Finite Group Databasebeta

← #15756457

Subgroups — #15756457

Order 3328.

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

normal subgroups only

This group has 394 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#13117438C211yesmaximal, characteristic
2#13113165C211yesmaximal, characteristic
3#13113165C211yesmaximal, characteristic
4#13112743C211yesmaximal, characteristic
5#13112742C211yesmaximal, characteristic
6#13112741C211yesmaximal, characteristic
7C13×#1305C211yesmaximal, characteristic
8C22×#6101C2211yescharacteristic
9C13×#407C2211yescharacteristic
10C13×#407C2211yescharacteristic
11C13×#380C2211yescharacteristic
12#11718873C2211yescharacteristic
13#11718868C2211yescharacteristic
14#11718868C2211yescharacteristic
15#11718639—22no—
16#11718604C412yes—
17C22⋊C4×Dic13C412yes—
18#11718316—22no—
19#11718061—22no—
20#11718061—22no—
21C23×C4×C13C2311yescharacteristic
22C23×Dic13C2×C411yescharacteristic
23C23×Dic13C2×C411yescharacteristic
24C2×C13×M16—21no—
25C2×C13×M16—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C22⋊C4C2×C412yes—
28C2×C22⋊Dic13C2×C412yes—
29C2×C4⋊Dic13—21no—
30C2×#6101—21no—
31C2×#6101—21no—
32C2×#6101—21no—
33C2×#6101—21no—
34C2×#6101D412yes—
35C2×#6101D412yes—
36C2×C4×Dic13—22no—
37C2×#6099—21no—
38C2×#6099—21no—
39C13×C22⋊C8—21no—
40C13×C22⋊C8—21no—
41C13×C22⋊C8—21no—
42C13×C22⋊C8—21no—
43C13×#95—21no—
44#88071—21no—
45#88071—22no—
46#88071—24no—
47C22⋊#1055—21no—
48C22⋊#1055—21no—
49C22⋊#1055—21no—
50C22⋊#1055—21no—
51#8758—131nomaximal, Sylow
52C24×C13C22×C411yescharacteristic
53C22×C4×C13—22no—
54C22×C4×C13—81no—
55C22×C4×C13C2×D411yescharacteristic
56C22×C4×C13C2×D411yescharacteristic
57C22×C4×C13#4111yescharacteristic
58C22×C4×C13#4111yescharacteristic
59C22×C4×C13#4111yescharacteristic
60C22×C4×C13#4111yescharacteristic
61C22×Dic13—21no—
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13—22no—
66C22×Dic13—41no—
67C22×Dic13—41no—
68C22×Dic13—81no—
69C22×Dic13C22⋊C412yes—
70C22×Dic13C22⋊C412yes—
71C13×M16—81no—
72C13×M16—81no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C13×C4⋊C4—81no—
76C13×C22⋊C4—42no—
77C22⋊Dic13—42no—
78C4⋊Dic13—81no—
79#6101—22no—
80#6101—22no—
81#6101—22no—
82#6101—22no—
83C4×Dic13—82no—
84#6099—81no—
85#6099—81no—
86C2×#1055—41no—
87C2×#1055—41no—
88#2313—131no—
89#1463—131no—
90#1463—131no—
91#1305—131no—
92#1305—131no—
93#1305—131no—
94#1305D1311yescharacteristic
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13C2×C22⋊C411yescharacteristic
100C23×C13#11711yescharacteristic
101C23×C13#11711yescharacteristic
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13#12311yescharacteristic
112C2×C4×C13#12311yescharacteristic
113C2×C4×C13#12311yescharacteristic
114C2×C4×C13#12311yescharacteristic
115C2×Dic13—22no—
116C2×Dic13—22no—
117C2×Dic13—22no—
118C2×Dic13—22no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124C2×Dic13—42no—
125C2×Dic13—81no—
126C2×Dic13—81no—
127C8×C13—81no—
128C8×C13—81no—
129#1055—81no—
130#1055—81no—
131C22×C4⋊C4—131no—
132#407—131no—
133#407—131no—
134#407C2×D1311yescharacteristic
135#407C2×D1311yescharacteristic
136#387—262no—
137#387—262no—
138#381—132no—
139#380—131no—
140#380C2×D1311yescharacteristic
141C4×C22⋊C4—132no—
142#324—262no—
143#324—262no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—21no—
