Subgroups — C₂×#13114955 #15863065

Order 3328.

1006 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718593	C₂	1	1	yes	maximal, characteristic
3	#13114955	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718142	C₂	1	4	yes	maximal
5	C₂²×C₁₃×C₄⋊C₈	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	C₂²	1	2	yes	—
9	C₂³×#1055	C₂²	1	2	yes	—
10	C₂×C₁₃×C₄⋊C₈	—	2	4	no	—
11	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
12	C₂×#88071	C₄	1	2	yes	—
13	C₂×#88071	C₄	1	2	yes	—
14	#11718593	C₄	1	4	yes	—
15	#11718593	C₂²	1	4	yes	—
16	C₂×C₄⋊#1055	—	2	4	no	—
17	C₂×C₄⋊#1055	C₂²	1	4	yes	—
18	#11718142	C₂²	1	16	yes	—
19	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
22	C₂³×Dic₁₃	C₂×C₄	1	4	yes	—
23	C₂²×C₈×C₁₃	—	2	4	no	—
24	C₂²×C₈×C₁₃	—	2	8	no	—
25	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
26	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₃	D₄	1	4	yes	—
28	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
29	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
30	C₂×C₄×Dic₁₃	—	2	4	no	—
31	C₂×C₄×Dic₁₃	—	2	4	no	—
32	C₂×C₄×Dic₁₃	C₂×C₄	1	4	yes	—
33	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
34	C₂²×#1055	—	2	4	no	—
35	C₂²×#1055	—	2	8	no	—
36	C₂²×#1055	C₂³	1	4	yes	—
37	C₁₃×C₄⋊C₈	—	2	8	no	—
38	#88071	C₂×C₄	1	8	yes	—
39	#88071	C₂×C₄	1	8	yes	—
40	C₄⋊#1055	—	2	8	no	—
41	C₂×#1832	—	13	1	no	maximal, Sylow
42	C₂⁴×C₁₃	C₂²×C₄	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	4	yes	—
46	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
47	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
49	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
51	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
52	C₂²×C₄×C₁₃	#41	1	4	yes	—
53	C₂²×C₄×C₁₃	#41	1	4	yes	—
54	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
55	C₂²×Dic₁₃	—	2	8	no	—
56	C₂²×Dic₁₃	—	2	8	no	—
57	C₂²×Dic₁₃	—	2	8	no	—
58	C₂²×Dic₁₃	C₂²×C₄	1	8	yes	—
59	C₂×C₈×C₁₃	—	2	4	no	—
60	C₂×C₈×C₁₃	—	2	8	no	—
61	C₂×C₈×C₁₃	—	4	8	no	—
62	C₄²×C₁₃	C₄⋊C₄	1	8	yes	—
63	C₄²×C₁₃	C₂×D₄	1	4	yes	—
64	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
65	C₄×Dic₁₃	—	2	8	no	—
66	C₄×Dic₁₃	—	2	4	no	—
67	C₄×Dic₁₃	—	2	4	no	—
68	C₂×#1055	—	2	4	no	—
69	C₂×#1055	—	2	8	no	—
70	C₂×#1055	—	4	8	no	—
71	C₂²×C₄⋊C₈	—	13	1	no	—
72	C₂²×C₄⋊C₈	D₁₃	1	1	yes	characteristic
73	C₂×#376	—	13	1	no	—
74	#1832	—	13	8	no	—
75	C₂×#336	—	13	4	no	—
76	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
77	C₂³×C₁₃	#117	1	4	yes	—
78	C₂³×C₁₃	#131	1	4	yes	—
79	C₂³×C₁₃	#131	1	4	yes	—
80	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₃	—	2	4	no	—
82	C₂×C₄×C₁₃	—	2	4	no	—
83	C₂×C₄×C₁₃	—	2	8	no	—
