Subgroups — #15828526

Order 3328.

834 conjugacy classes of subgroups.

The subgroup lattice has 222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718586	C₂	1	2	yes	maximal
2	#13113128	C₂	1	4	yes	maximal, complemented
3	#13113123	C₂	1	8	yes	maximal, complemented
4	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×M₁₆	C₄	1	2	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₄×C₁₃×M₁₆	C₄	1	4	yes	—
8	C₄×C₁₃×M₁₆	C₂²	1	4	yes	—
9	C₂×C₁₃×#97	C₄	1	2	yes	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
11	C₂×C₂²⋊#1055	C₄	1	4	yes	—
12	#11718586	C₄	1	4	yes	—
13	#11718586	C₄	1	4	yes	—
14	#11718586	C₂²	1	4	yes	—
15	#11718586	C₂²	1	4	yes	—
16	C₂×C₄⋊#1055	C₄	1	4	yes	—
17	C₂×C₄×#1055	C₂²	1	4	yes	—
18	#11718046	C₂²	1	16	yes	complemented
19	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
20	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₁₃×M₁₆	—	2	8	no	—
22	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	—
23	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
24	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
30	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
31	C₂²×#1055	C₂×C₄	1	8	yes	—
32	C₁₃×#97	C₂×C₄	1	8	yes	—
33	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
34	C₄×C₈×C₁₃	C₂³	1	4	yes	—
35	C₂²⋊#1055	C₂×C₄	1	8	yes	—
36	C₂²⋊#1055	C₂×C₄	1	8	yes	—
37	C₄⋊#1055	C₂×C₄	1	8	yes	—
38	C₄⋊#1055	C₂×C₄	1	8	yes	—
39	C₄×#1055	C₂×C₄	1	8	yes	—
40	C₄×#1055	C₂³	1	8	yes	—
41	#17319	—	13	1	no	maximal, Sylow
42	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	—	4	4	no	—
44	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
45	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
46	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
47	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
48	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	M₁₆	1	8	yes	—
50	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
51	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
52	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
53	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
55	C₁₃×M₁₆	—	2	16	no	—
56	C₂×C₈×C₁₃	—	2	8	no	—
57	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
58	C₄²×C₁₃	C₄²	1	1	yes	characteristic
59	C₄²×C₁₃	C₄²	1	2	yes	—
60	C₄²×C₁₃	C₄²	1	1	yes	characteristic
61	C₄²×C₁₃	C₄²	1	2	yes	—
62	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
63	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
64	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
65	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
67	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
68	C₂×#1055	—	4	8	no	—
69	C₂×#1055	C₂²×C₄	1	16	yes	—
70	C₂×#431	—	13	2	no	—
71	C₂×C₄×M₁₆	D₁₃	1	1	yes	characteristic
72	#1452	—	13	4	no	—
73	#1451	—	13	8	no	—
74	C₂³×C₁₃	—	4	2	no	—
75	C₂³×C₁₃	#97	1	4	yes	—
76	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
77	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
78	C₂×C₄×C₁₃	—	2	4	no	—
79	C₂×C₄×C₁₃	—	2	4	no	—
80	C₂×C₄×C₁₃	—	2	4	no	—
81	C₂×C₄×C₁₃	—	4	2	no	—
82	C₂×C₄×C₁₃	—	4	2	no	—
83	C₂×C₄×C₁₃	—	4	2	no	—
84	C₂×C₄×C₁₃	#97	1	8	yes	—
85	C₂×C₄×C₁₃	#97	1	4	yes	—
86	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
87	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
88	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
89	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
90	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
91	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
92	C₂×C₄×C₁₃	C₂×M₁₆	1	8	yes	—
93	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
95	C₈×C₁₃	—	2	8	no	—
96	#1055	—	2	16	no	—
97	C₂²×M₁₆	Dic₁₃	1	2	yes	—
98	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
99	#431	—	13	4	no	—
100	#431	—	13	4	no	—
101	#431	—	13	4	no	—
102	#431	—	13	4	no	—
103	C₂×C₄⋊C₈	—	13	4	no	—
104	C₂×C₂²⋊C₈	—	13	4	no	—
105	C₄×M₁₆	Dic₁₃	1	4	yes	—
106	C₄×M₁₆	C₂×D₁₃	1	4	yes	—
107	C₂×#97	Dic₁₃	1	2	yes	—
108	C₂×C₄×C₈	—	13	4	no	—
109	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
110	#322	—	13	16	no	—
111	C₂²×C₁₃	—	2	2	no	—
112	C₂²×C₁₃	—	2	2	no	—
113	C₂²×C₁₃	—	2	2	no	—
114	C₂²×C₁₃	—	4	4	no	—
115	C₂²×C₁₃	C₂×#97	1	2	yes	—
