Subgroups — #16789245

Order 3328.

414 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	C₄×D₁₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₄×C₈×#261	C₂	1	1	yes	maximal, characteristic
3	(C₂×#261)⋊C₁₆	C₂	1	4	yes	maximal
4	C₄×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₈×#261	C₄	1	2	yes	—
6	C₂×C₈×#261	C₂²	1	2	yes	—
7	C₂×D₁₃⋊C₁₆	C₂²	1	2	yes	—
8	C₄²×#261	C₄	1	1	yes	characteristic
9	C₄×D₁₃⋊C₈	C₄	1	1	yes	characteristic
10	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
11	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	#11718257	C₄	1	2	yes	complemented
13	C₄×#6092	C₄	1	2	yes	complemented
14	C₄×C₁₃×C₁₆	C₄	1	1	yes	characteristic, complemented
15	C₁₆×Dic₁₃	C₄	1	2	yes	complemented
16	C₄×#6090	C₄	1	1	yes	characteristic, complemented
17	C₂×C₄×#261	C₈	1	2	yes	—
18	C₂×C₄×#261	C₈	1	2	yes	—
19	C₂×C₄×#261	C₂×C₄	1	2	yes	—
20	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
21	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
23	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
24	C₄×#1057	C₈	1	2	yes	—
25	C₄×#1057	C₈	1	2	yes	—
26	C₂×#6092	C₂×C₄	1	4	yes	—
27	C₈×#261	—	2	4	no	—
28	C₈×#261	—	2	4	no	—
29	D₁₃⋊C₁₆	—	2	4	no	—
30	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
31	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
33	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂×#6090	C₂×C₄	1	2	yes	—
35	C₄×#1055	C₂×C₄	1	1	yes	characteristic
36	C₁₆×D₁₃	—	2	4	no	—
37	#12590	—	13	1	no	maximal, Sylow
38	C₂²×#261	C₂×C₈	1	4	yes	—
39	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
40	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
41	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×#1057	C₂×C₈	1	4	yes	—
43	C₄×#261	—	2	4	no	—
44	C₄×#261	—	2	2	no	—
45	C₄×#261	—	2	2	no	—
46	C₄×#261	C₁₆	1	8	yes	complemented
47	D₁₃⋊C₈	—	2	2	no	—
48	D₁₃⋊C₈	—	2	2	no	—
49	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
50	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
51	C₄²×C₁₃	C₄²	1	1	yes	characteristic
52	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
53	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
54	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
55	C₂×#1055	C₄²	1	1	yes	characteristic
56	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
57	C₈×D₁₃	M₁₆	1	4	yes	—
58	C₈×D₁₃	#41	1	4	yes	—
59	#6092	—	2	4	no	—
60	C₁₃×C₁₆	—	2	2	no	—
61	#6090	—	2	2	no	—
62	C₂×C₄×C₁₆	—	13	1	no	—
63	C₂×C₄×C₁₆	—	13	1	no	—
64	C₄²×C₈	—	13	1	no	—
65	#1374	—	13	4	no	—
66	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
67	C₂×#261	—	2	4	no	—
68	C₂×#261	—	2	4	no	—
69	C₂×#261	C₂×C₁₆	1	8	yes	—
70	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
73	C₂×Dic₁₃	C₄×C₈	1	1	yes	characteristic
74	C₂×Dic₁₃	C₄×C₈	1	1	yes	characteristic
75	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
76	C₄×D₁₃	C₂×C₁₆	1	4	yes	—
77	C₄×D₁₃	M₃₂	1	4	yes	—
78	C₄×D₁₃	#117	1	2	yes	—
79	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
80	#1057	—	2	4	no	—
81	C₈×C₁₃	#97	1	2	yes	—
82	C₈×C₁₃	#117	1	2	yes	—
83	#1055	#97	1	2	yes	—
84	#1055	#117	1	2	yes	—
85	C₂²×C₁₆	—	13	2	no	—
86	C₂²×C₁₆	—	13	2	no	—
87	C₂×C₄×C₈	—	13	1	no	—
88	C₂×C₄×C₈	—	13	1	no	—
89	C₂×C₄×C₈	—	13	2	no	—
90	C₂×C₄×C₈	—	13	2	no	—
91	C₄³	—	13	1	no	—
92	C₄×C₁₆	—	13	2	no	—
93	C₄×C₁₆	—	13	2	no	—
94	C₄×C₁₆	—	13	2	no	—
