Subgroups — C₂×#13114970 #15863116

Order 3328.

1054 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718596	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718597	C₂	1	1	yes	maximal, characteristic
3	#13114970	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718143	C₂	1	4	yes	maximal
5	C₂²×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
7	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₁₃	—	2	2	no	—
9	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
10	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
11	C₂×C₁₃×#97	C₄	1	8	yes	complemented
12	C₂×C₁₃×#97	C₂²	1	4	yes	—
13	C₂×#88071	—	2	2	no	—
14	#11718597	—	2	2	no	—
15	#11718597	C₂²	1	4	yes	—
16	#11718596	—	2	2	no	—
17	#11718596	C₂²	1	4	yes	—
18	#11718143	C₂²	1	16	yes	—
19	C₂³×C₄×C₁₃	D₄	1	2	yes	—
20	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
21	C₂³×Dic₁₃	—	2	2	no	—
22	C₂³×Dic₁₃	—	2	2	no	—
23	C₂²×C₈×C₁₃	—	2	4	no	—
24	C₂²×C₈×C₁₃	—	2	4	no	—
25	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	—
26	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
27	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
28	C₂×C₄²×C₁₃	D₄	1	2	yes	—
29	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
30	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
31	C₂×C₄⋊Dic₁₃	—	2	8	no	—
32	C₂×C₄⋊Dic₁₃	—	2	8	no	—
33	C₂×C₄⋊Dic₁₃	—	2	8	no	—
34	C₂×C₄⋊Dic₁₃	—	2	2	no	—
35	C₂×C₄⋊Dic₁₃	—	2	2	no	—
36	C₂×C₄⋊Dic₁₃	—	4	8	no	—
37	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
38	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
39	C₁₃×#97	C₂×C₄	1	16	yes	complemented
40	#88071	—	2	8	no	—
41	C₂×#1836	—	13	1	no	maximal, Sylow
42	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	—	2	4	no	—
44	C₂²×C₄×C₁₃	—	2	4	no	—
45	C₂²×C₄×C₁₃	C₄⋊C₄	1	8	yes	—
46	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
47	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
48	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
50	C₂²×C₄×C₁₃	#41	1	4	yes	—
51	C₂²×C₄×C₁₃	#41	1	4	yes	—
52	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
53	C₂²×Dic₁₃	—	2	4	no	—
54	C₂²×Dic₁₃	—	2	4	no	—
55	C₂²×Dic₁₃	—	4	4	no	—
56	C₂²×Dic₁₃	—	4	4	no	—
57	C₂²×Dic₁₃	—	4	8	no	—
58	C₂²×Dic₁₃	—	4	4	no	—
59	C₂²×Dic₁₃	—	4	4	no	—
60	C₂×C₈×C₁₃	—	2	16	no	—
61	C₂×C₈×C₁₃	—	2	4	no	—
62	C₂×C₈×C₁₃	—	2	4	no	—
63	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
64	C₄²×C₁₃	C₄⋊C₄	1	8	yes	—
65	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
66	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
67	C₄⋊Dic₁₃	—	2	8	no	—
68	C₄⋊Dic₁₃	—	2	8	no	—
69	C₄⋊Dic₁₃	—	4	16	no	—
70	C₄⋊Dic₁₃	—	4	4	no	—
71	C₄⋊Dic₁₃	—	4	4	no	—
72	C₂²×#97	D₁₃	1	1	yes	characteristic
73	C₂×#384	—	13	1	no	—
74	C₂×#382	—	13	1	no	—
75	#1836	—	13	8	no	—
76	C₂×#340	—	13	4	no	—
77	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
78	C₂³×C₁₃	#124	1	2	yes	—
79	C₂³×C₁₃	#124	1	2	yes	—
80	C₂³×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
