Finite Group Databasebeta

← #15758682

Subgroups — #15758682

Order 3328.

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

normal subgroups only

This group has 586 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#13123175C211yesmaximal, characteristic
2C2×#11718598C211yesmaximal, characteristic
3C2×#11718059C212yesmaximal
4#13112716C212yesmaximal
5C13×#1817C211yesmaximal, characteristic
6C22×C42×C13C2211yescharacteristic
7C2×#88178C2211yescharacteristic
8C2×C13×C22⋊C8C2212yes—
9#11718873C2211yescharacteristic
10#11718872—21no—
11#11718871—21no—
12C2×#88071—21no—
13C2×#88071—21no—
14C2×#88071C2212yes—
15#11718598—24no—
16#11718594—22no—
17#11718590C412yescomplemented
18#11718589C412yescomplemented
19C13×#336—22no—
20#11718059—24no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C23×Dic13—22no—
25C22×Dic26C2×C411yescharacteristic
26C22×C8×C13—22no—
27C2×C42×C13—22no—
28C2×C42×C13—22no—
29C2×C42×C13C2×C412yes—
30C2×C42×C13D412yes—
31C2×C22⋊Dic13—21no—
32C2×C22⋊Dic13—21no—
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13C2×C412yes—
35#88178—22no—
36#88178—22no—
37C2×#6101—22no—
38C2×#6101—21no—
39C13×C22⋊C8—22no—
40C13×C22⋊C8—22no—
41#88071—24no—
42#88071—24no—
43#88071—22no—
44#88071—22no—
45#88071—22no—
46#88071—21no—
47#88071—22no—
48#88071D414yes—
49#9153—131nomaximal, Sylow
50C24×C13C2×D411yescharacteristic
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—42no—
58C22×C4×C13—42no—
59C22×C4×C13C22⋊C412yes—
60C22×C4×C13C22⋊C412yes—
61C22×C4×C13C22×C411yescharacteristic
62C22×C4×C13C2×D412yes—
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13#4112yes—
65C22×Dic13—22no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13—24no—
69C22×Dic13—44no—
70C22×Dic13—44no—
71C22×Dic13—42no—
72C22×Dic13—42no—
73C2×Dic26—22no—
74C2×Dic26—42no—
75C2×C8×C13—44no—
76C2×C8×C13—42no—
77C42×C13—24no—
78C42×C13—24no—
79C22⋊Dic13—41no—
80C22⋊Dic13—41no—
81C22⋊Dic13—42no—
82C4⋊Dic13—22no—
83C4⋊Dic13—42no—
84#6101—44no—
85#6101—42no—
86#2855—131no—
87C2×#383—131no—
88#1817D1311yescharacteristic
89C2×#328—132no—
90#1294—132no—
91C23×C13—22no—
92C23×C13—22no—
93C23×C13C2×C22⋊C411yescharacteristic
94C23×C13#12011yescharacteristic
95C23×C13#12311yescharacteristic
96C23×C13#13512yes—
97C23×C13#13712yes—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13C4×D412yes—
113C2×C4×C13#12112yes—
114C2×Dic13—44no—
115C2×Dic13—44no—
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13—44no—
124C2×Dic13—84no—
125C2×Dic13—84no—
126Dic26—82no—
127C8×C13—82no—
128C2×C22⋊Q8—131no—
129C22×C42C2×D1311yescharacteristic
130C2×C22⋊C8C2×D1312yes—
131#391—132no—
132#389—132no—
133#387—262no—
134#385—261no—
135#383—264no—
136#381—261no—
137#380—131no—
138C2×#95—132no—
139C2×#95—261no—
140C2×#95—261no—
141#336—22no—
142#328—264no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—24no—
148C22×C13—24no—
149C22×C13#38611yescharacteristic
150C22×C13#41012yes—
151C22×C13#41611yescharacteristic
152C22×C13#41911yescharacteristic
153C22×C13#42112yes—
154C22×C13#45212yes—
