Subgroups — #16786582

Order 3328.

330 conjugacy classes of subgroups.

The subgroup lattice has 162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131042	C₂	1	1	yes	maximal, characteristic
2	#13130039	C₂	1	1	yes	maximal, characteristic
3	#13129747	C₂	1	2	yes	maximal, complemented
4	C₁₆×#1057	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
6	#11719119	C₄	1	2	yes	—
7	C₂×#88106	C₄	1	2	yes	—
8	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
9	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
10	C₂²×#6090	C₄	1	1	yes	characteristic
11	#11718258	C₄	1	2	yes	—
12	#11718257	C₂²	1	2	yes	—
13	#11718251	C₄	1	2	yes	—
14	C₈×#1057	C₂²	1	2	yes	—
15	C₁₆×Dic₁₃	C₄	1	1	yes	characteristic
16	C₁₆×Dic₁₃	C₄	1	1	yes	characteristic
17	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
18	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	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⋊#1057	C₈	1	4	yes	—
23	C₄⋊#1057	C₈	1	4	yes	—
24	C₄×#1057	C₂×C₄	1	4	yes	—
25	#88106	C₈	1	8	yes	complemented
26	C₂×#6092	C₂×C₄	1	4	yes	—
27	C₂×C₁₃×C₁₆	C₈	1	4	yes	complemented
28	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
29	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
30	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
31	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
32	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
33	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
34	C₂×#6090	C₈	1	4	yes	complemented
35	C₂×#6090	C₂×C₄	1	1	yes	characteristic
36	C₂×#6090	C₂×C₄	1	1	yes	characteristic
37	#11399	—	13	1	no	maximal, Sylow
38	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
39	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
40	C₂×#1057	C₂×C₈	1	8	yes	—
41	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
43	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
44	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
46	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
47	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
48	C₂×#1055	C₄²	1	1	yes	characteristic
49	C₂×#1055	C₂×C₈	1	4	yes	—
50	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
51	#6092	C₂×C₈	1	8	yes	—
52	C₁₃×C₁₆	C₂×C₈	1	2	yes	—
53	C₁₃×C₁₆	C₂×C₈	1	2	yes	—
54	#6090	C₂×C₈	1	2	yes	—
55	#6090	C₂×C₈	1	2	yes	—
56	C₄×M₃₂	—	13	1	no	—
57	C₂×C₄×C₁₆	—	13	1	no	—
58	#1450	—	13	1	no	—
59	#1311	—	13	2	no	—
60	C₈×C₁₆	—	13	2	no	—
61	C₂³×C₁₃	C₄×C₈	1	1	yes	characteristic
62	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
63	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
64	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
65	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
66	C₂×Dic₁₃	—	2	4	no	—
67	C₂×Dic₁₃	C₄×C₈	1	2	yes	—
68	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
69	#1057	—	2	8	no	—
70	C₈×C₁₃	C₄×C₈	1	2	yes	—
71	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
72	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
73	#1055	C₄×C₈	1	2	yes	—
74	#1055	C₂²×C₈	1	2	yes	—
75	C₂×M₃₂	—	13	2	no	—
76	C₂²×C₁₆	—	13	1	no	—
77	C₂²×C₁₆	#261	1	1	yes	characteristic
