Finite Group Databasebeta

← #16789473

Subgroups — #16789473

Order 3328.

512 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C2×#11718295C212yesmaximal
2#13130589C212yesmaximal, complemented
3#13129933C212yesmaximal, complemented
4#13117546C211yesmaximal, characteristic
5C2×#88190C2211yescharacteristic
6C2×D4×Dic13C411yescharacteristic
7C2×#88141C2211yescharacteristic
8C2×#88113C2214yes—
9C4×#6122—22no—
10C13×#390C411yescharacteristic
11#11718637C411yescharacteristic
12#11718607—22no—
13#11718606—22no—
14#11718593C411yescharacteristic
15#11718590C2211yescharacteristic
16#11718295C418yescomplemented
17#11718291—22no—
18C22×D4×C13C2×C411yescharacteristic
19C23×Dic13—21no—
20C22×Dic26C2311yescharacteristic
21C2×#6122—24no—
22C2×C13×C4⋊C4C2×C411yescharacteristic
23C2×C13×C22⋊C4—22no—
24C2×C42×C13C2×C411yescharacteristic
25C2×C22⋊Dic13—22no—
26C2×C22⋊Dic13—21no—
27#88190—22no—
28#88190C2×C414yes—
29D4×Dic13—42no—
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×#6101—22no—
32C2×#6101D412yes—
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13D412yes—
36#88141—42no—
37#88113—24no—
38#88113C2×C418yescomplemented
39#88110—42no—
40C4×#1057—42no—
41#88071—21no—
42#88071—21no—
43#88071—22no—
44#12632—131nomaximal, Sylow
45C24×C13—21no—
46C2×D4×C13—21no—
47C2×D4×C13—41no—
48C2×D4×C13—41no—
49C2×D4×C13C4212yes—
50C22×C4×C13—21no—
51C22×C4×C13C22⋊C412yes—
52C22×C4×C13C22×C411yescharacteristic
53C22×Dic13—21no—
54C22×Dic13—21no—
55C22×Dic13—42no—
56C22×Dic13—82no—
57C22×Dic13C22⋊C411yescharacteristic
58C22×Dic13C22⋊C411yescharacteristic
59C22×Dic13C2×D412yes—
60C2×Dic26—41no—
61C2×Dic26—41no—
62C2×Dic26C22×C412yes—
63C2×Dic26#4112yes—
64#6122—28no—
65#6122—44no—
66C2×#1057—44no—
67C13×C4⋊C4—41no—
68C13×C22⋊C4—82no—
69C42×C13—41no—
70C22⋊Dic13—28no—
71C22⋊Dic13—42no—
72C4⋊Dic13—41no—
73#6101—42no—
74#6101—82no—
75C4×Dic13—21no—
76C4×Dic13—22no—
77C4×Dic13—22no—
78C4×Dic13—22no—
79C4×Dic13C4212yes—
80#2326—131no—
81C2×#355—132no—
82C4×#101—132no—
83#1394—132no—
84C23×C13—22no—
85C23×C13—42no—
86C23×C13—42no—
87C23×C13—41no—
88C23×C13—41no—
89C23×C13C2×C22⋊C411yescharacteristic
90D4×C13—42no—
91D4×C13—42no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—42no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13C2×C4211yescharacteristic
100C2×C4×C13#11711yescharacteristic
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—21no—
105C2×Dic13—41no—
106C2×Dic13—41no—
107C2×Dic13—41no—
108C2×Dic13—41no—
109C2×Dic13—42no—
110C2×Dic13—41no—
111C2×Dic13—84no—
112C2×Dic13#9912yes—
113C2×Dic13C4×D414yes—
114Dic26—42no—
115Dic26—42no—
116#1057—48no—
117C2×#124—131no—
118C2×C4×Q8—131no—
119C2×C4×D4—131no—
120C2×#101—134no—
121C4×M16—262no—
122#391—131no—
123#390#26111yescharacteristic
124#388—262no—
125#385—262no—
126#384—131no—
127#376—131no—
128#355—138no—
129#343—262no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13—44no—
133C22×C13—42no—
134C22×C13—82no—
135C22×C13—81no—
136C22×C13—81no—
