Subgroups — C₂×#13113744 #15832682

Order 3328.

654 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718492	C₂	1	2	yes	maximal
2	C₂×C₄×Dic₅₂	C₂	1	1	yes	maximal, characteristic
3	#13113744	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718076	C₂	1	2	yes	maximal
5	C₂×#11718047	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#334	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₅₂	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₂₆	C₂²	1	2	yes	—
9	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×#88058	C₄	1	1	yes	characteristic
12	C₂×#88056	C₄	1	2	yes	—
13	C₂×#88055	—	2	2	no	—
14	C₂×#88054	—	2	2	no	—
15	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
16	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
17	#11718492	—	2	4	no	—
18	#11718492	C₂²	1	8	yes	—
19	C₄×Dic₅₂	C₄	1	4	yes	—
20	C₄×Dic₅₂	C₂²	1	4	yes	—
21	C₁₃×#334	C₂²	1	4	yes	—
22	#11718076	C₂²	1	8	yes	—
23	#11718047	C₂²	1	4	yes	—
24	C₂²×Dic₂₆	C₂×C₄	1	2	yes	—
25	C₂²×C₈×C₁₃	—	2	2	no	—
26	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
30	C₂×#6101	—	2	2	no	—
31	C₂×C₄×Dic₁₃	—	2	2	no	—
32	C₂²×#1055	—	2	1	no	—
33	C₂²×#1055	D₄	1	2	yes	—
34	C₂×Dic₅₂	—	2	4	no	—
35	C₂×Dic₅₂	C₂×C₄	1	4	yes	—
36	C₄×Dic₂₆	—	2	2	no	—
37	C₄×Dic₂₆	—	2	2	no	—
38	C₄×Dic₂₆	C₂×C₄	1	4	yes	—
39	C₄×Dic₂₆	C₂³	1	4	yes	—
40	C₁₃×C₄⋊C₈	—	2	2	no	—
41	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
42	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
43	C₄×C₈×C₁₃	C₂³	1	2	yes	—
44	#88058	C₂×C₄	1	4	yes	—
45	#88056	C₂×C₄	1	8	yes	—
46	#88055	—	2	8	no	—
47	#88054	—	2	8	no	—
48	C₄×#1055	—	2	1	no	—
49	C₄×#1055	D₄	1	2	yes	—
50	C₄×#1055	C₂³	1	2	yes	—
51	C₄×#1055	C₂³	1	2	yes	—
52	C₂×#1593	—	13	1	no	maximal, Sylow
53	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
56	C₂²×Dic₁₃	—	2	2	no	—
57	C₂²×Dic₁₃	—	2	2	no	—
58	C₂×Dic₂₆	—	2	4	no	—
59	C₂×Dic₂₆	—	2	4	no	—
60	C₂×Dic₂₆	—	2	2	no	—
61	C₂×Dic₂₆	C₂²×C₄	1	4	yes	—
62	C₂×C₈×C₁₃	—	2	2	no	—
63	C₂×C₈×C₁₃	—	2	4	no	—
64	C₂×C₈×C₁₃	—	4	4	no	—
65	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
66	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
67	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
68	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
69	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₃	#41	1	1	yes	characteristic
71	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
72	C₄⋊Dic₁₃	—	2	2	no	—
73	C₄⋊Dic₁₃	C₂²×C₄	1	4	yes	—
74	#6101	—	2	4	no	—
75	#6101	—	2	4	no	—
76	C₄×Dic₁₃	—	2	4	no	—
77	C₄×Dic₁₃	—	2	4	no	—
78	C₂×#1055	—	2	4	no	—
79	C₂×#1055	—	2	2	no	—
80	C₂×#1055	—	4	2	no	—
81	C₂×#1055	C₂×D₄	1	4	yes	—
82	Dic₅₂	—	2	8	no	—
83	C₂×#446	—	13	2	no	—
84	C₂×C₄×Q₁₆	—	13	1	no	—
