Finite Group Databasebeta

← #15756446

Subgroups — #15756446

Order 3328.

398 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 83 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#13117437C211yesmaximal, characteristic
2#13114914C211yesmaximal, characteristic
3#13114914C211yesmaximal, characteristic
4#13112745C211yesmaximal, characteristic
5#13112745C211yesmaximal, characteristic
6#13112744C211yesmaximal, characteristic
7C13×#1306C211yesmaximal, characteristic
8C22×C4⋊Dic13C2211yescharacteristic
9C13×#407C2211yescharacteristic
10C13×#407C2211yescharacteristic
11C13×#381C2211yescharacteristic
12#11718872C2211yescharacteristic
13#11718868C2211yescharacteristic
14#11718868C2211yescharacteristic
15#11718603C412yes—
16C22⋊C4×Dic13C412yes—
17#11718315—22no—
18#11718314—22no—
19#11718146—22no—
20#11718146—22no—
21C23×C4×C13C2311yescharacteristic
22C23×Dic13C2×C411yescharacteristic
23C23×Dic13C2×C411yescharacteristic
24C2×C13×M16—21no—
25C2×C13×M16—21no—
26C2×C13×C22⋊C4C2×C412yes—
27C2×C22⋊Dic13C2×C412yes—
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13D412yes—
33C2×C4⋊Dic13D412yes—
34C2×#6101—22no—
35C2×C4×Dic13—22no—
36C2×#6099—21no—
37C2×#6099—21no—
38C13×C22⋊C8—21no—
39C13×C22⋊C8—21no—
40C13×C22⋊C8—21no—
41C13×C22⋊C8—21no—
42C13×#95—21no—
43C13×#95—21no—
44#88071—21no—
45#88071—21no—
46#88071—22no—
47#88071—22no—
48C22⋊#1055—21no—
49C22⋊#1055—21no—
50C22⋊#1055—21no—
51C22⋊#1055—21no—
52#8755—131nomaximal, Sylow
53C24×C13C22×C411yescharacteristic
54C22×C4×C13—22no—
55C22×C4×C13—42no—
56C22×C4×C13C2×D411yescharacteristic
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13#4111yescharacteristic
59C22×C4×C13#4111yescharacteristic
60C22×C4×C13#4111yescharacteristic
61C22×C4×C13#4111yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13—22no—
67C22×Dic13—81no—
68C22×Dic13—81no—
69C22×Dic13C22⋊C412yes—
70C22×Dic13C22⋊C412yes—
71C13×M16—42no—
72C13×M16—42no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C13×C22⋊C4—42no—
76C22⋊Dic13—42no—
77C4⋊Dic13—22no—
78C4⋊Dic13—22no—
79C4⋊Dic13—22no—
80C4⋊Dic13—22no—
81#6101—82no—
82C4×Dic13—82no—
83#6099—42no—
84#6099—42no—
85C2×#1055—41no—
86C2×#1055—41no—
87#2313—131no—
88#1821—131no—
89#1821—131no—
90#1306—131no—
91#1306—131no—
92#1306—131no—
93#1306D1311yescharacteristic
94C23×C13—22no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13C2×C22⋊C411yescharacteristic
98C23×C13#11711yescharacteristic
99C23×C13#11711yescharacteristic
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13#12311yescharacteristic
110C2×C4×C13#12311yescharacteristic
111C2×C4×C13#12311yescharacteristic
112C2×C4×C13#12311yescharacteristic
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—42no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—81no—
121C2×Dic13—81no—
122C2×Dic13—81no—
123C2×Dic13—81no—
124C8×C13—81no—
125C8×C13—81no—
126#1055—81no—
127#1055—81no—
128C22×C4⋊C4—131no—
129#407—131no—
130#407—131no—
131#407C2×D1311yescharacteristic
132#407C2×D1311yescharacteristic
133#387—262no—
134#387—262no—
135#381—131no—
136#381C2×D1311yescharacteristic
137#380—132no—
138C4×C22⋊C4—132no—
139#343—262no—
