Finite Group Databasebeta

← #15772573

Subgroups — #15772573

Order 3328.

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

normal subgroups only

This group has 350 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#13120023C211yesmaximal, characteristic
2#13113180C211yesmaximal, characteristic
3#13112781C212yesmaximal
4#13112779C212yesmaximal
5C13×#1461C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88124C411yescharacteristic
8C13×#431—21no—
9#11718891C411yescharacteristic
10#11718891C411yescharacteristic
11#11718645—21no—
12#11718645—21no—
13#11718638C2211yescharacteristic
14#11718637C2211yescharacteristic
15C4×C4⋊Dic13C411yescharacteristic
16#11718594—21no—
17#11718594—21no—
18#11718587—21no—
19C13×#324—21no—
20C13×#324C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C4×Q8×C13—41no—
25C4×Q8×C13—41no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C4⋊C4C2311yescharacteristic
29C2×C42×C13C2×C411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13D411yescharacteristic
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13C2×C411yescharacteristic
41#88124—41no—
42#88124—41no—
43C13×C4⋊C8—41no—
44C13×C22⋊C8—22no—
45C4×C8×C13—41no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53C22⋊#1055—22no—
54C4⋊#1055—41no—
55#88043—41no—
56#11571—131nomaximal, Sylow
57C2×Q8×C13—22no—
58C2×Q8×C13—22no—
59C2×Q8×C13—41no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C2×C8×C13—42no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C42×C13—21no—
76C42×C13—21no—
77C42×C13—21no—
78C42×C13—21no—
79C42×C13—21no—
80C42×C13—21no—
81C4⋊Dic13—42no—
82C4⋊Dic13—41no—
83C4⋊Dic13—41no—
84#6101—42no—
85#6101—42no—
86#6101—42no—
87#6101—41no—
88#6101—41no—
89C4×Dic13—22no—
90C4×Dic13—22no—
91C2×#1055—42no—
92#2565—131no—
93#1467—131no—
94#1461D1311yescharacteristic
95#1325—132no—
96#1324—132no—
97C23×C13C2×C22⋊C411yescharacteristic
98Q8×C13—44no—
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—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13#9911yescharacteristic
114C2×C4×C13#9911yescharacteristic
115C2×C4×C13#10112yes—
116C2×C4×C13#13112yes—
117C2×Dic13—22no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—42no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C8×C13—82no—
129#1055—82no—
130C2×#125—131no—
131C2×C4×Q8C2×D1311yescharacteristic
132#432—261no—
133#431—21no—
134#398—261no—
135#398—261no—
136#391—131no—
137#391—131no—
138#387—261no—
139#387—261no—
140#384—131no—
141#382—131no—
142C4×C4⋊C4—131no—
143#324—21no—
144#324—132no—
145#324—261no—
146#324C2×D1312yes—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13#40811yescharacteristic
150C22×C13C2×#9911yescharacteristic
151C22×C13C2×#10111yescharacteristic
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—22no—
155C4×C13—22no—
156C4×C13—41no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—41no—
160Dic13—42no—
161Dic13—81no—
162Dic13—81no—
163Dic13—81no—
164C22×Q8C4×D1311yescharacteristic
165#125—521no—
166#125—521no—
167C4×Q8—41no—
168C4×Q8—41no—
169C2×C4⋊C4—131no—
170C2×C4⋊C4—131no—
171C2×C4⋊C4—261no—
172C2×C4⋊C4—261no—
173C2×C4⋊C4—261no—
174C2×C4⋊C4—261no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4D5211yescharacteristic
177C2×C4⋊C4C22⋊D1311yescharacteristic
178C2×C4⋊C4C22×D1311yescharacteristic
179C2×C42—131no—
180C2×C42—131no—
181C2×C42C4×D1311yescharacteristic
182C2×C42D5211yescharacteristic
183C2×C42C22⋊D1311yescharacteristic
184C4⋊C8—41no—
185C4⋊C8—521no—
186C22⋊C8—22no—
187C22⋊C8—262no—
188#97—521no—
189C4×C8—41no—
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#212611yescharacteristic
201C2×C13#213311yescharacteristic
202C2×Q8—22no—
203C2×Q8—22no—
204C2×Q8—41no—
205C22×C4—261no—
206C22×C4—261no—
207C22×C4—261no—
208C22×C4—261no—
209C22×C4#610311yescharacteristic
210C22×C4#610311yescharacteristic
211C22×C4#610311yescharacteristic
212C22×C4#610311yescharacteristic
213C22×C4C2×C4×D1311yescharacteristic
214C22×C4C2×D5211yescharacteristic
215C22×C4C2×C22⋊D1311yescharacteristic
216C2×C8—42no—
217C2×C8—522no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—521no—
222C4⋊C4—521no—
223C4⋊C4—522no—
224C4⋊C4—522no—
225C4⋊C4—522no—
226C4⋊C4—522no—
227C4⋊C4—521no—
228C4⋊C4—521no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—262no—
236C42—262no—
237C13#1157111yescharacteristic, complemented, Sylow
238C23C2×#610311yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—262no—
255C2×C4—521no—
256C2×C4—521no—
257C2×C4—521no—
258C2×C4—521no—
259C2×C4—521no—
260C2×C4—521no—
261C2×C4—522no—
262C2×C4—521no—
263C2×C4—521no—
264C2×C4—521no—
265C2×C4#8804611yescharacteristic
266C2×C4#8804611yescharacteristic
267C2×C4#8806412yes—
268C2×C4#8815512yes—
269C8—82no—
270C8—1042no—
271C22—21no—
272C22—21no—
273C22C2×#8804611yescharacteristic
274C22#1171877111yescharacteristic
275C22C2×#8806411yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—522no—
285C4—1041no—
286C4—1041no—
287C4—1041no—
288C2—21no—
289C2—21no—
290C2#1311319911yescharacteristic
291C2#1311649911yescharacteristic
292C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1461C2
socleC22×C13C2×#99
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1461D13
hypocenterC13#11571
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
237. C13#11571semidirect

Maximal subgroups

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

subgroupindex
#131200232
#131131802
#131127812
#131127792
C13×#14612
#1157113