Finite Group Databasebeta

← #15766004

Subgroups — #15766004

Order 3328.

454 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 101 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115664C211yesmaximal, characteristic
2#13113395C212yesmaximal
3#13112694C212yesmaximal, complemented
4#13112669C211yesmaximal, characteristic, complemented
5C13×#2862C211yesmaximal, characteristic, complemented
6C2×C13×C4⋊Q8—21no—
7#11719182C2211yescharacteristic
8C13×#391—24no—
9C13×#382—21no—
10C13×#382C2212yes—
11C43×C13C2211yescharacteristic
12C2×#88045—21no—
13C2×#88045—21no—
14#11718586C2212yes—
15#11718585C2211yescharacteristic
16#11718043—24no—
17C22×Q8×C13—22no—
18C2×#6127—21no—
19C13×C4⋊Q8—42no—
20C13×C4⋊Q8—42no—
21C2×C13×C4⋊C4—22no—
22C2×C13×C4⋊C4—22no—
23C2×C42×C13—22no—
24C2×C42×C13D411yescharacteristic
25C2×C42×C13D411yescharacteristic
26C2×C42×C13C2311yescharacteristic
27#88184—22no—
28C2×#6099—21no—
29#88129—21no—
30#88128Q811yescharacteristic, complemented
31C4×D52—22no—
32#88123Q811yescharacteristic, complemented
33C13×#95—24no—
34C13×#95—22no—
35C13×#95D414yes—
36C22⋊#1055—22no—
37#88045—42no—
38#88045—42no—
39C4⋊#1055—22no—
40C4⋊#1055—22no—
41C4×#1055—22no—
42#10362—131nomaximal, Sylow
43C2×Q8×C13—44no—
44C2×Q8×C13—48no—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13—24no—
48C22×C4×C13C2×D412yes—
49C22×C4×C13C2×D411yescharacteristic
50C2×C22⋊D13—41no—
51#6127—41no—
52#6127—41no—
53#6127—41no—
54#6127—41no—
55C2×D52—21no—
56C2×D52—22no—
57C2×C4×D13—41no—
58C2×Dic26—21no—
59C13×C4⋊C4—44no—
60C13×C4⋊C4—42no—
61C13×C4⋊C4—42no—
62C42×C13—21no—
63C42×C13—21no—
64C42×C13—44no—
65C42×C13D812yes—
66C42×C13SD1612yes—
67C42×C13C2×Q811yescharacteristic
68C42×C13#4112yes—
69C42×C13#4111yescharacteristic
70#6103—42no—
71C4⋊Dic13—22no—
72#6099—41no—
73#6099—41no—
74C2×#1055—42no—
75C2×#1055—41no—
76#2862D1311yescharacteristic, complemented
77#1962—131no—
78#1517—132no—
79#1286—132no—
80#1276—131no—
81C23×C13#12011yescharacteristic
82C22×D13—41no—
83Q8×C13—88no—
84C2×C4×C13—24no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13—48no—
90C2×C4×C13—44no—
91C2×C4×C13C22⋊Q812yes—
92C2×C4×C13C22⋊Q811yescharacteristic
93C2×C4×C13#12412yes—
94C2×C4×C13#12411yescharacteristic
95C2×C4×C13C2×D811yescharacteristic
96C2×C4×C13C2×SD1611yescharacteristic
97C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
98C2×C4×C13#13711yescharacteristic
99C22⋊D13—81no—
100C22⋊D13—81no—
101C2×Dic13—41no—
102D52—41no—
103D52—41no—
104D52—82no—
105C4×D13—81no—
106C4×D13—81no—
107Dic26—41no—
108Dic26—41no—
109#1055—82no—
110#1055—81no—
111#532—131no—
112C2×C4⋊Q8—21no—
113#431—132no—
114#423—131no—
115C2×#104—261no—
116C2×#104—261no—
117#391—24no—
118#382—21no—
119#382C2×D1312yes—
120C43C2×D1311yescharacteristic
121#327—264no—
122C22×C13—22no—
123C22×C13#39311yescharacteristic
124C22×C13#44711yescharacteristic
125C22×C13#44811yescharacteristic
126C2×D13—81no—
127C2×D13—82no—
128C4×C13—24no—
129C4×C13—22no—
130C4×C13—22no—
131C4×C13—42no—
132C4×C13—84no—
133C4×C13#47411yescharacteristic
