Finite Group Databasebeta

← #15833462

Subgroups — #15833462

Order 3328.

630 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125406C211yesmaximal, characteristic
2#13123811C212yesmaximal, complemented
3#13113734C211yesmaximal, characteristic, complemented
4#13113728C212yesmaximal, complemented
5#13113722C211yesmaximal, characteristic, complemented
6C8×Dic52C211yesmaximal, characteristic, complemented
7C8×#6095C212yesmaximal, complemented
8C8×D104C211yesmaximal, characteristic, complemented
9#13113599C211yesmaximal, characteristic, complemented
10#13113297C212yesmaximal, complemented
11C2×C82×C13C211yesmaximal, characteristic, complemented
12#11719184C2212yes—
13C2×C4×C8×C13C2211yescharacteristic
14C2×C4×C8×C13C2211yescharacteristic
15C2×C4×C8×C13C2211yescharacteristic
16#11718777C411yescharacteristic
17#11718776C411yescharacteristic
18#11718775C412yes—
19#11718772—22no—
20C8×C22⋊D13—22no—
21#11718587C2212yes—
22C4×Dic52C2211yescharacteristic
23#11718358C412yes—
24#11718357C411yescharacteristic
25C4×D104C2211yescharacteristic
26C4×#6095C2212yes—
27#11718351—22no—
28#11718350—22no—
29#11718349C2212yes—
30C8×D52C2212yes—
31#11718344C411yescharacteristic
32#11718340C2212yes—
33C8×Dic26C2212yes—
34C82×C13C2211yescharacteristic
35C82×C13C2211yescharacteristic
36C82×C13C2211yescharacteristic
37C82×C13C2211yescharacteristic
38#11718051C2212yes—
39#11718051C2212yes—
40#11718050C2211yescharacteristic
41#11718050C2211yescharacteristic
42#11718049C2212yes—
43#11718048C2212yes—
44#11718048C2212yes—
45C22×C8×C13—21no—
46C22×C8×C13C2×C411yescharacteristic
47C22×C8×C13C2×C411yescharacteristic
48C22×C8×C13D411yescharacteristic
49C22×C8×C13D411yescharacteristic
50C2×C42×C13C2311yescharacteristic
51#88184C2×C412yes—
52#88183—22no—
53C4×C22⋊D13—22no—
54#88178C2×C412yes—
55C2×Dic52C2×C411yescharacteristic
56C2×D104C2×C411yescharacteristic
57C2×#6095C2×C412yes—
58C2×#6094—22no—
59C2×C8×D13—22no—
60#88130—22no—
61#88129C2×C412yes—
62C4×D52C2312yes—
63#88126—22no—
64#88124C2×C412yes—
65C4×Dic26C2312yes—
66C4×C8×C13—21no—
67C4×C8×C13C2×C411yescharacteristic
68C4×C8×C13C2×C411yescharacteristic
69C4×C8×C13D411yescharacteristic
70C4×C8×C13D411yescharacteristic
71C4×C8×C13C2311yescharacteristic
72C4×C8×C13C2311yescharacteristic
73C4×C8×C13C2311yescharacteristic
74C4×C8×C13C2311yescharacteristic
75C4×C8×C13C2311yescharacteristic
76C4×C8×C13C2311yescharacteristic
77C22⋊#1055—22no—
78#88061C2×C412yes—
79#88061C2×C412yes—
80#88060—22no—
81#88060—22no—
82#88058C2×C411yescharacteristic
83#88058C2×C411yescharacteristic
84#88057C2×C412yes—
85#88056C2×C412yes—
86#88056C2×C412yes—
87#88055—22no—
88#88054—22no—
89#88054—22no—
90C8×Dic13—22no—
91C4⋊#1055C2312yes—
92C4⋊#1055C2312yes—
93#88043—22no—
94#17959—131nomaximal, Sylow
95C22×C4×C13C22×C411yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13#4111yescharacteristic
98C2×C22⋊D13—22no—
99C2×D52C22×C412yes—
100C2×C4×D13—22no—
101C2×Dic26C22×C412yes—
102C2×C8×C13—24no—
103C2×C8×C13—21no—
104C2×C8×C13—21no—
105C2×C8×C13—22no—
106C2×C8×C13—22no—
107C2×C8×C13—22no—
108C2×C8×C13—22no—
109C2×C8×C13C22×C411yescharacteristic
110C2×C8×C13C22×C411yescharacteristic
111C2×C8×C13C22×C411yescharacteristic
112C2×C8×C13C22×C411yescharacteristic
113C2×C8×C13C2×D411yescharacteristic
114C2×C8×C13C2×D411yescharacteristic
