Finite Group Databasebeta

← #15772118

Subgroups — #15772118

Order 3328.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11718379C211yesmaximal, characteristic
2#13116636C212yesmaximal, complemented
3#13112775C212yesmaximal, complemented
4#13112760C211yesmaximal, characteristic
5C13×#1314C211yesmaximal, characteristic
6C22×C4×Dic13C411yescharacteristic
7C2×C13×C22⋊C8C2211yescharacteristic
8C2×C22⋊#1055C411yescharacteristic
9C2×#88054C411yescharacteristic
10C2×#88054C2211yescharacteristic
11C2×C8×Dic13C411yescharacteristic
12C2×C8×Dic13C2211yescharacteristic
13#11718379—22no—
14#11718379—22no—
15C13×C22⋊C16C2212yes—
16C22⋊#6090C2212yes—
17#11718094—22no—
18#11718093—22no—
19C23×C4×C13C2×C411yescharacteristic
20C23×Dic13C811yescharacteristic
21C23×Dic13C811yescharacteristic
22C22×C8×C13C2×C411yescharacteristic
23C22×C8×C13C2311yescharacteristic
24C2×C4×Dic13—21no—
25C2×C4×Dic13—21no—
26C2×C4×Dic13—21no—
27C2×C4×Dic13—21no—
28C2×C4×Dic13C811yescharacteristic
29C2×C4×Dic13C811yescharacteristic
30C2×C4×Dic13C2×C411yescharacteristic
31C2×C4×Dic13C2×C411yescharacteristic
32C22×#1055C2×C411yescharacteristic
33C22×#1055C2×C411yescharacteristic
34C2×C13×C16—22no—
35C13×C22⋊C8—22no—
36C22⋊#1055—22no—
37#88054—22no—
38#88054—22no—
39C8×Dic13—21no—
40C8×Dic13—21no—
41C8×Dic13D412yes—
42C8×Dic13D412yes—
43C2×#6090—22no—
44#11460—131nomaximal, Sylow
45C24×C13C2×C811yescharacteristic
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13—41no—
49C22×C4×C13—41no—
50C22×C4×C13C2×C811yescharacteristic
51C22×C4×C13C22×C411yescharacteristic
52C22×Dic13—22no—
53C22×Dic13—21no—
54C22×Dic13—21no—
55C22×Dic13—22no—
56C22×Dic13—21no—
57C22×Dic13—21no—
58C22×Dic13—42no—
59C22×Dic13C2×C811yescharacteristic
60C22×Dic13C2×C811yescharacteristic
61C22×Dic13C2×C811yescharacteristic
62C22×Dic13C2×C811yescharacteristic
63C2×C8×C13—21no—
64C2×C8×C13—41no—
65C2×C8×C13—41no—
66C2×C8×C13C2×D412yes—
67C4×Dic13—21no—
68C4×Dic13—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#2163—132no—
85#1322—132no—
86#1314—131no—
87#1314D1311yescharacteristic
88C23×C13—21no—
89C23×C13—21no—
90C23×C13—41no—
91C23×C13—41no—
92C23×C13M3212yes—
93C23×C13C22×C811yescharacteristic
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—42no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13C2×C22⋊C411yescharacteristic
102C2×C4×C13C2×M1611yescharacteristic
103C2×Dic13—24no—
104C2×Dic13—24no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—22no—
110C2×Dic13—21no—
111C2×Dic13—42no—
112C2×Dic13—42no—
113C2×Dic13—41no—
114C2×Dic13C22⋊C811yescharacteristic
115C2×Dic13C22⋊C811yescharacteristic
116C2×Dic13C22⋊C811yescharacteristic
117C2×Dic13C22⋊C811yescharacteristic
118C2×Dic13M3212yes—
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⋊C8—131no—
128C2×C22⋊C8—131no—
129C2×C22⋊C8C2×D1311yescharacteristic
130C2×C4×C8—131no—
131C2×C4×C8—131no—
132C4⋊C16—262no—
133C22⋊C16—132no—
134C22⋊C16C2×D1312yes—
135#346—262no—
136C22×C13—21no—
137C22×C13—21no—
138C22×C13—22no—
139C22×C13—42no—
140C22×C13—42no—
141C22×C13—41no—
142C22×C13—41no—
