Finite Group Databasebeta

← #15772221

Subgroups — #15772221

Order 3328.

382 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 115 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#13116457C212yesmaximal, complemented
2#13112789C212yesmaximal, complemented
3#13112772C212yesmaximal, complemented
4C13×#2929C211yesmaximal, characteristic
5C2×C13×#131C2211yescharacteristic
6C23×C8×C13C411yescharacteristic
7C13×#525C411yescharacteristic
8C13×#435—22no—
9C8×D4×C13—22no—
10C13×#424C2211yescharacteristic
11C13×#408C411yescharacteristic
12C13×#407C2211yescharacteristic
13C13×#405C411yescharacteristic
14C2×#88052—22no—
15#11718145—22no—
16#11718145C2214yes—
17C2×C13×#41C2×C411yescharacteristic
18C23×C4×C13C2×C411yescharacteristic
19C13×#131—41no—
20C13×#131—41no—
21C2×C13×M16C2×C411yescharacteristic
22C2×C13×M16D412yes—
23C2×C13×M16C2311yescharacteristic
24C22×C8×C13—21no—
25C22×C8×C13—21no—
26C22×C8×C13—41no—
27C22×C8×C13—41no—
28C22×C8×C13C2×C411yescharacteristic
29C22×C8×C13C2×C411yescharacteristic
30C22×C8×C13D412yes—
31C13×#123C812yes—
32C13×C22⋊Q8—21no—
33C13×#121—21no—
34C13×#120C812yes—
35C4×D4×C13—22no—
36C13×#117C2×C411yescharacteristic
37C13×C4⋊C8—22no—
38C13×C22⋊C8—22no—
39C13×C22⋊C8—22no—
40C13×#97—21no—
41C4×C8×C13—21no—
42#88052—24no—
43#88052—42no—
44C2×#6090—42no—
45#11483—131nomaximal, Sylow
46C24×C13C2×C811yescharacteristic
47C13×#41—41no—
48C13×#41—41no—
49C2×Q8×C13M1611yescharacteristic
50C2×D4×C13—22no—
51C2×D4×C13C2×C812yes—
52C2×D4×C13M1611yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—41no—
56C22×C4×C13—41no—
57C22×C4×C13C22⋊C412yes—
58C22×C4×C13C2×C811yescharacteristic
59C22×C4×C13C22×C411yescharacteristic
60C13×M16—42no—
61C13×M16—41no—
62C13×M16—41no—
63C2×C8×C13—21no—
64C2×C8×C13—21no—
65C2×C8×C13—22no—
66C2×C8×C13—22no—
67C2×C8×C13—21no—
68C2×C8×C13—21no—
69C2×C8×C13—42no—
70C2×C8×C13—41no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C2×C8×C13C22⋊C411yescharacteristic
74C2×C8×C13C22⋊C411yescharacteristic
75C2×C8×C13C2×D412yes—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—21no—
78C13×C22⋊C4—22no—
79C13×C22⋊C4—22no—
80C13×C22⋊C4C2×C812yes—
81C42×C13—21no—
82#6090—44no—
83#2929D1311yescharacteristic
84#2115—132no—
85#1328—132no—
86#1320—132no—
87C23×C13—21no—
88C23×C13—41no—
89C23×C13—42no—
90C23×C13C22⋊C812yes—
91C23×C13C22×C811yescharacteristic
92Q8×C13—41no—
93D4×C13—42no—
94D4×C13—41no—
95D4×C13—44no—
96C2×C4×C13—21no—
97C2×C4×C13—22no—
98C2×C4×C13—21no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—21no—
102C2×C4×C13—42no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13C22⋊C812yes—
107C2×C4×C13C2×C22⋊C411yescharacteristic
108C2×C4×C13C2×M1611yescharacteristic
109C8×C13—22no—
110C8×C13—21no—
111C8×C13—41no—
112C8×C13—41no—
113C8×C13#9911yescharacteristic
114C8×C13#9911yescharacteristic
115C2×#131C2×D1311yescharacteristic
116C23×C8Dic1311yescharacteristic
117#525Dic1311yescharacteristic
118C2×M32—262no—
119#435—22no—
120C8×D4—22no—
121#424C2×D1311yescharacteristic
122#408Dic1311yescharacteristic
123#407C2×D1311yescharacteristic
124#405Dic1311yescharacteristic
125#349—134no—
126#349—262no—
127C22×C13—22no—
128C22×C13—21no—
129C22×C13—22no—
