Subgroups — #16789020

Order 3328.

478 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718216	C₂	1	2	yes	maximal
2	C₄×D₁₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×#261	C₂	1	2	yes	maximal
4	#13130492	C₂	1	1	yes	maximal, characteristic
5	D₁₃×#346	C₂	1	1	yes	maximal, characteristic
6	C₂×#88100	C₄	1	2	yes	—
7	C₂×C₈×#261	C₂²	1	2	yes	—
8	C₂×D₁₃⋊C₁₆	C₂²	1	1	yes	characteristic
9	C₂×D₁₃⋊C₁₆	C₂²	1	1	yes	characteristic
10	#11719057	C₄	1	1	yes	characteristic
11	#11719047	C₄	1	1	yes	characteristic
12	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
13	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
14	#11718257	C₄	1	2	yes	complemented
15	C₄×#6092	C₄	1	2	yes	complemented
16	#11718216	C₄	1	8	yes	complemented
17	C₁₆×#261	C₄	1	8	yes	complemented
18	C₁₃×#346	C₄	1	1	yes	characteristic, complemented
19	#11718094	C₄	1	2	yes	complemented
20	#11718053	C₄	1	1	yes	characteristic, complemented
21	C₂×C₄×#261	C₂×C₄	1	2	yes	—
22	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
23	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
25	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
26	(C₂×#261)⋊C₄	C₈	1	4	yes	—
27	#88110	C₈	1	4	yes	—
28	C₂×#6092	C₂×C₄	1	2	yes	—
29	C₂×#6092	C₂×C₄	1	2	yes	—
30	#88100	C₈	1	8	yes	—
31	C₈×#261	C₂×C₄	1	4	yes	—
32	C₈×#261	C₂×C₄	1	4	yes	—
33	D₁₃⋊C₁₆	C₂×C₄	1	4	yes	—
34	D₁₃⋊C₁₆	C₂×C₄	1	4	yes	—
35	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
36	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
38	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂×#6090	C₂×C₄	1	2	yes	—
40	C₄×#1055	C₂×C₄	1	1	yes	characteristic
41	C₁₆×D₁₃	C₂×C₄	1	4	yes	—
42	C₁₆×D₁₃	C₂×C₄	1	4	yes	—
43	#12539	—	13	1	no	maximal, Sylow
44	C₂²×#261	C₂×C₈	1	4	yes	—
45	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
46	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₂×#1057	C₂×C₈	1	4	yes	—
48	C₄×#261	C₄²	1	4	yes	—
49	C₄×#261	C₂×C₈	1	4	yes	—
50	D₁₃⋊C₈	C₄²	1	4	yes	—
51	D₁₃⋊C₈	C₂×C₈	1	4	yes	—
52	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
53	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
54	C₄²×C₁₃	C₄²	1	1	yes	characteristic
55	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
56	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
57	C₂×#1055	C₄²	1	1	yes	characteristic
58	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
59	C₈×D₁₃	C₂×C₈	1	4	yes	—
60	C₈×D₁₃	C₂²×C₄	1	2	yes	—
61	C₈×D₁₃	C₂²×C₄	1	2	yes	—
62	#6092	C₄²	1	4	yes	—
63	#6092	C₄²	1	4	yes	—
64	C₁₃×C₁₆	C₄²	1	4	yes	—
65	#6090	C₄²	1	4	yes	—
66	C₂×#346	—	13	2	no	—
67	C₂×#346	—	13	1	no	—
68	C₂×C₄×C₁₆	—	13	2	no	—
69	C₂×C₄×C₁₆	—	13	1	no	—
70	#1726	—	13	1	no	—
71	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
72	C₂×#261	—	2	8	no	—
73	C₂×#261	C₄×C₈	1	8	yes	—
74	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
75	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
76	C₂×Dic₁₃	C₄×C₈	1	2	yes	—
77	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
78	C₄×D₁₃	—	2	4	no	—
79	C₄×D₁₃	C₂×C₄²	1	2	yes	—
80	C₄×D₁₃	C₂²×C₈	1	2	yes	—
81	#1057	C₄×C₈	1	8	yes	—
82	C₈×C₁₃	C₄×C₈	1	2	yes	—
83	C₈×C₁₃	C₂×C₄²	1	2	yes	—
84	#1055	C₄×C₈	1	2	yes	—
85	#1055	C₂×C₄²	1	1	yes	characteristic
86	#1055	C₂×C₄²	1	1	yes	characteristic
87	C₂²×C₁₆	—	13	1	no	—
