Finite Group Databasebeta

← #16017714

Subgroups — #16017714

Order 3328.

590 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718767C211yesmaximal, characteristic, complemented
2#13117041C212yesmaximal, complemented
3#13117036C211yesmaximal, characteristic, complemented
4#13117031C211yesmaximal, characteristic, complemented
5#13117024C212yesmaximal, complemented
6#13117019C211yesmaximal, characteristic, complemented
7#13117014C211yesmaximal, characteristic, complemented
8#13116618C212yesmaximal, complemented
9#13116543C212yesmaximal, complemented
10C2×C22⋊#6090C211yesmaximal, characteristic, complemented
11C13×#3050C211yesmaximal, characteristic
12C2×C13×#135C2211yescharacteristic
13C23×C8×C13C2211yescharacteristic
14C13×#525—21no—
15C2×#88180—21no—
16C13×#467C2211yescharacteristic
17C13×#467C2211yescharacteristic
18C13×#466C2211yescharacteristic
19C13×#466C2211yescharacteristic
20C13×#465—21no—
21C13×#465—21no—
22C13×#427C2211yescharacteristic
23C13×#416—21no—
24#11718767—21no—
25#11718767—21no—
26#11718767C2212yes—
27#11718767C2212yes—
28C2×#88058C2211yescharacteristic
29C2×#88058C2211yescharacteristic
30C2×#88057—21no—
31C22×#6090C2212yes—
32#11718156C2212yescomplemented
33#11718156C2212yescomplemented
34#11718154C2212yescomplemented
35#11718154C2212yescomplemented
36C22⋊#6090C2211yescharacteristic
37C22⋊#6090C2211yescharacteristic
38C22⋊#6090C2212yes—
39#11718082C2212yescomplemented
40#11718082C2212yescomplemented
41#11718081C2212yescomplemented
42#11718081C2212yescomplemented
43C2×C13×#41—21no—
44C23×C4×C13D411yescharacteristic
45C13×#135—24no—
46C2×C13×Q16C2311yescharacteristic
47C2×C13×SD16—21no—
48C2×C13×D8C2311yescharacteristic
49C22×C8×C13—24no—
50C22×C8×C13D411yescharacteristic
51C22×C8×C13D411yescharacteristic
52C22×C8×C13D411yescharacteristic
53C22×C8×C13C2311yescharacteristic
54C22×C8×C13C2311yescharacteristic
55C22×C8×C13C2311yescharacteristic
56C13×#123—41no—
57C13×C22⋊Q8—21no—
58C13×C22⋊Q8—21no—
59C13×#121—21no—
60C13×#121—21no—
61C13×#120—41no—
62C4×D4×C13—41no—
63C4×D4×C13—41no—
64C13×#117—21no—
65C2×C22⋊Dic13—41no—
66#88180—22no—
67#88180—22no—
68#88180—41no—
69#88180—41no—
70C2×C4⋊Dic13—21no—
71C2×C4⋊Dic13—21no—
72C2×C4×Dic13—41no—
73C13×#107C2311yescharacteristic
74C13×#107C2311yescharacteristic
75C13×#106—21no—
76C13×#103—21no—
77C13×#103—21no—
78C13×#102—21no—
79C13×#102—21no—
80#88058—21no—
81#88058—21no—
82#88058C2312yes—
83#88058C2312yes—
84#88057—22no—
85#88057—22no—
86C2×#6090—24no—
87C2×#6090C2312yes—
88C2×#6090C2312yes—
89#33645—131nomaximal, Sylow
90C24×C13D811yescharacteristic
91C13×#41—42no—
92C13×#41—42no—
93C2×Q8×C13—21no—
94C2×D4×C13—21no—
95C2×D4×C13—41no—
96C2×D4×C13—41no—
97C2×D4×C13—41no—
98C22×C4×C13—22no—
99C22×C4×C13—22no—
100C22×C4×C13—41no—
101C22×C4×C13D811yescharacteristic
102C22×C4×C13D811yescharacteristic
103C22×C4×C13D811yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×Dic13—41no—
108C22×Dic13—41no—
109C13×Q16—22no—
110C13×SD16—42no—
111C13×D8—22no—
112C2×C8×C13—22no—
113C2×C8×C13—22no—
114C2×C8×C13—22no—
115C2×C8×C13—22no—
116C2×C8×C13—22no—
117C2×C8×C13C2×D411yescharacteristic
118C2×C8×C13C2×D411yescharacteristic
119C2×C8×C13C2×D411yescharacteristic
120C2×C8×C13#4114yes—
121C2×C8×C13C2411yescharacteristic
122C13×C4⋊C4—21no—
123C13×C4⋊C4—21no—
124C13×C4⋊C4—41no—
125C13×C4⋊C4—41no—