115C2×C8×C13C2×D411yescharacteristic
116C2×C8×C13C2×D411yescharacteristic
117C42×C13C22×C411yescharacteristic
118C42×C13C2×D411yescharacteristic
119C42×C13#4111yescharacteristic
120C42×C13C2411yescharacteristic
121C22⋊Dic13—22no—
122#6103—22no—
123#6103—22no—
124#6103—22no—
125#6103—22no—
126C4⋊Dic13C22×C412yes—
127C4⋊Dic13C22×C412yes—
128#6101—22no—
129#6101—22no—
130#6101—22no—
131#6101—22no—
132C4×Dic13—22no—
133C2×#1055—22no—
134C2×#1055—22no—
135Dic52—22no—
136D104—22no—
137#6095—24no—
138#6094—44no—
139C8×D13—44no—
140#3168—131no—
141#2966—132no—
142#1591—131no—
143#1590—132no—
144#1589—131no—
145C8×Q16—131no—
146C8×SD16—132no—
147C8×D8—131no—
148#1568—131no—
149#1494—132no—
150C2×C82D1311yescharacteristic, complemented
151C23×C13C4×D411yescharacteristic
152C22×D13—22no—
153C2×C4×C13—22no—
154C2×C4×C13—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13C4×D411yescharacteristic
159C2×C4×C13C4×D411yescharacteristic
160C2×C4×C13C4×D411yescharacteristic
161C2×C4×C13C23×C411yescharacteristic
162C2×C4×C13C22×D411yescharacteristic
163C2×C4×C13C2×#4111yescharacteristic
164C22⋊D13—44no—
165C2×Dic13—22no—
166C2×Dic13—22no—
167C2×Dic13—22no—
168D52—22no—
169D52—22no—
170C4×D13—42no—
171C4×D13—42no—
172Dic26—22no—
173Dic26—22no—
174C8×C13—22no—
175C8×C13—22no—
176C8×C13—21no—
177C8×C13—21no—
178C8×C13—21no—
179C8×C13—21no—
180C8×C13#13112yes—
181C8×C13#13112yes—
182C8×C13#13512yes—
183C8×C13#13512yes—
184#1055—42no—
185#1055—42no—
186#529—132no—
187#499—131no—
188#495—131no—
189#488—132no—
190#467—131no—
191#466—131no—
192#465—132no—
193#446—132no—
194C8×Q8—132no—
195C4×Q16—131no—
196C4×SD16—132no—
197C4×D8—131no—
198#436—132no—
199#435—262no—
200C8×D4—132no—
201C8×D4—262no—
202#433—262no—
203#432—132no—
204#405—262no—
205C2×C4×C8C2×D1311yescharacteristic
206C2×C4×C8C2×D1311yescharacteristic
207C2×C4×C8C2×D1311yescharacteristic
208#335—131no—
209#335—131no—
210#334—132no—
211Q8⋊C8—132no—
212Q8⋊C8—132no—
213D4⋊C8—132no—
214D4⋊C8—132no—
215C82C2×D1311yescharacteristic
216C82C2×D1311yescharacteristic
217C82C2×D1311yescharacteristic
218C82C2×D1311yescharacteristic
219C22×C13—21no—
220C22×C13—21no—
221C22×C13#44312yes—
222C22×C13C2×C4×D411yescharacteristic
223C2×D13—42no—
224C2×D13—42no—
225C2×D13—42no—
226C4×C13—21no—
227C4×C13—21no—
228C4×C13—21no—
229C4×C13—21no—
230C4×C13C2×#13111yescharacteristic
231C4×C13C2×#13111yescharacteristic
232C4×C13C2×#13511yescharacteristic
233C4×C13C2×#13511yescharacteristic
234Dic13—42no—
235Dic13—42no—
236Dic13—42no—
237C2×Q16—131no—
238C2×SD16—132no—
239C2×D8—131no—
240C2×M16—262no—
241C22×C8—21no—
242C22×C8—262no—
243C22×C8C4×D1311yescharacteristic
244C22×C8C4×D1311yescharacteristic
245C22×C8D5211yescharacteristic
246C22×C8D5211yescharacteristic
247#126—262no—
248#125—132no—
249#124—132no—
250#123—262no—
251C22⋊Q8—132no—
252#121—132no—
253C4×Q8—132no—
254C4×D4—132no—
255C4×D4—262no—
256#117—262no—
257C2×C42C22×D1311yescharacteristic
258#107—131no—
259#107—131no—
260#106—132no—
261C4⋊C8—132no—
262C4⋊C8—132no—
263C4⋊C8—262no—
264C4⋊C8—262no—
265#103—132no—
266#103—132no—
267#102—132no—
268#102—132no—
269C22⋊C8—262no—
270C22⋊C8—262no—
271C22⋊C8—262no—
272#97—262no—
273#97—262no—
274C4×C8—21no—
275C4×C8—262no—
276C4×C8C4×D1311yescharacteristic
277C4×C8C4×D1311yescharacteristic
278C4×C8D5211yescharacteristic
279C4×C8D5211yescharacteristic
