Subgroups — #16789015

Order 3328.

510 conjugacy classes of subgroups.

The subgroup lattice has 180 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	2	yes	maximal
3	C₂×#11718257	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	#11718257	C₄	1	8	yes	complemented
15	#11718231	C₄	1	8	yes	complemented
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×Dic₁₃	C₈	1	4	yes	—
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	C₂×C₄	1	8	yes	—
25	C₂×#6092	C₂×C₄	1	8	yes	—
26	C₂×#6092	C₂×C₄	1	8	yes	—
27	C₄×C₈×C₁₃	C₈	1	4	yes	—
28	C₈×Dic₁₃	C₈	1	4	yes	—
29	C₈×Dic₁₃	C₈	1	4	yes	—
30	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
31	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
32	C₄×#1055	C₂×C₄	1	4	yes	—
33	C₄×#346	—	13	1	no	maximal, Sylow
34	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
35	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
37	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
38	C₂×C₈×C₁₃	C₄²	1	2	yes	—
39	C₂×C₈×C₁₃	C₄²	1	2	yes	—
40	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
41	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
42	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
43	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
44	C₄²×C₁₃	C₄²	1	2	yes	—
45	C₄²×C₁₃	C₂×C₈	1	2	yes	—
46	C₄×Dic₁₃	—	2	8	no	—
47	C₄×Dic₁₃	C₄²	1	2	yes	—
48	C₄×Dic₁₃	C₄²	1	2	yes	—
49	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
50	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
51	C₂×#1055	C₄²	1	2	yes	—
52	C₂×#1055	C₂×C₈	1	2	yes	—
53	C₂×#1055	C₂×C₈	1	2	yes	—
54	C₂×#1055	C₂²×C₄	1	2	yes	—
55	C₂×#1055	C₂²×C₄	1	2	yes	—
56	C₂×#1055	C₂²×C₄	1	2	yes	—
57	#6092	C₄²	1	16	yes	complemented
58	C₂×#346	—	13	2	no	—
59	C₂×#346	—	13	2	no	—
60	C₂×C₄×C₁₆	—	13	2	no	—
61	C₄²×C₈	—	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	1	yes	characteristic
67	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
68	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
71	C₂×Dic₁₃	—	2	4	no	—
72	C₂×Dic₁₃	C₄×C₈	1	4	yes	—
73	C₂×Dic₁₃	C₄×C₈	1	4	yes	—
74	C₂×Dic₁₃	M₃₂	1	8	yes	—
75	C₈×C₁₃	C₄×C₈	1	4	yes	—
76	C₈×C₁₃	C₄×C₈	1	4	yes	—
77	#1055	C₄×C₈	1	4	yes	—
78	#1055	C₂×C₄²	1	4	yes	—
79	C₂²×C₁₆	—	13	4	no	—
80	C₂×C₄×C₈	—	13	1	no	—
81	C₂×C₄×C₈	—	13	1	no	—
82	C₂×C₄×C₈	—	13	1	no	—
83	C₂×C₄×C₈	—	13	1	no	—
84	C₂×C₄×C₈	—	13	1	no	—
85	C₂×C₄×C₈	#261	1	1	yes	characteristic
86	C₄³	—	13	1	no	—
87	#346	—	13	8	no	—
88	#346	—	13	8	no	—
89	C₄×C₁₆	—	13	8	no	—
90	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
91	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
92	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
93	C₂²×C₁₃	C₂×M₃₂	1	4	yes	—
94	C₄×C₁₃	—	2	4	no	—
95	C₄×C₁₃	C₄³	1	1	yes	characteristic
96	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
97	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
98	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
99	Dic₁₃	—	2	4	no	—
100	Dic₁₃	#346	1	8	yes	complemented
