Subgroups — #15756586

Order 3328.

378 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13114988	C₂	1	1	yes	maximal, characteristic
2	#13114953	C₂	1	1	yes	maximal, characteristic
3	#13112671	C₂	1	4	yes	maximal
4	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#97	C₄	1	2	yes	—
6	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
7	C₂×C₁₃×#97	C₄	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
9	C₄³×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊#1055	—	2	2	no	—
11	C₂×C₄⋊#1055	C₂²	1	2	yes	—
12	C₂×C₄⋊#1055	C₂²	1	2	yes	—
13	#11718116	—	2	2	no	—
14	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
15	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	D₄	1	2	yes	—
19	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
20	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
21	C₂²×#1055	—	2	2	no	—
22	C₂²×#1055	—	2	2	no	—
23	C₁₃×#97	—	2	4	no	—
24	C₁₃×#97	—	2	2	no	—
25	C₁₃×#97	C₈	1	4	yes	complemented
26	C₄×C₈×C₁₃	—	2	2	no	—
27	C₄×C₈×C₁₃	—	2	2	no	—
28	C₄⋊#1055	—	2	4	no	—
29	C₄⋊#1055	—	2	4	no	—
30	C₄⋊#1055	—	4	4	no	—
31	#8786	—	13	1	no	maximal, Sylow
32	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
33	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
34	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₈×C₁₃	—	2	2	no	—
38	C₂×C₈×C₁₃	—	2	2	no	—
39	C₂×C₈×C₁₃	—	2	2	no	—
40	C₂×C₈×C₁₃	—	2	2	no	—
41	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
42	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
43	C₄²×C₁₃	—	2	2	no	—
44	C₄²×C₁₃	—	2	2	no	—
45	C₄²×C₁₃	—	2	2	no	—
46	C₄²×C₁₃	—	4	2	no	—
47	C₄²×C₁₃	C₂×C₈	1	2	yes	—
48	C₄²×C₁₃	M₁₆	1	2	yes	—
49	C₄²×C₁₃	#41	1	2	yes	—
50	C₄²×C₁₃	#41	1	2	yes	—
51	C₂×#1055	—	4	2	no	—
52	C₂×#1055	—	4	2	no	—
53	C₂×#1055	—	4	2	no	—
54	C₂×#1055	—	4	4	no	—
55	C₂×#1055	—	4	2	no	—
56	#1842	—	13	1	no	—
57	#1831	—	13	1	no	—
58	C₄×#97	D₁₃	1	1	yes	characteristic
59	#1277	—	13	4	no	—
60	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₄×C₁₃	—	2	2	no	—
62	C₂×C₄×C₁₃	—	2	2	no	—
63	C₂×C₄×C₁₃	—	2	2	no	—
64	C₂×C₄×C₁₃	—	2	2	no	—
65	C₂×C₄×C₁₃	—	2	2	no	—
66	C₂×C₄×C₁₃	—	2	2	no	—
67	C₂×C₄×C₁₃	C₄⋊C₈	1	4	yes	—
68	C₂×C₄×C₁₃	#117	1	2	yes	—
69	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
70	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
71	C₂×C₄×C₁₃	#125	1	2	yes	—
72	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
74	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
75	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
76	C₂×C₄×C₁₃	#137	1	2	yes	—
77	C₈×C₁₃	—	2	4	no	—
78	C₈×C₁₃	—	2	4	no	—
79	#1055	—	8	2	no	—
80	#1055	—	8	2	no	—
81	C₂×C₄⋊C₈	—	13	2	no	—
82	C₂×C₄⋊C₈	—	13	2	no	—
83	C₂×C₄⋊C₈	—	26	2	no	—
84	C₂×#97	Dic₁₃	1	2	yes	—
85	C₂×#97	Dic₁₃	1	1	yes	characteristic
86	C₂×#97	Dic₁₃	1	1	yes	characteristic
87	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
88	C₄³	C₂×D₁₃	1	1	yes	characteristic
89	#336	—	26	2	no	—
90	C₂²×C₁₃	#382	1	1	yes	characteristic
91	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
92	C₂²×C₁₃	#423	1	1	yes	characteristic
93	C₂²×C₁₃	#428	1	2	yes	—
94	C₂²×C₁₃	#430	1	2	yes	—
95	C₄×C₁₃	—	2	4	no	—
96	C₄×C₁₃	—	2	2	no	—
97	C₄×C₁₃	—	4	2	no	—
98	C₄×C₁₃	#431	1	2	yes	—
99	C₄×C₁₃	#432	1	2	yes	—
