Subgroups — C₂×#13117059 #16018202

Order 3328.

726 conjugacy classes of subgroups.

The subgroup lattice has 236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718343	C₂	1	1	yes	maximal, characteristic, complemented
2	#13117059	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718154	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×#6090	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×D₈	—	2	1	no	—
7	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
8	C₂×C₁₃×#127	—	2	1	no	—
9	C₂×#88123	—	2	1	no	—
10	C₁₃×#493	—	2	2	no	—
11	C₁₃×#493	C₂²	1	4	yes	—
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×#88058	—	2	1	no	—
14	C₂×#88058	C₂²	1	2	yes	—
15	C₂²×#6090	C₂²	1	2	yes	—
16	#11718343	—	2	2	no	—
17	#11718343	C₂²	1	4	yes	complemented
18	#11718154	C₂²	1	16	yes	complemented
19	C₄×#6090	C₂²	1	4	yes	complemented
20	C₂²×D₄×C₁₃	—	2	2	no	—
21	C₂²×D₄×C₁₃	—	4	1	no	—
22	C₂²×D₄×C₁₃	—	4	1	no	—
23	C₂²×Dic₂₆	—	4	1	no	—
24	C₂×C₁₃×D₈	—	2	2	no	—
25	C₂×C₁₃×D₈	—	2	4	no	—
26	C₂×C₁₃×D₈	—	2	8	no	—
27	C₂×C₁₃×D₈	—	4	4	no	—
28	C₂×C₁₃×D₈	C₂³	1	4	yes	—
29	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
31	C₁₃×#127	—	2	4	no	—
32	C₁₃×#127	—	4	2	no	—
33	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
34	C₂×C₄⋊Dic₁₃	—	2	2	no	—
35	C₂×C₄⋊Dic₁₃	—	4	1	no	—
36	#88123	—	2	4	no	—
37	#88123	—	4	2	no	—
38	C₄×C₈×C₁₃	D₄	1	2	yes	—
39	C₄×C₈×C₁₃	C₂³	1	2	yes	—
40	#88058	—	2	4	no	—
41	#88058	—	2	2	no	—
42	#88058	C₂³	1	4	yes	—
43	C₂×#6090	—	2	4	no	—
44	C₂×#6090	C₂³	1	4	yes	—
45	C₂×#2240	—	13	1	no	maximal, Sylow
46	C₂⁴×C₁₃	—	4	2	no	—
47	C₂×D₄×C₁₃	—	2	4	no	—
48	C₂×D₄×C₁₃	—	4	4	no	—
49	C₂×D₄×C₁₃	—	4	4	no	—
50	C₂×D₄×C₁₃	—	4	4	no	—
51	C₂×D₄×C₁₃	—	4	2	no	—
52	C₂×D₄×C₁₃	—	4	4	no	—
53	C₂×D₄×C₁₃	—	8	4	no	—
54	C₂×D₄×C₁₃	—	8	4	no	—
55	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₂²×Dic₁₃	—	4	2	no	—
59	C₂×Dic₂₆	—	4	4	no	—
60	C₂×Dic₂₆	—	8	4	no	—
61	C₁₃×D₈	—	2	8	no	—
62	C₁₃×D₈	—	4	4	no	—
63	C₁₃×D₈	—	4	8	no	—
64	C₂×C₈×C₁₃	SD₁₆	1	4	yes	—
65	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
66	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
67	C₂×C₈×C₁₃	#41	1	4	yes	—
68	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
69	C₄²×C₁₃	D₈	1	2	yes	—
70	C₄²×C₁₃	C₂×D₄	1	2	yes	—
71	C₄⋊Dic₁₃	—	2	4	no	—
72	C₄⋊Dic₁₃	—	4	4	no	—
73	C₄⋊Dic₁₃	—	4	2	no	—
74	#6090	—	2	4	no	—
75	C₂×#500	—	13	1	no	—
76	C₂×#493	D₁₃	1	1	yes	characteristic
77	#2240	—	13	8	no	—
78	C₂×#357	—	13	4	no	—
79	C₂×C₄×C₁₆	—	13	1	no	—
80	C₂³×C₁₃	—	4	4	no	—
81	C₂³×C₁₃	—	8	4	no	—
82	C₂³×C₁₃	—	8	4	no	—
83	C₂³×C₁₃	—	8	4	no	—
84	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
85	D₄×C₁₃	—	4	4	no	—
86	D₄×C₁₃	—	4	4	no	—
