁₁	—	4	4	no	—
76	C₂×C₈×C₁₁	Q₁₆	1	4	yes	complemented
77	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
78	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
79	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₁₁	#41	1	1	yes	characteristic
82	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
83	C₄⋊Dic₁₁	—	2	1	no	—
84	C₄⋊Dic₁₁	—	2	4	no	—
85	C₄⋊Dic₁₁	—	2	4	no	—
86	C₄⋊Dic₁₁	—	4	2	no	—
87	C₄⋊Dic₁₁	—	4	2	no	—
88	C₄⋊Dic₁₁	C₂×D₄	1	2	yes	—
89	Dic₁₁⋊C₄	—	2	2	no	—
90	Dic₁₁⋊C₄	—	2	2	no	—
91	C₄×Dic₁₁	—	2	2	no	—
92	C₄×Dic₁₁	—	2	2	no	—
93	C₂×C₁₁⋊C₈	—	2	2	no	—
94	C₂×C₁₁⋊C₈	—	4	2	no	—
95	Dic₄₄	—	4	16	no	—
96	C₂×#500	—	11	1	no	—
97	C₂×#462	—	11	2	no	—
98	C₂×#446	—	11	1	no	—
99	#1694	—	11	8	no	—
100	C₂×#334	D₁₁	1	1	yes	characteristic
101	C₂×#332	—	11	2	no	—
102	C₂³×C₁₁	#121	1	1	yes	characteristic
103	C₂×C₄×C₁₁	—	2	2	no	—
104	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
105	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
106	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
107	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
108	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
109	C₂×C₄×C₁₁	#137	1	2	yes	—
110	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
111	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
112	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
113	C₂×Dic₁₁	—	2	2	no	—
114	C₂×Dic₁₁	—	2	2	no	—
115	C₂×Dic₁₁	—	4	2	no	—
116	C₂×Dic₁₁	—	4	2	no	—
117	C₂×Dic₁₁	—	4	4	no	—
118	C₂×Dic₁₁	—	8	4	no	—
119	Dic₂₂	—	2	4	no	—
120	Dic₂₂	—	4	2	no	—
121	Dic₂₂	—	4	4	no	—
122	Dic₂₂	—	4	4	no	—
123	Dic₂₂	—	8	4	no	—
124	C₈×C₁₁	—	2	2	no	—
125	C₈×C₁₁	—	4	4	no	—
126	C₈×C₁₁	C₂×Q₁₆	1	4	yes	complemented
127	C₁₁⋊C₈	—	4	2	no	—
128	C₂²×Q₁₆	—	22	2	no	—
129	C₂×C₄⋊Q₈	—	11	2	no	—
130	C₂×C₄×Q₈	—	11	1	no	—
131	#500	—	11	4	no	—
132	#500	—	22	2	no	—
133	#462	—	11	8	no	—
134	#462	—	22	4	no	—
135	#446	—	11	4	no	—
136	#446	—	22	2	no	—
137	C₂×#107	—	22	1	no	—
138	C₂×#107	—	22	1	no	—
139	C₂×C₄⋊C₈	—	11	1	no	—
140	C₂×C₄⋊C₈	—	22	1	no	—
141	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
142	C₂×#103	—	22	2	no	—
143	C₂×#97	—	22	1	no	—
144	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
145	#334	C₂×D₁₁	1	4	yes	—
146	#332	—	11	8	no	—
147	C₂²×C₁₁	#462	1	2	yes	—
148	C₂²×C₁₁	#469	1	2	yes	—
149	C₂²×C₁₁	#473	1	2	yes	—
150	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
151	C₄×C₁₁	—	2	1	no	—
152	C₄×C₁₁	—	2	1	no	—
153	C₄×C₁₁	#462	1	2	yes	—
154	C₄×C₁₁	#469	1	2	yes	—
155	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
156	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
157	C₄×C₁₁	C₂×#137	1	1	yes	characteristic
158	Dic₁₁	—	4	2	no	—
159	Dic₁₁	—	4	2	no	—
160	Dic₁₁	—	8	4	no	—
161	C₂²×Q₈	—	11	1	no	—
162	C₂²×Q₈	—	22	2	no	—
163	C₂×Q₁₆	—	22	8	no	—
164	C₂×Q₁₆	—	44	8	no	—
165	C₂²×C₈	—	2	2	no	—
166	C₂²×C₈	—	22	1	no	—
167	C₂²×C₈	D₄₄	1	1	yes	characteristic
168	C₂²×C₈	D₄₄	1	1	yes	characteristic
169	C₄⋊Q₈	—	11	4	no	—
170	C₄⋊Q₈	—	22	2	no	—
171	C₄⋊Q₈	—	22	2	no	—
172	C₄⋊Q₈	—	22	2	no	—
173	C₄×Q₈	—	11	2	no	—
174	C₄×Q₈	—	11	2	no	—
175	C₄×Q₈	—	22	1	no	—
176	C₄×Q₈	—	22	1	no	—
177	C₂×C₄⋊C₄	—	11	1	no	—
178	C₂×C₄⋊C₄	—	22	1	no	—
179	C₂×C₄⋊C₄	—	22	2	no	—
180	C₂×C₄⋊C₄	—	22	2	no	—
181	C₂×C₄²	—	22	1	no	—
182	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
183	#107	—	22	4	no	—
184	#107	—	22	4	no	—
185	C₄⋊C₈	—	2	2	no	—
186	C₄⋊C₈	—	11	2	no	—
187	C₄⋊C₈	—	22	4	no	—
188	C₄⋊C₈	—	22	1	no	—
