Subgroups — C₂×#13066664 #14665012

Order 2816.

414 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622312	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊(C₁₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	#13066664	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁×#335	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₄₄	—	2	1	no	—
6	C₂²×Dic₄₄	C₄	1	2	yes	—
7	C₂×#66922	—	2	1	no	—
8	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂²×C₁₁⋊C₁₆	—	2	1	no	—
11	#10622312	—	2	1	no	—
12	#10622312	—	2	1	no	—
13	#10622312	C₄	1	2	yes	—
14	#10622312	C₂²	1	2	yes	—
15	C₁₁×#335	—	2	1	no	—
16	C₁₁×#335	C₂²	1	2	yes	—
17	C₄⋊(C₁₁⋊C₁₆)	—	2	1	no	—
18	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	—
19	C₂²×Dic₂₂	—	2	2	no	—
20	C₂²×C₈×C₁₁	—	4	1	no	—
21	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₁	—	4	1	no	—
25	C₂×C₄⋊Dic₁₁	—	4	1	no	—
26	C₂×Dic₄₄	—	2	2	no	—
27	C₂×Dic₄₄	—	2	2	no	—
28	C₂×Dic₄₄	—	2	2	no	—
29	C₂×Dic₄₄	—	4	4	no	—
30	C₂×Dic₄₄	—	4	2	no	—
31	C₂×Dic₄₄	—	4	2	no	—
32	C₂×Dic₄₄	C₂×C₄	1	4	yes	—
33	#66922	—	2	2	no	—
34	#66922	—	2	2	no	—
35	#66922	—	4	1	no	—
36	#66922	—	4	1	no	—
37	C₁₁×C₄⋊C₈	—	2	2	no	—
38	C₁₁×C₄⋊C₈	—	4	1	no	—
39	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
43	C₂×C₁₁⋊C₁₆	—	2	2	no	—
44	C₂×C₁₁⋊C₁₆	—	4	2	no	—
45	C₂×#1362	—	11	1	no	maximal, Sylow
46	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
48	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
49	C₂²×Dic₁₁	—	4	2	no	—
50	C₂×Dic₂₂	—	2	4	no	—
51	C₂×Dic₂₂	—	4	4	no	—
52	C₂×Dic₂₂	—	4	4	no	—
53	C₂×Dic₂₂	—	4	2	no	—
54	C₂×C₈×C₁₁	—	2	2	no	—
55	C₂×C₈×C₁₁	—	4	2	no	—
56	C₂×C₈×C₁₁	—	8	2	no	—
57	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₈×C₁₁	D₈	1	2	yes	—
60	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
61	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
63	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
64	C₄²×C₁₁	D₈	1	1	yes	characteristic
65	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
66	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
67	C₄⋊Dic₁₁	—	4	2	no	—
68	C₄⋊Dic₁₁	—	4	2	no	—
69	C₄⋊Dic₁₁	—	4	2	no	—
70	C₄⋊Dic₁₁	—	4	2	no	—
71	Dic₄₄	—	4	4	no	—
72	Dic₄₄	—	4	4	no	—
73	Dic₄₄	—	4	4	no	—
74	Dic₄₄	—	4	2	no	—
75	Dic₄₄	—	4	2	no	—
76	C₁₁⋊C₁₆	—	4	2	no	—
77	C₂×#494	—	11	1	no	—
78	C₂×C₄⋊C₁₆	—	11	1	no	—
79	C₂×#335	D₁₁	1	1	yes	characteristic
80	#1362	—	11	4	no	—
81	C₂³×C₁₁	#102	1	1	yes	characteristic
82	C₂×C₄×C₁₁	—	2	2	no	—
83	C₂×C₄×C₁₁	#100	1	2	yes	—
84	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
85	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
86	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
87	C₂×C₄×C₁₁	#102	1	2	yes	—
