Finite Group Databasebeta

← #15775129

Subgroups — #15775129

Order 3328.

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

normal subgroups only

This group has 458 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#13113856C212yesmaximal
3#13112859C212yesmaximal, 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#11718695—22no—
12#11718610C2212yes—
13#11718608—21no—
14#11718316—22no—
15#11718307—22no—
16C13×#342C2211yescharacteristic
17#11718129—22no—
18#11718117C2212yes—
19C22×D4×C13—21no—
20C23×C4×C13D411yescharacteristic
21C22×Dic26—21no—
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×C4⋊Dic13D412yes—
34C2×#6101—22no—
35C2×C4×Dic13—21no—
36C2×C4×Dic13—21no—
37C13×#99—42no—
38C13×#95—22no—
39#88072—42no—
40#88071—22no—
41#88071—22no—
42#88071—21no—
43#88071D412yes—
44C22⋊#1055—22no—
45#88048—42no—
46#12122—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×C13SD1612yes—
64C22×C4×C13C2×D412yes—
65C22×Dic13—22no—
66C22×Dic13—22no—
67C2×Dic26—44no—
68C2×Dic26—81no—
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—
78C4⋊Dic13—42no—
79#6101—44no—
80C4×Dic13—81no—
81C4×Dic13—81no—
82C2×#1055—42no—
83#2607—131no—
84#2022D1311yescharacteristic
85#1613—132no—
86#1352—132no—
87#1317—131no—
88C23×C13—21no—
89C23×C13—21no—
90C23×C13—42no—
91C23×C13—41no—
92C23×C13—41no—
93C23×C13—41no—
94C23×C13—82no—
95C23×C13#12011yescharacteristic
96C23×C13C2×SD1611yescharacteristic
97C23×C13#13711yescharacteristic
98D4×C13—82no—
99D4×C13—81no—
100D4×C13—81no—
101D4×C13—81no—
102D4×C13—81no—
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—41no—
111C2×C4×C13—42no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—81no—
116C2×C4×C13—82no—
117C2×Dic13—24no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—42no—
122C2×Dic13—42no—
123Dic26—84no—
124#1055—82no—
125#534C2×D1311yescharacteristic
126C2×#123—21no—
127#481—262no—
128C2×#99—21no—
129#399—132no—
130#393—261no—
131#391—262no—
132#387—262no—
133#381C2×D1311yescharacteristic
134C4×C22⋊C4—261no—
135#342C2×D1311yescharacteristic
136#327—262no—
137#323—132no—
138C22×C13—22no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—41no—
142C22×C13—41no—
143C22×C13—42no—
144C22×C13—81no—
145C22×C13—82no—
146C22×C13—81no—
147C22×C13—82no—
148C22×C13—161no—
149C22×C13#44811yescharacteristic
150C22×C13#45311yescharacteristic
151C22×C13B(4,𝔽2)11yescharacteristic
152C4×C13—42no—
153C4×C13—42no—
154C4×C13—81no—
155C4×C13—82no—
156C4×C13—81no—
157Dic13—44no—
158Dic13—82no—
159C22×Q8—261no—
160C22×D4—21no—
161C23×C4C22⋊D1311yescharacteristic
162#123—42no—
163#123—41no—
164#123—42no—
165#121—22no—
166#120—41no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—132no—
169C2×C4⋊C4—262no—
170C2×C22⋊C4—21no—
171C2×C22⋊C4—41no—
172C2×C22⋊C4—262no—
173C2×C22⋊C4C22⋊D1311yescharacteristic
174C2×C22⋊C4C22×D1311yescharacteristic
175C2×C42—261no—
176C2×C42—261no—
177#106—522no—
178#102—522no—
179#99—42no—
180C22⋊C8—262no—
181#95—22no—
182#95—132no—
183#95—262no—
184#95—261no—
185#95—262no—
186C2×C13—21no—
187C2×C13—21no—
188C2×C13—41no—
189C2×C13—41no—
190C2×C13—161no—
191C2×C13#159611yescharacteristic
192C2×C13#219812yes—
193C24—21no—
194C24C2×C22⋊D1311yescharacteristic
195C2×Q8—524no—
196C2×Q8—1041no—
197C2×D4—22no—
198C2×D4—41no—
199C2×D4—41no—
200C2×D4—41no—
201C2×D4—41no—
202C2×D4—41no—
203C2×D4—41no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—262no—
212C22×C4—262no—
213C22×C4#610512yes—
214C22×C4D4×D1312yes—
215C2×C8—522no—
216C4⋊C4—22no—
217C4⋊C4—44no—
218C4⋊C4—522no—
219C4⋊C4—524no—
220C22⋊C4—22no—
221C22⋊C4—41no—
222C22⋊C4—42no—
223C22⋊C4—44no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C22⋊C4—524no—
227C42—1041no—
228C42—1041no—
229C13#1212211yescharacteristic, complemented, Sylow
230C23—21no—
231C23—21no—
232C23—42no—
233C23—41no—
234C23—41no—
235C23—41no—
236C23—82no—
237C23C2×#610511yescharacteristic
238C23#8819111yescharacteristic
239C23#8820511yescharacteristic
240Q8—1044no—
241D4—82no—
242D4—81no—
243D4—81no—
244D4—81no—
245D4—81no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—81no—
259C2×C4—82no—
260C2×C4—264no—
261C2×C4—522no—
262C2×C4—522no—
263C2×C4—522no—
264C2×C4—522no—
265C2×C4—522no—
266C8—1042no—
267C22—22no—
268C22—21no—
269C22—21no—
270C22—41no—
271C22—41no—
272C22—42no—
273C22—81no—
274C22—82no—
275C22—81no—
276C22—82no—
277C22—161no—
278C22#1171869311yescharacteristic
279C22#1171870111yescharacteristic
280C22#1171873811yescharacteristic
281C4—42no—
282C4—42no—
283C4—81no—
284C4—82no—
285C4—81no—
286C4—524no—
287C4—1042no—
288C2—21no—
289C2—21no—
290C2—41no—
291C2—41no—
292C2—161no—
293C2#1311375811yescharacteristic
294C2#1311683012yes—
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#12122
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. #13112859C2semidirect
4. #13112766C2semidirect
229. C13#12122semidirect

Maximal subgroups

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

subgroupindex
#131205012
#131138562
#131128592
#131127662
C13×#20222
#1212213