Subgroups — C₂×#13113139 #15828625

Order 3328.

994 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6099	C₂	1	2	yes	maximal
2	#13113139	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718046	C₂	1	2	yes	maximal, complemented
4	C₂×#11718047	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₈×#1055	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₃×M₁₆	C₄	1	2	yes	—
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×#6099	C₄	1	4	yes	—
10	C₄×C₁₃×M₁₆	C₄	1	4	yes	—
11	C₄×C₁₃×M₁₆	C₂²	1	4	yes	—
12	C₂×C₁₃×#97	C₄	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₄×#6099	C₄	1	8	yes	—
16	C₄×#6099	C₂²	1	8	yes	—
17	C₂×#88043	C₄	1	4	yes	—
18	C₂×C₄×#1055	C₂²	1	2	yes	—
19	C₂×C₄×#1055	C₂²	1	2	yes	—
20	#11718047	C₂²	1	4	yes	complemented
21	#11718046	C₂²	1	8	yes	complemented
22	C₈×#1055	C₂²	1	4	yes	complemented
23	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
24	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₁₃×M₁₆	—	2	8	no	—
26	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	—
27	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
28	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
31	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
33	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
34	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
35	C₂×#6099	—	2	16	no	—
36	C₂×#6099	C₂×C₄	1	16	yes	—
37	C₂²×#1055	C₂×C₄	1	4	yes	—
38	C₂²×#1055	C₂×C₄	1	4	yes	—
39	C₁₃×#97	C₂×C₄	1	8	yes	—
40	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
41	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
42	C₄×C₈×C₁₃	C₂³	1	2	yes	—
43	C₄×C₈×C₁₃	C₂³	1	2	yes	—
44	#88043	C₂×C₄	1	16	yes	—
45	C₄×#1055	C₂×C₄	1	4	yes	—
46	C₄×#1055	C₂×C₄	1	4	yes	—
47	C₄×#1055	C₂³	1	4	yes	—
48	C₄×#1055	C₂³	1	4	yes	—
49	C₂×#1455	—	13	1	no	maximal, Sylow
50	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	—	2	8	no	—
52	C₂²×C₄×C₁₃	—	2	4	no	—
53	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
55	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
56	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
57	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
58	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
59	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
60	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
61	C₁₃×M₁₆	—	2	16	no	—
62	C₂×C₈×C₁₃	—	2	4	no	—
63	C₂×C₈×C₁₃	M₁₆	1	8	yes	complemented
64	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
65	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
66	C₄²×C₁₃	C₄²	1	4	yes	—
67	C₄²×C₁₃	C₄²	1	2	yes	—
68	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
69	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
70	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
71	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
72	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
73	#6099	—	2	32	no	—
74	C₂×#1055	—	2	8	no	—
75	C₂×#1055	M₁₆	1	16	yes	complemented
76	C₂×#1055	C₂²×C₄	1	8	yes	—
77	C₂×#1055	C₂²×C₄	1	8	yes	—
78	C₂×C₄×M₁₆	—	13	2	no	—
79	C₂×C₄×M₁₆	D₁₃	1	1	yes	characteristic
80	#1455	—	13	8	no	—
81	C₂×#322	—	13	1	no	—
82	C₂×#322	—	13	2	no	—
83	C₂×C₈²	—	13	1	no	—
84	C₂³×C₁₃	—	2	4	no	—
85	C₂³×C₁₃	—	2	2	no	—
86	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
87	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
88	C₂×C₄×C₁₃	—	2	4	no	—
89	C₂×C₄×C₁₃	—	2	2	no	—
90	C₂×C₄×C₁₃	—	2	8	no	—
91	C₂×C₄×C₁₃	—	2	4	no	—
92	C₂×C₄×C₁₃	—	2	8	no	—
93	C₂×C₄×C₁₃	—	2	4	no	—
94	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
95	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
96	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
97	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
98	C₂×C₄×C₁₃	C₂×M₁₆	1	8	yes	—
99	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
100	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
101	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
102	C₈×C₁₃	—	2	4	no	—
103	C₈×C₁₃	C₂×M₁₆	1	8	yes	complemented
104	#1055	—	2	8	no	—
105	#1055	C₂×M₁₆	1	16	yes	complemented
106	C₂²×M₁₆	—	13	4	no	—
107	C₂²×M₁₆	Dic₁₃	1	2	yes	—
108	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
109	C₄×M₁₆	—	13	8	no	—
110	C₄×M₁₆	—	13	8	no	—
111	C₄×M₁₆	Dic₁₃	1	4	yes	—
112	C₄×M₁₆	C₂×D₁₃	1	4	yes	—
113	C₂×#97	—	13	4	no	—
114	C₂×#97	Dic₁₃	1	2	yes	—
115	C₂×C₄×C₈	—	13	2	no	—
116	C₂×C₄×C₈	—	13	2	no	—
117	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
118	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
119	#322	—	13	8	no	—
120	#322	—	13	4	no	—
121	C₈²	—	13	4	no	—
122	C₂²×C₁₃	—	2	4	no	—
123	C₂²×C₁₃	—	2	2	no	—
124	C₂²×C₁₃	—	4	4	no	—
125	C₂²×C₁₃	C₄×M₁₆	1	4	yes	—
126	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
