Subgroups — #16807039

Order 3328.

622 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131498	C₂	1	2	yes	maximal
2	#13131192	C₂	1	6	yes	maximal, complemented
3	C₂×#11718224	C₂	1	3	yes	maximal, complemented
4	D₁₃⋊#368	C₂	1	3	yes	maximal, complemented
5	D₁₃×#504	C₂	1	1	yes	maximal, characteristic
6	#11719629	—	2	2	no	—
7	D₁₃×#131	C₂²	1	1	yes	characteristic
8	#11719100	—	2	6	no	—
9	D₁₃⋊#108	C₂²	1	6	yes	—
10	C₂×#88104	C₂²	1	6	yes	—
11	C₁₃×#504	C₄	1	1	yes	characteristic
12	#11718801	C₄	1	1	yes	characteristic
13	#11718568	C₄	1	3	yes	—
14	D₁₃×M₃₂	C₂²	1	3	yes	—
15	#11718562	C₄	1	3	yes	—
16	C₂×C₁₆×D₁₃	C₂²	1	3	yes	—
17	#11718224	C₂²	1	1	yes	characteristic
18	#11718224	C₂²	1	3	yes	—
19	#11718224	C₂²	1	6	yes	—
20	#11718223	C₂²	1	6	yes	—
21	#41×D₁₃	D₄	1	1	yes	characteristic
22	#88240	—	4	2	no	—
23	#88238	—	4	6	no	—
24	D₁₃⋊M₁₆	—	2	6	no	—
25	C₂×#6118	—	2	6	no	—
26	C₁₃×#131	C₂×C₄	1	1	yes	characteristic
27	#88202	Q₈	1	1	yes	characteristic
28	#88161	Q₈	1	3	yes	—
29	M₁₆×D₁₃	D₄	1	3	yes	—
30	#88155	C₂×C₄	1	3	yes	—
31	C₂×C₈×D₁₃	C₂³	1	3	yes	—
32	#88104	—	2	6	no	—
33	#88104	C₂³	1	2	yes	—
34	#88104	C₂³	1	6	yes	—
35	#88103	—	2	6	no	—
36	C₁₃×M₃₂	C₂×C₄	1	3	yes	—
37	C₂×C₁₃×C₁₆	C₂×C₄	1	3	yes	—
38	#88052	C₂×C₄	1	3	yes	—
39	C₂×#6090	C₂×C₄	1	3	yes	—
40	#88038	C₂×C₄	1	6	yes	—
41	C₁₆×D₁₃	C₂×C₄	1	3	yes	—
42	C₁₆×D₁₃	C₂×C₄	1	3	yes	—
43	C₁₆×D₁₃	C₂³	1	3	yes	—
44	C₁₆×D₁₃	C₂³	1	1	yes	characteristic
45	#33414	—	13	1	no	maximal, Sylow
46	C₁₃×#41	C₄⋊C₄	1	1	yes	characteristic
47	#6131	D₈	1	1	yes	characteristic
48	Q₈×D₁₃	Q₁₆	1	1	yes	characteristic
49	#6129	D₈	1	3	yes	—
50	D₄×D₁₃	Q₁₆	1	3	yes	—
51	#6127	C₄⋊C₄	1	3	yes	—
52	C₂×C₄×D₁₃	C₂×D₄	1	3	yes	—
53	#6122	—	4	6	no	—
54	C₂×#1057	—	4	6	no	—
55	#6118	—	2	2	no	—
56	#6118	—	2	6	no	—
57	#6118	—	4	6	no	—
58	D₁₃⋊C₈	—	4	6	no	—
59	C₁₃×M₁₆	C₄⋊C₄	1	3	yes	—
60	C₂×C₈×C₁₃	C₂²×C₄	1	3	yes	—
61	#6099	C₄⋊C₄	1	3	yes	—
62	C₂×#1055	C₂×Q₈	1	3	yes	—
63	#6094	C₄⋊C₄	1	6	yes	—
64	C₈×D₁₃	C₂²×C₄	1	3	yes	—
65	C₈×D₁₃	C₂×D₄	1	3	yes	—
66	C₈×D₁₃	C₂×Q₈	1	3	yes	—
67	C₈×D₁₃	C₂⁴	1	1	yes	characteristic
68	C₁₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
