Finite Group Databasebeta

← #15751036

Subgroups — #15751036

Order 3328.

408 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88124C211yesmaximal, characteristic
2#13114953C211yesmaximal, characteristic
3#13112660C212yesmaximal
4#13112658C212yesmaximal
5C13×#1831C211yesmaximal, characteristic
6C2×#88124C411yescharacteristic
7C2×C13×C4⋊C8—21no—
8C43×C13C2211yescharacteristic
9#11718597C411yescharacteristic
10C4×C4⋊Dic13C411yescharacteristic
11C4×C4⋊Dic13C411yescharacteristic
12#11718594—21no—
13#11718594—21no—
14C4×#6101—21no—
15C4×#6101—21no—
16#11718589C2211yescharacteristic
17#11718589C2211yescharacteristic
18C2×C4⋊#1055—21no—
19C13×#336—21no—
20C13×#336C2212yes—
21#11718116—21no—
22#11718116C2212yes—
23C22×C8×C13—22no—
24C2×C42×C13C2×C411yescharacteristic
25C2×C42×C13C2×C411yescharacteristic
26C2×C42×C13D411yescharacteristic
27C2×C42×C13D411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C42×C13C2311yescharacteristic
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×C4×Dic13—21no—
40C2×C4×Dic13—21no—
41C22×#1055—22no—
42#88124—22no—
43#88124C814yescomplemented
44C13×C4⋊C8—42no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51C4⋊#1055—42no—
52#7602—131nomaximal, Sylow
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×Dic13—21no—
61C22×Dic13—21no—
62C22×Dic13—21no—
63C22×Dic13—21no—
64C2×C8×C13—42no—
65C2×C8×C13—42no—
66C2×C8×C13—42no—
67C42×C13—22no—
68C42×C13—21no—
69C42×C13—21no—
70C42×C13—21no—
71C42×C13—21no—
72C42×C13—41no—
73C42×C13—41no—
74C42×C13—41no—
75C42×C13C2×C812yes—
76C42×C13M1612yes—
77C4⋊Dic13—21no—
78C4⋊Dic13—21no—
79C4⋊Dic13—41no—
80C4⋊Dic13—41no—
81C4⋊Dic13C2×C812yes—
82C4⋊Dic13C2×C812yes—
83#6101—24no—
84#6101—24no—
85#6101—41no—
86#6101—41no—
87#6101—41no—
88#6101—41no—
89C4×Dic13—42no—
90C4×Dic13—42no—
91C2×#1055—42no—
92C2×#1055—42no—
93C2×#1055—42no—
94C4×#125—131no—
95#1831—131no—
96#1831D1311yescharacteristic
97#1271—132no—
98#1271—132no—
99C23×C13C2×C22⋊C411yescharacteristic
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×C13C22⋊C812yes—
116C2×C4×C13C22⋊C812yes—
117C2×C4×C13#10112yes—
118C2×C4×C13C22×C811yescharacteristic
119C2×C4×C13C2×M1611yescharacteristic
120C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
121C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C13#13711yescharacteristic
123C2×C4×C13#13711yescharacteristic
124C2×Dic13—22no—
125C2×Dic13—22no—
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—
135C2×Dic13—41no—
136C8×C13—82no—
137#1055—82no—
138C2×#125—131no—
139C2×C4⋊C8—21no—
140C2×C4⋊C8—261no—
141#389—131no—
142#389—131no—
143#387—261no—
144#387—261no—
145#382—131no—
146C4×C4⋊C4—131no—
147C4×C4⋊C4—131no—
148C4×C4⋊C4—261no—
149C4×C4⋊C4—261no—
150C43C2×D1311yescharacteristic
151#336—21no—
152#336—132no—
153#336—261no—
154#336C2×D1312yes—
155C22×C13C2×C22⋊C811yescharacteristic
156C22×C13#41011yescharacteristic
157C22×C13C2×#10111yescharacteristic
158C22×C13#41711yescharacteristic
159C22×C13#41711yescharacteristic
160C22×C13#42111yescharacteristic
161C22×C13#42111yescharacteristic
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—22no—
165C4×C13—22no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—22no—
171C4×C13—41no—
172Dic13—42no—
173Dic13—42no—
