Finite Group Databasebeta

← #15763512

Subgroups — #15763512

Order 3328.

632 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#11718704C212yesmaximal
2C2×#11718130C212yesmaximal
3#13113103C211yesmaximal, characteristic
4#13112679C211yesmaximal, characteristic
5C13×#2659C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2212yes—
7C22×C4⋊Dic13C2211yescharacteristic
8C13×#398—22no—
9C13×#395—22no—
10C13×#380—22no—
11C2×C13×#95C2211yescharacteristic
12C2×#88075—22no—
13C2×#88071—22no—
14C2×#88071C2211yescharacteristic
15C2×C22⋊#1055C2212yes—
16#11718704—24no—
17#11718704—24no—
18C2×#88048—22no—
19#11718130—24no—
20C22×Q8×C13D412yes—
21C23×C4×C13D412yes—
22C23×C4×C13C2311yescharacteristic
23C23×Dic13—21no—
24C23×Dic13—21no—
25C13×C22⋊Q8—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—22no—
28C13×C22⋊Q8—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4D412yes—
33C2×C13×C22⋊C4—22no—
34C2×C4⋊Dic13—22no—
35C2×C4⋊Dic13—22no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13D412yes—
38C22×#1055—22no—
39C13×#95—24no—
40C13×#95—22no—
41#88075—28no—
42#88071—22no—
43#88071—44no—
44C22⋊#1055—22no—
45C22⋊#1055D414yes—
46#88048—28no—
47#9973—131nomaximal, Sylow
48C24×C13C2×D411yescharacteristic
49C2×Q8×C13—22no—
50C2×Q8×C13—22no—
51C2×Q8×C13—44no—
52C22×C4×C13—22no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—42no—
57C22×C4×C13—42no—
58C22×C4×C13—42no—
59C22×C4×C13SD1614yes—
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D412yes—
62C22×C4×C13C2×D412yes—
63C22×C4×C13#4111yescharacteristic
64C22×Dic13—22no—
65C22×Dic13—22no—
66C22×Dic13—41no—
67C22×Dic13—42no—
68C22×Dic13—41no—
69C22×Dic13—41no—
70C22×Dic13—41no—
71C22×Dic13—42no—
72C22×Dic13—42no—
73C22×Dic13—42no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—22no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—42no—
78C13×C4⋊C4—82no—
79C13×C4⋊C4—82no—
80C13×C22⋊C4—42no—
81C13×C22⋊C4—42no—
82C4⋊Dic13—24no—
83C4⋊Dic13—42no—
84C2×#1055—24no—
85C2×#1055—44no—
86C2×#483—132no—
87#2659D1311yescharacteristic
88C2×#328—132no—
89#1445—131no—
90#1280—131no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—22no—
94C23×C13#12011yescharacteristic
95C23×C13#12111yescharacteristic
96C23×C13#12711yescharacteristic
97C23×C13C2×SD1612yes—
98C23×C13#13712yes—
99Q8×C13—44no—
100Q8×C13—82no—
101C2×C4×C13—24no—
102C2×C4×C13—24no—
103C2×C4×C13—41no—
104C2×C4×C13—42no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—44no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—44no—
114C2×C4×C13—82no—
115C2×C4×C13#12012yes—
116C2×C4×C13#12112yes—
117C2×Dic13—44no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—44no—
121C2×Dic13—82no—
122C2×Dic13—81no—
123C2×Dic13—82no—
124C2×Dic13—81no—
125C2×Dic13—81no—
126C2×Dic13—81no—
127#1055—44no—
128C2×C22⋊Q8C2×D1312yes—
129C22×C4⋊C4—131no—
130#483—264no—
131#483—264no—
132C2×#106—262no—
133C2×#103—262no—
134C2×C22⋊C8—132no—
135#398—22no—
136#395—22no—
137#380—22no—
138C2×#95—131no—
139C2×#95—262no—
140C2×#95C2×D1311yescharacteristic
141#328—264no—
142C22×C13—22no—
143C22×C13—22no—
144C22×C13—22no—
145C22×C13—22no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13#39211yescharacteristic
151C22×C13#44812yes—
