Subgroups — #16015507

Order 3328.

806 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718344	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718725	C₂	1	2	yes	maximal
3	#13123196	C₂	1	2	yes	maximal
4	#13115003	C₂	1	4	yes	maximal
5	#13115001	C₂	1	4	yes	maximal
6	C₄×#88055	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₃×#125	C₂²	1	2	yes	—
9	C₂×#88124	C₂²	1	2	yes	—
10	C₁₃×#499	—	2	4	no	—
11	C₂×C₁₃×#107	C₂²	1	2	yes	—
12	C₂×C₁₃×#106	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×#88058	C₂²	1	2	yes	—
15	C₂×#88057	C₂²	1	2	yes	—
16	C₂×#88055	C₂²	1	2	yes	—
17	C₂×#88055	C₂²	1	2	yes	—
18	#11718725	—	2	8	no	—
19	#11718638	C₂²	1	4	yes	—
20	#11718637	C₂²	1	4	yes	—
21	#11718633	—	2	8	no	—
22	C₂×#88048	C₂²	1	4	yes	—
23	C₂×#88047	C₂²	1	4	yes	—
24	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
26	#11718344	—	2	4	no	—
27	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
28	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
29	C₁₃×#125	—	2	4	no	—
30	C₁₃×#125	—	2	4	no	—
31	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
32	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
33	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
34	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
35	C₂×#6101	—	2	4	no	—
36	C₂×#6101	—	2	8	no	—
37	C₂×C₄×Dic₁₃	D₄	1	4	yes	—
38	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
39	C₂²×#1055	C₂³	1	2	yes	—
40	#88124	—	2	4	no	—
41	#88124	—	2	4	no	—
42	C₁₃×#107	—	2	4	no	—
43	C₁₃×#106	—	2	4	no	—
44	C₄×C₈×C₁₃	D₄	1	4	yes	—
45	#88071	—	2	8	no	—
46	#88058	—	2	4	no	—
47	#88057	—	2	4	no	—
48	#88055	Q₈	1	8	yes	—
49	#88055	Q₈	1	8	yes	—
50	#88048	—	2	8	no	—
51	#88047	—	2	8	no	—
52	C₄×#1055	D₄	1	4	yes	—
53	#33315	—	13	1	no	maximal, Sylow
54	C₂²×C₄×C₁₃	—	2	4	no	—
55	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
56	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
57	C₂²×Dic₁₃	—	2	4	no	—
58	C₂²×Dic₁₃	C₂×D₄	1	4	yes	—
59	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
60	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
61	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
62	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
63	C₁₃×C₄⋊C₄	—	2	4	no	—
64	C₁₃×C₄⋊C₄	—	2	4	no	—
65	C₁₃×C₄⋊C₄	—	4	8	no	—
66	C₄²×C₁₃	C₂×D₄	1	2	yes	—
67	C₄²×C₁₃	C₂×D₄	1	2	yes	—
68	C₄⋊Dic₁₃	—	2	4	no	—
69	C₄⋊Dic₁₃	—	2	4	no	—
70	#6101	—	4	16	no	—
71	#6101	—	4	8	no	—
72	C₄×Dic₁₃	—	4	4	no	—
73	C₄×Dic₁₃	C₂×Q₈	1	4	yes	—
74	C₄×Dic₁₃	C₂×Q₈	1	4	yes	—
75	C₂×#1055	C₂×D₄	1	4	yes	—
76	C₂×#1055	C₂×Q₈	1	4	yes	—
77	C₂×#1055	C₂×Q₈	1	4	yes	—
78	C₂×#499	—	13	1	no	—
79	C₂×#499	—	13	2	no	—
80	C₂×#499	D₁₃	1	1	yes	characteristic
81	#2859	—	13	2	no	—
82	#1847	—	13	4	no	—
83	#1847	—	13	4	no	—
84	C₄×#97	—	13	1	no	—
85	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
86	C₂×C₄×C₁₃	—	2	4	no	—
87	C₂×C₄×C₁₃	—	4	4	no	—
88	C₂×C₄×C₁₃	—	4	8	no	—
89	C₂×C₄×C₁₃	#127	1	4	yes	—
90	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
91	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
93	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
94	C₂×Dic₁₃	—	2	8	no	—
95	C₂×Dic₁₃	—	4	4	no	—
96	C₂×Dic₁₃	—	4	8	no	—
97	C₂×Dic₁₃	C₄⋊Q₈	1	8	yes	—
98	C₈×C₁₃	C₄⋊Q₈	1	4	yes	—
99	C₈×C₁₃	C₄⋊Q₈	1	4	yes	—
100	#1055	C₄⋊Q₈	1	8	yes	—
101	C₂×#125	—	13	2	no	—
102	C₂×#125	C₂×D₁₃	1	2	yes	—
103	#499	—	2	4	no	—
104	#499	—	26	8	no	—
105	#499	—	26	4	no	—
106	C₂×#107	—	13	2	no	—
107	C₂×#107	—	13	4	no	—
108	C₂×#107	C₂×D₁₃	1	2	yes	—
109	C₂×#106	—	13	2	no	—
110	C₂×#106	—	13	4	no	—
111	C₂×#106	C₂×D₁₃	1	2	yes	—
112	C₂×#97	—	13	2	no	—
113	C₂×#97	—	13	2	no	—
114	C₂×C₄×C₈	—	13	1	no	—
