Subgroups — #15768109

Order 3328.

870 conjugacy classes of subgroups.

The subgroup lattice has 178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6099	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	C₄×#6099	—	2	4	no	—
10	C₄×#6099	C₄	1	8	yes	—
11	C₂×#88043	—	2	2	no	—
12	C₂×C₄×#1055	—	2	2	no	—
13	#11718144	C₄	1	16	yes	complemented
14	C₂³×C₄×C₁₃	Q₈	1	2	yes	—
15	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	—	2	4	no	—
17	C₂²×C₈×C₁₃	—	2	4	no	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	—
19	C₂²×C₈×C₁₃	C₂×C₄	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	C₂×C₄	1	16	yes	—
27	C₂×#6099	C₂×C₄	1	8	yes	—
28	C₂²×#1055	—	2	4	no	—
29	C₁₃×#97	—	2	8	no	—
30	#88043	—	2	8	no	—
31	C₄×#1055	—	2	8	no	—
32	#10705	—	13	1	no	maximal, Sylow
33	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
34	C₂²×C₄×C₁₃	—	4	4	no	—
35	C₂²×C₄×C₁₃	C₄⋊C₄	1	8	yes	—
36	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
37	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
38	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
39	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₂×D₄	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	16	no	—
46	C₂×C₈×C₁₃	C₄²	1	8	yes	—
47	C₄²×C₁₃	C₄²	1	4	yes	—
48	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
49	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
50	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
51	#6099	—	2	8	no	—
52	#6099	—	2	16	no	—
53	#6099	C₄²	1	16	yes	—
54	C₂×#1055	—	2	8	no	—
55	C₂×#1055	—	2	16	no	—
56	C₂×C₄×M₁₆	—	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	C₄×Q₈	1	4	yes	—
63	C₂×C₄×C₁₃	—	2	8	no	—
64	C₂×C₄×C₁₃	—	4	8	no	—
65	C₂×C₄×C₁₃	#95	1	8	yes	—
66	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
67	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
68	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
69	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
70	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₁₃	#117	1	4	yes	—
72	C₂×C₄×C₁₃	#117	1	2	yes	—
73	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
74	C₂×C₄×C₁₃	C₄×D₄	1	8	yes	—
75	C₈×C₁₃	—	2	8	no	—
76	#1055	—	2	16	no	—
77	C₂²×M₁₆	—	13	4	no	—
78	C₂³×C₈	C₂×D₁₃	1	2	yes	—
79	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
80	C₄×M₁₆	—	13	8	no	—
81	C₄×M₁₆	—	26	4	no	—
82	C₂×#97	—	2	4	no	—
83	C₂×#97	—	26	2	no	—
84	C₂×#97	Dic₁₃	1	4	yes	—
85	C₂×C₄×C₈	—	26	2	no	—
86	#341	—	13	16	no	—
87	C₂²×C₁₃	—	2	4	no	—
88	C₂²×C₁₃	—	2	8	no	—
89	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
90	C₂²×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
91	C₂²×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
92	C₂²×C₁₃	#430	1	4	yes	—
93	C₄×C₁₃	—	2	8	no	—
94	C₄×C₁₃	C₄³	1	1	yes	characteristic
95	C₄×C₁₃	#376	1	1	yes	characteristic
96	C₄×C₁₃	C₄×C₂²⋊C₄	1	4	yes	—
97	C₄×C₁₃	C₄×C₂²⋊C₄	1	2	yes	—
