Finite Group Databasebeta

← #15763546

Subgroups — #15763546

Order 3328.

492 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 85 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#13124780C212yesmaximal
2#13114905C211yesmaximal, characteristic
3#13113200C212yesmaximal
4#13112713C211yesmaximal, characteristic
5C13×#3189C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2212yes—
7C2×#88180C2211yescharacteristic
8C13×#484—22no—
9C13×#467—22no—
10C13×#451—22no—
11C2×C13×C22⋊C8C2211yescharacteristic
12#11718886—22no—
13#11718868C2212yes—
14C2×C22⋊#1055C2211yescharacteristic
15#11718706—24no—
16#11718705—22no—
17#11718704—22no—
18#11718625—22no—
19#11718142—22no—
20#11718120—24no—
21C22×Q8×C13D412yes—
22C23×C4×C13C2311yescharacteristic
23C2×C13×Q16—22no—
24C22×C8×C13D412yes—
25C13×C22⋊Q8—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—22no—
28C13×C22⋊Q8—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4D412yes—
31C2×C13×C22⋊C4—22no—
32C2×C22⋊Dic13—21no—
33#88180—22no—
34#88180—22no—
35C2×C4⋊Dic13D411yescharacteristic
36C2×C4⋊Dic13D411yescharacteristic
37C2×C4×Dic13—21no—
38C2×#6099—22no—
39C22×#1055—21no—
40C13×#107—22no—
41C13×#103—24no—
42C13×C22⋊C8—22no—
43#88075—24no—
44#88075—24no—
45C22⋊#1055—22no—
46C22⋊#1055—22no—
47C22⋊#1055D414yes—
48#88048—24no—
49#88047—24no—
50#9979—131nomaximal, Sylow
51C24×C13#4111yescharacteristic
52C2×Q8×C13—22no—
53C2×Q8×C13—22no—
54C2×Q8×C13—44no—
55C22×C4×C13—22no—
56C22×C4×C13—22no—
57C22×C4×C13—42no—
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D412yes—
60C22×C4×C13C2×D412yes—
61C22×C4×C13C2×D411yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C13×Q16—82no—
65C2×C8×C13—22no—
66C2×C8×C13—42no—
67C13×C4⋊C4—22no—
68C13×C4⋊C4—22no—
69C13×C4⋊C4—42no—
70C13×C4⋊C4—42no—
71C13×C22⋊C4—42no—
72C13×C22⋊C4—42no—
73C22⋊Dic13—42no—
74C4⋊Dic13—22no—
75C4⋊Dic13—22no—
76C4×Dic13—41no—
77C4×Dic13—41no—
78#6099—44no—
79C2×#1055—24no—
80C2×#1055—42no—
81C2×#1055—41no—
82#3189D1311yescharacteristic
83#3095—132no—
84#1818—131no—
85#1472—132no—
86#1293—131no—
87C23×C13—22no—
88C23×C13—41no—
89C23×C13—41no—
90C23×C13#12112yes—
91C23×C13#12111yescharacteristic
92Q8×C13—44no—
93Q8×C13—44no—
94C2×C4×C13—22no—
95C2×C4×C13—24no—
96C2×C4×C13—41no—
97C2×C4×C13—42no—
98C2×C4×C13—44no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—82no—
102C2×C4×C13#12012yes—
103C2×C4×C13#12011yescharacteristic
104C2×C4×C13#12711yescharacteristic
105C2×Dic13—42no—
106C2×Dic13—41no—
107C2×Dic13—41no—
108C2×Dic13—42no—
109C8×C13—42no—
110#1055—44no—
111#1055—81no—
112C2×C22⋊Q8C2×D1312yes—
113C2×#117—131no—
114#485—264no—
115#484—22no—
116#484—262no—
117#483—262no—
118#467—22no—
119#451—22no—
120#428—262no—
121#419—262no—
122#407—132no—
123C2×C22⋊C8—131no—
124C2×C22⋊C8C2×D1311yescharacteristic
125#336—262no—
126#324—264no—
127C22×C13—21no—
128C22×C13—21no—
129C22×C13—22no—
130C22×C13—22no—
131C22×C13—22no—
132C22×C13—82no—
133C22×C13#39211yescharacteristic
134C22×C13#47312yes—
135C4×C13—22no—
136C4×C13—21no—
137C4×C13—82no—
138C4×C13—82no—
139C4×C13#45812yes—
140Dic13—81no—
141Dic13—81no—
142C22×Q8C22⋊D1312yes—
143C23×C4C22×D1311yescharacteristic
144C2×Q16—22no—
145C2×M16—262no—
146C22×C8—261no—
147C22×C8C22⋊D1312yes—
148C22⋊Q8—22no—
149C22⋊Q8—22no—
150C22⋊Q8—22no—
151C22⋊Q8—22no—
152#117—262no—
153#117—262no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—131no—
156C2×C4⋊C4—131no—
157C2×C4⋊C4C22⋊D1312yes—
158C2×C22⋊C4—22no—
159C2×C22⋊C4—261no—
160C2×C42—261no—
161#107—22no—
162#107—264no—
163#106—264no—
164#103—24no—
165#103—264no—
166#103—264no—
167C22⋊C8—22no—
168C22⋊C8—134no—
169C22⋊C8—262no—
170C22⋊C8—262no—
171C2×C13—22no—
172C2×C13—42no—
173C2×C13#201711yescharacteristic
174C2×C13#202011yescharacteristic
175C2×C13#202211yescharacteristic
176C24#612911yescharacteristic
177C2×Q8—22no—
178C2×Q8—22no—
179C2×Q8—44no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—42no—
183C22×C4—261no—
184C22×C4—261no—
185C22×C4D4×D1311yescharacteristic
186C22×C4D4×D1312yes—
187C22×C4C2×C22⋊D1312yes—
188C22×C4C2×C22⋊D1311yescharacteristic
189Q16—82no—
190M16—524no—
191C2×C8—22no—
192C2×C8—42no—
193C2×C8—264no—
194C2×C8—522no—
195C2×C8—521no—
196C4⋊C4—22no—
197C4⋊C4—22no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—262no—
201C4⋊C4—262no—
202C22⋊C4—42no—
203C22⋊C4—42no—
204C22⋊C4—522no—
205C42—521no—
206C42—521no—
207C13#997911yescharacteristic, complemented, Sylow
208C23—22no—
209C23—41no—
210C23—41no—
211C23#8819211yescharacteristic
212C23#8819312yes—
213Q8—44no—
214Q8—44no—
215C2×C4—22no—
216C2×C4—24no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—44no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—82no—
223C2×C4—522no—
224C2×C4—522no—
225C2×C4—521no—
226C2×C4—521no—
227C2×C4#8819112yes—
228C2×C4#8819411yescharacteristic
229C2×C4#8820711yescharacteristic
230C8—42no—
231C8—524no—
232C8—1041no—
233C22—21no—
234C22—21no—
235C22—22no—
236C22—22no—
237C22—22no—
238C22—82no—
239C22#1171885312yes—
240C22#1171888411yescharacteristic
241C4—22no—
242C4—21no—
243C4—82no—
244C4—82no—
245C4—1041no—
246C4—1041no—
247C4#1171890412yes—
248C2—22no—
249C2—42no—
250C2#1311593911yescharacteristic
251C2#1311595511yescharacteristic
252C2#1311596511yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#3189C2
socleC22×C13#392
prime radicalC24×C13#41
hypercenter#3189D13
hypocenterC13#9979
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
207. C13#9979semidirect

Maximal subgroups

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

subgroupindex
#131247802
#131149052
#131132002
#131127132
C13×#31892
#997913