Subgroups — C₂×#13066672 #14665052

Order 2816.

350 conjugacy classes of subgroups.

The subgroup lattice has 218 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×C₄⋊(C₁₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	#13066672	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁×#335	C₂	1	1	yes	maximal, characteristic
5	C₂×#66922	—	2	1	no	—
6	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×#66882	—	2	1	no	—
9	C₂×#66882	C₄	1	2	yes	—
10	C₂²×C₁₁⋊C₁₆	—	2	1	no	—
11	#10622295	—	2	1	no	—
12	#10622295	—	2	1	no	—
13	#10622295	C₄	1	2	yes	—
14	#10622295	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	—	4	1	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	—	2	2	no	—
25	C₂×C₄⋊Dic₁₁	—	4	1	no	—
26	#66922	—	2	2	no	—
27	#66922	—	2	2	no	—
28	#66922	—	4	1	no	—
29	#66922	—	4	1	no	—
30	C₁₁×C₄⋊C₈	—	2	2	no	—
31	C₁₁×C₄⋊C₈	—	4	1	no	—
32	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
34	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
35	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
36	#66882	—	2	2	no	—
37	#66882	—	2	2	no	—
38	#66882	—	2	2	no	—
39	#66882	C₂×C₄	1	4	yes	—
40	C₂×C₁₁⋊C₁₆	—	2	2	no	—
41	C₂×C₁₁⋊C₁₆	—	4	2	no	—
42	C₂×#1364	—	11	1	no	maximal, Sylow
43	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
45	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
46	C₂²×Dic₁₁	—	4	2	no	—
47	C₂×Dic₂₂	—	4	2	no	—
48	C₂×Dic₂₂	—	4	2	no	—
49	C₂×Dic₂₂	—	8	2	no	—
50	C₂×Dic₂₂	—	8	2	no	—
51	C₂×C₈×C₁₁	—	2	2	no	—
52	C₂×C₈×C₁₁	—	4	2	no	—
53	C₂×C₈×C₁₁	—	8	2	no	—
54	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
57	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
58	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
60	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
61	C₄²×C₁₁	D₈	1	1	yes	characteristic
62	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
63	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
64	C₄⋊Dic₁₁	—	2	4	no	—
65	C₄⋊Dic₁₁	—	4	2	no	—
66	C₄⋊Dic₁₁	—	4	2	no	—
67	C₄⋊Dic₁₁	—	4	2	no	—
68	C₁₁⋊C₁₆	—	4	2	no	—
69	C₂×#500	—	11	1	no	—
70	C₂×C₄⋊C₁₆	—	11	1	no	—
71	C₂×#335	D₁₁	1	1	yes	characteristic
72	#1364	—	11	4	no	—
73	C₂³×C₁₁	#102	1	1	yes	characteristic
74	C₂×C₄×C₁₁	—	2	2	no	—
75	C₂×C₄×C₁₁	#101	1	2	yes	—
76	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
77	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
78	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
79	C₂×C₄×C₁₁	#103	1	2	yes	—
80	C₂×C₄×C₁₁	D₁₆	1	2	yes	—
81	C₂×C₄×C₁₁	SD₃₂	1	2	yes	—
82	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
84	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
85	C₂×Dic₁₁	—	4	4	no	—
86	C₂×Dic₁₁	—	8	4	no	—
87	Dic₂₂	—	8	4	no	—
88	Dic₂₂	—	8	2	no	—
89	Dic₂₂	—	8	2	no	—
90	C₈×C₁₁	—	2	1	no	—
91	C₈×C₁₁	—	2	1	no	—
92	C₈×C₁₁	—	8	2	no	—
93	C₈×C₁₁	#103	1	2	yes	—
94	C₈×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
95	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
96	C₂×C₄⋊Q₈	—	22	1	no	—
97	C₂²×C₁₆	—	22	1	no	—
98	#500	—	11	2	no	—
99	#500	—	11	2	no	—
100	#500	—	22	1	no	—
101	#500	—	22	1	no	—
102	C₂×#107	—	11	2	no	—
103	C₂×#107	—	22	1	no	—
104	C₂×C₄⋊C₈	—	2	1	no	—
105	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
106	C₄⋊C₁₆	—	11	2	no	—
107	C₄⋊C₁₆	—	22	1	no	—
108	#335	—	2	1	no	—
109	#335	C₂×D₁₁	1	2	yes	—
110	C₂²×C₁₁	#332	1	2	yes	—
111	C₂²×C₁₁	#357	1	2	yes	—
112	C₂²×C₁₁	#362	1	2	yes	—
113	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
114	C₄×C₁₁	—	2	1	no	—
115	C₄×C₁₁	—	2	1	no	—
116	C₄×C₁₁	#332	1	2	yes	—
117	C₄×C₁₁	#357	1	2	yes	—
118	C₄×C₁₁	C₂×#101	1	1	yes	characteristic
119	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
120	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
