Subgroups — #15778247

Order 3328.

334 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13116592	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718104	C₂	1	2	yes	maximal
3	#13114522	C₂	1	1	yes	maximal, characteristic
4	#13112915	C₂	1	2	yes	maximal
5	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88055	C₂²	1	1	yes	characteristic
9	C₂×#88055	C₂²	1	1	yes	characteristic
10	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
12	C₂×#88052	C₂²	1	2	yes	—
13	#11718593	C₄	1	1	yes	characteristic
14	C₂×#88043	C₄	1	1	yes	characteristic
15	C₁₃×C₄⋊C₁₆	C₄	1	4	yes	complemented
16	#11718104	—	2	4	no	—
17	C₄⋊#6090	C₄	1	4	yes	complemented
18	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
20	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
24	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
25	C₁₃×M₃₂	—	2	2	no	—
26	C₁₃×M₃₂	—	2	2	no	—
27	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
28	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
29	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
30	#88071	—	2	2	no	—
31	#88055	—	2	1	no	—
32	#88055	—	2	1	no	—
33	#88055	D₄	1	2	yes	—
34	#88055	Q₈	1	2	yes	—
35	C₈×Dic₁₃	—	2	2	no	—
36	C₈×Dic₁₃	—	2	2	no	—
37	#88052	—	2	2	no	—
38	#88052	—	2	2	no	—
39	C₂×#6090	C₂×C₄	1	4	yes	—
40	#88043	—	2	2	no	—
41	#12657	—	13	1	no	maximal, Sylow
42	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
43	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
44	C₂²×Dic₁₃	—	2	1	no	—
45	C₂²×Dic₁₃	—	2	1	no	—
46	C₂×C₈×C₁₃	—	2	1	no	—
47	C₂×C₈×C₁₃	—	2	1	no	—
48	C₂×C₈×C₁₃	C₄²	1	2	yes	—
49	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
54	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
55	C₄²×C₁₃	C₄²	1	2	yes	—
56	C₄²×C₁₃	M₁₆	1	2	yes	—
57	C₄×Dic₁₃	—	2	1	no	—
58	C₄×Dic₁₃	—	2	1	no	—
59	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
60	C₄×Dic₁₃	M₁₆	1	2	yes	—
61	C₂×#1055	—	2	1	no	—
62	C₂×#1055	—	2	1	no	—
63	C₂×#1055	—	2	1	no	—
64	C₂×#1055	—	2	1	no	—
65	C₂×#1055	C₄⋊C₄	1	2	yes	—
66	C₂×#1055	M₁₆	1	2	yes	—
67	C₁₃×C₁₆	—	2	4	no	—
68	#6090	—	2	4	no	—
69	#2150	—	13	1	no	—
70	#2150	D₁₃	1	1	yes	characteristic
71	C₂×#347	—	13	2	no	—
72	#1726	—	13	1	no	—
73	#1375	—	13	2	no	—
74	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
75	C₂×C₄×C₁₃	—	4	2	no	—
76	C₂×C₄×C₁₃	#97	1	4	yes	—
77	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
81	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
83	C₂×Dic₁₃	—	2	2	no	—
84	C₂×Dic₁₃	—	2	2	no	—
85	C₂×Dic₁₃	—	4	2	no	—
86	C₂×Dic₁₃	—	4	2	no	—
87	C₈×C₁₃	—	2	2	no	—
88	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
89	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
90	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
91	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
92	#1055	—	2	2	no	—
93	#1055	—	2	2	no	—
94	C₂×M₃₂	—	13	2	no	—
95	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
96	C₂×#97	—	13	1	no	—
97	C₂×#97	—	13	1	no	—
98	C₂×#97	—	13	1	no	—
99	C₂×C₄×C₈	—	13	1	no	—
100	C₂×C₄×C₈	—	13	1	no	—
101	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
102	#376	—	13	1	no	—
103	C₄⋊C₁₆	—	13	4	no	—
104	C₄⋊C₁₆	Dic₁₃	1	4	yes	complemented
105	#347	—	26	4	no	—
106	C₂²×C₁₃	—	2	2	no	—
107	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
108	C₂²×C₁₃	#423	1	1	yes	characteristic
109	C₂²×C₁₃	#432	1	1	yes	characteristic
110	C₄×C₁₃	—	2	4	no	—
111	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
112	C₄×C₁₃	C₄×M₁₆	1	1	yes	characteristic
113	C₄×C₁₃	#423	1	1	yes	characteristic
114	C₄×C₁₃	#432	1	1	yes	characteristic
115	Dic₁₃	—	4	2	no	—
116	Dic₁₃	—	4	2	no	—
