Subgroups — C₂×#10622170 #13068321

Order 1408.

488 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#117	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#4318	C₂	1	1	yes	maximal, characteristic
4	#10622170	C₂	1	4	yes	maximal, direct product factor
5	C₂³×C₄×C₁₁	C₂²	1	1	yes	characteristic
6	C₂³×Dic₁₁	—	2	1	no	—
7	C₁₁×#117	—	2	1	no	—
8	C₁₁×#117	—	2	1	no	—
9	C₁₁×#117	C₄	1	2	yes	complemented
10	C₁₁×#117	C₂²	1	2	yes	—
11	C₂×C₁₁×C₄⋊C₄	C₄	1	2	yes	complemented
12	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
13	C₂×C₄²×C₁₁	—	2	1	no	—
14	C₂×C₄×Dic₁₁	—	2	2	no	—
15	C₂×C₄×Dic₁₁	—	2	1	no	—
16	C₂×C₄×Dic₁₁	C₄	1	4	yes	complemented
17	C₂×C₄×Dic₁₁	C₂²	1	2	yes	—
18	C₂×#4318	—	2	2	no	—
19	C₂×#4318	—	2	1	no	—
20	C₂×#4318	C₄	1	4	yes	complemented
21	C₂×#4318	C₂²	1	2	yes	—
22	C₂²×C₁₁⋊C₈	—	2	1	no	—
23	C₂⁴×C₁₁	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₁₁	—	2	2	no	—
25	C₂²×C₄×C₁₁	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₁₁	C₂×C₄	1	2	yes	—
27	C₂²×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₁	D₄	1	2	yes	—
31	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₁	Q₈	1	2	yes	—
34	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
35	C₂²×Dic₁₁	—	2	8	no	—
36	C₂²×Dic₁₁	—	2	4	no	—
37	C₂²×Dic₁₁	—	2	2	no	—
38	C₁₁×C₄⋊C₄	—	2	2	no	—
39	C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
40	C₁₁×C₂²⋊C₄	—	2	2	no	—
41	C₁₁×C₂²⋊C₄	—	2	2	no	—
42	C₄²×C₁₁	—	2	2	no	—
43	C₄²×C₁₁	—	2	2	no	—
44	C₄×Dic₁₁	—	2	4	no	—
45	C₄×Dic₁₁	—	2	2	no	—
46	C₄×Dic₁₁	C₂×C₄	1	4	yes	complemented
47	#4318	—	2	4	no	—
48	#4318	—	2	2	no	—
49	#4318	C₂×C₄	1	4	yes	complemented
50	C₂×C₁₁⋊C₈	—	2	4	no	—
51	C₂×C₁₁⋊C₈	—	2	2	no	—
52	C₂×#339	—	11	1	no	maximal, Sylow
53	C₂³×C₁₁	—	2	4	no	—
54	C₂³×C₁₁	C₂²⋊C₄	1	2	yes	—
55	C₂³×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
56	C₂³×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
57	C₂³×C₁₁	C₄⋊C₄	1	2	yes	—
58	C₂³×C₁₁	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₁₁	—	2	4	no	—
60	C₂×C₄×C₁₁	—	4	4	no	—
61	C₂×C₄×C₁₁	C₄²	1	2	yes	—
62	C₂×C₄×C₁₁	C₄²	1	2	yes	—
63	C₂×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
64	C₂×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
65	C₂×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
66	C₂×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
69	C₂×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
70	C₂×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
71	C₂×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
72	C₂×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
73	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
79	C₂×Dic₁₁	—	2	16	no	—
80	C₂×Dic₁₁	—	2	8	no	—
81	C₂×Dic₁₁	—	2	4	no	—
82	C₁₁⋊C₈	—	2	4	no	—
83	C₂²×M₁₆	—	11	1	no	—
84	C₂×#117	D₁₁	1	1	yes	characteristic
85	C₂²×C₄²	—	11	1	no	—
86	#339	—	11	4	no	—
87	C₂²×C₁₁	—	2	4	no	—
88	C₂²×C₁₁	—	2	4	no	—
89	C₂²×C₁₁	—	2	2	no	—
90	C₂²×C₁₁	—	2	2	no	—
91	C₂²×C₁₁	#95	1	2	yes	—
92	C₂²×C₁₁	#95	1	2	yes	—
93	C₂²×C₁₁	#104	1	4	yes	—
94	C₂²×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
97	C₄×C₁₁	—	4	4	no	—
98	C₄×C₁₁	#95	1	2	yes	—
99	C₄×C₁₁	#95	1	2	yes	—
100	C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
101	C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
103	C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
104	Dic₁₁	—	2	8	no	—
105	C₂³×C₄	—	22	1	no	—
106	C₂³×C₄	C₂×D₁₁	1	1	yes	characteristic
107	C₂×M₁₆	—	11	2	no	—
108	C₂×M₁₆	—	11	4	no	—
109	C₂×M₁₆	—	22	2	no	—
110	C₂×M₁₆	—	22	1	no	—
111	C₂²×C₈	—	22	1	no	—
112	#117	—	2	1	no	—
113	#117	—	2	1	no	—
114	#117	Dic₁₁	1	2	yes	complemented
115	#117	C₂×D₁₁	1	2	yes	—
116	C₂×C₄⋊C₄	Dic₁₁	1	2	yes	complemented
117	C₂×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₄²	—	2	1	no	—
119	C₂×C₄²	—	11	2	no	—
120	C₂×C₄²	—	11	4	no	—
121	C₂×C₄²	—	22	2	no	—
122	C₂×C₄²	—	22	1	no	—
123	C₂×C₁₁	—	2	1	no	—
124	C₂×C₁₁	—	2	2	no	—
125	C₂×C₁₁	—	2	1	no	—
126	C₂×C₁₁	#339	1	4	yes	complemented
127	C₂×C₁₁	C₂×#95	1	1	yes	characteristic
