Finite Group Databasebeta

← #15753846

Subgroups — #15753846

Order 3328.

444 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88124C211yesmaximal, characteristic
2#13114585C211yesmaximal, characteristic
3C2×#11718057C212yesmaximal
4#13112718C212yesmaximal
5C13×#1745C211yesmaximal, characteristic
6C2×#88124C2211yescharacteristic
7C2×C13×#97C2212yes—
8C43×C13C2211yescharacteristic
9#11718597C2211yescharacteristic
10C4×C4⋊Dic13C411yescharacteristic
11C4×C4⋊Dic13C411yescharacteristic
12#11718594—21no—
13#11718594—21no—
14C4×#6101—21no—
15C4×#6101—21no—
16#11718589C411yescharacteristic
17#11718589C411yescharacteristic
18C2×#88043C2212yes—
19C13×#336—21no—
20C13×#336—21no—
21#11718116—21no—
22#11718116—21no—
23#11718057C418yescomplemented
24C22×C8×C13—22no—
25C2×C42×C13C2×C411yescharacteristic
26C2×C42×C13C2×C411yescharacteristic
27C2×C42×C13D411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13C2311yescharacteristic
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×C4×Dic13—21no—
41C2×C4×Dic13—21no—
42C22×#1055—22no—
43#88124—22no—
44#88124C2×C414yes—
45C13×#97—22no—
46C13×#97C2×C414yes—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88043—22no—
54#88043C2×C414yes—
55#8225—131nomaximal, Sylow
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C2×C8×C13—24no—
68C2×C8×C13—42no—
69C2×C8×C13—42no—
70C42×C13—22no—
71C42×C13—41no—
72C42×C13—41no—
73C42×C13—41no—
74C42×C13—41no—
75C42×C13—41no—
76C42×C13C22×C412yes—
77C42×C13#4112yes—
78C4⋊Dic13—21no—
79C4⋊Dic13—21no—
80C4⋊Dic13—41no—
81C4⋊Dic13—41no—
82C4⋊Dic13C4212yes—
83C4⋊Dic13C4212yes—
84#6101—24no—
85#6101—24no—
86#6101—42no—
87#6101—42no—
88C4×Dic13—42no—
89C4×Dic13—42no—
90C2×#1055—24no—
91C2×#1055—42no—
92C2×#1055—42no—
93C4×#125—131no—
94#1745—131no—
95#1745D1311yescharacteristic
96C2×#330—132no—
97#1295—132no—
98C23×C13C2×C22⋊C411yescharacteristic
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13#10112yes—
117C2×C4×C13C2×C4211yescharacteristic
118C2×C4×C13#11711yescharacteristic
119C2×C4×C13C4×D412yes—
120C2×C4×C13C4×D412yes—
121C2×Dic13—22no—
122C2×Dic13—22no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C8×C13—44no—
134#1055—44no—
135C2×#125—131no—
136C2×#97—132no—
137C2×#97C2×D1312yes—
138#389—131no—
139#389—131no—
140#387—261no—
141#387—261no—
142#382—131no—
143C4×C4⋊C4—131no—
144C4×C4⋊C4—131no—
145C4×C4⋊C4—261no—
146C4×C4⋊C4—261no—
147C43C2×D1311yescharacteristic
148#336—21no—
149#336—21no—
150#336—261no—
151#336—261no—
152#330—138no—
153C22×C13C4×C22⋊C411yescharacteristic
154C22×C13C2×#10111yescharacteristic
155C22×C13#41311yescharacteristic
156C22×C13#42111yescharacteristic
157C22×C13#42111yescharacteristic
158C22×C13#42111yescharacteristic
159C22×C13#42111yescharacteristic
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—22no—
163C4×C13—22no—
164C4×C13—22no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—41no—
168Dic13—42no—
169Dic13—42no—
170Dic13—81no—
171Dic13—81no—
172C22×C8—22no—
173C22×C8—262no—
174#125—134no—
175#125—262no—
176C2×C4⋊C4—131no—
177C2×C4⋊C4—131no—
178C2×C4⋊C4—131no—
179C2×C4⋊C4—131no—
