Subgroups — #16789019

Order 3328.

478 conjugacy classes of subgroups.

The subgroup lattice has 164 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	C₂×#11718231	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718257	C₂	1	2	yes	maximal
4	C₂×C₄×#6092	C₂	1	1	yes	maximal, characteristic
5	#13114524	C₂	1	1	yes	maximal, characteristic
6	C₂²×#6092	C₂²	1	1	yes	characteristic
7	C₂²×#6092	C₂²	1	1	yes	characteristic
8	C₂²×#6092	C₂²	1	2	yes	—
9	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
10	C₂×#88055	C₄	1	2	yes	—
11	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
12	#11718593	C₄	1	1	yes	characteristic
13	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
14	#11718258	C₄	1	8	yes	complemented
15	#11718257	C₄	1	8	yes	complemented
16	#11718231	C₄	1	4	yes	complemented
17	C₄×#6092	C₄	1	4	yes	complemented
18	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
21	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
22	C₂²×#1055	C₂³	1	1	yes	characteristic
23	C₂×#6092	C₂×C₄	1	2	yes	—
24	C₂×#6092	C₂×C₄	1	2	yes	—
25	C₂×#6092	C₂×C₄	1	4	yes	—
26	C₂×#6092	C₂×C₄	1	4	yes	—
27	C₂×#6092	C₂×C₄	1	4	yes	—
28	C₂×#6092	C₂×C₄	1	4	yes	—
29	C₂×#6092	C₂×C₄	1	4	yes	—
30	C₁₃×#97	C₈	1	4	yes	—
31	#88071	C₈	1	4	yes	—
32	#88055	C₈	1	8	yes	—
33	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
34	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
35	C₄×#1055	C₂×C₄	1	2	yes	—
36	C₄×#1055	C₂×C₄	1	2	yes	—
37	#12539	—	13	1	no	maximal, Sylow
38	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
39	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
40	C₂²×Dic₁₃	C₂×C₈	1	4	yes	—
41	C₂×C₈×C₁₃	C₄²	1	4	yes	—
42	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
43	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
44	C₄²×C₁₃	C₄²	1	2	yes	—
45	C₄²×C₁₃	C₂×C₈	1	2	yes	—
46	C₄×Dic₁₃	C₄²	1	4	yes	—
47	C₄×Dic₁₃	C₂×C₈	1	4	yes	—
48	C₂×#1055	C₄²	1	2	yes	—
49	C₂×#1055	C₂×C₈	1	4	yes	—
50	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
51	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
52	C₂×#1055	C₂²×C₄	1	2	yes	—
53	C₂×#1055	C₂²×C₄	1	2	yes	—
54	#6092	C₄²	1	4	yes	—
55	#6092	C₄²	1	4	yes	—
56	#6092	C₄²	1	8	yes	—
57	C₂×#346	—	13	1	no	—
58	C₂×#346	—	13	2	no	—
59	C₂×C₄×C₁₆	—	13	1	no	—
60	C₂×C₄×C₁₆	—	13	2	no	—
61	#1726	—	13	1	no	—
62	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
63	C₂×C₄×C₁₃	—	2	4	no	—
64	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	—
65	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
66	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
67	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
68	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
69	C₂×Dic₁₃	—	2	8	no	—
70	C₂×Dic₁₃	C₄×C₈	1	8	yes	—
71	C₈×C₁₃	C₄×C₈	1	8	yes	—
72	#1055	C₄×C₈	1	4	yes	—
73	#1055	C₂×C₄²	1	1	yes	characteristic
74	#1055	C₂×C₄²	1	1	yes	characteristic
75	#1055	C₂×C₄²	1	2	yes	—
76	C₂²×C₁₆	—	13	1	no	—
77	C₂²×C₁₆	—	13	1	no	—
78	C₂²×C₁₆	—	13	2	no	—