127	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
128	C₄×C₁₃	—	2	4	no	—
129	C₄×C₁₃	—	2	2	no	—
130	C₄×C₁₃	C₄×M₁₆	1	4	yes	—
131	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
132	C₄×C₁₃	C₂²×M₁₆	1	4	yes	—
133	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
134	C₂³×C₄	C₄×D₁₃	1	2	yes	—
135	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
136	C₂×M₁₆	—	2	8	no	—
137	C₂×M₁₆	—	13	16	no	—
138	C₂×M₁₆	—	26	16	no	—
139	C₂×M₁₆	C₂×Dic₁₃	1	8	yes	—
140	C₂²×C₈	—	13	4	no	—
141	C₂²×C₈	—	13	4	no	—
142	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
143	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
144	C₂×C₄²	C₄×D₁₃	1	2	yes	—
145	C₂×C₄²	C₄×D₁₃	1	4	yes	—
146	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
147	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
148	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
149	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
150	#97	—	13	16	no	—
151	#97	C₂×Dic₁₃	1	8	yes	—
152	C₄×C₈	—	13	4	no	—
153	C₄×C₈	—	13	4	no	—
154	C₄×C₈	—	13	4	no	—
155	C₄×C₈	—	13	4	no	—
156	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
157	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
158	C₄×C₈	C₂²×D₁₃	1	2	yes	—
159	C₄×C₈	C₂²×D₁₃	1	2	yes	—
160	C₂×C₁₃	—	4	2	no	—
161	C₂×C₁₃	#1455	1	4	yes	complemented
162	C₂×C₁₃	C₂×C₄×M₁₆	1	2	yes	—
163	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
164	C₂⁴	C₄×Dic₁₃	1	1	yes	characteristic
165	C₂²×C₄	—	2	8	no	—
166	C₂²×C₄	—	2	4	no	—
167	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
168	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
169	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
170	C₂²×C₄	C₄×Dic₁₃	1	4	yes	—
171	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
172	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
173	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
174	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
175	M₁₆	—	2	16	no	—
176	M₁₆	—	26	32	no	—
177	C₂×C₈	—	2	4	no	—
178	C₂×C₈	—	13	16	no	—
179	C₂×C₈	—	13	8	no	—
180	C₂×C₈	—	13	8	no	—
181	C₂×C₈	—	26	8	no	—
182	C₂×C₈	#6099	1	8	yes	complemented
183	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
184	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
185	C₄²	C₄×Dic₁₃	1	4	yes	—
186	C₄²	C₄×Dic₁₃	1	2	yes	—
187	C₄²	C₂×C₄×D₁₃	1	2	yes	—
188	C₄²	C₂×C₄×D₁₃	1	4	yes	—
189	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
190	C₄²	C₂²×Dic₁₃	1	2	yes	—
191	C₄²	C₂³×D₁₃	1	1	yes	characteristic
192	C₁₃	C₂×#1455	1	1	yes	characteristic, complemented, Sylow
193	C₂³	—	2	4	no	—
194	C₂³	—	2	2	no	—
195	C₂³	C₂×C₄×Dic₁₃	1	2	yes	—
196	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	8	no	—
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	2	8	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	M₁₆×D₁₃	1	8	yes	—
204	C₂×C₄	C₂×#6099	1	4	yes	—
205	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
206	C₂×C₄	C₂×C₄×Dic₁₃	1	4	yes	—
207	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
208	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
209	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
210	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
211	C₈	—	2	4	no	—
212	C₈	—	13	16	no	—
213	C₈	—	26	8	no	—
214	C₈	C₂×#6099	1	8	yes	complemented
215	C₂²	—	2	4	no	—
216	C₂²	—	2	2	no	—
217	C₂²	—	4	4	no	—
218	C₂²	C₄×#6099	1	2	yes	—
219	C₂²	M₁₆×Dic₁₃	1	4	yes	—
220	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
221	C₄	—	2	4	no	—
222	C₄	—	2	2	no	—
223	C₄	C₄×#6099	1	2	yes	—
224	C₄	M₁₆×Dic₁₃	1	4	yes	—
225	C₄	C₂×M₁₆×D₁₃	1	4	yes	—
226	C₄	C₂²×#6099	1	2	yes	—
227	C₂	—	4	2	no	—
228	C₂	#13113139	1	4	yes	direct product factor
229	C₂	C₂×M₁₆×Dic₁₃	1	2	yes	—
230	C₂	C₂×C₄×#6099	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂²×C₄²
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₄×C₁₃×M₁₆	C₂
socle	C₂³×C₁₃	C₂×C₄²
prime radical	C₂⁴×C₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₁₃
hypocenter	C₁₃	C₂×#1455
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. #13113139	C₂	direct (N × H)
3. C₂×#11718046	C₂	semidirect
4. C₂×#11718047	C₂	semidirect
5. C₂×C₈×#1055	C₂	semidirect
20. #11718047	C₂²	semidirect
21. #11718046	C₂²	semidirect
22. C₈×#1055	C₂²	semidirect
63. C₂×C₈×C₁₃	M₁₆	semidirect
75. C₂×#1055	M₁₆	semidirect
103. C₈×C₁₃	C₂×M₁₆	semidirect
105. #1055	C₂×M₁₆	semidirect
161. C₂×C₁₃	#1455	semidirect
182. C₂×C₈	#6099	semidirect
192. C₁₃	C₂×#1455	semidirect
214. C₈	C₂×#6099	semidirect
228. C₂	#13113139	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×C₄×#6099	2
#13113139	2
C₂×#11718046	2
C₂×#11718047	2
C₂×C₈×#1055	2
C₂×C₄×C₁₃×M₁₆	2
C₂×#1455	13

Subgroups — C2×#13113139 #15828625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13113139 #15828625