Finite Group Databasebeta

← #15880819

Subgroups — #15880819

Order 3328.

680 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#13117234C211yesmaximal, characteristic
2#13115557C212yesmaximal, complemented
3#13115452C212yesmaximal
4#13115445C212yesmaximal
5#13114954C212yesmaximal, complemented
6#13114713C212yesmaximal, complemented
7#13114598C211yesmaximal, characteristic
8#13114586C212yesmaximal, complemented
9C13×#1797C211yesmaximal, characteristic
10C22×C42×C13C2211yescharacteristic
11C2×C13×C4⋊C8C2212yes—
12C2×C13×C22⋊C8C2211yescharacteristic
13C2×C13×C22⋊C8C2211yescharacteristic
14#11718873C411yescharacteristic
15#11718873C411yescharacteristic
16#11718872C412yes—
17C4×C22⋊Dic13C2212yes—
18C2×C22⋊#1055C2212yes—
19C2×#88055C2212yes—
20C2×#88054C2212yes—
21C2×#88054C2212yes—
22C2×C8×Dic13C2212yes—
23#11718598C412yes—
24#11718597C411yescharacteristic
25#11718597C411yescharacteristic
26C4×C4⋊Dic13C2211yescharacteristic
27C4×C4⋊Dic13C2211yescharacteristic
28#11718593C2212yes—
29C2×#88043C2212yes—
30C13×#336C2212yes—
31#11718142C2212yes—
32#11718142C2212yes—
33#11718142C2212yes—
34#11718142C2212yes—
35#11718116C2211yescharacteristic
36#11718116C2211yescharacteristic
37C23×C4×C13C2×C411yescharacteristic
38C23×C4×C13C2×C411yescharacteristic
39C23×C4×C13C2311yescharacteristic
40C22×C8×C13C2312yes—
41C22×C8×C13C2312yes—
42C2×C42×C13—24no—
43C2×C42×C13C2×C411yescharacteristic
44C2×C42×C13C2×C411yescharacteristic
45C2×C42×C13C2311yescharacteristic
46C2×C42×C13C2311yescharacteristic
47C2×C22⋊Dic13C2×C412yes—
48C2×C22⋊Dic13C2×C412yes—
49C2×C4⋊Dic13C2×C411yescharacteristic
50C2×C4⋊Dic13C2×C411yescharacteristic
51C2×C4⋊Dic13C2×C411yescharacteristic
52C2×C4⋊Dic13C2×C411yescharacteristic
53C2×C4×Dic13C2312yes—
54C2×C4×Dic13C2312yes—
55C22×#1055C2312yes—
56C22×#1055C2312yes—
57C13×C4⋊C8—24no—
58C13×C22⋊C8—41no—
59C13×C22⋊C8—41no—
60#88071C2×C412yes—
61#88071C2×C412yes—
62#88071C2×C412yes—
63#88071C2×C412yes—
64#88071C2×C412yes—
65#88071C2×C412yes—
66#88071C2×C412yes—
67#88071C2×C412yes—
68C22⋊#1055—24no—
69#88055—24no—
70#88054—42no—
71#88054—42no—
72C8×Dic13—24no—
73#88043—24no—
74#22635—131nomaximal, Sylow
75C24×C13C22×C411yescharacteristic
76C22×C4×C13—22no—
77C22×C4×C13—22no—
78C22×C4×C13—22no—
79C22×C4×C13—22no—
80C22×C4×C13—22no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—41no—
84C22×C4×C13—41no—
85C22×C4×C13—41no—
86C22×C4×C13C22×C411yescharacteristic
87C22×C4×C13C22×C411yescharacteristic
88C22×C4×C13C22×C411yescharacteristic
89C22×C4×C13C22×C411yescharacteristic
90C22×C4×C13C22×C411yescharacteristic
91C22×C4×C13C2411yescharacteristic
92C22×Dic13C22×C412yes—
93C22×Dic13C22×C412yes—
94C22×Dic13C22×C412yes—
95C22×Dic13C22×C412yes—
96C2×C8×C13—22no—
97C2×C8×C13—22no—
98C2×C8×C13—22no—
99C2×C8×C13—22no—
100C2×C8×C13—22no—
101C2×C8×C13—22no—
102C42×C13—22no—
103C42×C13—22no—
104C42×C13—22no—
105C42×C13#4114yes—
106C22⋊Dic13—24no—
107C22⋊Dic13—42no—
