Finite Group Databasebeta

← #15772116

Subgroups — #15772116

Order 3328.

386 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C2×#11718494C211yesmaximal, characteristic
2#13116632C212yesmaximal, complemented
3#13112776C211yesmaximal, characteristic, complemented
4#13112759C212yesmaximal
5C13×#1322C211yesmaximal, characteristic, complemented
6C2×C42×D13C411yescharacteristic
7C2×C13×C4⋊C8C2211yescharacteristic
8C2×#88060C411yescharacteristic
9C2×#88060C2211yescharacteristic
10C2×C8×Dic13C411yescharacteristic
11C2×C8×Dic13C2211yescharacteristic
12C2×C4⋊#1055C411yescharacteristic
13#11718494—22no—
14#11718494—22no—
15C13×C22⋊C16C2212yes—
16C22⋊#6090C2212yes—
17#11718093—22no—
18C16×Dic13—22no—
19C22×C4×D13C811yescharacteristic
20C22×C4×D13C811yescharacteristic
21C22×C4×D13C2×C411yescharacteristic
22C22×C8×C13C2×C411yescharacteristic
23C22×C8×C13C2311yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25C2×C4×Dic13C811yescharacteristic
26C2×C4×Dic13C811yescharacteristic
27C2×C4×Dic13C2×C411yescharacteristic
28C22×#1055C2×C411yescharacteristic
29C22×#1055C2×C411yescharacteristic
30C42×D13—21no—
31C42×D13—21no—
32C42×D13—21no—
33C42×D13—21no—
34C2×C13×C16—22no—
35C13×C4⋊C8—22no—
36#88060—22no—
37#88060—22no—
38C8×Dic13—21no—
39C8×Dic13—21no—
40C8×Dic13D412yes—
41C8×Dic13D412yes—
42C2×#6090—22no—
43C4⋊#1055—22no—
44#11459—131nomaximal, Sylow
45C23×D13C2×C811yescharacteristic
46C22×C4×C13C2×C811yescharacteristic
47C22×C4×C13C2×C811yescharacteristic
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13C2×C811yescharacteristic
50C22×Dic13C2×C811yescharacteristic
51C22×Dic13C2×C811yescharacteristic
52C2×C4×D13—21no—
53C2×C4×D13—21no—
54C2×C4×D13—22no—
55C2×C4×D13—21no—
56C2×C4×D13—21no—
57C2×C4×D13—21no—
58C2×C4×D13—21no—
59C2×C4×D13—42no—
60C2×C4×D13—41no—
61C2×C4×D13—41no—
62C2×C4×D13C1614yescomplemented
63C2×C8×C13—21no—
64C2×C8×C13—41no—
65C2×C8×C13—41no—
66C2×C8×C13C2×D412yes—
67C42×C13—21no—
68C42×C13—21no—
69C4×Dic13—21no—
70C4×Dic13—21no—
71C4×Dic13—21no—
72C4×Dic13—21no—
73C4×Dic13C22⋊C411yescharacteristic
74C4×Dic13C22⋊C411yescharacteristic
75C4×Dic13M1611yescharacteristic
76C4×Dic13M1611yescharacteristic
77C2×#1055—21no—
78C2×#1055—41no—
79C2×#1055—41no—
80C2×#1055C22⋊C412yes—
81C13×C16—42no—
82#6090—42no—
83C2×#431—131no—
84#2162—132no—
85#1322—131no—
86#1322D1311yescharacteristic, complemented
87#1314—132no—
88C23×C13C22×C811yescharacteristic
89C22×D13—21no—
90C22×D13—21no—
91C22×D13—41no—
92C22×D13—41no—
93C22×D13C2×C1612yes—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—41no—
100C2×C4×C13C2×C1612yes—
101C2×C4×C13C2×C22⋊C411yescharacteristic
102C2×C4×C13C2×M1611yescharacteristic
103C2×Dic13—22no—
104C2×Dic13—21no—
105C2×Dic13—41no—
106C2×Dic13C22⋊C811yescharacteristic
107C2×Dic13C22⋊C811yescharacteristic
108C2×Dic13C22⋊C811yescharacteristic
109C2×Dic13C22⋊C811yescharacteristic
110C2×Dic13C2×C1612yes—
111C2×Dic13M3212yes—
112C4×D13—24no—
113C4×D13—24no—
114C4×D13—42no—
115C4×D13—42no—
116C4×D13—41no—
117C4×D13—41no—
118C4×D13—42no—
119C8×C13—22no—
120C8×C13—41no—
121#1055—22no—
122#1055—41no—
123C22×C42—131no—
124#431—262no—
125#431—262no—
126C2×C4⋊C8—131no—
127C2×C4⋊C8C2×D1311yescharacteristic
128C2×C22⋊C8—131no—
129C2×C22⋊C8—131no—
130C2×C4×C8—131no—
131C2×C4×C8—131no—
132C4⋊C16—262no—
133C22⋊C16—132no—
134C22⋊C16C2×D1312yes—
135C4×C16—262no—
136C22×C13—21no—
137C22×C13—21no—
138C22×C13C2×C22⋊C811yescharacteristic
