Finite Group Databasebeta

← #16786900

Subgroups — #16786900

Order 3328.

460 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 90 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#13130078C212yesmaximal, complemented
2#13129776C212yesmaximal, complemented
3#13129765C212yesmaximal
4C4×#88129C211yesmaximal, characteristic
5C2×#88129C411yescharacteristic
6C2×C4×D52C411yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8#11719125—22no—
9C43×C13C411yescharacteristic
10#11718601—22no—
11#11718600C2211yescharacteristic
12C4×#6103—22no—
13#11718597C2211yescharacteristic
14#11718590C411yescharacteristic
15#11718286—22no—
16#11718285C2214yes—
17C22×D52C2×C411yescharacteristic
18C22×C4×D13—21no—
19C22×Dic26C2×C411yescharacteristic
20C2×C42×C13—21no—
21C2×C42×C13—21no—
22C2×C42×C13C2×C411yescharacteristic
23C2×C42×C13C2×C411yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25C2×#6103—22no—
26C2×#6103—21no—
27C2×#6103—22no—
28C2×C4⋊Dic13C2×C411yescharacteristic
29C2×C4⋊Dic13C2311yescharacteristic
30C2×#6101D412yes—
31C2×C4×Dic13D412yes—
32#88129—22no—
33#88129C814yescomplemented
34C4×D52—41no—
35C4×D52—41no—
36C4×Dic26—41no—
37C4×Dic26—41no—
38C22⋊#1057—24no—
39#88112—42no—
40C4×#1057—42no—
41#88071—22no—
42#88071—22no—
43#11476—131nomaximal, Sylow
44C23×D13—21no—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13C22⋊C411yescharacteristic
48C22×C4×C13C22⋊C411yescharacteristic
49C22×C4×C13C22×C411yescharacteristic
50C22×Dic13—21no—
51C22×Dic13C22⋊C412yes—
52C22×Dic13C2×D412yes—
53C2×D52—21no—
54C2×D52—41no—
55C2×D52—41no—
56C2×D52C2×C812yes—
57C2×C4×D13—44no—
58C2×C4×D13—41no—
59C2×C4×D13—41no—
60C2×Dic26—41no—
61C2×Dic26—41no—
62C2×Dic26C2×C812yes—
63C2×Dic26M1612yes—
64C2×#1057—44no—
65C42×C13—21no—
66C42×C13—21no—
67C42×C13—21no—
68C42×C13—41no—
69C42×C13—42no—
70C42×C13—42no—
71C42×C13C2×C812yes—
72#6103—28no—
73#6103—42no—
74#6103—44no—
75C4⋊Dic13—41no—
76C4⋊Dic13—41no—
77#6101—42no—
78C4×Dic13—22no—
79C4×Dic13—22no—
80C4×#124—131no—
81#1461—132no—
82#1324—132no—
83#1318—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—22no—
94C2×C4×C13—22no—
95C2×C4×C13—21no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13#9911yescharacteristic
102C2×C4×C13#9911yescharacteristic
103C2×C4×C13C22×C811yescharacteristic
104C2×C4×C13C2×M1611yescharacteristic
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—42no—
109C2×Dic13—42no—
110C2×Dic13—41no—
111C2×Dic13C22⋊C814yes—
112D52—42no—
113D52—42no—
114C4×D13—82no—
115C4×D13—82no—
116Dic26—42no—
117Dic26—42no—
118#1057—84no—
119C2×#124—131no—
120C2×C4×Q8—131no—
121C2×C4×D4—131no—
122#431—262no—
123#391—131no—
124#390—131no—
125#388—262no—
126#382—131no—
127C4×C22⋊C4—262no—
128C43#26111yescharacteristic
129#324—134no—
130#324—262no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13C2×C22⋊C811yescharacteristic
134C22×C13C2×#9911yescharacteristic
135C22×C13#41311yescharacteristic
136C2×D13—44no—
137C2×D13—42no—
138C2×D13—82no—
139C2×D13—81no—
140C2×D13—81no—
141C4×C13—21no—
142C4×C13—21no—
143C4×C13—21no—
144C4×C13—42no—
145C4×C13—42no—
