Finite Group Databasebeta

← #16785040

Subgroups — #16785040

Order 3328.

460 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130622C211yesmaximal, characteristic
2C4×#88112C211yesmaximal, characteristic
3#13129672C212yesmaximal
4#13129672C212yesmaximal
5#125×Dic13C211yesmaximal, characteristic
6C2×C13×#125C411yescharacteristic
7C2×#88112—21no—
8C2×#88110—21no—
9C2×C4⋊#1057C2212yes—
10C2×C4×#1057C2212yes—
11#11718646C411yescharacteristic
12#11718646C411yescharacteristic
13#11718642—21no—
14#11718642—21no—
15C4⋊C4×Dic13—21no—
16C4⋊C4×Dic13—21no—
17C4⋊C4×Dic13C2211yescharacteristic
18C4⋊C4×Dic13C2211yescharacteristic
19#11718597C411yescharacteristic
20C42×Dic13C2211yescharacteristic
21#11718290—21no—
22#11718290—21no—
23C22×#1057—22no—
24C22×#1057—22no—
25C13×#125—22no—
26C13×#125—22no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13C2311yescharacteristic
44#88112—24no—
45#88110—42no—
46C4⋊#1057—22no—
47C4⋊#1057Q814yes—
48C4×#1057—24no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#9867—131nomaximal, Sylow
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×Dic13—21no—
62C22×Dic13—21no—
63C22×Dic13C22⋊C411yescharacteristic
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C2×D411yescharacteristic
66C22×Dic13C2×D411yescharacteristic
67C2×#1057—24no—
68C2×#1057—24no—
69C2×#1057—42no—
70C2×#1057—42no—
71C2×#1057—42no—
72C2×#1057—42no—
73C13×C4⋊C4—24no—
74C13×C4⋊C4—24no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4M1612yes—
78C13×C4⋊C4M1612yes—
79C42×C13—21no—
80C42×C13—21no—
81C4⋊Dic13—22no—
82C4⋊Dic13—22no—
83C4⋊Dic13—42no—
84C4⋊Dic13—42no—
85C4×Dic13—22no—
86C4×Dic13—22no—
87C4×Dic13—22no—
88C4×Dic13—21no—
89C4×Dic13—21no—
90C4×Dic13—41no—
91C4×Dic13—42no—
92C4×Dic13—41no—
93C4×Dic13—41no—
94C4×Dic13C2×Q812yes—
95C4×Dic13#4112yes—
96C4×#125—131no—
97#1767—131no—
98C4×C4⋊C8—131no—
99#1279—132no—
100#1279—132no—
101C23×C13C2×C22⋊C411yescharacteristic
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13C4×Q812yes—
115C2×C4×C13C2×M1611yescharacteristic
116C2×C4×C13C2×M1611yescharacteristic
117C2×C4×C13#13112yes—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13#10412yes—
132C2×Dic13C22⋊Q812yes—
133C2×Dic13#12411yescharacteristic
134C2×Dic13C4⋊Q811yescharacteristic
135C2×Dic13#13512yes—
136C2×Dic13AGL(1,ℤ/8)11yescharacteristic
137C2×Dic13#13711yescharacteristic
138#1057—44no—
139#1057—44no—
140C2×#125#26111yescharacteristic
141C2×C4⋊C8—132no—
142C2×C4⋊C8—261no—
143C2×#97—261no—
144C2×C4×C8—132no—
145#389—131no—
146#389—131no—
147#387—261no—
148#387—261no—
149#382—131no—
150C4×C4⋊C4—131no—
151C4×C4⋊C4—131no—
152C4×C4⋊C4—261no—
153C4×C4⋊C4—261no—
154C43—131no—
155#336—261no—
156#336—261no—
157C22×C13#39111yescharacteristic
158C22×C13#40711yescharacteristic
159C22×C13#40811yescharacteristic
160C22×C13#41611yescharacteristic
161C22×C13#41711yescharacteristic
162C22×C13C2×#10411yescharacteristic
163C22×C13#42111yescharacteristic
164C4×C13—41no—
165C4×C13—42no—
166C4×C13—41no—
167C4×C13—42no—
168C4×C13#44612yes—
169C4×C13#44612yes—
170Dic13—21no—
171Dic13—21no—
172Dic13—22no—
