Subgroups — #15780940

Order 3328.

318 conjugacy classes of subgroups.

The subgroup lattice has 226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718055	C₂	1	2	yes	maximal
2	#13116592	C₂	1	1	yes	maximal, characteristic
3	C₄×#88052	C₂	1	1	yes	maximal, characteristic
4	#13112918	C₂	1	2	yes	maximal
5	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
10	C₂×#88052	C₂²	1	2	yes	—
11	C₂×#88052	C₂²	1	1	yes	characteristic
12	C₂×#88052	C₂²	1	1	yes	characteristic
13	C₁₃×#336	C₄	1	2	yes	—
14	#11718055	—	2	4	no	—
15	C₄⋊#6090	—	2	1	no	—
16	C₄⋊#6090	—	2	1	no	—
17	#11718053	—	2	1	no	—
18	C₄×#6090	—	2	1	no	—
19	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
21	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
23	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₁₃×C₄⋊C₈	C₈	1	2	yes	—
26	C₁₃×C₄⋊C₈	C₈	1	2	yes	—
27	C₄×C₈×C₁₃	—	2	2	no	—
28	C₄×C₈×C₁₃	—	2	2	no	—
29	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
30	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
31	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
32	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
33	C₁₃×#95	—	2	1	no	—
34	#88052	—	2	1	no	—
35	#88052	—	2	1	no	—
36	#88052	—	2	2	no	—
37	#88052	—	2	2	no	—
38	#88052	D₄	1	2	yes	—
39	#88052	Q₈	1	2	yes	—
40	C₂×#6090	—	2	1	no	—
41	C₂×#6090	—	2	1	no	—
42	C₂×#6090	—	2	2	no	—
43	#13163	—	13	1	no	maximal, Sylow
44	C₂²×C₄×C₁₃	—	2	2	no	—
45	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
48	C₂×C₈×C₁₃	—	2	2	no	—
49	C₂×C₈×C₁₃	—	2	1	no	—
50	C₂×C₈×C₁₃	—	2	1	no	—
51	C₂×C₈×C₁₃	—	2	2	no	—
52	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
55	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
58	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
59	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
60	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
61	C₁₃×C₄⋊C₄	—	2	4	no	—
62	C₄²×C₁₃	—	2	2	no	—
63	C₄²×C₁₃	—	2	2	no	—
64	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
65	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
66	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
67	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
68	#6090	—	2	2	no	—
69	#6090	—	2	2	no	—
70	#6090	—	4	2	no	—
71	C₂×#364	—	13	2	no	—
72	#2150	—	13	1	no	—
73	C₄×M₃₂	—	13	1	no	—
74	C₈×C₄⋊C₄	D₁₃	1	1	yes	characteristic
75	#1376	—	13	2	no	—
76	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
77	C₂×C₄×C₁₃	—	2	2	no	—
78	C₂×C₄×C₁₃	—	2	4	no	—
79	C₂×C₄×C₁₃	—	4	1	no	—
80	C₂×C₄×C₁₃	—	4	2	no	—
81	C₂×C₄×C₁₃	—	4	2	no	—
82	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
83	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
85	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
88	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
90	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
91	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
92	C₈×C₁₃	—	2	1	no	—
93	C₈×C₁₃	—	2	1	no	—
94	C₈×C₁₃	—	2	4	no	—
95	C₈×C₁₃	#121	1	1	yes	characteristic
96	C₈×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
97	C₈×C₁₃	#125	1	1	yes	characteristic
98	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
99	C₂×M₃₂	—	13	1	no	—
100	C₂×M₃₂	—	13	1	no	—
101	C₂×M₃₂	—	13	2	no	—
102	C₂×C₄⋊C₈	Dic₁₃	1	1	yes	characteristic
103	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
104	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
105	C₄×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
106	#364	—	26	4	no	—
107	C₄⋊C₁₆	—	26	1	no	—
108	C₄⋊C₁₆	—	26	1	no	—
109	#346	—	26	1	no	—
110	C₄×C₁₆	—	26	1	no	—
111	#336	Dic₁₃	1	2	yes	—
112	C₂²×C₁₃	—	2	1	no	—
113	C₂²×C₁₃	—	2	1	no	—
114	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
115	C₂²×C₁₃	#436	1	1	yes	characteristic
116	C₂²×C₁₃	#446	1	1	yes	characteristic
117	C₄×C₁₃	—	2	1	no	—
118	C₄×C₁₃	—	2	1	no	—
119	C₄×C₁₃	—	2	1	no	—
120	C₄×C₁₃	—	4	4	no	—
121	C₄×C₁₃	#364	1	2	yes	complemented
122	C₄×C₁₃	#389	1	1	yes	characteristic
123	C₄×C₁₃	#424	1	1	yes	characteristic
124	C₄×C₁₃	C₈×D₄	1	1	yes	characteristic
