Finite Group Databasebeta

← #16017718

Subgroups — #16017718

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
1#13124417C211yesmaximal, characteristic
2#13117044C212yesmaximal, complemented
3#13117038C211yesmaximal, characteristic, complemented
4#13117033C211yesmaximal, characteristic, complemented
5#13117027C212yesmaximal, complemented
6#13117021C211yesmaximal, characteristic, complemented
7#13117016C211yesmaximal, characteristic, complemented
8#13116618C212yesmaximal, complemented
9#13116541C212yesmaximal, complemented
10C2×C22⋊#6090C211yesmaximal, characteristic, complemented
11C2×C13×#427C211yesmaximal, characteristic, complemented
12C23×C8×C13C2211yescharacteristic
13C2×C13×#117—21no—
14#11719496—21no—
15C2×#88158C2211yescharacteristic
16C13×#427—21no—
17C13×#427—21no—
18C13×#427C2212yes—
19C13×#427C2212yes—
20C2×C13×#107C2211yescharacteristic
21C2×C13×#107C2211yescharacteristic
22C2×C13×#106—21no—
23#11718777C2211yescharacteristic
24#11718777C2211yescharacteristic
25#11718776C2211yescharacteristic
26#11718776C2211yescharacteristic
27#11718775—21no—
28#11718775—21no—
29#11718774—21no—
30#11718767C2211yescharacteristic
31C22×#6090C2212yes—
32C22⋊#6090C2211yescharacteristic
33C22⋊#6090C2211yescharacteristic
34C22⋊#6090C2212yes—
35#11718084C2212yescomplemented
36#11718084C2212yescomplemented
37#11718083C2212yescomplemented
38#11718083C2212yescomplemented
39#11718082C2212yescomplemented
40#11718082C2212yescomplemented
41#11718081C2212yescomplemented
42#11718081C2212yescomplemented
43C23×C4×C13D411yescharacteristic
44C2×#6127—21no—
45C22×C8×C13—24no—
46C22×C8×C13D411yescharacteristic
47C22×C8×C13D411yescharacteristic
48C22×C8×C13D411yescharacteristic
49C22×C8×C13C2311yescharacteristic
50C22×C8×C13C2311yescharacteristic
51C22×C8×C13C2311yescharacteristic
52C13×#117—22no—
53C13×#117—22no—
54C13×#117—41no—
55C13×#117—41no—
56C2×C13×C4⋊C4—21no—
57C2×C13×C4⋊C4—21no—
58C2×C13×C22⋊C4—41no—
59C2×C42×C13—41no—
60#88207—41no—
61#88184—21no—
62#88184—21no—
63#88183—41no—
64C4×C22⋊D13—41no—
65C4×C22⋊D13—41no—
66#88180—21no—
67#88178—21no—
68#88178—21no—
69C2×Dic52C2311yescharacteristic
70#88158—24no—
71C2×D104C2311yescharacteristic
72C2×#6095—21no—
73C13×#107—21no—
74C13×#107—21no—
75C13×#107C2312yes—
76C13×#107C2312yes—
77C13×#106—22no—
78C13×#106—22no—
79#88061—21no—
80#88061—21no—
81#88058C2311yescharacteristic
82#88058C2311yescharacteristic
83#88057—21no—
84#88056—21no—
85#88056—21no—
86C2×#6090—24no—
87C2×#6090C2312yes—
88C2×#6090C2312yes—
89#33645—131nomaximal, Sylow
90C24×C13D811yescharacteristic
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13—41no—
94C22×C4×C13—41no—
95C22×C4×C13D811yescharacteristic
96C22×C4×C13D811yescharacteristic
97C22×C4×C13D811yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C2×C22⋊D13—41no—
102C2×C22⋊D13—41no—
103C2×C22⋊D13—41no—
104#6127—42no—
105#6127—42no—
106C2×D52—21no—
107C2×C4×D13—41no—
108C2×Dic26—21no—
109C2×C8×C13—22no—
110C2×C8×C13—22no—
111C2×C8×C13—22no—
112C2×C8×C13—22no—
113C2×C8×C13—22no—
114C2×C8×C13C2×D411yescharacteristic
115C2×C8×C13C2×D411yescharacteristic
