Subgroups — C₂×Q₃₂×Dic₁₃ #16016194

Order 3328.

678 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	C₂×Q₁₆×Dic₁₃	C₂	1	2	yes	maximal
2	Q₃₂×Dic₁₃	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718096	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718156	C₂	1	2	yes	maximal
5	C₂×C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×Q₃₂	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
8	C₂×Q₈×Dic₁₃	—	2	2	no	—
9	C₂×C₁₃×Q₃₂	C₄	1	8	yes	complemented
10	C₂×C₁₃×Q₃₂	C₂²	1	4	yes	—
11	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
12	C₂×#88075	—	2	2	no	—
13	Q₁₆×Dic₁₃	—	2	4	no	—
14	Q₁₆×Dic₁₃	C₂²	1	8	yes	—
15	C₂×#88058	C₂²	1	2	yes	—
16	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
17	C₂²×#6090	C₂²	1	1	yes	characteristic
18	#11718156	C₂²	1	8	yes	—
19	#11718096	C₂²	1	4	yes	—
20	C₁₆×Dic₁₃	C₂²	1	4	yes	—
21	C₂²×Q₈×C₁₃	—	2	2	no	—
22	C₂×C₁₃×Q₁₆	—	2	2	no	—
23	C₂×C₁₃×Q₁₆	—	2	4	no	—
24	C₂×C₁₃×Q₁₆	C₂×C₄	1	8	yes	—
25	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
26	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
27	Q₈×Dic₁₃	—	2	8	no	—
28	Q₈×Dic₁₃	—	4	4	no	—
29	C₂×C₄⋊Dic₁₃	—	2	2	no	—
30	C₂×C₄⋊Dic₁₃	—	4	2	no	—
31	C₂×C₄×Dic₁₃	—	4	2	no	—
32	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
33	C₂²×#1055	D₄	1	1	yes	characteristic
34	C₁₃×Q₃₂	C₂×C₄	1	16	yes	complemented
35	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
36	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
37	#88075	—	2	8	no	—
38	#88058	—	2	2	no	—
39	#88058	C₂³	1	4	yes	—
40	C₈×Dic₁₃	D₄	1	2	yes	—
41	C₈×Dic₁₃	C₂³	1	2	yes	—
42	C₂×#6090	—	2	2	no	—
43	C₂×#6090	C₂³	1	2	yes	—
44	C₂×C₄×Q₃₂	—	13	1	no	maximal, Sylow
45	C₂×Q₈×C₁₃	—	2	8	no	—
46	C₂×Q₈×C₁₃	—	2	4	no	—
47	C₂×Q₈×C₁₃	—	4	2	no	—
48	C₂×Q₈×C₁₃	—	4	4	no	—
49	C₂²×C₄×C₁₃	—	4	2	no	—
50	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
51	C₂²×Dic₁₃	—	4	2	no	—
52	C₂²×Dic₁₃	D₈	1	1	yes	characteristic
53	C₂²×Dic₁₃	D₈	1	1	yes	characteristic
54	C₁₃×Q₁₆	—	2	8	no	—
55	C₁₃×Q₁₆	—	2	4	no	—
56	C₁₃×Q₁₆	C₂²×C₄	1	8	yes	—
57	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
58	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₁₃	#41	1	2	yes	—
60	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
61	C₄⋊Dic₁₃	—	2	4	no	—
62	C₄⋊Dic₁₃	—	4	2	no	—
63	C₄⋊Dic₁₃	—	4	8	no	—
64	C₄×Dic₁₃	—	4	8	no	—
65	C₄×Dic₁₃	D₈	1	2	yes	—
66	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
67	C₂×#1055	—	2	2	no	—
68	C₂×#1055	C₂×D₄	1	2	yes	—
69	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
70	#6090	—	2	2	no	—
71	C₂²×Q₃₂	D₁₃	1	1	yes	characteristic
72	C₂×C₄×Q₁₆	—	13	2	no	—
73	C₄×Q₃₂	—	13	8	no	—
74	C₂×#366	—	13	1	no	—