100	C₄×C₁₃	#489	1	2	yes	—
101	C₄×C₁₃	#490	1	1	yes	characteristic
102	C₄×C₁₃	#491	1	1	yes	characteristic
103	C₂²×C₈	—	26	2	no	—
104	C₂²×C₈	—	26	2	no	—
105	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
106	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
107	C₂×C₄²	Dic₂₆	1	2	yes	—
108	C₂×C₄²	D₅₂	1	2	yes	—
109	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
110	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
111	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
112	C₄⋊C₈	—	26	4	no	—
113	C₄⋊C₈	—	26	4	no	—
114	C₄⋊C₈	—	52	4	no	—
115	#97	—	2	4	no	—
116	#97	—	2	2	no	—
117	#97	#1055	1	4	yes	complemented
118	C₄×C₈	—	2	2	no	—
119	C₄×C₈	—	2	2	no	—
120	C₂×C₁₃	#1565	1	2	yes	—
121	C₂×C₁₃	#1569	1	2	yes	—
122	C₂×C₁₃	#1831	1	1	yes	characteristic
123	C₂×C₁₃	#1836	1	1	yes	characteristic
124	C₂×C₁₃	#1838	1	1	yes	characteristic
125	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
126	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
127	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
128	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
129	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
130	C₂×C₈	—	2	2	no	—
131	C₂×C₈	—	2	2	no	—
132	C₂×C₈	—	2	2	no	—
133	C₂×C₈	—	2	2	no	—
134	C₂×C₈	—	52	2	no	—
135	C₂×C₈	—	52	2	no	—
136	C₂×C₈	—	52	4	no	—
137	C₂×C₈	—	52	2	no	—
138	C₂×C₈	—	52	2	no	—
139	C₂×C₈	C₂×#1055	1	4	yes	—
140	C₂×C₈	#6099	1	4	yes	—
141	C₄²	—	2	2	no	—
142	C₄²	—	2	2	no	—
143	C₄²	—	2	2	no	—
144	C₄²	—	4	2	no	—
145	C₄²	C₂×#1055	1	2	yes	—
146	C₄²	#6099	1	2	yes	—
147	C₄²	#6127	1	2	yes	—
148	C₄²	#6127	1	2	yes	—
149	C₁₃	#8786	1	1	yes	characteristic, complemented, Sylow
150	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	C₄⋊#1055	1	4	yes	—
158	C₂×C₄	#88124	1	2	yes	—
159	C₂×C₄	#88129	1	1	yes	characteristic
160	C₂×C₄	#88129	1	1	yes	characteristic
161	C₂×C₄	#88162	1	2	yes	—
162	C₂×C₄	#88163	1	2	yes	—
163	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
164	C₂×C₄	C₂×#6099	1	2	yes	—
165	C₂×C₄	C₂×#6099	1	1	yes	characteristic
166	C₂×C₄	#88180	1	2	yes	—
167	C₈	—	2	4	no	—
168	C₈	—	2	4	no	—
169	C₈	—	104	2	no	—
170	C₈	—	104	2	no	—
171	C₂²	C₂×C₄⋊#1055	1	1	yes	characteristic
172	C₂²	#11718585	1	1	yes	characteristic
173	C₂²	#11718597	1	1	yes	characteristic
174	C₂²	#11718782	1	2	yes	—
175	C₂²	#11718786	1	2	yes	—
176	C₄	—	2	2	no	—
177	C₄	—	2	4	no	—
178	C₄	—	4	2	no	—
179	C₄	#11718364	1	1	yes	characteristic
180	C₄	#11718374	1	1	yes	characteristic
181	C₄	#11718375	1	2	yes	—
182	C₄	#11718586	1	2	yes	—
183	C₄	#11718587	1	2	yes	—
184	C₂	#13113588	1	2	yes	—
185	C₂	#13113603	1	2	yes	—
186	C₂	#13114953	1	1	yes	characteristic
187	C₂	#13114970	1	1	yes	characteristic
188	C₂	#13114977	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₄×C₁₃×#97	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₄×#97	D₁₃
hypocenter	C₁₃	#8786
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×#97

Complements

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

N	H ≅ G/N	type
25. C₁₃×#97	C₈	semidirect
117. #97	#1055	semidirect
149. C₁₃	#8786	semidirect

Maximal subgroups

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

subgroup	index
#13114988	2
#13114953	2
#13112671	2
C₄×C₁₃×#97	2
#8786	13