Finite Group Databasebeta

← #15781619

Subgroups — #15781619

Order 3328.

618 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88068C211yesmaximal, characteristic, complemented
2C2×#11718776C211yesmaximal, characteristic
3C2×#11718156C211yesmaximal, characteristic, complemented
4C2×#11718083C211yesmaximal, characteristic, complemented
5C2×C22⋊#6090C211yesmaximal, characteristic, complemented
6#13112927C211yesmaximal, characteristic, complemented
7C2×C13×#467C211yesmaximal, characteristic, complemented
8C22×C13×Q16C2211yescharacteristic
9C23×C8×C13C2211yescharacteristic
10C2×C13×C22⋊Q8—21no—
11C2×#88184—21no—
12C22×D104C2211yescharacteristic
13C13×#467—22no—
14C13×#467—22no—
15C2×C13×#107C2211yescharacteristic
16C2×C13×#103—21no—
17C2×#88068—22no—
18C2×#88068—22no—
19C2×#88068—22no—
20#11718776—22no—
21#11718776—22no—
22C2×#88061—21no—
23C2×#88058C2211yescharacteristic
24C22×#6090C2211yescharacteristic
25C22×#6090C2211yescharacteristic
26#11718156—22no—
27C22⋊#6090—22no—
28#11718083—22no—
29C22×Q8×C13—21no—
30C23×C4×C13D411yescharacteristic
31C22×C22⋊D13—41no—
32C22×D52—21no—
33C2×C13×Q16—21no—
34C2×C13×Q16—21no—
35C2×C13×Q16—21no—
36C2×C13×Q16—21no—
37C2×C13×Q16—21no—
38C2×C13×Q16D412yescomplemented
39C22×C8×C13—21no—
40C22×C8×C13—21no—
41C22×C8×C13—21no—
42C22×C8×C13—21no—
43C22×C8×C13—21no—
44C22×C8×C13—21no—
45C22×C8×C13D411yescharacteristic
46C22×C8×C13C2311yescharacteristic
47C13×C22⋊Q8—24no—
48C13×C22⋊Q8—42no—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—41no—
51C2×C13×C22⋊C4—41no—
52#88184—24no—
53#88184—42no—
54C2×#6103—41no—
55C2×C4⋊Dic13—21no—
56C2×D104—21no—
57C2×D104—21no—
58C2×D104—21no—
59C2×D104—21no—
60C2×D104—21no—
61C2×D104D412yes—
62C13×#107—21no—
63C13×#107D412yescomplemented
64C13×#103—24no—
65#88068—28no—
66#88061—24no—
67#88058—21no—
68#88058D412yes—
69C2×#6090—21no—
70C2×#6090—21no—
71C2×#6090—21no—
72C2×#6090—21no—
73C2×#6090—21no—
74C2×#6090D412yescomplemented
75#13305—131nomaximal, Sylow
76C24×C13D811yescharacteristic
77C23×D13—41no—
78C2×Q8×C13—22no—
79C2×Q8×C13—41no—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C2×Q8×C13—41no—
83C2×Q8×C13—41no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—41no—
91C22×C4×C13—41no—
92C22×C4×C13D811yescharacteristic
93C22×C4×C13C2×D411yescharacteristic
94C2×C22⋊D13—44no—
95C2×C22⋊D13—82no—
96C2×C22⋊D13—82no—
97C22×Dic13—41no—
98C2×D52—22no—
99C2×D52—41no—
100C2×D52—41no—
101C2×D52—41no—
102C2×D52—41no—
103C2×D52—41no—
104C13×Q16—22no—
105C13×Q16—22no—
106C13×Q16—41no—
107C13×Q16—41no—
108C2×C8×C13—21no—
109C2×C8×C13—21no—
110C2×C8×C13—21no—
111C2×C8×C13—41no—
112C2×C8×C13—41no—
113C2×C8×C13—41no—
114C2×C8×C13—41no—
115C2×C8×C13C2×D411yescharacteristic
116C2×C8×C13C2×D411yescharacteristic
117C2×C8×C13C2×D411yescharacteristic
118C2×C8×C13C2×D411yescharacteristic
119C2×C8×C13C2×D411yescharacteristic
120C2×C8×C13#4111yescharacteristic
121C13×C4⋊C4—22no—
122C13×C4⋊C4—44no—
123C13×C4⋊C4—41no—
124C13×C22⋊C4—44no—
125#6103—44no—
126C4⋊Dic13—22no—
127C4⋊Dic13—41no—
128D104—22no—
129D104—22no—
130D104—41no—
131D104—41no—
132#6090—22no—
133#6090—41no—
134C22×SD32—131no—
135C2×#467D1311yescharacteristic, complemented
136C2×#466—131no—
137C2×#358—131no—
138C2×#357—131no—
139C2×C22⋊C16—131no—
140#1380—131no—
141C23×C13—21no—
142C23×C13—21no—
143C23×C13—21no—
144C23×C13—21no—