75	C₂×#358	—	13	2	no	—
76	C₂×C₄×C₁₆	—	13	1	no	—
77	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
78	Q₈×C₁₃	—	2	8	no	—
79	Q₈×C₁₃	—	4	4	no	—
80	Q₈×C₁₃	—	4	8	no	—
81	C₂×C₄×C₁₃	—	4	4	no	—
82	C₂×C₄×C₁₃	—	4	8	no	—
83	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
84	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
85	C₂×C₄×C₁₃	#135	1	2	yes	—
86	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
87	C₂×Dic₁₃	—	2	2	no	—
88	C₂×Dic₁₃	—	4	4	no	—
89	C₂×Dic₁₃	—	8	4	no	—
90	C₂×Dic₁₃	Q₃₂	1	4	yes	direct product factor
91	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
92	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
93	C₈×C₁₃	C₄×D₄	1	2	yes	—
94	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
95	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
96	#1055	—	2	2	no	—
97	C₂²×Q₁₆	C₂×D₁₃	1	2	yes	—
98	C₂×C₄×Q₈	—	26	2	no	—
99	C₂×Q₃₂	Dic₁₃	1	8	yes	direct product factor
100	C₂×Q₃₂	C₂×D₁₃	1	4	yes	—
101	C₂²×C₁₆	—	13	1	no	—
102	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
103	C₄×Q₁₆	—	13	8	no	—
104	C₄×Q₁₆	—	26	4	no	—
105	C₂×#107	—	13	2	no	—
106	C₂×#103	—	26	2	no	—
107	C₂×C₄×C₈	—	13	1	no	—
108	#366	—	13	4	no	—
109	#358	—	13	8	no	—
110	C₄×C₁₆	—	13	4	no	—
111	C₂²×C₁₃	C₄×D₈	1	2	yes	—
112	C₂²×C₁₃	C₂×Q₃₂	1	2	yes	—
113	C₂²×C₁₃	#508	1	2	yes	—
114	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
115	C₄×C₁₃	—	4	8	no	—
116	C₄×C₁₃	C₄×D₈	1	2	yes	—
117	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
118	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
119	Dic₁₃	—	2	2	no	—
120	Dic₁₃	—	8	4	no	—
121	Dic₁₃	C₂×Q₃₂	1	4	yes	direct product factor
122	C₂²×Q₈	—	2	2	no	—
123	C₂×Q₁₆	—	2	2	no	—
124	C₂×Q₁₆	—	2	4	no	—
125	C₂×Q₁₆	C₂×Dic₁₃	1	8	yes	—
126	C₂×Q₁₆	C₂²×D₁₃	1	4	yes	—
127	C₂²×C₈	—	13	1	no	—
128	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
129	C₄×Q₈	—	26	8	no	—
130	C₄×Q₈	—	52	4	no	—
131	C₂×C₄⋊C₄	—	26	2	no	—
132	C₂×C₄⋊C₄	—	52	2	no	—
133	C₂×C₄²	—	13	1	no	—
134	C₂×C₄²	—	52	2	no	—
135	Q₃₂	C₂×Dic₁₃	1	16	yes	direct product factor
136	C₂×C₁₆	—	13	2	no	—
137	C₂×C₁₆	—	26	2	no	—
138	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	—
139	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
140	#107	—	13	4	no	—
141	#107	—	26	2	no	—
142	#103	—	26	8	no	—
143	C₄×C₈	—	13	2	no	—
144	C₄×C₈	—	13	2	no	—
145	C₂×C₁₃	C₄×Q₃₂	1	4	yes	complemented
146	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
147	C₂×C₁₃	C₂²×Q₃₂	1	1	yes	characteristic
148	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
149	C₂×Q₈	—	2	8	no	—
150	C₂×Q₈	—	2	4	no	—
151	C₂×Q₈	—	4	2	no	—
152	C₂×Q₈	—	4	4	no	—
153	C₂²×C₄	—	4	2	no	—
