Finite Group Databasebeta

← #15756242

Subgroups — #15756242

Order 3328.

1158 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13114746C212yesmaximal
2#13112679C214yesmaximal, complemented
3C22×C13×#95C211yesmaximal, characteristic
4C24×C4×C13C411yescharacteristic
5C24×C4×C13C411yescharacteristic
6C24×C4×C13C2211yescharacteristic
7C2×C13×#95—22no—
8C2×C13×#95—22no—
9C2×C13×#95C412yes—
10C2×C13×#95C2212yes—
11C2×C22⋊#1055—22no—
12C2×C22⋊#1055—22no—
13C2×C22⋊#1055C2214yes—
14C25×C13C2×C411yescharacteristic
15C23×C4×C13—21no—
16C23×C4×C13—21no—
17C23×C4×C13—21no—
18C23×C4×C13—21no—
19C23×C4×C13—22no—
20C23×C4×C13—24no—
21C23×C4×C13—24no—
22C23×C4×C13—42no—
23C23×C4×C13—42no—
24C23×C4×C13—42no—
25C23×C4×C13—42no—
26C23×C4×C13—42no—
27C23×C4×C13—42no—
28C23×C4×C13C814yescomplemented
29C23×C4×C13C2×C411yescharacteristic
30C23×C4×C13C2×C412yes—
31C23×C4×C13C2×C412yes—
32C23×C4×C13D412yes—
33C23×C4×C13D412yes—
34C23×C4×C13C2311yescharacteristic
35C22×#1055—24no—
36C13×#95—24no—
37C13×#95—24no—
38C22⋊#1055—28no—
39C22⋊#1055—44no—
40C22⋊#1055—44no—
41#8698—131nomaximal, Sylow
42C24×C13—22no—
43C24×C13—22no—
44C24×C13—22no—
45C24×C13—22no—
46C24×C13—22no—
47C24×C13—22no—
48C24×C13C22⋊C411yescharacteristic
49C24×C13C22⋊C411yescharacteristic
50C24×C13C2×C812yes—
51C24×C13M1612yes—
52C24×C13C22×C411yescharacteristic
53C22×C4×C13—24no—
54C22×C4×C13—24no—
55C22×C4×C13—24no—
56C22×C4×C13—24no—
57C22×C4×C13—24no—
58C22×C4×C13—24no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—22no—
64C22×C4×C13—24no—
65C22×C4×C13—24no—
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13—41no—
71C22×C4×C13—41no—
72C22×C4×C13—416no—
73C22×C4×C13—416no—
74C22×C4×C13—48no—
75C22×C4×C13—42no—
76C22×C4×C13—42no—
77C22×C4×C13—42no—
78C22×C4×C13—42no—
79C22×C4×C13—42no—
80C22×C4×C13—42no—
81C22×C4×C13—42no—
82C22×C4×C13—42no—
83C22×C4×C13—48no—
84C22×C4×C13—42no—
85C22×C4×C13—42no—
86C22×C4×C13—42no—
87C22×C4×C13—42no—
88C22×C4×C13C22⋊C412yes—
89C22×C4×C13C2×C814yes—
90C22×C4×C13M1614yes—
91C22×C4×C13C2×D412yes—
92C22×C4×C13#4114yes—
93C2×#1055—44no—
94C2×#1055—44no—
95C2×#1055—44no—
96C22×#95D1311yescharacteristic
97#1779—132no—
98#1280—134no—
99C23×C13—28no—
100C23×C13—28no—
101C23×C13—28no—
102C23×C13—28no—
103C23×C13—24no—
104C23×C13—24no—
105C23×C13—24no—
106C23×C13—24no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—24no—
120C23×C13—24no—
121C23×C13C22⋊C812yes—
122C23×C13C22⋊C812yes—
123C23×C13#9912yes—
124C23×C13#9912yes—
125C23×C13#10012yes—
126C23×C13#10112yes—
127C23×C13C2×C22⋊C411yescharacteristic
128C23×C13#11712yes—
129C23×C13C22×C811yescharacteristic
130C23×C13C2×M1611yescharacteristic
131C23×C13C2×M1612yes—
132C2×C4×C13—22no—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—24no—
136C2×C4×C13—24no—
137C2×C4×C13—22no—
138C2×C4×C13—22no—
139C2×C4×C13—44no—
140C2×C4×C13—48no—
141C2×C4×C13—48no—
142C2×C4×C13—44no—
143C2×C4×C13—48no—
144C2×C4×C13—44no—
145C2×C4×C13—48no—
146C2×C4×C13—48no—
147C2×C4×C13—44no—
148C2×C4×C13—48no—
149C2×C4×C13—42no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—44no—
154C2×C4×C13—44no—
155C2×C4×C13#12314yes—
156#1055—84no—
157C24×C4Dic1311yescharacteristic
158C24×C4Dic1311yescharacteristic
159C24×C4C2×D1311yescharacteristic
160C2×C22⋊C8—134no—
161C2×C22⋊C8—262no—
162C2×C22⋊C8—262no—
163C2×#95—22no—
164C2×#95—22no—
165C2×#95Dic1312yes—
166C2×#95C2×D1312yes—
167C22×C13—216no—
168C22×C13—216no—
169C22×C13—22no—
170C22×C13—22no—
171C22×C13—22no—
172C22×C13—22no—
173C22×C13—22no—
174C22×C13—22no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—22no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—22no—
184C22×C13—22no—
185C22×C13—22no—
186C22×C13—22no—
187C22×C13—22no—
188C22×C13—22no—
189C22×C13#32314yes—
190C22×C13#32414yes—
191C22×C13#38111yescharacteristic
192C22×C13C2×C22⋊C811yescharacteristic
193C22×C13#40711yescharacteristic
194C22×C13C2×#9911yescharacteristic
195C22×C13C2×#9911yescharacteristic