116C2×C8×C13C2×D411yescharacteristic
117C2×C8×C13#4114yes—
118C2×C8×C13C2411yescharacteristic
119C13×C4⋊C4—22no—
120C13×C4⋊C4—22no—
121C13×C4⋊C4—41no—
122C13×C4⋊C4—41no—
123C13×C22⋊C4—42no—
124C13×C22⋊C4—42no—
125C42×C13—42no—
126C42×C13—42no—
127C22⋊Dic13—41no—
128C22⋊Dic13—41no—
129C22⋊Dic13—41no—
130#6103—41no—
131#6103—41no—
132C4⋊Dic13—21no—
133C4⋊Dic13—21no—
134#6101—41no—
135#6101—41no—
136C4×Dic13—41no—
137Dic52—22no—
138D104—22no—
139#6095—42no—
140#6090—22no—
141#6090—22no—
142#3050—131no—
143C2×#427D1311yescharacteristic, complemented
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×C13C2×D811yescharacteristic
157C23×C13C2×D811yescharacteristic
158C23×C13C2×D811yescharacteristic
159C22×D13—41no—
160C2×C4×C13—22no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—22no—
166C2×C4×C13—22no—
167C2×C4×C13—42no—
168C2×C4×C13—42no—
169C2×C4×C13—82no—
170C2×C4×C13—82no—
171C2×C4×C13#12312yes—
172C2×C4×C13C2×D811yescharacteristic
173C2×C4×C13C2×D811yescharacteristic
174C2×C4×C13C2×D811yescharacteristic
175C2×C4×C13#13712yes—
176C2×C4×C13C22×D411yescharacteristic
177C22⋊D13—82no—
178C22⋊D13—82no—
179C22⋊D13—82no—
180C2×Dic13—41no—
181C2×Dic13—41no—
182C2×Dic13—41no—
183D52—41no—
184D52—41no—
185C4×D13—82no—
186Dic26—41no—
187Dic26—41no—
188C8×C13—21no—
189C8×C13—21no—
190C8×C13#12312yes—
191C8×C13C2×#4112yes—
192C2×#135—131no—
193C23×C8C2×D1311yescharacteristic
194#525—261no—
195C2×#117—21no—
196C22×C16—132no—
197#467—131no—
198#467—131no—
199#466—131no—
200#466—131no—
201#465—261no—
202#465—261no—
203#427—21no—
204#427—21no—
205#427—131no—
206#427C2×D1312yes—
207#427C2×D1312yes—
208C2×#107C2×D1311yescharacteristic
209C2×#107C2×D1311yescharacteristic
210C2×#106—21no—
211#416—261no—
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#48012yes—
232C22×C13#50812yes—
233C22×C13C22×D811yescharacteristic
234C2×D13—81no—
235C2×D13—81no—
236C2×D13—81no—
237C4×C13—21no—
238C4×C13—21no—
239C4×C13—82no—
240C4×C13—82no—
241C4×C13#48012yes—
242C4×C13C2×#12311yescharacteristic
243C4×C13C2×#13711yescharacteristic
244Dic13—81no—
245Dic13—81no—
246Dic13—81no—
247C2×#41—261no—
248C23×C4C22⋊D1311yescharacteristic
249#135—264no—
250C2×Q16—131no—
251C2×SD16—261no—
252C2×D8—131no—
253C22×C8—24no—
254C22×C8C22⋊D1311yescharacteristic
255C22×C8C22⋊D1311yescharacteristic
256C22×C8C22⋊D1311yescharacteristic
257C22×C8C22×D1311yescharacteristic
258C22×C8C22×D1311yescharacteristic
259C22×C8C22×D1311yescharacteristic
260#123—521no—
261C22⋊Q8—261no—
262C22⋊Q8—261no—
263#121—261no—
264#121—261no—
265#120—521no—
266C4×D4—521no—
267C4×D4—521no—
268#117—22no—
269#117—22no—
270#117—41no—
271#117—41no—
272#117—261no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C22⋊C4—41no—
276C2×C42—41no—
277C2×C16—132no—
278C2×C16—132no—
279C2×C16—264no—
280#107—21no—
281#107—21no—
282#107—131no—
283#107—131no—
284#107C22×D1312yes—
285#107C22×D1312yes—
286#106—22no—
287#106—22no—
288#106—261no—
289#103—261no—
290#103—261no—
291#102—261no—
292#102—261no—
293C2×C13—22no—
294C2×C13—22no—
295C2×C13—41no—
296C2×C13C2×#48011yescharacteristic
297C2×C13C2×#50811yescharacteristic