180C2×C4⋊C4—261no—
181C2×C4⋊C4—261no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C42—261no—
185C2×C42—261no—
186C2×C42C4×D1311yescharacteristic
187C2×C42C4×D1311yescharacteristic
188C2×C42D5211yescharacteristic
189C2×C42D5211yescharacteristic
190C2×C42C22⋊D1311yescharacteristic
191C2×C42C22⋊D1311yescharacteristic
192C2×C42C22×D1311yescharacteristic
193#97—22no—
194#97—134no—
195#97—262no—
196#97C4×D1314yes—
197#95—261no—
198#95—261no—
199#95—261no—
200#95—261no—
201#95—261no—
202#95—261no—
203C2×C13#153411yescharacteristic
204C2×C13#153511yescharacteristic
205C2×C13#153511yescharacteristic
206C2×C13#153711yescharacteristic
207C2×C13C4×#10111yescharacteristic
208C2×C13#175911yescharacteristic
209C2×C13#175911yescharacteristic
210C22×C4—261no—
211C22×C4—261no—
212C22×C4—261no—
213C22×C4—261no—
214C22×C4#610311yescharacteristic
215C22×C4#610311yescharacteristic
216C22×C4#610311yescharacteristic
217C22×C4#610311yescharacteristic
218C22×C4C2×C4×D1311yescharacteristic
219C22×C4C2×D5211yescharacteristic
220C22×C4C2×C22⋊D1311yescharacteristic
221C2×C8—24no—
222C2×C8—42no—
223C2×C8—42no—
224C2×C8—264no—
225C2×C8—522no—
226C2×C8—522no—
227C4⋊C4—132no—
228C4⋊C4—132no—
229C4⋊C4—261no—
230C4⋊C4—261no—
231C4⋊C4—264no—
232C4⋊C4—264no—
233C4⋊C4—521no—
234C4⋊C4—521no—
235C4⋊C4—522no—
236C4⋊C4—522no—
237C42—22no—
238C42—41no—
239C42—41no—
240C42—41no—
241C42—41no—
242C42—41no—
243C42—522no—
244C42—522no—
245C42C2×C4×D1312yes—
246C42#612712yes—
247C13#822511yescharacteristic, complemented, Sylow
248C23C2×#610311yescharacteristic
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—262no—
267C2×C4—262no—
268C2×C4—521no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4—521no—
275C2×C4—521no—
276C2×C4—521no—
277C2×C4—521no—
278C2×C4#8806412yes—
279C2×C4C42×D1311yescharacteristic
280C2×C4#8812611yescharacteristic
281C2×C4C4×D5212yes—
282C2×C4C4×C22⋊D1312yes—
283C8—44no—
284C8—524no—
285C22C4×#610311yescharacteristic
286C22#1171866611yescharacteristic
287C22#1171866611yescharacteristic
288C22#1171879311yescharacteristic
289C22C2×#8806411yescharacteristic
290C22#1171880011yescharacteristic
291C22#1171880011yescharacteristic
292C4—21no—
293C4—21no—
294C4—22no—
295C4—22no—
296C4—22no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—522no—
301C4—522no—
302C4—1041no—
303C4—1041no—
304C2#1311346211yescharacteristic
305C2#1311346511yescharacteristic
306C2#1311346811yescharacteristic
307C2#1311347311yescharacteristic
308C2C4×#8806411yescharacteristic
309C2#1311464711yescharacteristic
310C2#1311464911yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC2×C4×C13C2×C42
FrattiniC2×C42C22×D13
FittingC13×#1745C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1745D13
hypocenterC13#8225
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #1745

Complements

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

NH ≅ G/Ntype
23. #11718057C4semidirect
247. C13#8225semidirect

Maximal subgroups

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

subgroupindex
C4×#881242
#131145852
C2×#117180572
#131127182
C13×#17452
#822513