Subgroups — #15860344

Order 3328.

1978 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719524	C₂	1	2	yes	maximal
2	#13114563	C₂	1	6	yes	maximal, complemented
3	C₂×#11718144	C₂	1	6	yes	maximal, complemented
4	C₂²×C₁₃×#131	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
6	C₂×C₁₃×#131	—	2	8	no	—
7	C₂×C₁₃×#131	C₄	1	8	yes	—
8	C₂²×C₁₃×M₁₆	C₂²	1	3	yes	—
9	C₂³×C₈×C₁₃	C₂²	1	3	yes	—
10	#11719524	—	2	8	no	—
11	#11719524	C₄	1	16	yes	—
12	C₂×#88202	—	2	8	no	—
13	C₂²×#6099	C₂²	1	12	yes	—
14	#11718144	C₂²	1	4	yes	—
15	#11718144	C₂²	1	12	yes	—
16	C₂×C₁₃×#41	C₂×C₄	1	8	yes	—
17	C₂×C₁₃×#41	C₂×C₄	1	4	yes	—
18	C₂×C₁₃×#41	D₄	1	4	yes	—
19	C₂×C₁₃×#41	D₄	1	8	yes	—
20	C₂²×Q₈×C₁₃	Q₈	1	1	yes	characteristic
21	C₂²×D₄×C₁₃	Q₈	1	3	yes	—
22	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
23	C₁₃×#131	—	2	32	no	—
24	C₂×C₁₃×M₁₆	—	2	12	no	—
25	C₂×C₁₃×M₁₆	C₂×C₄	1	12	yes	—
26	C₂²×C₈×C₁₃	—	2	12	no	—
27	C₂²×C₈×C₁₃	C₂×C₄	1	12	yes	—
28	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
30	#88202	—	2	64	no	—
31	C₂×#6099	—	2	12	no	—
32	C₂×#6099	—	2	24	no	—
33	C₂×#6099	C₂×C₄	1	48	yes	—
34	C₂×#6099	C₂³	1	8	yes	—
35	C₂²×#1055	—	2	12	no	—
36	#20351	—	13	1	no	maximal, Sylow
37	C₂⁴×C₁₃	C₂×Q₈	1	3	yes	—
38	C₁₃×#41	C₄²	1	16	yes	—
39	C₁₃×#41	C₂²⋊C₄	1	32	yes	—
40	C₁₃×#41	C₂²⋊C₄	1	16	yes	—
41	C₂×Q₈×C₁₃	C₄⋊C₄	1	8	yes	—
42	C₂×Q₈×C₁₃	C₄⋊C₄	1	4	yes	—
43	C₂×D₄×C₁₃	C₄⋊C₄	1	24	yes	—
44	C₂×D₄×C₁₃	C₄⋊C₄	1	12	yes	—
45	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
46	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
47	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
48	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
49	C₂²×C₄×C₁₃	C₂×Q₈	1	3	yes	—
50	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
51	C₁₃×M₁₆	—	2	24	no	—
52	C₂×C₈×C₁₃	—	2	24	no	—
53	C₂×C₈×C₁₃	—	2	2	no	—
54	C₂×C₈×C₁₃	—	2	6	no	—
55	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
56	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
57	#6099	—	2	48	no	—
58	#6099	—	2	8	no	—
59	#6099	C₂²×C₄	1	16	yes	—
60	C₂×#1055	—	2	48	no	—
61	C₂×#1055	—	2	8	no	—
62	C₂×#568	—	13	2	no	—
63	C₂²×#131	D₁₃	1	1	yes	characteristic
64	#1738	—	13	6	no	—
65	C₂×#341	—	13	6	no	—
66	C₂³×C₁₃	—	4	6	no	—
67	C₂³×C₁₃	C₂×C₄⋊C₄	1	6	yes	—
68	C₂³×C₁₃	C₂×C₄⋊C₄	1	12	yes	—
69	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
70	Q₈×C₁₃	#95	1	16	yes	—
71	D₄×C₁₃	#95	1	48	yes	—
72	C₂×C₄×C₁₃	C₂×C₄²	1	12	yes	—
73	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	24	yes	—
74	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	12	yes	—
75	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	12	yes	—
76	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	6	yes	—
77	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
78	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
81	C₈×C₁₃	—	2	2	no	—
82	C₈×C₁₃	—	2	6	no	—
83	#1055	—	2	16	no	—
84	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
85	#568	—	13	16	no	—
86	#568	—	26	8	no	—
87	C₂×#131	—	2	8	no	—
88	C₂×#131	—	26	8	no	—
89	C₂×#131	Dic₁₃	1	8	yes	—
90	C₂²×M₁₆	—	13	12	no	—
91	C₂²×M₁₆	C₂×D₁₃	1	3	yes	—
92	C₂³×C₈	C₂×D₁₃	1	3	yes	—
93	#341	—	13	4	no	—
94	#341	—	13	12	no	—
95	C₂²×C₁₃	—	2	2	no	—
96	C₂²×C₁₃	—	2	12	no	—
97	C₂²×C₁₃	—	4	12	no	—
98	C₂²×C₁₃	C₂×#95	1	12	yes	—
99	C₂²×C₁₃	C₂²×C₄⋊C₄	1	2	yes	—
100	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
