Finite Group Databasebeta

← #16788234

Subgroups — #16788234

Order 3328.

378 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 88 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#13131195C211yesmaximal, characteristic, complemented
2#13130757C211yesmaximal, characteristic, complemented
3#13129823C214yesmaximal, complemented
4#13125416C211yesmaximal, characteristic
5#11719430—21no—
6#11719059—21no—
7C13×#500C411yescharacteristic, complemented
8#11718749—21no—
9#11718544—21no—
10#11718544C2212yes—
11#11718533—21no—
12#11718533C412yescomplemented
13#11718356C411yescharacteristic, complemented
14C4×C8×D13C2211yescharacteristic
15#11718265—21no—
16#11718265C2212yes—
17#11718260—21no—
18#11718259C2212yes—
19C4×#6092—21no—
20C2×#6131—41no—
21C2×C4⋊#261—22no—
22C2×C4⋊#261—41no—
23C2×C4⋊#261—41no—
24C13×C4⋊Q8—21no—
25#88201—41no—
26C2×D104—21no—
27C2×D104C2×C412yes—
28C2×C8×D13D411yescharacteristic
29C2×C8×D13C2311yescharacteristic
30#88149—22no—
31#88149—41no—
32#88147—22no—
33#88147—41no—
34#88128—21no—
35C42×D13D411yescharacteristic
36C2×#6092—22no—
37C13×#107—21no—
38C13×#107C2×C412yes—
39C4×C8×C13C2×C411yescharacteristic
40C8×Dic13C2×C411yescharacteristic
41C8×Dic13D411yescharacteristic
42#88049—22no—
43#88049—22no—
44C4×#1055D411yescharacteristic
45#11856—131nomaximal, Sylow
46C22×#261—42no—
47C2×Q8×C13—41no—
48#6131—82no—
49#6131—82no—
50C2×D52—22no—
51C2×D52—42no—
52C2×D52—41no—
53C2×D52—41no—
54C2×C4×D13—42no—
55C2×C4×D13D811yescharacteristic
56C2×C4×D13D811yescharacteristic
57C2×C4×D13C2×D411yescharacteristic
58C4⋊#261—42no—
59C4⋊#261—42no—
60C4⋊#261—82no—
61C4⋊#261—82no—
62C2×C8×C13C22⋊C411yescharacteristic
63C2×C8×C13C22×C411yescharacteristic
64C13×C4⋊C4—22no—
65C13×C4⋊C4—41no—
66C42×C13C22⋊C411yescharacteristic
67#6103—42no—
68#6103—42no—
69C4×Dic13C22⋊C411yescharacteristic
70C4×Dic13SD1611yescharacteristic
71C4×Dic13SD1611yescharacteristic
72C2×#1055C22⋊C411yescharacteristic
73C2×#1055C2×D411yescharacteristic
74D104—42no—
75D104—42no—
76C8×D13—41no—
77C8×D13—41no—
78#6092—42no—
79#3169—131no—
80#2162—131no—
81#1834—131no—
82#1347—134no—
83C22×D13—42no—
84C22×D13C2×D811yescharacteristic
85C2×#261—82no—
86C2×#261—82no—
87C2×#261—82no—
88Q8×C13—82no—
89C2×C4×C13—42no—
90C2×C4×C13#10211yescharacteristic
91C2×C4×C13#10211yescharacteristic
92C2×C4×C13C2×C22⋊C411yescharacteristic
93C2×Dic13#10211yescharacteristic
94C2×Dic13#10211yescharacteristic
95C2×Dic13C2×SD1611yescharacteristic
96D52—42no—
97D52—42no—
98D52—82no—
99D52—82no—
100D52—82no—
101D52—82no—
102C4×D13—22no—
103C4×D13—21no—
104C4×D13—21no—
105C4×D13—84no—
106C4×D13D1612yes—
107C4×D13SD3212yes—
108C8×C13—21no—
109C8×C13—21no—
110#1055—21no—
111#1055—21no—
112#532—261no—
113#500#26111yescharacteristic, complemented
114#493—131no—
115#486—261no—
116#466—132no—
117#466—261no—
118C4×D8—132no—
119C4×D8—261no—
120C2×C4×C8—131no—
121#384—261no—
122C4⋊C16—261no—
123C22⋊C16—132no—
124C4×C16—261no—
125#340—132no—
126#340—261no—
127C22×C13C2×#10211yescharacteristic
128C2×D13—21no—
129C2×D13—21no—
130C2×D13—82no—
131C2×D13—82no—
132C2×D13—82no—
133C2×D13C2×D1611yescharacteristic
