Subgroups — C₂×#13116617 #16015945

Order 3328.

694 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718541	C₂	1	2	yes	maximal
3	#13116617	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718082	C₂	1	2	yes	maximal, complemented
5	C₂×#11718096	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88146	—	2	2	no	—
9	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#107	C₂²	1	2	yes	—
11	C₂×#88058	C₂²	1	2	yes	—
12	C₂²×#6090	C₂²	1	1	yes	characteristic
13	C₂×#88048	—	2	2	no	—
14	C₂×C₁₆×D₁₃	C₄	1	8	yes	complemented
15	C₂×C₁₆×D₁₃	C₂²	1	4	yes	—
16	#11718541	—	2	4	no	—
17	#11718541	C₂²	1	8	yes	—
18	C₁₃×#366	C₂²	1	4	yes	complemented
19	#11718096	C₂²	1	4	yes	complemented
20	#11718082	C₂²	1	8	yes	complemented
21	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
24	C₂×#6103	—	4	2	no	—
25	C₂×C₄⋊Dic₁₃	—	2	2	no	—
26	C₂×C₄×Dic₁₃	—	4	2	no	—
27	C₂²×#1055	D₄	1	1	yes	characteristic
28	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
29	C₂×C₈×D₁₃	D₄	1	2	yes	—
30	C₂×C₈×D₁₃	Q₈	1	4	yes	—
31	C₂×C₈×D₁₃	C₂³	1	2	yes	—
32	#88146	—	2	8	no	—
33	#88146	—	4	4	no	—
34	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
35	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
36	C₁₃×#107	—	2	2	no	—
37	C₁₃×#107	C₂³	1	4	yes	—
38	#88058	—	2	2	no	—
39	#88058	C₂³	1	4	yes	—
40	C₂×#6090	C₂×C₄	1	4	yes	—
41	C₂×#6090	C₂³	1	2	yes	—
42	#88048	—	2	8	no	—
43	C₁₆×D₁₃	C₂×C₄	1	16	yes	complemented
44	C₂×#2158	—	13	1	no	maximal, Sylow
45	C₂³×D₁₃	D₈	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	—	4	2	no	—
47	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×Dic₁₃	—	4	2	no	—
49	C₂²×Dic₁₃	D₈	1	1	yes	characteristic
50	C₂×C₄×D₁₃	C₄⋊C₄	1	4	yes	—
51	C₂×C₄×D₁₃	D₈	1	2	yes	—
52	C₂×C₄×D₁₃	Q₁₆	1	4	yes	—
53	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
54	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
55	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
57	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
58	C₁₃×C₄⋊C₄	—	2	4	no	—
59	C₁₃×C₄⋊C₄	—	4	2	no	—
60	#6103	—	4	8	no	—
61	C₄⋊Dic₁₃	—	2	4	no	—
62	C₄⋊Dic₁₃	—	4	2	no	—
63	C₄×Dic₁₃	—	4	8	no	—
64	C₂×#1055	C₄⋊C₄	1	4	yes	—
65	C₂×#1055	C₂×D₄	1	2	yes	—
66	C₈×D₁₃	C₄⋊C₄	1	8	yes	—
67	C₈×D₁₃	C₂²×C₄	1	4	yes	—
68	C₈×D₁₃	C₂×Q₈	1	4	yes	—
69	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
70	#6090	C₂²×C₄	1	4	yes	—
71	C₂³×C₁₆	—	13	1	no	—
72	C₂×#427	—	13	2	no	—
73	#2158	—	13	8	no	—
74	C₂×#367	—	13	2	no	—
75	C₂×#366	—	13	1	no	—
76	C₂×#366	D₁₃	1	1	yes	characteristic, complemented
77	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
78	C₂²×D₁₃	—	2	2	no	—
79	C₂²×D₁₃	—	2	2	no	—
80	C₂²×D₁₃	#107	1	4	yes	—
81	C₂²×D₁₃	C₂×D₈	1	2	yes	—
82	C₂×C₄×C₁₃	—	4	4	no	—