116	C₂²×C₁₃	C₂×#97	1	4	yes	—
117	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
118	C₄×C₁₃	—	2	2	no	—
119	C₄×C₁₃	—	2	2	no	—
120	C₄×C₁₃	—	2	2	no	—
121	C₄×C₁₃	C₂×#97	1	2	yes	—
122	C₄×C₁₃	C₂×#97	1	4	yes	—
123	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
124	C₄×C₁₃	#568	1	4	yes	—
125	C₂³×C₄	C₄×D₁₃	1	2	yes	—
126	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
127	C₂×M₁₆	—	2	8	no	—
128	C₂×M₁₆	C₂×Dic₁₃	1	8	yes	—
129	C₂²×C₈	—	13	8	no	—
130	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
131	C₂×C₄²	C₄×D₁₃	1	2	yes	—
132	C₂×C₄²	C₄×D₁₃	1	2	yes	—
133	C₂×C₄²	C₄×D₁₃	1	2	yes	—
134	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
135	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
136	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
137	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
138	C₄⋊C₈	—	13	8	no	—
139	C₄⋊C₈	—	13	8	no	—
140	C₂²⋊C₈	—	13	8	no	—
141	C₂²⋊C₈	—	13	8	no	—
142	#97	C₂×Dic₁₃	1	8	yes	—
143	C₄×C₈	—	13	8	no	—
144	C₄×C₈	—	13	8	no	—
145	C₄×C₈	C₂×Dic₁₃	1	4	yes	—
146	C₄×C₈	C₂²×D₁₃	1	4	yes	—
147	C₂×C₁₃	—	2	4	no	—
148	C₂×C₁₃	—	2	2	no	—
149	C₂×C₁₃	C₂²×#97	1	1	yes	characteristic
150	C₂×C₁₃	#2873	1	2	yes	—
151	C₂⁴	C₄×Dic₁₃	1	1	yes	characteristic
152	C₂²×C₄	—	4	4	no	—
153	C₂²×C₄	#6099	1	8	yes	—
154	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
155	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
156	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
157	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
158	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
159	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
160	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
161	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
162	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
163	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
164	M₁₆	—	2	16	no	—
165	C₂×C₈	—	2	8	no	—
166	C₂×C₈	—	13	16	no	—
167	C₂×C₈	—	52	8	no	—
168	C₂×C₈	C₂²×Dic₁₃	1	8	yes	—
169	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
170	C₄²	C₄×Dic₁₃	1	2	yes	—
171	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
172	C₄²	C₄×Dic₁₃	1	2	yes	—
173	C₄²	C₂×C₄×D₁₃	1	2	yes	—
174	C₄²	C₂×C₄×D₁₃	1	2	yes	—
175	C₄²	C₂×C₄×D₁₃	1	2	yes	—
176	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
177	C₄²	C₂²×Dic₁₃	1	2	yes	—
178	C₄²	C₂³×D₁₃	1	1	yes	characteristic
179	C₁₃	#17319	1	1	yes	characteristic, complemented, Sylow
180	C₂³	—	4	2	no	—
181	C₂³	#88043	1	4	yes	—
182	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
183	C₂³	C₂×C₄×Dic₁₃	1	2	yes	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	—	2	4	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	4	2	no	—
190	C₂×C₄	#88043	1	8	yes	—
191	C₂×C₄	#88043	1	4	yes	—
192	C₂×C₄	C₂×#6099	1	4	yes	—
193	C₂×C₄	C₂×#6099	1	8	yes	—
194	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
195	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
196	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
197	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
198	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
199	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
200	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
201	C₈	—	2	8	no	—
202	C₈	—	26	16	no	—
203	C₂²	—	2	2	no	—
204	C₂²	—	2	2	no	—
205	C₂²	—	2	2	no	—
206	C₂²	—	4	4	no	—
207	C₂²	C₂×#88043	1	2	yes	—
208	C₂²	C₂×#88043	1	4	yes	—
209	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
210	C₄	—	2	2	no	—
211	C₄	—	2	2	no	—
212	C₄	—	2	2	no	—
213	C₄	C₂×#88043	1	2	yes	—
214	C₄	C₂×#88043	1	4	yes	—
215	C₄	#11719450	1	4	yes	—
216	C₄	C₂²×#6099	1	2	yes	—
217	C₂	—	2	4	no	—
218	C₂	—	2	2	no	—
219	C₂	C₂²×#88043	1	1	yes	characteristic
220	C₂	#13123254	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₂×C₄×C₁₃×M₁₆	C₂
prime radical	C₂⁴×C₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₁₃
hypocenter	C₁₃	#17319
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. #13113128	C₂	semidirect
3. #13113123	C₂	semidirect
18. #11718046	C₂²	semidirect
179. C₁₃	#17319	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718586	2
#13113128	2
#13113123	2
C₂×C₄×C₁₃×M₁₆	2
#17319	13