Subgroups — C₂×#13112930 #15777806

Order 3328.

574 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88059	C₂	1	2	yes	maximal
2	#13112930	C₂	1	4	yes	maximal, direct product factor
3	C₂³×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
5	C₂²×#6099	—	2	2	no	—
6	C₂²×C₁₃×C₁₆	—	2	4	no	—
7	C₂²×C₁₃×C₁₆	C₄	1	2	yes	—
8	C₂²×C₁₃×C₁₆	C₄	1	2	yes	—
9	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
10	C₂×#88059	—	2	4	no	—
11	C₂×#88059	—	2	2	no	—
12	C₂×#88059	C₄	1	8	yes	—
13	C₂×#88059	C₂²	1	4	yes	—
14	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	D₄	1	4	yes	—
20	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
23	C₂×#6099	—	2	8	no	—
24	C₂×#6099	—	2	4	no	—
25	C₂×#6099	—	4	2	no	—
26	C₂×#6099	—	4	4	no	—
27	C₂²×#1055	—	4	2	no	—
28	C₂×C₁₃×C₁₆	—	2	4	no	—
29	C₂×C₁₃×C₁₆	—	2	4	no	—
30	C₂×C₁₃×C₁₆	—	2	4	no	—
31	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
32	#88059	—	2	8	no	—
33	#88059	—	2	4	no	—
34	#88059	C₂×C₄	1	8	yes	—
35	C₂×#1381	—	13	1	no	maximal, Sylow
36	C₂⁴×C₁₃	Q₁₆	1	1	yes	characteristic
37	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
38	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
43	C₂²×C₄×C₁₃	Q₁₆	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₄²	1	2	yes	—
46	C₂×C₈×C₁₃	C₄²	1	2	yes	—
47	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
48	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
49	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
50	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
53	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
54	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
56	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
57	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
58	#6099	—	2	8	no	—
59	#6099	—	4	8	no	—
60	#6099	—	4	4	no	—
61	C₂×#1055	—	4	8	no	—
62	C₂×#1055	—	4	4	no	—
63	C₁₃×C₁₆	—	2	4	no	—
64	C₂³×C₁₆	D₁₃	1	1	yes	characteristic
65	C₂²×#108	—	13	2	no	—
66	#1381	—	13	4	no	—
67	C₂³×C₁₃	—	2	4	no	—
68	C₂³×C₁₃	#103	1	4	yes	—
69	C₂³×C₁₃	#107	1	1	yes	characteristic
70	C₂³×C₁₃	#107	1	1	yes	characteristic
71	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
72	C₂×C₄×C₁₃	#95	1	2	yes	—
73	C₂×C₄×C₁₃	#95	1	2	yes	—
74	C₂×C₄×C₁₃	#102	1	4	yes	—
75	C₂×C₄×C₁₃	#102	1	4	yes	—
76	C₂×C₄×C₁₃	#103	1	4	yes	—
77	C₂×C₄×C₁₃	#106	1	2	yes	—
78	C₂×C₄×C₁₃	#106	1	2	yes	—
79	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
80	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
81	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
82	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
85	C₈×C₁₃	#95	1	2	yes	—
86	C₈×C₁₃	#95	1	2	yes	—
87	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
88	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
89	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
90	#1055	—	4	8	no	—
91	C₂²×M₁₆	—	26	2	no	—
92	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
93	C₂²×C₁₆	—	2	4	no	—
94	C₂²×C₁₆	Dic₁₃	1	2	yes	—
95	C₂²×C₁₆	Dic₁₃	1	2	yes	—
96	C₂²×C₁₆	C₂×D₁₃	1	2	yes	—
97	C₂×#108	—	13	8	no	—
98	C₂×#108	—	13	4	no	—
99	C₂×#108	—	26	2	no	—
100	C₂×#108	—	26	4	no	—
101	C₂²×C₁₃	—	2	8	no	—
102	C₂²×C₁₃	—	2	2	no	—
103	C₂²×C₁₃	—	2	2	no	—
104	C₂²×C₁₃	#340	1	2	yes	—
105	C₂²×C₁₃	#340	1	2	yes	—
106	C₂²×C₁₃	#368	1	4	yes	—
107	C₂²×C₁₃	C₂×#103	1	2	yes	—
108	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
109	C₄×C₁₃	#340	1	2	yes	—
110	C₄×C₁₃	#340	1	2	yes	—
111	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
112	C₄×C₁₃	C₂×#102	1	2	yes	—
113	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
114	C₂³×C₄	D₅₂	1	1	yes	characteristic
115	C₂×M₁₆	—	26	8	no	—
116	C₂×M₁₆	—	26	4	no	—
117	C₂×M₁₆	—	52	4	no	—
118	C₂×M₁₆	—	52	2	no	—
119	C₂²×C₈	—	52	2	no	—
120	C₂²×C₈	Dic₂₆	1	1	yes	characteristic
121	C₂²×C₈	Dic₂₆	1	1	yes	characteristic
122	C₂²×C₈	C₄×D₁₃	1	4	yes	—
123	C₂²×C₈	D₅₂	1	1	yes	characteristic
124	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
