Subgroups — #15777809

Order 3328.

554 conjugacy classes of subgroups.

The subgroup lattice has 174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88059	C₂	1	2	yes	maximal
2	#13112930	C₂	1	4	yes	maximal, complemented
3	C₂²×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
5	C₂²×#6099	—	2	2	no	—
6	C₂×C₁₃×M₃₂	—	2	4	no	—
7	C₂×C₁₃×M₃₂	C₄	1	4	yes	—
8	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
9	C₂×#88059	—	2	4	no	—
10	C₂×#88059	—	2	2	no	—
11	C₂×#88059	C₄	1	8	yes	—
12	C₂×#88059	C₂²	1	4	yes	—
13	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
15	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
16	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	D₄	1	4	yes	—
18	C₂²×C₈×C₁₃	Q₈	1	2	yes	—
19	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
20	C₂×#6099	—	2	8	no	—
21	C₂×#6099	—	2	4	no	—
22	C₂×#6099	—	4	2	no	—
23	C₂×#6099	—	4	4	no	—
24	C₂²×#1055	—	4	2	no	—
25	C₁₃×M₃₂	—	2	8	no	—
26	C₂×C₁₃×C₁₆	—	2	4	no	—
27	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
28	#88059	—	2	8	no	—
29	#88059	—	2	4	no	—
30	#88059	C₂×C₄	1	8	yes	—
31	#12559	—	13	1	no	maximal, Sylow
32	C₂⁴×C₁₃	Q₁₆	1	1	yes	characteristic
33	C₂²×C₄×C₁₃	C₂²⋊C₄	1	4	yes	—
34	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
35	C₂²×C₄×C₁₃	D₈	1	2	yes	—
36	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	—
37	C₂²×C₄×C₁₃	Q₁₆	1	1	yes	characteristic
38	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₄²	1	4	yes	—
40	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
41	C₂×C₈×C₁₃	C₂²⋊C₄	1	4	yes	—
42	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
43	C₂×C₈×C₁₃	C₄⋊C₄	1	8	yes	—
44	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
46	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
47	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
48	#6099	—	2	8	no	—
49	#6099	—	4	8	no	—
50	#6099	—	4	4	no	—
51	C₂×#1055	—	4	8	no	—
52	C₂×#1055	—	4	4	no	—
53	C₁₃×C₁₆	—	2	4	no	—
54	C₂²×M₃₂	D₁₃	1	1	yes	characteristic
55	C₂²×#108	—	13	2	no	—
56	#1381	—	13	4	no	—
57	C₂³×C₁₃	—	4	2	no	—
58	C₂³×C₁₃	#103	1	4	yes	—
59	C₂³×C₁₃	#107	1	2	yes	—
60	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
61	C₂×C₄×C₁₃	#95	1	4	yes	—
62	C₂×C₄×C₁₃	#102	1	4	yes	—
63	C₂×C₄×C₁₃	#102	1	4	yes	—
64	C₂×C₄×C₁₃	#103	1	4	yes	—
65	C₂×C₄×C₁₃	#106	1	4	yes	—
66	C₂×C₄×C₁₃	#107	1	2	yes	—
67	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
68	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
71	C₈×C₁₃	#95	1	4	yes	—
72	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
73	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
75	#1055	—	4	8	no	—
76	C₂²×M₁₆	—	26	2	no	—
77	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
78	C₂×M₃₂	—	2	4	no	—
79	C₂×M₃₂	Dic₁₃	1	4	yes	—
80	C₂²×C₁₆	C₂×D₁₃	1	2	yes	—
81	C₂×#108	—	13	8	no	—
82	C₂×#108	—	13	4	no	—
83	C₂×#108	—	26	2	no	—
84	C₂×#108	—	26	4	no	—
85	C₂²×C₁₃	—	2	4	no	—
86	C₂²×C₁₃	—	2	2	no	—
87	C₂²×C₁₃	—	4	4	no	—
88	C₂²×C₁₃	#340	1	4	yes	—
89	C₂²×C₁₃	C₂×#103	1	2	yes	—
90	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
91	C₄×C₁₃	#340	1	4	yes	—
92	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
93	C₄×C₁₃	C₂×#102	1	2	yes	—