83	C₂×C₄×C₁₃	—	8	4	no	—
84	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
85	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
87	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
88	C₂×Dic₁₃	—	4	4	no	—
89	C₂×Dic₁₃	—	8	4	no	—
90	C₂×Dic₁₃	#107	1	4	yes	—
91	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
92	C₄×D₁₃	#107	1	8	yes	—
93	C₄×D₁₃	C₂×C₄⋊C₄	1	4	yes	—
94	C₄×D₁₃	C₂×Q₁₆	1	4	yes	—
95	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
96	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
97	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
98	#1055	C₂×C₄⋊C₄	1	4	yes	—
99	C₂³×C₈	—	13	1	no	—
100	C₂×#117	—	26	2	no	—
101	C₂²×C₁₆	—	13	1	no	—
102	C₂²×C₁₆	—	13	8	no	—
103	C₂²×C₁₆	—	13	4	no	—
104	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
105	#427	—	13	8	no	—
106	#427	—	26	4	no	—
107	C₂×#107	—	13	2	no	—
108	C₂×#107	C₂×D₁₃	1	2	yes	—
109	C₂×#106	—	26	2	no	—
110	#367	—	13	8	no	—
111	#366	—	13	4	no	—
112	#366	C₂×D₁₃	1	4	yes	complemented
113	C₂²×C₁₃	C₂×#107	1	2	yes	—
114	C₂²×C₁₃	#508	1	2	yes	—
115	C₂²×C₁₃	#508	1	2	yes	—
116	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
117	C₂×D₁₃	—	2	2	no	—
118	C₂×D₁₃	—	2	2	no	—
119	C₂×D₁₃	—	2	8	no	—
120	C₂×D₁₃	C₂×#107	1	4	yes	—
121	C₄×C₁₃	—	8	4	no	—
122	C₄×C₁₃	C₂×#107	1	2	yes	—
123	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
124	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
125	Dic₁₃	—	8	4	no	—
126	Dic₁₃	C₂×#107	1	4	yes	—
127	C₂³×C₄	—	13	1	no	—
128	C₂²×C₈	—	13	1	no	—
129	C₂²×C₈	—	13	4	no	—
130	C₂²×C₈	—	13	2	no	—
131	C₂²×C₈	—	13	4	no	—
132	C₂²×C₈	—	13	2	no	—
133	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
134	#117	—	26	8	no	—
135	#117	—	52	4	no	—
136	C₂×C₄⋊C₄	—	2	2	no	—
137	C₂×C₄⋊C₄	—	26	2	no	—
138	C₂×C₂²⋊C₄	—	52	2	no	—
139	C₂×C₄²	—	52	2	no	—
140	C₂×C₁₆	—	13	4	no	—
141	C₂×C₁₆	—	13	2	no	—
142	C₂×C₁₆	—	13	16	no	—
143	C₂×C₁₆	C₄×D₁₃	1	4	yes	—
144	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
145	#107	—	2	2	no	—
146	#107	—	13	4	no	—
147	#107	—	26	2	no	—
148	#107	C₂²×D₁₃	1	4	yes	—
149	#106	—	26	8	no	—
150	C₂×C₁₃	#2158	1	4	yes	complemented
151	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
152	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
153	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
154	D₁₃	—	2	4	no	—
155	C₂⁴	—	13	1	no	—
156	C₂²×C₄	—	4	2	no	—
157	C₂²×C₄	—	13	1	no	—
158	C₂²×C₄	—	13	4	no	—
159	C₂²×C₄	—	13	2	no	—
160	C₂²×C₄	—	13	4	no	—
161	C₂²×C₄	—	13	2	no	—
162	C₂²×C₄	—	52	2	no	—
163	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
164	C₂×C₈	—	13	4	no	—
165	C₂×C₈	—	13	2	no	—
166	C₂×C₈	—	13	8	no	—
167	C₂×C₈	—	13	4	no	—
168	C₂×C₈	—	13	4	no	—
