Subgroups — #15861038

Order 3328.

994 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88059	C₂	1	2	yes	maximal
2	#13123255	C₂	1	2	yes	maximal
3	#13114742	C₂	1	4	yes	maximal, complemented
4	C₄×#88059	C₂	1	4	yes	maximal, complemented
5	#13114563	C₂	1	2	yes	maximal
6	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
10	C₂²×#6099	C₂²	1	4	yes	—
11	C₁₃×#405	C₄	1	8	yes	—
12	C₂×C₁₃×#97	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
14	C₂×#88059	C₄	1	16	yes	complemented
15	C₂×#88059	C₂²	1	4	yes	—
16	C₂×#88059	C₂²	1	4	yes	—
17	#11718658	—	2	8	no	—
18	C₄×#6099	C₂²	1	8	yes	—
19	#11718144	C₂²	1	8	yes	—
20	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
21	C₂×C₁₃×M₁₆	—	2	4	no	—
22	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
23	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	—
24	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
25	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
26	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
28	C₁₃×#117	C₂×C₄	1	4	yes	—
29	C₁₃×#117	D₄	1	4	yes	—
30	C₂×C₁₃×C₄⋊C₄	Q₈	1	2	yes	—
31	C₂×C₁₃×C₂²⋊C₄	Q₈	1	2	yes	—
32	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
33	C₂×#6099	—	2	4	no	—
34	C₂×#6099	—	2	8	no	—
35	C₂×#6099	C₂×C₄	1	16	yes	—
36	C₂×#6099	C₂³	1	8	yes	—
37	C₂²×#1055	—	2	4	no	—
38	C₁₃×#97	C₂×C₄	1	8	yes	—
39	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	—
40	#88059	C₂×C₄	1	16	yes	—
41	#88059	C₂×C₄	1	16	yes	—
42	#88043	—	2	8	no	—
43	C₄×#1055	—	2	8	no	—
44	#20460	—	13	1	no	maximal, Sylow
45	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
47	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
49	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
50	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	#41	1	4	yes	—
52	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
53	C₁₃×M₁₆	—	2	8	no	—
54	C₂×C₈×C₁₃	—	2	4	no	—
55	C₂×C₈×C₁₃	C₄²	1	16	yes	—
56	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
57	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
58	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
59	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
60	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
61	C₁₃×C₄⋊C₄	C₄⋊C₄	1	8	yes	—
62	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
63	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
64	C₄²×C₁₃	C₂×D₄	1	4	yes	—
65	#6099	—	2	16	no	—
66	#6099	—	2	8	no	—
67	#6099	C₂²×C₄	1	16	yes	—
68	C₂×#1055	—	2	16	no	—
69	C₂×#1055	—	2	8	no	—
70	C₂²×#108	—	13	2	no	—
71	#2873	—	13	2	no	—
72	C₂×#405	D₁₃	1	1	yes	characteristic
73	#1778	—	13	4	no	—
74	C₄×#108	—	13	4	no	—
75	#1738	—	13	2	no	—
76	C₂³×C₁₃	—	4	2	no	—
77	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
78	C₂³×C₁₃	C₄×Q₈	1	4	yes	—
79	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
80	C₂×C₄×C₁₃	—	4	4	no	—
81	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
82	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
83	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
84	C₂×C₄×C₁₃	#117	1	4	yes	—
85	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
86	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
87	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
88	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
90	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
91	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
92	C₈×C₁₃	—	2	4	no	—
93	C₈×C₁₃	C₂×C₄²	1	4	yes	—
94	C₈×C₁₃	C₂×C₄²	1	4	yes	—
95	#1055	—	2	16	no	—
96	C₂²×M₁₆	—	13	4	no	—
97	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
98	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
99	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
100	C₂×#108	—	13	16	no	—
101	C₂×#108	—	13	4	no	—
102	C₂×#108	—	13	4	no	—
103	#405	—	26	8	no	—
104	#405	Dic₁₃	1	8	yes	—
105	C₄×M₁₆	—	13	8	no	—
106	C₂×#97	C₂×D₁₃	1	2	yes	—
107	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
108	#341	—	13	8	no	—
109	C₂²×C₁₃	—	2	2	no	—
110	C₂²×C₁₃	—	2	4	no	—
111	C₂²×C₁₃	—	4	4	no	—
112	C₂²×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
