Finite Group Databasebeta

← #15766172

Subgroups — #15766172

Order 3328.

542 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 75 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#13123089C211yesmaximal, characteristic
2#13114910C212yesmaximal
3#13112740C212yesmaximal
4#13112740C211yesmaximal, characteristic
5C13×#1819C211yesmaximal, characteristic
6C22×C13×C22⋊C4C2211yescharacteristic
7C13×#379C2211yescharacteristic
8C13×#379C2211yescharacteristic
9#11718908C2212yes—
10#11718908C2212yes—
11#11718608—22no—
12#11718608—24no—
13C13×#342—22no—
14#11718118—24no—
15C25×C13C2311yescharacteristic
16C23×C4×C13Q812yescomplemented
17C22×Dic26—22no—
18C2×C13×C22⋊C4—21no—
19C2×C13×C22⋊C4—22no—
20C2×C13×C22⋊C4—21no—
21C2×C13×C22⋊C4—22no—
22C2×C13×C22⋊C4—21no—
23C2×C13×C22⋊C4—22no—
24C2×C13×C22⋊C4—22no—
25C2×C13×C22⋊C4D412yes—
26C2×C22⋊Dic13—22no—
27C2×C22⋊Dic13—22no—
28C2×C22⋊Dic13—22no—
29C2×C22⋊Dic13—22no—
30C2×C22⋊Dic13—22no—
31C2×C22⋊Dic13D414yes—
32#88071—26no—
33#10391—131nomaximal, Sylow
34C24×C13—42no—
35C24×C13—82no—
36C24×C13C2×D412yes—
37C24×C13C2×D411yescharacteristic
38C24×C13C2×Q811yescharacteristic
39C24×C13#4111yescharacteristic
40C24×C13#4112yes—
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13—41no—
46C22×C4×C13—82no—
47C22×Dic13—24no—
48C22×Dic13—42no—
49C2×Dic26—84no—
50C2×Dic26—82no—
51C13×C22⋊C4—41no—
52C13×C22⋊C4—42no—
53C13×C22⋊C4—41no—
54C13×C22⋊C4—42no—
55C13×C22⋊C4—42no—
56C13×C22⋊C4—82no—
57C13×C22⋊C4—82no—
58C22⋊Dic13—44no—
59C22⋊Dic13—44no—
60C22⋊Dic13—82no—
61C22⋊Dic13—82no—
62C22⋊Dic13—82no—
63C22⋊Dic13—82no—
64#2840—131no—
65#1819—132no—
66#1819D1311yescharacteristic
67#1304—132no—
68#1304—131no—
69C23×C13—24no—
70C23×C13—22no—
71C23×C13—42no—
72C23×C13—41no—
73C23×C13—42no—
74C23×C13—42no—
75C23×C13—42no—
76C23×C13—42no—
77C23×C13—42no—
78C23×C13—42no—
79C23×C13—41no—
80C23×C13—42no—
81C23×C13—88no—
82C23×C13#12011yescharacteristic
83C23×C13C22⋊Q812yes—
84C23×C13C22⋊Q811yescharacteristic
85C23×C13#12412yes—
86C23×C13#12411yescharacteristic
87C2×C4×C13—44no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—82no—
91C2×C4×C13—82no—
92C2×C4×C13—82no—
93C2×C4×C13—81no—
94C2×C4×C13—82no—
95C2×Dic13—44no—
96C2×Dic13—44no—
97C2×Dic13—44no—
98C2×Dic13—82no—
99C2×Dic13—82no—
100C2×Dic13—82no—
101Dic26—88no—
102C22×C22⋊C4C2×D1311yescharacteristic
103#393—264no—
104#393—262no—
105#379—132no—
106#379—132no—
107#379C2×D1311yescharacteristic
108#379C2×D1311yescharacteristic
109#342—22no—
110#342—264no—
111C22×C13—22no—
112C22×C13—22no—
113C22×C13—21no—
114C22×C13—22no—
115C22×C13—21no—
116C22×C13—22no—
117C22×C13—22no—
118C22×C13—22no—
119C22×C13—22no—
120C22×C13—22no—
121C22×C13—22no—
122C22×C13—44no—
123C22×C13—84no—
