Subgroups — C₂×#13116631 #16015975

Order 3328.

642 conjugacy classes of subgroups.

The subgroup lattice has 216 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	#13116631	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718098	C₂	1	4	yes	maximal, complemented
4	C₂²×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×#6099	—	2	2	no	—
7	C₂×C₁₃×M₃₂	C₄	1	4	yes	—
8	C₂×C₁₃×M₃₂	C₄	1	4	yes	—
9	C₂×C₁₃×M₃₂	C₂²	1	4	yes	—
10	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
11	C₂×#88059	—	2	2	no	—
12	C₂×#88059	—	2	4	no	—
13	C₂×#88059	C₂²	1	4	yes	—
14	C₂×#88059	C₂²	1	8	yes	—
15	#11718098	C₂²	1	16	yes	complemented
16	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
19	C₂²×C₈×C₁₃	D₄	1	2	yes	—
20	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	Q₈	1	2	yes	—
22	C₂²×C₈×C₁₃	Q₈	1	2	yes	—
23	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
25	C₂×#6099	—	2	4	no	—
26	C₂×#6099	—	2	8	no	—
27	C₂×#6099	—	4	2	no	—
28	C₂×#6099	—	4	4	no	—
29	C₂²×#1055	—	4	2	no	—
30	C₁₃×M₃₂	C₂×C₄	1	16	yes	—
31	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
32	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
33	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
34	#88059	—	2	4	no	—
35	#88059	—	2	8	no	—
36	#88059	C₂³	1	8	yes	—
37	C₂×#2161	—	13	1	no	maximal, Sylow
38	C₂⁴×C₁₃	Q₁₆	1	1	yes	characteristic
39	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
40	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
41	C₂²×C₄×C₁₃	D₈	1	2	yes	—
42	C₂²×C₄×C₁₃	D₈	1	2	yes	—
43	C₂²×C₄×C₁₃	Q₁₆	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	Q₁₆	1	2	yes	—
45	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
46	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
48	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
49	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
50	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
51	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
53	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
54	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
55	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
56	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
57	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
58	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
59	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
60	#6099	—	2	8	no	—
61	#6099	—	4	8	no	—
62	#6099	—	4	4	no	—
63	C₂×#1055	—	4	8	no	—
64	C₂×#1055	—	4	4	no	—
65	C₁₃×C₁₆	C₂²×C₄	1	8	yes	—
66	C₂²×M₃₂	D₁₃	1	1	yes	characteristic
67	C₂²×#108	—	13	2	no	—
68	#2161	—	13	8	no	—
69	C₂×#368	—	13	4	no	—
70	C₂³×C₁₃	—	4	2	no	—
71	C₂³×C₁₃	#107	1	2	yes	—
72	C₂³×C₁₃	#107	1	2	yes	—
73	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
74	C₂³×C₁₃	C₂×Q₁₆	1	2	yes	—
75	C₂×C₄×C₁₃	#107	1	4	yes	—
76	C₂×C₄×C₁₃	#107	1	2	yes	—
77	C₂×C₄×C₁₃	#107	1	4	yes	—
78	C₂×C₄×C₁₃	#107	1	2	yes	—
79	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
81	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
83	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
85	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
86	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
88	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
89	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
90	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
91	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
92	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
93	#1055	—	4	8	no	—
94	C₂²×M₁₆	—	26	2	no	—
95	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
96	C₂×M₃₂	Dic₁₃	1	4	yes	—
97	C₂×M₃₂	Dic₁₃	1	4	yes	—
98	C₂×M₃₂	C₂×D₁₃	1	4	yes	—
99	C₂²×C₁₆	C₂×D₁₃	1	2	yes	—
100	C₂×#108	—	13	4	no	—
101	C₂×#108	—	13	8	no	—
102	C₂×#108	—	26	4	no	—
103	C₂×#108	—	26	2	no	—
104	#368	—	13	16	no	—
105	C₂²×C₁₃	—	2	4	no	—
106	C₂²×C₁₃	—	2	2	no	—
107	C₂²×C₁₃	—	4	2	no	—
108	C₂²×C₁₃	—	4	2	no	—
109	C₂²×C₁₃	C₂×#107	1	4	yes	—
110	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
111	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
112	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
113	C₄×C₁₃	C₂×#107	1	4	yes	—
114	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
115	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
116	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
117	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
118	C₂³×C₄	D₅₂	1	1	yes	characteristic
