Finite Group Databasebeta

← #15760466

Subgroups — #15760466

Order 3328.

422 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 99 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#13125378C211yesmaximal, characteristic
2#13113553C211yesmaximal, characteristic
3#13113386C211yesmaximal, characteristic
4#13113386C211yesmaximal, characteristic
5#13112700C211yesmaximal, characteristic
6#13112700C211yesmaximal, characteristic
7C13×#2381C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9#11719175C2211yescharacteristic
10C13×#391—22no—
11C13×#387—22no—
12C13×#387—22no—
13C13×#383C2211yescharacteristic
14C13×#383C2211yescharacteristic
15#11718741—22no—
16#11718740C412yescomplemented
17#11718739C412yescomplemented
18#11718625—22no—
19#11718587C2211yescharacteristic
20#11718587C2211yescharacteristic
21C4×#6099C2211yescharacteristic
22#11718139—22no—
23#11718044—22no—
24#11718044—22no—
25C22×Q8×C13—21no—
26C13×C4⋊Q8—21no—
27C13×C4⋊Q8—21no—
28C13×C4⋊Q8C2×C412yes—
29C13×C4⋊Q8D412yes—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4D412yes—
33C2×C42×C13—22no—
34C2×C42×C13C2311yescharacteristic
35#88180—21no—
36#88178—21no—
37#88178—21no—
38C2×#6099—21no—
39#88124—21no—
40#88123C2×C411yescharacteristic
41#88123C2×C411yescharacteristic
42C4×Dic26—21no—
43C4×Dic26—21no—
44C13×#95—24no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95D412yes—
50C13×#95D412yes—
51C22⋊#1055—21no—
52C22⋊#1055—21no—
53#88048—24no—
54#88047—24no—
55C4⋊#1055—21no—
56C4⋊#1055—21no—
57#88043—21no—
58#88043—21no—
59#88043—21no—
60C4×#1055C2×C412yes—
61#9427—131nomaximal, Sylow
62C2×Q8×C13—22no—
63C2×Q8×C13—22no—
64C2×Q8×C13—81no—
65C2×Q8×C13—81no—
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C2×Dic26—21no—
73C2×Dic26—21no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—22no—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—82no—
78C13×C4⋊C4C22⋊C414yes—
79C42×C13—82no—
80C42×C13C22×C411yescharacteristic
81C42×C13C2×D411yescharacteristic
82C42×C13#4111yescharacteristic
83C42×C13#4111yescharacteristic
84C22⋊Dic13—41no—
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89#6101—41no—
90#6101—41no—
91C4×Dic13—41no—
92#6099—24no—
93C2×#1055—22no—
94C2×#1055—41no—
95C2×#1055—41no—
96#3165—131no—
97#2381D1311yescharacteristic
98#1556—131no—
99#1515—131no—
100#1515—131no—
101#1288—131no—
102#1288—131no—
103C23×C13#12011yescharacteristic
104Q8×C13—82no—
105Q8×C13—82no—
106C2×C4×C13—22no—
107C2×C4×C13—24no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13C2×C22⋊C411yescharacteristic
119C2×C4×C13C4×D411yescharacteristic
120C2×C4×C13C4×D411yescharacteristic
121C2×C4×C13#12111yescharacteristic
122C2×C4×C13#12111yescharacteristic
123C2×C4×C13#12311yescharacteristic
124C2×Dic13—41no—
125C2×Dic13—41no—
126Dic26—81no—
127Dic26—81no—
128#1055—24no—
129#1055—81no—
130#1055—81no—
131#533—131no—
132C2×C4⋊Q8C2×D1311yescharacteristic
133#501—262no—
134#500—132no—
135#498—132no—
136#432—131no—
137#432—131no—
138#428—262no—
139C4×M16—131no—
140#391—22no—
141#387—22no—
142#387—22no—
143#383C2×D1311yescharacteristic
144#383C2×D1311yescharacteristic
145#332—262no—
146#328—262no—
147#328—262no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13#38611yescharacteristic
151C22×C13#45612yes—
152C4×C13—21no—
153C4×C13—21no—
154C4×C13—21no—
155C4×C13—21no—
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—44no—
159C4×C13—82no—
160C4×C13—82no—
161Dic13—81no—
162Dic13—81no—
163C22×Q8—21no—
164C2×M16—261no—
165C4⋊Q8—21no—
166C4⋊Q8—21no—
167C4⋊Q8—131no—
168C4⋊Q8—131no—
169C4⋊Q8C4×D1312yes—
170C4⋊Q8D5212yes—
171#125—261no—
172C22⋊Q8—261no—
173C22⋊Q8—261no—
174C4×Q8—261no—
175C4×Q8—261no—
176#117—261no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4C22⋊D1312yes—
180C2×C42—22no—
181C2×C42C22×D1311yescharacteristic
182#107—264no—
183#106—264no—
184C4⋊C8—261no—
185C4⋊C8—261no—
186C22⋊C8—261no—
187C22⋊C8—261no—
188#97—261no—
189#97—261no—
190#97—261no—
191C4×C8—132no—
192#95—24no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95C22⋊D1312yes—
198#95C22⋊D1312yes—
199C2×C13—22no—
200C2×C13#188611yescharacteristic
201C2×C13#190411yescharacteristic
202C2×C13#190511yescharacteristic
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—81no—
206C2×Q8—81no—
207C2×Q8—261no—
208C2×Q8—261no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—22no—
212C22×C4C2×C22⋊D1311yescharacteristic
213C22×C4C2×C22⋊D1311yescharacteristic
214C22×C4C2×C22⋊D1311yescharacteristic
215M16—264no—
216C2×C8—262no—
217C2×C8—521no—
218C2×C8—521no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4—22no—
222C4⋊C4—82no—
223C4⋊C4—261no—
224C4⋊C4—261no—
225C4⋊C4—261no—
226C4⋊C4—261no—
227C4⋊C4—521no—
228C4⋊C4—521no—
229C4⋊C4#610314yes—
230C22⋊C4—521no—
231C42—82no—
232C42—521no—
233C42C2×C4×D1311yescharacteristic
234C42C2×D5211yescharacteristic
235C42#612711yescharacteristic
236C42#612711yescharacteristic
237C13#942711yescharacteristic, complemented, Sylow
238C23#8820711yescharacteristic
239Q8—82no—
240Q8—82no—
241Q8—1041no—
242Q8—1041no—
243C2×C4—22no—
244C2×C4—24no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—521no—
256C2×C4—521no—
257C2×C4C2×#610311yescharacteristic
258C2×C4C4×C22⋊D1311yescharacteristic
259C2×C4C4×C22⋊D1311yescharacteristic
260C2×C4#8818311yescharacteristic
261C2×C4#8818411yescharacteristic
262C2×C4#8818411yescharacteristic
263C8—264no—
264C8—1041no—
265C8—1041no—
266C22—21no—
267C22—21no—
268C22#1171887411yescharacteristic
269C22#1171890712yes—
270C4—21no—
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—44no—
277C4—82no—
278C4—82no—
279C4—1041no—
280C4—1041no—
281C2—22no—
282C2#1311522911yescharacteristic
283C2#1311532311yescharacteristic
284C2#1311533011yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2381C2
socleC22×C13#386
prime radicalC23×C13#120
cosocleC2×C42×C13C23
hypercenter#2381D13
hypocenterC13#9427
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2381

Complements

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

NH ≅ G/Ntype
16. #11718740C4semidirect
17. #11718739C4semidirect
237. C13#9427semidirect

Maximal subgroups

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

subgroupindex
#131253782
#131135532
#131133862
#131127002
C13×#23812
#942713