174Dic13—81no—
175Dic13—81no—
176C22×C8—22no—
177C22×C8—262no—
178#125—134no—
179#125—262no—
180C2×C4⋊C4—131no—
181C2×C4⋊C4—131no—
182C2×C4⋊C4—131no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—261no—
188C2×C42—261no—
189C2×C42—261no—
190C2×C42C4×D1311yescharacteristic
191C2×C42C4×D1311yescharacteristic
192C2×C42D5211yescharacteristic
193C2×C42D5211yescharacteristic
194C2×C42C22⋊D1311yescharacteristic
195C2×C42C22⋊D1311yescharacteristic
196C2×C42C22×D1311yescharacteristic
197C4⋊C8—42no—
198C4⋊C8—522no—
199#95—261no—
200#95—261no—
201#95—261no—
202#95—261no—
203#95—261no—
204#95—261no—
205C2×C13#146111yescharacteristic
206C2×C13#147711yescharacteristic
207C2×C13#147711yescharacteristic
208C2×C13#151211yescharacteristic
209C2×C13#151211yescharacteristic
210C2×C13#153411yescharacteristic
211C2×C13#156111yescharacteristic
212C22×C4—261no—
213C22×C4—261no—
214C22×C4—261no—
215C22×C4—261no—
216C22×C4#610311yescharacteristic
217C22×C4#610311yescharacteristic
218C22×C4#610311yescharacteristic
219C22×C4#610311yescharacteristic
220C22×C4C2×C4×D1311yescharacteristic
221C22×C4C2×D5211yescharacteristic
222C22×C4C2×C22⋊D1311yescharacteristic
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—42no—
226C2×C8—522no—
227C2×C8—522no—
228C2×C8—522no—
229C4⋊C4—132no—
230C4⋊C4—132no—
231C4⋊C4—261no—
232C4⋊C4—261no—
233C4⋊C4—264no—
234C4⋊C4—264no—
235C4⋊C4—521no—
236C4⋊C4—521no—
237C4⋊C4—521no—
238C4⋊C4—521no—
239C4⋊C4—521no—
240C4⋊C4—521no—
241C42—22no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—41no—
247C42—41no—
248C42—41no—
249C42—522no—
250C42—522no—
251C42C8×D1312yes—
252C42#609412yes—
253C13#760211yescharacteristic, complemented, Sylow
254C23C2×#610311yescharacteristic
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—21no—
269C2×C4—21no—
270C2×C4—262no—
271C2×C4—262no—
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—521no—
281C2×C4—521no—
282C2×C4#8806012yes—
283C2×C4#8806012yes—
284C2×C4#8806412yes—
285C2×C4C2×C8×D1311yescharacteristic
286C2×C4C2×#609411yescharacteristic
287C2×C4#8816211yescharacteristic
288C2×C4#8816311yescharacteristic
289C2×C4#8818611yescharacteristic
290C2×C4#8819611yescharacteristic
291C8—82no—
292C8—1042no—
293C22#1171862711yescharacteristic
294C22#1171866611yescharacteristic
295C22#1171866711yescharacteristic
296C22C2×#8806011yescharacteristic
297C22#1171879411yescharacteristic
298C22C2×#8806411yescharacteristic
299C22#1171880011yescharacteristic
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—21no—
306C4—22no—
307C4—22no—
308C4—22no—
309C4—41no—
310C4—522no—
311C4—522no—
312C4—1041no—
313C4—1041no—
314C2#1311315911yescharacteristic
315C2#1311322111yescharacteristic
316C2#1311322411yescharacteristic
317C2#1311337211yescharacteristic
318C2#1311337511yescharacteristic
319C2#1311346211yescharacteristic
320C2#1311357311yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1831C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1831D13
hypocenterC13#7602
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
43. #88124C8semidirect
253. C13#7602semidirect

Maximal subgroups

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

subgroupindex
C4×#881242
#131149532
#131126602
#131126582
C13×#18312
#760213