Subgroups — #16789255

Order 3328.

358 conjugacy classes of subgroups.

The subgroup lattice has 194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718258	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718257	C₂	1	1	yes	maximal, characteristic
3	#13129875	C₂	1	2	yes	maximal
4	#13129874	C₂	1	2	yes	maximal
5	#13114524	C₂	1	1	yes	maximal, characteristic
6	C₂²×#6092	C₂²	1	2	yes	—
7	C₂²×#6092	C₂²	1	2	yes	—
8	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
9	C₂×#88055	C₄	1	1	yes	characteristic
10	C₂×#88055	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
13	#11718593	C₄	1	1	yes	characteristic
14	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
15	#11718258	C₄	1	4	yes	complemented
16	#11718257	C₄	1	4	yes	complemented
17	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
23	C₂²×#1055	C₂³	1	1	yes	characteristic
24	C₂×#6092	—	2	2	no	—
25	C₂×#6092	—	2	2	no	—
26	C₂×#6092	—	2	2	no	—
27	C₂×#6092	—	2	2	no	—
28	C₂×#6092	C₂×C₄	1	4	yes	—
29	C₂×#6092	C₂×C₄	1	4	yes	—
30	C₁₃×#97	—	2	2	no	—
31	#88071	C₈	1	4	yes	—
32	#88055	—	2	2	no	—
33	#88055	C₈	1	4	yes	—
34	C₈×Dic₁₃	—	2	2	no	—
35	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
36	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
37	C₄×#1055	—	2	2	no	—
38	#12592	—	13	1	no	maximal, Sylow
39	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
40	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
42	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
43	C₂×C₈×C₁₃	—	2	1	no	—
44	C₂×C₈×C₁₃	—	2	1	no	—
45	C₂×C₈×C₁₃	C₄²	1	2	yes	—
46	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
47	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
48	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
49	C₄²×C₁₃	—	2	1	no	—
50	C₄²×C₁₃	—	2	1	no	—
51	C₄×Dic₁₃	—	2	1	no	—
52	C₄×Dic₁₃	—	2	1	no	—
53	C₄×Dic₁₃	C₄²	1	2	yes	—
54	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
55	C₂×#1055	—	2	1	no	—
56	C₂×#1055	—	2	1	no	—
57	C₂×#1055	C₂×C₈	1	2	yes	—
58	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
59	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
60	C₂×#1055	#41	1	2	yes	—
61	C₂×#1055	#41	1	2	yes	—
62	#6092	—	2	4	no	—
63	#6092	—	2	4	no	—
64	C₂×#346	—	13	1	no	—
65	C₂×C₄×C₁₆	—	13	1	no	—
66	#1726	—	13	1	no	—
67	#1374	—	13	2	no	—
68	#1374	—	13	2	no	—
69	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
70	C₂×C₄×C₁₃	—	2	2	no	—
71	C₂×C₄×C₁₃	—	2	4	no	—
72	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
73	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
74	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
75	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
76	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
78	C₂×Dic₁₃	—	2	4	no	—
79	C₂×Dic₁₃	—	2	2	no	—
80	C₂×Dic₁₃	—	2	4	no	—
81	C₂×Dic₁₃	C₄×C₈	1	4	yes	—
82	C₈×C₁₃	—	2	2	no	—
83	C₈×C₁₃	#97	1	4	yes	—
84	#1055	—	2	2	no	—
85	#1055	#117	1	2	yes	—
86	#1055	#117	1	2	yes	—
87	C₂²×C₁₆	—	13	2	no	—
88	C₂²×C₁₆	—	13	2	no	—
89	C₂×#97	—	13	1	no	—
90	C₂×#97	—	13	1	no	—
91	C₂×#97	#261	1	1	yes	characteristic
92	C₂×C₄×C₈	—	13	1	no	—
93	C₂×C₄×C₈	—	13	1	no	—
94	C₂×C₄×C₈	—	13	1	no	—
95	#376	—	13	1	no	—
96	#346	—	13	4	no	—
97	C₄×C₁₆	—	13	4	no	—
98	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