134C4×C13#47611yescharacteristic
135C4×C13#48611yescharacteristic
136C4×C13#48911yescharacteristic
137Dic13—81no—
138C2×#41—261no—
139C22×Q8—22no—
140C2×M16—261no—
141C4⋊Q8—42no—
142C4⋊Q8—42no—
143C4⋊Q8—131no—
144#127—131no—
145#124—261no—
146#121—262no—
147C4×D4—262no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C42—22no—
151C2×C42C22⋊D1311yescharacteristic
152C2×C42C22⋊D1311yescharacteristic
153C2×C42C22×D1311yescharacteristic
154C4⋊C8—262no—
155C4⋊C8—262no—
156#104—522no—
157#104—522no—
158C22⋊C8—262no—
159C4×C8—262no—
160#95—24no—
161#95—22no—
162#95C22⋊D1314yes—
163C2×C13—21no—
164C2×C13—21no—
165C2×C13#202311yescharacteristic
166C2×C13#203112yes—
167D13—161no—
168#41—521no—
169#41—521no—
170#41—521no—
171#41—521no—
172C2×Q8—44no—
173C2×Q8—48no—
174C2×Q8—261no—
175C2×D4—261no—
176C2×D4—262no—
177C2×D4—521no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—24no—
181C22×C4—521no—
182C22×C4C2×C22⋊D1312yes—
183C22×C4C2×C22⋊D1311yescharacteristic
184M16—521no—
185M16—521no—
186C2×C8—522no—
187C2×C8—521no—
188C4⋊C4—44no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—262no—
192C22⋊C4—522no—
193C42—21no—
194C42—21no—
195C42—44no—
196C42#610412yes—
197C42#610612yes—
198C42Q8×D1311yescharacteristic
199C42#613111yescharacteristic
200C42#613112yes—
201C13#1036211yescharacteristic, complemented, Sylow
202C23—521no—
203C23#8820711yescharacteristic
204Q8—88no—
205Q8—521no—
206Q8—521no—
207D4—521no—
208D4—521no—
209D4—1042no—
210D4—1041no—
211D4—1041no—
212C2×C4—24no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—48no—
218C2×C4—44no—
219C2×C4—521no—
220C2×C4—1041no—
221C2×C4—1041no—
222C2×C4C2×#610411yescharacteristic
223C2×C4#8818611yescharacteristic
224C2×C4C2×#610611yescharacteristic
225C2×C4#8819611yescharacteristic
226C2×C4#8820012yes—
227C2×C4#8820011yescharacteristic
228C2×C4#8820112yes—
229C2×C4#8820111yescharacteristic
230C8—1042no—
231C8—1041no—
232C22—22no—
233C22—1041no—
234C22—1042no—
235C22#1171887811yescharacteristic
236C22#1171888811yescharacteristic
237C22#1171889211yescharacteristic
238C4—24no—
239C4—22no—
240C4—22no—
241C4—42no—
242C4—84no—
243C4—1041no—
244C4#1171874511yescharacteristic
245C4#1171874811yescharacteristic
246C4#1171874911yescharacteristic
247C4#1171875011yescharacteristic
248C2—21no—
249C2—21no—
250C2—2081no—
251C2#1311596911yescharacteristic
252C2#1311600512yes—
subgroupG/H
centerC22#11718892
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2862C2
socleC22×C13#393
prime radical#11719182C22
hypercenter#2862D13
hypocenterC13#10362
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2862

Complements

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

NH ≅ G/Ntype
3. #13112694C2semidirect
4. #13112669C2semidirect
5. C13×#2862C2semidirect
30. #88128Q8semidirect
32. #88123Q8semidirect
76. #2862D13semidirect
201. C13#10362semidirect

Maximal subgroups

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

subgroupindex
#131156642
#131133952
#131126942
#131126692
C13×#28622
#1036213