Finite Group Databasebeta

← #15757953

Subgroups — #15757953

Order 3328.

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

normal subgroups only

This group has 572 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
1C2×#11718647C211yesmaximal, characteristic
2#13114924C212yesmaximal
3C2×#11718120C211yesmaximal, characteristic
4#13112714C212yesmaximal
5C13×#2313C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C22×C4⋊Dic13C2211yescharacteristic
8C13×#387—24no—
9C13×#381—21no—
10C13×#380C2212yes—
11C4×C13×C22⋊C4—21no—
12C2×#88071—21no—
13C2×#88071—21no—
14C2×#88071C2211yescharacteristic
15C2×C22⋊#1055C2212yes—
16#11718647—22no—
17#11718647C414yescomplemented
18#11718121—24no—
19#11718120—22no—
20C23×C4×C13D411yescharacteristic
21C23×C4×C13D411yescharacteristic
22C23×C4×C13C2311yescharacteristic
23C23×Dic13—21no—
24C23×Dic13—21no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4C2×C412yes—
28C2×C13×C4⋊C4D412yes—
29C2×C13×C4⋊C4D414yes—
30C2×C13×C22⋊C4—22no—
31C2×C42×C13—22no—
32C2×C4⋊Dic13—22no—
33C2×C4⋊Dic13—22no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C412yes—
36C22×#1055—22no—
37C13×#95—22no—
38C13×#95—24no—
39C13×#95—22no—
40#88071—24no—
41#88071—24no—
42#88071—21no—
43#88071C2×C412yes—
44C22⋊#1055—22no—
45C22⋊#1055—22no—
46#9022—131nomaximal, Sylow
47C24×C13C2×D411yescharacteristic
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—21no—
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—21no—
54C22×C4×C13—24no—
55C22×C4×C13—42no—
56C22×C4×C13—42no—
57C22×C4×C13C22⋊C412yes—
58C22×C4×C13C22⋊C412yes—
59C22×C4×C13C22×C411yescharacteristic
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D412yes—
62C22×C4×C13#4112yes—
63C22×Dic13—22no—
64C22×Dic13—22no—
65C22×Dic13—42no—
66C22×Dic13—42no—
67C22×Dic13—44no—
68C22×Dic13—41no—
69C22×Dic13—41no—
70C22×Dic13—42no—
71C13×C4⋊C4—24no—
72C13×C4⋊C4—24no—
73C13×C4⋊C4—44no—
74C13×C22⋊C4—42no—
75C13×C22⋊C4—42no—
76C42×C13—82no—
77C4⋊Dic13—24no—
78C4⋊Dic13—42no—
79C2×#1055—44no—
80C2×#1055—42no—
81C2×#400—131no—
82#2313D1311yescharacteristic
83#1824—132no—
84C2×#324—131no—
85#1294—132no—
86C23×C13—22no—
87C23×C13—22no—
88C23×C13C2×C22⋊C411yescharacteristic
89C23×C13#12011yescharacteristic
90C23×C13#12311yescharacteristic
91C23×C13#13512yes—
92C23×C13#13712yes—
93C2×C4×C13—24no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13—44no—
106C2×C4×C13—44no—
107C2×C4×C13—44no—
108C2×C4×C13—81no—
109C2×C4×C13C4×D412yes—
110C2×C4×C13#12112yes—
111C2×Dic13—42no—
112C2×Dic13—42no—
113C2×Dic13—44no—
114C2×Dic13—42no—
115C2×Dic13—42no—
116C2×Dic13—84no—
117C2×Dic13—82no—
118C2×Dic13—82no—
119#1055—82no—
120C22×C4⋊C4—131no—
121C22×C4⋊C4C2×D1311yescharacteristic
122C2×C22⋊C8—132no—
123#400—134no—
124#400—262no—
125#387—24no—
126#381—21no—
127#380C2×D1312yes—
128C4×C22⋊C4—21no—
129C2×#95—131no—
130C2×#95—261no—
131C2×#95—261no—
132#340—264no—
133#324—262no—
134C22×C13—24no—
135C22×C13—24no—
136C22×C13—21no—
137C22×C13—21no—
138C22×C13—21no—
139C22×C13—21no—
140C22×C13#38611yescharacteristic
141C22×C13#41611yescharacteristic
142C22×C13#41911yescharacteristic