108C4⋊Dic13—41no—
109C4⋊Dic13—41no—
110C4⋊Dic13—41no—
111C4⋊Dic13—41no—
112C4×Dic13—22no—
113C4×Dic13—22no—
114C4×Dic13—22no—
115C4×Dic13—22no—
116C2×#1055—22no—
117C2×#1055—22no—
118C2×#1055—22no—
119C2×#1055—22no—
120C2×#1055—22no—
121C2×#1055#4114yes—
122#2283—131no—
123#1940—132no—
124#1924—132no—
125#1923—132no—
126#1832—132no—
127#1797D1311yescharacteristic
128#1771—132no—
129#1749—131no—
130#1746—132no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13—21no—
134C23×C13—21no—
135C23×C13—21no—
136C23×C13—21no—
137C23×C13#13112yes—
138C23×C13C23×C411yescharacteristic
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—44no—
153C2×C4×C13—44no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13#11712yes—
157C2×C4×C13#11712yes—
158C2×C4×C13C2×#4112yes—
159C2×C4×C13C2×#4112yes—
160C2×C4×C13H(5,𝔽2)11yescharacteristic
161C2×C4×C132−1+411yescharacteristic
162C2×Dic13—22no—
163C2×Dic13—22no—
164C2×Dic13—22no—
165C2×Dic13—22no—
166C2×Dic13—22no—
167C2×Dic13—22no—
168C2×Dic13—22no—
169C2×Dic13—22no—
170C2×Dic13—22no—
171C2×Dic13—22no—
172C2×Dic13—22no—
173C2×Dic13—22no—
174C8×C13—42no—
175C8×C13—42no—
176#1055—24no—
177#1055—42no—
178C22×C42C2×D1311yescharacteristic
179C2×C4⋊C8—132no—
180C2×C4⋊C8—132no—
181C2×C4⋊C8C2×D1312yes—
182C2×C22⋊C8—132no—
183C2×C22⋊C8C2×D1311yescharacteristic
184C2×C22⋊C8C2×D1311yescharacteristic
185C2×#97—132no—
186C2×#97—132no—
187C2×C4×C8—132no—
188#383—132no—
189#382—131no—
190#382—131no—
191#381—132no—
192#380—131no—
193#380—131no—
194C4×C4⋊C4—131no—
195C4×C4⋊C4—131no—
196C4×C22⋊C4—132no—
197#376—132no—
198#336—132no—
199#336—132no—
200#336—132no—
201#336—132no—
202#336—131no—
203#336—131no—
204#336C2×D1312yes—
205C22×C13—22no—
206C22×C13—22no—
207C22×C13—22no—
208C22×C13—41no—
209C22×C13—41no—
210C22×C13—41no—
211C22×C13—41no—
212C22×C13C2×#11711yescharacteristic
213C22×C13C4×#4111yescharacteristic
214C22×C13#52011yescharacteristic
215C22×C13C2×#13111yescharacteristic
216C22×C13#56811yescharacteristic
217C22×C13#56811yescharacteristic
218C22×C13#56811yescharacteristic
219C4×C13—22no—
220C4×C13—22no—
221C4×C13—41no—
222C4×C13—41no—
223C4×C13—41no—
224C4×C13#55212yes—
225C4×C13#55512yes—
226Dic13—42no—
227Dic13—42no—
228Dic13—42no—
229Dic13—42no—
230C23×C4C4×D1311yescharacteristic
231C23×C4C4×D1311yescharacteristic
232C23×C4C22×D1311yescharacteristic
233C22×C8—132no—
234C22×C8—132no—
235C22×C8C22×D1312yes—
236C22×C8C22×D1312yes—
237C2×C4⋊C4—131no—
238C2×C4⋊C4—131no—
239C2×C4⋊C4—131no—
240C2×C4⋊C4—131no—
241C2×C22⋊C4—132no—
242C2×C22⋊C4—132no—
243C2×C42—24no—
244C2×C42—132no—
245C2×C42—132no—
246C2×C42C4×D1311yescharacteristic
247C2×C42C4×D1311yescharacteristic
248C2×C42C22×D1311yescharacteristic
249C2×C42C22×D1311yescharacteristic
250C4⋊C8—24no—
251C4⋊C8—522no—
252C4⋊C8—522no—
253C22⋊C8—41no—
254C22⋊C8—41no—
255C22⋊C8—264no—
256#97—264no—
257#97—264no—
258C4×C8—264no—
259#95—132no—
260#95—132no—
261#95—132no—
262#95—132no—
