Finite Group Databasebeta

← #15775037

Subgroups — #15775037

Order 3328.

424 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 67 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#13125611C211yesmaximal, characteristic
2#13116770C212yesmaximal, complemented
3#13112847C212yesmaximal, complemented
4#13112760C211yesmaximal, characteristic
5C13×#2001C211yesmaximal, characteristic
6C22×C13×Q16C2211yescharacteristic
7C2×C13×C22⋊Q8—21no—
8C2×#88178—21no—
9C2×C13×#103—21no—
10C2×C13×C22⋊C8C2211yescharacteristic
11C2×#88069—22no—
12#11718777—21no—
13#11718777C2212yes—
14#11718400—22no—
15#11718383—22no—
16C13×#340C2211yescharacteristic
17#11718156—22no—
18C22⋊#6090C2212yes—
19C22×Q8×C13—21no—
20C23×C4×C13D411yescharacteristic
21C22×Dic26—21no—
22C2×C13×Q16—22no—
23C2×C13×Q16—42no—
24C22×C8×C13D411yescharacteristic
25C22×C8×C13C2311yescharacteristic
26C13×C22⋊Q8—42no—
27C13×C22⋊Q8—42no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—41no—
30C2×C13×C22⋊C4—41no—
31C2×C22⋊Dic13—41no—
32C2×C4⋊Dic13—21no—
33#88178—22no—
34#88178—22no—
35#88178—41no—
36#88178—41no—
37C2×#6101—41no—
38C2×Dic52—21no—
39C2×Dic52D412yes—
40C13×#103—42no—
41C13×C22⋊C8—22no—
42#88069—44no—
43#88058—21no—
44#88058D412yes—
45#88056—22no—
46#88056—22no—
47C2×#6090—22no—
48#12106—131nomaximal, Sylow
49C24×C13D811yescharacteristic
50C2×Q8×C13—22no—
51C2×Q8×C13—41no—
52C2×Q8×C13—41no—
53C2×Q8×C13—41no—
54C2×Q8×C13—41no—
55C2×Q8×C13—41no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—41no—
59C22×C4×C13—41no—
60C22×C4×C13—41no—
61C22×C4×C13—41no—
62C22×C4×C13D811yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13—41no—
65C22×Dic13—41no—
66C2×Dic26—22no—
67C2×Dic26—41no—
68C2×Dic26—81no—
69C2×Dic26—81no—
70C13×Q16—24no—
71C13×Q16—42no—
72C2×C8×C13—21no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C2×C8×C13C2×D412yes—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—44no—
79C13×C22⋊C4—44no—
80C22⋊Dic13—42no—
81C22⋊Dic13—42no—
82C4⋊Dic13—22no—
83C4⋊Dic13—41no—
84#6101—42no—
85#6101—42no—
86Dic52—42no—
87Dic52—81no—
88#6090—42no—
89#3189—131no—
90#2188—132no—
91#2001D1311yescharacteristic
92#1348—132no—
93#1314—131no—
94C23×C13—21no—
95C23×C13—21no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13Q3212yescomplemented
99C23×C13C2×D811yescharacteristic
100Q8×C13—42no—
101Q8×C13—42no—
102Q8×C13—81no—
103Q8×C13—81no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—81no—
113C2×C4×C13—81no—
114C2×C4×C13—81no—
115C2×C4×C13—81no—
116C2×C4×C13—81no—
117C2×C4×C13#12011yescharacteristic
118C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13—82no—
122C2×Dic13—82no—
123Dic26—42no—
124Dic26—42no—
125Dic26—82no—
126C8×C13—22no—
127C8×C13—41no—
128C22×Q16C2×D1311yescharacteristic
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—261no—
131C2×Q32—262no—
132#484—262no—
133#467—132no—
134#467—261no—
135#451—262no—
136C2×#103—21no—
137C2×C22⋊C8C2×D1311yescharacteristic
138#358—262no—
139C22⋊C16—132no—
140#340C2×D1311yescharacteristic
141C22×C13—21no—
142C22×C13—21no—
143C22×C13—22no—
144C22×C13—42no—
145C22×C13—41no—
146C22×C13—41no—
147C22×C13—81no—
148C22×C13#44711yescharacteristic
