Finite Group Databasebeta

← #15751336

Subgroups — #15751336

Order 3328.

384 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123218C211yesmaximal, characteristic
2#13114979C211yesmaximal, characteristic
3#13112661C212yesmaximal
4#13112658C212yesmaximal
5C4×C13×C4⋊C8C211yesmaximal, characteristic
6C2×C13×C4⋊C8—21no—
7C2×C4×C8×C13—21no—
8C43×C13C2211yescharacteristic
9#11718598—21no—
10#11718594—21no—
11#11718594—21no—
12#11718594—21no—
13#11718590C411yescharacteristic
14#11718590C411yescharacteristic
15#11718590C2211yescharacteristic
16#11718589C411yescharacteristic
17#11718589C411yescharacteristic
18#11718589C2211yescharacteristic
19C13×#336C2212yes—
20#11718116—21no—
21#11718116—21no—
22#11718116C2212yes—
23C22×Dic26C2×C411yescharacteristic
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×#6101—21no—
36C2×#6101—21no—
37C2×#6101—21no—
38C22×#1055—22no—
39C13×C4⋊C8—24no—
40C4×C8×C13—42no—
41#88071—21no—
42#88071—21no—
43#88071—21no—
44#88071—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#7673—131nomaximal, Sylow
51C22×C4×C13C22⋊C411yescharacteristic
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C22×C4×C13C2×D411yescharacteristic
57C22×C4×C13C2×D411yescharacteristic
58C22×Dic13—21no—
59C22×Dic13—21no—
60C22×Dic13—21no—
61C22×Dic13—21no—
62C2×Dic26—22no—
63C2×Dic26—41no—
64C2×Dic26—41no—
65C2×C8×C13—24no—
66C2×C8×C13—42no—
67C2×C8×C13—42no—
68C42×C13—22no—
69C42×C13—22no—
70C42×C13—22no—
71C42×C13—41no—
72C42×C13—41no—
73C42×C13—41no—
74C42×C13SD1612yes—
75C42×C13Q1612yes—
76C4⋊Dic13—22no—
77C4⋊Dic13—41no—
78C4⋊Dic13—41no—
79#6101—42no—
80#6101—42no—
81#6101—42no—
82C2×#1055—42no—
83C2×#1055—42no—
84C2×#1055—42no—
85#2863—131no—
86#1839—131no—
87C4×C4⋊C8D1311yescharacteristic
88#1272—132no—
89#1271—132no—
90C23×C13C2×C22⋊C411yescharacteristic
91C2×C4×C13—21no—
92C2×C4×C13—21no—
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—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13#10312yes—
107C2×C4×C13#10312yes—
108C2×C4×C13#10412yes—
109C2×C4×C13#13112yes—
110C2×C4×C13C2×SD1611yescharacteristic
111C2×C4×C13C2×Q1611yescharacteristic
112C2×C4×C13#13512yes—
113C2×Dic13—41no—
114C2×Dic13—41no—
115C2×Dic13—41no—
116C2×Dic13—41no—
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125Dic26—82no—
126C8×C13—44no—
127#1055—82no—
128C2×C4⋊C8—21no—
129C2×C4×C8—21no—
130#391—131no—
131#391—131no—
132#391—131no—
133#389—131no—
134#389—131no—
135#389—131no—
136#387—261no—
137#387—261no—
138#387—261no—
139#383—261no—
140C43C2×D1311yescharacteristic
141#336—132no—
142#336—261no—
143#336—261no—
144#336C2×D1312yes—
145C22×C13#40811yescharacteristic
146C22×C13#41011yescharacteristic
147C22×C13#41311yescharacteristic
148C22×C13C2×#10311yescharacteristic
149C22×C13#41611yescharacteristic
150C22×C13C2×#10411yescharacteristic
151C22×C13#42111yescharacteristic
152C4×C13—22no—
153C4×C13—22no—
154C4×C13—22no—
155C4×C13—22no—
156C4×C13—21no—
157C4×C13—21no—
158C4×C13—22no—
159C4×C13—41no—
160Dic13—81no—
161Dic13—81no—
162Dic13—81no—
163Dic13—81no—
164C22×Q8—131no—
165C22×C8—22no—
166C22×C8—262no—
167C2×C4⋊C4—131no—
168C2×C4⋊C4—131no—
