Subgroups — C₂×#13117110 #16018395

Order 3328.

558 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718535	C₂	1	2	yes	maximal
2	#13117110	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718096	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718081	C₂	1	2	yes	maximal
5	C₂×C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#366	C₂	1	1	yes	maximal, characteristic
7	C₂×#88142	—	2	2	no	—
8	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×#107	C₂²	1	2	yes	—
10	C₂×#88058	C₂²	1	2	yes	—
11	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂²×#6090	C₂²	1	1	yes	characteristic
13	C₂×#88047	—	2	2	no	—
14	#11718535	—	2	4	no	—
15	#11718535	C₂²	1	8	yes	—
16	C₁₃×#366	C₂²	1	4	yes	—
17	#11718096	C₂²	1	4	yes	—
18	C₁₆×Dic₁₃	C₂²	1	4	yes	—
19	#11718081	C₂²	1	8	yes	—
20	C₂²×Dic₂₆	—	4	2	no	—
21	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
23	C₂×C₄⋊Dic₁₃	—	2	2	no	—
24	C₂×#6101	—	4	2	no	—
25	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
26	C₂²×#1055	D₄	1	1	yes	characteristic
27	#88142	—	2	8	no	—
28	#88142	—	4	4	no	—
29	C₂×C₁₃×C₁₆	Q₈	1	4	yes	complemented
30	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
31	C₁₃×#107	—	2	2	no	—
32	C₁₃×#107	C₂³	1	4	yes	—
33	#88058	—	2	2	no	—
34	#88058	C₂³	1	4	yes	—
35	C₈×Dic₁₃	D₄	1	2	yes	—
36	C₈×Dic₁₃	C₂³	1	2	yes	—
37	C₂×#6090	Q₈	1	4	yes	complemented
38	C₂×#6090	C₂³	1	2	yes	—
39	#88047	—	2	8	no	—
40	C₂×#2252	—	13	1	no	maximal, Sylow
41	C₂²×C₄×C₁₃	—	4	2	no	—
42	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×Dic₁₃	—	4	2	no	—
44	C₂²×Dic₁₃	D₈	1	1	yes	characteristic
45	C₂²×Dic₁₃	D₈	1	1	yes	characteristic
46	C₂×Dic₂₆	—	4	8	no	—
47	C₂×Dic₂₆	—	8	8	no	—
48	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
50	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
51	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
52	C₁₃×C₄⋊C₄	—	2	4	no	—
53	C₁₃×C₄⋊C₄	—	4	2	no	—
54	C₄⋊Dic₁₃	—	2	4	no	—
55	C₄⋊Dic₁₃	—	4	2	no	—
56	#6101	—	4	8	no	—
57	C₄×Dic₁₃	D₈	1	2	yes	—
58	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
59	C₂×#1055	Q₁₆	1	4	yes	—
60	C₂×#1055	C₂×D₄	1	2	yes	—
61	C₁₃×C₁₆	C₂×Q₈	1	4	yes	complemented
62	#6090	C₂×Q₈	1	4	yes	complemented
63	C₂×#500	—	13	2	no	—
64	#2252	—	13	8	no	—
65	C₂×#366	—	13	1	no	—
66	C₂×#366	—	13	2	no	—
67	C₂×#366	D₁₃	1	1	yes	characteristic
68	C₂×C₄×C₁₆	—	13	1	no	—
69	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
70	C₂×C₄×C₁₃	—	4	4	no	—
71	C₂×C₄×C₁₃	—	8	4	no	—
72	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
73	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
75	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
76	C₂×Dic₁₃	—	4	4	no	—
77	C₂×Dic₁₃	—	8	4	no	—
78	C₂×Dic₁₃	D₁₆	1	4	yes	—
79	C₂×Dic₁₃	Q₃₂	1	4	yes	—
80	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
81	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
82	Dic₂₆	—	8	16	no	—
83	C₈×C₁₃	C₄⋊Q₈	1	2	yes	—
84	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
85	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
86	#1055	C₂×Q₁₆	1	4	yes	—
87	C₂×C₄⋊Q₈	—	26	2	no	—
88	C₂²×C₁₆	—	13	1	no	—
89	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
90	#500	—	13	8	no	—
91	#500	—	26	4	no	—
92	C₂×#107	—	13	2	no	—
93	C₂×#107	—	26	2	no	—
94	C₂×#107	C₂×D₁₃	1	2	yes	—
95	C₂×C₄×C₈	—	13	1	no	—
96	#366	—	13	4	no	—
97	#366	—	13	8	no	—
98	#366	C₂×D₁₃	1	4	yes	—
99	C₄×C₁₆	—	13	4	no	—
100	C₂²×C₁₃	#500	1	2	yes	—
101	C₂²×C₁₃	C₂×D₁₆	1	2	yes	—
102	C₂²×C₁₃	C₂×Q₃₂	1	2	yes	—
103	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
104	C₄×C₁₃	—	8	4	no	—
105	C₄×C₁₃	#500	1	2	yes	—