81	C₂³×C₁₃	#137	1	4	yes	—
82	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
83	C₂×C₄×C₁₃	—	2	4	no	—
84	C₂×C₄×C₁₃	—	2	4	no	—
85	C₂×C₄×C₁₃	—	2	16	no	—
86	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
87	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
88	C₂×C₄×C₁₃	#117	1	8	yes	—
89	C₂×C₄×C₁₃	#124	1	2	yes	—
90	C₂×C₄×C₁₃	#124	1	2	yes	—
91	C₂×C₄×C₁₃	#125	1	8	yes	—
92	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
94	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
95	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
96	C₂×Dic₁₃	—	4	4	no	—
97	C₂×Dic₁₃	—	4	4	no	—
98	C₂×Dic₁₃	—	4	8	no	—
99	C₂×Dic₁₃	—	4	4	no	—
100	C₂×Dic₁₃	—	4	4	no	—
101	C₂×Dic₁₃	—	8	8	no	—
102	C₂×Dic₁₃	—	8	8	no	—
103	C₈×C₁₃	—	2	8	no	—
104	C₂³×C₈	C₂×D₁₃	1	2	yes	—
105	C₂²×C₄⋊C₄	—	13	2	no	—
106	C₂²×C₄⋊C₄	—	13	2	no	—
107	C₂²×C₄⋊C₄	—	26	2	no	—
108	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
109	C₂×#97	Dic₁₃	1	8	yes	complemented
110	C₂×#97	C₂×D₁₃	1	4	yes	—
111	#384	—	13	4	no	—
112	#384	—	26	2	no	—
113	#382	—	13	4	no	—
114	#382	—	26	2	no	—
115	C₂×#95	—	26	2	no	—
116	#340	—	13	16	no	—
117	C₂²×C₁₃	#382	1	4	yes	—
118	C₂²×C₁₃	#428	1	8	yes	—
119	C₂²×C₁₃	#489	1	8	yes	—
120	C₂²×C₁₃	#490	1	4	yes	—
121	C₂²×C₁₃	#491	1	4	yes	—
122	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
123	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
124	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
125	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
126	C₂²×C₁₃	C₂×#137	1	2	yes	—
127	C₄×C₁₃	—	2	8	no	—
128	C₄×C₁₃	#382	1	4	yes	—
129	C₄×C₁₃	C₂×#117	1	2	yes	—
130	C₄×C₁₃	C₂×#125	1	2	yes	—
131	Dic₁₃	—	8	4	no	—
132	Dic₁₃	—	8	4	no	—
133	C₂³×C₄	—	26	2	no	—
134	C₂³×C₄	—	26	2	no	—
135	C₂³×C₄	D₅₂	1	2	yes	—
136	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
137	C₂²×C₈	—	2	4	no	—
138	C₂²×C₈	—	2	4	no	—
139	C₂²×C₈	C₂×Dic₁₃	1	8	yes	—
140	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
141	C₂×C₄⋊C₄	—	13	4	no	—
142	C₂×C₄⋊C₄	—	13	4	no	—
143	C₂×C₄⋊C₄	—	26	8	no	—
144	C₂×C₄⋊C₄	—	26	8	no	—
145	C₂×C₄⋊C₄	—	26	2	no	—
146	C₂×C₄⋊C₄	—	26	2	no	—
147	C₂×C₄⋊C₄	—	26	8	no	—
148	C₂×C₄⋊C₄	—	52	8	no	—
149	C₂×C₄²	Dic₂₆	1	4	yes	—
150	C₂×C₄²	D₅₂	1	2	yes	—
151	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
152	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
153	#97	C₂×Dic₁₃	1	16	yes	complemented
154	#95	—	26	8	no	—
155	C₂×C₁₃	#1836	1	8	yes	complemented
156	C₂×C₁₃	C₂×#382	1	1	yes	characteristic
157	C₂×C₁₃	C₂×#428	1	2	yes	—
158	C₂×C₁₃	C₂×#489	1	2	yes	—
159	C₂×C₁₃	C₂×#490	1	1	yes	characteristic
160	C₂×C₁₃	C₂×#491	1	1	yes	characteristic
161	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
162	C₂²×C₄	—	2	4	no	—
163	C₂²×C₄	—	2	4	no	—
164	C₂²×C₄	—	26	4	no	—
165	C₂²×C₄	—	26	4	no	—
166	C₂²×C₄	—	52	4	no	—
167	C₂²×C₄	—	52	4	no	—
168	C₂²×C₄	—	52	8	no	—
169	C₂²×C₄	—	52	4	no	—
170	C₂²×C₄	—	52	4	no	—
171	C₂²×C₄	C₄⋊Dic₁₃	1	8	yes	—