113	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
114	C₂²×C₁₃	C₂×C₄×Q₈	1	2	yes	—
115	C₄×C₁₃	—	2	8	no	—
116	C₄×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
117	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
118	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
119	C₄×C₁₃	C₂×C₄×D₄	1	2	yes	—
120	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
121	C₂×M₁₆	—	2	4	no	—
122	C₂×M₁₆	—	13	16	no	—
123	C₂×M₁₆	—	13	8	no	—
124	C₂×M₁₆	—	26	4	no	—
125	C₂×M₁₆	—	26	8	no	—
126	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
127	C₂²×C₈	—	26	4	no	—
128	C₂²×C₈	C₄×D₁₃	1	8	yes	—
129	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
130	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
131	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
132	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
133	#117	D₅₂	1	4	yes	—
134	#117	C₂×Dic₁₃	1	4	yes	—
135	C₂×C₄⋊C₄	Dic₂₆	1	2	yes	—
136	C₂×C₂²⋊C₄	Dic₂₆	1	2	yes	—
137	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
138	#108	—	13	16	no	—
139	#108	—	13	16	no	—
140	#97	—	26	8	no	—
141	#97	C₂×Dic₁₃	1	8	yes	—
142	C₄×C₈	—	26	8	no	—
143	C₄×C₈	C₂×Dic₁₃	1	8	yes	—
144	C₂×C₁₃	—	2	2	no	—
145	C₂×C₁₃	—	2	4	no	—
146	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₁₃	#2916	1	2	yes	—
148	C₂⁴	C₂×Dic₂₆	1	1	yes	characteristic
149	C₂²×C₄	C₂×Dic₂₆	1	4	yes	—
150	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
151	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
152	C₂²×C₄	C₂×D₅₂	1	2	yes	—
153	C₂²×C₄	#6127	1	4	yes	—
154	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
155	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
156	M₁₆	—	2	8	no	—
157	M₁₆	—	13	16	no	—
158	M₁₆	—	26	16	no	—
159	M₁₆	—	26	8	no	—
160	C₂×C₈	—	2	4	no	—
161	C₂×C₈	—	26	16	no	—
162	C₂×C₈	—	26	8	no	—
163	C₂×C₈	C₄×Dic₁₃	1	16	yes	—
164	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
165	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
166	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
167	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
168	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
169	C₄⋊C₄	C₄⋊Dic₁₃	1	8	yes	—
170	C₂²⋊C₄	C₄⋊Dic₁₃	1	8	yes	—
171	C₄²	C₂×D₅₂	1	4	yes	—
172	C₄²	C₂²×Dic₁₃	1	4	yes	—
173	C₁₃	#20460	1	1	yes	characteristic, complemented, Sylow
174	C₂³	—	4	2	no	—
175	C₂³	C₄×Dic₂₆	1	4	yes	—
176	C₂³	C₂×C₄⋊Dic₁₃	1	2	yes	—
177	C₂³	C₂²×Dic₂₆	1	1	yes	characteristic
178	C₂×C₄	—	4	4	no	—
179	C₂×C₄	C₄×Dic₂₆	1	4	yes	—
180	C₂×C₄	C₄×D₅₂	1	4	yes	—
181	C₂×C₄	C₄×D₅₂	1	4	yes	—
182	C₂×C₄	C₂×C₄×Dic₁₃	1	4	yes	—
183	C₂×C₄	C₂×C₄⋊Dic₁₃	1	8	yes	—
184	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
185	C₂×C₄	#88180	1	4	yes	—
186	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
187	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
188	C₂×C₄	C₂×#6127	1	2	yes	—
189	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
190	C₈	—	2	4	no	—
191	C₈	—	26	16	no	—
192	C₈	C₂×C₄×Dic₁₃	1	4	yes	—
193	C₈	C₂×C₄×Dic₁₃	1	4	yes	—
194	C₂²	—	2	2	no	—
195	C₂²	—	2	4	no	—
196	C₂²	—	4	4	no	—
197	C₂²	C₄×C₄⋊Dic₁₃	1	4	yes	—
198	C₂²	C₂×C₄×Dic₂₆	1	2	yes	—
199	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
200	C₄	—	2	8	no	—
201	C₄	C₄×C₄⋊Dic₁₃	1	4	yes	—
202	C₄	C₂×C₄×D₅₂	1	2	yes	—
203	C₄	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
204	C₄	C₂×#88180	1	1	yes	characteristic
205	C₂	—	2	2	no	—
206	C₂	—	2	4	no	—
207	C₂	C₂×C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
208	C₂	#13123447	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₂
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#405	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#405	D₁₃
hypocenter	C₁₃	#20460
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117 ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
3. #13114742	C₂	semidirect
4. C₄×#88059	C₂	semidirect
14. C₂×#88059	C₄	semidirect
173. C₁₃	#20460	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#88059	2
#13123255	2
#13114742	2
C₄×#88059	2
#13114563	2
C₂×C₁₃×#405	2
#20460	13