78	#431	—	13	2	no	—
79	C₂×C₄×C₈	—	13	1	no	—
80	#346	—	13	2	no	—
81	C₄×C₁₆	—	13	2	no	—
82	C₄×C₁₆	—	13	1	no	—
83	C₄×C₁₆	—	13	1	no	—
84	C₄×C₁₆	—	13	1	no	—
85	C₄×C₁₆	—	13	1	no	—
86	#322	—	13	2	no	—
87	C₈²	—	13	2	no	—
88	C₂²×C₁₃	—	2	2	no	—
89	C₂²×C₁₃	C₈²	1	2	yes	—
90	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
91	C₄×C₁₃	C₈²	1	2	yes	—
92	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
93	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
94	Dic₁₃	—	2	2	no	—
95	Dic₁₃	#504	1	4	yes	—
96	C₂²×C₈	—	13	1	no	—
97	C₂²×C₈	C₂×#261	1	1	yes	characteristic
98	C₂×C₄²	—	13	1	no	—
99	M₃₂	—	13	8	no	—
100	C₂×C₁₆	—	13	4	no	—
101	C₂×C₁₆	—	13	4	no	—
102	C₂×C₁₆	—	13	1	no	—
103	C₂×C₁₆	—	13	1	no	—
104	C₂×C₁₆	#1057	1	4	yes	complemented
105	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
106	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
107	C₄⋊C₈	—	13	4	no	—
108	C₂²⋊C₈	—	13	4	no	—
109	C₄×C₈	—	13	4	no	—
110	C₄×C₈	—	13	1	no	—
111	C₄×C₈	—	13	1	no	—
112	C₄×C₈	—	13	1	no	—
113	C₄×C₈	—	13	1	no	—
114	C₂×C₁₃	—	2	2	no	—
115	C₂×C₁₃	C₂×C₈²	1	1	yes	characteristic
116	C₂×C₁₃	#2108	1	2	yes	—
117	C₂²×C₄	—	13	2	no	—
118	C₂²×C₄	C₄×#261	1	1	yes	characteristic
119	C₂×C₈	—	13	4	no	—
120	C₂×C₈	—	13	1	no	—
121	C₂×C₈	—	13	1	no	—
122	C₂×C₈	—	13	8	no	—
123	C₂×C₈	D₁₃⋊C₈	1	2	yes	—
124	C₂×C₈	C₄×#261	1	1	yes	characteristic
125	C₂×C₈	C₂×#1057	1	2	yes	—
126	C₂×C₈	C₂²×#261	1	1	yes	characteristic
127	C₄²	—	13	2	no	—
128	C₄²	—	13	1	no	—
129	C₄²	—	13	1	no	—
130	C₁₆	—	13	8	no	—
131	C₁₆	—	13	2	no	—
132	C₁₆	—	13	2	no	—
133	C₁₆	C₂×#1057	1	2	yes	—
134	C₁₆	C₂×#1057	1	2	yes	—
135	C₁₃	#11399	1	1	yes	characteristic, complemented, Sylow
136	C₂³	C₈×#261	1	1	yes	characteristic
137	C₂×C₄	—	13	2	no	—
138	C₂×C₄	—	13	2	no	—
139	C₂×C₄	—	26	4	no	—
140	C₂×C₄	C₈×#261	1	1	yes	characteristic
141	C₂×C₄	C₈×#261	1	2	yes	—
142	C₂×C₄	C₄×#1057	1	2	yes	—
143	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
144	C₈	—	13	2	no	—
145	C₈	—	13	2	no	—
146	C₈	—	26	8	no	—
147	C₈	C₄×#1057	1	2	yes	—
148	C₈	C₂×D₁₃⋊C₈	1	1	yes	characteristic
149	C₈	C₂²×#1057	1	1	yes	characteristic
150	C₂²	—	2	2	no	—
151	C₂²	C₈×#1057	1	2	yes	—
152	C₂²	C₂×C₈×#261	1	1	yes	characteristic
153	C₄	—	13	4	no	—
154	C₄	—	26	2	no	—
155	C₄	C₈×#1057	1	2	yes	—
156	C₄	C₂×C₈×#261	1	1	yes	characteristic
157	C₄	C₂×C₄×#1057	1	1	yes	characteristic
158	C₂	—	2	2	no	—
159	C₂	C₂×C₈×#1057	1	1	yes	characteristic
160	C₂	#13131044	1	2	yes	—

	subgroup	G/H
center	C₂×C₁₆	C₂×#261
commutator	C₂×C₁₃	C₂×C₈²
Frattini	C₂×C₈	C₂²×#261
Fitting	C₂²×C₁₃×C₁₆	C₄
socle	C₂²×C₁₃	C₂×C₄×C₈
prime radical	C₂³×C₁₃	C₄×C₈
cosocle	C₈×Dic₁₃	C₂³
hypercenter	C₂²×C₁₆	#261
hypocenter	C₁₃	#11399
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
3. #13129747	C₂	semidirect
4. C₁₆×#1057	C₂	semidirect
25. #88106	C₈	semidirect
27. C₂×C₁₃×C₁₆	C₈	semidirect
34. C₂×#6090	C₈	semidirect
104. C₂×C₁₆	#1057	semidirect
135. C₁₃	#11399	semidirect

Maximal subgroups

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

subgroup	index
#13131042	2
#13130039	2
#13129747	2
C₁₆×#1057	2
C₂×C₁₆×Dic₁₃	2
#11399	13