Finite Group Databasebeta

← #16789472

Subgroups — #16789472

Order 3328.

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

normal subgroups only

This group has 512 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
1C2×#11718228C212yesmaximal
2C4×#88113C212yesmaximal, complemented
3#13129933C212yesmaximal, complemented
4#13117547C211yesmaximal, characteristic
5C2×#88129C2211yescharacteristic
6C2×C4×D52C411yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8C2×#88113C2214yes—
9C4×#6122—22no—
10C13×#376C411yescharacteristic
11#11718600C411yescharacteristic
12#11718596C411yescharacteristic
13#11718590C2211yescharacteristic
14#11718331—22no—
15#11718329—22no—
16#11718291—22no—
17#11718228C418yescomplemented
18C22×D52C2×C411yescharacteristic
19C22×C4×D13—21no—
20C22×Dic26C2311yescharacteristic
21C2×#6122—24no—
22C2×C42×C13C2×C411yescharacteristic
23C2×C42×C13C2×C411yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25C2×#6103—22no—
26C2×#6103—21no—
27C2×#6103—22no—
28C2×C4⋊Dic13—22no—
29C2×C4⋊Dic13C2×C411yescharacteristic
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×#6101D412yes—
32C2×C4×Dic13D412yes—
33#88129—22no—
34#88129C2×C414yes—
35C4×D52—42no—
36C4×Dic26—42no—
37#88113—24no—
38#88113C2×C418yescomplemented
39#88110—42no—
40C4×#1057—42no—
41C13×#95—21no—
42C13×#95—21no—
43#88071—22no—
44#12632—131nomaximal, Sylow
45C23×D13—21no—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13C22⋊C411yescharacteristic
49C22×C4×C13C22⋊C411yescharacteristic
50C22×C4×C13C22×C411yescharacteristic
51C22×Dic13—21no—
52C22×Dic13C22⋊C412yes—
53C22×Dic13C2×D412yes—
54C2×D52—21no—
55C2×D52—41no—
56C2×D52—41no—
57C2×D52C4212yes—
58C2×C4×D13—42no—
59C2×C4×D13—82no—
60C2×Dic26—41no—
61C2×Dic26—41no—
62C2×Dic26C22×C412yes—
63C2×Dic26#4112yes—
64#6122—28no—
65#6122—44no—
66C2×#1057—44no—
67C42×C13—22no—
68C42×C13—21no—
69C42×C13—41no—
70C42×C13C4212yes—
71#6103—28no—
72#6103—42no—
73#6103—82no—
74C4⋊Dic13—41no—
75C4⋊Dic13—41no—
76C4⋊Dic13—82no—
77#6101—42no—
78C4×Dic13—22no—
79C4×Dic13—22no—
80#2326—131no—
81C2×#355—132no—
82C4×#101—132no—
83#1394—132no—
84C23×C13C2×C22⋊C411yescharacteristic
85C22×D13—22no—
86C22×D13—42no—
87C22×D13—42no—
88C22×D13—41no—
89C22×D13—41no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—41no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13#9912yes—
102C2×C4×C13C2×C4211yescharacteristic
103C2×C4×C13#11711yescharacteristic
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109C2×Dic13—41no—
110C2×Dic13C4×D414yes—
111D52—42no—
112D52—42no—
113C4×D13—84no—
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—131no—
124#388—262no—
125#385—262no—
126#384—131no—
127#376#26111yescharacteristic
128#355—138no—
129#343—262no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13C4×C22⋊C411yescharacteristic
133C22×C13C2×#9911yescharacteristic
134C22×C13#41011yescharacteristic
135C2×D13—44no—
136C2×D13—42no—
137C2×D13—82no—
138C2×D13—81no—
139C2×D13—81no—
140C4×C13—22no—
141C4×C13—21no—
142C4×C13—21no—
143C4×C13—42no—
144C4×C13—41no—
145C4×C13—81no—
146Dic13—24no—
147Dic13—42no—
148Dic13—81no—
149C22×Q8—131no—
150C22×D4—131no—
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—131no—
160C2×C4⋊C4—262no—
161C2×C22⋊C4—262no—
162C2×C22⋊C4—261no—
163C2×C22⋊C4—262no—
164C2×C42—132no—
165C2×C42C2×#26111yescharacteristic
166C2×C42C2×#26111yescharacteristic
167C2×C42C2×#26111yescharacteristic
168#101—138no—
169#101—264no—
170#97—522no—
171C4×C8—522no—
172#95—21no—
173#95—21no—
174#95—262no—
175C2×C13—21no—
176C2×C13—21no—
177C2×C13C4×#9911yescharacteristic
178C2×C13#213311yescharacteristic
179C2×C13#213411yescharacteristic
180D13—82no—
181C24—261no—
182C2×Q8—132no—
183C2×Q8—132no—
184C2×Q8—521no—
185C2×Q8—521no—
186C2×D4—132no—
187C2×D4—261no—
188C2×D4—521no—
189C2×D4—521no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—132no—
193C22×C4—132no—
194C22×C4—261no—
195C22×C4—522no—
196C22×C4—1042no—
197C22×C4C22⋊#26111yescharacteristic
198C22×C4C22⋊#26111yescharacteristic
199C22×C4C22×#26111yescharacteristic
200M16—268no—
201M16—524no—
202C2×C8—524no—
203C4⋊C4—522no—
204C4⋊C4—521no—
205C4⋊C4—521no—
206C4⋊C4—1042no—
207C22⋊C4—268no—
208C22⋊C4—522no—
209C22⋊C4—1042no—
210C42—22no—
211C42—21no—
212C42—41no—
213C42—262no—
214C42—262no—
215C42C4×#26112yes—
216C13#1263211yescharacteristic, complemented, Sylow
217C23—262no—
218C23—522no—
219C23—522no—
220C23—521no—
221C23—521no—
222C23C2×C22⋊#26111yescharacteristic
223Q8—522no—
224Q8—522no—
225D4—522no—
226D4—522no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—134no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4—262no—
242C2×C4—522no—
243C2×C4—522no—
244C2×C4—521no—
245C2×C4—1044no—
246C2×C4#8810712yes—
247C2×C4C2×C4×#26111yescharacteristic
248C2×C4#8823711yescharacteristic
249C8—528no—
250C22—21no—
251C22—21no—
252C22—524no—
253C22—522no—
254C22—1042no—
255C22—1041no—
256C22—1041no—
257C22C2×#8810711yescharacteristic
258C22#1171911611yescharacteristic
259C22C4×C22⋊#26111yescharacteristic
260C4—21no—
261C4—21no—
262C4—22no—
263C4—42no—
264C4—41no—
265C4—81no—
266C4—264no—
267C4—522no—
268C4—1041no—
269C2—21no—
270C2—21no—
271C2—1042no—
272C2C4×#8810711yescharacteristic
273C2#1313113311yescharacteristic
274C2#1313113711yescharacteristic
subgroupG/H
centerC22C2×#88107
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#376C4
socleC22×C13C2×#99
prime radicalC22×D52C2×C4
cosocleC22×Dic26C23
hypercenter#376#261
hypocenterC13#12632
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. C4×#88113C2semidirect
3. #13129933C2semidirect
17. #11718228C4semidirect
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×#117182282
C4×#881132
#131299332
#131175472
#1263213