Finite Group Databasebeta

← #16786941

Subgroups — #16786941

Order 3328.

364 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 86 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#13131072C212yesmaximal, complemented
2#13129783C212yesmaximal, complemented
3#13129771C212yesmaximal, complemented
4#13123551C211yesmaximal, characteristic
5#11719537C411yescharacteristic
6C2×#88202C2211yescharacteristic
7C2×#88161C411yescharacteristic
8C2×#88106—22no—
9C13×#408C411yescharacteristic
10#11718779C2211yescharacteristic
11#11718771C2211yescharacteristic
12C2×#88055C411yescharacteristic
13#11718391—22no—
14#11718389—22no—
15#11718284—22no—
16#11718284C2214yes—
17C2×C13×#41C2×C411yescharacteristic
18C2×#6127C2×C411yescharacteristic
19C2×C13×M16C2×C411yescharacteristic
20C22×C8×C13C2×C411yescharacteristic
21#88202—42no—
22#88201C811yescharacteristic
23#88198C811yescharacteristic
24#88194C811yescharacteristic
25#88193—22no—
26#88190C811yescharacteristic
27C4×C22⋊D13—22no—
28C2×C4×Dic13C2×C411yescharacteristic
29C2×#6099D412yes—
30C2×#6099C2311yescharacteristic
31C22×#1055C2×C411yescharacteristic
32C22×#1055D412yes—
33#88161—42no—
34C2×#6094—21no—
35C2×C8×D13—21no—
36#88106—24no—
37#88106—42no—
38C2×#6092—42no—
39C13×C22⋊C8—22no—
40#88060—22no—
41#88055—21no—
42#88055—21no—
43#88054—22no—
44#11486—131nomaximal, Sylow
45C13×#41—41no—
46C13×#41—41no—
47C2×Q8×C13C2×C811yescharacteristic
48C2×D4×C13C2×C811yescharacteristic
49C2×D4×C13M1612yes—
50C22×C4×C13C22⋊C412yes—
51C22×C4×C13C22×C411yescharacteristic
52C2×C22⋊D13—21no—
53C2×C22⋊D13—22no—
54C22×Dic13—21no—
55#6127—41no—
56#6127—41no—
57C2×D52C2×C811yescharacteristic
58C2×C4×D13—21no—
59C2×Dic26C2×C811yescharacteristic
60C13×M16—41no—
61C2×C8×C13—21no—
62C2×C8×C13—21no—
63C2×C8×C13—41no—
64C22⋊Dic13—22no—
65#6103—22no—
66#6101—22no—
67C4×Dic13—21no—
68C4×Dic13C2×C811yescharacteristic
69C4×Dic13C2×C811yescharacteristic
70#6099—42no—
71#6099—41no—
72C2×#1055—22no—
73C2×#1055—22no—
74C2×#1055—22no—
75C2×#1055C22⋊C411yescharacteristic
76C2×#1055C22⋊C411yescharacteristic
77C2×#1055C2×D412yes—
78#6094—42no—
79C8×D13—42no—
80#6092—44no—
81#2932—131no—
82#2115—132no—
83#1327—132no—
84#1321—132no—
85C23×C13C22⋊C812yes—
86C23×C13C2×M1611yescharacteristic
87C22×D13—21no—
88Q8×C13—41no—
89D4×C13—41no—
90D4×C13—42no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13C22⋊C812yes—
96C2×C4×C13C2×C22⋊C411yescharacteristic
97C2×C4×C13C22×C811yescharacteristic
98C22⋊D13—42no—
99C22⋊D13—82no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—81no—
104D52—41no—
105C4×D13—41no—
106C4×D13—41no—
107Dic26—41no—
108C8×C13—41no—
109C8×C13—41no—
110#1055—22no—
111#1055—21no—
112#1055#9912yes—
113C2×#131—131no—
114C2×#131—131no—
115#532—131no—
116C2×M32—262no—
117#435—262no—
118#435—262no—
119#423—131no—
120#408—131no—
121#408#26111yescharacteristic
122C2×#97—131no—