189	C₄⋊C₈	C₂²×D₁₁	1	4	yes	—
190	#103	—	22	8	no	—
191	#97	—	22	4	no	—
192	C₄×C₈	D₄₄	1	2	yes	—
193	C₄×C₈	C₂²×D₁₁	1	2	yes	—
194	C₂×C₁₁	#1694	1	4	yes	complemented
195	C₂×C₁₁	C₂×#462	1	1	yes	characteristic
196	C₂×C₁₁	C₂×#469	1	1	yes	characteristic
197	C₂×C₁₁	C₂×#473	1	1	yes	characteristic
198	C₂×Q₈	—	11	2	no	—
199	C₂×Q₈	—	22	1	no	—
200	C₂×Q₈	—	22	4	no	—
201	C₂×Q₈	—	22	4	no	—
202	C₂×Q₈	—	44	2	no	—
203	C₂×Q₈	—	44	4	no	—
204	C₂×Q₈	—	44	4	no	—
205	C₂²×C₄	—	22	1	no	—
206	C₂²×C₄	—	22	1	no	—
207	C₂²×C₄	—	44	2	no	—
208	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
209	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
210	C₂²×C₄	#4343	1	1	yes	characteristic
211	Q₁₆	—	44	16	no	—
212	C₂×C₈	—	2	2	no	—
213	C₂×C₈	—	2	4	no	—
214	C₂×C₈	—	4	4	no	—
215	C₂×C₈	—	22	2	no	—
216	C₂×C₈	—	44	2	no	—
217	C₂×C₈	Dic₄₄	1	4	yes	complemented
218	C₂×C₈	C₂×D₄₄	1	2	yes	—
219	C₂×C₈	C₂×D₄₄	1	2	yes	—
220	C₄⋊C₄	—	11	2	no	—
221	C₄⋊C₄	—	22	1	no	—
222	C₄⋊C₄	—	22	2	no	—
223	C₄⋊C₄	—	22	2	no	—
224	C₄⋊C₄	—	22	4	no	—
225	C₄⋊C₄	—	22	4	no	—
226	C₄⋊C₄	—	44	2	no	—
227	C₄⋊C₄	—	44	2	no	—
228	C₄²	—	22	2	no	—
229	C₄²	—	22	2	no	—
230	C₄²	C₂×D₄₄	1	1	yes	characteristic
231	C₄²	D₄×D₁₁	1	1	yes	characteristic
232	C₄²	#4343	1	1	yes	characteristic
233	C₄²	C₂³×D₁₁	1	1	yes	characteristic
234	C₁₁	C₂×#1694	1	1	yes	characteristic, complemented, Sylow
235	C₂³	#66948	1	1	yes	characteristic
236	Q₈	—	22	4	no	—
237	Q₈	—	44	2	no	—
238	Q₈	—	44	4	no	—
239	Q₈	—	44	4	no	—
240	Q₈	—	88	4	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	22	2	no	—
243	C₂×C₄	—	22	2	no	—
244	C₂×C₄	—	44	2	no	—
245	C₂×C₄	—	44	2	no	—
246	C₂×C₄	—	44	4	no	—
247	C₂×C₄	—	88	4	no	—
248	C₂×C₄	#66948	1	1	yes	characteristic
249	C₂×C₄	#66948	1	1	yes	characteristic
250	C₂×C₄	#66948	1	1	yes	characteristic
251	C₂×C₄	C₂×Dic₄₄	1	2	yes	—
252	C₂×C₄	#66962	1	2	yes	—
253	C₂×C₄	#66967	1	4	yes	—
254	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
255	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
256	C₂×C₄	C₂×#4343	1	1	yes	characteristic
257	C₈	—	2	2	no	—
258	C₈	—	4	4	no	—
259	C₈	—	44	2	no	—
260	C₈	C₂×Dic₄₄	1	4	yes	complemented
261	C₂²	#10622462	1	2	yes	—
262	C₂²	#10622478	1	2	yes	—
263	C₂²	#10622509	1	2	yes	—
264	C₂²	C₂×#66948	1	1	yes	characteristic
265	C₄	—	2	1	no	—
266	C₄	—	2	1	no	—
267	C₄	—	44	2	no	—
268	C₄	—	44	2	no	—
269	C₄	—	88	4	no	—
270	C₄	#10622462	1	2	yes	—
271	C₄	#10622478	1	2	yes	—
272	C₄	C₂²×Dic₄₄	1	1	yes	characteristic
273	C₄	C₂×#66962	1	1	yes	characteristic
274	C₄	C₂×#66967	1	2	yes	—
275	C₂	#13068135	1	4	yes	direct product factor
276	C₂	C₂×#10622462	1	1	yes	characteristic
277	C₂	C₂×#10622478	1	1	yes	characteristic
278	C₂	C₂×#10622509	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#66948
commutator, cosocle	C₄²×C₁₁	C₂⁴
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂×C₁₁×#334	C₂
socle, prime radical	C₂³×C₁₁	#121
hypercenter	C₂×#334	D₁₁
hypocenter	C₁₁	C₂×#1694
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
4. #13068135	C₂	direct (N × H)
76. C₂×C₈×C₁₁	Q₁₆	semidirect
126. C₈×C₁₁	C₂×Q₁₆	semidirect
194. C₂×C₁₁	#1694	semidirect
217. C₂×C₈	Dic₄₄	semidirect
234. C₁₁	C₂×#1694	semidirect
260. C₈	C₂×Dic₄₄	semidirect
275. C₂	#13068135	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
C₂×#10622462	2
C₂×#10622292	2
#13068135	2
C₂×#10622120	2
C₂×C₁₁×#334	2
C₂×#1694	11

Subgroups — C2×#13068135 #14736402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13068135 #14736402