130C22×C13—42no—
131C22×C13—41no—
132C22×C13—41no—
133C22×C13—42no—
134C22×C13—42no—
135C22×C13—41no—
136C22×C13C2×C22⋊C811yescharacteristic
137C4×C13—21no—
138C4×C13—22no—
139C4×C13—42no—
140C4×C13—41no—
141C4×C13C2×#9911yescharacteristic
142C4×C13#41311yescharacteristic
143C2×#41C2×Dic1311yescharacteristic
144C23×C4C2×Dic1311yescharacteristic
145#131—41no—
146#131—41no—
147C2×M16C2×Dic1311yescharacteristic
148C2×M16C22⋊D1312yes—
149C2×M16C22×D1311yescharacteristic
150C22×C8—21no—
151C22×C8—21no—
152C22×C8—41no—
153C22×C8—41no—
154C22×C8C2×Dic1311yescharacteristic
155C22×C8C2×Dic1311yescharacteristic
156C22×C8C22⋊D1312yes—
157#123#105512yes—
158C22⋊Q8—21no—
159#121—21no—
160#120#105512yes—
161C4×D4—22no—
162#117C2×Dic1311yescharacteristic
163M32—264no—
164M32—522no—
165C2×C16—522no—
166C4⋊C8—22no—
167C22⋊C8—22no—
168C22⋊C8—22no—
169#97—21no—
170C4×C8—21no—
171C2×C13—21no—
172C2×C13—42no—
173C2×C13—42no—
174C2×C13—41no—
175C2×C13#145911yescharacteristic
176C24C2×#105511yescharacteristic
177#41—41no—
178#41—41no—
179C2×Q8#609911yescharacteristic
180C2×D4—22no—
181C2×D4C2×#105512yes—
182C2×D4#609911yescharacteristic
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4C2×#105511yescharacteristic
188C22×C4C22⋊Dic1312yes—
189C22×C4C22×Dic1311yescharacteristic
190M16—42no—
191M16—41no—
192M16—41no—
193C2×C8—22no—
194C2×C8—21no—
195C2×C8—22no—
196C2×C8—21no—
197C2×C8—21no—
198C2×C8—21no—
199C2×C8—42no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—41no—
203C2×C8C22⋊Dic1311yescharacteristic
204C2×C8C22⋊Dic1311yescharacteristic
205C2×C8C2×C22⋊D1312yes—
206C4⋊C4—22no—
207C4⋊C4—21no—
208C22⋊C4—22no—
209C22⋊C4—22no—
210C22⋊C4C2×#105512yes—
211C42—21no—
212C16—524no—
213C13#1148311yescharacteristic, complemented, Sylow
214C23—21no—
215C23—41no—
216C23—42no—
217C23C22⋊#105512yes—
218C23C22×#105511yescharacteristic
219Q8—41no—
220D4—42no—
221D4—41no—
222D4—44no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—42no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4C22⋊#105512yes—
234C2×C4C2×#609911yescharacteristic
235C2×C4C2×C22⋊Dic1311yescharacteristic
236C8—22no—
237C8—21no—
238C8—41no—
239C8—41no—
240C8#8807411yescharacteristic
241C8#8807411yescharacteristic
242C22—22no—
243C22—21no—
244C22—22no—
245C22—42no—
246C22—41no—
247C22—41no—
248C22—42no—
249C22—42no—
250C22—41no—
251C22C2×C22⋊#105511yescharacteristic
252C4—21no—
253C4—22no—
254C4—42no—
255C4—41no—
256C4C2×#8807411yescharacteristic
257C4#1171889811yescharacteristic
258C2—21no—
259C2—42no—
260C2—41no—
261C2—42no—
262C2#1311315411yescharacteristic
subgroupG/H
centerC8#88074
commutatorC23×C13C22×C8
FrattiniC2×M16C22×D13
FittingC13×#2929C2
socleC2×C13#1459
prime radicalC13×#525C4
cosocleC2×C13×M16C23
hypercenter#2929D13
hypocenterC13#11483
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C2×C8 ◁ C2×#131 ◁ #2929

Complements

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

NH ≅ G/Ntype
1. #13116457C2semidirect
2. #13112789C2semidirect
3. #13112772C2semidirect
213. C13#11483semidirect

Maximal subgroups

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

subgroupindex
#131164572
#131127892
#131127722
C13×#29292
#1148313