88	C₂×C₄×C₁₁	SD₃₂	1	2	yes	—
89	C₂×C₄×C₁₁	Q₃₂	1	2	yes	—
90	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
92	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
93	C₂×Dic₁₁	—	4	4	no	—
94	C₂×Dic₁₁	—	8	4	no	—
95	Dic₂₂	—	4	4	no	—
96	Dic₂₂	—	4	4	no	—
97	Dic₂₂	—	8	4	no	—
98	C₈×C₁₁	—	2	1	no	—
99	C₈×C₁₁	—	2	1	no	—
100	C₈×C₁₁	—	8	2	no	—
101	C₈×C₁₁	#102	1	2	yes	—
102	C₈×C₁₁	C₂×D₈	1	1	yes	characteristic
103	C₈×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
104	C₂²×Q₁₆	—	11	2	no	—
105	C₂²×Q₁₆	—	22	1	no	—
106	C₂×C₄⋊Q₈	—	22	1	no	—
107	C₂²×C₁₆	—	22	1	no	—
108	#494	—	11	2	no	—
109	#494	—	11	2	no	—
110	#494	—	22	1	no	—
111	#494	—	22	1	no	—
112	C₂×C₄⋊C₈	—	2	1	no	—
113	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
114	C₄⋊C₁₆	—	11	2	no	—
115	C₄⋊C₁₆	—	22	1	no	—
116	#335	—	2	1	no	—
117	#335	C₂×D₁₁	1	2	yes	—
118	C₂²×C₁₁	#331	1	2	yes	—
119	C₂²×C₁₁	#358	1	2	yes	—
120	C₂²×C₁₁	#362	1	2	yes	—
121	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
122	C₄×C₁₁	—	2	1	no	—
123	C₄×C₁₁	—	2	1	no	—
124	C₄×C₁₁	#331	1	2	yes	—
125	C₄×C₁₁	#358	1	2	yes	—
126	C₄×C₁₁	C₂×#100	1	1	yes	characteristic
127	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
128	C₄×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
129	C₄×C₁₁	C₂×Q₃₂	1	1	yes	characteristic
130	Dic₁₁	—	8	4	no	—
131	C₂²×Q₈	—	22	2	no	—
132	C₂×Q₁₆	—	11	4	no	—
133	C₂×Q₁₆	—	22	2	no	—
134	C₂×Q₁₆	—	22	2	no	—
135	C₂×Q₁₆	—	22	2	no	—
136	C₂×Q₁₆	—	44	4	no	—
137	C₂×Q₁₆	—	44	2	no	—
138	C₂×Q₁₆	—	44	2	no	—
139	C₂²×C₈	—	4	1	no	—
140	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
141	C₂²×C₈	D₄₄	1	1	yes	characteristic
142	C₄⋊Q₈	—	22	2	no	—
143	C₄⋊Q₈	—	22	2	no	—
144	C₄⋊Q₈	—	44	1	no	—
145	C₄⋊Q₈	—	44	1	no	—
146	C₂×C₄⋊C₄	—	44	1	no	—
147	C₂×C₄⋊C₄	—	44	1	no	—
148	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
149	C₂×C₁₆	—	22	2	no	—
150	C₂×C₁₆	—	44	2	no	—
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	4	1	no	—
153	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
154	C₄×C₈	D₄₄	1	1	yes	characteristic
155	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
156	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
157	C₂×C₁₁	#1362	1	4	yes	complemented
158	C₂×C₁₁	C₂×#331	1	1	yes	characteristic
159	C₂×C₁₁	C₂×#358	1	1	yes	characteristic
160	C₂×C₁₁	C₂×#362	1	1	yes	characteristic
161	C₂×Q₈	—	22	4	no	—
162	C₂×Q₈	—	44	2	no	—
163	C₂×Q₈	—	44	4	no	—
164	C₂×Q₈	—	44	4	no	—
165	C₂²×C₄	—	44	2	no	—
166	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
167	C₂²×C₄	#4323	1	1	yes	characteristic
168	C₂²×C₄	#4325	1	1	yes	characteristic
169	Q₁₆	—	44	4	no	—
170	Q₁₆	—	44	4	no	—
171	Q₁₆	—	44	4	no	—
172	Q₁₆	—	44	2	no	—
173	Q₁₆	—	44	2	no	—
