Subgroups — #15761585

Order 3328.

370 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13115595	C₂	1	2	yes	maximal
2	#13114993	C₂	1	1	yes	maximal, characteristic
3	#13114703	C₂	1	1	yes	maximal, characteristic
4	#13112720	C₂	1	2	yes	maximal
5	C₂×C₁₃×#335	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88058	—	2	2	no	—
9	C₂×#88057	—	2	1	no	—
10	C₂×#88057	—	2	1	no	—
11	C₂×#88055	—	2	1	no	—
12	#11718596	C₂²	1	2	yes	—
13	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
15	C₁₃×#335	C₄	1	4	yes	complemented
16	#11718143	—	2	2	no	—
17	#11718142	—	2	1	no	—
18	C₂²×C₈×C₁₃	—	2	2	no	—
19	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₃	—	2	2	no	—
23	C₂×C₄⋊Dic₁₃	—	2	2	no	—
24	C₂×C₄⋊Dic₁₃	—	2	2	no	—
25	C₂×C₄⋊Dic₁₃	D₄	1	2	yes	—
26	C₂×C₄×Dic₁₃	—	2	1	no	—
27	C₂²×#1055	—	2	1	no	—
28	C₁₃×C₄⋊C₈	—	2	2	no	—
29	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
30	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
31	C₄×C₈×C₁₃	Q₈	1	2	yes	—
32	#88071	—	2	1	no	—
33	#88058	—	4	4	no	—
34	#88057	—	4	2	no	—
35	#88057	—	4	2	no	—
36	#88055	—	4	2	no	—
37	C₄⋊#1055	—	2	1	no	—
38	C₄⋊#1055	Q₈	1	2	yes	—
39	#9617	—	13	1	no	maximal, Sylow
40	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
43	C₂²×Dic₁₃	—	2	2	no	—
44	C₂²×Dic₁₃	—	4	2	no	—
45	C₂×C₈×C₁₃	—	2	1	no	—
46	C₂×C₈×C₁₃	—	2	1	no	—
47	C₂×C₈×C₁₃	—	2	4	no	—
48	C₂×C₈×C₁₃	—	4	2	no	—
49	C₂×C₈×C₁₃	—	4	2	no	—
50	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
51	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
52	C₂×C₈×C₁₃	D₈	1	2	yes	—
53	C₂×C₈×C₁₃	Q₁₆	1	2	yes	—
54	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
55	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
56	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
57	C₄²×C₁₃	#41	1	1	yes	characteristic
58	C₄⋊Dic₁₃	—	2	2	no	—
59	C₄⋊Dic₁₃	—	2	2	no	—
60	C₄⋊Dic₁₃	—	4	2	no	—
61	C₄⋊Dic₁₃	—	4	2	no	—
62	C₄⋊Dic₁₃	—	4	2	no	—
63	C₄⋊Dic₁₃	—	4	2	no	—
64	C₄⋊Dic₁₃	—	8	2	no	—
65	C₄×Dic₁₃	—	4	1	no	—
66	C₄×Dic₁₃	—	4	1	no	—
67	C₂×#1055	—	2	2	no	—
68	C₂×#1055	—	4	1	no	—
69	C₂×#1055	—	4	1	no	—
70	#1947	—	13	2	no	—
71	#1844	—	13	1	no	—
72	#1770	—	13	1	no	—
73	C₂×#335	D₁₃	1	1	yes	characteristic
74	#1296	—	13	2	no	—
75	C₂³×C₁₃	#121	1	1	yes	characteristic
76	C₂×C₄×C₁₃	—	2	2	no	—
77	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₁₃	#125	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
83	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
85	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
86	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
87	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
88	C₂×C₄×C₁₃	#137	1	2	yes	—
89	C₂×Dic₁₃	—	4	2	no	—
90	C₂×Dic₁₃	—	4	2	no	—
91	C₂×Dic₁₃	—	4	2	no	—
92	C₂×Dic₁₃	—	8	2	no	—
93	C₂×Dic₁₃	—	8	2	no	—
94	C₂×Dic₁₃	—	8	2	no	—
95	C₈×C₁₃	—	2	2	no	—
96	C₈×C₁₃	—	4	4	no	—
97	C₈×C₁₃	#107	1	4	yes	complemented
98	#1055	—	4	2	no	—
99	C₂×#107	—	26	2	no	—
100	C₂×#106	—	26	1	no	—
101	C₂×#106	—	26	1	no	—
102	C₂×C₄⋊C₈	—	13	1	no	—
103	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
104	C₂×#97	—	26	1	no	—
105	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
106	#384	—	13	2	no	—
107	C₄×C₄⋊C₄	—	13	1	no	—
108	#340	—	26	2	no	—
109	#336	—	26	1	no	—
110	#335	Dic₁₃	1	4	yes	complemented
111	C₂²×C₁₃	#389	1	1	yes	characteristic
112	C₂²×C₁₃	#459	1	1	yes	characteristic
113	C₂²×C₁₃	#462	1	1	yes	characteristic
114	C₂²×C₁₃	#468	1	2	yes	—
115	C₂²×C₁₃	#471	1	2	yes	—
116	C₄×C₁₃	—	2	1	no	—
117	C₄×C₁₃	—	2	1	no	—
118	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
119	C₄×C₁₃	#428	1	1	yes	characteristic
120	C₄×C₁₃	#441	1	1	yes	characteristic
121	C₄×C₁₃	#442	1	1	yes	characteristic
122	C₄×C₁₃	#474	1	1	yes	characteristic
123	C₄×C₁₃	#477	1	1	yes	characteristic
124	C₄×C₁₃	#501	1	2	yes	—
125	Dic₁₃	—	8	2	no	—
126	Dic₁₃	—	16	2	no	—
127	C₂²×C₈	—	2	2	no	—
128	C₂²×C₈	—	26	1	no	—