154	C₂²×C₄	—	13	1	no	—
155	C₂²×C₄	—	13	1	no	—
156	C₂²×C₄	—	52	2	no	—
157	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
158	Q₁₆	—	2	8	no	—
159	Q₁₆	—	2	4	no	—
160	Q₁₆	C₂²×Dic₁₃	1	8	yes	—
161	C₂×C₈	—	13	2	no	—
162	C₂×C₈	—	26	2	no	—
163	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
164	C₂×C₈	#6129	1	2	yes	—
165	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
166	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
167	C₄⋊C₄	—	26	4	no	—
168	C₄⋊C₄	—	52	8	no	—
169	C₄⋊C₄	—	52	2	no	—
170	C₄²	—	13	2	no	—
171	C₄²	—	13	2	no	—
172	C₄²	—	52	8	no	—
173	C₁₆	—	26	2	no	—
174	C₁₆	C₂²×Dic₁₃	1	4	yes	—
175	C₁₃	C₂×C₄×Q₃₂	1	1	yes	characteristic, complemented, Sylow
176	C₂³	D₈×D₁₃	1	1	yes	characteristic
177	Q₈	—	2	8	no	—
178	Q₈	—	4	4	no	—
179	Q₈	—	4	8	no	—
180	C₂×C₄	—	4	4	no	—
181	C₂×C₄	—	4	8	no	—
182	C₂×C₄	—	13	2	no	—
183	C₂×C₄	—	13	4	no	—
184	C₂×C₄	—	13	2	no	—
185	C₂×C₄	—	26	2	no	—
186	C₂×C₄	—	52	4	no	—
187	C₂×C₄	—	104	4	no	—
188	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
189	C₂×C₄	#88166	1	2	yes	—
190	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
191	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
192	C₈	—	26	2	no	—
193	C₈	D₄×Dic₁₃	1	2	yes	—
194	C₈	C₂×#6129	1	1	yes	characteristic
195	C₈	C₂³×Dic₁₃	1	1	yes	characteristic
196	C₂²	D₁₃×Q₃₂	1	2	yes	—
197	C₂²	#11718580	1	2	yes	—
198	C₂²	D₈×Dic₁₃	1	2	yes	—
199	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
200	C₄	—	4	8	no	—
201	C₄	—	13	4	no	—
202	C₄	—	26	2	no	—
203	C₄	—	104	4	no	—
204	C₄	D₈×Dic₁₃	1	2	yes	—
205	C₄	C₂×#88166	1	1	yes	characteristic
206	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
207	C₂	Q₃₂×Dic₁₃	1	4	yes	direct product factor
208	C₂	C₂×D₈×Dic₁₃	1	1	yes	characteristic
209	C₂	C₂×D₁₃×Q₃₂	1	1	yes	characteristic
210	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	C₂²×C₁₃×Q₃₂	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂²×Q₃₂	D₁₃
hypocenter	C₁₃	C₂×C₄×Q₃₂
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×Q₃₂

Complements

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

N	H ≅ G/N	type
2. Q₃₂×Dic₁₃	C₂	direct (N × H)
9. C₂×C₁₃×Q₃₂	C₄	semidirect
34. C₁₃×Q₃₂	C₂×C₄	semidirect
90. C₂×Dic₁₃	Q₃₂	direct (N × H)
99. C₂×Q₃₂	Dic₁₃	direct (N × H)
121. Dic₁₃	C₂×Q₃₂	direct (N × H)
135. Q₃₂	C₂×Dic₁₃	direct (N × H)
145. C₂×C₁₃	C₄×Q₃₂	semidirect
175. C₁₃	C₂×C₄×Q₃₂	semidirect
207. C₂	Q₃₂×Dic₁₃	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×Q₁₆×Dic₁₃	2
Q₃₂×Dic₁₃	2
C₂×#11718096	2
C₂×#11718156	2
C₂×C₁₆×Dic₁₃	2
C₂²×C₁₃×Q₃₂	2
C₂×C₄×Q₃₂	13

Subgroups — C2×Q32×Dic13 #16016194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₃₂×Dic₁₃ #16016194