Subgroups — #16789251

Order 3328.

390 conjugacy classes of subgroups.

The subgroup lattice has 196 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	2	yes	maximal
2	#13129875	C₂	1	2	yes	maximal
3	#13129874	C₂	1	2	yes	maximal
4	C₄×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#6092	C₂²	1	4	yes	—
6	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
7	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
8	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
9	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
11	C₄²×Dic₁₃	C₄	1	1	yes	characteristic
12	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
13	#11718258	C₄	1	8	yes	complemented
14	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₁₃	C₈	1	2	yes	—
18	C₂×C₄×Dic₁₃	C₈	1	2	yes	—
19	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
22	C₂²×#1055	C₂³	1	1	yes	characteristic
23	C₂×#6092	—	2	4	no	—
24	C₂×#6092	—	2	4	no	—
25	C₂×#6092	C₂×C₄	1	8	yes	—
26	C₄×C₈×C₁₃	—	2	2	no	—
27	C₈×Dic₁₃	—	2	2	no	—
28	C₈×Dic₁₃	—	2	2	no	—
29	C₈×Dic₁₃	C₈	1	4	yes	—
30	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
31	C₄×#1055	—	2	2	no	—
32	#12591	—	13	1	no	maximal, Sylow
33	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
34	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
36	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
37	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
38	C₂×C₈×C₁₃	—	2	1	no	—
39	C₂×C₈×C₁₃	—	2	1	no	—
40	C₂×C₈×C₁₃	C₄²	1	2	yes	—
41	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
42	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
43	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
44	C₄²×C₁₃	—	2	1	no	—
45	C₄²×C₁₃	—	2	1	no	—
46	C₄×Dic₁₃	—	2	4	no	—
47	C₄×Dic₁₃	—	2	1	no	—
48	C₄×Dic₁₃	—	2	1	no	—
49	C₄×Dic₁₃	—	2	4	no	—
50	C₄×Dic₁₃	C₄²	1	2	yes	—
51	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
52	C₂×#1055	—	2	1	no	—
53	C₂×#1055	—	2	1	no	—
54	C₂×#1055	C₂×C₈	1	2	yes	—
55	C₂×#1055	C₂²×C₄	1	2	yes	—
56	C₂×#1055	#41	1	2	yes	—
57	C₂×#1055	#41	1	2	yes	—
58	#6092	—	2	8	no	—
59	C₂×#346	—	13	2	no	—
60	C₄²×C₈	—	13	1	no	—
61	#1374	—	13	2	no	—
62	#1374	—	13	2	no	—
63	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
64	C₂×C₄×C₁₃	—	2	2	no	—
65	C₂×C₄×C₁₃	—	2	2	no	—
66	C₂×C₄×C₁₃	M₃₂	1	4	yes	—
67	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
68	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
69	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
73	C₂×Dic₁₃	—	2	2	no	—
74	C₂×Dic₁₃	—	2	2	no	—
75	C₂×Dic₁₃	—	2	2	no	—
76	C₂×Dic₁₃	—	2	2	no	—
77	C₂×Dic₁₃	C₄×C₈	1	2	yes	—
78	C₂×Dic₁₃	C₄×C₈	1	2	yes	—
79	C₂×Dic₁₃	M₃₂	1	4	yes	—
80	C₈×C₁₃	—	2	2	no	—
81	C₈×C₁₃	#97	1	4	yes	—
82	#1055	—	2	2	no	—
83	#1055	#117	1	4	yes	—
84	C₂²×C₁₆	—	13	4	no	—
85	C₂×C₄×C₈	—	13	1	no	—
86	C₂×C₄×C₈	—	13	1	no	—
87	C₂×C₄×C₈	—	13	1	no	—
88	C₂×C₄×C₈	—	13	1	no	—
89	C₂×C₄×C₈	—	13	1	no	—
90	C₂×C₄×C₈	#261	1	1	yes	characteristic
91	C₄³	—	13	1	no	—
92	#346	—	13	8	no	—
93	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
94	C₂²×C₁₃	#431	1	1	yes	characteristic
95	C₂²×C₁₃	#431	1	1	yes	characteristic