69	C₁₃×C₁₆	C₂²×C₄	1	3	yes	—
70	#6090	C₂²×C₄	1	1	yes	characteristic
71	#6090	C₂²×C₄	1	3	yes	—
72	C₂×#504	—	13	1	no	—
73	#2916	—	13	2	no	—
74	#2161	—	13	6	no	—
75	C₂×#368	—	13	3	no	—
76	C₂×#368	—	13	3	no	—
77	C₂²×D₁₃	C₂×Q₁₆	1	3	yes	—
78	Q₈×C₁₃	#107	1	1	yes	characteristic
79	D₄×C₁₃	#107	1	3	yes	—
80	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
81	C₂²⋊D₁₃	#107	1	6	yes	—
82	C₂×Dic₁₃	C₂×D₈	1	3	yes	—
83	D₅₂	#107	1	3	yes	—
84	C₄×D₁₃	C₂×C₄⋊C₄	1	3	yes	—
85	C₄×D₁₃	C₂×D₈	1	3	yes	—
86	C₄×D₁₃	C₂×Q₁₆	1	3	yes	—
87	C₄×D₁₃	C₂²×D₄	1	1	yes	characteristic
88	Dic₂₆	#107	1	3	yes	—
89	#1057	—	4	2	no	—
90	#1057	—	4	6	no	—
91	C₈×C₁₃	C₂×C₄⋊C₄	1	3	yes	—
92	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
93	#1055	C₂×C₄⋊C₄	1	3	yes	—
94	#1055	C₂²×Q₈	1	1	yes	characteristic
95	#568	—	26	2	no	—
96	C₂×#131	—	13	1	no	—
97	#504	—	13	1	no	—
98	#504	—	13	3	no	—
99	#504	—	13	3	no	—
100	#504	#261	1	1	yes	characteristic
101	C₂×M₃₂	—	13	3	no	—
102	C₂²×C₁₆	—	13	3	no	—
103	#430	—	26	6	no	—
104	C₂×#108	—	13	6	no	—
105	C₂×#108	—	13	6	no	—
106	#368	—	13	6	no	—
107	#368	—	13	1	no	—
108	#368	—	13	3	no	—
109	#368	—	13	6	no	—
110	C₂²×C₁₃	C₂×#107	1	3	yes	—
111	C₂×D₁₃	—	4	3	no	—
112	C₂×D₁₃	C₂×#107	1	3	yes	—
113	C₂×D₁₃	C₂²×Q₁₆	1	1	yes	characteristic
114	C₄×C₁₃	C₂×#107	1	3	yes	—
115	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
116	Dic₁₃	C₂×#107	1	3	yes	—
117	Dic₁₃	C₂²×D₈	1	1	yes	characteristic
118	C₂×#41	—	13	1	no	—
119	#131	—	13	1	no	—
120	#131	—	13	3	no	—
121	#131	—	13	3	no	—
122	#131	—	52	6	no	—
123	#131	—	52	2	no	—
124	#131	C₂×#261	1	1	yes	characteristic
125	C₂×M₁₆	—	13	3	no	—
126	C₂×M₁₆	—	26	6	no	—
127	C₂×M₁₆	—	26	6	no	—
128	C₂²×C₈	—	13	3	no	—
129	M₃₂	—	13	3	no	—
130	M₃₂	—	13	6	no	—
131	M₃₂	C₂×#261	1	3	yes	—
132	C₂×C₁₆	—	13	3	no	—
133	C₂×C₁₆	—	13	1	no	—
134	C₂×C₁₆	—	13	3	no	—
135	C₂×C₁₆	—	13	3	no	—
136	C₂×C₁₆	—	13	3	no	—
137	C₂×C₁₆	C₂×#261	1	3	yes	—
138	#108	—	13	2	no	—
139	#108	—	13	6	no	—
140	#108	—	26	6	no	—
141	#108	—	26	6	no	—
142	C₂×C₁₃	—	2	3	no	—
143	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
144	D₁₃	—	2	1	no	—