263#95—132no—
264#95—132no—
265#95—132no—
266#95—132no—
267C2×C13—42no—
268C2×C13#234611yescharacteristic
269C2×C13#292111yescharacteristic
270C2×C13#292411yescharacteristic
271C2×C13#296711yescharacteristic
272C2×C13#296811yescharacteristic
273C2×C13#299211yescharacteristic
274C2×C13#299511yescharacteristic
275C24C2×C4×D1311yescharacteristic
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—132no—
287C22×C4—132no—
288C22×C4—132no—
289C22×C4—132no—
290C22×C4C2×C4×D1311yescharacteristic
291C22×C4C2×C4×D1311yescharacteristic
292C22×C4C2×C4×D1311yescharacteristic
293C22×C4C2×C4×D1311yescharacteristic
294C22×C4C2×C4×D1311yescharacteristic
295C22×C4C23×D1311yescharacteristic
296C2×C8—22no—
297C2×C8—22no—
298C2×C8—22no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—22no—
302C2×C8—134no—
303C2×C8—262no—
304C2×C8—262no—
305C2×C8—262no—
306C2×C8—262no—
307C2×C8—262no—
308C4⋊C4—521no—
309C4⋊C4—521no—
310C4⋊C4—521no—
311C4⋊C4—521no—
312C22⋊C4—264no—
313C22⋊C4—522no—
314C42—22no—
315C42—22no—
316C42—22no—
317C42—262no—
318C42—262no—
319C42—262no—
320C42—262no—
321C42#612914yes—
322C13#2263511yescharacteristic, complemented, Sylow
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23#8815512yes—
330C23C22×C4×D1311yescharacteristic
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—262no—
349C2×C4—262no—
350C2×C4—262no—
351C2×C4—262no—
352C2×C4—262no—
353C2×C4—262no—
354C2×C4—262no—
355C2×C4—262no—
356C2×C4—262no—
357C2×C4—262no—
358C2×C4—262no—
359C2×C4—262no—
360C2×C4#8813112yes—
361C2×C4#8813112yes—
362C2×C4C2×#612912yes—
363C2×C4#8825111yescharacteristic
364C2×C4#8825411yescharacteristic
365C2×C4#41×D1312yes—
366C8—42no—
367C8—42no—
368C8—264no—
369C8—522no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22C2×#8813111yescharacteristic
378C22#1171920911yescharacteristic
379C22#1171922711yescharacteristic
380C22C2×#8815511yescharacteristic
381C22#1171945011yescharacteristic
382C22#1171945011yescharacteristic
383C22#1171945011yescharacteristic
384C4—22no—
385C4—22no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—522no—
390C4—522no—
391C4—522no—
392C4—522no—
393C4#1171932112yes—
394C4#1171934412yes—
395C2—42no—
396C2#1311772311yescharacteristic
397C2#1312347111yescharacteristic
398C2#1312349011yescharacteristic
399C2#1312381611yescharacteristic
400C2#1312382511yescharacteristic
401C2#1312397211yescharacteristic
402C2#1312400311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC13×#1797C2
prime radicalC24×C13C22×C4
cosocleC22×C4×C13C24
hypercenter#1797D13
hypocenterC13#22635
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. #13115557C2semidirect
5. #13114954C2semidirect
6. #13114713C2semidirect
8. #13114586C2semidirect
322. C13#22635semidirect

Maximal subgroups

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

subgroupindex
#131172342
#131155572
#131154522
#131154452
#131149542
#131147132
#131145982
#131145862
C13×#17972
#2263513