115	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
116	#389	—	26	8	no	—
117	#384	—	13	4	no	—
118	#382	—	13	4	no	—
119	C₄³	—	13	1	no	—
120	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
121	C₂²×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
122	C₂²×C₁₃	#575	1	4	yes	—
123	C₄×C₁₃	—	2	4	no	—
124	C₄×C₁₃	—	8	4	no	—
125	C₄×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
126	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
127	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
128	Dic₁₃	—	2	8	no	—
129	Dic₁₃	—	8	4	no	—
130	C₂²×C₈	—	13	2	no	—
131	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
132	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
133	#125	—	2	4	no	—
134	#125	—	2	4	no	—
135	#125	—	26	4	no	—
136	#125	—	26	4	no	—
137	C₂×C₄⋊C₄	—	2	4	no	—
138	C₂×C₄⋊C₄	—	13	4	no	—
139	C₂×C₄⋊C₄	—	26	8	no	—
140	C₂×C₄⋊C₄	—	26	4	no	—
141	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
142	C₂×C₄²	—	13	2	no	—
143	C₂×C₄²	—	13	4	no	—
144	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
145	#107	—	2	4	no	—
146	#107	—	26	8	no	—
147	#107	—	26	4	no	—
148	#106	—	2	4	no	—
149	#106	—	26	8	no	—
150	#106	—	26	4	no	—
151	#97	—	13	8	no	—
152	#97	—	13	8	no	—
153	C₄×C₈	—	13	4	no	—
154	C₄×C₈	C₂²⋊D₁₃	1	4	yes	—
155	#95	—	26	8	no	—
156	C₂×C₁₃	#2868	1	1	yes	characteristic
157	C₂×C₁₃	#3150	1	2	yes	—
158	C₂×C₁₃	#3166	1	4	yes	—
159	C₂²×C₄	—	2	4	no	—
160	C₂²×C₄	—	13	4	no	—
161	C₂²×C₄	—	26	4	no	—
162	C₂²×C₄	D₄×D₁₃	1	2	yes	—
163	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
164	C₂×C₈	—	13	4	no	—
165	C₂×C₈	—	13	4	no	—
166	C₂×C₈	—	13	4	no	—
167	C₂×C₈	Q₈×D₁₃	1	4	yes	—
168	C₂×C₈	Q₈×D₁₃	1	4	yes	—
169	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
170	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
171	C₄⋊C₄	—	2	4	no	—
172	C₄⋊C₄	—	2	4	no	—
173	C₄⋊C₄	—	4	8	no	—
174	C₄⋊C₄	—	26	4	no	—
175	C₄⋊C₄	—	26	4	no	—
176	C₄⋊C₄	—	52	16	no	—
177	C₄⋊C₄	—	52	8	no	—
178	C₄²	—	13	4	no	—
179	C₄²	—	13	4	no	—
180	C₄²	—	52	4	no	—
181	C₄²	D₄×D₁₃	1	2	yes	—
182	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
183	C₁₃	#33315	1	1	yes	characteristic, complemented, Sylow
184	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	—	4	8	no	—
187	C₂×C₄	—	4	4	no	—
188	C₂×C₄	—	13	8	no	—
189	C₂×C₄	—	26	8	no	—
190	C₂×C₄	—	52	8	no	—
191	C₂×C₄	—	52	4	no	—
192	C₂×C₄	#88194	1	4	yes	—
193	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
194	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
195	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
196	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
197	C₈	—	13	8	no	—
198	C₈	#88198	1	4	yes	—
199	C₈	#88198	1	4	yes	—
200	C₂²	D₁₃×C₄⋊Q₈	1	2	yes	—
201	C₂²	#11719473	1	4	yes	—
202	C₂²	C₂×#88194	1	1	yes	characteristic
203	C₄	—	2	4	no	—
204	C₄	—	8	4	no	—
205	C₄	—	26	8	no	—
206	C₄	—	104	4	no	—
207	C₄	D₁₃×C₄⋊Q₈	1	2	yes	—
208	C₄	C₂×#88198	1	1	yes	characteristic
209	C₄	C₂×#88198	1	1	yes	characteristic
210	C₂	#13123232	1	1	yes	characteristic
211	C₂	#13125279	1	2	yes	—
212	C₂	#13125384	1	4	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₁₃
commutator, cosocle	C₂²×C₄×C₁₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#499	C₂
socle, prime radical	C₂³×C₁₃	C₂²×D₄
hypercenter	C₂×#499	D₁₃
hypocenter	C₁₃	#33315
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#499

Complements

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

N	H ≅ G/N	type
183. C₁₃	#33315	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718344	2
C₂×#11718725	2
#13123196	2
#13115003	2
#13115001	2
C₄×#88055	2
C₂×C₁₃×#499	2
#33315	13