Finite Group Databasebeta

← #15753857

Subgroups — #15753857

Order 3328.

488 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88124C211yesmaximal, characteristic
2C4×#88043C211yesmaximal, 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×#88043—21no—
19C2×#88043C2212yes—
20C2×C4×#1055—21no—
21C13×#336—21no—
22C13×#336—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—24no—
54#88043—22no—
55#88043C2×C414yes—
56C4×#1055—24no—
57#8227—131nomaximal, Sylow
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×C4×C13C2×D411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13—21no—
69C2×C8×C13—24no—
70C2×C8×C13—42no—
71C2×C8×C13—42no—
72C42×C13—22no—
73C42×C13—22no—
74C42×C13—22no—
75C42×C13—41no—
76C42×C13—41no—
77C42×C13—41no—
78C42×C13C22×C412yes—
79C42×C13#4112yes—
80C4⋊Dic13—21no—
81C4⋊Dic13—21no—
82C4⋊Dic13—41no—
83C4⋊Dic13—41no—
84C4⋊Dic13C4212yes—
85C4⋊Dic13C4212yes—
86#6101—24no—
87#6101—24no—
88#6101—42no—
89#6101—42no—
90C4×Dic13—42no—
91C4×Dic13—42no—
92C2×#1055—24no—
93C2×#1055—24no—
94C2×#1055—24no—
95C4×#125—131no—
96#1745D1311yescharacteristic
97C4×#97—131no—
98C2×#330—132no—
99#1295—132no—
100C23×C13C2×C22⋊C411yescharacteristic
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×C13#10412yes—
118C2×C4×C13#10412yes—
119C2×C4×C13C2×C4211yescharacteristic
120C2×C4×C13#11711yescharacteristic
121C2×C4×C13C4×D412yes—
122C2×C4×C13C4×D412yes—
123C2×Dic13—22no—
124C2×Dic13—22no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C8×C13—44no—
136#1055—28no—
137C2×#125—131no—
138C2×#97—132no—
139C2×#97—261no—
140C2×#97C2×D1312yes—
141C2×C4×C8—261no—
142#389—131no—
143#389—131no—
144#387—261no—
145#387—261no—
146#382—131no—
147C4×C4⋊C4—131no—
148C4×C4⋊C4—131no—
149C4×C4⋊C4—261no—
150C4×C4⋊C4—261no—
151C43C2×D1311yescharacteristic
152#336—21no—
153#336—21no—
154#330—138no—
155C22×C13C4×C22⋊C411yescharacteristic
156C22×C13C2×#10111yescharacteristic
157C22×C13#41311yescharacteristic
158C22×C13C2×#10411yescharacteristic
159C22×C13C2×#10411yescharacteristic
160C22×C13#42111yescharacteristic
161C22×C13#42111yescharacteristic
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—22no—
165C4×C13—22no—
166C4×C13—22no—
167C4×C13—22no—
168C4×C13—22no—
169C4×C13—41no—
170Dic13—42no—
171Dic13—42no—
172Dic13—81no—
173Dic13—81no—
174C22×C8—22no—
175C22×C8—262no—
176#125—134no—
177#125—262no—
178C2×C4⋊C4—131no—
179C2×C4⋊C4—131no—
180C2×C4⋊C4—131no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4—261no—
186C2×C42—261no—
187C2×C42—261no—
188C2×C42C4×D1311yescharacteristic
189C2×C42C4×D1311yescharacteristic
190C2×C42D5211yescharacteristic
191C2×C42D5211yescharacteristic
192C2×C42C22⋊D1311yescharacteristic
193C2×C42C22⋊D1311yescharacteristic
194C2×C42C22×D1311yescharacteristic
195#97—22no—
196#97—134no—
197#97—264no—
198#97—262no—
199#97C4×D1314yes—
200C4×C8—264no—
201#95—261no—
202#95—261no—
203#95—261no—
204#95—261no—
205#95—261no—
206#95—261no—
207C2×C13#152811yescharacteristic
208C2×C13#152911yescharacteristic
209C2×C13#153111yescharacteristic
210C2×C13#153211yescharacteristic
211C2×C13C4×#10111yescharacteristic
212C2×C13C4×#10411yescharacteristic
213C2×C13#175911yescharacteristic
214C22×C4—261no—
215C22×C4—261no—
216C22×C4—261no—
217C22×C4—261no—
218C22×C4#610311yescharacteristic
219C22×C4#610311yescharacteristic
220C22×C4#610311yescharacteristic
221C22×C4#610311yescharacteristic
222C22×C4C2×C4×D1311yescharacteristic
223C22×C4C2×D5211yescharacteristic
224C22×C4C2×C22⋊D1311yescharacteristic
225C2×C8—24no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—264no—
229C2×C8—264no—
230C2×C8—264no—
231C4⋊C4—132no—
232C4⋊C4—132no—
233C4⋊C4—261no—
234C4⋊C4—261no—
235C4⋊C4—264no—
236C4⋊C4—264no—
237C4⋊C4—521no—
238C4⋊C4—521no—
239C4⋊C4—522no—
240C4⋊C4—522no—
241C42—22no—
242C42—22no—
243C42—22no—
244C42—41no—
245C42—41no—
246C42—41no—
247C42—522no—
248C42—522no—
249C42C2×C4×D1312yes—
250C42#612712yes—
251C13#822711yescharacteristic, complemented, Sylow
252C23C2×#610311yescharacteristic
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—21no—
267C2×C4—21no—
268C2×C4—262no—
269C2×C4—262no—
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—521no—
279C2×C4—521no—
280C2×C4#8806412yes—
281C2×C4#8806512yes—
282C2×C4#8806512yes—
283C2×C4C42×D1311yescharacteristic
284C2×C4#8812611yescharacteristic
285C2×C4C4×D5212yes—
286C2×C4C4×C22⋊D1312yes—
287C8—44no—
288C8—268no—
289C22C4×#610311yescharacteristic
290C22#1171866611yescharacteristic
291C22#1171866611yescharacteristic
292C22#1171879311yescharacteristic
293C22C2×#8806411yescharacteristic
294C22C2×#8806511yescharacteristic
295C22C2×#8806511yescharacteristic
296C4—21no—
297C4—21no—
298C4—22no—
299C4—22no—
300C4—22no—
301C4—22no—
302C4—22no—
303C4—41no—
304C4—522no—
305C4—522no—
306C4—1041no—
307C4—1041no—
308C2#1311343911yescharacteristic
309C2#1311344411yescharacteristic
310C2#1311345211yescharacteristic
311C2#1311345711yescharacteristic
312C2C4×#8806411yescharacteristic
313C2C4×#8806511yescharacteristic
314C2#1311464711yescharacteristic
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#8227
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
251. C13#8227semidirect

Maximal subgroups

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

subgroupindex
C4×#881242
C4×#880432
C2×#117180572
#131127182
C13×#17452
#822713