145	D₁₃	—	2	3	no	—
146	#41	—	13	1	no	—
147	#41	—	13	3	no	—
148	#41	—	13	3	no	—
149	#41	C₄⋊#261	1	1	yes	characteristic
150	C₂×Q₈	—	13	1	no	—
151	C₂×D₄	—	13	3	no	—
152	C₂²×C₄	—	13	3	no	—
153	M₁₆	—	13	3	no	—
154	M₁₆	—	13	6	no	—
155	M₁₆	—	26	2	no	—
156	M₁₆	—	26	6	no	—
157	M₁₆	—	52	6	no	—
158	M₁₆	—	52	6	no	—
159	M₁₆	C₄⋊#261	1	3	yes	—
160	C₂×C₈	—	13	3	no	—
161	C₂×C₈	—	13	3	no	—
162	C₂×C₈	—	13	3	no	—
163	C₂×C₈	—	13	1	no	—
164	C₂×C₈	—	13	3	no	—
165	C₂×C₈	—	52	6	no	—
166	C₂×C₈	—	52	6	no	—
167	C₂×C₈	C₂²×#261	1	3	yes	—
168	C₁₆	—	13	1	no	—
169	C₁₆	—	13	3	no	—
170	C₁₆	C₂²×#261	1	1	yes	characteristic
171	C₁₆	C₂²×#261	1	3	yes	—
172	C₁₃	#33414	1	1	yes	characteristic, complemented, Sylow
173	C₂³	—	13	3	no	—
174	Q₈	—	13	3	no	—
175	Q₈	#88102	1	1	yes	characteristic
176	D₄	—	13	6	no	—
177	D₄	—	13	3	no	—
178	D₄	#88102	1	3	yes	—
179	C₂×C₄	—	13	3	no	—
180	C₂×C₄	—	13	3	no	—
181	C₂×C₄	—	13	3	no	—
182	C₂×C₄	—	13	1	no	—
183	C₂×C₄	—	13	3	no	—
184	C₂×C₄	C₂×C₄⋊#261	1	3	yes	—
185	C₈	—	13	3	no	—
186	C₈	—	13	1	no	—
187	C₈	—	52	2	no	—
188	C₈	—	52	6	no	—
189	C₈	C₂×C₄⋊#261	1	3	yes	—
190	C₈	C₂³×#261	1	1	yes	characteristic
191	C₂²	—	13	1	no	—
192	C₂²	—	13	3	no	—
193	C₂²	—	52	3	no	—
194	C₂²	C₂×#88102	1	3	yes	—
195	C₄	—	13	1	no	—
196	C₄	—	13	3	no	—
197	C₄	C₂×#88102	1	3	yes	—
198	C₄	C₂²×C₄⋊#261	1	1	yes	characteristic
199	C₂	—	2	3	no	—
200	C₂	—	26	1	no	—
201	C₂	—	26	3	no	—
202	C₂	C₂²×#88102	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×#88102
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₈	C₂³×#261
Fitting	C₁₃×#504	C₄
socle	C₂×C₁₃	C₂²×#107
prime radical	#41×D₁₃	D₄
cosocle	C₈×D₁₃	C₂⁴
hypercenter	#504	#261
hypocenter	C₁₃	#33414
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131 ◁ #504

Complements

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

N	H ≅ G/N	type
2. #13131192	C₂	semidirect
3. C₂×#11718224	C₂	semidirect
4. D₁₃⋊#368	C₂	semidirect
172. C₁₃	#33414	semidirect

Maximal subgroups

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

subgroup	index
#13131498	2
#13131192	2
C₂×#11718224	2
D₁₃⋊#368	2
D₁₃×#504	2
#33414	13