119	C₂×M₁₆	—	26	8	no	—
120	C₂×M₁₆	—	26	4	no	—
121	C₂×M₁₆	—	52	4	no	—
122	C₂×M₁₆	—	52	2	no	—
123	C₂²×C₈	—	52	2	no	—
124	C₂²×C₈	Dic₂₆	1	2	yes	—
125	C₂²×C₈	Dic₂₆	1	2	yes	—
126	C₂²×C₈	D₅₂	1	2	yes	—
127	C₂²×C₈	D₅₂	1	1	yes	characteristic
128	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
129	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
130	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
131	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
132	M₃₂	C₂×Dic₁₃	1	16	yes	—
133	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	—
134	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	—
135	C₂×C₁₆	C₂²×D₁₃	1	4	yes	—
136	#108	—	13	8	no	—
137	#108	—	26	4	no	—
138	#108	—	26	8	no	—
139	C₂×C₁₃	—	2	1	no	—
140	C₂×C₁₃	—	2	4	no	—
141	C₂×C₁₃	—	2	1	no	—
142	C₂×C₁₃	#2161	1	2	yes	complemented
143	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
144	C₂⁴	Dic₅₂	1	1	yes	characteristic
145	C₂²×C₄	D₁₀₄	1	2	yes	—
146	C₂²×C₄	D₁₀₄	1	2	yes	—
147	C₂²×C₄	Dic₅₂	1	1	yes	characteristic
148	C₂²×C₄	Dic₅₂	1	2	yes	—
149	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
150	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
151	C₂²×C₄	C₂×D₅₂	1	2	yes	—
152	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
153	M₁₆	—	26	8	no	—
154	M₁₆	—	52	8	no	—
155	M₁₆	—	52	4	no	—
156	C₂×C₈	—	52	8	no	—
157	C₂×C₈	—	52	4	no	—
158	C₂×C₈	C₄⋊Dic₁₃	1	4	yes	—
159	C₂×C₈	C₄⋊Dic₁₃	1	4	yes	—
160	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
161	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
162	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
163	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
164	C₂×C₈	C₂×Dic₂₆	1	4	yes	—
165	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
166	C₂×C₈	C₂×D₅₂	1	2	yes	—
167	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
168	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
169	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
170	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
171	C₁₆	C₂²×Dic₁₃	1	8	yes	—
172	C₁₃	C₂×#2161	1	1	yes	characteristic, complemented, Sylow
173	C₂³	—	4	2	no	—
174	C₂³	#88058	1	2	yes	—
175	C₂³	#88058	1	2	yes	—
176	C₂³	C₂×Dic₅₂	1	1	yes	characteristic
177	C₂³	C₂×Dic₅₂	1	2	yes	—
178	C₂×C₄	#88058	1	2	yes	—
179	C₂×C₄	#88058	1	4	yes	—
180	C₂×C₄	#88058	1	2	yes	—
181	C₂×C₄	#88058	1	4	yes	—
182	C₂×C₄	C₂×D₁₀₄	1	4	yes	—
183	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
184	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
185	C₂×C₄	C₂×Dic₅₂	1	2	yes	—
186	C₂×C₄	C₂×Dic₅₂	1	1	yes	characteristic
187	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
188	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
189	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
190	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
191	C₈	—	52	8	no	—
192	C₈	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
193	C₈	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
194	C₈	C₂×C₄⋊Dic₁₃	1	4	yes	—
195	C₈	C₂²×Dic₂₆	1	1	yes	characteristic
196	C₈	C₂³×Dic₁₃	1	1	yes	characteristic
197	C₂²	—	2	2	no	—
198	C₂²	—	2	4	no	—
199	C₂²	—	4	2	no	—
200	C₂²	—	4	2	no	—
201	C₂²	C₂×#88058	1	4	yes	—
202	C₂²	C₂×#88058	1	1	yes	characteristic
203	C₂²	C₂×#88058	1	1	yes	characteristic
204	C₂²	C₂²×Dic₅₂	1	1	yes	characteristic
205	C₄	C₂×#88058	1	4	yes	—
206	C₄	C₂×#88058	1	1	yes	characteristic
207	C₄	C₂×#88058	1	1	yes	characteristic
208	C₄	C₂²×D₁₀₄	1	1	yes	characteristic
209	C₄	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
210	C₂	—	2	1	no	—
211	C₂	—	2	1	no	—
212	C₂	—	2	4	no	—
213	C₂	#13116631	1	2	yes	direct product factor
214	C₂	C₂²×#88058	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₁₀₄
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂²×C₁₃×M₃₂	C₂
socle	C₂²×C₁₃	C₂×#107
prime radical	C₂⁴×C₁₃	Q₁₆
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂²×M₃₂	D₁₃
hypocenter	C₁₃	C₂×#2161
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂²×M₃₂

Complements

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

N	H ≅ G/N	type
2. #13116631	C₂	direct (N × H)
3. C₂×#11718098	C₂	semidirect
15. #11718098	C₂²	semidirect
142. C₂×C₁₃	#2161	semidirect
172. C₁₃	C₂×#2161	semidirect
213. C₂	#13116631	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
#13116631	2
C₂×#11718098	2
C₂²×C₁₃×M₃₂	2
C₂×#2161	13

Subgroups — C2×#13116631 #16015975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116631 #16015975