Finite Group Databasebeta

← #16785039

Subgroups — #16785039

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×C4⋊#1057C211yesmaximal, characteristic
3#13129672C212yesmaximal
4#13129672C212yesmaximal
5#13117395C211yesmaximal, characteristic
6C2×#88144C411yescharacteristic
7C2×#88110—21no—
8C2×C4⋊#1057—21no—
9C2×C4⋊#1057C2212yes—
10C2×C4×#1057C2212yes—
11C13×#389C411yescharacteristic
12#11718639—21no—
13#11718638C411yescharacteristic
14C4⋊C4×Dic13—21no—
15C4⋊C4×Dic13C2211yescharacteristic
16C4⋊C4×Dic13C2211yescharacteristic
17C42×Dic13C2211yescharacteristic
18#11718589C411yescharacteristic
19#11718314—21no—
20#11718310—21no—
21#11718290—21no—
22#11718290—21no—
23C22×#1057—22no—
24C22×#1057—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—21no—
33C2×#6101—21no—
34C2×C4×Dic13—21no—
35C2×C4×Dic13—21no—
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13C2311yescharacteristic
42#88144—22no—
43#88144—22no—
44#88110—42no—
45C4⋊#1057—24no—
46C4⋊#1057—22no—
47C4⋊#1057Q814yes—
48C4×#1057—24no—
49C13×#95—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—21no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4M1612yes—
77C42×C13—22no—
78C4⋊Dic13—24no—
79C4⋊Dic13—21no—
80C4⋊Dic13—22no—
81C4⋊Dic13M1612yes—
82#6101—24no—
83#6101—42no—
84C4×Dic13—22no—
85C4×Dic13—21no—
86C4×Dic13—21no—
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—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13#10412yes—
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—22no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
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—131no—
141C2×C4⋊C8—132no—
142C2×C4⋊C8—261no—
143C2×#97—261no—
144C2×C4×C8—132no—
145#389—131no—
146#389#26111yescharacteristic
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—22no—
165C4×C13—42no—
166C4×C13—41no—
167C4×C13—81no—
168C4×C13#44612yes—
169C4×C13#44612yes—
170Dic13—21no—
171Dic13—21no—
172Dic13—41no—
173Dic13—42no—
174Dic13—41no—
175Dic13—81no—
176Dic13#47812yes—
177Dic13#47912yes—
178C22×C8—262no—
179C22×C8—262no—
180#125—262no—
181#125—262no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—131no—
185C2×C4⋊C4—261no—
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—21no—
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—21no—
235C4⋊C4—22no—
236C4⋊C4—42no—
237C4⋊C4—132no—
238C4⋊C4—264no—
239C4⋊C4—264no—
240C4⋊C4—261no—
241C4⋊C4—262no—
242C4⋊C4—522no—
243C4⋊C4#611812yes—
244C42—22no—
245C42—132no—
246C42—132no—
247C42—261no—
248C42—262no—
249C42—261no—
250C42—262no—
251C42—261no—
252C42—261no—
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—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—132no—
271C2×C4—131no—
272C2×C4—131no—
273C2×C4—132no—
274C2×C4—131no—
275C2×C4—131no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—262no—
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#8811612yes—
291C2×C4C2×#611811yescharacteristic
292C2×C4D13⋊M1611yescharacteristic
293C2×C4#8823812yes—
294C2×C4Q8×#26112yes—
295C8—524no—
296C8—524no—
297C22#1171912711yescharacteristic
298C22C2×#8811611yescharacteristic
299C22#1171914611yescharacteristic
300C22#1171915511yescharacteristic
301C22(C2×#261)⋊Q811yescharacteristic
302C22#1171916411yescharacteristic
303C22#1171916511yescharacteristic
304C4—22no—
305C4—42no—
306C4—41no—
307C4—81no—
308C4—132no—
309C4—132no—
310C4—261no—
311C4—261no—
312C4—521no—
313C4—522no—
314C4—521no—
315C4—1041no—
316C4#1171907812yes—
317C4#1171908012yes—
318C2#1313017011yescharacteristic
319C2#1313017211yescharacteristic
320C2#1313018711yescharacteristic
321C2#1313019311yescharacteristic
322C2#1313100911yescharacteristic
323C2#1313101211yescharacteristic
324C2#1313101611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#389C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#9867
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

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×C4⋊#10572
#131296722
#131173952
#986713