298C2×C13#341411yescharacteristic
299D13—161no—
300C24#610411yescharacteristic
301#41—522no—
302#41—522no—
303C2×Q8—261no—
304C2×D4—261no—
305C2×D4—521no—
306C2×D4—521no—
307C2×D4—521no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—41no—
311C22×C4—41no—
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—262no—
320SD16—522no—
321D8—262no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8#612714yes—
328C2×C8C2×C22⋊D1311yescharacteristic
329C2×C8C2×C22⋊D1311yescharacteristic
330C2×C8C2×C22⋊D1311yescharacteristic
331C2×C8C23×D1311yescharacteristic
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—41no—
335C4⋊C4—41no—
336C4⋊C4—261no—
337C4⋊C4—261no—
338C4⋊C4—521no—
339C4⋊C4—521no—
340C22⋊C4—42no—
341C22⋊C4—42no—
342C22⋊C4—521no—
343C22⋊C4—521no—
344C22⋊C4—521no—
345C22⋊C4—521no—
346C22⋊C4—521no—
347C42—42no—
348C42—42no—
349C42—521no—
350C16—262no—
351C16—262no—
352C13#3364511yescharacteristic, complemented, Sylow
353C23—22no—
354C23—22no—
355C23—41no—
356C23—521no—
357C23C2×#610411yescharacteristic
358C23C2×#610411yescharacteristic
359C23C2×#610411yescharacteristic
360Q8—521no—
361Q8—521no—
362D4—521no—
363D4—521no—
364D4—1042no—
365D4—1042no—
366D4—1042no—
367C2×C4—22no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—521no—
379C2×C4—521no—
380C2×C4—521no—
381C2×C4—1042no—
382C2×C4#8818312yes—
383C2×C4C2×#610411yescharacteristic
384C2×C4C2×#610411yescharacteristic
385C2×C4C2×#610411yescharacteristic
386C2×C4#8819612yes—
387C2×C4C22×C22⋊D1311yescharacteristic
388C8—21no—
389C8—21no—
390C8#8818312yes—
391C8C2×#612712yes—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—44no—
400C22—1041no—
401C22—1041no—
402C22—1041no—
403C22#1171862812yes—
404C22#1171885512yes—
405C22C22×#610411yescharacteristic
406C4—21no—
407C4—21no—
408C4—82no—
409C4—82no—
410C4—1041no—
411C4—1041no—
412C4—1041no—
413C4#1171862812yes—
414C4C2×#8818311yescharacteristic
415C4C2×#8819611yescharacteristic
416C2—22no—
417C2—22no—
418C2—41no—
419C2—2081no—
420C2C2×#1171862811yescharacteristic
421C2C2×#1171885511yescharacteristic
422C2#1312797011yescharacteristic
subgroupG/H
centerC2×C4C2×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×#427C2
socleC22×C13C22×D8
prime radical#13124417C2
hypercenterC2×#427D13
hypocenterC13#33645
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. #13117044C2semidirect
3. #13117038C2semidirect
4. #13117033C2semidirect
5. #13117027C2semidirect
6. #13117021C2semidirect
7. #13117016C2semidirect
8. #13116618C2semidirect
9. #13116541C2semidirect
10. C2×C22⋊#6090C2semidirect
11. C2×C13×#427C2semidirect
35. #11718084C22semidirect
36. #11718084C22semidirect
37. #11718083C22semidirect
38. #11718083C22semidirect
39. #11718082C22semidirect
40. #11718082C22semidirect
41. #11718081C22semidirect
42. #11718081C22semidirect
143. C2×#427D13semidirect
352. C13#33645semidirect

Maximal subgroups

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

subgroupindex
#131244172
#131170442
#131170382
#131170332
#131170272
#131170212
#131170162
#131166182
#131165412
C2×C22⋊#60902
C2×C13×#4272
#3364513