125	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
126	C₂²×C₈	C₂²⋊D₁₃	1	4	yes	—
127	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
128	C₂×C₁₆	—	2	4	no	—
129	C₂×C₁₆	—	2	4	no	—
130	C₂×C₁₆	—	2	4	no	—
131	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	—
132	#108	—	13	8	no	—
133	#108	—	26	8	no	—
134	#108	—	26	4	no	—
135	C₂×C₁₃	—	2	2	no	—
136	C₂×C₁₃	—	2	2	no	—
137	C₂×C₁₃	#1381	1	4	yes	complemented
138	C₂×C₁₃	C₂×#340	1	1	yes	characteristic
139	C₂×C₁₃	C₂×#368	1	2	yes	—
140	C₂⁴	Dic₅₂	1	1	yes	characteristic
141	C₂²×C₄	#6095	1	4	yes	—
142	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
143	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
144	C₂²×C₄	Dic₅₂	1	1	yes	characteristic
145	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
146	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
147	C₂²×C₄	#6103	1	4	yes	—
148	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
149	M₁₆	—	26	8	no	—
150	M₁₆	—	52	4	no	—
151	M₁₆	—	52	8	no	—
152	C₂×C₈	—	52	4	no	—
153	C₂×C₈	—	52	8	no	—
154	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
155	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
156	C₂×C₈	#6101	1	4	yes	—
157	C₂×C₈	#6101	1	4	yes	—
158	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
159	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
160	C₂×C₈	#6103	1	4	yes	—
161	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
162	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
163	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
164	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
165	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
166	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
167	C₁₆	—	2	4	no	—
168	C₁₃	C₂×#1381	1	1	yes	characteristic, complemented, Sylow
169	C₂³	—	2	4	no	—
170	C₂³	#88056	1	4	yes	—
171	C₂³	#88058	1	1	yes	characteristic
172	C₂³	#88058	1	1	yes	characteristic
173	C₂³	C₂×Dic₅₂	1	1	yes	characteristic
174	C₂×C₄	#88056	1	4	yes	—
175	C₂×C₄	#88057	1	2	yes	—
176	C₂×C₄	#88057	1	2	yes	—
177	C₂×C₄	#88058	1	1	yes	characteristic
178	C₂×C₄	#88058	1	1	yes	characteristic
179	C₂×C₄	#88061	1	4	yes	—
180	C₂×C₄	#88061	1	4	yes	—
181	C₂×C₄	#88071	1	2	yes	—
182	C₂×C₄	#88071	1	2	yes	—
183	C₂×C₄	C₂×#6095	1	2	yes	—
184	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
185	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
186	C₂×C₄	C₂×#6103	1	2	yes	—
187	C₈	—	52	8	no	—
188	C₈	#88071	1	2	yes	—
189	C₈	#88071	1	2	yes	—
190	C₈	C₂×C₄×Dic₁₃	1	1	yes	characteristic
191	C₈	C₂×#6101	1	2	yes	—
192	C₈	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
193	C₂²	—	2	8	no	—
194	C₂²	—	2	2	no	—
195	C₂²	—	2	2	no	—
196	C₂²	#11718098	1	4	yes	—
197	C₂²	#11718143	1	2	yes	—
198	C₂²	#11718143	1	2	yes	—
199	C₂²	C₂×#88056	1	2	yes	—
200	C₂²	C₂×#88058	1	1	yes	characteristic
201	C₄	#11718143	1	2	yes	—
202	C₄	#11718143	1	2	yes	—
203	C₄	C₂×#88057	1	1	yes	characteristic
204	C₄	C₂×#88061	1	2	yes	—
205	C₄	C₂×#88071	1	1	yes	characteristic
206	C₂	—	2	2	no	—
207	C₂	—	2	2	no	—
208	C₂	#13112930	1	4	yes	direct product factor
209	C₂	C₂×#11718143	1	1	yes	characteristic
210	C₂	C₂×#11718098	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₁₀₄
commutator	C₈×C₁₃	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂³×C₁₃×C₁₆	C₂
socle	C₂³×C₁₃	#107
prime radical	C₂⁴×C₁₃	Q₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂³×C₁₆	D₁₃
hypocenter	C₁₃	C₂×#1381
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂³×C₁₆

Complements

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

N	H ≅ G/N	type
2. #13112930	C₂	direct (N × H)
137. C₂×C₁₃	#1381	semidirect
168. C₁₃	C₂×#1381	semidirect
208. C₂	#13112930	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×#88059	2
#13112930	2
C₂³×C₁₃×C₁₆	2
C₂×#1381	13

Subgroups — C2×#13112930 #15777806

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112930 #15777806