Finite Group Databasebeta

← #15750967

Subgroups — #15750967

Order 3328.

426 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88124C211yesmaximal, characteristic
2C4×C4⋊#1055C211yesmaximal, characteristic
3#13112660C212yesmaximal
4#13112658C212yesmaximal
5C13×#1839C211yesmaximal, characteristic
6C2×#88124C411yescharacteristic
7C43×C13C2211yescharacteristic
8#11718597C411yescharacteristic
9C4×C4⋊Dic13C411yescharacteristic
10C4×C4⋊Dic13C411yescharacteristic
11#11718594—21no—
12#11718594—21no—
13C4×#6101—21no—
14C4×#6101—21no—
15#11718589C2211yescharacteristic
16#11718589C2211yescharacteristic
17C2×C4⋊#1055—21no—
18C2×C4×#1055—21no—
19C13×#336—21no—
20C13×#336—21no—
21C13×#336C2212yes—
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
44#88071—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50C4⋊#1055—24no—
51C4×#1055—42no—
52#7585—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—22no—
69C42×C13—22no—
70C42×C13—21no—
71C42×C13—21no—
72C42×C13—41no—
73C42×C13—41no—
74C42×C13C2×C812yes—
75C42×C13M1612yes—
76C4⋊Dic13—21no—
77C4⋊Dic13—21no—
78C4⋊Dic13—41no—
79C4⋊Dic13—41no—
80C4⋊Dic13C2×C812yes—
81C4⋊Dic13C2×C812yes—
82#6101—24no—
83#6101—24no—
84#6101—42no—
85#6101—41no—
86#6101—41no—
87C4×Dic13—42no—
88C4×Dic13—42no—
89C2×#1055—24no—
90C2×#1055—42no—
91C2×#1055—42no—
92C4×#125—131no—
93#1839D1311yescharacteristic
94C4×C4⋊C8—131no—
95#1271—132no—
96#1271—132no—
97C23×C13C2×C22⋊C411yescharacteristic
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—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13C22⋊C812yes—
113C2×C4×C13C22⋊C812yes—
114C2×C4×C13#10112yes—
115C2×C4×C13#10412yes—
116C2×C4×C13C22×C811yescharacteristic
117C2×C4×C13C2×M1611yescharacteristic
118C2×C4×C13#13512yes—
119C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C13#13711yescharacteristic
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—82no—
134#1055—44no—
135C2×#125—131no—
136C2×C4⋊C8—261no—
137C2×C4×C8—261no—
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—132no—
151#336C2×D1312yes—
152C22×C13C2×C22⋊C811yescharacteristic
153C22×C13#41011yescharacteristic
154C22×C13C2×#10111yescharacteristic
155C22×C13#41611yescharacteristic
156C22×C13#41711yescharacteristic
157C22×C13C2×#10411yescharacteristic
158C22×C13#42111yescharacteristic
159C4×C13—22no—
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—22no—
163C4×C13—22no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—22no—
167C4×C13—22no—
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
193C4⋊C8—264no—
194C4×C8—522no—
195#95—261no—
196#95—261no—
197#95—261no—
198#95—261no—
199#95—261no—
200#95—261no—
201C2×C13#146111yescharacteristic
202C2×C13#147611yescharacteristic
203C2×C13#147711yescharacteristic
204C2×C13#150911yescharacteristic
205C2×C13#152111yescharacteristic
206C2×C13#152811yescharacteristic
207C2×C13#155211yescharacteristic
208C22×C4—261no—
209C22×C4—261no—
210C22×C4—261no—
211C22×C4—261no—
212C22×C4#610311yescharacteristic
213C22×C4#610311yescharacteristic
214C22×C4#610311yescharacteristic
215C22×C4#610311yescharacteristic
216C22×C4C2×C4×D1311yescharacteristic
217C22×C4C2×D5211yescharacteristic
218C22×C4C2×C22⋊D1311yescharacteristic
219C2×C8—42no—
220C2×C8—42no—
221C2×C8—42no—
222C2×C8—264no—
223C2×C8—522no—
224C2×C8—522no—
225C4⋊C4—132no—
226C4⋊C4—132no—
227C4⋊C4—261no—
228C4⋊C4—261no—
229C4⋊C4—264no—
230C4⋊C4—264no—
231C4⋊C4—521no—
232C4⋊C4—521no—
233C4⋊C4—521no—
234C4⋊C4—521no—
235C4⋊C4—522no—
236C42—22no—
237C42—22no—
238C42—21no—
239C42—21no—
240C42—22no—
241C42—41no—
242C42—41no—
243C42—522no—
244C42—522no—
245C42C8×D1312yes—
246C42#609412yes—
247C13#758511yescharacteristic, 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—262no—
264C2×C4—262no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4—521no—
268C2×C4—521no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4—521no—
275C2×C4#8806012yes—
276C2×C4#8806012yes—
277C2×C4#8806412yes—
278C2×C4#8806512yes—
279C2×C4C2×C8×D1311yescharacteristic
280C2×C4C2×#609411yescharacteristic
281C2×C4#8816211yescharacteristic
282C2×C4#8816311yescharacteristic
283C2×C4#8820412yes—
284C8—82no—
285C8—524no—
286C22#1171866311yescharacteristic
287C22#1171866611yescharacteristic
288C22#1171866711yescharacteristic
289C22C2×#8806011yescharacteristic
290C22#1171879411yescharacteristic
291C22C2×#8806411yescharacteristic
292C22C2×#8806511yescharacteristic
293C4—21no—
294C4—21no—
295C4—22no—
296C4—21no—
297C4—21no—
298C4—22no—
299C4—22no—
300C4—22no—
301C4—22no—
302C4—522no—
303C4—522no—
304C4—1041no—
305C4—1041no—
306C2#1311315911yescharacteristic
307C2#1311321611yescharacteristic
308C2#1311322411yescharacteristic
309C2#1311336211yescharacteristic
310C2#1311341111yescharacteristic
311C2#1311343911yescharacteristic
312C2#1311353711yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC2×C4×C13C22×C8
FrattiniC2×C42C22×D13
FittingC13×#1839C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1839D13
hypocenterC13#7585
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #1839

Complements

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

NH ≅ G/Ntype
43. #88124C8semidirect
247. C13#7585semidirect

Maximal subgroups

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

subgroupindex
C4×#881242
C4×C4⋊#10552
#131126602
#131126582
C13×#18392
#758513