152C22×C13#45511yescharacteristic
153C22×C13#45611yescharacteristic
154C22×C13#45812yes—
155C22×C13#46112yes—
156C22×C13#49211yescharacteristic
157C22×C13#49711yescharacteristic
158C4×C13—22no—
159C4×C13—22no—
160C4×C13—44no—
161C4×C13—82no—
162C4×C13—82no—
163Dic13—82no—
164Dic13—82no—
165C22×Q8C22⋊D1312yes—
166C23×C4—261no—
167C23×C4—261no—
168C23×C4C22⋊D1312yes—
169C23×C4C22×D1311yescharacteristic
170C22×C8—262no—
171C22⋊Q8—22no—
172C22⋊Q8—22no—
173C22⋊Q8—22no—
174C22⋊Q8—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—132no—
179C2×C4⋊C4—262no—
180C2×C4⋊C4—262no—
181C2×C4⋊C4—261no—
182C2×C4⋊C4C22⋊D1312yes—
183C2×C22⋊C4—22no—
184#106—268no—
185#103—268no—
186C22⋊C8—134no—
187C22⋊C8—262no—
188#95—24no—
189#95—22no—
190#95—262no—
191#95—524no—
192C2×C13—21no—
193C2×C13—22no—
194C2×C13—21no—
195C2×C13#160812yes—
196C2×C13#161112yes—
197C2×C13#200711yescharacteristic
198C2×C13#201311yescharacteristic
199C2×C13#202211yescharacteristic
200C24C2×C22⋊D1311yescharacteristic
201C2×Q8—22no—
202C2×Q8—22no—
203C2×Q8—44no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—262no—
212C22×C4—262no—
213C22×C4—521no—
214C22×C4—522no—
215C22×C4—521no—
216C22×C4—521no—
217C22×C4—522no—
218C22×C4—522no—
219C22×C4—522no—
220C22×C4—521no—
221C22×C4#610614yes—
222C22×C4D4×D1311yescharacteristic
223C22×C4D4×D1312yes—
224C22×C4#612911yescharacteristic
225C22×C4C2×C22⋊D1312yes—
226C2×C8—264no—
227C2×C8—524no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—82no—
233C4⋊C4—82no—
234C4⋊C4—264no—
235C4⋊C4—522no—
236C22⋊C4—42no—
237C22⋊C4—42no—
238C13#997311yescharacteristic, complemented, Sylow
239C23—21no—
240C23—22no—
241C23—21no—
242C23#8819211yescharacteristic
243C23#8819411yescharacteristic
244C23C2×#610612yes—
245C23#8819612yes—
246C23#8820711yescharacteristic
247Q8—44no—
248Q8—82no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—44no—
261C2×C4—42no—
262C2×C4—82no—
263C2×C4—522no—
264C2×C4—524no—
265C2×C4—524no—
266C2×C4—522no—
267C2×C4—1041no—
268C2×C4—1042no—
269C2×C4—1041no—
270C2×C4—1041no—
271C2×C4—1041no—
272C2×C4—1042no—
273C2×C4#8819112yes—
274C2×C4#8819312yes—
275C8—524no—
276C22—21no—
277C22—21no—
278C22—22no—
279C22—22no—
280C22—21no—
281C22—21no—
282C22—22no—
283C22—22no—
284C22#1171874412yes—
285C22#1171874611yescharacteristic
286C22#1171874711yescharacteristic
287C22#1171888411yescharacteristic
288C22#1171888812yes—
289C22#1171890311yescharacteristic
290C22#1171890412yes—
291C22#1171890711yescharacteristic
292C4—22no—
293C4—22no—
294C4—44no—
295C4—82no—
296C4—82no—
297C4—1042no—
298C4—1042no—
299C2—21no—
300C2—22no—
301C2—21no—
302C2#1311382712yes—
303C2#1311384412yes—
304C2#1311588311yescharacteristic
305C2#1311591911yescharacteristic
306C2#1311596511yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#2659C2
socleC23×C13#120
prime radicalC24×C13C2×D4
hypercenter#2659D13
hypocenterC13#9973
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2659

Complements

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

NH ≅ G/Ntype
238. C13#9973semidirect

Maximal subgroups

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

subgroupindex
C2×#117187042
C2×#117181302
#131131032
#131126792
C13×#26592
#997313