Finite Group Databasebeta

← #15772591

Subgroups — #15772591

Order 3328.

554 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 87 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#13118201C211yesmaximal, characteristic
2#13113177C211yesmaximal, characteristic
3#13112783C214yesmaximal, complemented
4C13×#1459C211yesmaximal, characteristic
5C23×Dic26C411yescharacteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88178—21no—
8C2×C13×C22⋊C8—21no—
9#11718881C412yes—
10#11718873C411yescharacteristic
11#11718640—21no—
12#11718608—21no—
13#11718607C2212yes—
14#11718590—21no—
15#11718587—21no—
16C13×#324—21no—
17C13×#323C2212yes—
18#11718117—21no—
19#11718117C2212yes—
20C22×D4×C13C2×C411yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×Dic13C2×C412yes—
24C22×Dic26—21no—
25C22×Dic26—21no—
26C22×Dic26—44no—
27C22×Dic26—41no—
28C22×Dic26—41no—
29C22×C8×C13—41no—
30C4×D4×C13—41no—
31C4×D4×C13—41no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C13×C22⋊C4C2311yescharacteristic
35C2×C42×C13D411yescharacteristic
36C2×C22⋊Dic13—22no—
37C2×C22⋊Dic13C2×C412yes—
38C2×C4⋊Dic13—21no—
39#88178—44no—
40C2×#6101—22no—
41C13×C22⋊C8—22no—
42C13×C22⋊C8—41no—
43#88071—22no—
44#88071—21no—
45#88071—22no—
46C22⋊#1055—22no—
47C4⋊#1055—41no—
48#88043—41no—
49#11575—131nomaximal, Sylow
50C24×C13C22⋊C411yescharacteristic
51C24×C13C22×C411yescharacteristic
52C2×D4×C13—22no—
53C2×D4×C13—22no—
54C2×D4×C13—41no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—42no—
60C22×C4×C13—42no—
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—22no—
67C22×Dic13—22no—
68C22×Dic13—44no—
69C22×Dic13—42no—
70C2×Dic26—24no—
71C2×Dic26—44no—
72C2×Dic26—42no—
73C2×Dic26—42no—
74C2×Dic26—48no—
75C2×Dic26—44no—
76C2×Dic26—41no—
77C2×Dic26—41no—
78C2×Dic26—44no—
79C2×C8×C13—42no—
80C2×C8×C13—82no—
81C13×C4⋊C4—41no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—41no—
84C42×C13—21no—
85C42×C13—21no—
86C22⋊Dic13—24no—
87C22⋊Dic13—44no—
88C4⋊Dic13—42no—
89#6101—44no—
90C2×#1055—42no—
91#2409—131no—
92#1466—131no—
93#1459D1311yescharacteristic
94#1326—134no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13#10112yes—
104C23×C13C2×C22⋊C411yescharacteristic
105C23×C13#13112yes—
106D4×C13—44no—
107C2×C4×C13—22no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—81no—
121C2×C4×C13#9911yescharacteristic
122C2×C4×C13#9911yescharacteristic
123C2×Dic13—24no—
124C2×Dic13—42no—
125C2×Dic13—44no—
126C2×Dic13—42no—
127C2×Dic13—44no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—42no—
131Dic26—44no—
132Dic26—48no—
133Dic26—44no—
134C8×C13—82no—
135#1055—82no—
136C23×Q8—131no—
137C2×C22⋊Q8—261no—
138C2×C4×D4C2×D1311yescharacteristic
139#432—261no—
140C2×C22⋊C8—21no—
141#395—261no—
142#393—261no—
143#391—261no—
144#386—132no—
145#385—132no—
146#380—131no—
147#324—21no—
148#323—132no—
149#323—261no—
150#323C2×D1312yes—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—22no—
154C22×C13—22no—
155C22×C13—42no—
156C22×C13—42no—
157C22×C13—42no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—81no—
163C22×C13#40811yescharacteristic
164C22×C13C2×#9911yescharacteristic
165C22×C13C2×#10111yescharacteristic
166C4×C13—21no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13AΣL(1,𝔽16)12yes—
172Dic13—44no—
173Dic13—82no—
174C22×Q8—261no—
175C22×Q8—261no—
176C22×Q8—521no—
177C22×Q8—521no—
178C22×Q8—524no—
179C22×D4C4×D1311yescharacteristic
180C23×C4—132no—
181C23×C4C4×D1311yescharacteristic
182C23×C4C22⋊D1311yescharacteristic
183C22×C8—41no—
184C22⋊Q8—524no—
185C4×D4—41no—
186C4×D4—41no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4—262no—
189C2×C4⋊C4C22⋊D1311yescharacteristic
190C2×C22⋊C4—132no—
191C2×C22⋊C4—262no—
192C2×C22⋊C4D5211yescharacteristic
193C2×C22⋊C4C22×D1311yescharacteristic
194C2×C42D5211yescharacteristic
195C4⋊C8—521no—
196C22⋊C8—22no—
197C22⋊C8—41no—
198C22⋊C8—262no—
199#97—521no—
200#95—261no—
201#95—262no—
202#95—262no—
203C2×C13—21no—
204C2×C13—21no—
205C2×C13—42no—
206C2×C13—42no—
207C2×C13#147211yescharacteristic
208C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
209C2×C13#212311yescharacteristic
210C24#610311yescharacteristic
211C24C2×C4×D1311yescharacteristic
212C2×Q8—264no—
213C2×Q8—522no—
214C2×Q8—522no—
215C2×Q8—524no—
216C2×Q8—524no—
217C2×Q8—528no—
218C2×Q8—524no—
219C2×Q8—521no—
220C2×Q8—521no—
221C2×D4—22no—
222C2×D4—22no—
223C2×D4—41no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—262no—
231C22×C4—262no—
232C22×C4—524no—
233C22×C4—522no—
234C22×C4#610311yescharacteristic
235C22×C4#610311yescharacteristic
236C22×C4#610311yescharacteristic
237C22×C4C2×D5211yescharacteristic
238C22×C4C2×C22⋊D1311yescharacteristic
239C2×C8—42no—
240C2×C8—82no—
241C2×C8—522no—
242C4⋊C4—41no—
243C4⋊C4—522no—
244C4⋊C4—524no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—264no—
248C22⋊C4—524no—
249C42—21no—
250C42—21no—
251C13#1157511yescharacteristic, complemented, Sylow
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23#8806412yes—
261C23#8815512yes—
262C23C2×#610311yescharacteristic
263Q8—524no—
264Q8—528no—
265Q8—524no—
266D4—44no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—81no—
281C2×C4—264no—
282C2×C4—522no—
283C2×C4—524no—
284C2×C4—522no—
285C2×C4—524no—
286C2×C4—522no—
287C2×C4—522no—
288C2×C4—522no—
289C2×C4#8804611yescharacteristic
290C2×C4#8804611yescharacteristic
291C8—82no—
292C8—1042no—
293C22—21no—
294C22—21no—
295C22—22no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—81no—
305C22C2×#8804611yescharacteristic
306C22#1171877111yescharacteristic
307C22C2×#8806411yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—524no—
314C4—1042no—
315C4#1171806312yes—
316C2—21no—
317C2—21no—
318C2—42no—
319C2—42no—
320C2#1311319911yescharacteristic
321C2C2×#1171806311yescharacteristic
322C2#1311649111yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC24×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1459C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C22⋊C4C23
hypercenter#1459D13
hypocenterC13#11575
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #13112783C2semidirect
251. C13#11575semidirect

Maximal subgroups

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

subgroupindex
#131182012
#131131772
#131127832
C13×#14592
#1157513