87	D₄×C₁₃	—	8	4	no	—
88	D₄×C₁₃	—	8	8	no	—
89	D₄×C₁₃	—	8	8	no	—
90	C₂×C₄×C₁₃	D₁₆	1	4	yes	—
91	C₂×C₄×C₁₃	SD₃₂	1	4	yes	—
92	C₂×C₄×C₁₃	#124	1	2	yes	—
93	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
94	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
95	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
96	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
97	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
98	C₂×Dic₁₃	—	4	4	no	—
99	C₂×Dic₁₃	—	8	4	no	—
100	Dic₂₆	—	8	8	no	—
101	C₈×C₁₃	#124	1	2	yes	—
102	C₈×C₁₃	C₂×SD₁₆	1	4	yes	—
103	C₈×C₁₃	C₂×#41	1	2	yes	—
104	C₂²×D₈	—	2	1	no	—
105	C₂²×D₈	C₂×D₁₃	1	2	yes	—
106	C₂×C₄⋊Q₈	—	26	1	no	—
107	C₂×#127	—	2	1	no	—
108	C₂²×C₁₆	—	13	2	no	—
109	#500	—	13	4	no	—
110	#500	—	26	2	no	—
111	#493	—	2	2	no	—
112	#493	C₂×D₁₃	1	4	yes	—
113	C₂×#107	—	13	2	no	—
114	C₂×#107	—	26	1	no	—
115	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
116	#357	—	13	16	no	—
117	C₄×C₁₆	—	13	4	no	—
118	C₂²×C₁₃	—	8	4	no	—
119	C₂²×C₁₃	—	8	4	no	—
120	C₂²×C₁₃	—	8	4	no	—
121	C₂²×C₁₃	—	16	8	no	—
122	C₂²×C₁₃	#486	1	2	yes	—
123	C₂²×C₁₃	C₂×D₁₆	1	2	yes	—
124	C₂²×C₁₃	C₂×SD₃₂	1	2	yes	—
125	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
126	C₄×C₁₃	#486	1	2	yes	—
127	C₄×C₁₃	C₂×D₁₆	1	4	yes	—
128	C₄×C₁₃	C₂×SD₃₂	1	4	yes	—
129	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
130	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
131	Dic₁₃	—	8	4	no	—
132	C₂²×Q₈	—	52	1	no	—
133	C₂²×D₄	—	2	2	no	—
134	C₂²×D₄	—	4	1	no	—
135	C₂²×D₄	—	4	1	no	—
136	C₂×D₈	—	2	8	no	—
137	C₂×D₈	—	2	4	no	—
138	C₂×D₈	—	2	2	no	—
139	C₂×D₈	—	4	4	no	—
140	C₂×D₈	C₂²×D₁₃	1	4	yes	—
141	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
142	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
143	C₄⋊Q₈	—	26	4	no	—
144	C₄⋊Q₈	—	52	2	no	—
145	#127	—	2	4	no	—
146	#127	—	4	2	no	—
147	C₂×C₄⋊C₄	—	26	2	no	—
148	C₂×C₄⋊C₄	—	52	1	no	—
149	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
150	C₂×C₁₆	—	13	4	no	—
151	C₂×C₁₆	—	26	4	no	—
152	#107	—	13	4	no	—
153	#107	—	26	2	no	—
154	#107	—	26	4	no	—
155	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
156	C₄×C₈	C₂²×D₁₃	1	2	yes	—
157	C₂×C₁₃	—	16	4	no	—
158	C₂×C₁₃	#2240	1	4	yes	complemented
159	C₂×C₁₃	C₂×#486	1	1	yes	characteristic
160	C₂×C₁₃	C₂²×D₁₆	1	1	yes	characteristic
161	C₂×C₁₃	C₂²×SD₃₂	1	1	yes	characteristic
162	C₂⁴	—	4	2	no	—
163	C₂×Q₈	—	52	4	no	—
164	C₂×Q₈	—	104	4	no	—
165	C₂×D₄	—	2	4	no	—
166	C₂×D₄	—	4	4	no	—
167	C₂×D₄	—	4	4	no	—
168	C₂×D₄	—	4	2	no	—
169	C₂×D₄	—	4	4	no	—
170	C₂×D₄	—	4	4	no	—
171	C₂×D₄	—	8	4	no	—
172	C₂×D₄	—	8	4	no	—
173	C₂²×C₄	—	52	2	no	—
174	C₂²×C₄	#6104	1	1	yes	characteristic
