Finite Group Databasebeta

← #15756428

Subgroups — #15756428

Order 3328.

538 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 538 conjugacy classes of subgroups — too many to draw. Only its 91 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#13117434C211yesmaximal, characteristic
2#13114910C211yesmaximal, characteristic
3#13112740C212yesmaximal
4#13112740C212yesmaximal
5C13×#1819C211yesmaximal, characteristic
6C22×C13×C22⋊C4C2211yescharacteristic
7C13×#379C2212yes—
8#11718908C2212yes—
9#11718908C2211yescharacteristic
10#11718908C2211yescharacteristic
11#11718873C412yescomplemented
12C4×C22⋊Dic13C412yescomplemented
13#11718612—22no—
14#11718612—22no—
15C13×#342—22no—
16#11718118—22no—
17C25×C13C2311yescharacteristic
18C23×C4×C13C2×C411yescharacteristic
19C23×C4×C13C2×C411yescharacteristic
20C2×C13×C22⋊C4—22no—
21C2×C13×C22⋊C4—22no—
22C2×C13×C22⋊C4—22no—
23C2×C13×C22⋊C4—22no—
24C2×C13×C22⋊C4—22no—
25C2×C13×C22⋊C4D412yes—
26C2×C13×C22⋊C4D412yes—
27C2×C22⋊Dic13—22no—
28C2×C22⋊Dic13—21no—
29C2×C22⋊Dic13—21no—
30C2×C22⋊Dic13—21no—
31C2×C22⋊Dic13—21no—
32C2×C22⋊Dic13—22no—
33C2×C22⋊Dic13—22no—
34C2×C22⋊Dic13C2×C412yes—
35C2×C22⋊Dic13C2×C412yes—
36C2×C4⋊Dic13—22no—
37C2×C4×Dic13—22no—
38#88071—22no—
39#88071—22no—
40#8750—131nomaximal, Sylow
41C24×C13—42no—
42C24×C13—81no—
43C24×C13—81no—
44C24×C13C22×C411yescharacteristic
45C24×C13C2×D411yescharacteristic
46C24×C13C2×D411yescharacteristic
47C24×C13#4112yes—
48C24×C13#4112yes—
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—42no—
54C22×C4×C13—81no—
55C22×C4×C13—81no—
56C22×C4×C13C22⋊C412yes—
57C22×C4×C13C22⋊C412yes—
58C22×Dic13—22no—
59C22×Dic13—22no—
60C22×Dic13—42no—
61C13×C22⋊C4—24no—
62C13×C22⋊C4—24no—
63C13×C22⋊C4—44no—
64C13×C22⋊C4—82no—
65C13×C22⋊C4—82no—
66C22⋊Dic13—42no—
67C22⋊Dic13—42no—
68C22⋊Dic13—44no—
69C22⋊Dic13—81no—
70C22⋊Dic13—81no—
71C22⋊Dic13—81no—
72C22⋊Dic13—81no—
73C22⋊Dic13—82no—
74C22⋊Dic13—82no—
75C4⋊Dic13—82no—
76C4×Dic13—82no—
77#2312—131no—
78#1819—131no—
79#1819D1311yescharacteristic
80#1304—132no—
81#1304—132no—
82C23×C13—22no—
83C23×C13—22no—
84C23×C13—22no—
85C23×C13—41no—
86C23×C13—41no—
87C23×C13—41no—
88C23×C13—41no—
89C23×C13—41no—
90C23×C13—41no—
91C23×C13—42no—
92C23×C13—42no—
93C23×C13—42no—
94C23×C13—42no—
95C23×C13—42no—
96C23×C13—42no—
97C23×C13—88no—
98C23×C13C2×C22⋊C411yescharacteristic
99C23×C13#11711yescharacteristic
100C23×C13#11711yescharacteristic
101C23×C13#12312yes—
102C23×C13#12312yes—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—42no—
106C2×C4×C13—42no—
107C2×C4×C13—81no—
108C2×C4×C13—81no—
109C2×C4×C13—81no—
110C2×C4×C13—81no—
111C2×C4×C13—82no—
112C2×C4×C13—82no—
113C2×C4×C13—82no—
114C2×Dic13—42no—
115C2×Dic13—42no—
116C2×Dic13—42no—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—82no—
121C2×Dic13—82no—
122C2×Dic13—82no—
123C22×C22⋊C4C2×D1311yescharacteristic
124#388—262no—
125#388—262no—
126#380—132no—
127#379—131no—
128#379—131no—
129#379—132no—
130#379C2×D1312yes—
131C4×C22⋊C4—132no—
132#342—22no—
133#342—262no—
134C22×C13—21no—
135C22×C13—21no—
136C22×C13—22no—
137C22×C13—22no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13—22no—