101	C₂²×C₈	—	13	1	no	—
102	C₂²×C₈	—	13	1	no	—
103	C₂²×C₈	C₂×#261	1	1	yes	characteristic
104	C₂²×C₈	C₂×#261	1	1	yes	characteristic
105	C₂×C₄²	—	13	1	no	—
106	C₂×C₄²	—	13	1	no	—
107	C₂×C₄²	—	13	4	no	—
108	C₂×C₄²	C₂×#261	1	1	yes	characteristic
109	C₂×C₁₆	—	13	8	no	—
110	C₂×C₁₆	—	13	8	no	—
111	C₂×C₁₆	—	13	8	no	—
112	C₄×C₈	—	13	4	no	—
113	C₄×C₈	—	13	4	no	—
114	C₄×C₈	—	13	4	no	—
115	C₄×C₈	—	13	4	no	—
116	C₄×C₈	—	13	4	no	—
117	C₄×C₈	#1057	1	4	yes	—
118	C₂×C₁₃	C₄²×C₈	1	1	yes	characteristic
119	C₂×C₁₃	C₂×#346	1	2	yes	—
120	C₂×C₁₃	C₄×M₃₂	1	2	yes	—
121	C₂×C₁₃	C₄×M₃₂	1	2	yes	—
122	C₂²×C₄	—	13	2	no	—
123	C₂²×C₄	—	13	2	no	—
124	C₂²×C₄	D₁₃⋊C₈	1	2	yes	—
125	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
126	C₂×C₈	—	13	2	no	—
127	C₂×C₈	—	13	2	no	—
128	C₂×C₈	—	13	2	no	—
129	C₂×C₈	—	13	2	no	—
130	C₂×C₈	—	13	2	no	—
131	C₂×C₈	—	13	2	no	—
132	C₂×C₈	D₁₃⋊C₈	1	2	yes	—
133	C₂×C₈	D₁₃⋊C₈	1	2	yes	—
134	C₂×C₈	C₄×#261	1	2	yes	—
135	C₂×C₈	C₄×#261	1	2	yes	—
136	C₂×C₈	C₂×#1057	1	2	yes	—
137	C₂×C₈	C₂×#1057	1	2	yes	—
138	C₄²	—	13	2	no	—
139	C₄²	—	13	2	no	—
140	C₄²	—	13	2	no	—
141	C₄²	—	13	2	no	—
142	C₄²	—	26	8	no	—
143	C₄²	C₄×#261	1	2	yes	—
144	C₄²	C₂×#1057	1	2	yes	—
145	C₁₆	—	13	16	no	—
146	C₁₃	C₄×#346	1	1	yes	characteristic, complemented, Sylow
147	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
148	C₂×C₄	—	2	4	no	—
149	C₂×C₄	—	13	4	no	—
150	C₂×C₄	—	13	8	no	—
151	C₂×C₄	—	13	4	no	—
152	C₂×C₄	—	26	4	no	—
153	C₂×C₄	C₄×#1057	1	4	yes	—
154	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
155	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
156	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
157	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
158	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
159	C₂×C₄	C₂²×#1057	1	1	yes	characteristic
160	C₈	—	13	4	no	—
161	C₈	—	13	4	no	—
162	C₈	C₄×#1057	1	4	yes	—
163	C₈	C₄×#1057	1	4	yes	—
164	C₂²	C₄×D₁₃⋊C₈	1	1	yes	characteristic
165	C₂²	C₄×D₁₃⋊C₈	1	1	yes	characteristic
166	C₂²	D₁₃⋊M₃₂	1	4	yes	—
167	C₂²	C₂×C₄×#1057	1	1	yes	characteristic
168	C₄	—	2	4	no	—
169	C₄	—	13	8	no	—
170	C₄	—	26	4	no	—
171	C₄	C₄×D₁₃⋊C₈	1	1	yes	characteristic
172	C₄	C₄²×#261	1	1	yes	characteristic
173	C₄	C₂×C₄×#1057	1	1	yes	characteristic
174	C₄	C₂×C₄×#1057	1	1	yes	characteristic
175	C₂	C₄²×#1057	1	1	yes	characteristic
176	C₂	#13131037	1	2	yes	—
177	C₂	#13131042	1	2	yes	—
178	C₂	#13131043	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂×#261
commutator	C₂×C₁₃	C₄²×C₈
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle, prime radical	C₂³×C₁₃	C₂²×C₈
cosocle	C₂²×#1055	C₂³
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₄×#346
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
13. #11718258	C₄	semidirect
14. #11718257	C₄	semidirect
15. #11718231	C₄	semidirect
57. #6092	C₄²	semidirect
100. Dic₁₃	#346	semidirect
146. C₁₃	C₄×#346	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
C₄×C₈×Dic₁₃	2
C₄×#346	13