196C22×C13C2×#10011yescharacteristic
197C22×C13C2×#10111yescharacteristic
198C22×C13#43112yes—
199C22×C13#43212yes—
200C4×C13—24no—
201C4×C13—42no—
202C4×C13—44no—
203C4×C13—44no—
204C25C2×Dic1311yescharacteristic
205C23×C4—22no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—24no—
211C23×C4—24no—
212C23×C4—42no—
213C23×C4—42no—
214C23×C4—42no—
215C23×C4—42no—
216C23×C4—42no—
217C23×C4—42no—
218C23×C4#105514yescomplemented
219C23×C4C2×Dic1312yes—
220C23×C4C2×Dic1312yes—
221C23×C4C2×Dic1311yescharacteristic
222C23×C4C22⋊D1312yes—
223C23×C4C22⋊D1312yes—
224C23×C4C22×D1311yescharacteristic
225C22×C8—264no—
226C22⋊C8—268no—
227C22⋊C8—524no—
228C22⋊C8—524no—
229#95—24no—
230#95—24no—
231C2×C13—24no—
232C2×C13—24no—
233C2×C13—22no—
234C2×C13—22no—
235C2×C13C2×#32311yescharacteristic
236C2×C13C2×#32411yescharacteristic
237C2×C13#146211yescharacteristic
238C2×C13#146311yescharacteristic
239C2×C13#181711yescharacteristic
240C2×C13#181911yescharacteristic
241C2×C13#182111yescharacteristic
242C24—22no—
243C24—22no—
244C24—22no—
245C24—22no—
246C24—22no—
247C24—22no—
248C24C2×#105512yes—
249C24#609912yes—
250C24C22⋊Dic1311yescharacteristic
251C24C22⋊Dic1311yescharacteristic
252C24C22×Dic1311yescharacteristic
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—41no—
267C22×C4—41no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—416no—
273C22×C4—416no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4—48no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—48no—
284C22×C4—42no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4C2×#105514yes—
289C22×C4#609914yes—
290C22×C4C22⋊Dic1312yes—
291C22×C4#612714yes—
292C22×C4C2×C22⋊D1312yes—
293C2×C8—524no—
294C2×C8—524no—
295C2×C8—524no—
296C13#869811yescharacteristic, complemented, Sylow
297C23—28no—
298C23—28no—
299C23—28no—
300C23—28no—
301C23—24no—
302C23—24no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—24no—
314C23—24no—
315C23—21no—
316C23—21no—
317C23—24no—
318C23—24no—
319C23C22⋊#105512yes—
320C23C22⋊#105512yes—
321C23#8807312yes—
322C23#8807412yes—
323C23#8807412yes—
324C23#8807612yes—
325C23C22×#105511yescharacteristic
326C23C2×#609912yes—
327C23C2×#609911yescharacteristic
328C23#8818012yes—
329C23C2×C22⋊Dic1311yescharacteristic
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—44no—
338C2×C4—48no—
339C2×C4—48no—
340C2×C4—44no—
341C2×C4—48no—
342C2×C4—44no—
343C2×C4—48no—
344C2×C4—48no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—48no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4#8818314yes—
354C8—1044no—
355C22—216no—
356C22—216no—
357C22—22no—
358C22—22no—
359C22—22no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22—22no—
366C22—21no—
367C22—21no—
368C22—22no—
369C22—21no—
370C22—21no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22#1171811714yes—
378C22#1171812014yes—
379C22#1171858612yes—
380C22#1171858712yes—
381C22C2×C22⋊#105511yescharacteristic
382C22#1171886811yescharacteristic
383C22#1171887211yescharacteristic
384C22C2×#8807311yescharacteristic
385C22C2×#8807411yescharacteristic
386C22C2×#8807411yescharacteristic
387C22C2×#8807611yescharacteristic
388C4—24no—
389C4—42no—
390C4—44no—
391C4—44no—
392C2—22no—
393C2—22no—
394C2—24no—
395C2—24no—
396C2C2×#1171811711yescharacteristic
397C2C2×#1171812011yescharacteristic
398C2#1311316311yescharacteristic
399C2#1311316611yescharacteristic
400C2#1311490411yescharacteristic
401C2#1311491011yescharacteristic
402C2#1311491611yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC23×C13C22×C8
FrattiniC23×C4C22×D13
FittingC22×C13×#95C2
socleC23×C13C2×C22⋊C4
prime radicalC25×C13C2×C4
cosocleC23×C4×C13C23
hypercenterC22×#95D13
hypocenterC13#8698
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
2. #13112679C2semidirect
28. C23×C4×C13C8semidirect
218. C23×C4#1055semidirect
296. C13#8698semidirect

Maximal subgroups

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

subgroupindex
#131147462
#131126792
C22×C13×#952
#869813