106	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
107	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
108	Dic₁₃	—	8	4	no	—
109	Dic₁₃	C₂×D₁₆	1	4	yes	—
110	Dic₁₃	C₂×Q₃₂	1	4	yes	—
111	C₂²×Q₈	—	52	2	no	—
112	C₂²×C₈	—	13	1	no	—
113	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
114	C₄⋊Q₈	—	26	8	no	—
115	C₄⋊Q₈	—	52	4	no	—
116	C₂×C₄⋊C₄	—	2	2	no	—
117	C₂×C₄⋊C₄	—	26	2	no	—
118	C₂×C₄⋊C₄	—	52	2	no	—
119	C₂×C₄²	—	13	1	no	—
120	C₂×C₁₆	—	13	4	no	—
121	C₂×C₁₆	—	13	2	no	—
122	C₂×C₁₆	Dic₂₆	1	4	yes	complemented
123	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
124	#107	—	2	2	no	—
125	#107	—	13	4	no	—
126	#107	—	26	8	no	—
127	#107	—	26	2	no	—
128	#107	C₂²×D₁₃	1	4	yes	—
129	C₄×C₈	—	13	2	no	—
130	C₄×C₈	—	13	2	no	—
131	C₂×C₁₃	#2252	1	4	yes	complemented
132	C₂×C₁₃	C₂×#500	1	1	yes	characteristic
133	C₂×C₁₃	C₂²×D₁₆	1	1	yes	characteristic
134	C₂×C₁₃	C₂²×Q₃₂	1	1	yes	characteristic
135	C₂×Q₈	—	52	8	no	—
136	C₂×Q₈	—	104	8	no	—
137	C₂²×C₄	—	4	2	no	—
138	C₂²×C₄	—	13	1	no	—
139	C₂²×C₄	—	13	1	no	—
140	C₂²×C₄	—	52	2	no	—
141	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
142	C₂×C₈	—	13	4	no	—
143	C₂×C₈	—	13	2	no	—
144	C₂×C₈	C₂×Dic₂₆	1	2	yes	—
145	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
146	C₂×C₈	Q₈×D₁₃	1	2	yes	—
147	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
148	C₄⋊C₄	—	2	4	no	—
149	C₄⋊C₄	—	4	2	no	—
150	C₄⋊C₄	—	26	4	no	—
151	C₄⋊C₄	—	52	8	no	—
152	C₄⋊C₄	—	52	2	no	—
153	C₄²	—	13	2	no	—
154	C₄²	—	13	2	no	—
155	C₁₆	—	13	4	no	—
156	C₁₆	C₂×Dic₂₆	1	4	yes	complemented
157	C₁₃	C₂×#2252	1	1	yes	characteristic, complemented, Sylow
158	C₂³	D₈×D₁₃	1	1	yes	characteristic
159	Q₈	—	104	16	no	—
160	C₂×C₄	—	4	4	no	—
161	C₂×C₄	—	8	4	no	—
162	C₂×C₄	—	13	2	no	—
163	C₂×C₄	—	13	2	no	—
164	C₂×C₄	—	13	4	no	—
165	C₂×C₄	—	13	4	no	—
166	C₂×C₄	—	52	4	no	—
167	C₂×C₄	—	104	4	no	—
168	C₂×C₄	#88142	1	2	yes	—
169	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
170	C₂×C₄	Q₁₆×D₁₃	1	2	yes	—
171	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
172	C₈	—	13	4	no	—
173	C₈	#88142	1	2	yes	—
174	C₈	C₂²×Dic₂₆	1	1	yes	characteristic
175	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
176	C₂²	#11718535	1	2	yes	—
177	C₂²	D₁₃×D₁₆	1	2	yes	—
178	C₂²	D₁₃×Q₃₂	1	2	yes	—
179	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
180	C₄	—	8	4	no	—
181	C₄	—	13	4	no	—
182	C₄	—	13	4	no	—
183	C₄	—	104	4	no	—
184	C₄	#11718535	1	2	yes	—
185	C₄	C₂×#88142	1	1	yes	characteristic
186	C₄	C₂×Q₁₆×D₁₃	1	1	yes	characteristic
187	C₂	#13117110	1	4	yes	direct product factor
188	C₂	C₂×#11718535	1	1	yes	characteristic
189	C₂	C₂×D₁₃×D₁₆	1	1	yes	characteristic
190	C₂	C₂×D₁₃×Q₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₈×D₁₃
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#366	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₈
hypercenter	C₂×#366	D₁₃
hypocenter	C₁₃	C₂×#2252
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

Complements

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

N	H ≅ G/N	type
2. #13117110	C₂	direct (N × H)
29. C₂×C₁₃×C₁₆	Q₈	semidirect
37. C₂×#6090	Q₈	semidirect
61. C₁₃×C₁₆	C₂×Q₈	semidirect
62. #6090	C₂×Q₈	semidirect
122. C₂×C₁₆	Dic₂₆	semidirect
131. C₂×C₁₃	#2252	semidirect
156. C₁₆	C₂×Dic₂₆	semidirect
157. C₁₃	C₂×#2252	semidirect
187. C₂	#13117110	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×#11718535	2
#13117110	2
C₂×#11718096	2
C₂×#11718081	2
C₂×C₁₆×Dic₁₃	2
C₂×C₁₃×#366	2
C₂×#2252	13

Subgroups — C2×#13117110 #16018395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13117110 #16018395