85	#1593	—	13	8	no	—
86	C₂×#334	D₁₃	1	1	yes	characteristic
87	C₂×Q₈⋊C₈	—	13	2	no	—
88	C₂×#322	—	13	1	no	—
89	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
90	C₂×C₄×C₁₃	—	2	2	no	—
91	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
93	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
95	C₂×C₄×C₁₃	#131	1	2	yes	—
96	C₂×C₄×C₁₃	#137	1	4	yes	—
97	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
100	C₂×Dic₁₃	—	2	4	no	—
101	C₂×Dic₁₃	—	2	4	no	—
102	C₂×Dic₁₃	—	4	4	no	—
103	C₂×Dic₁₃	—	4	4	no	—
104	Dic₂₆	—	2	4	no	—
105	Dic₂₆	—	2	4	no	—
106	Dic₂₆	—	4	4	no	—
107	C₈×C₁₃	—	2	2	no	—
108	C₈×C₁₃	—	4	4	no	—
109	C₈×C₁₃	C₂×M₁₆	1	4	yes	—
110	#1055	—	2	4	no	—
111	#1055	—	4	2	no	—
112	C₂²×Q₁₆	—	13	1	no	—
113	C₂×C₄×Q₈	—	13	2	no	—
114	#446	—	13	8	no	—
115	#446	—	26	4	no	—
116	C₄×Q₁₆	—	13	4	no	—
117	C₄×Q₁₆	—	13	4	no	—
118	C₂×#107	—	13	1	no	—
119	C₂×C₄⋊C₈	—	26	2	no	—
120	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
121	C₂×#103	—	13	2	no	—
122	C₂×#97	—	26	2	no	—
123	C₂×C₄×C₈	—	13	1	no	—
124	C₂×C₄×C₈	—	13	1	no	—
125	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
126	#334	C₂×D₁₃	1	4	yes	—
127	Q₈⋊C₈	—	13	8	no	—
128	#322	—	13	4	no	—
129	C₂²×C₁₃	#436	1	2	yes	—
130	C₂²×C₁₃	#441	1	2	yes	—
131	C₂²×C₁₃	#444	1	2	yes	—
132	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
133	C₄×C₁₃	—	2	1	no	—
134	C₄×C₁₃	—	2	1	no	—
135	C₄×C₁₃	#436	1	2	yes	—
136	C₄×C₁₃	#441	1	2	yes	—
137	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
138	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
139	C₄×C₁₃	C₂×#137	1	2	yes	—
140	Dic₁₃	—	4	4	no	—
141	Dic₁₃	—	4	4	no	—
142	C₂²×Q₈	—	13	2	no	—
143	C₂×Q₁₆	—	13	4	no	—
144	C₂×Q₁₆	—	26	4	no	—
145	C₂²×C₈	—	2	2	no	—
146	C₂²×C₈	—	13	2	no	—
147	C₂²×C₈	—	26	1	no	—
148	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
149	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
150	C₄×Q₈	—	13	4	no	—
151	C₄×Q₈	—	13	4	no	—
152	C₄×Q₈	—	26	2	no	—
153	C₄×Q₈	—	26	2	no	—
154	C₂×C₄⋊C₄	—	13	2	no	—
155	C₂×C₄⋊C₄	—	26	2	no	—
156	C₂×C₄²	—	26	2	no	—
157	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
158	#107	—	13	4	no	—
159	C₄⋊C₈	—	2	2	no	—
160	C₄⋊C₈	—	26	8	no	—
161	C₄⋊C₈	C₂²×D₁₃	1	4	yes	—
162	#103	—	13	8	no	—
163	#97	—	26	8	no	—
164	C₄×C₈	—	13	2	no	—
165	C₄×C₈	—	13	2	no	—
166	C₄×C₈	—	13	2	no	—
167	C₄×C₈	—	26	1	no	—
168	C₄×C₈	C₄×D₁₃	1	2	yes	—
169	C₄×C₈	C₂²×D₁₃	1	2	yes	—
170	C₂×C₁₃	#1593	1	4	yes	complemented
171	C₂×C₁₃	C₂×#436	1	1	yes	characteristic
172	C₂×C₁₃	C₂×#441	1	1	yes	characteristic
173	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
174	C₂×Q₈	—	13	4	no	—
175	C₂×Q₈	—	26	2	no	—
176	C₂×Q₈	—	26	4	no	—
177	C₂×Q₈	—	26	4	no	—
178	C₂²×C₄	—	26	2	no	—
179	C₂²×C₄	—	26	2	no	—