126C13×C22⋊C4—41no—
127C13×C22⋊C4—41no—
128C13×C22⋊C4—41no—
129C13×C22⋊C4—41no—
130C13×C22⋊C4—41no—
131C42×C13—41no—
132C22⋊Dic13—42no—
133C22⋊Dic13—42no—
134C4⋊Dic13—22no—
135C4⋊Dic13—22no—
136C4⋊Dic13—41no—
137C4⋊Dic13—41no—
138C4×Dic13—42no—
139C4×Dic13—42no—
140#6090—22no—
141#6090—22no—
142#3050D1311yescharacteristic
143C2×#427—131no—
144#2237—132no—
145#2236—131no—
146#2235—131no—
147#2234—132no—
148#2233—131no—
149#2232—131no—
150#2158—132no—
151#2138—132no—
152C2×C22⋊C16—131no—
153C23×C13—22no—
154C23×C13—22no—
155C23×C13—41no—
156C23×C13—41no—
157C23×C13C2×D811yescharacteristic
158C23×C13C2×D811yescharacteristic
159C23×C13C2×D811yescharacteristic
160Q8×C13—41no—
161Q8×C13—41no—
162D4×C13—41no—
163D4×C13—41no—
164D4×C13—82no—
165D4×C13—82no—
166D4×C13—82no—
167C2×C4×C13—22no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—21no—
172C2×C4×C13—22no—
173C2×C4×C13—22no—
174C2×C4×C13—41no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—82no—
178C2×C4×C13#12312yes—
179C2×C4×C13C2×D811yescharacteristic
180C2×C4×C13C2×D811yescharacteristic
181C2×C4×C13C2×D811yescharacteristic
182C2×C4×C13#13712yes—
183C2×C4×C13C22×D411yescharacteristic
184C2×Dic13—42no—
185C2×Dic13—42no—
186C2×Dic13—82no—
187C2×Dic13—82no—
188C8×C13—21no—
189C8×C13—21no—
190C8×C13#12312yes—
191C8×C13C2×#4112yes—
192C2×#135C2×D1311yescharacteristic
193C23×C8C2×D1311yescharacteristic
194#525—21no—
195C2×#117—261no—
196C22×C16—132no—
197#467C2×D1311yescharacteristic
198#467C2×D1311yescharacteristic
199#466C2×D1311yescharacteristic
200#466C2×D1311yescharacteristic
201#465—21no—
202#465—21no—
203#427—132no—
204#427—132no—
205#427—261no—
206#427—261no—
207#427C2×D1311yescharacteristic
208C2×#107—131no—
209C2×#107—131no—
210C2×#106—261no—
211#416—21no—
212#367—132no—
213#367—132no—
214#366—132no—
215#366—132no—
216#358—132no—
217#358—132no—
218#357—132no—
219#357—132no—
220C22⋊C16—131no—
221C22⋊C16—131no—
222C22⋊C16—132no—
223C22×C13—21no—
224C22×C13—21no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13—21no—
230C22×C13—44no—
231C22×C13—81no—
232C22×C13—81no—
233C22×C13—81no—
234C22×C13#48012yes—
235C22×C13#50812yes—
236C22×C13C22×D811yescharacteristic
237C4×C13—21no—
238C4×C13—21no—
239C4×C13—81no—
240C4×C13—81no—
241C4×C13—81no—
242C4×C13#48012yes—
243C4×C13C2×#12311yescharacteristic
244C4×C13C2×#13711yescharacteristic
245Dic13—82no—
246Dic13—82no—
247C2×#41—21no—
248C23×C4C22⋊D1311yescharacteristic
249#135—24no—
250C2×Q16C22×D1311yescharacteristic
251C2×SD16—21no—
252C2×D8C22×D1311yescharacteristic
253C22×C8—24no—
254C22×C8C22⋊D1311yescharacteristic
255C22×C8C22⋊D1311yescharacteristic
256C22×C8C22⋊D1311yescharacteristic
257C22×C8C22×D1311yescharacteristic
258C22×C8C22×D1311yescharacteristic
259C22×C8C22×D1311yescharacteristic
260#123—41no—
261C22⋊Q8—21no—
262C22⋊Q8—21no—
263#121—21no—
264#121—21no—
265#120—41no—
266C4×D4—41no—
267C4×D4—41no—
268#117—21no—
269#117—262no—
270#117—262no—
271#117—521no—
272#117—521no—
273C2×C4⋊C4—261no—
274C2×C4⋊C4—261no—
275C2×C22⋊C4—521no—
276C2×C42—521no—
277C2×C16—132no—
278C2×C16—132no—
279C2×C16—264no—
280#107—132no—
281#107—132no—
282#107—261no—
283#107—261no—
284#107C22×D1311yescharacteristic
285#107C22×D1311yescharacteristic
286#106—21no—
287#106—262no—
288#106—262no—
289#103—21no—
290#103—21no—
291#102—21no—
