Subgroups — C₂×#13112817 #15772733

Order 3328.

346 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×#11718340	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718053	C₂	1	1	yes	maximal, characteristic
3	#13112817	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×Dic₂₆	C₄	1	1	yes	characteristic
6	C₂²×C₁₃×C₁₆	—	2	1	no	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88055	—	2	1	no	—
9	C₂×#88054	—	2	1	no	—
10	C₂²×#6090	—	2	1	no	—
11	C₂×C₄⋊#1055	C₄	1	1	yes	characteristic
12	#11718340	—	2	1	no	—
13	#11718340	—	2	1	no	—
14	#11718340	C₄	1	2	yes	—
15	#11718340	C₂²	1	2	yes	—
16	C₁₃×C₄⋊C₁₆	—	2	1	no	—
17	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
18	#11718053	—	2	1	no	—
19	#11718053	C₂²	1	2	yes	—
20	C₂²×Dic₂₆	C₈	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₃	C₈	1	1	yes	characteristic
25	C₂×#6101	—	2	1	no	—
26	C₂×C₄×Dic₁₃	—	2	1	no	—
27	C₂²×#1055	—	2	1	no	—
28	C₄×Dic₂₆	—	2	1	no	—
29	C₄×Dic₂₆	—	2	1	no	—
30	C₄×Dic₂₆	C₈	1	2	yes	—
31	C₄×Dic₂₆	C₂×C₄	1	2	yes	—
32	C₂×C₁₃×C₁₆	—	2	2	no	—
33	C₂×C₁₃×C₁₆	—	4	2	no	—
34	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
36	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
37	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
38	#88055	—	2	2	no	—
39	#88055	—	2	2	no	—
40	#88054	—	2	2	no	—
41	#88054	—	2	2	no	—
42	C₂×#6090	—	2	4	no	—
43	C₂×#6090	—	2	2	no	—
44	C₄⋊#1055	—	2	1	no	—
45	C₄⋊#1055	C₂×C₄	1	2	yes	—
46	C₂×#1338	—	13	1	no	maximal, Sylow
47	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
50	C₂²×Dic₁₃	—	2	1	no	—
51	C₂²×Dic₁₃	—	2	1	no	—
52	C₂×Dic₂₆	—	2	1	no	—
53	C₂×Dic₂₆	—	4	2	no	—
54	C₂×Dic₂₆	C₂×C₈	1	2	yes	—
55	C₂×C₈×C₁₃	—	2	2	no	—
56	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
57	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
59	C₂×C₈×C₁₃	Q₁₆	1	2	yes	—
60	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
61	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
62	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
64	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
65	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₄⋊Dic₁₃	—	2	1	no	—
67	C₄⋊Dic₁₃	C₂×C₈	1	2	yes	—
68	#6101	—	2	2	no	—
69	#6101	—	2	2	no	—
70	C₄×Dic₁₃	—	2	2	no	—
71	C₄×Dic₁₃	—	2	2	no	—
72	C₂×#1055	—	2	2	no	—
73	C₂×#1055	—	4	2	no	—
74	C₁₃×C₁₆	—	4	2	no	—
75	#6090	—	2	4	no	—
76	C₂×#446	—	13	1	no	—
77	C₂×C₄⋊C₁₆	D₁₃	1	1	yes	characteristic
78	C₂×#346	—	13	1	no	—
79	#1338	—	13	4	no	—
80	C₂³×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
81	C₂×C₄×C₁₃	—	2	2	no	—
82	C₂×C₄×C₁₃	—	2	2	no	—
83	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
85	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
86	C₂×C₄×C₁₃	#103	1	2	yes	—
87	C₂×C₄×C₁₃	#104	1	2	yes	—
88	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
91	C₂×Dic₁₃	—	2	2	no	—
92	C₂×Dic₁₃	—	2	2	no	—
93	C₂×Dic₁₃	—	4	2	no	—
94	C₂×Dic₁₃	—	4	2	no	—
95	Dic₂₆	—	4	2	no	—
96	Dic₂₆	—	4	2	no	—
97	C₈×C₁₃	—	2	1	no	—
98	C₈×C₁₃	—	2	1	no	—
99	C₈×C₁₃	#103	1	2	yes	—
100	C₈×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
101	C₈×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
102	#1055	—	4	2	no	—
103	C₂×C₄×Q₈	—	13	1	no	—
104	C₂²×C₁₆	—	2	1	no	—
105	C₂²×C₁₆	—	26	1	no	—
106	#446	—	13	2	no	—
107	#446	—	13	2	no	—
108	#446	—	26	1	no	—
109	#446	—	26	1	no	—
110	C₂×C₄⋊C₈	—	13	1	no	—
111	C₂×C₄⋊C₈	—	26	1	no	—
112	C₂×#97	—	26	1	no	—
113	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
114	C₄⋊C₁₆	—	2	1	no	—
115	C₄⋊C₁₆	C₂×D₁₃	1	2	yes	—
116	#346	—	13	2	no	—
117	#346	—	26	1	no	—
118	C₂²×C₁₃	Q₈⋊C₈	1	2	yes	—
119	C₂²×C₁₃	#349	1	2	yes	—
120	C₂²×C₁₃	#350	1	2	yes	—
121	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
122	C₄×C₁₃	—	2	1	no	—
123	C₄×C₁₃	—	2	1	no	—
124	C₄×C₁₃	—	2	1	no	—
125	C₄×C₁₃	—	2	1	no	—
126	C₄×C₁₃	Q₈⋊C₈	1	2	yes	—
127	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
128	C₄×C₁₃	C₂×#104	1	1	yes	characteristic