143C22×C13C2×C22⋊C811yescharacteristic
144C22×C13C2×M3211yescharacteristic
145C22×C13C2×M3211yescharacteristic
146C4×C13—21no—
147C4×C13—41no—
148C4×C13#41011yescharacteristic
149C4×C13#41311yescharacteristic
150Dic13—21no—
151Dic13—21no—
152Dic13—22no—
153Dic13—21no—
154Dic13—41no—
155Dic13#34912yes—
156C23×C4—131no—
157C23×C4—131no—
158C23×C4C4×D1311yescharacteristic
159C22×C8—131no—
160C22×C8—131no—
161C22×C8C4×D1311yescharacteristic
162C22×C8C22×D1311yescharacteristic
163C2×C42—131no—
164C2×C42—131no—
165C2×C42—131no—
166C2×C42—131no—
167C2×C42—261no—
168C2×C42—261no—
169C2×C42—261no—
170C2×C42—261no—
171C2×C16—22no—
172C2×C16—262no—
173C4⋊C8—262no—
174C4⋊C8—262no—
175C22⋊C8—22no—
176C22⋊C8—262no—
177C4×C8—132no—
178C4×C8—132no—
179C4×C8—261no—
180C4×C8—261no—
181C2×C13—21no—
182C2×C13—21no—
183C2×C13—42no—
184C2×C13#145811yescharacteristic
185C2×C13#211211yescharacteristic
186C2×C13C2×#34911yescharacteristic
187C24C8×D1311yescharacteristic
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—131no—
193C22×C4—131no—
194C22×C4—131no—
195C22×C4—131no—
196C22×C4—261no—
197C22×C4—261no—
198C22×C4—262no—
199C22×C4—261no—
200C22×C4—261no—
201C22×C4—262no—
202C22×C4—522no—
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—131no—
214C42—131no—
215C42—131no—
216C42—131no—
217C42—261no—
218C42—261no—
219C42—261no—
220C42—261no—
221C42—261no—
222C42—261no—
223C16—42no—
224C16—522no—
225C13#1146011yescharacteristic, complemented, Sylow
226C23—21no—
227C23—21no—
228C23—41no—
229C23—41no—
230C23#8803812yes—
231C23C2×C8×D1311yescharacteristic
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—131no—
240C2×C4—132no—
241C2×C4—131no—
242C2×C4—131no—
243C2×C4—131no—
244C2×C4—262no—
245C2×C4—264no—
246C2×C4—264no—
247C2×C4—261no—
248C2×C4—261no—
249C2×C4—261no—
250C2×C4—261no—
251C2×C4—261no—
252C2×C4—522no—
253C2×C4—522no—
254C2×C4—521no—
255C2×C4C22⋊C4×D1311yescharacteristic
256C2×C4M16×D1311yescharacteristic
257C8—22no—
258C8—41no—
259C8—262no—
260C8—521no—
261C22—21no—
262C22—21no—
263C22—22no—
264C22—42no—
265C22—42no—
266C22—41no—
267C22—41no—
268C22D13×C22⋊C811yescharacteristic
269C22C2×#8803811yescharacteristic
270C22D13×M3211yescharacteristic
271C4—21no—
272C4—41no—
273C4—132no—
274C4—261no—
275C4—261no—
276C4—262no—
277C4—261no—
278C4—521no—
279C4#1171840111yescharacteristic
280C4#1171840611yescharacteristic
281C2—21no—
282C2—21no—
283C2—42no—
284C2#1311314711yescharacteristic
285C2#1311644511yescharacteristic
286C2D13×#34911yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D13
commutatorC23×C13C22×C8
FrattiniC22×C8C22×D13
FittingC13×#1314C2
socleC22×C13C2×C22⋊C8
prime radicalC24×C13C2×C8
cosocleC22×C8×C13C23
hypercenter#1314D13
hypocenterC13#11460
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1314

Complements

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

NH ≅ G/Ntype
2. #13116636C2semidirect
3. #13112775C2semidirect
225. C13#11460semidirect

Maximal subgroups

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

subgroupindex
C2×#117183792
#131166362
#131127752
#131127602
C13×#13142
#1146013