Subgroups — #15756585

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	C₄×#88043	C₂	1	1	yes	maximal, characteristic
3	#13112670	C₂	1	4	yes	maximal
4	C₁₃×#1831	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
6	C₄³×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊#1055	—	2	2	no	—
8	C₂×C₄⋊#1055	C₂²	1	2	yes	—
9	C₂×#88043	C₄	1	2	yes	—
10	C₂×#88043	C₄	1	1	yes	characteristic
11	C₂×#88043	C₄	1	1	yes	characteristic
12	C₂×C₄×#1055	C₂²	1	2	yes	—
13	C₁₃×#336	—	2	2	no	—
14	C₂²×C₈×C₁₃	—	2	2	no	—
15	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	D₄	1	2	yes	—
18	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
19	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
20	C₂²×#1055	—	2	2	no	—
21	C₂²×#1055	C₂×C₄	1	2	yes	—
22	C₂²×#1055	C₂×C₄	1	2	yes	—
23	C₁₃×C₄⋊C₈	—	2	4	no	—
24	C₄⋊#1055	—	2	4	no	—
25	C₄⋊#1055	—	4	4	no	—
26	#88043	—	2	2	no	—
27	#88043	—	2	4	no	—
28	#88043	C₈	1	4	yes	complemented
29	C₄×#1055	—	2	2	no	—
30	C₄×#1055	—	2	2	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	—	4	2	no	—
38	C₂×C₈×C₁₃	—	4	2	no	—
39	C₂×C₈×C₁₃	—	4	2	no	—
40	C₄²×C₁₃	—	2	2	no	—
41	C₄²×C₁₃	—	2	2	no	—
42	C₄²×C₁₃	—	2	2	no	—
43	C₄²×C₁₃	—	4	2	no	—
44	C₄²×C₁₃	C₂×C₈	1	2	yes	—
45	C₄²×C₁₃	M₁₆	1	2	yes	—
46	C₄²×C₁₃	#41	1	2	yes	—
47	C₄²×C₁₃	#41	1	2	yes	—
48	C₂×#1055	—	2	2	no	—
49	C₂×#1055	—	2	2	no	—
50	C₂×#1055	—	2	2	no	—
51	C₂×#1055	—	2	2	no	—
52	C₂×#1055	—	4	2	no	—
53	C₂×#1055	—	4	4	no	—
54	C₂×#1055	C₂×C₈	1	4	yes	—
55	C₂×#1055	M₁₆	1	4	yes	—
56	#1842	—	13	1	no	—
57	#1831	D₁₃	1	1	yes	characteristic
58	C₄×#97	—	13	1	no	—
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	—	8	2	no	—
78	#1055	—	2	4	no	—
79	#1055	—	2	4	no	—
80	#1055	—	8	2	no	—
81	C₂×C₄⋊C₈	—	13	2	no	—
82	C₂×C₄⋊C₈	—	26	2	no	—
83	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
84	C₂×#97	—	13	1	no	—
85	C₂×#97	—	13	2	no	—
86	C₂×#97	—	13	1	no	—
87	C₂×C₄×C₈	—	13	2	no	—
88	C₄³	C₂×D₁₃	1	1	yes	characteristic
89	#336	—	2	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	—	2	2	no	—
104	C₂²×C₈	—	13	2	no	—
105	C₂²×C₈	—	13	2	no	—
106	C₂²×C₈	—	26	2	no	—
107	C₂×C₄²	Dic₂₆	1	2	yes	—
108	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
109	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
110	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
111	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
112	C₄⋊C₈	—	2	4	no	—
113	C₄⋊C₈	—	26	4	no	—
114	C₄⋊C₈	—	52	4	no	—
115	#97	—	13	4	no	—
116	#97	—	26	4	no	—
117	#97	—	26	2	no	—
118	C₄×C₈	—	26	2	no	—
119	C₄×C₈	—	26	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	#6101	1	2	yes	—
126	C₂²×C₄	#6101	1	2	yes	—
127	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
128	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
129	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
130	C₂×C₈	—	4	2	no	—
131	C₂×C₈	—	4	2	no	—
132	C₂×C₈	—	4	2	no	—
133	C₂×C₈	—	13	4	no	—
134	C₂×C₈	—	13	4	no	—
135	C₂×C₈	—	26	2	no	—
136	C₂×C₈	—	26	2	no	—
137	C₂×C₈	—	26	2	no	—
138	C₂×C₈	—	26	2	no	—
139	C₂×C₈	—	52	2	no	—
140	C₂×C₈	—	52	4	no	—
141	C₄²	—	2	2	no	—
142	C₄²	—	2	2	no	—
143	C₄²	—	2	2	no	—
144	C₄²	—	4	2	no	—
145	C₄²	C₈×D₁₃	1	2	yes	—
146	C₄²	#6094	1	2	yes	—
147	C₄²	#6129	1	2	yes	—
148	C₄²	#6131	1	2	yes	—
149	C₁₃	#8786	1	1	yes	characteristic, complemented, Sylow
150	C₂³	C₂×#6101	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	#88054	1	4	yes	—
158	C₂×C₄	#88144	1	2	yes	—
159	C₂×C₄	#88146	1	2	yes	—
160	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
161	C₂×C₄	C₂×#6094	1	1	yes	characteristic
162	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
163	C₂×C₄	#88190	1	1	yes	characteristic
164	C₂×C₄	#88201	1	1	yes	characteristic
165	C₂×C₄	#88203	1	2	yes	—
166	C₂×C₄	#88205	1	2	yes	—
167	C₈	—	8	2	no	—
168	C₈	—	26	4	no	—
169	C₈	—	26	4	no	—
170	C₈	—	104	2	no	—
171	C₂²	#11718638	1	1	yes	characteristic
172	C₂²	#11718656	1	2	yes	—
173	C₂²	C₂×#88054	1	1	yes	characteristic
174	C₂²	#11718779	1	1	yes	characteristic
175	C₂²	#11718785	1	2	yes	—
176	C₄	—	2	2	no	—
177	C₄	—	2	4	no	—
178	C₄	—	4	2	no	—
179	C₄	#11718494	1	2	yes	—
180	C₄	#11718496	1	2	yes	—
181	C₄	#11718716	1	2	yes	—
182	C₄	#11718728	1	1	yes	characteristic
183	C₄	#11718730	1	1	yes	characteristic
184	C₂	#13113589	1	2	yes	—
185	C₂	#13113604	1	2	yes	—
186	C₂	#13114952	1	1	yes	characteristic
187	C₂	#13114969	1	1	yes	characteristic
188	C₂	#13114976	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1831	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#1831	D₁₃
hypocenter	C₁₃	#8786
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1831

Complements

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

N	H ≅ G/N	type
28. #88043	C₈	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
C₄×#88043	2
#13112670	2
C₁₃×#1831	2
#8786	13