128	C₂×C₁₁	C₂×#104	1	2	yes	—
129	C₂⁴	C₂²⋊D₁₁	1	1	yes	characteristic
130	C₂²×C₄	—	2	2	no	—
131	C₂²×C₄	—	22	8	no	—
132	C₂²×C₄	—	22	4	no	—
133	C₂²×C₄	—	22	2	no	—
134	C₂²×C₄	Dic₂₂	1	2	yes	—
135	C₂²×C₄	C₄×D₁₁	1	2	yes	—
136	C₂²×C₄	C₄×D₁₁	1	2	yes	—
137	C₂²×C₄	D₄₄	1	2	yes	—
138	C₂²×C₄	C₂×Dic₁₁	1	1	yes	characteristic
139	C₂²×C₄	C₂×Dic₁₁	1	1	yes	characteristic
140	C₂²×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
141	C₂²×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
142	C₂²×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
143	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
144	M₁₆	—	11	4	no	—
145	M₁₆	—	22	4	no	—
146	M₁₆	—	22	2	no	—
147	C₂×C₈	—	22	4	no	—
148	C₂×C₈	—	22	2	no	—
149	C₄⋊C₄	—	2	2	no	—
150	C₄⋊C₄	C₂×Dic₁₁	1	4	yes	complemented
151	C₂²⋊C₄	—	2	2	no	—
152	C₂²⋊C₄	—	2	2	no	—
153	C₄²	—	2	2	no	—
154	C₄²	—	2	2	no	—
155	C₄²	—	11	4	no	—
156	C₄²	—	22	4	no	—
157	C₄²	—	22	2	no	—
158	C₁₁	C₂×#339	1	1	yes	characteristic, complemented, Sylow
159	C₂³	—	2	4	no	—
160	C₂³	Dic₁₁⋊C₄	1	2	yes	—
161	C₂³	(C₂×D₁₁)⋊C₄	1	2	yes	—
162	C₂³	C₂²⋊Dic₁₁	1	1	yes	characteristic
163	C₂³	C₂²⋊Dic₁₁	1	1	yes	characteristic
164	C₂³	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
165	C₂×C₄	—	2	4	no	—
166	C₂×C₄	—	4	4	no	—
167	C₂×C₄	—	22	8	no	—
168	C₂×C₄	—	22	16	no	—
169	C₂×C₄	—	22	4	no	—
170	C₂×C₄	C₄×Dic₁₁	1	2	yes	—
171	C₂×C₄	C₄×Dic₁₁	1	2	yes	—
172	C₂×C₄	Dic₁₁⋊C₄	1	2	yes	—
173	C₂×C₄	Dic₁₁⋊C₄	1	2	yes	—
174	C₂×C₄	Dic₁₁⋊C₄	1	2	yes	—
175	C₂×C₄	C₄⋊Dic₁₁	1	2	yes	—
176	C₂×C₄	C₄⋊Dic₁₁	1	2	yes	—
177	C₂×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
178	C₂×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
179	C₂×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
180	C₂×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
181	C₂×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
182	C₂×C₄	C₂×Dic₂₂	1	1	yes	characteristic
183	C₂×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
184	C₂×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
185	C₂×C₄	C₂×D₄₄	1	1	yes	characteristic
186	C₂×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
187	C₂×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
188	C₈	—	22	4	no	—
189	C₂²	—	2	2	no	—
190	C₂²	—	2	2	no	—
191	C₂²	—	2	4	no	—
192	C₂²	—	2	4	no	—
193	C₂²	C₁₁⋊#95	1	2	yes	—
194	C₂²	C₁₁⋊#95	1	2	yes	—
195	C₂²	#66901	1	4	yes	—
196	C₂²	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
197	C₂²	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
198	C₂²	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
199	C₄	—	4	4	no	—
200	C₄	—	22	8	no	—
201	C₄	C₁₁⋊#95	1	2	yes	—
202	C₄	C₁₁⋊#95	1	2	yes	—
203	C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
204	C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
205	C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
206	C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
207	C₂	—	2	1	no	—
208	C₂	—	2	2	no	—
209	C₂	—	2	1	no	—
210	C₂	#10622170	1	4	yes	direct product factor
211	C₂	C₂×C₁₁⋊#95	1	1	yes	characteristic
212	C₂	C₂×#66901	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₁
Fitting	C₂×C₁₁×#117	C₂
socle	C₂³×C₁₁	C₂²⋊C₄
prime radical	C₂⁴×C₁₁	D₄
cosocle	C₂²×C₄×C₁₁	C₂³
hypercenter	C₂×#117	D₁₁
hypocenter	C₁₁	C₂×#339
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
4. #10622170	C₂	direct (N × H)
9. C₁₁×#117	C₄	semidirect
11. C₂×C₁₁×C₄⋊C₄	C₄	semidirect
16. C₂×C₄×Dic₁₁	C₄	semidirect
20. C₂×#4318	C₄	semidirect
39. C₁₁×C₄⋊C₄	C₂×C₄	semidirect
46. C₄×Dic₁₁	C₂×C₄	semidirect
49. #4318	C₂×C₄	semidirect
114. #117	Dic₁₁	semidirect
116. C₂×C₄⋊C₄	Dic₁₁	semidirect
126. C₂×C₁₁	#339	semidirect
150. C₄⋊C₄	C₂×Dic₁₁	semidirect
158. C₁₁	C₂×#339	semidirect
210. C₂	#10622170	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×C₁₁×#117	2
C₂²×C₄×Dic₁₁	2
C₂²×#4318	2
#10622170	2
C₂×#339	11

Subgroups — C2×#10622170 #13068321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10622170 #13068321