134C2×D13C2×SD3211yescharacteristic
135#261—162no—
136C4×C13—82no—
137C4×C13#35712yes—
138C4×C13#36012yes—
139C4×C13#41011yescharacteristic
140C4×C13#42111yescharacteristic
141Dic13—21no—
142Dic13—21no—
143Dic13#35712yes—
144C2×#41—521no—
145C2×D8—132no—
146C2×D8—261no—
147C22×C8—131no—
148C22×C8—131no—
149C4⋊Q8—21no—
150#127—261no—
151#124—521no—
152#121—262no—
153#121—521no—
154C4×D4—262no—
155C4×D4—521no—
156C2×C4⋊C4—262no—
157C2×C4⋊C4—521no—
158C2×C4⋊C4—521no—
159C2×C42—131no—
160C2×C16—262no—
161#107—21no—
162#107C2×#26112yes—
163#102—262no—
164#102—262no—
165C4×C8—131no—
166C4×C8—131no—
167C4×C8—131no—
168C4×C8C2×#26111yescharacteristic
169C2×C13#151711yescharacteristic
170C2×C13C2×#35711yescharacteristic
171C2×C13C2×#36011yescharacteristic
172D13—21no—
173D13—21no—
174D13—162no—
175#41—1042no—
176#41—1042no—
177C2×Q8—41no—
178C2×D4—262no—
179C2×D4—522no—
180C2×D4—521no—
181C2×D4—521no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—131no—
185C22×C4—522no—
186C22×C4—522no—
187D8—522no—
188D8—522no—
189C2×C8—131no—
190C2×C8—131no—
191C2×C8—521no—
192C2×C8—521no—
193C2×C8C22⋊#26111yescharacteristic
194C2×C8C22×#26111yescharacteristic
195C4⋊C4—22no—
196C4⋊C4—41no—
197C4⋊C4—522no—
198C4⋊C4—522no—
199C4⋊C4—1042no—
200C4⋊C4—1042no—
201C22⋊C4—522no—
202C22⋊C4—522no—
203C42—131no—
204C42—131no—
205C42—131no—
206C42C22⋊#26111yescharacteristic
207C16—522no—
208C13#1185611yescharacteristic, complemented, Sylow
209C23—131no—
210C23—522no—
211Q8—82no—
212D4—522no—
213D4—522no—
214D4—1042no—
215D4—1042no—
216D4—1042no—
217D4—1042no—
218C2×C4—42no—
219C2×C4—131no—
220C2×C4—132no—
221C2×C4—132no—
222C2×C4—131no—
223C2×C4—131no—
224C2×C4—262no—
225C2×C4—261no—
226C2×C4—261no—
227C2×C4—1044no—
228C2×C4—1042no—
229C2×C4—1042no—
230C2×C4—1042no—
231C2×C4#8811511yescharacteristic
232C2×C4#8811511yescharacteristic
233C2×C4C2×C22⋊#26111yescharacteristic
234C8—21no—
235C8—21no—
236C8—261no—
237C8—261no—
238C22—131no—
239C22—131no—
240C22—261no—
241C22—261no—
242C22—1042no—
243C22—1042no—
244C22—1042no—
245C22C2×#8811511yescharacteristic
246C4—82no—
247C4—132no—
248C4—261no—
249C4—261no—
250C4—2082no—
251C4#1171827612yes—
252C4#1171827912yes—
253C4#1171915511yescharacteristic
254C4#1171915611yescharacteristic
255C2—261no—
256C2—261no—
257C2—2082no—
258C2#1313026711yescharacteristic
259C2C2×#1171827611yescharacteristic
260C2C2×#1171827911yescharacteristic
subgroupG/H
centerC22C2×#88115
commutatorC2×C8×C13C22×C4
FrattiniC2×C8C22×#261
FittingC13×#500C4
socleC22×C13C2×#102
prime radical#13125416C2
cosocleC2×C8×D13C23
hypercenter#500#261
hypocenterC13#11856
LCSG ▷ C2×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #500

Complements

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

NH ≅ G/Ntype
1. #13131195C2semidirect
2. #13130757C2semidirect
3. #13129823C2semidirect
7. C13×#500C4semidirect
12. #11718533C4semidirect
13. #11718356C4semidirect
113. #500#261semidirect
208. C13#11856semidirect

Maximal subgroups

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

subgroupindex
#131311952
#131307572
#131298232
#131254162
#1185613