Finite Group Databasebeta

← #15758977

Subgroups — #15758977

Order 3328.

516 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 115 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#13120649C211yesmaximal, characteristic
2#13113407C212yesmaximal
3C2×#11718120C211yesmaximal, characteristic
4#13112703C212yesmaximal
5C13×#2313C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88178C2211yescharacteristic
8C13×#387—24no—
9C13×#381—21no—
10C13×#380C2212yes—
11C4×C13×C22⋊C4—21no—
12#11718873C2211yescharacteristic
13#11718872—21no—
14#11718871—21no—
15C2×C22⋊#1055C2212yes—
16#11718647C412yescomplemented
17#11718645—22no—
18#11718640C412yescomplemented
19#11718120—22no—
20#11718044—24no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C22×Dic26C2×C411yescharacteristic
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C13×C4⋊C4D412yes—
30C2×C13×C22⋊C4—22no—
31C2×C42×C13—22no—
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36#88178—22no—
37#88178—22no—
38C2×#6101—21no—
39C2×#6101—22no—
40C22×#1055—22no—
41C13×#95—22no—
42C13×#95—24no—
43C13×#95D414yes—
44#88071—22no—
45#88071—22no—
46#88071—22no—
47#88071C2×C412yes—
48C22⋊#1055—22no—
49C22⋊#1055—22no—
50#9202—131nomaximal, Sylow
51C24×C13C2×D411yescharacteristic
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—21no—
58C22×C4×C13—24no—
59C22×C4×C13—81no—
60C22×C4×C13—81no—
61C22×C4×C13C22⋊C412yes—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13C22×C411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13C2×D412yes—
66C22×C4×C13#4112yes—
67C22×Dic13—21no—
68C22×Dic13—22no—
69C22×Dic13—21no—
70C2×Dic26—22no—
71C2×Dic26—81no—
72C13×C4⋊C4—24no—
73C13×C4⋊C4—24no—
74C13×C4⋊C4—82no—
75C13×C22⋊C4—42no—
76C13×C22⋊C4—42no—
77C42×C13—82no—
78C22⋊Dic13—41no—
79C22⋊Dic13—41no—
80C22⋊Dic13—42no—
81C4⋊Dic13—22no—
82C4⋊Dic13—81no—
83#6101—42no—
84#6101—82no—
85C2×#1055—42no—
86C2×#1055—82no—
87#2627—131no—
88#2313D1311yescharacteristic
89#1520—132no—
90C2×#324—131no—
91#1289—132no—
92C23×C13—41no—
93C23×C13—41no—
94C23×C13C2×C22⋊C411yescharacteristic
95C23×C13#12011yescharacteristic
96C23×C13#12311yescharacteristic
97C23×C13#13512yes—
98C23×C13#13712yes—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—42no—
104C2×C4×C13—41no—
105C2×C4×C13—42no—
106C2×C4×C13—41no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—44no—
112C2×C4×C13—44no—
113C2×C4×C13—44no—
114C2×C4×C13—81no—
115C2×C4×C13C4×D412yes—
116C2×C4×C13#12112yes—
117C2×Dic13—42no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—42no—
124Dic26—82no—
125#1055—82no—
126C2×C22⋊Q8—131no—
127C22×C4⋊C4C2×D1311yescharacteristic
128C2×C22⋊C8—132no—
129#400—132no—
130#398—262no—
131#395—132no—
132#387—24no—
133#385—261no—
134#381—21no—
135#381—261no—
136#380—131no—
137#380C2×D1312yes—
138C4×C22⋊C4—21no—
139#328—264no—
140#324—262no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—21no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—42no—
148C22×C13—42no—
149C22×C13#38611yescharacteristic
150C22×C13#41611yescharacteristic
151C22×C13#41911yescharacteristic
152C22×C13#45212yes—
153C22×C13#48512yes—
154C4×C13—22no—
155C4×C13—22no—
156C4×C13—42no—
157C4×C13—42no—
158C4×C13—84no—
159Dic13—82no—
160Dic13—81no—
161Dic13—81no—
162C22×Q8—131no—
163C23×C4C22⋊D1311yescharacteristic
164C23×C4C22⋊D1311yescharacteristic
165C23×C4C22×D1311yescharacteristic
166C22×C8—262no—
167C22⋊Q8—262no—
168C22⋊Q8—262no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—131no—
173C2×C4⋊C4—261no—
174C2×C4⋊C4—262no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4C4×D1312yes—
177C2×C4⋊C4D5212yes—
178C2×C22⋊C4—22no—
179C2×C22⋊C4—261no—
180C2×C22⋊C4—261no—
181C2×C42—22no—
182C22⋊C8—262no—
183C22⋊C8—262no—
184#95—22no—
185#95—24no—
186#95—132no—
187#95—262no—
188#95—262no—
189#95—262no—
190#95C22⋊D1314yes—
191C2×C13—21no—
192C2×C13—22no—
193C2×C13—21no—
194C2×C13—22no—
195C2×C13#187311yescharacteristic
196C2×C13#191211yescharacteristic
197C2×C13#191311yescharacteristic
198C24C2×C22⋊D1311yescharacteristic
199C2×Q8—262no—
200C2×Q8—1041no—
201C22×C4—21no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—24no—
208C22×C4—81no—
209C22×C4—81no—
210C22×C4—262no—
211C22×C4—261no—
212C22×C4—261no—
213C22×C4#610312yes—
214C22×C4#610312yes—
215C22×C4C2×C4×D1311yescharacteristic
216C22×C4C2×D5211yescharacteristic
217C22×C4#612712yes—
218C22×C4C2×C22⋊D1312yes—
219C2×C8—522no—
220C2×C8—1042no—
221C4⋊C4—24no—
222C4⋊C4—24no—
223C4⋊C4—82no—
224C4⋊C4—262no—
225C4⋊C4—522no—
226C4⋊C4—1042no—
227C4⋊C4—1041no—
228C22⋊C4—42no—
229C22⋊C4—42no—
230C22⋊C4—521no—
231C22⋊C4—522no—
232C22⋊C4—521no—
233C42—82no—
234C13#920211yescharacteristic, complemented, Sylow
235C23—41no—
236C23—41no—
237C23C2×#610311yescharacteristic
238C23#8818311yescharacteristic
239C23#8820412yes—
240C23#8820512yes—
241C23#8820711yescharacteristic
242Q8—1042no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—44no—
257C2×C4—44no—
258C2×C4—81no—
259C2×C4—522no—
260C2×C4—522no—
261C2×C4—522no—
262C2×C4—522no—
263C2×C4—522no—
264C2×C4—521no—
265C2×C4—521no—
266C2×C4C4×C22⋊D1312yes—
267C2×C4#8818412yes—
268C8—1042no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—42no—
276C22—42no—
277C22#1171865712yes—
278C22#1171866311yescharacteristic
279C22#1171866511yescharacteristic
280C22#1171887411yescharacteristic
281C22#1171890012yes—
282C4—22no—
283C4—22no—
284C4—42no—
285C4—42no—
286C4—84no—
287C4—1042no—
288C4—1041no—
289C4—1041no—
290C2—22no—
291C2—21no—
292C2—22no—
293C2—21no—
294C2#1311514811yescharacteristic
295C2#1311537311yescharacteristic
296C2#1311537811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2313C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2313D13
hypocenterC13#9202
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
16. #11718647C4semidirect
18. #11718640C4semidirect
234. C13#9202semidirect

Maximal subgroups

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

subgroupindex
#131206492
#131134072
C2×#117181202
#131127032
C13×#23132
#920213