292#102—21no—
293C2×C13—22no—
294C2×C13—22no—
295C2×C13—41no—
296C2×C13—161no—
297C2×C13C2×#48011yescharacteristic
298C2×C13C2×#50811yescharacteristic
299C2×C13#341411yescharacteristic
300C24#610411yescharacteristic
301#41—42no—
302#41—42no—
303C2×Q8—21no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—41no—
307C2×D4—41no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—41no—
311C22×C4—521no—
312C22×C4—521no—
313C22×C4#610411yescharacteristic
314C22×C4#610411yescharacteristic
315C22×C4#610411yescharacteristic
316C22×C4C2×C22⋊D1311yescharacteristic
317C22×C4C2×C22⋊D1311yescharacteristic
318C22×C4C2×C22⋊D1311yescharacteristic
319Q16—22no—
320SD16—42no—
321D8—22no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8#612914yes—
328C2×C8C2×C22⋊D1311yescharacteristic
329C2×C8C2×C22⋊D1311yescharacteristic
330C2×C8C2×C22⋊D1311yescharacteristic
331C2×C8C23×D1311yescharacteristic
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—262no—
337C4⋊C4—262no—
338C4⋊C4—521no—
339C4⋊C4—521no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—522no—
346C22⋊C4—522no—
347C42—41no—
348C42—522no—
349C42—522no—
350C16—262no—
351C16—262no—
352C13#3364511yescharacteristic, complemented, Sylow
353C23—22no—
354C23—22no—
355C23—41no—
356C23—41no—
357C23C2×#610411yescharacteristic
358C23C2×#610411yescharacteristic
359C23C2×#610411yescharacteristic
360Q8—41no—
361Q8—41no—
362D4—41no—
363D4—41no—
364D4—82no—
365D4—82no—
366D4—82no—
367C2×C4—22no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—82no—
378C2×C4—522no—
379C2×C4—522no—
380C2×C4—1042no—
381C2×C4—1042no—
382C2×C4C2×#610411yescharacteristic
383C2×C4C2×#610411yescharacteristic
384C2×C4C2×#610411yescharacteristic
385C2×C4#8818912yes—
386C2×C4#8820512yes—
387C2×C4C22×C22⋊D1311yescharacteristic
388C8—21no—
389C8—21no—
390C8#8818912yes—
391C8C2×#612912yes—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—44no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22#1171869412yes—
404C22#1171885512yes—
405C22C22×#610411yescharacteristic
406C4—21no—
407C4—21no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—1042no—
412C4—1042no—
413C4#1171869412yes—
414C4C2×#8818911yescharacteristic
415C4C2×#8820511yescharacteristic
416C2—22no—
417C2—22no—
418C2—41no—
419C2—161no—
420C2C2×#1171869411yescharacteristic
421C2C2×#1171885511yescharacteristic
422C2#1312797011yescharacteristic
subgroupG/H
centerC2×C4C2×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
Fitting, prime radicalC13×#3050C2
socleC22×C13C22×D8
hypercenter#3050D13
hypocenterC13#33645
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C2×#11718767C2semidirect
2. #13117041C2semidirect
3. #13117036C2semidirect
4. #13117031C2semidirect
5. #13117024C2semidirect
6. #13117019C2semidirect
7. #13117014C2semidirect
8. #13116618C2semidirect
9. #13116543C2semidirect
10. C2×C22⋊#6090C2semidirect
32. #11718156C22semidirect
33. #11718156C22semidirect
34. #11718154C22semidirect
35. #11718154C22semidirect
39. #11718082C22semidirect
40. #11718082C22semidirect
41. #11718081C22semidirect
42. #11718081C22semidirect
352. C13#33645semidirect

Maximal subgroups

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

subgroupindex
C2×#117187672
#131170412
#131170362
#131170312
#131170242
#131170192
#131170142
#131166182
#131165432
C2×C22⋊#60902
C13×#30502
#3364513