Finite Group Databasebeta

← #15760691

Subgroups — #15760691

Order 3328.

598 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 131 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#13123860C211yesmaximal, characteristic
2#13119144C211yesmaximal, characteristic
3#13114920C212yesmaximal, complemented
4#13112703C212yesmaximal, complemented
5C13×#1799C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88189—21no—
8C22×C4⋊Dic13C2211yescharacteristic
9C2×C13×#99—21no—
10C13×#380C2212yes—
11#11718873—21no—
12#11718873C2211yescharacteristic
13C2×C22⋊#1055—21no—
14C2×C22⋊#1055C2212yes—
15D4×#1055—24no—
16#11718644C412yescomplemented
17#11718614C412yescomplemented
18#11718604—21no—
19#11718589—21no—
20#11718586—21no—
21C13×#342—21no—
22#11718121—24no—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C23×Dic13—21no—
27C4×D4×C13—22no—
28C4×D4×C13—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C22⋊Dic13—22no—
36C2×C22⋊Dic13—21no—
37#88189—42no—
38#88189—42no—
39C2×C4⋊Dic13—22no—
40C2×C4⋊Dic13—22no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13C2×C412yes—
44C2×#6101—22no—
45C22×#1055—22no—
46C22×#1055D414yes—
47C13×#99—42no—
48C13×#95—22no—
49#88071—22no—
50#88071—22no—
51#88071C2×C412yes—
52C22⋊#1055—22no—
53C22⋊#1055—22no—
54C22⋊#1055—22no—
55C4⋊#1055—22no—
56C4×#1055—22no—
57#9470—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C2×D411yescharacteristic
60C2×D4×C13—22no—
61C2×D4×C13—22no—
62C2×D4×C13D812yes—
63C2×D4×C13SD1612yes—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—42no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13C2×D412yes—
75C22×C4×C13#4112yes—
76C22×Dic13—22no—
77C22×Dic13—22no—
78C22×Dic13—42no—
79C22×Dic13—41no—
80C22×Dic13—41no—
81C22×Dic13—42no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—44no—
84C13×C22⋊C4—22no—
85C13×C22⋊C4—22no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C42×C13—21no—
89C42×C13—21no—
90C22⋊Dic13—44no—
91C22⋊Dic13—41no—
92C22⋊Dic13—41no—
93C4⋊Dic13—24no—
94C4⋊Dic13—42no—
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97#6101—44no—
98C2×#1055—24no—
99C2×#1055—44no—
100C2×#1055—82no—
101#2972—131no—
102#2486—131no—
103#1823—132no—
104#1799D1311yescharacteristic
105#1289—132no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13#10212yes—
113C23×C13C2×C22⋊C411yescharacteristic
114C23×C13#12112yes—
115C23×C13C2×D811yescharacteristic
116C23×C13C2×SD1611yescharacteristic
117C23×C13#13512yes—
118D4×C13—24no—
119D4×C13—24no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—24no—
123C2×C4×C13—22no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—41no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—81no—
132C2×C4×C13—82no—
133C2×C4×C13—82no—
134C2×C4×C13—82no—
135C2×C4×C13#10212yes—
136C2×C4×C13C4×D412yes—
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13#12311yescharacteristic
139C2×Dic13—42no—
140C2×Dic13—42no—
141C2×Dic13—42no—
142C2×Dic13—42no—
143C2×Dic13—42no—
144C2×Dic13—42no—
145C2×Dic13—82no—
146C2×Dic13—82no—
147#1055—44no—
148C2×#123—261no—
149C2×C4×D4C2×D1311yescharacteristic
150C22×C4⋊C4—131no—
151C8×D4—264no—
152#431—261no—
153C2×#99—21no—
154C2×C22⋊C8—132no—
155C2×C22⋊C8—261no—
156#398—132no—
157#397—132no—
158#389—261no—
159#381—261no—
160#380—131no—
161#380—261no—
162#380C2×D1312yes—
163#342—21no—
164#340—264no—
165C22×C13—21no—
166C22×C13—22no—
167C22×C13—21no—
168C22×C13—22no—
169C22×C13—22no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—42no—
173C22×C13—42no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—81no—
177C22×C13#38611yescharacteristic
178C22×C13C2×#10211yescharacteristic
179C22×C13#41611yescharacteristic
180C22×C13#46512yes—
