Subgroups — #16015978

Order 3328.

622 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718568	C₂	1	1	yes	maximal, characteristic
2	#13123444	C₂	1	2	yes	maximal
3	#13116631	C₂	1	1	yes	maximal, characteristic, complemented
4	#13116629	C₂	1	4	yes	maximal, complemented
5	C₂×#11718085	C₂	1	2	yes	maximal, complemented
6	D₁₃×#368	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2161	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719450	—	2	2	no	—
9	C₂×#88155	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#108	C₂²	1	2	yes	—
12	#11718785	—	2	2	no	—
13	C₂×#88059	C₂²	1	2	yes	—
14	C₂²×#6090	C₂²	1	1	yes	characteristic
15	#11718568	C₄	1	8	yes	—
16	C₂×#88038	C₂²	1	2	yes	—
17	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
18	#11718554	—	2	4	no	—
19	D₁₃×#108	C₂²	1	8	yes	—
20	C₁₃×#368	C₂²	1	4	yes	—
21	#11718098	C₂²	1	4	yes	—
22	#11718085	C₂²	1	4	yes	—
23	#11718085	C₂²	1	4	yes	—
24	C₂×#6127	D₄	1	1	yes	characteristic
25	C₂×C₁₃×M₁₆	—	2	2	no	—
26	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
27	C₂×#6099	—	2	2	no	—
28	C₂×#6099	D₄	1	1	yes	characteristic
29	#88161	—	4	4	no	—
30	M₁₆×D₁₃	—	2	8	no	—
31	#88155	—	4	4	no	—
32	#88155	C₂×C₄	1	4	yes	—
33	#88155	Q₈	1	4	yes	—
34	C₂×#6094	D₄	1	2	yes	—
35	C₂×C₈×D₁₃	C₂³	1	2	yes	—
36	C₁₃×M₃₂	C₂×C₄	1	4	yes	—
37	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
38	C₁₃×#108	—	2	2	no	—
39	C₁₃×#108	C₂³	1	4	yes	—
40	#88062	—	2	8	no	—
41	#88059	—	2	2	no	—
42	#88059	C₂³	1	4	yes	—
43	C₂×#6090	C₂×C₄	1	4	yes	—
44	C₂×#6090	C₂³	1	1	yes	characteristic
45	C₂×#6090	C₂³	1	1	yes	characteristic
46	#88038	C₂×C₄	1	8	yes	—
47	C₁₆×D₁₃	C₂×C₄	1	8	yes	—
48	#33414	—	13	1	no	maximal, Sylow
49	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂×C₂²⋊D₁₃	Q₁₆	1	2	yes	—
51	#6127	C₄⋊C₄	1	4	yes	—
52	#6127	D₈	1	4	yes	—
53	C₂×D₅₂	Q₁₆	1	1	yes	characteristic
54	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
55	C₂×Dic₂₆	Q₁₆	1	1	yes	characteristic
56	C₁₃×M₁₆	—	2	4	no	—
57	C₁₃×M₁₆	—	4	2	no	—
58	C₂×C₈×C₁₃	—	4	2	no	—
59	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
60	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
61	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
62	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
63	#6099	—	2	4	no	—
64	#6099	—	4	2	no	—
65	#6099	C₄⋊C₄	1	4	yes	—
66	C₂×#1055	—	4	2	no	—
67	C₂×#1055	C₂×D₄	1	2	yes	—
68	#6094	—	4	8	no	—
69	#6094	C₄⋊C₄	1	8	yes	—
70	C₈×D₁₃	—	4	8	no	—
71	C₈×D₁₃	C₂²×C₄	1	4	yes	—
72	C₈×D₁₃	C₂×Q₈	1	4	yes	—
73	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
74	#6090	C₂²×C₄	1	2	yes	—
75	#6090	C₂²×C₄	1	2	yes	—
76	C₂×#504	—	13	1	no	—
77	#2916	—	13	2	no	—
78	#2161	—	13	1	no	—
79	#2161	—	13	4	no	—
80	#2161	D₁₃	1	1	yes	characteristic, complemented
81	C₂×#368	—	13	2	no	—
82	C₂×#368	—	13	4	no	—
83	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
84	C₂²×D₁₃	C₂×Q₁₆	1	2	yes	—
85	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
86	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
87	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
88	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
89	C₂²⋊D₁₃	#107	1	8	yes	—
90	C₂×Dic₁₃	C₂×Q₁₆	1	2	yes	—
91	D₅₂	#107	1	4	yes	—
92	C₄×D₁₃	C₂×C₄⋊C₄	1	4	yes	—
93	C₄×D₁₃	C₂×D₈	1	4	yes	—
94	Dic₂₆	#107	1	4	yes	—
95	C₈×C₁₃	—	4	4	no	—
96	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
97	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
98	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
99	#1055	—	4	4	no	—
100	#1055	C₂×C₄⋊C₄	1	4	yes	—
101	#568	—	26	2	no	—
102	C₂×#131	—	13	1	no	—
103	#504	—	13	8	no	—
104	C₂×M₃₂	—	13	2	no	—
105	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
106	C₂²×C₁₆	—	13	1	no	—
107	C₂²×C₁₆	—	13	2	no	—
108	#430	—	26	4	no	—
109	#430	—	26	2	no	—