149C22×C13C2×Q3211yescharacteristic
150C22×C13#51011yescharacteristic
151C4×C13—21no—
152C4×C13—41no—
153C4×C13—82no—
154C4×C13—82no—
155C4×C13#45311yescharacteristic
156C4×C13B(4,𝔽2)11yescharacteristic
157Dic13—82no—
158Dic13—82no—
159C22×Q8—21no—
160C22×Q8—261no—
161C23×C4C22⋊D1311yescharacteristic
162C2×Q16—22no—
163C2×Q16—42no—
164C2×Q16—132no—
165C2×Q16—261no—
166C22×C8C22⋊D1311yescharacteristic
167C22×C8C22×D1311yescharacteristic
168C22⋊Q8—42no—
169C22⋊Q8—42no—
170C22⋊Q8—262no—
171C22⋊Q8—262no—
172C22⋊Q8—521no—
173C22⋊Q8—521no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—41no—
176C2×C4⋊C4—261no—
177C2×C4⋊C4—521no—
178C2×C22⋊C4—41no—
179C2×C22⋊C4—521no—
180Q32—524no—
181C2×C16—262no—
182#107—132no—
183#107—261no—
184#103—42no—
185#103—262no—
186#103—262no—
187C22⋊C8—22no—
188C2×C13—21no—
189C2×C13—21no—
190C2×C13—42no—
191C2×C13#159511yescharacteristic
192C2×C13#218811yescharacteristic
193C2×C13#219111yescharacteristic
194C24#610411yescharacteristic
195C2×Q8—22no—
196C2×Q8—41no—
197C2×Q8—41no—
198C2×Q8—41no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8—262no—
202C2×Q8—521no—
203C2×Q8—1041no—
204C2×Q8—1041no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—521no—
212C22×C4—521no—
213C22×C4#610411yescharacteristic
214C22×C4C2×C22⋊D1311yescharacteristic
215Q16—24no—
216Q16—42no—
217Q16—522no—
218Q16—1041no—
219C2×C8—21no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8D4×D1312yes—
223C4⋊C4—22no—
224C4⋊C4—41no—
225C4⋊C4—44no—
226C4⋊C4—262no—
227C4⋊C4—521no—
228C4⋊C4—522no—
229C4⋊C4—522no—
230C22⋊C4—44no—
231C22⋊C4—522no—
232C22⋊C4—522no—
233C16—522no—
234C13#1210611yescharacteristic, complemented, Sylow
235C23—21no—
236C23—21no—
237C23—41no—
238C23—41no—
239C23#8806912yescomplemented
240C23C2×#610411yescharacteristic
241Q8—42no—
242Q8—42no—
243Q8—81no—
244Q8—81no—
245Q8—522no—
246Q8—522no—
247Q8—1042no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—522no—
262C2×C4—522no—
263C2×C4—1042no—
264C2×C4—1042no—
265C2×C4#8819111yescharacteristic
266C2×C4#8820311yescharacteristic
267C8—22no—
268C8—41no—
269C22—21no—
270C22—21no—
271C22—22no—
272C22—42no—
273C22—41no—
274C22—41no—
275C22—81no—
276C22#1171869711yescharacteristic
277C22C2×#8806911yescharacteristic
278C22#1171885611yescharacteristic
279C4—21no—
280C4—41no—
281C4—82no—
282C4—82no—
283C4—1042no—
284C4—1042no—
285C4#1171869311yescharacteristic
286C4#1171873811yescharacteristic
287C2—21no—
288C2—21no—
289C2—42no—
290C2#1311375311yescharacteristic
291C2#1311676911yescharacteristic
292C2#1311678611yescharacteristic
subgroupG/H
centerC22#11718697
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC13×#2001C2
socleC22×C13#447
prime radicalC24×C13D8
hypercenter#2001D13
hypocenterC13#12106
LCSG ▷ C22×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8 ◁ #2001

Complements

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

NH ≅ G/Ntype
2. #13116770C2semidirect
3. #13112847C2semidirect
98. C23×C13Q32semidirect
234. C13#12106semidirect
239. C23#88069semidirect

Maximal subgroups

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

subgroupindex
#131256112
#131167702
#131128472
#131127602
C13×#20012
#1210613