Finite Group Databasebeta

← #16787249

Subgroups — #16787249

Order 3328.

358 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 72 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#13130099C211yesmaximal, characteristic
2#13130079C211yesmaximal, characteristic
3#13129777C212yesmaximal
4#13129776C212yesmaximal
5#13120053C211yesmaximal, characteristic
6C2×Q8×Dic13C2211yescharacteristic
7C2×#88142C411yescharacteristic
8#11719128—21no—
9#11719119—21no—
10C13×#391C411yescharacteristic
11#11718891C411yescharacteristic
12#11718638C2211yescharacteristic
13#11718597C2211yescharacteristic
14C4×#6101C411yescharacteristic
15#11718321—21no—
16#11718321—21no—
17#11718307—21no—
18#11718307—21no—
19#11718285—21no—
20#11718285—21no—
21#11718285C2212yes—
22#11718285C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×Dic26—21no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C42×C13C2×C411yescharacteristic
27Q8×Dic13—41no—
28Q8×Dic13—41no—
29C2×C4⋊Dic13C2×C411yescharacteristic
30C2×C4⋊Dic13D411yescharacteristic
31C2×C4⋊Dic13D411yescharacteristic
32C2×C4⋊Dic13C2311yescharacteristic
33C2×#6101—21no—
34C2×#6101—21no—
35C2×C4×Dic13C2×C411yescharacteristic
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39#88142—41no—
40#88142—41no—
41C22⋊#1057—22no—
42C22⋊#1057—22no—
43#88112—41no—
44#88110—41no—
45C4⋊#1057—41no—
46C4×#1057—41no—
47C13×#95—21no—
48C13×#95—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#11573—131nomaximal, Sylow
57C2×Q8×C13—22no—
58C2×Q8×C13—22no—
59C2×Q8×C13—41no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13C22⋊C411yescharacteristic
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C2×D411yescharacteristic
70C22×Dic13C2×D411yescharacteristic
71C2×Dic26—44no—
72C2×Dic26—41no—
73C2×Dic26—41no—
74C2×#1057—42no—
75C2×#1057—42no—
76C13×C4⋊C4—41no—
77C42×C13—22no—
78C4⋊Dic13—41no—
79C4⋊Dic13—41no—
80C4⋊Dic13—41no—
81C4⋊Dic13—41no—
82#6101—42no—
83#6101—42no—
84C4×Dic13—21no—
85C4×Dic13—21no—
86C4×Dic13—21no—
87C4×Dic13—21no—
88C4×Dic13—21no—
89C4×Dic13—21no—
90C4×Dic13—22no—
91#2568—131no—
92#1467—131no—
93#1461—131no—
94#1324—132no—
95#1324—132no—
96C23×C13C2×C22⋊C411yescharacteristic
97Q8×C13—44no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13#10112yes—
111C2×C4×C13#13112yes—
112C2×Dic13—22no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—42no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13#9911yescharacteristic
125C2×Dic13#9911yescharacteristic
126Dic26—82no—
127Dic26—82no—
128#1057—82no—
129#1057—82no—
130C2×C4⋊Q8—131no—
131C2×C4×Q8—131no—
132#432—261no—
133#431—261no—
134#400—261no—
135#400—261no—
136#391—131no—
137#391—261no—
138#391—261no—
139#391#26111yescharacteristic
140#382—131no—
141#382—131no—
142C4×C4⋊C4—131no—
143#324—132no—
144#324—132no—
145#324—261no—
146#324—261no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13#40811yescharacteristic
150C22×C13C2×#9911yescharacteristic
151C22×C13C2×#10111yescharacteristic
152C4×C13—22no—
153C4×C13—22no—
154C4×C13—41no—
155C4×C13—81no—
156C4×C13—81no—
157Dic13—21no—
158Dic13—41no—
159Dic13—41no—
160Dic13—41no—
161Dic13—81no—
162Dic13—81no—
163Dic13#35512yes—
164C22×Q8—261no—
165C22×Q8C2×#26111yescharacteristic
166C4⋊Q8—521no—
167C4⋊Q8—521no—
168C4×Q8—521no—
169C4×Q8—521no—
170C2×C4⋊C4—131no—
171C2×C4⋊C4—131no—
172C2×C4⋊C4—131no—
173C2×C4⋊C4—131no—
174C2×C4⋊C4—261no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4C2×#26111yescharacteristic
177C2×C42—131no—
178C2×C42—131no—
179C2×C42—131no—
180C2×C42—131no—
181C2×C42C2×#26111yescharacteristic
182C4⋊C8—521no—
183C4⋊C8—521no—
184C22⋊C8—262no—
185C22⋊C8—262no—
186#97—521no—
187C4×C8—521no—
188#95—21no—
189#95—21no—
190#95—261no—
191#95—261no—
192#95—261no—
193#95—261no—
194#95—261no—
195#95—261no—
196#95—261no—
197C2×C13—21no—
198C2×C13—21no—
199C2×C13#147211yescharacteristic
200C2×C13#212911yescharacteristic
201C2×C13C2×#35511yescharacteristic
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—41no—
205C2×Q8—521no—
206C2×Q8—521no—
207C2×Q8—524no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—131no—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4—131no—
214C22×C4—261no—
215C22×C4—261no—
216C22×C4C22⋊#26111yescharacteristic
217C22×C4C22⋊#26111yescharacteristic
218C22×C4C22×#26111yescharacteristic
219C2×C8—522no—
220C2×C8—522no—
221C4⋊C4—41no—
222C4⋊C4—521no—
223C4⋊C4—521no—
224C4⋊C4—521no—
225C4⋊C4—521no—
226C4⋊C4—522no—
227C4⋊C4—522no—
228C42—22no—
229C42—261no—
230C42—261no—
231C42—261no—
232C42—261no—
233C42—261no—
234C42—261no—
235C42—262no—
236C13#1157311yescharacteristic, complemented, Sylow
237C23C2×C22⋊#26111yescharacteristic
238Q8—44no—
239Q8—1042no—
240Q8—1042no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—131no—
254C2×C4—131no—
255C2×C4—262no—
256C2×C4—261no—
257C2×C4—261no—
258C2×C4—261no—
259C2×C4—521no—
260C2×C4—521no—
261C2×C4—521no—
262C2×C4—521no—
263C2×C4—521no—
264C2×C4—522no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4#8811312yes—
268C2×C4#8823812yes—
269C8—1042no—
270C8—1042no—
271C22—21no—
272C22—21no—
273C22C2×#8811311yescharacteristic
274C22D13⋊#9911yescharacteristic
275C22#1171914611yescharacteristic
276C4—22no—
277C4—22no—
278C4—41no—
279C4—81no—
280C4—81no—
281C4—132no—
282C4—261no—
283C4—521no—
284C4—521no—
285C4—521no—
286C4—1041no—
287C4—1041no—
288C2—21no—
289C2—21no—
290C2#1313011511yescharacteristic
291C2#1313111911yescharacteristic
292C2D13⋊#35511yescharacteristic
subgroupG/H
centerC22D13⋊#99
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#391C4
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4⋊Dic13C23
hypercenter#391#261
hypocenterC13#11573
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #391

Complements

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

NH ≅ G/Ntype
236. C13#11573semidirect

Maximal subgroups

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

subgroupindex
#131300992
#131300792
#131297772
#131297762
#131200532
#1157313