95	C₄×C₁₆	—	13	1	no	—
96	C₄×C₁₆	#261	1	1	yes	characteristic, complemented
97	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
98	C₂×D₁₃	#431	1	2	yes	—
99	C₂×D₁₃	C₂²×C₁₆	1	2	yes	—
100	C₂×D₁₃	C₂×M₃₂	1	2	yes	—
101	#261	—	2	8	no	—
102	C₄×C₁₃	C₄×C₁₆	1	2	yes	—
103	C₄×C₁₃	#346	1	2	yes	—
104	C₄×C₁₃	#376	1	1	yes	characteristic
105	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
106	Dic₁₃	C₄×C₁₆	1	2	yes	—
107	Dic₁₃	#346	1	2	yes	—
108	Dic₁₃	#431	1	2	yes	—
109	C₂²×C₈	—	13	1	no	—
110	C₂²×C₈	—	13	1	no	—
111	C₂²×C₈	—	13	2	no	—
112	C₂×C₄²	—	13	2	no	—
113	C₂×C₄²	—	13	1	no	—
114	C₂×C₄²	—	13	2	no	—
115	C₂×C₄²	—	13	2	no	—
116	C₂×C₁₆	—	13	4	no	—
117	C₂×C₁₆	—	13	2	no	—
118	C₂×C₁₆	—	26	4	no	—
119	C₂×C₁₆	—	26	4	no	—
120	C₂×C₁₆	C₂×#261	1	2	yes	—
121	C₄×C₈	—	13	2	no	—
122	C₄×C₈	—	13	2	no	—
123	C₄×C₈	—	13	1	no	—
124	C₄×C₈	—	13	1	no	—
125	C₄×C₈	—	13	1	no	—
126	C₄×C₈	—	26	4	no	—
127	C₄×C₈	—	26	4	no	—
128	C₄×C₈	C₂×#261	1	1	yes	characteristic
129	C₂×C₁₃	#1744	1	1	yes	characteristic
130	C₂×C₁₃	C₂×C₄×C₁₆	1	1	yes	characteristic
131	C₂×C₁₃	C₂×#346	1	1	yes	characteristic
132	D₁₃	#2162	1	4	yes	—
133	C₂²×C₄	—	13	1	no	—
134	C₂²×C₄	—	13	1	no	—
135	C₂²×C₄	—	13	1	no	—
136	C₂²×C₄	—	13	4	no	—
137	C₂×C₈	—	13	1	no	—
138	C₂×C₈	—	13	1	no	—
139	C₂×C₈	—	13	4	no	—
140	C₂×C₈	—	13	4	no	—
141	C₂×C₈	—	13	4	no	—
142	C₂×C₈	—	26	2	no	—
143	C₂×C₈	—	26	2	no	—
144	C₂×C₈	C₄×#261	1	1	yes	characteristic
145	C₂×C₈	C₂²×#261	1	1	yes	characteristic
146	C₄²	—	13	8	no	—
147	C₄²	—	13	1	no	—
148	C₄²	—	13	1	no	—
149	C₄²	—	13	1	no	—
150	C₄²	—	26	2	no	—
151	C₄²	—	26	2	no	—
152	C₄²	—	26	4	no	—
153	C₄²	C₄×#261	1	1	yes	characteristic
154	C₁₆	—	2	2	no	—
155	C₁₆	—	26	4	no	—
156	C₁₆	—	26	2	no	—
157	C₁₃	#12590	1	1	yes	characteristic, complemented, Sylow
158	C₂³	—	13	1	no	—
159	C₂×C₄	—	13	1	no	—
160	C₂×C₄	—	13	1	no	—
161	C₂×C₄	—	13	1	no	—
162	C₂×C₄	—	13	4	no	—
163	C₂×C₄	—	13	4	no	—
164	C₂×C₄	—	13	2	no	—
165	C₂×C₄	—	13	2	no	—
166	C₂×C₄	—	13	8	no	—
167	C₂×C₄	—	26	4	no	—
168	C₂×C₄	—	26	4	no	—
169	C₂×C₄	C₈×#261	1	1	yes	characteristic
170	C₂×C₄	C₈×#261	1	1	yes	characteristic
171	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
172	C₈	—	13	2	no	—
173	C₈	—	13	2	no	—
174	C₈	—	26	4	no	—
175	C₈	#88100	1	2	yes	—
176	C₈	#88237	1	2	yes	—
177	C₂²	—	13	2	no	—
178	C₂²	—	13	2	no	—
179	C₂²	—	13	2	no	—
180	C₂²	C₂×C₈×#261	1	1	yes	characteristic
181	C₄	—	13	2	no	—
182	C₄	—	13	2	no	—
183	C₄	—	13	2	no	—
184	C₄	—	26	8	no	—
185	C₄	C₁₆×#261	1	2	yes	—
186	C₄	#11718216	1	2	yes	—
187	C₄	#11719057	1	1	yes	characteristic
188	C₄	C₂×#88100	1	1	yes	characteristic
189	C₂	—	13	4	no	—
190	C₂	#13130549	1	1	yes	characteristic
191	C₂	C₂×C₁₆×#261	1	1	yes	characteristic
192	C₂	C₂×#11718216	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂×#261
commutator	C₂×C₁₃	C₂×C₄×C₁₆
Frattini	C₂×C₈	C₂²×#261
Fitting	C₄×C₁₃×C₁₆	C₄
socle	C₂²×C₁₃	C₂×C₄×C₈
prime radical	C₂²×D₁₃	C₂²×C₈
cosocle	C₂×C₈×D₁₃	C₂³
hypercenter	C₄×C₁₆	#261
hypocenter	C₁₃	#12590
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
12. #11718257	C₄	semidirect
13. C₄×#6092	C₄	semidirect
14. C₄×C₁₃×C₁₆	C₄	semidirect
15. C₁₆×Dic₁₃	C₄	semidirect
16. C₄×#6090	C₄	semidirect
46. C₄×#261	C₁₆	semidirect
96. C₄×C₁₆	#261	semidirect
157. C₁₃	#12590	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₁₃⋊C₁₆	2
C₄×C₈×#261	2
(C₂×#261)⋊C₁₆	2
C₄×C₁₆×D₁₃	2
#12590	13