169	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
170	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
171	C₂×C₈	Q₈×D₁₃	1	2	yes	—
172	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
173	C₄⋊C₄	—	2	4	no	—
174	C₄⋊C₄	—	4	2	no	—
175	C₄⋊C₄	—	26	4	no	—
176	C₄⋊C₄	—	52	2	no	—
177	C₂²⋊C₄	—	52	8	no	—
178	C₄²	—	52	8	no	—
179	C₁₆	—	13	4	no	—
180	C₁₆	C₂×C₄×D₁₃	1	4	yes	—
181	C₁₃	C₂×#2158	1	1	yes	characteristic, complemented, Sylow
182	C₂³	—	13	2	no	—
183	C₂³	—	13	4	no	—
184	C₂³	—	26	2	no	—
185	C₂³	—	26	2	no	—
186	C₂³	D₈×D₁₃	1	1	yes	characteristic
187	C₂×C₄	—	4	4	no	—
188	C₂×C₄	—	8	4	no	—
189	C₂×C₄	—	13	2	no	—
190	C₂×C₄	—	13	4	no	—
191	C₂×C₄	—	13	4	no	—
192	C₂×C₄	—	13	4	no	—
193	C₂×C₄	—	13	8	no	—
194	C₂×C₄	—	52	4	no	—
195	C₂×C₄	—	104	4	no	—
196	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
197	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
198	C₂×C₄	Q₁₆×D₁₃	1	2	yes	—
199	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
200	C₈	—	13	4	no	—
201	C₈	C₄⋊C₄×D₁₃	1	2	yes	—
202	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
203	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
204	C₂²	—	13	4	no	—
205	C₂²	—	26	2	no	—
206	C₂²	—	26	2	no	—
207	C₂²	—	26	8	no	—
208	C₂²	D₁₃×#107	1	2	yes	—
209	C₂²	#11718573	1	2	yes	—
210	C₂²	#11718580	1	2	yes	—
211	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
212	C₄	—	8	4	no	—
213	C₄	—	13	4	no	—
214	C₄	—	104	4	no	—
215	C₄	D₁₃×#107	1	2	yes	—
216	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
217	C₄	C₂×Q₁₆×D₁₃	1	1	yes	characteristic
218	C₂	—	26	4	no	—
219	C₂	#13116617	1	4	yes	direct product factor
220	C₂	C₂×D₁₃×#107	1	1	yes	characteristic
221	C₂	C₂×#11718573	1	1	yes	characteristic
222	C₂	C₂×#11718580	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₈×D₁₃
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#366	C₂
socle	C₂³×C₁₃	C₂×D₈
prime radical	C₂³×D₁₃	D₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂×#366	D₁₃
hypocenter	C₁₃	C₂×#2158
LCS	G ▷ 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
3. #13116617	C₂	direct (N × H)
4. C₂×#11718082	C₂	semidirect
5. C₂×#11718096	C₂	semidirect
6. C₂×C₁₃×#366	C₂	semidirect
14. C₂×C₁₆×D₁₃	C₄	semidirect
18. C₁₃×#366	C₂²	semidirect
19. #11718096	C₂²	semidirect
20. #11718082	C₂²	semidirect
43. C₁₆×D₁₃	C₂×C₄	semidirect
76. C₂×#366	D₁₃	semidirect
112. #366	C₂×D₁₃	semidirect
150. C₂×C₁₃	#2158	semidirect
181. C₁₃	C₂×#2158	semidirect
219. C₂	#13116617	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×C₁₆×D₁₃	2
C₂×#11718541	2
#13116617	2
C₂×#11718082	2
C₂×#11718096	2
C₂×C₁₃×#366	2
C₂×#2158	13

Subgroups — C2×#13116617 #16015945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116617 #16015945