121	C₄×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
122	Dic₁₁	—	8	4	no	—
123	C₂²×Q₈	—	44	1	no	—
124	C₂²×C₈	—	4	1	no	—
125	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
126	C₂²×C₈	D₄₄	1	1	yes	characteristic
127	C₄⋊Q₈	—	22	2	no	—
128	C₄⋊Q₈	—	22	2	no	—
129	C₄⋊Q₈	—	44	1	no	—
130	C₄⋊Q₈	—	44	1	no	—
131	C₂×C₄⋊C₄	—	22	2	no	—
132	C₂×C₄⋊C₄	—	44	1	no	—
133	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
134	C₂×C₁₆	—	22	2	no	—
135	C₂×C₁₆	—	44	2	no	—
136	#107	—	11	4	no	—
137	#107	—	22	2	no	—
138	#107	—	22	2	no	—
139	#107	—	22	2	no	—
140	C₄⋊C₈	—	2	2	no	—
141	C₄⋊C₈	—	4	1	no	—
142	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
143	C₄×C₈	D₄₄	1	1	yes	characteristic
144	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
145	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
146	C₂×C₁₁	#1364	1	4	yes	complemented
147	C₂×C₁₁	C₂×#332	1	1	yes	characteristic
148	C₂×C₁₁	C₂×#357	1	1	yes	characteristic
149	C₂×C₁₁	C₂×#362	1	1	yes	characteristic
150	C₂×Q₈	—	44	2	no	—
151	C₂×Q₈	—	44	2	no	—
152	C₂×Q₈	—	88	2	no	—
153	C₂×Q₈	—	88	2	no	—
154	C₂²×C₄	—	44	2	no	—
155	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
156	C₂²×C₄	#4323	1	1	yes	characteristic
157	C₂²×C₄	#4325	1	1	yes	characteristic
158	C₂×C₈	—	2	2	no	—
159	C₂×C₈	—	4	2	no	—
160	C₂×C₈	—	8	2	no	—
161	C₂×C₈	#4314	1	2	yes	—
162	C₂×C₈	Dic₄₄	1	2	yes	—
163	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
164	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
165	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
166	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
167	C₄⋊C₄	—	22	4	no	—
168	C₄⋊C₄	—	44	2	no	—
169	C₄⋊C₄	—	44	2	no	—
170	C₄⋊C₄	—	44	2	no	—
171	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
172	C₄²	#4323	1	1	yes	characteristic
173	C₄²	#4325	1	1	yes	characteristic
174	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
175	C₁₆	—	44	2	no	—
176	C₁₁	C₂×#1364	1	1	yes	characteristic, complemented, Sylow
177	C₂³	#66873	1	1	yes	characteristic
178	Q₈	—	88	2	no	—
179	Q₈	—	88	2	no	—
180	Q₈	—	88	4	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	44	4	no	—
183	C₂×C₄	—	88	4	no	—
184	C₂×C₄	#66873	1	1	yes	characteristic
185	C₂×C₄	#66873	1	1	yes	characteristic
186	C₂×C₄	#66873	1	1	yes	characteristic
187	C₂×C₄	#66880	1	2	yes	—
188	C₂×C₄	#66888	1	2	yes	—
189	C₂×C₄	#66890	1	2	yes	—
190	C₂×C₄	#66892	1	2	yes	—
191	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
192	C₂×C₄	C₂×#4323	1	1	yes	characteristic
193	C₂×C₄	C₂×#4325	1	1	yes	characteristic
194	C₈	—	2	1	no	—
195	C₈	—	2	1	no	—
196	C₈	—	8	2	no	—
197	C₈	#66880	1	2	yes	—
198	C₈	C₂×#4314	1	1	yes	characteristic
199	C₈	C₂×Dic₄₄	1	1	yes	characteristic
200	C₂²	#10622120	1	2	yes	—
201	C₂²	#10622129	1	2	yes	—
202	C₂²	#10622134	1	2	yes	—
203	C₂²	C₂×#66873	1	1	yes	characteristic
204	C₄	—	2	1	no	—
205	C₄	—	2	1	no	—
206	C₄	—	88	4	no	—
207	C₄	#10622120	1	2	yes	—
208	C₄	#10622129	1	2	yes	—
209	C₄	C₂×#66880	1	1	yes	characteristic
210	C₄	C₂×#66888	1	1	yes	characteristic
211	C₄	C₂×#66890	1	1	yes	characteristic
212	C₄	C₂×#66892	1	1	yes	characteristic
213	C₂	#13066672	1	4	yes	direct product factor
214	C₂	C₂×#10622120	1	1	yes	characteristic
215	C₂	C₂×#10622129	1	1	yes	characteristic
216	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×#1364
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. #13066672	C₂	direct (N × H)
146. C₂×C₁₁	#1364	semidirect
176. C₁₁	C₂×#1364	semidirect
213. C₂	#13066672	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×C₄⋊(C₁₁⋊C₁₆)	2
#13066672	2
C₂×C₁₁×#335	2
C₂×#1364	11

Subgroups — C2×#13066672 #14665052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066672 #14665052