155C22×C13#48512yes—
156C4×C13—22no—
157C4×C13—22no—
158C4×C13—42no—
159C4×C13—42no—
160Dic13—84no—
161Dic13—81no—
162Dic13—81no—
163Dic13—82no—
164C22×Q8—131no—
165C23×C4—262no—
166C23×C4D5211yescharacteristic
167C23×C4D5211yescharacteristic
168C23×C4C22×D1311yescharacteristic
169C22×C8—22no—
170C22⋊Q8—262no—
171C22⋊Q8—262no—
172C2×C4⋊C4—131no—
173C2×C4⋊C4—132no—
174C2×C4⋊C4—262no—
175C2×C4⋊C4—261no—
176C2×C22⋊C4—261no—
177C2×C22⋊C4—261no—
178C2×C42—22no—
179C2×C42—22no—
180C2×C42C4×D1312yes—
181C2×C42C22⋊D1312yes—
182C22⋊C8—22no—
183C22⋊C8—22no—
184#95—134no—
185#95—264no—
186#95—264no—
187#95—262no—
188#95—262no—
189#95—262no—
190#95—262no—
191#95—261no—
192C2×C13—22no—
193C2×C13—22no—
194C2×C13#151512yes—
195C2×C13#152112yes—
196C2×C13#187311yescharacteristic
197C2×C13#189711yescharacteristic
198C2×C13#189911yescharacteristic
199C24C2×D5211yescharacteristic
200C2×Q8—262no—
201C2×Q8—522no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—264no—
211C22×C4—262no—
212C22×C4—261no—
213C22×C4—261no—
214C22×C4—524no—
215C22×C4—524no—
216C22×C4—522no—
217C22×C4—522no—
218C22×C4#610312yes—
219C22×C4#610312yes—
220C22×C4C2×C4×D1311yescharacteristic
221C22×C4D4×D1312yes—
222C22×C4#612912yes—
223C22×C4C2×C22⋊D1311yescharacteristic
224C2×C8—44no—
225C2×C8—42no—
226C4⋊C4—262no—
227C4⋊C4—522no—
228C4⋊C4—524no—
229C4⋊C4—522no—
230C22⋊C4—521no—
231C22⋊C4—521no—
232C22⋊C4—522no—
233C42—24no—
234C42—24no—
235C13#915311yescharacteristic, complemented, Sylow
236C23—22no—
237C23—22no—
238C23#8813611yescharacteristic
239C23#8814011yescharacteristic
240C23#8815812yes—
241C23#8816312yes—
242C23C2×#610311yescharacteristic
243Q8—1042no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—524no—
259C2×C4—524no—
260C2×C4—522no—
261C2×C4—522no—
262C2×C4—522no—
263C2×C4—522no—
264C2×C4—522no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4—524no—
268C2×C4—1044no—
269C2×C4—1044no—
270C2×C4#8813512yes—
271C2×C4#8819312yes—
272C8—82no—
273C22—24no—
274C22—24no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22#1171838412yes—
280C22#1171839412yes—
281C22#1171861911yescharacteristic
282C22#1171866712yes—
283C22#1171877411yescharacteristic
284C22#1171878111yescharacteristic
285C22#1171880012yes—
286C4—22no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—1044no—
291C4—1042no—
292C4—1041no—
293C4—1041no—
294C2—22no—
295C2—22no—
296C2#1311338812yes—
297C2#1311341412yes—
298C2#1311514611yescharacteristic
299C2#1311528211yescharacteristic
300C2#1311529211yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1817C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#1817D13
hypocenterC13#9153
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1817

Complements

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

NH ≅ G/Ntype
17. #11718590C4semidirect
18. #11718589C4semidirect
235. C13#9153semidirect

Maximal subgroups

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

subgroupindex
#131231752
C2×#117185982
C2×#117180592
#131127162
C13×#18172
#915313