141C22×C13—22no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—22no—
147C22×C13—22no—
148C22×C13—44no—
149C22×C13—82no—
150C22×C13—82no—
151C22×C13—84no—
152C22×C13—84no—
153C22×C13#38111yescharacteristic
154C22×C13#41012yes—
155C4×C13—42no—
156C4×C13—42no—
157C4×C13—162no—
158Dic13—82no—
159Dic13—82no—
160Dic13—162no—
161C25C22×D1311yescharacteristic
162C23×C4C4×D1311yescharacteristic
163C23×C4C4×D1311yescharacteristic
164C2×C4⋊C4—262no—
165C2×C22⋊C4—22no—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—22no—
170C2×C22⋊C4—132no—
171C2×C22⋊C4—132no—
172C2×C22⋊C4—262no—
173C2×C22⋊C4—261no—
174C2×C22⋊C4—261no—
175C2×C22⋊C4—261no—
176C2×C22⋊C4—261no—
177C2×C22⋊C4—262no—
178C2×C22⋊C4—262no—
179C2×C22⋊C4D5212yes—
180C2×C22⋊C4C22⋊D1312yes—
181C2×C42—262no—
182#95—262no—
183#95—262no—
184C2×C13—22no—
185C2×C13—42no—
186C2×C13—42no—
187C2×C13—41no—
188C2×C13—41no—
189C2×C13#182011yescharacteristic
190C2×C13#182811yescharacteristic
191C2×C13#182811yescharacteristic
192C24—42no—
193C24—81no—
194C24—81no—
195C24C2×C4×D1311yescharacteristic
196C24C2×D5211yescharacteristic
197C24#612912yes—
198C24#612912yes—
199C24C2×C22⋊D1311yescharacteristic
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—42no—
205C22×C4—81no—
206C22×C4—81no—
207C22×C4—262no—
208C22×C4—262no—
209C22×C4—522no—
210C22×C4#610312yes—
211C22×C4#610312yes—
212C4⋊C4—1042no—
213C22⋊C4—24no—
214C22⋊C4—24no—
215C22⋊C4—44no—
216C22⋊C4—82no—
217C22⋊C4—82no—
218C22⋊C4—522no—
219C22⋊C4—522no—
220C22⋊C4—524no—
221C22⋊C4—1041no—
222C22⋊C4—1041no—
223C22⋊C4—1041no—
224C22⋊C4—1041no—
225C22⋊C4—1042no—
226C22⋊C4—1042no—
227C42—1042no—
228C13#875011yescharacteristic, complemented, Sylow
229C23—22no—
230C23—22no—
231C23—22no—
232C23—41no—
233C23—41no—
234C23—42no—
235C23—42no—
236C23—41no—
237C23—41no—
238C23—42no—
239C23—42no—
240C23—41no—
241C23—41no—
242C23—42no—
243C23—42no—
244C23—88no—
245C23#8813111yescharacteristic
246C23#8813111yescharacteristic
247C23#8814012yes—
248C23C2×#610311yescharacteristic
249C23#8818912yes—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4—522no—
262C2×C4—522no—
263C2×C4—522no—
264C2×C4—522no—
265C2×C4—522no—
266C2×C4—522no—
267C2×C4—1042no—
268C2×C4—1042no—
269C2×C4—1042no—
270C22—21no—
271C22—21no—
272C22—22no—
273C22—22no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—22no—
284C22—44no—
285C22—82no—
286C22—82no—
287C22—84no—
288C22—84no—
289C22#1171860411yescharacteristic
290C22#1171866712yes—
291C4—42no—
292C4—42no—
293C4—162no—
294C4—1042no—
295C4—1042no—
296C4—2082no—
297C2—22no—
298C2—42no—
299C2—42no—
300C2—41no—
301C2—41no—
302C2#1311491111yescharacteristic
303C2#1311494211yescharacteristic
304C2#1311494211yescharacteristic
subgroupG/H
centerC22#11718604
commutatorC24×C13C22×C4
FrattiniC25C22×D13
FittingC13×#1819C2
socleC22×C13#381
prime radical, cosocleC25×C13C23
hypercenter#1819D13
hypocenterC13#8750
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
11. #11718873C4semidirect
12. C4×C22⋊Dic13C4semidirect
228. C13#8750semidirect

Maximal subgroups

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

subgroupindex
#131174342
#131149102
#131127402
C13×#18192
#875013