145C23×C13—21no—
146C23×C13—21no—
147C23×C13SD3212yescomplemented
148C23×C13C2×D811yescharacteristic
149C22×D13—42no—
150C22×D13—81no—
151C22×D13—81no—
152C22×D13—81no—
153C22×D13—81no—
154C22×D13—81no—
155C22×D13—81no—
156Q8×C13—42no—
157Q8×C13—42no—
158Q8×C13—81no—
159Q8×C13—81no—
160C2×C4×C13—21no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—42no—
168C2×C4×C13—42no—
169C2×C4×C13—81no—
170C2×C4×C13—81no—
171C2×C4×C13—81no—
172C2×C4×C13—81no—
173C2×C4×C13#12011yescharacteristic
174C2×C4×C13#12011yescharacteristic
175C2×C4×C13#12111yescharacteristic
176C2×C4×C13#13511yescharacteristic
177C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
179C22⋊D13—88no—
180C2×Dic13—42no—
181C2×Dic13—81no—
182C2×Dic13—81no—
183D52—42no—
184D52—42no—
185D52—81no—
186D52—81no—
187C8×C13—41no—
188C8×C13#12011yescharacteristic
189C8×C13#12111yescharacteristic
190C8×C13#12111yescharacteristic
191C8×C13#12711yescharacteristic
192C22×Q16C2×D1311yescharacteristic
193C22×D8—131no—
194C23×C8C2×D1311yescharacteristic
195C2×C22⋊Q8—21no—
196C2×#121—261no—
197C2×SD32—262no—
198C2×SD32—262no—
199C2×SD32—262no—
200C22×C16—131no—
201C22×C16—131no—
202#467—22no—
203#467—22no—
204#466—262no—
205#466—262no—
206C2×#107—131no—
207C2×#107C2×D1311yescharacteristic
208C2×#103—21no—
209C2×#102—261no—
210#358—262no—
211#357—262no—
212C22⋊C16—262no—
213C22×C13—22no—
214C22×C13—22no—
215C22×C13—22no—
216C22×C13—41no—
217C22×C13—41no—
218C22×C13—41no—
219C22×C13—41no—
220C22×C13#44711yescharacteristic
221C22×C13#44711yescharacteristic
222C22×C13#46611yescharacteristic
223C22×C13C2×SD3211yescharacteristic
224C22×C13#50811yescharacteristic
225C22×C13#50911yescharacteristic
226C22×C13#51011yescharacteristic
227C2×D13—82no—
228C2×D13—82no—
229C2×D13—82no—
230C2×D13—161no—
231C2×D13—161no—
232C2×D13—161no—
233C2×D13—161no—
234C4×C13—41no—
235C4×C13—82no—
236C4×C13—82no—
237C4×C13#39211yescharacteristic
238C4×C13#44911yescharacteristic
239C4×C13#44911yescharacteristic
240C4×C13#46911yescharacteristic
241Dic13—82no—
242C22×Q8—21no—
243C22×D4—261no—
244C22×D4—521no—
245C23×C4C22⋊D1311yescharacteristic
246C2×Q16—21no—
247C2×Q16—21no—
248C2×Q16—21no—
249C2×Q16—21no—
250C2×Q16—21no—
251C2×Q16C22⋊D1312yescomplemented
252C2×D8—132no—
253C2×D8—261no—
254C2×D8—261no—
255C2×D8—261no—
256C2×D8—261no—
257C2×D8—261no—
258C22×C8—21no—
259C22×C8—21no—
260C22×C8—21no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8C22⋊D1311yescharacteristic
265C22×C8C22×D1311yescharacteristic
266C22⋊Q8—24no—
267C22⋊Q8—42no—
268#121—264no—
269#121—522no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—41no—
272C2×C4⋊C4—261no—
273C2×C22⋊C4—41no—
274C2×C22⋊C4—521no—
275SD32—268no—
276C2×C16—132no—
277C2×C16—261no—
278C2×C16—261no—
279C2×C16—261no—
280C2×C16—261no—
281C2×C16—261no—
282#107—21no—
283#107—132no—
284#107—261no—
285#107C22⋊D1312yescomplemented
286#103—24no—
287#102—264no—
288C2×C13—42no—
289C2×C13#199911yescharacteristic
290C2×C13#218511yescharacteristic
291C2×C13#218611yescharacteristic
292C2×C13#218711yescharacteristic
293C2×C13#218911yescharacteristic
294C2×C13#221711yescharacteristic
295C2×C13#222011yescharacteristic
296D13—162no—
297C24—521no—
298C24#610411yescharacteristic
299C2×Q8—22no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×D4—262no—
306C2×D4—524no—
307C2×D4—521no—
308C2×D4—521no—
