Finite Group Databasebeta

← #15756485

Subgroups — #15756485

Order 3328.

498 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 131 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#13114828C211yesmaximal, characteristic
2#13113157C211yesmaximal, characteristic
3#13112739C212yesmaximal, complemented
4#13112694C212yesmaximal, complemented
5C13×#2349C211yesmaximal, characteristic
6C2×C4×D4×C13—21no—
7C2×C4×D4×C13C2211yescharacteristic
8C13×#389—21no—
9C13×#385—22no—
10C13×#382C2211yescharacteristic
11C13×#380C412yes—
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×C13×#95C412yes—
14C2×#88073—21no—
15#11718586C2212yes—
16#11718585C2212yes—
17#11718122—21no—
18#11718117—22no—
19C22×D4×C13D411yescharacteristic
20C23×C4×C13—22no—
21C23×C4×C13C2×C412yes—
22C4×D4×C13—22no—
23C4×D4×C13—22no—
24C4×D4×C13—42no—
25C4×D4×C13—42no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4D412yes—
32C2×C42×C13—21no—
33C2×C42×C13C2311yescharacteristic
34C2×#6099—22no—
35C13×#95—22no—
36C13×#95—21no—
37C13×#95C2×C411yescharacteristic
38C13×#95C2×C411yescharacteristic
39C13×#95C2×C412yes—
40#88073—42no—
41C22⋊#1055—22no—
42C4⋊#1055—22no—
43C4⋊#1055—22no—
44C4⋊#1055—22no—
45C4×#1055—22no—
46#8764—131nomaximal, Sylow
47C24×C13C22⋊C412yes—
48C2×D4×C13—22no—
49C2×D4×C13—22no—
50C2×D4×C13D812yes—
51C2×D4×C13SD1612yes—
52C22×C4×C13—21no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—21no—
57C22×C4×C13—44no—
58C22×C4×C13—44no—
59C22×C4×C13—82no—
60C22×C4×C13—82no—
61C22×C4×C13C22⋊C412yes—
62C22×C4×C13C22×C411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C13×C4⋊C4—22no—
66C13×C4⋊C4—42no—
67C13×C4⋊C4—41no—
68C13×C4⋊C4—41no—
69C13×C4⋊C4—82no—
70C13×C22⋊C4—24no—
71C13×C22⋊C4—44no—
72C42×C13—41no—
73C42×C13—41no—
74C42×C13#4112yes—
75C42×C13#4112yes—
76#6099—42no—
77#6099—42no—
78C2×#1055—42no—
79C2×#1055—42no—
80#2349D1311yescharacteristic
81#1800—131no—
82#1460—131no—
83#1303—132no—
84#1286—132no—
85C23×C13—22no—
86C23×C13—22no—
87C23×C13—42no—
88C23×C13—42no—
89C23×C13#10214yes—
90C23×C13C2×C22⋊C411yescharacteristic
91D4×C13—24no—
92D4×C13—24no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—42no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—41no—
105C2×C4×C13—42no—
106C2×C4×C13—82no—
107C2×C4×C13—82no—
108C2×C4×C13—88no—
109C2×C4×C13#11711yescharacteristic
110C2×C4×C13#11711yescharacteristic
111C2×C4×C13#12312yes—
112C2×C4×C13#12312yes—
113C2×C4×C13C2×D811yescharacteristic
114C2×C4×C13C2×SD1611yescharacteristic
115C2×C4×C13#13712yes—
116#1055—82no—
117#1055—82no—
118C2×C4×D4—21no—
119C2×C4×D4C2×D1311yescharacteristic
120#431—132no—
121#423—132no—
122C2×#100—261no—
123#389—21no—
124#385—22no—
125#382C2×D1311yescharacteristic
126#380Dic1312yes—
127C4×C4⋊C4C2×D1311yescharacteristic
128C2×#95Dic1312yes—
129#343—261no—
130#323—262no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13—24no—
134C22×C13—44no—
135C22×C13—44no—
136C22×C13—42no—
137C22×C13—42no—
138C22×C13#38111yescharacteristic
139C22×C13C2×#10211yescharacteristic