129	Dic₁₃	—	4	2	no	—
130	Dic₁₃	—	4	2	no	—
131	C₂²×Q₈	—	13	1	no	—
132	C₂²×C₈	—	26	1	no	—
133	C₂²×C₈	D₅₂	1	1	yes	characteristic
134	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
135	C₄×Q₈	—	13	2	no	—
136	C₄×Q₈	—	13	2	no	—
137	C₄×Q₈	—	26	1	no	—
138	C₄×Q₈	—	26	1	no	—
139	C₂×C₄⋊C₄	—	13	1	no	—
140	C₂×C₄⋊C₄	—	26	1	no	—
141	C₂×C₄²	—	26	1	no	—
142	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
143	C₂×C₁₆	—	2	2	no	—
144	C₂×C₁₆	—	4	2	no	—
145	C₂×C₁₆	—	26	4	no	—
146	C₂×C₁₆	—	26	2	no	—
147	C₄⋊C₈	—	13	2	no	—
148	C₄⋊C₈	—	26	2	no	—
149	C₄⋊C₈	—	26	2	no	—
150	C₄⋊C₈	—	26	1	no	—
151	#97	—	26	2	no	—
152	#97	—	26	2	no	—
153	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
154	C₄×C₈	D₅₂	1	1	yes	characteristic
155	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
156	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
157	C₂×C₁₃	#1338	1	4	yes	complemented
158	C₂×C₁₃	C₂×Q₈⋊C₈	1	1	yes	characteristic
159	C₂×C₁₃	C₂×#349	1	1	yes	characteristic
160	C₂×C₁₃	C₂×#350	1	1	yes	characteristic
161	C₂×Q₈	—	13	2	no	—
162	C₂×Q₈	—	26	1	no	—
163	C₂×Q₈	—	52	2	no	—
164	C₂²×C₄	—	26	1	no	—
165	C₂²×C₄	—	26	1	no	—
166	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
167	C₂²×C₄	#6094	1	1	yes	characteristic
168	C₂²×C₄	#6103	1	1	yes	characteristic
169	C₂×C₈	—	2	2	no	—
170	C₂×C₈	—	26	2	no	—
171	C₂×C₈	—	52	2	no	—
172	C₂×C₈	#6103	1	1	yes	characteristic
173	C₂×C₈	#6103	1	1	yes	characteristic
174	C₂×C₈	#6105	1	2	yes	—
175	C₂×C₈	#6107	1	2	yes	—
176	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
177	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
178	C₄⋊C₄	—	13	2	no	—
179	C₄⋊C₄	—	26	2	no	—
180	C₄⋊C₄	—	26	1	no	—
181	C₄⋊C₄	—	26	2	no	—
182	C₄²	—	26	2	no	—
183	C₄²	—	26	2	no	—
184	C₄²	C₈×D₁₃	1	1	yes	characteristic
185	C₄²	#6094	1	1	yes	characteristic
186	C₄²	#6103	1	1	yes	characteristic
187	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
188	C₁₆	—	4	2	no	—
189	C₁₆	—	26	4	no	—
190	C₁₃	C₂×#1338	1	1	yes	characteristic, complemented, Sylow
191	C₂³	#88060	1	1	yes	characteristic
192	Q₈	—	52	2	no	—
193	Q₈	—	52	2	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	26	2	no	—
197	C₂×C₄	—	26	2	no	—
198	C₂×C₄	—	52	2	no	—
199	C₂×C₄	—	52	2	no	—
200	C₂×C₄	#88050	1	2	yes	—
201	C₂×C₄	#88060	1	1	yes	characteristic
202	C₂×C₄	#88060	1	1	yes	characteristic
203	C₂×C₄	#88060	1	1	yes	characteristic
204	C₂×C₄	#88065	1	2	yes	—
205	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
206	C₂×C₄	C₂×#6094	1	1	yes	characteristic
207	C₂×C₄	C₂×#6103	1	1	yes	characteristic
208	C₈	—	2	1	no	—
209	C₈	—	2	1	no	—
210	C₈	—	52	2	no	—
211	C₈	#88050	1	2	yes	—
212	C₈	C₂×#6105	1	1	yes	characteristic
213	C₈	C₂×#6107	1	1	yes	characteristic
214	C₂²	#11718076	1	2	yes	—
215	C₂²	#11718100	1	2	yes	—
216	C₂²	#11718106	1	2	yes	—
217	C₂²	C₂×#88060	1	1	yes	characteristic
218	C₄	—	2	1	no	—
219	C₄	—	2	1	no	—
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	52	2	no	—
223	C₄	—	52	2	no	—
224	C₄	#11718076	1	2	yes	—
225	C₄	C₂×#88050	1	1	yes	characteristic
226	C₄	C₂×#88065	1	1	yes	characteristic
227	C₂	#13112817	1	4	yes	direct product factor
228	C₂	C₂×#11718076	1	1	yes	characteristic
229	C₂	C₂×#11718106	1	1	yes	characteristic
230	C₂	C₂×#11718100	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#6103
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×C₄⋊C₁₆	C₂
socle, prime radical	C₂³×C₁₃	C₂²⋊C₈
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	C₂×C₄⋊C₁₆	D₁₃
hypocenter	C₁₃	C₂×#1338
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
3. #13112817	C₂	direct (N × H)
157. C₂×C₁₃	#1338	semidirect
190. C₁₃	C₂×#1338	semidirect
227. C₂	#13112817	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×#11718340	2
C₂×#11718053	2
#13112817	2
C₂×C₁₃×C₄⋊C₁₆	2
C₂×#1338	13

Subgroups — C2×#13112817 #15772733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112817 #15772733