169C2×C4⋊C4—131no—
170C2×C4⋊C4—261no—
171C2×C4⋊C4—261no—
172C2×C4⋊C4—261no—
173C2×C42C4×D1311yescharacteristic
174C2×C42C4×D1311yescharacteristic
175C2×C42D5211yescharacteristic
176C2×C42D5211yescharacteristic
177C2×C42C22⋊D1311yescharacteristic
178C2×C42C22⋊D1311yescharacteristic
179C2×C42C22×D1311yescharacteristic
180C4⋊C8—24no—
181C4×C8—42no—
182#95—261no—
183#95—261no—
184#95—261no—
185#95—261no—
186#95—261no—
187#95—261no—
188#95—261no—
189#95—261no—
190#95—261no—
191C2×C13#147311yescharacteristic
192C2×C13#148111yescharacteristic
193C2×C13#149411yescharacteristic
194C2×C13#150311yescharacteristic
195C2×C13#152111yescharacteristic
196C2×C13#152911yescharacteristic
197C2×C13#154211yescharacteristic
198C2×Q8—262no—
199C2×Q8—521no—
200C2×Q8—521no—
201C22×C4—261no—
202C22×C4—261no—
203C22×C4—261no—
204C22×C4—261no—
205C22×C4#610311yescharacteristic
206C22×C4#610311yescharacteristic
207C22×C4#610311yescharacteristic
208C22×C4#610311yescharacteristic
209C22×C4C2×C4×D1311yescharacteristic
210C22×C4C2×D5211yescharacteristic
211C22×C4C2×C22⋊D1311yescharacteristic
212C2×C8—24no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—522no—
216C2×C8—522no—
217C2×C8—522no—
218C4⋊C4—262no—
219C4⋊C4—521no—
220C4⋊C4—521no—
221C4⋊C4—522no—
222C4⋊C4—522no—
223C4⋊C4—522no—
224C42—22no—
225C42—22no—
226C42—22no—
227C42—41no—
228C42—41no—
229C42—41no—
230C42#610512yes—
231C42#610712yes—
232C13#767311yescharacteristic, complemented, Sylow
233C23C2×#610311yescharacteristic
234Q8—1042no—
235C2×C4—21no—
236C2×C4—21no—
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—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—521no—
251C2×C4—521no—
252C2×C4—521no—
253C2×C4—521no—
254C2×C4—521no—
255C2×C4—521no—
256C2×C4—521no—
257C2×C4—521no—
258C2×C4—521no—
259C2×C4—521no—
260C2×C4—521no—
261C2×C4—521no—
262C2×C4#8804512yes—
263C2×C4#8805012yes—
264C2×C4#8805012yes—
265C2×C4#8815512yes—
266C2×C4#8815812yes—
267C2×C4C2×#610511yescharacteristic
268C2×C4C2×#610711yescharacteristic
269C8—44no—
270C8—1042no—
271C22C2×#8804511yescharacteristic
272C22C2×#8805011yescharacteristic
273C22#1171866711yescharacteristic
274C22#1171877111yescharacteristic
275C22#1171877411yescharacteristic
276C22#1171879311yescharacteristic
277C22#1171880011yescharacteristic
278C4—22no—
279C4—22no—
280C4—22no—
281C4—22no—
282C4—22no—
283C4—21no—
284C4—21no—
285C4—41no—
286C4—1041no—
287C4—1041no—
288C4—1041no—
289C4—1041no—
290C2#1311320311yescharacteristic
291C2#1311323811yescharacteristic
292C2#1311329711yescharacteristic
293C2#1311333411yescharacteristic
294C2#1311341411yescharacteristic
295C2#1311344111yescharacteristic
296C2#1311349411yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC4×C13×C4⋊C8C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenterC4×C4⋊C8D13
hypocenterC13#7673
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊C8

Complements

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

NH ≅ G/Ntype
232. C13#7673semidirect

Maximal subgroups

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

subgroupindex
#131232182
#131149792
#131126612
#131126582
C4×C13×C4⋊C82
#767313