175	C₂²×C₄	#6104	1	1	yes	characteristic
176	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
177	D₈	—	2	8	no	—
178	D₈	—	4	8	no	—
179	D₈	—	4	4	no	—
180	C₂×C₈	#6105	1	4	yes	—
181	C₂×C₈	#6129	1	4	yes	—
182	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
183	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
184	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
185	C₄⋊C₄	—	26	4	no	—
186	C₄⋊C₄	—	52	2	no	—
187	C₄⋊C₄	—	52	4	no	—
188	C₄²	#6104	1	2	yes	—
189	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
190	C₁₆	—	26	4	no	—
191	C₁₃	C₂×#2240	1	1	yes	characteristic, complemented, Sylow
192	C₂³	—	4	4	no	—
193	C₂³	—	8	4	no	—
194	C₂³	—	8	4	no	—
195	C₂³	—	8	4	no	—
196	C₂³	C₂×#6104	1	1	yes	characteristic
197	Q₈	—	104	8	no	—
198	D₄	—	4	4	no	—
199	D₄	—	4	4	no	—
200	D₄	—	8	4	no	—
201	D₄	—	8	8	no	—
202	D₄	—	8	8	no	—
203	C₂×C₄	—	52	4	no	—
204	C₂×C₄	—	104	4	no	—
205	C₂×C₄	#88066	1	4	yes	—
206	C₂×C₄	#88067	1	4	yes	—
207	C₂×C₄	C₂×#6104	1	1	yes	characteristic
208	C₂×C₄	C₂×#6104	1	2	yes	—
209	C₂×C₄	C₂×#6104	1	2	yes	—
210	C₂×C₄	C₂×#6105	1	2	yes	—
211	C₂×C₄	#88190	1	2	yes	—
212	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
213	C₈	C₂×#6105	1	4	yes	—
214	C₈	#88190	1	2	yes	—
215	C₈	C₂×#6129	1	2	yes	—
216	C₂²	—	8	4	no	—
217	C₂²	—	8	4	no	—
218	C₂²	—	8	4	no	—
219	C₂²	—	16	8	no	—
220	C₂²	#11718731	1	2	yes	—
221	C₂²	C₂×#88066	1	2	yes	—
222	C₂²	C₂×#88067	1	2	yes	—
223	C₂²	C₂²×#6104	1	1	yes	characteristic
224	C₄	—	104	4	no	—
225	C₄	#11718731	1	2	yes	—
226	C₄	C₂×#88066	1	4	yes	—
227	C₄	C₂×#88067	1	4	yes	—
228	C₄	C₂²×#6105	1	1	yes	characteristic
229	C₄	C₂×#88190	1	1	yes	characteristic
230	C₂	—	16	4	no	—
231	C₂	#13117059	1	4	yes	direct product factor
232	C₂	C₂×#11718731	1	1	yes	characteristic
233	C₂	C₂²×#88066	1	1	yes	characteristic
234	C₂	C₂²×#88067	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting, prime radical	C₂×C₁₃×#493	C₂
socle	C₂³×C₁₃	C₂×D₈
hypercenter	C₂×#493	D₁₃
hypocenter	C₁₃	C₂×#2240
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#493

Complements

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

N	H ≅ G/N	type
1. C₂×#11718343	C₂	semidirect
2. #13117059	C₂	direct (N × H)
3. C₂×#11718154	C₂	semidirect
4. C₂×C₄×#6090	C₂	semidirect
17. #11718343	C₂²	semidirect
18. #11718154	C₂²	semidirect
19. C₄×#6090	C₂²	semidirect
158. C₂×C₁₃	#2240	semidirect
191. C₁₃	C₂×#2240	semidirect
231. C₂	#13117059	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×#11718343	2
#13117059	2
C₂×#11718154	2
C₂×C₄×#6090	2
C₂×C₁₃×#493	2
C₂×#2240	13

Subgroups — C2×#13117059 #16018202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13117059 #16018202