Finite Group Databasebeta

← #16784689

Subgroups — #16784689

Order 3328.

456 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 102 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#13130621C211yesmaximal, characteristic
2#13130553C211yesmaximal, characteristic
3C2×#11718242C214yesmaximal
4#13123197C211yesmaximal, characteristic
5C2×#88144C2212yes—
6C2×#88112—21no—
7C2×#88110C2212yes—
8C2×#88110C2212yes—
9C13×#384C411yescharacteristic
10#11718646—21no—
11#11718646—21no—
12#11718638C412yes—
13#11718634—21no—
14#11718634—21no—
15#11718596C411yescharacteristic
16C42×Dic13C2211yescharacteristic
17#11718290—21no—
18#11718290—21no—
19#11718290—21no—
20#11718242—28no—
21C22×#1057—22no—
22C22×#1057—22no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—21no—
25C2×C13×C4⋊C4C2×C412yes—
26C2×C42×C13C2×C411yescharacteristic
27C2×C4⋊Dic13—21no—
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13—22no—
30C2×C4⋊Dic13C2×C412yes—
31C2×#6101—22no—
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13D411yescharacteristic
34C2×C4×Dic13D411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13D411yescharacteristic
37C2×C4×Dic13C2311yescharacteristic
38#88144—24no—
39#88144—24no—
40#88112—24no—
41#88110—24no—
42#88110—22no—
43#88110D414yes—
44#88071—22no—
45#88071—22no—
46#9690—131nomaximal, Sylow
47C22×C4×C13—22no—
48C22×C4×C13C22⋊C411yescharacteristic
49C22×C4×C13C22⋊C411yescharacteristic
50C22×C4×C13C22×C411yescharacteristic
51C22×Dic13—22no—
52C22×Dic13C22⋊C411yescharacteristic
53C22×Dic13C22⋊C411yescharacteristic
54C22×Dic13C2×D411yescharacteristic
55C22×Dic13C2×D411yescharacteristic
56C2×#1057—24no—
57C2×#1057—24no—
58C2×#1057—42no—
59C2×#1057—42no—
60C2×#1057—42no—
61C2×#1057—42no—
62C13×C4⋊C4—24no—
63C13×C4⋊C4—42no—
64C13×C4⋊C4—42no—
65C42×C13—22no—
66C4⋊Dic13—24no—
67C4⋊Dic13—42no—
68C4⋊Dic13—42no—
69C4⋊Dic13—44no—
70#6101—42no—
71#6101—42no—
72C4×Dic13—22no—
73C4×Dic13—22no—
74C4×Dic13—41no—
75C4×Dic13—41no—
76C4×Dic13—41no—
77C4×Dic13C2×D412yes—
78C4×Dic13#4112yes—
79#2859—131no—
80#1767—131no—
81#1745—131no—
82C2×#330—134no—
83C23×C13C2×C22⋊C411yescharacteristic
84C2×C4×C13—21no—
85C2×C4×C13—21no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13#10112yes—
94C2×C4×C13#10412yes—
95C2×C4×C13C4×D412yes—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—21no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108C2×Dic13#10112yes—
109C2×Dic13#12112yes—
110C2×Dic13#12411yescharacteristic
111C2×Dic13#12711yescharacteristic
112#1057—44no—
113#1057—44no—
114C2×#125—132no—
115C2×C4⋊C8—261no—
116C2×#97—132no—
117C2×#97—132no—
118#389—261no—
119#389—261no—
120#389—261no—
121#389—261no—
122#384—131no—
123#384#26111yescharacteristic
124#382—132no—
125C43—131no—
126#336—261no—
127#336—261no—
128#336—261no—
129#330—268no—
130C22×C13#39011yescharacteristic
131C22×C13C2×#10111yescharacteristic
132C22×C13C2×#10111yescharacteristic
133C22×C13C2×#10411yescharacteristic
134C22×C13#42111yescharacteristic
135C22×C13#42111yescharacteristic
136C22×C13#42111yescharacteristic
137C4×C13—22no—
138C4×C13—22no—
139C4×C13—22no—
140C4×C13—82no—
141Dic13—22no—
142Dic13—21no—
143Dic13—21no—
144Dic13—22no—
145Dic13—41no—
146Dic13—82no—
147C22×C8—262no—
148C22×C8—262no—
149#125—264no—
150#125—264no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—132no—
154C2×C4⋊C4—262no—
155C2×C4⋊C4—262no—
156C2×C4⋊C4—261no—
157C2×C4⋊C4—261no—
158C2×C4⋊C4C2×#26112yes—
159C2×C42—131no—
160C2×C42—131no—
161C2×C42—131no—
162C2×C42—131no—
163C2×C42—131no—
164C2×C42—131no—
165C2×C42C2×#26111yescharacteristic
166C4⋊C8—264no—
167#97—134no—
168#97—262no—
169#97—264no—
170#95—262no—
171#95—262no—
172C2×C13#152811yescharacteristic
173C2×C13#153111yescharacteristic
174C2×C13#153411yescharacteristic
175C2×C13#153711yescharacteristic
176C2×C13#196311yescharacteristic
177C2×C13#196611yescharacteristic
178C2×C13#198011yescharacteristic
179C22×C4—22no—
180C22×C4—131no—
181C22×C4—131no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—262no—
185C22×C4C22⋊#26111yescharacteristic
186C22×C4C22⋊#26111yescharacteristic
187C22×C4C22×#26111yescharacteristic
188C2×C8—264no—
189C2×C8—264no—
190C2×C8—522no—
191C2×C8—522no—
192C2×C8—522no—
193C2×C8—522no—
194C4⋊C4—24no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—264no—
198C4⋊C4—522no—
199C4⋊C4—522no—
200C4⋊C4—522no—
201C4⋊C4—522no—
202C4⋊C4—524no—
203C42—22no—
204C42—132no—
205C42—132no—
206C42—262no—
207C42—262no—
208C42—521no—
209C42—521no—
210C42—521no—
211C13#969011yescharacteristic, complemented, Sylow
212C23C2×C22⋊#26111yescharacteristic
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—132no—
223C2×C4—131no—
224C2×C4—131no—
225C2×C4—132no—
226C2×C4—261no—
227C2×C4—261no—
228C2×C4—261no—
229C2×C4—261no—
230C2×C4—261no—
231C2×C4—261no—
232C2×C4—261no—
233C2×C4—261no—
234C2×C4—261no—
235C2×C4—522no—
236C2×C4—522no—
237C2×C4—522no—
238C2×C4#8811312yes—
239C2×C4#8811612yes—
240C2×C4D4×#26112yes—
241C8—524no—
242C8—524no—
243C22C2×#8811311yescharacteristic
244C22C2×#8811611yescharacteristic
245C22#1171914011yescharacteristic
246C22#1171915111yescharacteristic
247C22#1171915511yescharacteristic
248C22#1171915511yescharacteristic
249C22D13⋊#10111yescharacteristic
250C4—22no—
251C4—22no—
252C4—22no—
253C4—82no—
254C4—262no—
255C4—262no—
256C4—261no—
257C4—261no—
258C4—521no—
259C4—1042no—
260C2#1313029811yescharacteristic
261C2#1313030911yescharacteristic
262C2#1313031811yescharacteristic
263C2#1313032811yescharacteristic
264C2#1313097211yescharacteristic
265C2#1313097911yescharacteristic
266C2#1313100011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#384C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#384#261
hypocenterC13#9690
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
211. C13#9690semidirect

Maximal subgroups

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

subgroupindex
#131306212
#131305532
C2×#117182422
#131231972
#969013