117	C₂²×C₈	—	13	1	no	—
118	C₂²×C₈	—	13	1	no	—
119	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
120	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
121	C₂×C₄²	—	13	1	no	—
122	C₂×C₄²	—	13	1	no	—
123	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
124	M₃₂	—	2	2	no	—
125	M₃₂	—	2	2	no	—
126	M₃₂	—	26	2	no	—
127	M₃₂	—	26	2	no	—
128	C₂×C₁₆	—	13	4	no	—
129	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	—
130	#97	—	13	2	no	—
131	#97	—	13	2	no	—
132	#97	—	26	1	no	—
133	#97	—	26	1	no	—
134	#97	—	26	2	no	—
135	C₄×C₈	—	26	2	no	—
136	C₄×C₈	—	26	2	no	—
137	C₄×C₈	C₄×D₁₃	1	2	yes	—
138	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
139	#95	—	26	2	no	—
140	C₂×C₁₃	—	2	1	no	—
141	C₂×C₁₃	—	2	1	no	—
142	C₂×C₁₃	#1767	1	1	yes	characteristic
143	C₂×C₁₃	#2110	1	2	yes	—
144	C₂²×C₄	—	26	1	no	—
145	C₂²×C₄	—	26	1	no	—
146	C₂²×C₄	#6094	1	2	yes	—
147	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
148	C₂×C₈	—	2	1	no	—
149	C₂×C₈	—	2	1	no	—
150	C₂×C₈	—	13	2	no	—
151	C₂×C₈	—	13	2	no	—
152	C₂×C₈	—	26	1	no	—
153	C₂×C₈	—	26	1	no	—
154	C₂×C₈	—	26	1	no	—
155	C₂×C₈	—	26	1	no	—
156	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
157	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
158	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
159	C₂×C₈	#6129	1	1	yes	characteristic
160	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
161	C₂×C₈	#6131	1	1	yes	characteristic
162	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
163	C₄²	—	13	2	no	—
164	C₄²	—	13	2	no	—
165	C₄²	—	26	1	no	—
166	C₄²	—	26	1	no	—
167	C₄²	#6094	1	2	yes	—
168	C₄²	C₄×Dic₁₃	1	2	yes	—
169	C₁₆	—	2	4	no	—
170	C₁₆	—	26	4	no	—
171	C₁₃	#12657	1	1	yes	characteristic, complemented, Sylow
172	C₂³	C₂×#6094	1	1	yes	characteristic
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	—	26	2	no	—
175	C₂×C₄	—	26	2	no	—
176	C₂×C₄	—	52	2	no	—
177	C₂×C₄	—	52	2	no	—
178	C₂×C₄	#88055	1	4	yes	—
179	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
180	C₂×C₄	#88146	1	1	yes	characteristic
181	C₂×C₄	C₂×#6094	1	1	yes	characteristic
182	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
183	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
184	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
185	C₈	—	2	2	no	—
186	C₈	—	26	2	no	—
187	C₈	—	26	2	no	—
188	C₈	#88141	1	1	yes	characteristic
189	C₈	#88147	1	1	yes	characteristic
190	C₈	D₄×Dic₁₃	1	1	yes	characteristic
191	C₈	Q₈×Dic₁₃	1	1	yes	characteristic
192	C₂²	—	2	2	no	—
193	C₂²	#11718496	1	1	yes	characteristic
194	C₂²	#11718498	1	1	yes	characteristic
195	C₂²	C₂×#88055	1	1	yes	characteristic
196	C₄	—	2	4	no	—
197	C₄	—	52	2	no	—
198	C₄	—	52	2	no	—
199	C₄	#11718496	1	1	yes	characteristic
200	C₄	#11718498	1	1	yes	characteristic
201	C₄	C₄⋊C₄×Dic₁₃	1	1	yes	characteristic
202	C₄	M₁₆×Dic₁₃	1	1	yes	characteristic
203	C₂	—	2	1	no	—
204	C₂	—	2	1	no	—
205	C₂	#13114691	1	1	yes	characteristic
206	C₂	#13116440	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₄×Dic₁₃
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#2150	C₂
socle	C₂²×C₁₃	C₂×#97
prime radical	C₂³×C₁₃	C₂×M₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#2150	D₁₃
hypocenter	C₁₃	#12657
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #2150

Complements

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

N	H ≅ G/N	type
15. C₁₃×C₄⋊C₁₆	C₄	semidirect
17. C₄⋊#6090	C₄	semidirect
104. C₄⋊C₁₆	Dic₁₃	semidirect
171. C₁₃	#12657	semidirect

Maximal subgroups

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

subgroup	index
#13116592	2
C₂×#11718104	2
#13114522	2
#13112915	2
C₁₃×#2150	2
#12657	13