Subgroups — #15762751

Order 3328.

510 conjugacy classes of subgroups.

The subgroup lattice has 218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718343	C₂	1	1	yes	maximal, characteristic
2	#13115796	C₂	1	2	yes	maximal
3	#13115637	C₂	1	2	yes	maximal
4	C₂×#11718047	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1844	C₂	1	1	yes	maximal, characteristic
6	C₂×#88123	C₂²	1	2	yes	—
7	C₂×C₁₃×#106	—	2	2	no	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#384	C₂²	1	2	yes	—
10	C₂×#88058	—	2	2	no	—
11	C₂×#88050	—	2	4	no	—
12	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
13	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
14	#11718343	—	2	2	no	—
15	#11718343	C₄	1	4	yes	complemented
16	#11718121	—	2	4	no	—
17	#11718047	—	2	2	no	—
18	C₂²×Dic₂₆	—	2	2	no	—
19	C₂²×C₈×C₁₃	D₄	1	2	yes	—
20	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
21	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
22	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
23	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₃	—	2	2	no	—
25	C₂×C₄⋊Dic₁₃	—	2	2	no	—
26	C₂²×#1055	D₄	1	2	yes	—
27	C₂²×#1055	D₄	1	2	yes	—
28	#88123	—	2	2	no	—
29	#88123	—	2	2	no	—
30	#88123	—	2	2	no	—
31	#88123	C₂×C₄	1	4	yes	—
32	C₁₃×#106	—	4	4	no	—
33	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
34	C₄×C₈×C₁₃	D₄	1	2	yes	—
35	#88058	—	2	8	no	—
36	#88050	—	4	8	no	—
37	C₄×#1055	—	2	1	no	—
38	C₄×#1055	—	2	1	no	—
39	C₄×#1055	—	2	1	no	—
40	C₄×#1055	—	2	1	no	—
41	#9836	—	13	1	no	maximal, Sylow
42	C₂²×C₄×C₁₃	—	4	2	no	—
43	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
46	C₂²×Dic₁₃	—	4	2	no	—
47	C₂×Dic₂₆	—	2	4	no	—
48	C₂×Dic₂₆	—	4	4	no	—
49	C₂×Dic₂₆	—	4	4	no	—
50	C₂×Dic₂₆	—	4	2	no	—
51	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
52	C₂×C₈×C₁₃	SD₁₆	1	4	yes	—
53	C₂×C₈×C₁₃	Q₁₆	1	4	yes	—
54	C₁₃×C₄⋊C₄	—	4	4	no	—
55	C₁₃×C₄⋊C₄	—	4	4	no	—
56	C₁₃×C₄⋊C₄	—	4	4	no	—
57	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
58	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₄²×C₁₃	#41	1	1	yes	characteristic
60	C₄²×C₁₃	#41	1	1	yes	characteristic
61	C₄⋊Dic₁₃	—	2	4	no	—
62	C₄⋊Dic₁₃	—	2	4	no	—
63	C₄⋊Dic₁₃	—	4	2	no	—
64	C₄⋊Dic₁₃	—	4	2	no	—
65	C₂×#1055	—	2	2	no	—
66	C₂×#1055	—	2	2	no	—
67	C₂×#1055	—	2	4	no	—
68	C₂×#1055	—	2	4	no	—
69	C₂×#500	—	13	1	no	—
70	#1990	—	13	2	no	—
71	#1956	—	13	2	no	—
72	#1844	D₁₃	1	1	yes	characteristic
73	C₂×#322	—	13	1	no	—
74	C₂³×C₁₃	#127	1	1	yes	characteristic
75	C₂×C₄×C₁₃	—	8	2	no	—
76	C₂×C₄×C₁₃	—	8	2	no	—
77	C₂×C₄×C₁₃	—	8	2	no	—
78	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
81	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
82	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
83	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
85	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
86	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
87	C₂×C₄×C₁₃	#137	1	4	yes	—
88	C₂×Dic₁₃	—	4	4	no	—
89	C₂×Dic₁₃	—	8	2	no	—
90	C₂×Dic₁₃	—	8	2	no	—
91	Dic₂₆	—	4	8	no	—
92	Dic₂₆	—	8	4	no	—
93	C₈×C₁₃	#103	1	8	yes	complemented
94	#1055	—	4	2	no	—
95	#1055	—	4	2	no	—
96	C₂×C₄⋊Q₈	—	13	2	no	—
97	#500	—	13	4	no	—
98	#500	—	26	2	no	—
99	C₂×#107	—	26	2	no	—
100	C₂×#106	—	2	2	no	—
101	C₂×#103	—	26	4	no	—
102	C₂×C₄×C₈	—	13	1	no	—
103	C₂×C₄×C₈	—	13	1	no	—
104	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
105	#384	C₂×D₁₃	1	2	yes	—
106	#340	—	26	4	no	—
107	#322	—	26	2	no	—
108	C₂²×C₁₃	#390	1	1	yes	characteristic
109	C₂²×C₁₃	#492	1	1	yes	characteristic
110	C₂²×C₁₃	#494	1	1	yes	characteristic
111	C₂²×C₁₃	#496	1	2	yes	—
112	C₂²×C₁₃	#497	1	2	yes	—
113	C₄×C₁₃	—	16	2	no	—
114	C₄×C₁₃	C₂×#103	1	2	yes	—