101	C₄×C₁₃	C₂×#95	1	12	yes	—
102	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
103	C₄×C₁₃	C₂²×C₂²⋊C₄	1	2	yes	—
104	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
105	C₂×#41	C₄×D₁₃	1	8	yes	—
106	C₂×#41	D₅₂	1	4	yes	—
107	C₂×#41	C₂×Dic₁₃	1	4	yes	—
108	C₂×#41	C₂²⋊D₁₃	1	8	yes	—
109	C₂²×Q₈	Dic₂₆	1	1	yes	characteristic
110	C₂²×D₄	Dic₂₆	1	3	yes	—
111	C₂³×C₄	C₂²×D₁₃	1	3	yes	—
112	#131	—	2	32	no	—
113	#131	—	26	64	no	—
114	C₂×M₁₆	—	2	12	no	—
115	C₂×M₁₆	—	13	48	no	—
116	C₂×M₁₆	—	13	8	no	—
117	C₂×M₁₆	—	26	12	no	—
118	C₂×M₁₆	—	26	24	no	—
119	C₂×M₁₆	C₂×Dic₁₃	1	12	yes	—
120	C₂²×C₈	—	2	12	no	—
121	C₂²×C₈	—	26	12	no	—
122	C₂²×C₈	C₂×Dic₁₃	1	12	yes	—
123	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
124	C₂²×C₈	C₂²×D₁₃	1	3	yes	—
125	C₂×C₁₃	—	2	2	no	—
126	C₂×C₁₃	—	2	12	no	—
127	C₂×C₁₃	C₂²×#95	1	1	yes	characteristic
128	C₂×C₁₃	#2916	1	2	yes	—
129	C₂⁴	C₂×Dic₂₆	1	3	yes	—
130	#41	C₄×Dic₁₃	1	16	yes	—
131	#41	#6103	1	32	yes	—
132	#41	C₂²⋊Dic₁₃	1	16	yes	—
133	C₂×Q₈	#6101	1	8	yes	—
134	C₂×Q₈	C₄⋊Dic₁₃	1	4	yes	—
135	C₂×D₄	#6101	1	24	yes	—
136	C₂×D₄	C₄⋊Dic₁₃	1	12	yes	—
137	C₂²×C₄	C₂×Dic₂₆	1	3	yes	—
138	C₂²×C₄	C₂×C₄×D₁₃	1	12	yes	—
139	C₂²×C₄	C₂×D₅₂	1	6	yes	—
140	C₂²×C₄	C₂²×Dic₁₃	1	6	yes	—
141	C₂²×C₄	C₂×C₂²⋊D₁₃	1	12	yes	—
142	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
143	M₁₆	—	2	24	no	—
144	M₁₆	—	13	16	no	—
145	M₁₆	—	26	48	no	—
146	M₁₆	—	26	8	no	—
147	C₂×C₈	—	2	24	no	—
148	C₂×C₈	—	2	2	no	—
149	C₂×C₈	—	2	6	no	—
150	C₂×C₈	—	26	48	no	—
151	C₂×C₈	—	26	8	no	—
152	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
153	C₂×C₈	C₂²×Dic₁₃	1	6	yes	—
154	C₁₃	#20351	1	1	yes	characteristic, complemented, Sylow
155	C₂³	—	4	6	no	—
156	C₂³	C₂×#6101	1	12	yes	—
157	C₂³	C₂×C₄⋊Dic₁₃	1	6	yes	—
158	C₂³	C₂²×Dic₂₆	1	1	yes	characteristic
159	Q₈	#88071	1	16	yes	—
160	D₄	#88071	1	48	yes	—
161	C₂×C₄	C₂×C₄×Dic₁₃	1	12	yes	—
162	C₂×C₄	C₂×#6101	1	12	yes	—
163	C₂×C₄	C₂×C₄⋊Dic₁₃	1	6	yes	—
164	C₂×C₄	C₂×#6103	1	24	yes	—
165	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	12	yes	—
166	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
167	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
168	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
169	C₂×C₄	C₂²×C₂²⋊D₁₃	1	2	yes	—
170	C₈	—	2	2	no	—
171	C₈	—	2	6	no	—
172	C₈	—	26	16	no	—
173	C₂²	—	2	2	no	—
174	C₂²	—	2	12	no	—
175	C₂²	—	4	12	no	—
176	C₂²	C₂×#88071	1	12	yes	—
177	C₂²	C₂²×#6101	1	2	yes	—
178	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
179	C₄	C₂×#88071	1	12	yes	—
180	C₄	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
181	C₄	C₂²×#6103	1	2	yes	—
182	C₄	C₂²×C₂²⋊Dic₁₃	1	1	yes	characteristic
183	C₂	—	2	2	no	—
184	C₂	—	2	12	no	—
185	C₂	C₂²×#88071	1	1	yes	characteristic
186	C₂	#13123447	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₂
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂²×C₁₃×#131	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂²×C₁₃×#41	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂²×#131	D₁₃
hypocenter	C₁₃	#20351
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41 ◁ C₂²×#131

Complements

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

N	H ≅ G/N	type
2. #13114563	C₂	semidirect
3. C₂×#11718144	C₂	semidirect
154. C₁₃	#20351	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11719524	2
#13114563	2
C₂×#11718144	2
C₂²×C₁₃×#131	2
#20351	13