98	C₂³×C₄	Dic₂₆	1	2	yes	—
99	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
100	C₂×M₁₆	—	13	16	no	—
101	C₂×M₁₆	—	13	8	no	—
102	C₂×M₁₆	—	26	8	no	—
103	C₂×M₁₆	—	26	4	no	—
104	C₂²×C₈	—	2	4	no	—
105	C₂²×C₈	—	2	4	no	—
106	C₂²×C₈	—	26	4	no	—
107	C₂²×C₈	C₄×D₁₃	1	8	yes	—
108	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
109	C₂×C₄²	C₄×D₁₃	1	4	yes	—
110	C₂×C₄²	D₅₂	1	2	yes	—
111	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
112	C₂×C₄²	C₂²⋊D₁₃	1	4	yes	—
113	#97	—	2	8	no	—
114	#97	—	26	8	no	—
115	C₄×C₈	—	26	8	no	—
116	C₂×C₁₃	—	2	4	no	—
117	C₂×C₁₃	C₄×#95	1	1	yes	characteristic
118	C₂×C₁₃	#1738	1	2	yes	—
119	C₂×C₁₃	#1778	1	4	yes	—
120	C₂⁴	C₂×Dic₂₆	1	1	yes	characteristic
121	C₂²×C₄	—	4	4	no	—
122	C₂²×C₄	#6101	1	8	yes	—
123	C₂²×C₄	C₄⋊Dic₁₃	1	4	yes	—
124	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
125	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
126	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
127	C₂²×C₄	#6127	1	4	yes	—
128	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
129	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
130	M₁₆	—	13	16	no	—
131	M₁₆	—	26	8	no	—
132	M₁₆	—	26	16	no	—
133	C₂×C₈	—	2	4	no	—
134	C₂×C₈	—	2	16	no	—
135	C₂×C₈	—	2	4	no	—
136	C₂×C₈	—	26	16	no	—
137	C₂×C₈	—	26	8	no	—
138	C₂×C₈	C₄×Dic₁₃	1	8	yes	—
139	C₄²	C₄×Dic₁₃	1	4	yes	—
140	C₄²	#6103	1	4	yes	—
141	C₄²	#6103	1	4	yes	—
142	C₄²	C₂²⋊Dic₁₃	1	4	yes	—
143	C₁₃	#10705	1	1	yes	characteristic, complemented, Sylow
144	C₂³	—	2	4	no	—
145	C₂³	C₄×Dic₂₆	1	4	yes	—
146	C₂³	C₂×#6101	1	2	yes	—
147	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
148	C₂×C₄	—	2	8	no	—
149	C₂×C₄	—	4	8	no	—
150	C₂×C₄	#88071	1	8	yes	—
151	C₂×C₄	C₄²×D₁₃	1	4	yes	—
152	C₂×C₄	#88126	1	4	yes	—
153	C₂×C₄	C₄×D₅₂	1	4	yes	—
154	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
155	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
156	C₂×C₄	#88180	1	2	yes	—
157	C₂×C₄	C₂×#6103	1	2	yes	—
158	C₂×C₄	C₄×C₂²⋊D₁₃	1	8	yes	—
159	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
160	C₈	—	2	8	no	—
161	C₈	—	26	16	no	—
162	C₂²	—	2	8	no	—
163	C₂²	—	2	4	no	—
164	C₂²	C₄×#6101	1	4	yes	—
165	C₂²	C₄×C₄⋊Dic₁₃	1	2	yes	—
166	C₂²	#11718786	1	4	yes	—
167	C₂²	C₂×#88071	1	1	yes	characteristic
168	C₄	—	2	8	no	—
169	C₄	C₄²×Dic₁₃	1	1	yes	characteristic
170	C₄	#11718593	1	1	yes	characteristic
171	C₄	C₄×#6103	1	4	yes	—
172	C₄	C₄×C₂²⋊Dic₁₃	1	2	yes	—
173	C₂	—	2	4	no	—
174	C₂	C₄×#88071	1	1	yes	characteristic
175	C₂	#13114563	1	2	yes	—
176	C₂	#13114742	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator	C₄×C₁₃	C₄³
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	#10705
LCS	G ▷ 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
13. #11718144	C₄	semidirect
143. C₁₃	#10705	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#6099	2
C₂×#11718144	2
C₂²×C₁₃×#97	2
#10705	13