115	C₄×C₁₃	#441	1	2	yes	—
116	C₄×C₁₃	#442	1	2	yes	—
117	C₄×C₁₃	#469	1	2	yes	—
118	C₄×C₁₃	#470	1	2	yes	—
119	C₄×C₁₃	#487	1	2	yes	—
120	Dic₁₃	—	8	4	no	—
121	C₂²×Q₈	—	26	2	no	—
122	C₂²×C₈	—	13	2	no	—
123	C₂²×C₈	—	13	2	no	—
124	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
125	C₄⋊Q₈	—	13	4	no	—
126	C₄⋊Q₈	—	26	2	no	—
127	C₄⋊Q₈	—	26	2	no	—
128	C₄⋊Q₈	—	26	2	no	—
129	C₂×C₄⋊C₄	—	2	2	no	—
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	—	2	2	no	—
132	C₂×C₄⋊C₄	—	26	2	no	—
133	C₂×C₄⋊C₄	—	26	2	no	—
134	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
135	#107	—	26	8	no	—
136	#106	—	4	4	no	—
137	#103	—	52	8	no	—
138	C₄×C₈	—	26	1	no	—
139	C₄×C₈	—	26	1	no	—
140	C₄×C₈	—	26	1	no	—
141	C₄×C₈	—	26	1	no	—
142	C₄×C₈	C₄×D₁₃	1	2	yes	—
143	C₄×C₈	D₅₂	1	2	yes	—
144	C₂×C₁₃	#1714	1	2	yes	—
145	C₂×C₁₃	#1723	1	2	yes	—
146	C₂×C₁₃	#1956	1	1	yes	characteristic
147	C₂×C₁₃	#1971	1	1	yes	characteristic
148	C₂×C₁₃	#1972	1	1	yes	characteristic
149	C₂×Q₈	—	26	4	no	—
150	C₂×Q₈	—	52	2	no	—
151	C₂×Q₈	—	52	4	no	—
152	C₂×Q₈	—	52	4	no	—
153	C₂²×C₄	—	4	2	no	—
154	C₂²×C₄	—	52	2	no	—
155	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
156	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
157	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
158	C₂×C₈	—	26	2	no	—
159	C₂×C₈	—	26	2	no	—
160	C₂×C₈	—	26	4	no	—
161	C₂×C₈	—	26	4	no	—
162	C₂×C₈	#6103	1	4	yes	—
163	C₂×C₈	#6105	1	4	yes	—
164	C₂×C₈	#6107	1	4	yes	—
165	C₄⋊C₄	—	4	4	no	—
166	C₄⋊C₄	—	4	4	no	—
167	C₄⋊C₄	—	4	4	no	—
168	C₄⋊C₄	—	26	4	no	—
169	C₄⋊C₄	—	26	4	no	—
170	C₄⋊C₄	—	52	2	no	—
171	C₄⋊C₄	—	52	2	no	—
172	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
173	C₄²	C₂×D₅₂	1	1	yes	characteristic
174	C₄²	#6131	1	1	yes	characteristic
175	C₄²	#6131	1	1	yes	characteristic
176	C₁₃	#9836	1	1	yes	characteristic, complemented, Sylow
177	C₂³	#88194	1	1	yes	characteristic
178	Q₈	—	52	8	no	—
179	Q₈	—	104	4	no	—
180	C₂×C₄	—	8	2	no	—
181	C₂×C₄	—	8	2	no	—
182	C₂×C₄	—	8	2	no	—
183	C₂×C₄	—	52	4	no	—
184	C₂×C₄	—	104	2	no	—
185	C₂×C₄	—	104	2	no	—
186	C₂×C₄	#88147	1	1	yes	characteristic
187	C₂×C₄	#88147	1	1	yes	characteristic
188	C₂×C₄	#88149	1	1	yes	characteristic
189	C₂×C₄	#88149	1	1	yes	characteristic
190	C₂×C₄	#88168	1	4	yes	—
191	C₂×C₄	#88169	1	4	yes	—
192	C₂×C₄	C₂×#6103	1	1	yes	characteristic
193	C₂×C₄	C₂×#6105	1	2	yes	—
194	C₂×C₄	C₂×#6107	1	2	yes	—
195	C₂×C₄	#88201	1	1	yes	characteristic
196	C₈	—	52	2	no	—
197	C₈	—	52	2	no	—
198	C₈	#88050	1	8	yes	complemented
199	C₂²	#11718649	1	1	yes	characteristic
200	C₂²	#11718737	1	1	yes	characteristic
201	C₂²	#11718753	1	1	yes	characteristic
202	C₂²	#11718828	1	2	yes	—
203	C₂²	#11718837	1	2	yes	—
204	C₄	—	16	2	no	—
205	C₄	—	104	4	no	—
206	C₄	#11718514	1	2	yes	—
207	C₄	#11718526	1	2	yes	—
208	C₄	#11718529	1	2	yes	—
209	C₄	#11718530	1	2	yes	—
210	C₄	C₂×#88050	1	2	yes	—
211	C₄	#11718754	1	2	yes	—
212	C₂	#13114455	1	2	yes	—
213	C₂	#13114510	1	2	yes	—
214	C₂	#13115637	1	1	yes	characteristic
215	C₂	#13115705	1	1	yes	characteristic
216	C₂	#13115710	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#88194
commutator	C₄²×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1844	C₂
socle, prime radical	C₂³×C₁₃	#127
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1844	D₁₃
hypocenter	C₁₃	#9836
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

Complements

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

N	H ≅ G/N	type
15. #11718343	C₄	semidirect
93. C₈×C₁₃	#103	semidirect
176. C₁₃	#9836	semidirect
198. C₈	#88050	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718343	2
#13115796	2
#13115637	2
C₂×#11718047	2
C₁₃×#1844	2
#9836	13