124C22×C13—82no—
125C22×C13—82no—
126C22×C13—84no—
127C22×C13#39311yescharacteristic
128C22×C13#45812yes—
129C4×C13—82no—
130C4×C13—82no—
131C4×C13—161no—
132Dic13—84no—
133Dic13—162no—
134C25C22×D1311yescharacteristic
135C22×Q8—262no—
136C23×C4Dic2612yescomplemented
137C2×C22⋊C4—21no—
138C2×C22⋊C4—22no—
139C2×C22⋊C4—22no—
140C2×C22⋊C4—21no—
141C2×C22⋊C4—21no—
142C2×C22⋊C4—22no—
143C2×C22⋊C4—22no—
144C2×C22⋊C4—134no—
145C2×C22⋊C4—262no—
146C2×C22⋊C4—262no—
147C2×C22⋊C4—262no—
148C2×C22⋊C4—262no—
149C2×C22⋊C4—262no—
150C2×C22⋊C4C22⋊D1312yes—
151#95—266no—
152C2×C13—22no—
153C2×C13—42no—
154C2×C13—41no—
155C2×C13—42no—
156C2×C13—41no—
157C2×C13#203011yescharacteristic
158C2×C13#203212yes—
159C24—42no—
160C24—82no—
161C24C2×Dic2611yescharacteristic
162C24#612711yescharacteristic
163C24D4×D1312yes—
164C24#612912yes—
165C24C2×C22⋊D1311yescharacteristic
166C2×Q8—1044no—
167C2×Q8—1042no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—41no—
173C22×C4—82no—
174C22×C4—264no—
175C22×C4—522no—
176C22⋊C4—42no—
177C22⋊C4—41no—
178C22⋊C4—41no—
179C22⋊C4—42no—
180C22⋊C4—42no—
181C22⋊C4—82no—
182C22⋊C4—82no—
183C22⋊C4—524no—
184C22⋊C4—524no—
185C22⋊C4—1042no—
186C22⋊C4—1042no—
187C22⋊C4—1042no—
188C22⋊C4—1042no—
189C13#1039111yescharacteristic, complemented, Sylow
190C23—22no—
191C23—24no—
192C23—42no—
193C23—41no—
194C23—42no—
195C23—42no—
196C23—42no—
197C23—42no—
198C23—42no—
199C23—42no—
200C23—41no—
201C23—42no—
202C23—88no—
203C23#8813212yes—
204C23#8813912yes—
205C23#8817811yescharacteristic
206C23#8819011yescharacteristic
207C23#8819111yescharacteristic
208Q8—1048no—
209C2×C4—44no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—82no—
213C2×C4—82no—
214C2×C4—82no—
215C2×C4—81no—
216C2×C4—82no—
217C2×C4—524no—
218C2×C4—524no—
219C2×C4—524no—
220C2×C4—1042no—
221C2×C4—1042no—
222C2×C4—1042no—
223C22—22no—
224C22—21no—
225C22—22no—
226C22—22no—
227C22—21no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—44no—
235C22—82no—
236C22—84no—
237C22—84no—
238C22—82no—
239C22#1171860811yescharacteristic
240C22#1171871412yes—
241C4—82no—
242C4—82no—
243C4—161no—
244C4—1044no—
245C4—2082no—
246C2—22no—
247C2—41no—
248C2—42no—
249C2—42no—
250C2—41no—
251C2#1311600311yescharacteristic
252C2#1311601312yes—
subgroupG/H
centerC22#11718608
commutator, prime radical, cosocleC25×C13C23
FrattiniC25C22×D13
FittingC13×#1819C2
socleC22×C13#393
hypercenter#1819D13
hypocenterC13#10391
LCSG ▷ C25×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
16. C23×C4×C13Q8semidirect
136. C23×C4Dic26semidirect
189. C13#10391semidirect

Maximal subgroups

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

subgroupindex
#131230892
#131149102
#131127402
C13×#18192
#1039113