Subgroups — #16015484

Order 3328.

1006 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718516	C₂	1	4	yes	maximal
2	#13123233	C₂	1	2	yes	maximal
3	#13114993	C₂	1	1	yes	maximal, characteristic
4	#13114992	C₂	1	2	yes	maximal
5	#13114991	C₂	1	4	yes	maximal
6	C₄×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1844	C₂	1	1	yes	maximal, characteristic
8	C₂×#88142	—	2	4	no	—
9	C₂×#88142	C₂²	1	4	yes	—
10	C₂×C₁₃×#106	C₂²	1	4	yes	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#384	C₂²	1	2	yes	—
13	C₂×#88057	C₂²	1	4	yes	—
14	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
15	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
16	#11718637	—	2	4	no	—
17	#11718637	C₂²	1	4	yes	—
18	C₂×#88048	C₂²	1	8	yes	—
19	#11718596	C₂²	1	2	yes	—
20	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
22	#11718516	—	2	16	no	—
23	C₂²×Dic₂₆	—	2	4	no	—
24	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
26	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
27	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₃	—	2	4	no	—
29	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
30	C₂×#6101	—	2	8	no	—
31	C₂×#6101	—	2	4	no	—
32	C₂×C₄×Dic₁₃	D₄	1	4	yes	—
33	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
34	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
35	C₂²×#1055	C₂³	1	2	yes	—
36	#88142	—	2	16	no	—
37	#88142	—	4	16	no	—
38	C₁₃×#106	—	2	8	no	—
39	C₄×C₈×C₁₃	Q₈	1	4	yes	complemented
40	#88057	—	2	8	no	—
41	C₈×Dic₁₃	D₄	1	8	yes	—
42	C₈×Dic₁₃	Q₈	1	8	yes	complemented
43	#88048	—	2	16	no	—
44	C₄×#1055	Q₈	1	4	yes	complemented
45	#33310	—	13	1	no	maximal, Sylow
46	C₂²×C₄×C₁₃	—	2	4	no	—
47	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
49	C₂²×Dic₁₃	—	2	4	no	—
50	C₂²×Dic₁₃	C₂×D₄	1	2	yes	—
51	C₂²×Dic₁₃	C₂×D₄	1	2	yes	—
52	C₂×Dic₂₆	—	4	8	no	—
53	C₂×Dic₂₆	—	4	16	no	—
54	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
55	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
56	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
57	C₁₃×C₄⋊C₄	—	2	8	no	—
58	C₁₃×C₄⋊C₄	—	4	8	no	—
59	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
60	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
61	C₄⋊Dic₁₃	—	2	8	no	—
62	C₄⋊Dic₁₃	—	4	8	no	—
63	#6101	—	4	8	no	—
64	#6101	—	4	16	no	—
65	C₄×Dic₁₃	SD₁₆	1	16	yes	—
66	C₄×Dic₁₃	C₂×D₄	1	4	yes	—
67	C₄×Dic₁₃	C₂×Q₈	1	4	yes	—
68	C₂×#1055	C₂×D₄	1	4	yes	—
69	C₂×#1055	C₂×Q₈	1	4	yes	—
70	C₂×#1055	C₂×Q₈	1	4	yes	—
71	C₂×#498	—	13	4	no	—
72	#2868	—	13	2	no	—
73	#1844	—	13	4	no	—
74	#1844	—	13	1	no	—
75	#1844	—	13	2	no	—
76	#1844	D₁₃	1	1	yes	characteristic
77	C₄²×C₈	—	13	1	no	—
78	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
79	C₂×C₄×C₁₃	—	4	4	no	—
80	C₂×C₄×C₁₃	—	4	8	no	—
81	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
82	C₂×C₄×C₁₃	C₂×SD₁₆	1	8	yes	—
83	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
84	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
85	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
87	C₂×Dic₁₃	—	4	4	no	—
88	C₂×Dic₁₃	—	4	8	no	—
89	C₂×Dic₁₃	#127	1	4	yes	—
90	C₂×Dic₁₃	C₄⋊Q₈	1	4	yes	—
91	C₂×Dic₁₃	C₂×SD₁₆	1	8	yes	—
92	C₂×Dic₁₃	C₂×SD₁₆	1	8	yes	—
93	Dic₂₆	—	8	16	no	—
94	C₈×C₁₃	C₄⋊Q₈	1	8	yes	complemented
95	#1055	C₄⋊Q₈	1	8	yes	complemented
96	C₂×C₄⋊Q₈	—	13	4	no	—
97	C₂×C₄⋊Q₈	—	26	4	no	—
98	#498	—	26	16	no	—
99	C₂×#106	—	13	4	no	—
100	C₂×#106	—	13	8	no	—
101	C₂×#106	C₂×D₁₃	1	4	yes	—
102	C₂×C₄×C₈	—	13	2	no	—
103	C₂×C₄×C₈	—	13	2	no	—
104	C₂×C₄×C₈	—	13	1	no	—
105	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
106	#384	—	13	4	no	—
107	#384	—	13	2	no	—
108	#384	—	26	4	no	—
109	#384	C₂×D₁₃	1	2	yes	—
110	C₄³	—	13	1	no	—
111	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