309C2×D4—521no—
310C2×D4—521no—
311C2×D4—521no—
312C2×D4—1042no—
313C2×D4—1042no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—521no—
323C22×C4#610411yescharacteristic
324C22×C4C2×C22⋊D1311yescharacteristic
325Q16—22no—
326Q16—22no—
327Q16—41no—
328Q16—41no—
329D8—262no—
330D8—262no—
331D8—521no—
332D8—521no—
333C2×C8—21no—
334C2×C8—21no—
335C2×C8—21no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C2×C8D4×D1311yescharacteristic
341C2×C8D4×D1311yescharacteristic
342C2×C8D4×D1311yescharacteristic
343C2×C8#612911yescharacteristic
344C2×C8C2×C22⋊D1311yescharacteristic
345C2×C8C2×C22⋊D1311yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—44no—
348C4⋊C4—41no—
349C4⋊C4—262no—
350C4⋊C4—521no—
351C22⋊C4—44no—
352C22⋊C4—524no—
353C16—262no—
354C16—521no—
355C13#1330511yescharacteristic, complemented, Sylow
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—522no—
363C23—1041no—
364C23—1041no—
365C23—1041no—
366C23—1041no—
367C23—1041no—
368C23—1041no—
369C23#8806812yescomplemented
370C23C2×#610411yescharacteristic
371Q8—42no—
372Q8—42no—
373Q8—81no—
374Q8—81no—
375D4—522no—
376D4—522no—
377D4—1048no—
378D4—1041no—
379D4—1041no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—522no—
394C2×C4—1041no—
395C2×C4—1041no—
396C2×C4#8818611yescharacteristic
397C2×C4#8819111yescharacteristic
398C2×C4#8819311yescharacteristic
399C2×C4#8820311yescharacteristic
400C2×C4#8820411yescharacteristic
401C2×C4#8820711yescharacteristic
402C8—41no—
403C8#8819111yescharacteristic
404C8#8819211yescharacteristic
405C8#8819311yescharacteristic
406C8#8819411yescharacteristic
407C22—22no—
408C22—22no—
409C22—22no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—1042no—
415C22—1042no—
416C22—1042no—
417C22—2081no—
418C22—2081no—
419C22—2081no—
420C22—2081no—
421C22#1171869711yescharacteristic
422C22#1171869911yescharacteristic
423C22C2×#8806811yescharacteristic
424C22#1171884011yescharacteristic
425C22#1171885411yescharacteristic
426C22#1171885511yescharacteristic
427C22#1171887811yescharacteristic
428C4—41no—
429C4—82no—
430C4—82no—
431C4—1042no—
432C4#1171869811yescharacteristic
433C4#1171870011yescharacteristic
434C4#1171888411yescharacteristic
435C4#1171889911yescharacteristic
436C2—42no—
437C2—2082no—
438C2#1311583211yescharacteristic
439C2#1311675311yescharacteristic
440C2#1311675911yescharacteristic
441C2#1311676411yescharacteristic
442C2#1311677411yescharacteristic
443C2#1311693411yescharacteristic
444C2#1311695111yescharacteristic
subgroupG/H
centerC23C2×#6104
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC2×C13×#467C2
socleC23×C13C2×D8
prime radicalC2×#11718776C2
hypercenterC2×#467D13
hypocenterC13#13305
LCSG ▷ C22×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
1. C22×#88068C2semidirect
3. C2×#11718156C2semidirect
4. C2×#11718083C2semidirect
5. C2×C22⋊#6090C2semidirect
6. #13112927C2semidirect
7. C2×C13×#467C2semidirect
38. C2×C13×Q16D4semidirect
63. C13×#107D4semidirect
74. C2×#6090D4semidirect
135. C2×#467D13semidirect
147. C23×C13SD32semidirect
251. C2×Q16C22⋊D13semidirect
285. #107C22⋊D13semidirect
355. C13#13305semidirect
369. C23#88068semidirect

Maximal subgroups

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

subgroupindex
C22×#880682
C2×#117187762
C2×#117181562
C2×#117180832
C2×C22⋊#60902
#131129272
C2×C13×#4672
#1330513