140C22×C13#41911yescharacteristic
141C4×C13—22no—
142C4×C13—21no—
143C4×C13—21no—
144C4×C13—42no—
145C4×C13—42no—
146C4×C13—81no—
147C4×C13—82no—
148C4×C13#48012yes—
149C4×C13#48312yes—
150C22×D4C22⋊D1311yescharacteristic
151C23×C4—22no—
152C23×C4C2×Dic1312yes—
153C2×M16—262no—
154C4×D4—22no—
155C4×D4—22no—
156C4×D4—42no—
157C4×D4—42no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4C22⋊D1311yescharacteristic
162C2×C22⋊C4—22no—
163C2×C22⋊C4C22⋊D1312yes—
164C2×C42—21no—
165C2×C42C22×D1311yescharacteristic
166C4⋊C8—262no—
167C4⋊C8—262no—
168C4⋊C8—262no—
169#100—522no—
170C22⋊C8—262no—
171C4×C8—262no—
172#95—22no—
173#95—21no—
174#95C2×Dic1311yescharacteristic
175#95C2×Dic1312yes—
176#95C2×Dic1311yescharacteristic
177C2×C13—21no—
178C2×C13—21no—
179C2×C13—44no—
180C2×C13#182311yescharacteristic
181C2×C13#182711yescharacteristic
182C2×C13#182911yescharacteristic
183C24C22⋊Dic1312yes—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4#610412yes—
187C2×D4#610512yes—
188C22×C4—21no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—21no—
193C22×C4—44no—
194C22×C4—44no—
195C22×C4—82no—
196C22×C4—82no—
197C22×C4C22⋊Dic1312yes—
198C22×C4C22×Dic1311yescharacteristic
199C22×C4C2×C22⋊D1311yescharacteristic
200C22×C4C2×C22⋊D1311yescharacteristic
201M16—522no—
202M16—522no—
203C2×C8—522no—
204C2×C8—522no—
205C4⋊C4—22no—
206C4⋊C4—42no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—82no—
210C22⋊C4—24no—
211C22⋊C4—44no—
212C42—41no—
213C42—41no—
214C42#612712yes—
215C42#612712yes—
216C13#876411yescharacteristic, complemented, Sylow
217C23—22no—
218C23—22no—
219C23—42no—
220C23—42no—
221C23#8807214yes—
222C23C2×C22⋊Dic1311yescharacteristic
223D4—24no—
224D4—24no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4—88no—
241C2×C4#8818011yescharacteristic
242C2×C4#8818011yescharacteristic
243C2×C4#8818312yes—
244C2×C4#8818312yes—
245C2×C4C2×#610411yescharacteristic
246C2×C4C2×#610511yescharacteristic
247C2×C4#8819612yes—
248C8—1042no—
249C8—1042no—
250C22—21no—
251C22—21no—
252C22—24no—
253C22—44no—
254C22—44no—
255C22—42no—
256C22—42no—
257C22#1171887211yescharacteristic
258C22C2×#8807211yescharacteristic
259C22#1171888611yescharacteristic
260C4—22no—
261C4—21no—
262C4—21no—
263C4—42no—
264C4—42no—
265C4—81no—
266C4—82no—
267C4#1171862812yes—
268C4#1171863212yes—
269C2—21no—
270C2—21no—
271C2—44no—
272C2#1311492211yescharacteristic
273C2#1311494011yescharacteristic
274C2#1311494711yescharacteristic
subgroupG/H
centerC22#11718872
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2349C2
socleC22×C13#381
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenter#2349D13
hypocenterC13#8764
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2349

Complements

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

NH ≅ G/Ntype
3. #13112739C2semidirect
4. #13112694C2semidirect
216. C13#8764semidirect

Maximal subgroups

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

subgroupindex
#131148282
#131131572
#131127392
#131126942
C13×#23492
#876413