181C22×C13#46612yes—
182C4×C13—21no—
183C4×C13—22no—
184C4×C13—22no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—162no—
188C4×C13#45812yes—
189Dic13—82no—
190Dic13—82no—
191C22×D4C22⋊D1311yescharacteristic
192C23×C4—261no—
193C23×C4D5211yescharacteristic
194C23×C4C22×D1311yescharacteristic
195C22×C8—134no—
196C22×C8—262no—
197#123—522no—
198#123—522no—
199C4×D4—22no—
200C4×D4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—132no—
203C2×C4⋊C4—262no—
204C2×C4⋊C4—262no—
205C2×C4⋊C4—262no—
206C2×C4⋊C4—261no—
207C2×C4⋊C4—261no—
208C2×C4⋊C4C4×D1311yescharacteristic
209C2×C22⋊C4—22no—
210C2×C22⋊C4—262no—
211C2×C22⋊C4—261no—
212C2×C22⋊C4C4×D1311yescharacteristic
213C2×C22⋊C4C22⋊D1311yescharacteristic
214C2×C42D5211yescharacteristic
215C4⋊C8—262no—
216#99—42no—
217C22⋊C8—262no—
218C22⋊C8—262no—
219C22⋊C8—262no—
220C4×C8—262no—
221#95—22no—
222#95—132no—
223#95—262no—
224#95—262no—
225C2×C13—21no—
226C2×C13—22no—
227C2×C13—21no—
228C2×C13—22no—
229C2×C13—42no—
230C2×C13#189011yescharacteristic
231C2×C13#189311yescharacteristic
232C2×C13#190911yescharacteristic
233C24#610311yescharacteristic
234C24C2×C22⋊D1311yescharacteristic
235C2×D4—22no—
236C2×D4—22no—
237C2×D4#610412yes—
238C2×D4#610612yes—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4—262no—
245C22×C4—262no—
246C22×C4—521no—
247C22×C4—522no—
248C22×C4—521no—
249C22×C4—522no—
250C22×C4#610311yescharacteristic
251C22×C4#610311yescharacteristic
252C22×C4#610311yescharacteristic
253C22×C4C2×C4×D1311yescharacteristic
254C22×C4C2×D5211yescharacteristic
255C22×C4D4×D1312yes—
256C22×C4#612912yes—
257C2×C8—264no—
258C2×C8—524no—
259C2×C8—1042no—
260C4⋊C4—22no—
261C4⋊C4—44no—
262C4⋊C4—264no—
263C4⋊C4—522no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C4⋊C4—524no—
267C22⋊C4—22no—
268C22⋊C4—22no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C22⋊C4—521no—
272C22⋊C4—521no—
273C22⋊C4—524no—
274C42—21no—
275C42—21no—
276C13#947011yescharacteristic, complemented, Sylow
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23#8804912yes—
284C23C2×#610311yescharacteristic
285C23C2×#610411yescharacteristic
286C23#8819312yes—
287C23C2×#610611yescharacteristic
288C23#8820412yes—
289D4—24no—
290D4—24no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—24no—
294C2×C4—22no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—81no—
303C2×C4—82no—
304C2×C4—82no—
305C2×C4—82no—
306C2×C4—522no—
307C2×C4—522no—
308C2×C4—522no—
309C2×C4—522no—
310C2×C4—522no—
311C2×C4—522no—
312C2×C4—1042no—
313C2×C4—1042no—
314C2×C4#8804912yes—
315C2×C4#8813512yes—
316C2×C4#8813611yescharacteristic
317C2×C4#8814011yescharacteristic
318C8—524no—
319C22—21no—
320C22—22no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—42no—
327C22—42no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22#1171861911yescharacteristic
332C22C2×#8804911yescharacteristic
333C22#1171866311yescharacteristic
334C22#1171869912yes—
335C22#1171870912yes—
336C4—21no—
337C4—22no—
338C4—22no—
339C4—41no—
340C4—41no—
341C4—162no—
342C4—1042no—
343C4—1042no—
344C4#1171840312yes—
345C2—22no—
346C2—21no—
347C2—21no—
348C2—22no—
349C2—42no—
350C2#1311524711yescharacteristic
351C2#1311526211yescharacteristic
352C2#1311535611yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1799C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#1799D13
hypocenterC13#9470
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #13114920C2semidirect
4. #13112703C2semidirect
16. #11718644C4semidirect
17. #11718614C4semidirect
276. C13#9470semidirect

Maximal subgroups

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

subgroupindex
#131238602
#131191442
#131149202
#131127032
C13×#17992
#947013