Finite Group Databasebeta

← #15775124

Subgroups — #15775124

Order 3328.

470 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 59 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#13120501C211yesmaximal, characteristic, complemented
2#13113788C212yesmaximal
3#13112856C212yesmaximal, complemented
4#13112766C211yesmaximal, characteristic, complemented
5C13×#2022C211yesmaximal, characteristic
6C13×#534C2211yescharacteristic
7C2×C13×#123—21no—
8C2×C13×#99—21no—
9C13×#381C2211yescharacteristic
10C4×C22⋊Dic13—21no—
11#11718701—22no—
12#11718610—21no—
13#11718608C2212yes—
14#11718316—22no—
15#11718307—22no—
16C13×#342C2211yescharacteristic
17#11718129—22no—
18#11718117C2212yes—
19C22×D4×C13—21no—
20C23×C4×C13D411yescharacteristic
21C22×Dic26D412yes—
22C13×#123—42no—
23C13×#123—41no—
24C13×#123—42no—
25C13×#121—22no—
26C13×#120—41no—
27C2×C13×C4⋊C4—41no—
28C2×C13×C22⋊C4—21no—
29C2×C13×C22⋊C4—41no—
30C2×C13×C22⋊C4D411yescharacteristic
31C2×C13×C22⋊C4C2311yescharacteristic
32C2×C22⋊Dic13—22no—
33C2×#6105—42no—
34C2×C4⋊Dic13—21no—
35C2×#6101—22no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C13×#99—42no—
39C13×#95—22no—
40#88071—21no—
41#88071—22no—
42#88071—22no—
43#88071D412yes—
44C22⋊#1055—22no—
45#88050—42no—
46#12121—131nomaximal, Sylow
47C24×C13—21no—
48C24×C13C2×D411yescharacteristic
49C2×D4×C13—22no—
50C2×D4×C13—41no—
51C2×D4×C13—41no—
52C2×D4×C13—41no—
53C2×D4×C13—41no—
54C2×D4×C13—41no—
55C2×D4×C13—41no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—41no—
61C22×C4×C13—41no—
62C22×C4×C13—41no—
63C22×C4×C13SD1612yescomplemented
64C22×C4×C13C2×D412yes—
65C22×Dic13—22no—
66C22×Dic13—22no—
67C2×Dic26—42no—
68C2×Dic26—44no—
69C13×C4⋊C4—22no—
70C13×C4⋊C4—44no—
71C13×C22⋊C4—22no—
72C13×C22⋊C4—41no—
73C13×C22⋊C4—42no—
74C13×C22⋊C4—44no—
75C13×C22⋊C4—41no—
76C13×C22⋊C4—41no—
77C22⋊Dic13—44no—
78#6105—84no—
79C4⋊Dic13—81no—
80#6101—44no—
81C4×Dic13—81no—
82C4×Dic13—81no—
83C2×#1055—42no—
84#2607—131no—
85#2022D1311yescharacteristic
86#1601—132no—
87#1351—132no—
88#1317—131no—
89C23×C13—21no—
90C23×C13—21no—
91C23×C13—42no—
92C23×C13—41no—
93C23×C13—41no—
94C23×C13—41no—
95C23×C13—82no—
96C23×C13#12011yescharacteristic
97C23×C13C2×SD1611yescharacteristic
98C23×C13#13711yescharacteristic
99D4×C13—82no—
100D4×C13—81no—
101D4×C13—81no—
102D4×C13—81no—
103D4×C13—81no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—81no—
117C2×C4×C13—82no—
118C2×Dic13—24no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124Dic26—44no—
125Dic26—82no—
126#1055—82no—
127#534C2×D1311yescharacteristic
128C2×#123—21no—
129#448—262no—
130C2×#99—21no—
131#399—261no—
132#393—132no—
133#391—262no—
134#387—262no—
135#381C2×D1311yescharacteristic
136C4×C22⋊C4—261no—
137#342C2×D1311yescharacteristic
138#327—262no—
139#323—132no—
140C22×C13—22no—
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—41no—
144C22×C13—41no—
145C22×C13—42no—
146C22×C13—81no—
147C22×C13—82no—
148C22×C13—81no—
149C22×C13—82no—
150C22×C13—161no—
151C22×C13#44811yescharacteristic
