Finite Group Databasebeta

← #15750132

Subgroups — #15750132

Order 3328.

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

normal subgroups only

This group has 402 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#13115635C211yesmaximal, characteristic
2C4×#88074C211yesmaximal, characteristic
3C4×C13×#99C211yesmaximal, characteristic
4C2×C4×D4×C13C2211yescharacteristic
5C2×C13×#99—21no—
6C4×C13×C22⋊C4—21no—
7C2×#88074—21no—
8C4×C22⋊Dic13—21no—
9C2×C22⋊#1055—21no—
10C2×C22⋊#1055—21no—
11C2×C4⋊#1055C411yescharacteristic, complemented
12C2×#88043C411yescharacteristic, complemented
13C13×#342C412yescomplemented
14#11718118C412yescomplemented
15C22×D4×C13D411yescharacteristic
16C23×C4×C13D411yescharacteristic
17C23×C4×C13D411yescharacteristic
18C4×D4×C13—41no—
19C4×D4×C13—41no—
20C2×C13×C4⋊C4Q811yescharacteristic
21C2×C13×C22⋊C4—22no—
22C2×C13×C22⋊C4C2×C411yescharacteristic
23C2×C13×C22⋊C4C2×C411yescharacteristic
24C2×C42×C13—41no—
25C2×C42×C13C2×C411yescharacteristic
26C2×C22⋊Dic13—22no—
27C2×C4×Dic13—41no—
28C22×#1055—21no—
29C22×#1055—21no—
30C13×#99—24no—
31C13×#95—41no—
32#88074—24no—
33#88071—41no—
34C22⋊#1055—42no—
35C22⋊#1055—42no—
36C4⋊#1055—41no—
37#88043—41no—
38#7283—131nomaximal, Sylow
39C24×C13C22⋊C411yescharacteristic
40C24×C13C22⋊C411yescharacteristic
41C2×D4×C13—22no—
42C2×D4×C13—22no—
43C2×D4×C13—41no—
44C22×C4×C13—21no—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13—41no—
49C22×C4×C13—41no—
50C22×C4×C13—41no—
51C22×C4×C13—41no—
52C22×C4×C13—42no—
53C22×C4×C13C4211yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C4⋊C411yescharacteristic
56C22×C4×C13C4⋊C411yescharacteristic
57C22×C4×C13C4⋊C411yescharacteristic
58C22×Dic13—42no—
59C13×C4⋊C4—41no—
60C13×C22⋊C4—24no—
61C13×C22⋊C4—41no—
62C13×C22⋊C4—41no—
63C13×C22⋊C4—42no—
64C42×C13—21no—
65C42×C13—21no—
66C42×C13—81no—
67C42×C13—81no—
68C22⋊Dic13—24no—
69C22⋊Dic13—42no—
70C4×Dic13—81no—
71C4×Dic13—81no—
72C2×#1055—22no—
73C2×#1055—41no—
74C2×#1055—41no—
75C2×#1055—41no—
76C2×#1055—41no—
77C2×#1055—41no—
78#1955—131no—
79C4×#99—131no—
80C4×#99D1311yescharacteristic
81C23×C13—21no—
82C23×C13—21no—
83C23×C13—21no—
84C23×C13—21no—
85C23×C13—41no—
86C23×C13—41no—
87C23×C13—41no—
88C23×C13—41no—
89C23×C13#9511yescharacteristic
90C23×C13#10412yes—
91C23×C13#10412yes—
92D4×C13—44no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—44no—
109C2×C4×C13—81no—
110C2×C4×C13—81no—
111C2×C4×C13—82no—
112C2×C4×C13—82no—
113C2×C4×C13#9911yescharacteristic
114C2×C4×C13#9911yescharacteristic
115C2×Dic13—44no—
116C2×Dic13—82no—
117C2×Dic13—82no—
118#1055—42no—
119#1055—81no—
120C2×C4×D4C2×D1311yescharacteristic
121C2×C4⋊C8—131no—
122C2×#99—21no—
123C2×#99—261no—
124C2×C22⋊C8—261no—
125C2×C22⋊C8—261no—
126C2×#97—131no—
127C4×C22⋊C4—21no—
128C4×C22⋊C4—261no—
129#342—132no—
130#342Dic1312yescomplemented
131C22×C13—21no—
132C22×C13—21no—
133C22×C13—22no—
134C22×C13—22no—
135C22×C13—42no—
136C22×C13—42no—
137C22×C13—41no—
138C22×C13—41no—
139C22×C13—41no—
140C22×C13—41no—
141C22×C13—81no—
142C22×C13—81no—
143C22×C13#33911yescharacteristic
144C22×C13#33911yescharacteristic
145C22×C13#34211yescharacteristic