125	C₄×C₁₃	C₈×Q₈	1	1	yes	characteristic
126	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
127	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
128	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
129	C₂×C₄⋊C₄	—	2	1	no	—
130	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
131	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
132	M₃₂	—	13	2	no	—
133	M₃₂	—	13	2	no	—
134	M₃₂	—	26	1	no	—
135	M₃₂	—	26	1	no	—
136	M₃₂	—	26	2	no	—
137	M₃₂	—	26	2	no	—
138	C₂×C₁₆	—	26	1	no	—
139	C₂×C₁₆	—	26	1	no	—
140	C₂×C₁₆	—	26	2	no	—
141	C₄⋊C₈	#1055	1	2	yes	—
142	C₄⋊C₈	#1055	1	2	yes	—
143	C₄×C₈	—	2	2	no	—
144	C₄×C₈	—	2	2	no	—
145	C₄×C₈	Dic₂₆	1	1	yes	characteristic
146	C₄×C₈	Dic₂₆	1	1	yes	characteristic
147	C₄×C₈	D₅₂	1	1	yes	characteristic
148	C₄×C₈	D₅₂	1	1	yes	characteristic
149	#95	—	2	1	no	—
150	C₂×C₁₃	—	2	1	no	—
151	C₂×C₁₃	—	2	1	no	—
152	C₂×C₁₃	#1939	1	1	yes	characteristic
153	C₂×C₁₃	C₂×#364	1	1	yes	characteristic
154	C₂×C₁₃	#2153	1	1	yes	characteristic
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	#6099	1	1	yes	characteristic
157	C₂²×C₄	#6099	1	1	yes	characteristic
158	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
159	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	2	1	no	—
161	C₂×C₈	—	2	1	no	—
162	C₂×C₈	—	2	2	no	—
163	C₂×C₈	C₂×#1055	1	4	yes	—
164	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
165	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
166	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
167	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
168	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
169	C₂×C₈	#6129	1	1	yes	characteristic
170	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
171	C₂×C₈	#6131	1	1	yes	characteristic
172	C₄⋊C₄	—	2	4	no	—
173	C₄²	—	2	2	no	—
174	C₄²	—	2	2	no	—
175	C₄²	C₂×#1055	1	1	yes	characteristic
176	C₄²	C₂×#1055	1	1	yes	characteristic
177	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
178	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
179	C₁₆	—	26	2	no	—
180	C₁₆	—	26	2	no	—
181	C₁₆	—	52	2	no	—
182	C₁₃	#13163	1	1	yes	characteristic, complemented, Sylow
183	C₂³	C₂×#6099	1	1	yes	characteristic
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	—	4	1	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	C₄⋊#1055	1	1	yes	characteristic
190	C₂×C₄	C₄⋊#1055	1	1	yes	characteristic
191	C₂×C₄	C₄⋊#1055	1	1	yes	characteristic
192	C₂×C₄	C₄⋊#1055	1	1	yes	characteristic
193	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
194	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
195	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
196	C₂×C₄	Q₈×Dic₁₃	1	1	yes	characteristic
197	C₂×C₄	#88202	1	1	yes	characteristic
198	C₂×C₄	#88202	1	1	yes	characteristic
199	C₈	—	2	1	no	—
200	C₈	—	2	1	no	—
201	C₈	—	2	4	no	—
202	C₈	#88142	1	1	yes	characteristic
203	C₈	#88144	1	1	yes	characteristic
204	C₈	#88149	1	1	yes	characteristic
205	C₈	#88151	1	1	yes	characteristic
206	C₂²	—	2	1	no	—
207	C₂²	—	2	1	no	—
208	C₂²	C₂×C₄⋊#1055	1	1	yes	characteristic
209	C₂²	#11718673	1	1	yes	characteristic
210	C₂²	#11718685	1	1	yes	characteristic
211	C₄	—	2	1	no	—
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	4	4	no	—
215	C₄	#11718055	1	2	yes	complemented
216	C₄	#11718646	1	1	yes	characteristic
217	C₄	#11718660	1	1	yes	characteristic
218	C₄	D₄×#1055	1	1	yes	characteristic
219	C₄	Q₈×#1055	1	1	yes	characteristic
220	C₂	—	2	1	no	—
221	C₂	—	2	1	no	—
222	C₂	#13115555	1	1	yes	characteristic
223	C₂	C₂×#11718055	1	1	yes	characteristic
224	C₂	#13116602	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₈×C₁₃×C₄⋊C₄	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂³×C₁₃	C₂×M₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₈×C₄⋊C₄	D₁₃
hypocenter	C₁₃	#13163
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
121. C₄×C₁₃	#364	semidirect
182. C₁₃	#13163	semidirect
215. C₄	#11718055	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718055	2
#13116592	2
C₄×#88052	2
#13112918	2
C₈×C₁₃×C₄⋊C₄	2
#13163	13