143C22×C13#45212yes—
144C22×C13#45412yes—
145C22×C13#45812yes—
146C22×C13#48512yes—
147C4×C13—22no—
148C4×C13—22no—
149C4×C13—42no—
150C4×C13—42no—
151C4×C13—84no—
152Dic13—82no—
153Dic13—82no—
154C23×C4—261no—
155C23×C4—261no—
156C23×C4C22⋊D1311yescharacteristic
157C23×C4C22⋊D1311yescharacteristic
158C23×C4C22×D1311yescharacteristic
159C22×C8—262no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—132no—
163C2×C4⋊C4—262no—
164C2×C4⋊C4—262no—
165C2×C4⋊C4—261no—
166C2×C4⋊C4C4×D1312yes—
167C2×C4⋊C4D5212yes—
168C2×C4⋊C4C22⋊D1314yes—
169C2×C22⋊C4—22no—
170C2×C42—22no—
171C22⋊C8—262no—
172C22⋊C8—262no—
173#95—22no—
174#95—24no—
175#95—22no—
176#95—132no—
177#95—264no—
178#95—264no—
179#95—261no—
180C2×C13—21no—
181C2×C13—21no—
182C2×C13—22no—
183C2×C13#161514yes—
184C2×C13#187311yescharacteristic
185C2×C13#188811yescharacteristic
186C2×C13#189011yescharacteristic
187C24C2×C22⋊D1311yescharacteristic
188C22×C4—21no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—24no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—262no—
198C22×C4—262no—
199C22×C4—522no—
200C22×C4—522no—
201C22×C4—524no—
202C22×C4—521no—
203C22×C4—522no—
204C22×C4—521no—
205C22×C4#610312yes—
206C22×C4#610312yes—
207C22×C4C2×C4×D1311yescharacteristic
208C22×C4C2×D5211yescharacteristic
209C22×C4#612712yes—
210C22×C4C2×C22⋊D1312yes—
211C2×C8—524no—
212C2×C8—522no—
213C4⋊C4—24no—
214C4⋊C4—24no—
215C4⋊C4—44no—
216C4⋊C4—264no—
217C4⋊C4—522no—
218C22⋊C4—42no—
219C22⋊C4—42no—
220C42—82no—
221C13#902211yescharacteristic, complemented, Sylow
222C23—22no—
223C23—22no—
224C23C2×#610311yescharacteristic
225C23#8818311yescharacteristic
226C23#8820412yes—
227C23#8820512yes—
228C23#8820711yescharacteristic
229C2×C4—24no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—44no—
242C2×C4—44no—
243C2×C4—44no—
244C2×C4—81no—
245C2×C4—522no—
246C2×C4—522no—
247C2×C4—524no—
248C2×C4—522no—
249C2×C4—522no—
250C2×C4—1044no—
251C2×C4—1042no—
252C2×C4—1042no—
253C2×C4C4×C22⋊D1312yes—
254C2×C4#8818412yes—
255C8—1042no—
256C22—24no—
257C22—24no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22#1171865712yes—
263C22#1171866311yescharacteristic
264C22#1171866511yescharacteristic
265C22#1171887411yescharacteristic
266C22#1171890012yes—
267C22#1171890412yes—
268C22#1171890612yes—
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—84no—
274C4—1042no—
275C4—1042no—
276C2—21no—
277C2—22no—
278C2—21no—
279C2#1311386714yes—
280C2#1311514811yescharacteristic
281C2#1311523911yescharacteristic
282C2#1311524911yescharacteristic
subgroupG/H
centerC23#88207
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2313C2
socleC23×C13#120
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2313D13
hypocenterC13#9022
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2313

Complements

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

NH ≅ G/Ntype
17. #11718647C4semidirect
221. C13#9022semidirect

Maximal subgroups

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

subgroupindex
C2×#117186472
#131149242
C2×#117181202
#131127142
C13×#23132
#902213