123#349—134no—
124#349—262no—
125C22×C13—21no—
126C22×C13—22no—
127C22×C13—41no—
128C22×C13—42no—
129C22×C13C2×C22⋊C811yescharacteristic
130C2×D13—42no—
131C2×D13—41no—
132C4×C13—21no—
133C4×C13—22no—
134C4×C13C2×#9911yescharacteristic
135C4×C13#41311yescharacteristic
136Dic13—41no—
137Dic13—41no—
138Dic13—41no—
139C2×#41—131no—
140C2×#41C2×#26111yescharacteristic
141#131—522no—
142#131—522no—
143C2×M16—132no—
144C2×M16—131no—
145C2×M16—261no—
146C2×M16C2×#26111yescharacteristic
147C22×C8—132no—
148C22×C8—131no—
149C22×C8—261no—
150C22×C8C2×#26111yescharacteristic
151C4⋊Q8—131no—
152#127—131no—
153#124—131no—
154#124—131no—
155#121—262no—
156C4×D4—262no—
157C2×C42—131no—
158M32—264no—
159M32—522no—
160C2×C16—522no—
161C4⋊C8—262no—
162C22⋊C8—22no—
163C22⋊C8—262no—
164#97—261no—
165#97—261no—
166C2×C13—21no—
167C2×C13—41no—
168C2×C13—42no—
169C2×C13#145911yescharacteristic
170D13—81no—
171#41—41no—
172#41—41no—
173#41—521no—
174#41—521no—
175C2×Q8—131no—
176C2×Q8D13⋊C811yescharacteristic
177C2×D4—131no—
178C2×D4—261no—
179C2×D4—262no—
180C2×D4D13⋊C811yescharacteristic
181C2×D4#611812yes—
182C22×C4—261no—
183C22×C4—261no—
184C22×C4C22⋊#26112yes—
185C22×C4C22×#26111yescharacteristic
186M16—41no—
187M16—522no—
188M16—521no—
189M16—522no—
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—41no—
193C2×C8—131no—
194C2×C8—131no—
195C2×C8—132no—
196C2×C8—262no—
197C2×C8—262no—
198C2×C8—262no—
199C2×C8—522no—
200C4⋊C4—262no—
201C22⋊C4—262no—
202C22⋊C4—262no—
203C42—131no—
204C42—131no—
205C42—261no—
206C16—524no—
207C13#1148611yescharacteristic, complemented, Sylow
208C23—261no—
209C23#8811112yes—
210C23C2×#611811yescharacteristic
211Q8—41no—
212Q8—521no—
213D4—41no—
214D4—42no—
215D4—521no—
216D4—522no—
217D4—1042no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—261no—
223C2×C4—261no—
224C2×C4—261no—
225C2×C4—521no—
226C2×C4—521no—
227C2×C4—1041no—
228C2×C4#8811112yes—
229C2×C4C2×D13⋊C811yescharacteristic
230C2×C4C2×C22⋊#26111yescharacteristic
231C8—41no—
232C8—41no—
233C8—132no—
234C8—262no—
235C8—261no—
236C22—21no—
237C22—22no—
238C22—41no—
239C22—42no—
240C22—522no—
241C22—521no—
242C22C2×#8811111yescharacteristic
243C4—22no—
244C4—21no—
245C4—521no—
246C4—521no—
247C4—521no—
248C4D13⋊#9911yescharacteristic
249C4#1171914811yescharacteristic
250C2—21no—
251C2—41no—
252C2—42no—
253C2—1041no—
254C2#1313007411yescharacteristic
subgroupG/H
centerC4D13⋊#99
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#408C4
socleC2×C13#1459
prime radical#11719537C4
cosocleC2×#6099C23
hypercenter#408#261
hypocenterC13#11486
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #13131072C2semidirect
2. #13129783C2semidirect
3. #13129771C2semidirect
207. C13#11486semidirect

Maximal subgroups

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

subgroupindex
#131310722
#131297832
#131297712
#131235512
#1148613