Subgroups — #16015490

Order 3328.

830 conjugacy classes of subgroups.

The subgroup lattice has 220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718539	C₂	1	4	yes	maximal
2	#13123197	C₂	1	2	yes	maximal
3	#13114999	C₂	1	4	yes	maximal
4	#13114996	C₂	1	1	yes	maximal, characteristic
5	#13114992	C₂	1	2	yes	maximal
6	C₄×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic
8	C₂×#88144	C₂²	1	4	yes	—
9	C₂×C₁₃×#107	C₂²	1	4	yes	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#384	C₂²	1	2	yes	—
12	C₂×#88058	C₂²	1	4	yes	—
13	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
14	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
15	#11718646	—	2	4	no	—
16	#11718638	C₂²	1	4	yes	—
17	#11718634	—	2	4	no	—
18	C₂×#88048	C₂²	1	8	yes	—
19	#11718596	C₂²	1	2	yes	—
20	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
22	#11718539	—	2	16	no	—
23	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
24	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
25	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
26	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₃	—	2	4	no	—
28	C₂×C₄⋊Dic₁₃	—	2	4	no	—
29	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
30	C₂×#6101	—	2	4	no	—
31	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
32	C₂×C₄×Dic₁₃	D₄	1	2	yes	—
33	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
34	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
35	C₂²×#1055	C₂³	1	2	yes	—
36	#88144	—	2	16	no	—
37	C₁₃×#107	—	2	8	no	—
38	C₄×C₈×C₁₃	Q₈	1	4	yes	—
39	#88071	—	2	8	no	—
40	#88058	—	2	8	no	—
41	C₈×Dic₁₃	D₄	1	8	yes	—
42	C₈×Dic₁₃	Q₈	1	8	yes	—
43	#88048	—	2	16	no	—
44	C₄×#1055	Q₈	1	4	yes	—
45	#33311	—	13	1	no	maximal, Sylow
46	C₂²×C₄×C₁₃	—	2	4	no	—
47	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
49	C₂²×Dic₁₃	—	2	4	no	—
50	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
51	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×Dic₁₃	C₂×D₄	1	2	yes	—
53	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
54	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
55	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
56	C₁₃×C₄⋊C₄	—	2	8	no	—
57	C₁₃×C₄⋊C₄	—	4	8	no	—
58	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
59	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
60	C₄⋊Dic₁₃	—	2	8	no	—
61	C₄⋊Dic₁₃	—	4	8	no	—
62	C₄⋊Dic₁₃	—	4	8	no	—
63	#6101	—	4	8	no	—
64	C₄×Dic₁₃	—	2	4	no	—
65	C₄×Dic₁₃	—	2	4	no	—
66	C₄×Dic₁₃	C₂×D₄	1	4	yes	—
67	C₄×Dic₁₃	C₂×Q₈	1	4	yes	—
68	C₂×#1055	C₂×D₄	1	4	yes	—
69	C₂×#1055	C₂×Q₈	1	4	yes	—
70	C₂×#1055	C₂×Q₈	1	4	yes	—
71	C₂×#499	—	13	4	no	—
72	#2859	—	13	2	no	—
73	#1846	—	13	4	no	—
74	#1845	—	13	1	no	—
75	#1845	D₁₃	1	1	yes	characteristic
76	#1844	—	13	2	no	—
77	C₄²×C₈	—	13	1	no	—
78	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
79	C₂×C₄×C₁₃	—	4	4	no	—
80	C₂×C₄×C₁₃	—	4	8	no	—
81	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
82	C₂×C₄×C₁₃	#135	1	4	yes	—
83	C₂×C₄×C₁₃	#135	1	4	yes	—
84	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
85	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
88	C₂×Dic₁₃	—	2	2	no	—
89	C₂×Dic₁₃	—	2	2	no	—
90	C₂×Dic₁₃	—	2	2	no	—
91	C₂×Dic₁₃	—	2	2	no	—
92	C₂×Dic₁₃	—	4	4	no	—
93	C₂×Dic₁₃	—	4	8	no	—
94	C₂×Dic₁₃	#127	1	2	yes	—
95	C₂×Dic₁₃	#127	1	2	yes	—
96	C₂×Dic₁₃	C₄⋊Q₈	1	4	yes	—
97	C₈×C₁₃	C₄⋊Q₈	1	8	yes	—
98	#1055	C₄⋊Q₈	1	8	yes	—
99	C₂×#125	—	13	4	no	—
100	#499	—	26	16	no	—
101	C₂×#107	—	13	4	no	—
102	C₂×#107	C₂×D₁₃	1	4	yes	—
103	C₂×#106	—	13	8	no	—
104	C₂×C₄×C₈	—	13	2	no	—
105	C₂×C₄×C₈	—	13	2	no	—
106	C₂×C₄×C₈	—	13	1	no	—
107	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
108	#389	—	26	4	no	—
109	#389	—	26	4	no	—
110	#384	—	13	2	no	—
111	#384	C₂×D₁₃	1	2	yes	—
112	#382	—	13	4	no	—
113	C₄³	—	13	1	no	—