173Dic13—41no—
174Dic13—81no—
175Dic13—81no—
176Dic13#47812yes—
177Dic13#47912yes—
178C22×C8—262no—
179C22×C8—262no—
180#125—22no—
181#125—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—131no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4C2×#26111yescharacteristic
189C2×C4⋊C4C2×#26111yescharacteristic
190C2×C42—131no—
191C2×C42—131no—
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—131no—
195C2×C42—131no—
196C2×C42—261no—
197C2×C42—261no—
198C2×C42C2×#26111yescharacteristic
199C4⋊C8—134no—
200C4⋊C8—262no—
201C4⋊C8—264no—
202#97—522no—
203C4×C8—264no—
204#95—261no—
205#95—261no—
206#95—261no—
207#95—261no—
208#95—261no—
209#95—261no—
210C2×C13#148811yescharacteristic
211C2×C13#148911yescharacteristic
212C2×C13#149411yescharacteristic
213C2×C13#149511yescharacteristic
214C2×C13#198511yescharacteristic
215C2×C13#198611yescharacteristic
216C2×C13#198911yescharacteristic
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—131no—
220C22×C4—131no—
221C22×C4—131no—
222C22×C4—131no—
223C22×C4—261no—
224C22×C4—261no—
225C22×C4C22⋊#26111yescharacteristic
226C22×C4C22⋊#26111yescharacteristic
227C22×C4C22×#26111yescharacteristic
228C2×C8—264no—
229C2×C8—264no—
230C2×C8—522no—
231C2×C8—522no—
232C2×C8—522no—
233C2×C8—522no—
234C4⋊C4—24no—
235C4⋊C4—24no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—262no—
239C4⋊C4—262no—
240C4⋊C4—522no—
241C4⋊C4—522no—
242C4⋊C4#612212yes—
243C4⋊C4#612212yes—
244C42—21no—
245C42—21no—
246C42—132no—
247C42—132no—
248C42—261no—
249C42—262no—
250C42—261no—
251C42—262no—
252C42—262no—
253C42—521no—
254C42—521no—
255C42—521no—
256C42—522no—
257C13#986711yescharacteristic, complemented, Sylow
258C23C2×C22⋊#26111yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—132no—
272C2×C4—131no—
273C2×C4—131no—
274C2×C4—132no—
275C2×C4—131no—
276C2×C4—131no—
277C2×C4—132no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4#8824012yes—
292C2×C4Q8×#26112yes—
293C2×C4C2×#612211yescharacteristic
294C2×C4C2×#612211yescharacteristic
295C8—524no—
296C8—524no—
297C22#1171915911yescharacteristic
298C22(C2×#261)⋊Q811yescharacteristic
299C22D13⋊#10411yescharacteristic
300C22#1171916411yescharacteristic
301C22#1171916511yescharacteristic
302C22#1171916611yescharacteristic
303C22#1171916911yescharacteristic
304C4—41no—
305C4—42no—
306C4—41no—
307C4—42no—
308C4—132no—
309C4—132no—
310C4—261no—
311C4—261no—
312C4—262no—
313C4—521no—
314C4—1041no—
315C4—1041no—
316C4#1171915812yes—
317C4#1171915812yes—
318C2#1313016711yescharacteristic
319C2#1313017111yescharacteristic
320C2#1313019011yescharacteristic
321C2#1313019411yescharacteristic
322C2#1313101011yescharacteristic
323C2#1313101311yescharacteristic
324C2#1313101611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#125C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#125#261
hypocenterC13#9867
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
257. C13#9867semidirect

Maximal subgroups

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

subgroupindex
#131306222
C4×#881122
#131296722
#125×Dic132
#986713