99	C₂²×C₁₃	#431	1	1	yes	characteristic
100	C₂²×C₁₃	#431	1	1	yes	characteristic
101	C₂²×C₁₃	#504	1	4	yes	—
102	C₄×C₁₃	—	4	2	no	—
103	C₄×C₁₃	#376	1	1	yes	characteristic
104	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
105	C₄×C₁₃	#431	1	1	yes	characteristic
106	C₄×C₁₃	#431	1	1	yes	characteristic
107	Dic₁₃	—	2	4	no	—
108	Dic₁₃	—	4	2	no	—
109	C₂²×C₈	—	13	1	no	—
110	C₂²×C₈	—	13	1	no	—
111	C₂²×C₈	C₂×#261	1	1	yes	characteristic
112	C₂²×C₈	C₂×#261	1	1	yes	characteristic
113	C₂×C₄²	—	13	1	no	—
114	C₂×C₄²	—	13	1	no	—
115	C₂×C₄²	C₂×#261	1	1	yes	characteristic
116	C₂×C₁₆	—	13	4	no	—
117	C₂×C₁₆	—	13	4	no	—
118	C₂×C₁₆	—	26	2	no	—
119	C₂×C₁₆	—	26	2	no	—
120	C₂×C₁₆	—	26	2	no	—
121	C₂×C₁₆	—	26	2	no	—
122	#97	—	2	2	no	—
123	#97	—	13	4	no	—
124	#97	—	26	2	no	—
125	C₄×C₈	—	13	2	no	—
126	C₄×C₈	—	13	2	no	—
127	C₄×C₈	—	26	2	no	—
128	C₄×C₈	—	26	2	no	—
129	#95	—	13	4	no	—
130	C₂×C₁₃	#1744	1	1	yes	characteristic
131	C₂×C₁₃	#2108	1	2	yes	—
132	C₂×C₁₃	#2164	1	2	yes	—
133	C₂×C₁₃	#2164	1	2	yes	—
134	C₂²×C₄	—	13	2	no	—
135	C₂²×C₄	—	13	2	no	—
136	C₂²×C₄	D₁₃⋊C₈	1	2	yes	—
137	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
138	C₂×C₈	—	2	1	no	—
139	C₂×C₈	—	2	1	no	—
140	C₂×C₈	—	13	1	no	—
141	C₂×C₈	—	13	1	no	—
142	C₂×C₈	—	13	2	no	—
143	C₂×C₈	—	13	2	no	—
144	C₂×C₈	—	13	2	no	—
145	C₂×C₈	—	26	1	no	—
146	C₂×C₈	—	26	1	no	—
147	C₂×C₈	D₁₃⋊C₈	1	2	yes	—
148	C₂×C₈	#6118	1	2	yes	—
149	C₂×C₈	C₄×#261	1	2	yes	—
150	C₂×C₈	#6122	1	2	yes	—
151	C₄²	—	2	1	no	—
152	C₄²	—	2	1	no	—
153	C₄²	—	13	2	no	—
154	C₄²	—	13	2	no	—
155	C₄²	—	26	1	no	—
156	C₄²	—	26	1	no	—
157	C₁₆	—	26	4	no	—
158	C₁₆	—	26	4	no	—
159	C₁₃	#12592	1	1	yes	characteristic, complemented, Sylow
160	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
161	C₂×C₄	—	2	4	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	13	4	no	—
164	C₂×C₄	—	26	4	no	—
165	C₂×C₄	—	26	2	no	—
166	C₂×C₄	—	26	4	no	—
167	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
168	C₂×C₄	C₂×#6118	1	1	yes	characteristic
169	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
170	C₂×C₄	#88237	1	1	yes	characteristic
171	C₂×C₄	#88237	1	1	yes	characteristic
172	C₂×C₄	C₂×#6122	1	1	yes	characteristic
173	C₈	—	2	2	no	—
174	C₈	—	13	2	no	—
175	C₈	—	13	2	no	—
176	C₈	—	26	2	no	—
177	C₈	#88110	1	4	yes	—
178	C₂²	C₄×D₁₃⋊C₈	1	1	yes	characteristic
179	C₂²	#11719051	1	1	yes	characteristic
180	C₂²	#11719096	1	4	yes	—
181	C₂²	#11719125	1	1	yes	characteristic
182	C₄	—	4	2	no	—
183	C₄	—	26	4	no	—
184	C₄	—	52	2	no	—
185	C₄	#11719051	1	1	yes	characteristic
186	C₄	#11719057	1	1	yes	characteristic
187	C₄	C₂×#88110	1	1	yes	characteristic
188	C₄	#11719125	1	1	yes	characteristic
189	C₂	#13130551	1	1	yes	characteristic
190	C₂	#13131046	1	2	yes	—
191	C₂	#13131202	1	2	yes	—
192	C₂	#13131204	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#261
commutator	C₂²×C₁₃	C₂×C₄×C₈
Fitting	C₂×C₁₃×#97	C₄
socle, prime radical	C₂³×C₁₃	C₂²×C₈
cosocle	C₂²×#1055	C₂³
hypercenter	C₂×#97	#261
hypocenter	C₁₃	#12592
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
15. #11718258	C₄	semidirect
16. #11718257	C₄	semidirect
159. C₁₃	#12592	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718258	2
C₂×#11718257	2
#13129875	2
#13129874	2
#13114524	2
#12592	13