Finite Group Databasebeta

← #15760771

Subgroups — #15760771

Order 3328.

542 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 127 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#13123917C211yesmaximal, characteristic, complemented
2#13119741C211yesmaximal, characteristic
3#13113260C212yesmaximal
4#13112696C212yesmaximal, complemented
5C13×#1801C211yesmaximal, characteristic, complemented
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88200—21no—
8C2×C4×D52C2211yescharacteristic
9C13×#423C2212yes—
10C2×C13×#101—21no—
11Q8×#1055—24no—
12#11718652C412yes—
13#11718648—21no—
14#11718644C412yes—
15#11718601—22no—
16#11718597C2211yescharacteristic
17#11718586—22no—
18#11718586C2212yes—
19C13×#343—21no—
20#11718075—24no—
21C22×Q8×C13D411yescharacteristic
22C22×D52C2×C411yescharacteristic
23C22×C4×D13—21no—
24C2×C13×M16—22no—
25C4×Q8×C13—22no—
26C4×Q8×C13—22no—
27C2×C13×C4⋊C4C2×C412yes—
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C42×C13D412yes—
30C2×C42×C13C2311yescharacteristic
31#88200—42no—
32#88200—42no—
33C2×#6103—22no—
34C2×#6103—22no—
35C2×#6103—21no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×#6101—22no—
39C4×D52—22no—
40C4×D52—22no—
41C13×C4⋊C8—22no—
42C13×C4⋊C8—22no—
43C13×#101—42no—
44#88071—22no—
45#88071—21no—
46#88071C2×C412yes—
47C22⋊#1055—22no—
48C4⋊#1055—24no—
49C4⋊#1055—22no—
50C4×#1055—24no—
51C4×#1055D414yes—
52#9486—131nomaximal, Sylow
53C23×D13—21no—
54C2×Q8×C13—22no—
55C2×Q8×C13—22no—
56C2×Q8×C13D812yes—
57C2×Q8×C13SD1612yes—
58C22×C4×C13C22⋊C412yes—
59C22×C4×C13C22⋊C412yes—
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×Dic13—22no—
64C22×Dic13—21no—
65C2×D52—22no—
66C2×D52—42no—
67C2×C4×D13—42no—
68C2×C4×D13—41no—
69C2×C4×D13—41no—
70C2×C4×D13—42no—
71C13×M16—42no—
72C13×M16—42no—
73C2×C8×C13—42no—
74C13×C4⋊C4—24no—
75C13×C4⋊C4—22no—
76C42×C13—22no—
77C42×C13—22no—
78C42×C13C2×D412yes—
79C42×C13#4112yes—
80#6103—44no—
81#6103—44no—
82#6103—41no—
83#6103—41no—
84C4⋊Dic13—22no—
85C4⋊Dic13—41no—
86C4⋊Dic13—41no—
87#6101—44no—
88C2×#1055—24no—
89#2982—131no—
90#2536—131no—
91#1801D1311yescharacteristic, complemented
92#1486—132no—
93#1286—132no—
94C23×C13C2×C22⋊C411yescharacteristic
95C22×D13—22no—
96C22×D13—41no—
97C22×D13—41no—
98C22×D13—41no—
99C22×D13—41no—
100C22×D13—41no—
101C22×D13—41no—
102Q8×C13—24no—
103Q8×C13—24no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—42no—
110C2×C4×C13#10214yes—
111C2×C4×C13C4×D412yes—
112C2×C4×C13#12011yescharacteristic
113C2×C4×C13#12112yes—
114C2×C4×C13#12311yescharacteristic
115C2×C4×C13C2×D811yescharacteristic
116C2×C4×C13C2×SD1611yescharacteristic
117C2×C4×C13#13512yes—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—42no—
123C2×Dic13—41no—
124D52—24no—
125D52—42no—
126C4×D13—82no—
127C4×D13—82no—
128C8×C13—82no—
129#1055—44no—
130C2×C22⋊Q8—261no—
131C2×C4×Q8C2×D1311yescharacteristic
132C2×C4×D4—131no—
133C8×Q8—264no—
134#431—132no—
135#431—262no—
136#423C2×D1312yes—
137C2×#101—21no—
138#398—132no—
139#394—132no—
140#388—262no—
141#382—131no—
142#380—261no—
143#343—21no—
144D4⋊C8—264no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13#38611yescharacteristic
148C22×C13C2×#10211yescharacteristic
149C22×C13#41611yescharacteristic
150C2×D13—42no—
151C2×D13—42no—
152C2×D13—42no—