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	—	4	2	no	—
176	C₂×C₈	—	8	2	no	—
177	C₂×C₈	#4314	1	2	yes	—
178	C₂×C₈	D₈₈	1	2	yes	—
179	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
180	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
181	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
182	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
183	C₄⋊C₄	—	44	2	no	—
184	C₄⋊C₄	—	44	2	no	—
185	C₄⋊C₄	—	44	2	no	—
186	C₄⋊C₄	—	44	2	no	—
187	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
188	C₄²	#4323	1	1	yes	characteristic
189	C₄²	#4325	1	1	yes	characteristic
190	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
191	C₁₆	—	44	2	no	—
192	C₁₁	C₂×#1362	1	1	yes	characteristic, complemented, Sylow
193	C₂³	#66873	1	1	yes	characteristic
194	Q₈	—	44	4	no	—
195	Q₈	—	44	4	no	—
196	Q₈	—	88	4	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	44	4	no	—
199	C₂×C₄	—	88	4	no	—
200	C₂×C₄	#66873	1	1	yes	characteristic
201	C₂×C₄	#66873	1	1	yes	characteristic
202	C₂×C₄	#66873	1	1	yes	characteristic
203	C₂×C₄	#66885	1	2	yes	—
204	C₂×C₄	#66887	1	2	yes	—
205	C₂×C₄	#66891	1	2	yes	—
206	C₂×C₄	#66893	1	2	yes	—
207	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
208	C₂×C₄	C₂×#4323	1	1	yes	characteristic
209	C₂×C₄	C₂×#4325	1	1	yes	characteristic
210	C₈	—	2	1	no	—
211	C₈	—	2	1	no	—
212	C₈	—	8	2	no	—
213	C₈	#66885	1	2	yes	—
214	C₈	C₂×#4314	1	1	yes	characteristic
215	C₈	C₂×D₈₈	1	1	yes	characteristic
216	C₂²	#10622123	1	2	yes	—
217	C₂²	#10622130	1	2	yes	—
218	C₂²	#10622134	1	2	yes	—
219	C₂²	C₂×#66873	1	1	yes	characteristic
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	88	4	no	—
223	C₄	#10622123	1	2	yes	—
224	C₄	#10622130	1	2	yes	—
225	C₄	C₂×#66885	1	1	yes	characteristic
226	C₄	C₂×#66887	1	1	yes	characteristic
227	C₄	C₂×#66891	1	1	yes	characteristic
228	C₄	C₂×#66893	1	1	yes	characteristic
229	C₂	#13066664	1	4	yes	direct product factor
230	C₂	C₂×#10622123	1	1	yes	characteristic
231	C₂	C₂×#10622130	1	1	yes	characteristic
232	C₂	C₂×#10622134	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#66873
commutator	C₂×C₈×C₁₁	C₂²×C₄
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₂×C₁₁×#335	C₂
socle, prime radical	C₂³×C₁₁	#102
cosocle	C₄×C₈×C₁₁	C₂³
hypercenter	C₂×#335	D₁₁
hypocenter	C₁₁	C₂×#1362
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
3. #13066664	C₂	direct (N × H)
157. C₂×C₁₁	#1362	semidirect
192. C₁₁	C₂×#1362	semidirect
229. C₂	#13066664	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×#10622312	2
C₂×C₄⋊(C₁₁⋊C₁₆)	2
#13066664	2
C₂×C₁₁×#335	2
C₂×#1362	11

Subgroups — C2×#13066664 #14665012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066664 #14665012