114	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
115	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
116	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
117	C₂²×C₁₃	C₂×#135	1	2	yes	—
118	C₂²×C₁₃	C₂×#135	1	2	yes	—
119	C₄×C₁₃	—	8	4	no	—
120	C₄×C₁₃	#499	1	8	yes	complemented
121	C₄×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
122	C₄×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
123	Dic₁₃	—	2	2	no	—
124	Dic₁₃	—	2	2	no	—
125	Dic₁₃	—	2	4	no	—
126	Dic₁₃	—	8	4	no	—
127	C₂²×C₈	—	13	2	no	—
128	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
129	#125	—	26	16	no	—
130	C₂×C₄⋊C₄	—	2	4	no	—
131	C₂×C₄⋊C₄	—	13	4	no	—
132	C₂×C₄⋊C₄	—	26	4	no	—
133	C₂×C₄⋊C₄	—	26	4	no	—
134	C₂×C₄⋊C₄	—	26	4	no	—
135	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
136	C₂×C₄²	—	13	1	no	—
137	C₂×C₄²	—	13	1	no	—
138	C₂×C₄²	—	13	2	no	—
139	C₂×C₄²	—	13	2	no	—
140	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
141	#107	—	2	8	no	—
142	#107	—	26	8	no	—
143	#106	—	26	16	no	—
144	C₄×C₈	—	13	8	no	—
145	C₄×C₈	—	13	8	no	—
146	C₄×C₈	—	13	4	no	—
147	C₄×C₈	Dic₂₆	1	4	yes	—
148	#95	—	26	8	no	—
149	C₂×C₁₃	#2868	1	1	yes	characteristic
150	C₂×C₁₃	#3147	1	1	yes	characteristic
151	C₂×C₁₃	#3147	1	1	yes	characteristic
152	C₂×C₁₃	C₂×#499	1	2	yes	—
153	C₂×C₁₃	#3160	1	2	yes	—
154	C₂²×C₄	—	2	4	no	—
155	C₂²×C₄	—	13	2	no	—
156	C₂²×C₄	—	13	1	no	—
157	C₂²×C₄	—	13	1	no	—
158	C₂²×C₄	—	26	4	no	—
159	C₂²×C₄	D₄×D₁₃	1	2	yes	—
160	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
161	C₂×C₈	—	13	4	no	—
162	C₂×C₈	—	13	4	no	—
163	C₂×C₈	—	13	4	no	—
164	C₂×C₈	C₂×Dic₂₆	1	4	yes	—
165	C₂×C₈	D₄×D₁₃	1	4	yes	—
166	C₂×C₈	Q₈×D₁₃	1	4	yes	—
167	C₄⋊C₄	—	2	8	no	—
168	C₄⋊C₄	—	4	8	no	—
169	C₄⋊C₄	—	26	8	no	—
170	C₄⋊C₄	—	52	8	no	—
171	C₄⋊C₄	—	52	8	no	—
172	C₄⋊C₄	—	52	8	no	—
173	C₄²	—	13	4	no	—
174	C₄²	—	13	4	no	—
175	C₄²	—	26	4	no	—
176	C₄²	—	26	4	no	—
177	C₄²	C₂×Dic₂₆	1	2	yes	—
178	C₄²	Q₈×D₁₃	1	2	yes	—
179	C₁₃	#33311	1	1	yes	characteristic, complemented, Sylow
180	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
181	C₂×C₄	—	4	8	no	—
182	C₂×C₄	—	4	4	no	—
183	C₂×C₄	—	13	4	no	—
184	C₂×C₄	—	13	2	no	—
185	C₂×C₄	—	13	2	no	—
186	C₂×C₄	—	26	2	no	—
187	C₂×C₄	—	26	2	no	—
188	C₂×C₄	—	26	2	no	—
189	C₂×C₄	—	26	2	no	—
190	C₂×C₄	—	52	8	no	—
191	C₂×C₄	—	52	4	no	—
192	C₂×C₄	#88142	1	4	yes	—
193	C₂×C₄	#88166	1	4	yes	—
194	C₂×C₄	#88173	1	4	yes	—
195	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
196	C₂×C₄	C₂×D₄×D₁₃	1	2	yes	—
197	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
198	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
199	C₈	—	13	8	no	—
200	C₈	#88142	1	8	yes	—
201	C₂²	C₂×#88142	1	1	yes	characteristic
202	C₂²	D₁₃×#127	1	1	yes	characteristic
203	C₂²	D₁₃×C₄⋊Q₈	1	1	yes	characteristic
204	C₂²	C₂×#88166	1	2	yes	—
205	C₂²	C₂×#88173	1	2	yes	—
206	C₄	—	8	4	no	—
207	C₄	—	26	2	no	—
208	C₄	—	26	2	no	—
209	C₄	—	26	4	no	—
210	C₄	—	104	4	no	—
211	C₄	#11718539	1	8	yes	complemented
212	C₄	C₂×#88142	1	2	yes	—
213	C₄	D₁₃×C₄⋊Q₈	1	2	yes	—
214	C₂	#13123233	1	1	yes	characteristic
215	C₂	#13125263	1	1	yes	characteristic
216	C₂	#13125265	1	1	yes	characteristic
217	C₂	C₂×#11718539	1	2	yes	—
218	C₂	#13125347	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₁₃
commutator, cosocle	C₂²×C₄×C₁₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1845	C₂
socle, prime radical	C₂³×C₁₃	C₂²×D₄
hypercenter	#1845	D₁₃
hypocenter	C₁₃	#33311
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

Complements

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

N	H ≅ G/N	type
120. C₄×C₁₃	#499	semidirect
179. C₁₃	#33311	semidirect
211. C₄	#11718539	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718539	2
#13123197	2
#13114999	2
#13114996	2
#13114992	2
C₄×C₈×Dic₁₃	2
C₁₃×#1845	2
#33311	13