79	C₂×#97	—	13	2	no	—
80	C₂×#97	#261	1	1	yes	characteristic
81	C₂×C₄×C₈	—	13	2	no	—
82	C₂×C₄×C₈	—	13	1	no	—
83	#376	—	13	1	no	—
84	#346	—	13	4	no	—
85	#346	—	13	8	no	—
86	C₄×C₁₆	—	13	4	no	—
87	C₄×C₁₆	—	13	8	no	—
88	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
89	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
90	C₂²×C₁₃	#504	1	4	yes	—
91	C₄×C₁₃	—	2	4	no	—
92	C₄×C₁₃	C₄³	1	1	yes	characteristic
93	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
94	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
95	Dic₁₃	—	2	8	no	—
96	C₂²×C₈	—	13	1	no	—
97	C₂²×C₈	—	13	1	no	—
98	C₂²×C₈	C₂×#261	1	2	yes	—
99	C₂×C₄²	—	13	2	no	—
100	C₂×C₄²	C₂×#261	1	1	yes	characteristic
101	C₂×C₁₆	—	13	2	no	—
102	C₂×C₁₆	—	13	2	no	—
103	C₂×C₁₆	—	13	4	no	—
104	C₂×C₁₆	—	13	4	no	—
105	C₂×C₁₆	—	13	4	no	—
106	C₂×C₁₆	—	13	4	no	—
107	C₂×C₁₆	—	13	4	no	—
108	#97	—	13	8	no	—
109	#97	#1057	1	4	yes	—
110	C₄×C₈	—	13	4	no	—
111	C₄×C₈	—	13	4	no	—
112	C₄×C₈	—	13	2	no	—
113	C₄×C₈	—	13	2	no	—
114	#95	—	13	4	no	—
115	C₂×C₁₃	C₄²×C₈	1	1	yes	characteristic
116	C₂×C₁₃	#2108	1	4	yes	—
117	C₂×C₁₃	#2108	1	2	yes	—
118	C₂²×C₄	—	13	4	no	—
119	C₂²×C₄	D₁₃⋊C₈	1	2	yes	—
120	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
121	C₂×C₈	—	13	4	no	—
122	C₂×C₈	—	13	1	no	—
123	C₂×C₈	—	13	1	no	—
124	C₂×C₈	—	13	2	no	—
125	C₂×C₈	—	13	2	no	—
126	C₂×C₈	—	13	2	no	—
127	C₂×C₈	D₁₃⋊C₈	1	4	yes	—
128	C₂×C₈	C₄×#261	1	4	yes	—
129	C₂×C₈	C₂×#1057	1	4	yes	—
130	C₄²	—	13	4	no	—
131	C₄²	—	13	4	no	—
132	C₄²	C₄×#261	1	2	yes	—
133	C₄²	C₂×#1057	1	2	yes	—
134	C₁₆	—	13	4	no	—
135	C₁₆	—	13	4	no	—
136	C₁₆	—	13	8	no	—
137	C₁₃	#12539	1	1	yes	characteristic, complemented, Sylow
138	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
139	C₂×C₄	—	2	4	no	—
140	C₂×C₄	—	13	8	no	—
141	C₂×C₄	—	26	8	no	—
142	C₂×C₄	C₄×#1057	1	4	yes	—
143	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
144	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
145	C₂×C₄	C₂×C₄×#261	1	2	yes	—
146	C₂×C₄	C₂²×#1057	1	1	yes	characteristic
147	C₈	—	13	4	no	—
148	C₈	—	13	1	no	—
149	C₈	—	13	1	no	—
150	C₈	—	13	2	no	—
151	C₈	C₄×#1057	1	8	yes	—
152	C₂²	C₄×D₁₃⋊C₈	1	2	yes	—
153	C₂²	#11719096	1	4	yes	—
154	C₂²	C₂×C₄×#1057	1	1	yes	characteristic
155	C₄	—	2	4	no	—
156	C₄	—	26	8	no	—
157	C₄	C₄×D₁₃⋊C₈	1	1	yes	characteristic
158	C₄	C₄²×#261	1	1	yes	characteristic
159	C₄	C₂×C₄×#1057	1	2	yes	—
160	C₂	C₄²×#1057	1	1	yes	characteristic
161	C₂	#13131046	1	4	yes	—
162	C₂	#13131047	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#261
commutator	C₂×C₁₃	C₄²×C₈
Fitting	C₂×C₁₃×#97	C₄
socle, prime radical	C₂³×C₁₃	C₂²×C₈
cosocle	C₂²×#1055	C₂³
hypercenter	C₂×#97	#261
hypocenter	C₁₃	#12539
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
14. #11718258	C₄	semidirect
15. #11718257	C₄	semidirect
16. #11718231	C₄	semidirect
17. C₄×#6092	C₄	semidirect
137. 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×#11718258	2
C₂×#11718231	2
C₂×#11718257	2
C₂×C₄×#6092	2
#13114524	2
#12539	13