Finite Group Databasebeta

← #16785052

Subgroups — #16785052

Order 3328.

494 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130753C211yesmaximal, characteristic
2C42×#1057C211yesmaximal, characteristic
3#13129672C212yesmaximal
4#13129672C212yesmaximal
5#13117395C211yesmaximal, characteristic
6C2×#88144C411yescharacteristic
7C2×C4⋊#1057C2212yes—
8C2×C4×#1057—21no—
9C2×C4×#1057—21no—
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#88144C814yescomplemented
44C4⋊#1057—24no—
45C4×#1057—24no—
46C4×#1057—24no—
47C4×#1057—22no—
48C4×#1057Q814yes—
49C13×#95—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#9871—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—24no—
70C2×#1057—42no—
71C2×#1057—42no—
72C2×#1057—42no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4C2×C812yes—
77C42×C13—22no—
78C4⋊Dic13—21no—
79C4⋊Dic13—24no—
80C4⋊Dic13—22no—
81C4⋊Dic13C2×C812yes—
82#6101—24no—
83#6101—42no—
84C4×Dic13—22no—
85C4×Dic13—22no—
86C4×Dic13—22no—
87C4×Dic13—22no—
88C4×Dic13—42no—
89C4×Dic13—42no—
90C4×Dic13C2×C812yes—
91C4×Dic13M1612yes—
92C4×Dic13C2×Q812yes—
93C4×Dic13#4112yes—
94C4×#125—131no—
95#1831—131no—
96C42×C8—131no—
97#1279—132no—
98#1279—132no—
99C23×C13C2×C22⋊C411yescharacteristic
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—22no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13#10412yes—
111C2×C4×C13#10412yes—
112C2×C4×C13C4×Q812yes—
113C2×C4×C13C22×C811yescharacteristic
114C2×C4×C13C2×M1611yescharacteristic
115C2×C4×C13#13112yes—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—22no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13C22⋊C812yes—
129C2×Dic13C22⋊C812yes—
130C2×Dic13C22⋊Q812yes—
131C2×Dic13#12411yescharacteristic
132C2×Dic13C4⋊Q811yescharacteristic
133C2×Dic13#13512yes—
134C2×Dic13#13512yes—
135#1057—28no—
136#1057—82no—
137C2×#125—131no—
138C2×C4⋊C8—132no—
139C2×C4×C8—132no—
140C2×C4×C8—261no—
141C2×C4×C8—261no—
142#389—131no—
143#389#26111yescharacteristic
144#387—261no—
145#387—261no—
146#382—131no—
147C4×C4⋊C4—131no—
148C4×C4⋊C4—131no—
149C4×C4⋊C4—261no—
150C4×C4⋊C4—261no—
151C43—131no—
152#336—261no—
153#336—261no—
154C22×C13#39111yescharacteristic
155C22×C13C2×C22⋊C811yescharacteristic
156C22×C13#40811yescharacteristic
157C22×C13#41611yescharacteristic
158C22×C13#41611yescharacteristic
159C22×C13C2×#10411yescharacteristic
160C22×C13C2×#10411yescharacteristic
161C4×C13—22no—
162C4×C13—22no—
163C4×C13—42no—
164C4×C13—81no—
165C4×C13C8×Q812yes—
166C4×C13#44612yes—
167Dic13—22no—
168Dic13—22no—
169Dic13—22no—
170Dic13—42no—
171Dic13—81no—
172Dic13#48812yes—
173Dic13#49912yes—
174C22×C8—262no—
175C22×C8—262no—
176#125—134no—
177#125—262no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—131no—
180C2×C4⋊C4—131no—
181C2×C4⋊C4—261no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4C2×#26111yescharacteristic
185C2×C4⋊C4C2×#26111yescharacteristic
186C2×C42—131no—
187C2×C42—131no—
188C2×C42—131no—
189C2×C42—131no—
190C2×C42—131no—
191C2×C42—131no—
192C2×C42—261no—
193C2×C42—261no—
194C2×C42C2×#26111yescharacteristic
195C4⋊C8—264no—
196C4×C8—134no—
197C4×C8—262no—
198C4×C8—264no—
199C4×C8—264no—
200#95—21no—
201#95—261no—
202#95—261no—
203#95—261no—
204#95—261no—
205#95—261no—
206C2×C13#147611yescharacteristic
207C2×C13#147611yescharacteristic
208C2×C13#149411yescharacteristic
209C2×C13#149411yescharacteristic
210C2×C13#198411yescharacteristic
211C2×C13#199111yescharacteristic
212C2×C13#199411yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—131no—
216C22×C4—131no—
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—261no—
220C22×C4—261no—
221C22×C4C22⋊#26111yescharacteristic
222C22×C4C22⋊#26111yescharacteristic
223C22×C4C22×#26111yescharacteristic
224C2×C8—264no—
225C2×C8—264no—
226C2×C8—264no—
227C2×C8—522no—
228C2×C8—522no—
229C2×C8—522no—
230C4⋊C4—21no—
231C4⋊C4—22no—
232C4⋊C4—42no—
233C4⋊C4—132no—
234C4⋊C4—264no—
235C4⋊C4—264no—
236C4⋊C4—261no—
237C4⋊C4—262no—
238C4⋊C4—522no—
239C4⋊C4D13⋊C812yes—
240C42—22no—
241C42—132no—
242C42—132no—
243C42—132no—
244C42—132no—
245C42—262no—
246C42—262no—
247C42—262no—
248C42—262no—
249C42—522no—
250C42—522no—
251C13#987111yescharacteristic, complemented, Sylow
252C23C2×C22⋊#26111yescharacteristic
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—131no—
264C2×C4—131no—
265C2×C4—132no—
266C2×C4—132no—
267C2×C4—132no—
268C2×C4—132no—
269C2×C4—132no—
270C2×C4—261no—
271C2×C4—261no—
272C2×C4—261no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—262no—
277C2×C4—521no—
278C2×C4—521no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4#8811612yes—
283C2×C4#8811812yes—
284C2×C4C2×D13⋊C811yescharacteristic
285C2×C4D13⋊M1611yescharacteristic
286C2×C4#8823812yes—
287C2×C4Q8×#26112yes—
288C8—268no—
289C8—1042no—
290C22D13⋊(C22⋊C8)11yescharacteristic
291C22C2×#8811611yescharacteristic
292C22#1171914611yescharacteristic
293C22C2×#8811811yescharacteristic
294C22(C2×#261)⋊Q811yescharacteristic
295C22#1171916511yescharacteristic
296C22#1171916511yescharacteristic
297C4—22no—
298C4—22no—
299C4—42no—
300C4—81no—
301C4—132no—
302C4—132no—
303C4—262no—
304C4—262no—
305C4—262no—
306C4—522no—
307C4—1041no—
308C4#1171907412yes—
309C4#1171907812yes—
310C2#1313012811yescharacteristic
311C2#1313013011yescharacteristic
312C2#1313018711yescharacteristic
313C2#1313018911yescharacteristic
314C2#1313100711yescharacteristic
315C2#1313101811yescharacteristic
316C2#1313102111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#389C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#9871
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
43. #88144C8semidirect
251. C13#9871semidirect

Maximal subgroups

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

subgroupindex
#131307532
C42×#10572
#131296722
#131173952
#987113