94	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
95	C₂³×C₄	D₅₂	1	1	yes	characteristic
96	C₂×M₁₆	—	26	8	no	—
97	C₂×M₁₆	—	26	4	no	—
98	C₂×M₁₆	—	52	4	no	—
99	C₂×M₁₆	—	52	2	no	—
100	C₂²×C₈	—	52	2	no	—
101	C₂²×C₈	Dic₂₆	1	2	yes	—
102	C₂²×C₈	C₄×D₁₃	1	4	yes	—
103	C₂²×C₈	D₅₂	1	1	yes	characteristic
104	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
105	C₂²×C₈	C₂²⋊D₁₃	1	4	yes	—
106	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
107	M₃₂	—	2	8	no	—
108	C₂×C₁₆	—	2	4	no	—
109	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	—
110	#108	—	13	8	no	—
111	#108	—	26	8	no	—
112	#108	—	26	4	no	—
113	C₂×C₁₃	—	2	4	no	—
114	C₂×C₁₃	—	2	2	no	—
115	C₂×C₁₃	C₂×#340	1	1	yes	characteristic
116	C₂×C₁₃	#2161	1	2	yes	—
117	C₂⁴	Dic₅₂	1	1	yes	characteristic
118	C₂²×C₄	#6095	1	4	yes	—
119	C₂²×C₄	D₁₀₄	1	2	yes	—
120	C₂²×C₄	Dic₅₂	1	1	yes	characteristic
121	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
122	C₂²×C₄	#6103	1	4	yes	—
123	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
124	M₁₆	—	26	8	no	—
125	M₁₆	—	52	4	no	—
126	M₁₆	—	52	8	no	—
127	C₂×C₈	—	52	4	no	—
128	C₂×C₈	—	52	8	no	—
129	C₂×C₈	C₄×Dic₁₃	1	4	yes	—
130	C₂×C₈	#6101	1	8	yes	—
131	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
132	C₂×C₈	#6103	1	4	yes	—
133	C₂×C₈	C₂²⋊Dic₁₃	1	4	yes	—
134	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
135	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
136	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
137	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
138	C₁₆	—	2	4	no	—
139	C₁₃	#12559	1	1	yes	characteristic, complemented, Sylow
140	C₂³	—	4	2	no	—
141	C₂³	#88056	1	4	yes	—
142	C₂³	#88058	1	2	yes	—
143	C₂³	C₂×Dic₅₂	1	1	yes	characteristic
144	C₂×C₄	#88056	1	4	yes	—
145	C₂×C₄	#88057	1	4	yes	—
146	C₂×C₄	#88058	1	2	yes	—
147	C₂×C₄	#88061	1	4	yes	—
148	C₂×C₄	#88061	1	4	yes	—
149	C₂×C₄	#88071	1	4	yes	—
150	C₂×C₄	C₂×#6095	1	2	yes	—
151	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
152	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
153	C₂×C₄	C₂×#6103	1	2	yes	—
154	C₈	—	52	8	no	—
155	C₈	#88071	1	4	yes	—
156	C₈	C₂×C₄×Dic₁₃	1	1	yes	characteristic
157	C₈	C₂×#6101	1	2	yes	—
158	C₈	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
159	C₂²	—	2	2	no	—
160	C₂²	—	2	4	no	—
161	C₂²	—	4	4	no	—
162	C₂²	#11718143	1	4	yes	—
163	C₂²	C₂×#88056	1	2	yes	—
164	C₂²	C₂×#88058	1	1	yes	characteristic
165	C₄	#11718143	1	4	yes	—
166	C₄	C₂×#88057	1	1	yes	characteristic
167	C₄	C₂×#88061	1	2	yes	—
168	C₄	C₂×#88071	1	1	yes	characteristic
169	C₂	—	2	2	no	—
170	C₂	—	2	4	no	—
171	C₂	C₂×#11718143	1	1	yes	characteristic
172	C₂	#13116631	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₀₄
commutator	C₈×C₁₃	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂²×C₁₃×M₃₂	C₂
socle	C₂²×C₁₃	C₂×#107
prime radical	C₂⁴×C₁₃	Q₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂²×M₃₂	D₁₃
hypocenter	C₁₃	#12559
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂²×M₃₂

Complements

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

N	H ≅ G/N	type
2. #13112930	C₂	semidirect
139. C₁₃	#12559	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#88059	2
#13112930	2
C₂²×C₁₃×M₃₂	2
#12559	13