110	C₂×#108	—	13	2	no	—
111	C₂×#108	—	13	8	no	—
112	C₂×#108	C₂×D₁₃	1	2	yes	—
113	#368	—	13	4	no	—
114	#368	—	13	4	no	—
115	#368	—	13	4	no	—
116	#368	C₂×D₁₃	1	4	yes	—
117	C₂²×C₁₃	—	4	1	no	—
118	C₂²×C₁₃	C₂×#107	1	2	yes	—
119	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
120	C₂×D₁₃	—	4	2	no	—
121	C₂×D₁₃	C₂×#107	1	4	yes	—
122	C₄×C₁₃	C₂×#107	1	2	yes	—
123	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
124	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
125	Dic₁₃	C₂×#107	1	4	yes	—
126	C₂×#41	—	13	1	no	—
127	#131	—	13	4	no	—
128	#131	—	13	4	no	—
129	#131	—	52	4	no	—
130	#131	—	52	4	no	—
131	C₂×M₁₆	—	2	2	no	—
132	C₂×M₁₆	—	13	1	no	—
133	C₂×M₁₆	—	13	2	no	—
134	C₂×M₁₆	—	26	8	no	—
135	C₂×M₁₆	—	26	2	no	—
136	C₂²×C₈	—	13	2	no	—
137	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
138	M₃₂	—	13	8	no	—
139	M₃₂	C₄×D₁₃	1	4	yes	—
140	C₂×C₁₆	—	13	4	no	—
141	C₂×C₁₆	—	13	1	no	—
142	C₂×C₁₆	—	13	1	no	—
143	C₂×C₁₆	—	13	8	no	—
144	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
145	#108	—	2	2	no	—
146	#108	—	13	4	no	—
147	#108	—	26	8	no	—
148	#108	—	26	2	no	—
149	#108	C₂²×D₁₃	1	4	yes	—
150	C₂×C₁₃	—	2	1	no	—
151	C₂×C₁₃	—	2	2	no	—
152	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
153	D₁₃	—	2	4	no	—
154	#41	—	13	4	no	—
155	#41	—	13	4	no	—
156	C₂×Q₈	—	13	1	no	—
157	C₂×D₄	—	13	2	no	—
158	C₂×D₄	—	13	1	no	—
159	C₂²×C₄	—	13	2	no	—
160	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
161	M₁₆	—	2	4	no	—
162	M₁₆	—	4	2	no	—
163	M₁₆	—	13	4	no	—
164	M₁₆	—	13	8	no	—
165	M₁₆	—	26	4	no	—
166	M₁₆	—	52	8	no	—
167	M₁₆	—	52	2	no	—
168	C₂×C₈	—	4	2	no	—
169	C₂×C₈	—	13	2	no	—
170	C₂×C₈	—	13	4	no	—
171	C₂×C₈	—	13	4	no	—
172	C₂×C₈	—	52	8	no	—
173	C₂×C₈	—	52	2	no	—
174	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
175	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
176	C₂×C₈	Q₈×D₁₃	1	2	yes	—
177	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
178	C₁₆	—	13	2	no	—
179	C₁₆	—	13	2	no	—
180	C₁₆	C₂×C₄×D₁₃	1	4	yes	—
181	C₁₃	#33414	1	1	yes	characteristic, complemented, Sylow
182	C₂³	—	13	2	no	—
183	C₂³	Q₁₆×D₁₃	1	1	yes	characteristic
184	Q₈	—	13	4	no	—
185	D₄	—	13	8	no	—
186	D₄	—	13	4	no	—
187	C₂×C₄	—	13	2	no	—
188	C₂×C₄	—	13	4	no	—
189	C₂×C₄	—	13	4	no	—
190	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
191	C₂×C₄	D₈×D₁₃	1	2	yes	—
192	C₂×C₄	Q₁₆×D₁₃	1	1	yes	characteristic
193	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
194	C₈	—	4	4	no	—
195	C₈	—	13	4	no	—
196	C₈	—	52	4	no	—
197	C₈	C₄⋊C₄×D₁₃	1	2	yes	—
198	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
199	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
200	C₂²	—	4	1	no	—
201	C₂²	—	13	4	no	—
202	C₂²	—	52	2	no	—
203	C₂²	D₁₃×#107	1	2	yes	—
204	C₂²	C₂×Q₁₆×D₁₃	1	1	yes	characteristic
205	C₄	—	13	4	no	—
206	C₄	D₁₃×#107	1	2	yes	—
207	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
208	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
209	C₂	—	2	1	no	—
210	C₂	—	2	2	no	—
211	C₂	—	26	4	no	—
212	C₂	C₂×D₁₃×#107	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₈×D₁₃
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#2161	C₂
socle	C₂×C₁₃	C₂²×#107
prime radical	C₂×#6127	D₄
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2161	D₁₃
hypocenter	C₁₃	#33414
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2161

Complements

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

N	H ≅ G/N	type
3. #13116631	C₂	semidirect
4. #13116629	C₂	semidirect
5. C₂×#11718085	C₂	semidirect
6. D₁₃×#368	C₂	semidirect
7. C₁₃×#2161	C₂	semidirect
80. #2161	D₁₃	semidirect
181. C₁₃	#33414	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718568	2
#13123444	2
#13116631	2
#13116629	2
C₂×#11718085	2
D₁₃×#368	2
C₁₃×#2161	2
#33414	13