146C4×C13—21no—
147C4×C13—41no—
148C4×C13—41no—
149C4×C13—41no—
150C4×C13—41no—
151C4×C13—84no—
152C4×C13#35311yescharacteristic
153C4×C13#35411yescharacteristic
154Dic13—84no—
155C22×D4C22⋊D1311yescharacteristic
156C23×C4D5211yescharacteristic
157C23×C4C22⋊D1311yescharacteristic
158C22×C8—261no—
159C22×C8—261no—
160C4×D4—41no—
161C4×D4—41no—
162C2×C4⋊C4Dic2611yescharacteristic
163C2×C22⋊C4—22no—
164C2×C22⋊C4—262no—
165C2×C22⋊C4C4×D1311yescharacteristic
166C2×C22⋊C4C2×Dic1311yescharacteristic
167C2×C42—41no—
168C2×C42—521no—
169C2×C42C4×D1311yescharacteristic
170C4⋊C8—521no—
171#99—24no—
172#99—264no—
173C22⋊C8—522no—
174C22⋊C8—522no—
175#97—521no—
176#95—41no—
177#95—521no—
178C2×C13—21no—
179C2×C13—21no—
180C2×C13—42no—
181C2×C13—42no—
182C2×C13#129711yescharacteristic
183C2×C13#139111yescharacteristic
184C2×C13#139311yescharacteristic
185C24#610311yescharacteristic
186C24C22⋊Dic1311yescharacteristic
187C2×D4—22no—
188C2×D4—22no—
189C2×D4—41no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—42no—
199C22×C4—522no—
200C22×C4C4×Dic1311yescharacteristic
201C22×C4#610111yescharacteristic
202C22×C4#610111yescharacteristic
203C22×C4C4⋊Dic1311yescharacteristic
204C22×C4#610311yescharacteristic
205C2×C8—262no—
206C2×C8—521no—
207C2×C8—521no—
208C2×C8—521no—
209C2×C8—521no—
210C2×C8—521no—
211C4⋊C4—41no—
212C22⋊C4—24no—
213C22⋊C4—41no—
214C22⋊C4—41no—
215C22⋊C4—42no—
216C22⋊C4—264no—
217C22⋊C4—522no—
218C42—21no—
219C42—21no—
220C42—81no—
221C42—81no—
222C42—1041no—
223C42—1041no—
224C13#728311yescharacteristic, complemented, Sylow
225C23—21no—
226C23—21no—
227C23—21no—
228C23—21no—
229C23—41no—
230C23—41no—
231C23—41no—
232C23—41no—
233C23#8804512yes—
234C23#8807111yescharacteristic
235C23#8807712yes—
236D4—44no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—44no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—82no—
256C2×C4—82no—
257C2×C4—524no—
258C2×C4—1042no—
259C2×C4—1042no—
260C2×C4#8804611yescharacteristic
261C2×C4#8804611yescharacteristic
262C8—522no—
263C8—1041no—
264C22—21no—
265C22—21no—
266C22—22no—
267C22—22no—
268C22—42no—
269C22—42no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—81no—
275C22—81no—
276C22#1171811511yescharacteristic
277C22#1171811911yescharacteristic
278C22#1171812411yescharacteristic
279C4—21no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—84no—
285C4—1044no—
286C4#1171806511yescharacteristic
287C4#1171806611yescharacteristic
288C2—21no—
289C2—21no—
290C2—42no—
291C2—42no—
292C2#1311272211yescharacteristic
293C2#1311295611yescharacteristic
294C2#1311296011yescharacteristic
subgroupG/H
centerC2×C4#88046
commutatorC22×C4×C13C42
FrattiniC2×C4×D4C2×D13
FittingC4×C13×#99C2
socleC22×C13#342
prime radicalC22×D4×C13D4
cosocleC2×C4×D4×C13C22
hypercenterC4×#99D13
hypocenterC13#7283
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
11. C2×C4⋊#1055C4semidirect
12. C2×#88043C4semidirect
13. C13×#342C4semidirect
14. #11718118C4semidirect
130. #342Dic13semidirect
224. C13#7283semidirect

Maximal subgroups

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

subgroupindex
#131156352
C4×#880742
C4×C13×#992
#728313