84	C₂×C₄×C₁₃	—	2	8	no	—
85	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
86	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
87	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
88	C₂×C₄×C₁₃	#117	1	4	yes	—
89	C₂×C₄×C₁₃	#124	1	4	yes	—
90	C₂×C₄×C₁₃	#124	1	4	yes	—
91	C₂×C₄×C₁₃	#125	1	8	yes	—
92	C₂×C₄×C₁₃	C₂²×D₄	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	—	2	8	no	—
97	C₂×Dic₁₃	—	2	8	no	—
98	C₂×Dic₁₃	—	2	8	no	—
99	C₂×Dic₁₃	—	4	16	no	—
100	C₈×C₁₃	—	4	4	no	—
101	#1055	—	4	4	no	—
102	C₂³×C₈	—	13	2	no	—
103	C₂³×C₈	C₂×D₁₃	1	2	yes	—
104	C₂²×C₄²	—	13	2	no	—
105	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
106	C₂×C₄⋊C₈	—	2	4	no	—
107	C₂×C₄⋊C₈	—	13	4	no	—
108	C₂×C₄⋊C₈	—	26	4	no	—
109	C₂×C₄⋊C₈	C₂×D₁₃	1	4	yes	—
110	#376	—	13	4	no	—
111	#376	—	13	4	no	—
112	C₂×#95	—	13	2	no	—
113	C₂×#95	—	13	2	no	—
114	#336	—	13	16	no	—
115	C₂²×C₁₃	#382	1	4	yes	—
116	C₂²×C₁₃	#424	1	4	yes	—
117	C₂²×C₁₃	#424	1	4	yes	—
118	C₂²×C₁₃	#433	1	16	yes	—
119	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
120	C₂²×C₁₃	C₂×#117	1	2	yes	—
121	C₂²×C₁₃	C₂×#131	1	2	yes	—
122	C₂²×C₁₃	C₂×#131	1	2	yes	—
123	C₄×C₁₃	—	2	4	no	—
124	C₄×C₁₃	—	2	4	no	—
125	C₄×C₁₃	#382	1	4	yes	—
126	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
127	C₄×C₁₃	C₂×#124	1	1	yes	characteristic
128	C₄×C₁₃	C₂×#125	1	2	yes	—
129	Dic₁₃	—	4	8	no	—
130	C₂³×C₄	—	13	4	no	—
131	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
132	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
133	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
134	C₂²×C₈	—	2	8	no	—
135	C₂²×C₈	—	2	4	no	—
136	C₂²×C₈	—	13	4	no	—
137	C₂²×C₈	—	26	8	no	—
138	C₂²×C₈	—	26	4	no	—
139	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
140	C₂×C₄²	—	13	4	no	—
141	C₂×C₄²	—	13	4	no	—
142	C₂×C₄²	—	26	4	no	—
143	C₂×C₄²	—	26	4	no	—
144	C₂×C₄²	Dic₂₆	1	4	yes	—
145	C₂×C₄²	C₄×D₁₃	1	2	yes	—
146	C₂×C₄²	C₂²⋊D₁₃	1	4	yes	—
147	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
148	C₄⋊C₈	—	2	8	no	—
149	C₄⋊C₈	—	26	8	no	—
150	#95	—	13	8	no	—
151	#95	—	13	8	no	—
152	C₂×C₁₃	#1832	1	8	yes	complemented
153	C₂×C₁₃	C₂×#382	1	1	yes	characteristic
154	C₂×C₁₃	C₂×#424	1	1	yes	characteristic
155	C₂×C₁₃	C₂×#424	1	1	yes	characteristic
156	C₂×C₁₃	C₂×#433	1	4	yes	—
157	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
158	C₂²×C₄	—	2	4	no	—
159	C₂²×C₄	—	2	4	no	—
160	C₂²×C₄	—	13	8	no	—
161	C₂²×C₄	—	26	8	no	—
162	C₂²×C₄	—	26	8	no	—
163	C₂²×C₄	—	26	8	no	—
164	C₂²×C₄	#6101	1	4	yes	—
165	C₂²×C₄	#6101	1	4	yes	—
166	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
167	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
