Subgroups — #15768751

Order 3328.

774 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718585	C₂	1	2	yes	maximal
2	C₂×#11718144	C₂	1	4	yes	maximal
3	C₂²×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
5	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×#6099	C₂²	1	4	yes	—
7	C₂×C₁₃×#97	—	2	4	no	—
8	C₂×C₁₃×#97	C₄	1	4	yes	—
9	#11718585	—	2	4	no	—
10	#11718585	C₄	1	8	yes	—
11	C₂×C₄⋊#1055	—	2	4	no	—
12	#11718144	—	2	8	no	—
13	C₂³×C₄×C₁₃	Q₈	1	2	yes	—
14	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	—	2	4	no	—
16	C₂²×C₈×C₁₃	—	2	4	no	—
17	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
18	C₂²×C₈×C₁₃	D₄	1	4	yes	—
19	C₂²×C₈×C₁₃	Q₈	1	4	yes	—
20	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
21	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₃	D₄	1	2	yes	—
23	C₂×C₄²×C₁₃	D₄	1	4	yes	—
24	C₂×#6099	—	2	4	no	—
25	C₂×#6099	—	2	8	no	—
26	C₂×#6099	—	2	8	no	—
27	C₂×#6099	C₂×C₄	1	8	yes	—
28	C₂²×#1055	—	2	4	no	—
29	C₁₃×#97	—	2	8	no	—
30	C₄⋊#1055	—	2	16	no	—
31	#10845	—	13	1	no	maximal, Sylow
32	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
33	C₂²×C₄×C₁₃	—	4	4	no	—
34	C₂²×C₄×C₁₃	C₄⋊C₄	1	8	yes	—
35	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
36	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
37	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
39	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
41	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
42	C₂²×C₄×C₁₃	#41	1	4	yes	—
43	C₂×C₈×C₁₃	—	2	4	no	—
44	C₂×C₈×C₁₃	—	2	4	no	—
45	C₂×C₈×C₁₃	—	2	8	no	—
46	C₂×C₈×C₁₃	—	2	8	no	—
47	C₂×C₈×C₁₃	C₄⋊C₄	1	8	yes	—
48	C₄²×C₁₃	C₄²	1	4	yes	—
49	C₄²×C₁₃	C₂²⋊C₄	1	8	yes	—
50	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
51	#6099	—	2	16	no	—
52	#6099	—	4	8	no	—
53	C₂×#1055	—	2	8	no	—
54	C₂×#1055	—	4	4	no	—
55	C₂×#1055	—	4	4	no	—
56	C₂×#423	—	13	2	no	—
57	C₂²×#97	D₁₃	1	1	yes	characteristic
58	C₂×#341	—	13	4	no	—
59	C₂³×C₁₃	—	2	4	no	—
60	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
61	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₂³×C₁₃	#125	1	2	yes	—
63	C₂³×C₁₃	C₄⋊Q₈	1	2	yes	—
64	C₂×C₄×C₁₃	—	2	8	no	—
65	C₂×C₄×C₁₃	—	4	8	no	—
66	C₂×C₄×C₁₃	#95	1	8	yes	—
67	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
68	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
70	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
71	C₂×C₄×C₁₃	#117	1	2	yes	—
72	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
73	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
74	C₂×C₄×C₁₃	#121	1	4	yes	—
75	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
76	C₂×C₄×C₁₃	#124	1	2	yes	—
77	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
79	C₈×C₁₃	—	2	8	no	—
80	#1055	—	4	8	no	—
81	C₂²×M₁₆	—	13	4	no	—
82	C₂³×C₈	C₂×D₁₃	1	2	yes	—
83	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
84	#423	—	13	8	no	—
85	#423	—	26	4	no	—
86	C₂×C₄⋊C₈	—	26	4	no	—
87	C₂×#97	—	2	4	no	—
88	C₂×#97	Dic₁₃	1	4	yes	—
89	#341	—	26	8	no	—
90	C₂²×C₁₃	—	2	4	no	—
91	C₂²×C₁₃	—	2	4	no	—
92	C₂²×C₁₃	—	2	4	no	—
93	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
94	C₂²×C₁₃	#382	1	1	yes	characteristic
95	C₂²×C₁₃	#384	1	1	yes	characteristic
96	C₂²×C₁₃	#389	1	4	yes	—
97	C₂²×C₁₃	#430	1	4	yes	—
98	C₄×C₁₃	—	2	8	no	—
99	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