280C4×C8C22×D1311yescharacteristic
281C4×C8C22×D1311yescharacteristic
282C4×C8C22×D1311yescharacteristic
283C4×C8C22×D1311yescharacteristic
284C4×C8C22×D1311yescharacteristic
285C4×C8C22×D1311yescharacteristic
286C2×C13—22no—
287C2×C13#293111yescharacteristic
288C2×C13C4×#13511yescharacteristic
289C2×C13C2×#44311yescharacteristic
290D13—82no—
291C2×Q8—132no—
292C2×D4—132no—
293C2×D4—262no—
294C22×C4—262no—
295C22×C4C2×C4×D1311yescharacteristic
296C22×C4C2×D5211yescharacteristic
297C22×C4#612711yescharacteristic
298Q16—262no—
299SD16—264no—
300D8—262no—
301M16—524no—
302C2×C8—24no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8—262no—
310C2×C8—262no—
311C2×C8—524no—
312C2×C8C2×C4×D1311yescharacteristic
313C2×C8C2×C4×D1311yescharacteristic
314C2×C8C2×C4×D1311yescharacteristic
315C2×C8C2×C4×D1311yescharacteristic
316C2×C8C2×D5211yescharacteristic
317C2×C8C2×D5211yescharacteristic
318C2×C8C2×D5211yescharacteristic
319C2×C8C2×D5211yescharacteristic
320C4⋊C4—132no—
321C4⋊C4—132no—
322C4⋊C4—262no—
323C4⋊C4—262no—
324C4⋊C4—262no—
325C4⋊C4—262no—
326C22⋊C4—262no—
327C22⋊C4—262no—
328C22⋊C4—262no—
329C22⋊C4—262no—
330C22⋊C4—262no—
331C42—262no—
332C42C2×C4×D1311yescharacteristic
333C42C2×D5211yescharacteristic
334C42#612711yescharacteristic
335C42C23×D1311yescharacteristic
336C13#1795911yescharacteristic, complemented, Sylow
337C23—262no—
338C23C4×D5211yescharacteristic
339Q8—262no—
340Q8—262no—
341D4—262no—
342D4—262no—
343D4—524no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—262no—
350C2×C4—262no—
351C2×C4—262no—
352C2×C4—522no—
353C2×C4—522no—
354C2×C4C4×D5211yescharacteristic
355C2×C4C4×D5211yescharacteristic
356C2×C4C4×D5211yescharacteristic
357C2×C4C22×C4×D1311yescharacteristic
358C2×C4C22×D5211yescharacteristic
359C2×C4C2×#612711yescharacteristic
360C8—22no—
361C8—22no—
362C8—21no—
363C8—21no—
364C8—21no—
365C8—21no—
366C8—522no—
367C8—522no—
368C8#8815512yes—
369C8#8815512yes—
370C8#8815812yes—
371C8#8815812yes—
372C22—21no—
373C22—21no—
374C22—522no—
375C22—522no—
376C22—522no—
377C22#1171836112yes—
378C22C2×C4×D5211yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—21no—
383C4—522no—
384C4—522no—
385C4—522no—
386C4C2×#8815511yescharacteristic
387C4C2×#8815511yescharacteristic
388C4C2×#8815811yescharacteristic
389C4C2×#8815811yescharacteristic
390C2—22no—
391C2—1042no—
392C2#1312354911yescharacteristic
393C2C4×#8815811yescharacteristic
394C2C2×#1171836111yescharacteristic
subgroupG/H
centerC2×C8C2×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC2×C82×C13C2
socleC22×C13C2×C4×D4
prime radical#11718776C4
cosocleC42×C13C24
hypercenterC2×C82D13
hypocenterC13#17959
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C2×C4×C8 ◁ C2×C82

Complements

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

NH ≅ G/Ntype
2. #13123811C2semidirect
3. #13113734C2semidirect
4. #13113728C2semidirect
5. #13113722C2semidirect
6. C8×Dic52C2semidirect
7. C8×#6095C2semidirect
8. C8×D104C2semidirect
9. #13113599C2semidirect
10. #13113297C2semidirect
11. C2×C82×C13C2semidirect
150. C2×C82D13semidirect
336. C13#17959semidirect

Maximal subgroups

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

subgroupindex
#131254062
#131238112
#131137342
#131137282
#131137222
C8×Dic522
C8×#60952
C8×D1042
#131135992
#131132972
C2×C82×C132
#1795913