180	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
181	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
182	C₂²×C₄	#6131	1	1	yes	characteristic
183	Q₁₆	—	26	8	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	2	4	no	—
186	C₂×C₈	—	4	4	no	—
187	C₂×C₈	—	13	4	no	—
188	C₂×C₈	—	26	4	no	—
189	C₂×C₈	—	26	2	no	—
190	C₂×C₈	—	52	2	no	—
191	C₂×C₈	#6094	1	4	yes	—
192	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
193	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
194	C₄⋊C₄	—	13	4	no	—
195	C₄⋊C₄	—	26	2	no	—
196	C₄⋊C₄	—	26	4	no	—
197	C₄⋊C₄	—	26	4	no	—
198	C₄²	—	26	4	no	—
199	C₄²	—	26	4	no	—
200	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
201	C₄²	D₄×D₁₃	1	1	yes	characteristic
202	C₄²	#6131	1	1	yes	characteristic
203	C₄²	C₂³×D₁₃	1	1	yes	characteristic
204	C₁₃	C₂×#1593	1	1	yes	characteristic, complemented, Sylow
205	C₂³	#88147	1	1	yes	characteristic
206	Q₈	—	26	4	no	—
207	Q₈	—	26	4	no	—
208	Q₈	—	52	4	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	26	4	no	—
211	C₂×C₄	—	26	4	no	—
212	C₂×C₄	—	52	4	no	—
213	C₂×C₄	—	52	4	no	—
214	C₂×C₄	#88147	1	1	yes	characteristic
215	C₂×C₄	#88147	1	1	yes	characteristic
216	C₂×C₄	#88147	1	1	yes	characteristic
217	C₂×C₄	C₂×#6094	1	2	yes	—
218	C₂×C₄	#88161	1	2	yes	—
219	C₂×C₄	#88169	1	4	yes	—
220	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
221	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
222	C₂×C₄	C₂×#6131	1	1	yes	characteristic
223	C₈	—	2	2	no	—
224	C₈	—	4	4	no	—
225	C₈	—	26	4	no	—
226	C₈	—	52	2	no	—
227	C₈	C₂×#6094	1	4	yes	—
228	C₂²	#11718499	1	2	yes	—
229	C₂²	#11718514	1	2	yes	—
230	C₂²	#11718555	1	2	yes	—
231	C₂²	C₂×#88147	1	1	yes	characteristic
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	52	4	no	—
235	C₄	—	52	4	no	—
236	C₄	#11718499	1	2	yes	—
237	C₄	#11718514	1	2	yes	—
238	C₄	C₂²×#6094	1	1	yes	characteristic
239	C₄	C₂×#88161	1	1	yes	characteristic
240	C₄	C₂×#88169	1	2	yes	—
241	C₂	#13113744	1	4	yes	direct product factor
242	C₂	C₂×#11718499	1	1	yes	characteristic
243	C₂	C₂×#11718514	1	1	yes	characteristic
244	C₂	C₂×#11718555	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₁₃×#334	C₂
socle, prime radical	C₂³×C₁₃	C₄×D₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×#334	D₁₃
hypocenter	C₁₃	C₂×#1593
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
3. #13113744	C₂	direct (N × H)
170. C₂×C₁₃	#1593	semidirect
204. C₁₃	C₂×#1593	semidirect
241. C₂	#13113744	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×#11718492	2
C₂×C₄×Dic₅₂	2
#13113744	2
C₂×#11718076	2
C₂×#11718047	2
C₂×C₁₃×#334	2
C₂×#1593	13

Subgroups — C2×#13113744 #15832682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13113744 #15832682