152C22×C13#45311yescharacteristic
153C22×C13B(4,𝔽2)11yescharacteristic
154C4×C13—42no—
155C4×C13—42no—
156C4×C13—81no—
157C4×C13—82no—
158C4×C13—81no—
159Dic13—44no—
160Dic13—82no—
161C22×Q8—132no—
162C22×D4—21no—
163C23×C4C22⋊D1311yescharacteristic
164C2×SD16—522no—
165#123—42no—
166#123—41no—
167#123—42no—
168#121—22no—
169#120—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—262no—
172C2×C4⋊C4—261no—
173C2×C22⋊C4—21no—
174C2×C22⋊C4—41no—
175C2×C22⋊C4—262no—
176C2×C22⋊C4C22⋊D1311yescharacteristic
177C2×C22⋊C4C22×D1311yescharacteristic
178C2×C42—261no—
179C2×C42—261no—
180#103—522no—
181#99—42no—
182C22⋊C8—262no—
183#95—22no—
184#95—132no—
185#95—262no—
186#95—261no—
187#95—262no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13—41no—
191C2×C13—41no—
192C2×C13—161no—
193C2×C13#159611yescharacteristic
194C2×C13#219712yes—
195C24—21no—
196C24C2×C22⋊D1311yescharacteristic
197C2×Q8—522no—
198C2×Q8—524no—
199C2×D4—22no—
200C2×D4—41no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4—41no—
205C2×D4—41no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—262no—
214C22×C4—262no—
215C22×C4#610512yescomplemented
216C22×C4D4×D1312yes—
217SD16—1044no—
218C2×C8—522no—
219C4⋊C4—22no—
220C4⋊C4—44no—
221C4⋊C4—524no—
222C4⋊C4—1041no—
223C22⋊C4—22no—
224C22⋊C4—41no—
225C22⋊C4—42no—
226C22⋊C4—44no—
227C22⋊C4—41no—
228C22⋊C4—41no—
229C22⋊C4—524no—
230C42—1041no—
231C42—1041no—
232C13#1212111yescharacteristic, complemented, Sylow
233C23—21no—
234C23—21no—
235C23—42no—
236C23—41no—
237C23—41no—
238C23—41no—
239C23—82no—
240C23C2×#610511yescharacteristic
241C23#8819111yescharacteristic
242C23#8820511yescharacteristic
243Q8—524no—
244Q8—1042no—
245D4—82no—
246D4—81no—
247D4—81no—
248D4—81no—
249D4—81no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—81no—
263C2×C4—82no—
264C2×C4—264no—
265C2×C4—522no—
266C2×C4—522no—
267C2×C4—522no—
268C2×C4—522no—
269C2×C4—522no—
270C8—1042no—
271C22—22no—
272C22—21no—
273C22—21no—
274C22—41no—
275C22—41no—
276C22—42no—
277C22—81no—
278C22—82no—
279C22—82no—
280C22—81no—
281C22—161no—
282C22#1171869311yescharacteristic
283C22#1171870111yescharacteristic
284C22#1171873811yescharacteristic
285C4—42no—
286C4—42no—
287C4—81no—
288C4—82no—
289C4—81no—
290C4—524no—
291C4—1042no—
292C2—21no—
293C2—21no—
294C2—41no—
295C2—41no—
296C2—161no—
297C2#1311375811yescharacteristic
298C2#1311682312yes—
subgroupG/H
centerC22#11718693
commutator, cosocleC2×C13×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2022C2
socleC22×C13B(4,𝔽2)
prime radicalC13×#534C22
hypercenter#2022D13
hypocenterC13#12121
LCSG ▷ C2×C13×C22⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2022

Complements

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

NH ≅ G/Ntype
1. #13120501C2semidirect
3. #13112856C2semidirect
4. #13112766C2semidirect
63. C22×C4×C13SD16semidirect
215. C22×C4#6105semidirect
232. C13#12121semidirect

Maximal subgroups

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

subgroupindex
#131205012
#131137882
#131128562
#131127662
C13×#20222
#1212113