146C4×C13—41no—
147C4×C13#35512yes—
148Dic13—24no—
149Dic13—42no—
150Dic13—81no—
151C22×Q8—131no—
152C22×D4—131no—
153C23×C4—261no—
154#124—134no—
155#124—262no—
156C4×Q8—521no—
157C4×Q8—521no—
158C4×D4—521no—
159C4×D4—521no—
160C2×C4⋊C4—132no—
161C2×C4⋊C4—131no—
162C2×C4⋊C4—131no—
163C2×C22⋊C4—262no—
164C2×C22⋊C4—262no—
165C2×C22⋊C4—261no—
166C2×C42—21no—
167C2×C42—21no—
168C2×C42—132no—
169C2×C42C2×#26111yescharacteristic
170C2×C42C2×#26111yescharacteristic
171C2×C42C2×#26111yescharacteristic
172C4⋊C8—522no—
173C22⋊C8—264no—
174C4×C8—522no—
175#95—262no—
176#95—262no—
177C2×C13—21no—
178C2×C13—21no—
179C2×C13#145911yescharacteristic
180C2×C13#212611yescharacteristic
181C2×C13C2×#35511yescharacteristic
182D13—82no—
183C24—261no—
184C2×Q8—132no—
185C2×Q8—132no—
186C2×Q8—521no—
187C2×Q8—521no—
188C2×D4—132no—
189C2×D4—261no—
190C2×D4—521no—
191C2×D4—521no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—132no—
195C22×C4—132no—
196C22×C4—261no—
197C22×C4—524no—
198C22×C4—521no—
199C22×C4—521no—
200C22×C4C22⋊#26111yescharacteristic
201C22×C4C22⋊#26111yescharacteristic
202C22×C4C22×#26111yescharacteristic
203C2×C8—524no—
204C4⋊C4—522no—
205C4⋊C4—521no—
206C4⋊C4—521no—
207C22⋊C4—268no—
208C22⋊C4—522no—
209C22⋊C4—524no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—41no—
214C42—42no—
215C42—42no—
216C42—262no—
217C42—262no—
218C42D13⋊C812yes—
219C13#1147611yescharacteristic, complemented, Sylow
220C23—262no—
221C23—522no—
222C23—522no—
223C23—521no—
224C23—521no—
225C23C2×C22⋊#26111yescharacteristic
226Q8—522no—
227Q8—522no—
228D4—522no—
229D4—522no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—22no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—134no—
242C2×C4—262no—
243C2×C4—262no—
244C2×C4—262no—
245C2×C4—522no—
246C2×C4—522no—
247C2×C4—521no—
248C2×C4—1042no—
249C2×C4—1042no—
250C2×C4#8810711yescharacteristic
251C2×C4#8810711yescharacteristic
252C2×C4C2×D13⋊C811yescharacteristic
253C2×C4D13⋊M1611yescharacteristic
254C8—1044no—
255C22—21no—
256C22—21no—
257C22—524no—
258C22—522no—
259C22—1042no—
260C22—1041no—
261C22—1041no—
262C22C2×#8810711yescharacteristic
263C22D13⋊(C22⋊C8)11yescharacteristic
264C22#1171913211yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—42no—
269C4—42no—
270C4—41no—
271C4—264no—
272C4—522no—
273C4—1041no—
274C4#1171822812yes—
275C2—21no—
276C2—21no—
277C2—1042no—
278C2#1313007311yescharacteristic
279C2#1313110911yescharacteristic
280C2C2×#1171822811yescharacteristic
subgroupG/H
centerC2×C4#88107
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC43×C13C4
socleC22×C13C2×#99
prime radicalC22×D52C2×C4
cosocleC2×C4⋊Dic13C23
hypercenterC43#261
hypocenterC13#11476
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C43

Complements

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

NH ≅ G/Ntype
1. #13130078C2semidirect
2. #13129776C2semidirect
33. #88129C8semidirect
219. C13#11476semidirect

Maximal subgroups

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

subgroupindex
#131300782
#131297762
#131297652
C4×#881292
#1147613