96	C₂²×C₁₃	C₂×M₃₂	1	2	yes	—
97	C₂²×C₁₃	C₂×M₃₂	1	2	yes	—
98	C₄×C₁₃	—	2	4	no	—
99	C₄×C₁₃	#376	1	1	yes	characteristic
100	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
101	C₄×C₁₃	#431	1	1	yes	characteristic
102	C₄×C₁₃	#431	1	1	yes	characteristic
103	Dic₁₃	—	2	2	no	—
104	Dic₁₃	—	2	2	no	—
105	Dic₁₃	—	2	4	no	—
106	C₂²×C₈	—	13	1	no	—
107	C₂²×C₈	—	13	1	no	—
108	C₂²×C₈	C₂×#261	1	1	yes	characteristic
109	C₂²×C₈	C₂×#261	1	1	yes	characteristic
110	C₂×C₄²	—	13	1	no	—
111	C₂×C₄²	—	13	2	no	—
112	C₂×C₄²	—	13	2	no	—
113	C₂×C₄²	—	13	1	no	—
114	C₂×C₄²	C₂×#261	1	1	yes	characteristic
115	C₂×C₁₆	—	13	8	no	—
116	C₂×C₁₆	—	26	4	no	—
117	C₂×C₁₆	—	26	4	no	—
118	C₄×C₈	—	2	2	no	—
119	C₄×C₈	—	13	4	no	—
120	C₄×C₈	—	13	4	no	—
121	C₄×C₈	—	26	2	no	—
122	C₄×C₈	—	26	2	no	—
123	C₄×C₈	—	26	2	no	—
124	C₂×C₁₃	#1744	1	1	yes	characteristic
125	C₂×C₁₃	C₄×M₃₂	1	1	yes	characteristic
126	C₂×C₁₃	C₄×M₃₂	1	1	yes	characteristic
127	C₂×C₁₃	#2163	1	2	yes	—
128	C₂×C₁₃	#2163	1	2	yes	—
129	C₂²×C₄	—	13	1	no	—
130	C₂²×C₄	—	13	1	no	—
131	C₂²×C₄	—	13	2	no	—
132	C₂²×C₄	D₁₃⋊C₈	1	2	yes	—
133	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
134	C₂×C₈	—	2	1	no	—
135	C₂×C₈	—	2	1	no	—
136	C₂×C₈	—	13	2	no	—
137	C₂×C₈	—	13	2	no	—
138	C₂×C₈	—	13	2	no	—
139	C₂×C₈	—	13	2	no	—
140	C₂×C₈	—	26	1	no	—
141	C₂×C₈	—	26	1	no	—
142	C₂×C₈	D₁₃⋊C₈	1	2	yes	—
143	C₂×C₈	#6118	1	2	yes	—
144	C₂×C₈	C₄×#261	1	2	yes	—
145	C₂×C₈	#6122	1	2	yes	—
146	C₄²	—	2	1	no	—
147	C₄²	—	2	1	no	—
148	C₄²	—	13	2	no	—
149	C₄²	—	13	2	no	—
150	C₄²	—	26	4	no	—
151	C₄²	—	26	4	no	—
152	C₄²	—	26	1	no	—
153	C₄²	—	26	1	no	—
154	C₁₆	—	26	8	no	—
155	C₁₃	#12591	1	1	yes	characteristic, complemented, Sylow
156	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	13	2	no	—
160	C₂×C₄	—	13	2	no	—
161	C₂×C₄	—	13	4	no	—
162	C₂×C₄	—	26	2	no	—
163	C₂×C₄	—	26	2	no	—
164	C₂×C₄	—	26	2	no	—
165	C₂×C₄	—	26	2	no	—
166	C₂×C₄	#88098	1	4	yes	—
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	4	no	—
175	C₈	—	26	2	no	—
176	C₈	#88110	1	4	yes	—
177	C₂²	C₄×D₁₃⋊C₈	1	1	yes	characteristic
178	C₂²	#11719051	1	1	yes	characteristic
179	C₂²	C₂×#88098	1	2	yes	—
180	C₂²	D₁₃⋊M₃₂	1	2	yes	—
181	C₂²	#11719125	1	1	yes	characteristic
182	C₄	—	2	4	no	—
183	C₄	—	26	2	no	—
184	C₄	—	26	2	no	—
185	C₄	—	26	4	no	—
186	C₄	#11719051	1	1	yes	characteristic
187	C₄	#11719057	1	1	yes	characteristic
188	C₄	C₂×#88110	1	1	yes	characteristic
189	C₄	#11719125	1	1	yes	characteristic
190	C₂	#13130551	1	1	yes	characteristic
191	C₂	C₄×#88098	1	1	yes	characteristic
192	C₂	#13131043	1	1	yes	characteristic
193	C₂	#13131198	1	2	yes	—
194	C₂	#13131200	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#261
commutator	C₂²×C₁₃	C₂×C₄×C₈
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle, prime radical	C₂³×C₁₃	C₂²×C₈
cosocle	C₂²×#1055	C₂³
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	#12591
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
13. #11718258	C₄	semidirect
155. C₁₃	#12591	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
#13129875	2
#13129874	2
C₄×C₈×Dic₁₃	2
#12591	13