152C22×C13—42no—
153C22×C13—42no—
154C22×C13#38111yescharacteristic
155C22×C13#41311yescharacteristic
156C22×C13#41311yescharacteristic
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—82no—
162Dic13—42no—
163Dic13—42no—
164Dic13—82no—
165C23×C4—131no—
166C23×C4—131no—
167C23×C4C22×D1311yescharacteristic
168C2×M16—21no—
169C2×M16—21no—
170C2×M16—261no—
171C2×M16—261no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—132no—
174C2×C4⋊C4—132no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4—261no—
177C2×C4⋊C4—261no—
178C2×C4⋊C4—261no—
179C2×C4⋊C4—261no—
180C2×C22⋊C4—132no—
181C2×C22⋊C4C4×D1312yes—
182C2×C42—262no—
183C22⋊C8—21no—
184C22⋊C8—21no—
185C22⋊C8—21no—
186C22⋊C8—21no—
187C22⋊C8—261no—
188C22⋊C8—261no—
189C22⋊C8—261no—
190C22⋊C8—261no—
191#95—21no—
192#95—262no—
193#95—264no—
194#95—261no—
195C2×C13—21no—
196C2×C13—21no—
197C2×C13—41no—
198C2×C13—41no—
199C2×C13#182211yescharacteristic
200C2×C13#182811yescharacteristic
201C2×C13#183011yescharacteristic
202C24C2×C4×D1311yescharacteristic
203C22×C4—22no—
204C22×C4—81no—
205C22×C4—132no—
206C22×C4—132no—
207C22×C4—261no—
208C22×C4—261no—
209C22×C4—261no—
210C22×C4—261no—
211C22×C4—262no—
212C22×C4—521no—
213C22×C4—521no—
214C22×C4—1041no—
215C22×C4#612711yescharacteristic
216C22×C4#612711yescharacteristic
217C22×C4D4×D1311yescharacteristic
218C22×C4D4×D1311yescharacteristic
219C22×C4#612911yescharacteristic
220C22×C4#613111yescharacteristic
221M16—81no—
222M16—81no—
223M16—1041no—
224M16—1041no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—521no—
228C2×C8—521no—
229C4⋊C4—81no—
230C4⋊C4—262no—
231C4⋊C4—262no—
232C4⋊C4—262no—
233C4⋊C4—262no—
234C4⋊C4—1041no—
235C22⋊C4—42no—
236C22⋊C4—522no—
237C42—1042no—
238C13#875811yescharacteristic, complemented, Sylow
239C23—21no—
240C23—21no—
241C23—41no—
242C23—41no—
243C23#8812611yescharacteristic
244C23C22⋊C4×D1311yescharacteristic
245C23#8814611yescharacteristic
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—262no—
256C2×C4—262no—
257C2×C4—262no—
258C2×C4—262no—
259C2×C4—522no—
260C2×C4—522no—
261C2×C4—522no—
262C2×C4—522no—
263C2×C4—522no—
264C2×C4—522no—
265C2×C4—1041no—
266C2×C4—1041no—
267C2×C4#8813711yescharacteristic
268C2×C4#8813711yescharacteristic
269C2×C4#8814811yescharacteristic
270C2×C4#8814811yescharacteristic
271C8—81no—
272C8—81no—
273C8—1041no—
274C8—1041no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—42no—
284C22—42no—
285C22#1171832511yescharacteristic
286C22#1171840611yescharacteristic
287C22#1171841211yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—82no—
293C4—522no—
294C4—522no—
295C4—1042no—
296C2—21no—
297C2—21no—
298C2—41no—
299C2—41no—
300C2#1311491811yescharacteristic
301C2#1311494311yescharacteristic
302C2#1311494911yescharacteristic
subgroupG/H
centerC22#11718325
commutator, prime radicalC24×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1305C2
socleC22×C13#381
cosocleC23×C4×C13C23
hypercenter#1305D13
hypocenterC13#8758
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1305

Complements

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

NH ≅ G/Ntype
238. C13#8758semidirect

Maximal subgroups

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

subgroupindex
#131174382
#131131652
#131127432
#131127422
#131127412
C13×#13052
#875813