172	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
173	C₂²×C₄	C₂×D₅₂	1	4	yes	—
174	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
175	C₂²×C₄	#6127	1	4	yes	—
176	C₂²×C₄	#6127	1	4	yes	—
177	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
178	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
179	C₂×C₈	—	2	16	no	—
180	C₂×C₈	—	2	4	no	—
181	C₂×C₈	—	2	4	no	—
182	C₂×C₈	C₂²×Dic₁₃	1	8	yes	—
183	C₄⋊C₄	—	26	8	no	—
184	C₄⋊C₄	—	26	8	no	—
185	C₄⋊C₄	—	52	16	no	—
186	C₄⋊C₄	—	52	4	no	—
187	C₄⋊C₄	—	52	4	no	—
188	C₄²	C₄⋊Dic₁₃	1	8	yes	—
189	C₄²	C₂×Dic₂₆	1	4	yes	—
190	C₄²	C₂²×Dic₁₃	1	4	yes	—
191	C₁₃	C₂×#1836	1	1	yes	characteristic, complemented, Sylow
192	C₂³	#88129	1	2	yes	—
193	C₂³	#88129	1	2	yes	—
194	C₂³	#88162	1	4	yes	—
195	C₂³	#88163	1	4	yes	—
196	C₂³	C₂×C₄⋊Dic₁₃	1	2	yes	—
197	C₂³	C₂²×D₅₂	1	1	yes	characteristic
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	4	no	—
200	C₂×C₄	—	2	16	no	—
201	C₂×C₄	—	52	4	no	—
202	C₂×C₄	—	52	4	no	—
203	C₂×C₄	—	52	8	no	—
204	C₂×C₄	—	52	4	no	—
205	C₂×C₄	—	52	4	no	—
206	C₂×C₄	—	104	8	no	—
207	C₂×C₄	—	104	8	no	—
208	C₂×C₄	#88124	1	8	yes	—
209	C₂×C₄	#88129	1	2	yes	—
210	C₂×C₄	#88129	1	2	yes	—
211	C₂×C₄	C₂×C₄⋊Dic₁₃	1	8	yes	—
212	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
213	C₂×C₄	#88180	1	8	yes	—
214	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
215	C₂×C₄	C₂×#6127	1	2	yes	—
216	C₂×C₄	C₂×#6127	1	2	yes	—
217	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
218	C₈	—	2	8	no	—
219	C₂²	#11718364	1	4	yes	—
220	C₂²	#11718374	1	4	yes	—
221	C₂²	#11718375	1	8	yes	—
222	C₂²	#11718597	1	4	yes	—
223	C₂²	#11718782	1	8	yes	—
224	C₂²	C₂×#88129	1	1	yes	characteristic
225	C₂²	C₂×#88129	1	1	yes	characteristic
226	C₂²	C₂×#88162	1	2	yes	—
227	C₂²	C₂×#88163	1	2	yes	—
228	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
229	C₄	—	2	8	no	—
230	C₄	—	104	4	no	—
231	C₄	—	104	4	no	—
232	C₄	#11718597	1	4	yes	—
233	C₄	C₂×#88124	1	2	yes	—
234	C₄	C₂×#88180	1	2	yes	—
235	C₂	#13114970	1	8	yes	direct product factor
236	C₂	C₂×#11718597	1	1	yes	characteristic
237	C₂	C₂×#11718782	1	2	yes	—
238	C₂	C₂×#11718375	1	2	yes	—
239	C₂	C₂×#11718374	1	1	yes	characteristic
240	C₂	C₂×#11718364	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂²×C₁₃×#97	C₂
socle, prime radical	C₂⁴×C₁₃	C₂×D₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂²×#97	D₁₃
hypocenter	C₁₃	C₂×#1836
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
3. #13114970	C₂	direct (N × H)
11. C₂×C₁₃×#97	C₄	semidirect
39. C₁₃×#97	C₂×C₄	semidirect
109. C₂×#97	Dic₁₃	semidirect
153. #97	C₂×Dic₁₃	semidirect
155. C₂×C₁₃	#1836	semidirect
191. C₁₃	C₂×#1836	semidirect
235. C₂	#13114970	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×#11718596	2
C₂×#11718597	2
#13114970	2
C₂×#11718143	2
C₂²×C₁₃×#97	2
C₂×#1836	13

Subgroups — C2×#13114970 #15863116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13114970 #15863116