100	C₄×C₁₃	#380	1	2	yes	—
101	C₄×C₁₃	#390	1	2	yes	—
102	C₄×C₁₃	#391	1	2	yes	—
103	C₂³×C₄	Dic₂₆	1	2	yes	—
104	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
105	C₂×M₁₆	—	13	8	no	—
106	C₂×M₁₆	—	26	4	no	—
107	C₂×M₁₆	—	26	8	no	—
108	C₂×M₁₆	—	26	8	no	—
109	C₂²×C₈	—	2	4	no	—
110	C₂²×C₈	—	2	4	no	—
111	C₂²×C₈	—	26	4	no	—
112	C₂²×C₈	Dic₂₆	1	4	yes	—
113	C₂²×C₈	D₅₂	1	4	yes	—
114	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
115	C₂×C₄²	C₄×D₁₃	1	4	yes	—
116	C₂×C₄²	D₅₂	1	2	yes	—
117	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
118	C₂×C₄²	C₂²⋊D₁₃	1	4	yes	—
119	C₄⋊C₈	—	26	16	no	—
120	#97	—	2	8	no	—
121	C₂×C₁₃	—	2	4	no	—
122	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
123	C₂×C₁₃	#1738	1	2	yes	—
124	C₂×C₁₃	#1838	1	2	yes	—
125	C₂×C₁₃	#1849	1	2	yes	—
126	C₂⁴	C₂×Dic₂₆	1	1	yes	characteristic
127	C₂²×C₄	—	4	4	no	—
128	C₂²×C₄	#6101	1	8	yes	—
129	C₂²×C₄	C₄⋊Dic₁₃	1	4	yes	—
130	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
131	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
132	C₂²×C₄	C₂×D₅₂	1	2	yes	—
133	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
134	C₂²×C₄	#6127	1	4	yes	—
135	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
136	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
137	M₁₆	—	26	16	no	—
138	M₁₆	—	52	8	no	—
139	C₂×C₈	—	2	8	no	—
140	C₂×C₈	—	2	4	no	—
141	C₂×C₈	—	2	8	no	—
142	C₂×C₈	—	2	4	no	—
143	C₂×C₈	—	26	8	no	—
144	C₂×C₈	—	52	4	no	—
145	C₂×C₈	—	52	4	no	—
146	C₂×C₈	C₄⋊Dic₁₃	1	8	yes	—
147	C₄²	C₄×Dic₁₃	1	4	yes	—
148	C₄²	#6103	1	8	yes	—
149	C₄²	C₂²⋊Dic₁₃	1	4	yes	—
150	C₁₃	#10845	1	1	yes	characteristic, complemented, Sylow
151	C₂³	—	2	4	no	—
152	C₂³	#88123	1	2	yes	—
153	C₂³	#88124	1	2	yes	—
154	C₂³	C₂×#6101	1	2	yes	—
155	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
156	C₂×C₄	—	2	8	no	—
157	C₂×C₄	—	4	8	no	—
158	C₂×C₄	#88071	1	8	yes	—
159	C₂×C₄	C₄×Dic₂₆	1	4	yes	—
160	C₂×C₄	#88123	1	1	yes	characteristic
161	C₂×C₄	C₄×D₅₂	1	4	yes	—
162	C₂×C₄	#88128	1	1	yes	characteristic
163	C₂×C₄	#88129	1	2	yes	—
164	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
165	C₂×C₄	#88178	1	4	yes	—
166	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
167	C₂×C₄	#88180	1	2	yes	—
168	C₂×C₄	C₂×#6103	1	2	yes	—
169	C₂×C₄	#88184	1	4	yes	—
170	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
171	C₈	—	2	8	no	—
172	C₈	—	52	8	no	—
173	C₂²	—	2	4	no	—
174	C₂²	—	2	4	no	—
175	C₂²	—	2	4	no	—
176	C₂²	#11718589	1	4	yes	—
177	C₂²	#11718596	1	1	yes	characteristic
178	C₂²	#11718597	1	1	yes	characteristic
179	C₂²	#11718786	1	4	yes	—
180	C₂²	C₂×#88071	1	1	yes	characteristic
181	C₄	—	2	8	no	—
182	C₄	#11718590	1	2	yes	—
183	C₄	C₄×C₄⋊Dic₁₃	1	2	yes	—
184	C₄	#11718600	1	2	yes	—
185	C₄	#11718873	1	2	yes	—
186	C₂	—	2	4	no	—
187	C₂	#13113066	1	1	yes	characteristic
188	C₂	#13114563	1	2	yes	—
189	C₂	#13114977	1	2	yes	—
190	C₂	#13115011	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂²×C₁₃×#97	C₂
socle	C₂³×C₁₃	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₂×Q₈
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂²×#97	D₁₃
hypocenter	C₁₃	#10845
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
150. C₁₃	#10845	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718585	2
C₂×#11718144	2
C₂²×C₁₃×#97	2
#10845	13