140#343—262no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—44no—
150C22×C13#38111yescharacteristic
151C22×C13#41012yes—
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—21no—
155C4×C13—21no—
156C4×C13—82no—
157Dic13—42no—
158Dic13—42no—
159Dic13—82no—
160C23×C4—131no—
161C23×C4—131no—
162C23×C4C22×D1311yescharacteristic
163C2×M16—21no—
164C2×M16—21no—
165C2×M16—261no—
166C2×M16—261no—
167C2×C4⋊C4—132no—
168C2×C4⋊C4—132no—
169C2×C4⋊C4—261no—
170C2×C4⋊C4—261no—
171C2×C4⋊C4—261no—
172C2×C4⋊C4—261no—
173C2×C4⋊C4—262no—
174C2×C22⋊C4—132no—
175C2×C22⋊C4C4×D1312yes—
176C2×C42—262no—
177C22⋊C8—21no—
178C22⋊C8—21no—
179C22⋊C8—21no—
180C22⋊C8—21no—
181C22⋊C8—261no—
182C22⋊C8—261no—
183C22⋊C8—261no—
184C22⋊C8—261no—
185#95—21no—
186#95—21no—
187#95—262no—
188#95—262no—
189#95—261no—
190#95—261no—
191C2×C13—22no—
192C2×C13—41no—
193C2×C13—41no—
194C2×C13#182011yescharacteristic
195C2×C13#182911yescharacteristic
196C2×C13#183011yescharacteristic
197C24C2×C4×D1311yescharacteristic
198C22×C4—22no—
199C22×C4—42no—
200C22×C4—132no—
201C22×C4—132no—
202C22×C4—261no—
203C22×C4—261no—
204C22×C4—261no—
205C22×C4—261no—
206C22×C4—262no—
207C22×C4—1041no—
208C22×C4—1041no—
209C22×C4#612711yescharacteristic
210C22×C4#612711yescharacteristic
211C22×C4D4×D1311yescharacteristic
212C22×C4D4×D1311yescharacteristic
213C22×C4#612911yescharacteristic
214C22×C4#613111yescharacteristic
215M16—42no—
216M16—42no—
217M16—522no—
218M16—522no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—521no—
222C2×C8—521no—
223C4⋊C4—262no—
224C4⋊C4—262no—
225C4⋊C4—262no—
226C4⋊C4—262no—
227C4⋊C4—1042no—
228C22⋊C4—42no—
229C22⋊C4—522no—
230C42—1042no—
231C13#875511yescharacteristic, complemented, Sylow
232C23—22no—
233C23—41no—
234C23—41no—
235C23#8812611yescharacteristic
236C23C22⋊C4×D1311yescharacteristic
237C23#8814611yescharacteristic
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—262no—
248C2×C4—262no—
249C2×C4—522no—
250C2×C4—522no—
251C2×C4—522no—
252C2×C4—522no—
253C2×C4—522no—
254C2×C4—1041no—
255C2×C4—1041no—
256C2×C4—1041no—
257C2×C4—1041no—
258C2×C4#8813711yescharacteristic
259C2×C4#8813711yescharacteristic
260C2×C4#8814811yescharacteristic
261C2×C4#8814811yescharacteristic
262C8—81no—
263C8—81no—
264C8—1041no—
265C8—1041no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—44no—
275C22#1171832511yescharacteristic
276C22#1171840112yes—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—82no—
282C4—522no—
283C4—522no—
284C4—1042no—
285C2—22no—
286C2—41no—
287C2—41no—
288C2#1311491211yescharacteristic
289C2#1311494611yescharacteristic
290C2#1311494911yescharacteristic
subgroupG/H
centerC22#11718325
commutator, prime radicalC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1306C2
socleC22×C13#381
cosocleC23×C4×C13C23
hypercenter#1306D13
hypocenterC13#8755
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1306

Complements

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

NH ≅ G/Ntype
231. C13#8755semidirect

Maximal subgroups

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

subgroupindex
#131174372
#131149142
#131127452
#131127442
C13×#13062
#875513