88	C₂²×C₁₆	—	13	1	no	—
89	C₂²×C₁₆	—	13	2	no	—
90	C₂×#97	—	13	1	no	—
91	C₂×#97	—	13	2	no	—
92	C₂×C₄×C₈	—	13	2	no	—
93	C₂×C₄×C₈	—	13	1	no	—
94	#376	—	13	1	no	—
95	#346	—	13	8	no	—
96	#346	—	13	2	no	—
97	#346	—	13	1	no	—
98	#346	#261	1	1	yes	characteristic, complemented
99	C₄×C₁₆	—	13	8	no	—
100	C₄×C₁₆	—	13	2	no	—
101	C₄×C₁₆	—	13	2	no	—
102	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
103	C₂×D₁₃	C₂×C₄×C₈	1	2	yes	—
104	C₂×D₁₃	#504	1	4	yes	—
105	#261	—	2	8	no	—
106	C₄×C₁₃	—	2	2	no	—
107	C₄×C₁₃	C₄³	1	1	yes	characteristic
108	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
109	Dic₁₃	—	2	2	no	—
110	Dic₁₃	C₂×C₄×C₈	1	2	yes	—
111	C₂²×C₈	—	13	2	no	—
112	C₂²×C₈	—	13	1	no	—
113	C₂²×C₈	—	13	1	no	—
114	C₂×C₄²	—	13	2	no	—
115	C₂×C₄²	—	13	1	no	—
116	C₂×C₁₆	—	13	4	no	—
117	C₂×C₁₆	—	13	4	no	—
118	C₂×C₁₆	—	13	2	no	—
119	C₂×C₁₆	—	13	2	no	—
120	C₂×C₁₆	—	13	2	no	—
121	C₂×C₁₆	—	13	4	no	—
122	C₂×C₁₆	—	13	4	no	—
123	C₂×C₁₆	C₂×#261	1	2	yes	—
124	#97	—	13	8	no	—
125	#97	—	13	4	no	—
126	C₄×C₈	—	13	4	no	—
127	C₄×C₈	—	13	4	no	—
128	C₄×C₈	—	13	1	no	—
129	C₄×C₈	—	13	1	no	—
130	C₄×C₈	—	13	1	no	—
131	C₄×C₈	C₂×#261	1	1	yes	characteristic
132	#95	—	13	4	no	—
133	C₂×C₁₃	C₄²×C₈	1	1	yes	characteristic
134	C₂×C₁₃	#2108	1	2	yes	—
135	D₁₃	#2108	1	4	yes	—
136	C₂²×C₄	—	13	1	no	—
137	C₂²×C₄	—	13	4	no	—
138	C₂²×C₄	—	13	2	no	—
139	C₂×C₈	—	13	4	no	—
140	C₂×C₈	—	13	4	no	—
141	C₂×C₈	—	13	4	no	—
142	C₂×C₈	—	13	1	no	—
143	C₂×C₈	—	13	1	no	—
144	C₂×C₈	—	13	4	no	—
145	C₂×C₈	—	13	2	no	—
146	C₂×C₈	—	13	2	no	—
147	C₂×C₈	C₄×#261	1	1	yes	characteristic
148	C₂×C₈	C₂²×#261	1	1	yes	characteristic
149	C₄²	—	13	4	no	—
150	C₄²	—	13	4	no	—
151	C₄²	—	13	2	no	—
152	C₄²	—	13	1	no	—
153	C₄²	C₄×#261	1	1	yes	characteristic
154	C₁₆	—	13	4	no	—
155	C₁₆	—	13	4	no	—
156	C₁₆	—	13	4	no	—
157	C₁₆	C₄×#261	1	4	yes	—
158	C₁₃	#12539	1	1	yes	characteristic, complemented, Sylow
159	C₂³	—	13	1	no	—
160	C₂×C₄	—	13	1	no	—
161	C₂×C₄	—	13	2	no	—
162	C₂×C₄	—	13	2	no	—
163	C₂×C₄	—	13	8	no	—
164	C₂×C₄	—	13	2	no	—
165	C₂×C₄	—	26	4	no	—
166	C₂×C₄	—	26	8	no	—
167	C₂×C₄	C₈×#261	1	2	yes	—
168	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
169	C₈	—	13	8	no	—
170	C₈	—	13	1	no	—
171	C₈	—	13	1	no	—
172	C₈	—	13	2	no	—
173	C₈	C₈×#261	1	2	yes	—
174	C₈	C₂×C₄×#261	1	2	yes	—
175	C₂²	—	13	4	no	—
176	C₂²	—	13	2	no	—
177	C₂²	C₂×C₈×#261	1	1	yes	characteristic
178	C₄	—	2	2	no	—
179	C₄	—	13	2	no	—
180	C₄	—	26	8	no	—
181	C₄	—	26	2	no	—
182	C₄	C₄²×#261	1	1	yes	characteristic
183	C₄	C₂×C₈×#261	1	1	yes	characteristic
184	C₂	—	13	4	no	—
185	C₂	C₄×C₈×#261	1	1	yes	characteristic
186	C₂	#13131048	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#261
commutator	C₂×C₁₃	C₄²×C₈
Fitting	C₁₃×#346	C₄
socle	C₂²×C₁₃	C₂×C₄×C₈
prime radical	C₂²×D₁₃	C₂²×C₈
cosocle	C₂×C₈×D₁₃	C₂³
hypercenter	#346	#261
hypocenter	C₁₃	#12539
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
14. #11718257	C₄	semidirect
15. C₄×#6092	C₄	semidirect
16. #11718216	C₄	semidirect
17. C₁₆×#261	C₄	semidirect
18. C₁₃×#346	C₄	semidirect
19. #11718094	C₄	semidirect
20. #11718053	C₄	semidirect
98. #346	#261	semidirect
158. C₁₃	#12539	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718216	2
C₄×D₁₃⋊C₁₆	2
C₂×C₁₆×#261	2
#13130492	2
D₁₃×#346	2
#12539	13