129	C₂²×C₈	D₅₂	1	1	yes	characteristic
130	C₂²×C₈	D₅₂	1	1	yes	characteristic
131	C₂×C₄⋊C₄	—	13	2	no	—
132	C₂×C₄⋊C₄	—	26	2	no	—
133	C₂×C₄⋊C₄	—	26	2	no	—
134	C₂×C₄⋊C₄	—	26	2	no	—
135	C₂×C₄²	—	26	1	no	—
136	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
137	#107	—	52	4	no	—
138	#106	—	52	2	no	—
139	#106	—	52	2	no	—
140	C₄⋊C₈	—	2	2	no	—
141	C₄⋊C₈	—	13	2	no	—
142	C₄⋊C₈	—	26	1	no	—
143	C₄⋊C₈	C₂×Dic₁₃	1	4	yes	—
144	#97	—	52	2	no	—
145	C₄×C₈	Dic₂₆	1	2	yes	—
146	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
147	#95	—	26	1	no	—
148	C₂×C₁₃	#1685	1	2	yes	—
149	C₂×C₁₃	#1692	1	2	yes	—
150	C₂×C₁₃	#1943	1	1	yes	characteristic
151	C₂×C₁₃	#1947	1	1	yes	characteristic
152	C₂×C₁₃	#1951	1	1	yes	characteristic
153	C₂²×C₄	—	26	2	no	—
154	C₂²×C₄	—	52	2	no	—
155	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
156	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
157	C₂²×C₄	#6131	1	1	yes	characteristic
158	C₂×C₈	—	2	1	no	—
159	C₂×C₈	—	2	1	no	—
160	C₂×C₈	—	2	4	no	—
161	C₂×C₈	—	4	2	no	—
162	C₂×C₈	—	4	2	no	—
163	C₂×C₈	—	26	2	no	—
164	C₂×C₈	—	52	1	no	—
165	C₂×C₈	—	52	1	no	—
166	C₂×C₈	D₁₀₄	1	2	yes	—
167	C₂×C₈	Dic₅₂	1	2	yes	—
168	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
169	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
170	C₄⋊C₄	—	26	2	no	—
171	C₄⋊C₄	—	26	2	no	—
172	C₄⋊C₄	—	52	2	no	—
173	C₄⋊C₄	—	52	2	no	—
174	C₄⋊C₄	—	52	2	no	—
175	C₄⋊C₄	—	52	2	no	—
176	C₄⋊C₄	—	104	2	no	—
177	C₄²	—	52	1	no	—
178	C₄²	—	52	1	no	—
179	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
180	C₄²	#6129	1	1	yes	characteristic
181	C₄²	Q₈×D₁₃	1	1	yes	characteristic
182	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
183	C₁₃	#9617	1	1	yes	characteristic, complemented, Sylow
184	C₂³	#88149	1	1	yes	characteristic
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	52	2	no	—
187	C₂×C₄	—	52	2	no	—
188	C₂×C₄	—	52	2	no	—
189	C₂×C₄	—	104	2	no	—
190	C₂×C₄	—	104	2	no	—
191	C₂×C₄	—	104	2	no	—
192	C₂×C₄	#88142	1	1	yes	characteristic
193	C₂×C₄	#88144	1	1	yes	characteristic
194	C₂×C₄	#88151	1	1	yes	characteristic
195	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
196	C₂×C₄	C₂×Dic₅₂	1	1	yes	characteristic
197	C₂×C₄	#88162	1	1	yes	characteristic
198	C₂×C₄	#88163	1	1	yes	characteristic
199	C₂×C₄	#88165	1	2	yes	—
200	C₂×C₄	#88172	1	2	yes	—
201	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
202	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
203	C₂×C₄	Q₈×Dic₁₃	1	1	yes	characteristic
204	C₈	—	2	2	no	—
205	C₈	—	4	4	no	—
206	C₈	—	52	2	no	—
207	C₈	#88058	1	4	yes	complemented
208	C₂²	#11718504	1	1	yes	characteristic
209	C₂²	#11718510	1	1	yes	characteristic
210	C₂²	#11718547	1	2	yes	—
211	C₂²	#11718559	1	2	yes	—
212	C₂²	#11718646	1	1	yes	characteristic
213	C₄	—	2	1	no	—
214	C₄	—	2	1	no	—
215	C₄	—	104	2	no	—
216	C₄	—	208	2	no	—
217	C₄	#11718507	1	1	yes	characteristic
218	C₄	#11718511	1	1	yes	characteristic
219	C₄	#11718537	1	2	yes	—
220	C₄	C₂×#88058	1	1	yes	characteristic
221	C₄	#11718782	1	1	yes	characteristic
222	C₄	#11718813	1	1	yes	characteristic
223	C₄	#11718845	1	1	yes	characteristic
224	C₂	#13114302	1	2	yes	—
225	C₂	#13114343	1	2	yes	—
226	C₂	#13115575	1	1	yes	characteristic
227	C₂	#13115595	1	1	yes	characteristic
228	C₂	#13115617	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#88149
commutator	C₄²×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₁₃×#335	C₂
socle, prime radical	C₂³×C₁₃	#121
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×#335	D₁₃
hypocenter	C₁₃	#9617
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
15. C₁₃×#335	C₄	semidirect
97. C₈×C₁₃	#107	semidirect
110. #335	Dic₁₃	semidirect
183. C₁₃	#9617	semidirect
207. C₈	#88058	semidirect

Maximal subgroups

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

subgroup	index
#13115595	2
#13114993	2
#13114703	2
#13112720	2
C₂×C₁₃×#335	2
#9617	13