153C2×D13—81no—
154C2×D13—81no—
155C2×D13—81no—
156C2×D13—81no—
157C4×C13—22no—
158C4×C13—24no—
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—42no—
162C4×C13#46512yes—
163C4×C13#46612yes—
164Dic13—82no—
165Dic13—81no—
166C22×Q8C22⋊D1311yescharacteristic
167C22×D4—131no—
168C23×C4—261no—
169C2×M16—22no—
170C22⋊Q8—522no—
171C22⋊Q8—522no—
172C4×Q8—22no—
173C4×Q8—22no—
174C4×D4—262no—
175C4×D4—262no—
176C2×C4⋊C4—131no—
177C2×C4⋊C4—262no—
178C2×C4⋊C4—261no—
179C2×C4⋊C4C4×D1312yes—
180C2×C4⋊C4C22⋊D1311yescharacteristic
181C2×C22⋊C4—262no—
182C2×C22⋊C4—262no—
183C2×C22⋊C4—261no—
184C2×C42D5212yes—
185C2×C42C22×D1311yescharacteristic
186C4⋊C8—22no—
187C4⋊C8—22no—
188C4⋊C8—264no—
189C4⋊C8—262no—
190#101—42no—
191C22⋊C8—262no—
192C4×C8—134no—
193C4×C8—264no—
194#95—132no—
195#95—262no—
196#95—261no—
197C2×C13—21no—
198C2×C13—21no—
199C2×C13#189111yescharacteristic
200C2×C13#189311yescharacteristic
201C2×C13#191211yescharacteristic
202D13—82no—
203C24—261no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8#610412yes—
207C2×Q8#610612yes—
208C2×D4—262no—
209C2×D4—522no—
210C22×C4—262no—
211C22×C4—261no—
212C22×C4—521no—
213C22×C4—522no—
214C22×C4—521no—
215C22×C4—522no—
216C22×C4#610312yes—
217C22×C4#610312yes—
218C22×C4C2×C4×D1311yescharacteristic
219C22×C4C2×D5211yescharacteristic
220C22×C4C2×C22⋊D1311yescharacteristic
221M16—42no—
222M16—42no—
223C2×C8—42no—
224C2×C8—264no—
225C4⋊C4—24no—
226C4⋊C4—22no—
227C4⋊C4—262no—
228C4⋊C4—521no—
229C4⋊C4—521no—
230C4⋊C4—524no—
231C22⋊C4—524no—
232C22⋊C4—521no—
233C22⋊C4—521no—
234C22⋊C4—524no—
235C42—22no—
236C42—22no—
237C42D4×D1312yes—
238C42#612912yes—
239C13#948611yescharacteristic, complemented, Sylow
240C23—262no—
241C23—521no—
242C23—521no—
243C23—521no—
244C23—521no—
245C23—521no—
246C23—521no—
247C23C2×#610311yescharacteristic
248Q8—24no—
249Q8—24no—
250D4—264no—
251D4—522no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—522no—
259C2×C4—522no—
260C2×C4—521no—
261C2×C4—521no—
262C2×C4—522no—
263C2×C4—521no—
264C2×C4—1042no—
265C2×C4—1042no—
266C2×C4#8804914yes—
267C2×C4#8813512yes—
268C2×C4#8813611yescharacteristic
269C2×C4#8814011yescharacteristic
270C2×C4C2×#610411yescharacteristic
271C2×C4#8819312yes—
272C2×C4C2×#610611yescharacteristic
273C2×C4#8820412yes—
274C8—82no—
275C8—524no—
276C22—21no—
277C22—21no—
278C22—522no—
279C22—522no—
280C22—522no—
281C22—1041no—
282C22—1041no—
283C22—1041no—
284C22—1041no—
285C22#1171861911yescharacteristic
286C22C2×#8804911yescharacteristic
287C22#1171866311yescharacteristic
288C4—22no—
289C4—24no—
290C4—21no—
291C4—21no—
292C4—42no—
293C4—1042no—
294C4—1041no—
295C4#1171869912yes—
296C4#1171870912yes—
297C2—21no—
298C2—21no—
299C2—1042no—
300C2#1311525211yescharacteristic
301C2#1311526211yescharacteristic
302C2#1311537111yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1801C2
socleC22×C13#386
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1801D13
hypocenterC13#9486
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
1. #13123917C2semidirect
4. #13112696C2semidirect
5. C13×#1801C2semidirect
91. #1801D13semidirect
239. C13#9486semidirect

Maximal subgroups

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

subgroupindex
#131239172
#131197412
#131132602
#131126962
C13×#18012
#948613