137C22×C13C4×C22⋊C411yescharacteristic
138C22×C13C2×#9911yescharacteristic
139C22×C13#41011yescharacteristic
140C4×C13—21no—
141C4×C13—21no—
142C4×C13—42no—
143C4×C13—81no—
144Dic13—22no—
145Dic13—24no—
146Dic13—42no—
147Dic13—41no—
148Dic13—81no—
149C22×Q8—131no—
150C22×D4C2×#26111yescharacteristic
151C23×C4—261no—
152C2×M16—264no—
153#124—134no—
154#124—262no—
155C4×Q8—522no—
156C4×D4—522no—
157C2×C4⋊C4—132no—
158C2×C4⋊C4—131no—
159C2×C4⋊C4—262no—
160C2×C4⋊C4C2×#26111yescharacteristic
161C2×C22⋊C4—22no—
162C2×C22⋊C4—262no—
163C2×C22⋊C4—261no—
164C2×C42—131no—
165C2×C42—132no—
166C2×C42—131no—
167C2×C42C2×#26111yescharacteristic
168#101—138no—
169#101—264no—
170#97—522no—
171C4×C8—522no—
172#95—261no—
173#95—261no—
174#95—262no—
175C2×C13—21no—
176C2×C13—21no—
177C2×C13—82no—
178C2×C13C4×#9911yescharacteristic
179C2×C13#213311yescharacteristic
180C2×C13#213411yescharacteristic
181C24—21no—
182C2×Q8—132no—
183C2×Q8—132no—
184C2×Q8—521no—
185C2×Q8—521no—
186C2×D4—21no—
187C2×D4—41no—
188C2×D4—41no—
189C2×D4C4×#26112yes—
190C22×C4—21no—
191C22×C4—132no—
192C22×C4—131no—
193C22×C4—131no—
194C22×C4—261no—
195C22×C4—261no—
196C22×C4—522no—
197C22×C4—1042no—
198C22×C4C22⋊#26112yes—
199C22×C4C22×#26111yescharacteristic
200M16—268no—
201M16—524no—
202C2×C8—524no—
203C4⋊C4—41no—
204C4⋊C4—522no—
205C4⋊C4—521no—
206C4⋊C4—1042no—
207C22⋊C4—82no—
208C22⋊C4—268no—
209C22⋊C4—522no—
210C42—41no—
211C42—132no—
212C42—262no—
213C42—262no—
214C42—262no—
215C42—261no—
216C13#1263211yescharacteristic, complemented, Sylow
217C23—22no—
218C23—42no—
219C23—42no—
220C23—41no—
221C23—41no—
222C23C2×C22⋊#26111yescharacteristic
223Q8—522no—
224Q8—522no—
225D4—42no—
226D4—42no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—134no—
235C2×C4—132no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—261no—
240C2×C4—521no—
241C2×C4—521no—
242C2×C4—521no—
243C2×C4—521no—
244C2×C4—522no—
245C2×C4—521no—
246C2×C4—1044no—
247C2×C4C2×C4×#26111yescharacteristic
248C2×C4#8823711yescharacteristic
249C8—528no—
250C22—21no—
251C22—21no—
252C22—44no—
253C22—42no—
254C22—82no—
255C22—81no—
256C22—81no—
257C22C4×C22⋊#26111yescharacteristic
258C22D13⋊#9911yescharacteristic
259C22#1171914211yescharacteristic
260C4—21no—
261C4—21no—
262C4—42no—
263C4—81no—
264C4—264no—
265C4—262no—
266C4—522no—
267C4—521no—
268C4—1041no—
269C2—21no—
270C2—21no—
271C2—82no—
272C2#1313058311yescharacteristic
273C2#1313113211yescharacteristic
274C2#1313113611yescharacteristic
subgroupG/H
centerC22D13⋊#99
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#390C4
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC22×Dic26C23
hypercenter#390#261
hypocenterC13#12632
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. #13130589C2semidirect
3. #13129933C2semidirect
16. #11718295C4semidirect
38. #88113C2×C4semidirect
216. C13#12632semidirect

Maximal subgroups

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

subgroupindex
C2×#117182952
#131305892
#131299332
#131175462
#1263213