112	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
113	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
114	C₂²×C₁₃	C₂²×SD₁₆	1	4	yes	—
115	C₄×C₁₃	—	8	4	no	—
116	C₄×C₁₃	#498	1	8	yes	complemented
117	C₄×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
118	C₄×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
119	Dic₁₃	—	8	4	no	—
120	Dic₁₃	#492	1	8	yes	—
121	Dic₁₃	#498	1	8	yes	complemented
122	C₂²×Q₈	—	26	4	no	—
123	C₂²×C₈	—	13	2	no	—
124	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
125	C₄⋊Q₈	—	26	16	no	—
126	C₄⋊Q₈	—	52	16	no	—
127	C₂×C₄⋊C₄	—	2	4	no	—
128	C₂×C₄⋊C₄	—	13	4	no	—
129	C₂×C₄⋊C₄	—	26	4	no	—
130	C₂×C₄⋊C₄	—	26	8	no	—
131	C₂×C₄⋊C₄	—	26	4	no	—
132	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
133	C₂×C₄²	—	13	4	no	—
134	C₂×C₄²	—	13	1	no	—
135	C₂×C₄²	—	13	1	no	—
136	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
137	#106	—	2	8	no	—
138	#106	—	26	16	no	—
139	#106	—	26	8	no	—
140	C₄×C₈	—	13	8	no	—
141	C₄×C₈	—	13	8	no	—
142	C₄×C₈	—	13	4	no	—
143	C₄×C₈	Dic₂₆	1	4	yes	complemented
144	C₂×C₁₃	#2868	1	1	yes	characteristic
145	C₂×C₁₃	C₂×#492	1	2	yes	—
146	C₂×C₁₃	C₂×#498	1	2	yes	—
147	C₂×C₁₃	C₂×#498	1	2	yes	—
148	C₂×Q₈	—	52	8	no	—
149	C₂×Q₈	—	52	16	no	—
150	C₂²×C₄	—	2	4	no	—
151	C₂²×C₄	—	13	2	no	—
152	C₂²×C₄	—	13	2	no	—
153	C₂²×C₄	—	26	4	no	—
154	C₂²×C₄	D₄×D₁₃	1	2	yes	—
155	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
156	C₂×C₈	—	13	4	no	—
157	C₂×C₈	—	13	4	no	—
158	C₂×C₈	—	13	4	no	—
159	C₂×C₈	C₂×Dic₂₆	1	4	yes	—
160	C₂×C₈	D₄×D₁₃	1	4	yes	—
161	C₂×C₈	Q₈×D₁₃	1	4	yes	—
162	C₄⋊C₄	—	2	8	no	—
163	C₄⋊C₄	—	4	8	no	—
164	C₄⋊C₄	—	26	8	no	—
165	C₄⋊C₄	—	52	8	no	—
166	C₄⋊C₄	—	52	16	no	—
167	C₄⋊C₄	—	52	8	no	—
168	C₄²	—	13	16	no	—
169	C₄²	—	13	4	no	—
170	C₄²	—	13	4	no	—
171	C₄²	C₂×Dic₂₆	1	2	yes	—
172	C₄²	Q₈×D₁₃	1	2	yes	—
173	C₁₃	#33310	1	1	yes	characteristic, complemented, Sylow
174	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
175	Q₈	—	104	16	no	—
176	C₂×C₄	—	4	8	no	—
177	C₂×C₄	—	4	4	no	—
178	C₂×C₄	—	13	4	no	—
179	C₂×C₄	—	13	8	no	—
180	C₂×C₄	—	13	8	no	—
181	C₂×C₄	—	13	4	no	—
182	C₂×C₄	—	52	8	no	—
183	C₂×C₄	—	52	4	no	—
184	C₂×C₄	#88142	1	4	yes	—
185	C₂×C₄	SD₁₆×D₁₃	1	8	yes	—
186	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
187	C₂×C₄	C₂×D₄×D₁₃	1	2	yes	—
188	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
189	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
190	C₈	—	13	8	no	—
191	C₈	#88142	1	8	yes	complemented
192	C₂²	C₂×#88142	1	1	yes	characteristic
193	C₂²	D₁₃×#127	1	1	yes	characteristic
194	C₂²	D₁₃×C₄⋊Q₈	1	1	yes	characteristic
195	C₂²	C₂×SD₁₆×D₁₃	1	4	yes	—
196	C₄	—	8	4	no	—
197	C₄	—	13	8	no	—
198	C₄	—	13	8	no	—
199	C₄	—	104	4	no	—
200	C₄	#11718516	1	8	yes	complemented
201	C₄	C₂×#88142	1	2	yes	—
202	C₄	D₁₃×C₄⋊Q₈	1	2	yes	—
203	C₂	#13123233	1	1	yes	characteristic
204	C₂	D₁₃×#492	1	2	yes	—
205	C₂	D₁₃×#498	1	2	yes	—
206	C₂	C₂×#11718516	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₁₃
commutator, cosocle	C₂²×C₄×C₁₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1844	C₂
socle, prime radical	C₂³×C₁₃	C₂²×D₄
hypercenter	#1844	D₁₃
hypocenter	C₁₃	#33310
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

Complements

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

N	H ≅ G/N	type
39. C₄×C₈×C₁₃	Q₈	semidirect
42. C₈×Dic₁₃	Q₈	semidirect
44. C₄×#1055	Q₈	semidirect
94. C₈×C₁₃	C₄⋊Q₈	semidirect
95. #1055	C₄⋊Q₈	semidirect
116. C₄×C₁₃	#498	semidirect
121. Dic₁₃	#498	semidirect
143. C₄×C₈	Dic₂₆	semidirect
173. C₁₃	#33310	semidirect
191. C₈	#88142	semidirect
200. C₄	#11718516	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#11718516	2
#13123233	2
#13114993	2
#13114992	2
#13114991	2
C₄×C₈×Dic₁₃	2
C₁₃×#1844	2
#33310	13