168	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
169	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
170	C₂²×C₄	#6129	1	4	yes	—
171	C₂²×C₄	#6131	1	4	yes	—
172	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
173	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
174	C₂×C₈	—	2	8	no	—
175	C₂×C₈	—	2	4	no	—
176	C₂×C₈	—	4	8	no	—
177	C₂×C₈	—	26	8	no	—
178	C₂×C₈	—	26	4	no	—
179	C₂×C₈	—	52	8	no	—
180	C₄²	—	26	8	no	—
181	C₄²	—	26	4	no	—
182	C₄²	—	26	4	no	—
183	C₄²	#6101	1	8	yes	—
184	C₄²	C₂×Dic₂₆	1	4	yes	—
185	C₄²	C₂×C₂²⋊D₁₃	1	4	yes	—
186	C₁₃	C₂×#1832	1	1	yes	characteristic, complemented, Sylow
187	C₂³	#88146	1	4	yes	—
188	C₂³	#88155	1	4	yes	—
189	C₂³	#88161	1	4	yes	—
190	C₂³	C₂×#6101	1	2	yes	—
191	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
192	C₂×C₄	—	2	4	no	—
193	C₂×C₄	—	2	4	no	—
194	C₂×C₄	—	2	8	no	—
195	C₂×C₄	—	2	8	no	—
196	C₂×C₄	—	26	8	no	—
197	C₂×C₄	—	26	8	no	—
198	C₂×C₄	—	26	8	no	—
199	C₂×C₄	—	52	16	no	—
200	C₂×C₄	#88144	1	8	yes	—
201	C₂×C₄	#88146	1	4	yes	—
202	C₂×C₄	C₂×#6101	1	4	yes	—
203	C₂×C₄	C₂×#6101	1	4	yes	—
204	C₂×C₄	C₂×#6101	1	2	yes	—
205	C₂×C₄	#88190	1	4	yes	—
206	C₂×C₄	#88201	1	4	yes	—
207	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
208	C₂×C₄	C₂×#6129	1	2	yes	—
209	C₂×C₄	C₂×#6131	1	2	yes	—
210	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
211	C₈	—	4	4	no	—
212	C₈	—	52	4	no	—
213	C₂²	#11718501	1	16	yes	—
214	C₂²	#11718638	1	4	yes	—
215	C₂²	#11718763	1	4	yes	—
216	C₂²	#11718780	1	4	yes	—
217	C₂²	C₂×#88146	1	2	yes	—
218	C₂²	C₂×#88155	1	2	yes	—
219	C₂²	C₂×#88161	1	2	yes	—
220	C₂²	C₂²×#6101	1	1	yes	characteristic
221	C₄	—	2	4	no	—
222	C₄	—	2	4	no	—
223	C₄	—	52	8	no	—
224	C₄	#11718638	1	4	yes	—
225	C₄	C₂×#88144	1	2	yes	—
226	C₄	C₂×#88190	1	1	yes	characteristic
227	C₄	C₂×#88201	1	1	yes	characteristic
228	C₂	#13114955	1	8	yes	direct product factor
229	C₂	C₂×#11718638	1	1	yes	characteristic
230	C₂	C₂×#11718763	1	1	yes	characteristic
231	C₂	C₂×#11718780	1	1	yes	characteristic
232	C₂	C₂×#11718501	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₁₃
commutator	C₂³×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂²×C₁₃×C₄⋊C₈	C₂
socle, prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂²×C₄⋊C₈	D₁₃
hypocenter	C₁₃	C₂×#1832
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #13114955	C₂	direct (N × H)
152. C₂×C₁₃	#1832	semidirect
186. C₁₃	C₂×#1832	semidirect
228. C₂	#13114955	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₄⋊#1055	2
C₂×#11718593	2
#13114955	2
C₂×#11718142	2
C₂²×C₁₃×C₄⋊C₈	2
C₂×#1832	13

Subgroups — C2×#13114955 #15863065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13114955 #15863065