139C22×C13C22×C1611yescharacteristic
140C22×C13C2×M3211yescharacteristic
141C2×D13—22no—
142C2×D13—42no—
143C2×D13—41no—
144C2×D13—41no—
145C2×D13—42no—
146C4×C13—22no—
147C4×C13—21no—
148C4×C13—41no—
149C4×C13#41011yescharacteristic
150C4×C13#41311yescharacteristic
151Dic13—21no—
152Dic13—41no—
153Dic13C22⋊C1612yes—
154Dic13C22⋊C1612yes—
155Dic13#34912yes—
156C23×C4—131no—
157C23×C4—131no—
158C23×C4—131no—
159C22×C8—131no—
160C22×C8—131no—
161C22×C8C4×D1311yescharacteristic
162C22×C8C22×D1311yescharacteristic
163C2×C42—131no—
164C2×C42—131no—
165C2×C42—131no—
166C2×C42—261no—
167C2×C42—261no—
168C2×C42—261no—
169C2×C42—261no—
170C2×C42C4×D1311yescharacteristic
171C2×C16—22no—
172C2×C16—262no—
173C4⋊C8—22no—
174C4⋊C8—262no—
175C22⋊C8—262no—
176C22⋊C8—262no—
177C4×C8—132no—
178C4×C8—132no—
179C4×C8—261no—
180C4×C8—261no—
181C2×C13—21no—
182C2×C13—21no—
183C2×C13#145811yescharacteristic
184C2×C13C2×C22⋊C1611yescharacteristic
185C2×C13C2×#34911yescharacteristic
186D13—42no—
187C24—131no—
188C22×C4—131no—
189C22×C4—131no—
190C22×C4—134no—
191C22×C4—131no—
192C22×C4—261no—
193C22×C4—261no—
194C22×C4—262no—
195C22×C4—261no—
196C22×C4—261no—
197C22×C4—261no—
198C22×C4—261no—
199C22×C4—521no—
200C22×C4—521no—
201C22×C4—522no—
202C22×C4C8×D1311yescharacteristic
203C22×C4C8×D1311yescharacteristic
204C22×C4C2×C4×D1311yescharacteristic
205C2×C8—21no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—132no—
209C2×C8—261no—
210C2×C8—521no—
211C2×C8—521no—
212C2×C8D4×D1312yes—
213C42—21no—
214C42—21no—
215C42—131no—
216C42—131no—
217C42—131no—
218C42—131no—
219C42—261no—
220C42—261no—
221C42—261no—
222C42—261no—
223C16—42no—
224C16—522no—
225C13#1145911yescharacteristic, complemented, Sylow
226C23—132no—
227C23—261no—
228C23—261no—
229C23—521no—
230C23—521no—
231C23C2×C8×D1311yescharacteristic
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—132no—
239C2×C4—132no—
240C2×C4—131no—
241C2×C4—131no—
242C2×C4—131no—
243C2×C4—131no—
244C2×C4—264no—
245C2×C4—264no—
246C2×C4—262no—
247C2×C4—261no—
248C2×C4—522no—
249C2×C4—522no—
250C2×C4—522no—
251C2×C4—521no—
252C2×C4—521no—
253C2×C4—521no—
254C2×C4C16×D1312yes—
255C2×C4C22⋊C4×D1311yescharacteristic
256C2×C4M16×D1311yescharacteristic
257C8—22no—
258C8—41no—
259C8—262no—
260C8—521no—
261C22—21no—
262C22—21no—
263C22—262no—
264C22—522no—
265C22—522no—
266C22—521no—
267C22—521no—
268C22D13×C22⋊C811yescharacteristic
269C22C2×C16×D1311yescharacteristic
270C22D13×M3211yescharacteristic
271C4—22no—
272C4—21no—
273C4—41no—
274C4—132no—
275C4—132no—
276C4—132no—
277C4—261no—
278C4—521no—
279C4#1171840111yescharacteristic
280C4#1171841211yescharacteristic
281C2—21no—
282C2—21no—
283C2—522no—
284C2#1311314911yescharacteristic
285C2D13×C22⋊C1611yescharacteristic
286C2D13×#34911yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC22×C13C22×C16
FrattiniC22×C8C22×D13
FittingC13×#1322C2
socleC22×C13C2×C22⋊C8
prime radicalC23×D13C2×C8
cosocleC22×C8×C13C23
hypercenter#1322D13
hypocenterC13#11459
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1322

Complements

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

NH ≅ G/Ntype
2. #13116632C2semidirect
3. #13112776C2semidirect
5. C13×#1322C2semidirect
62. C2×C4×D13C16semidirect
86. #1322D13semidirect
225. C13#11459semidirect

Maximal subgroups

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

subgroupindex
C2×#117184942
#131166322
#131127762
#131127592
C13×#13222
#1145913