Finite Group Databasebeta

← #16017783

Subgroups — #16017783

Order 3328.

568 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124506C211yesmaximal, characteristic
2#13117044C212yesmaximal, complemented
3#13117038C212yesmaximal, complemented
4#13117027C212yesmaximal, complemented
5#13117016C212yesmaximal, complemented
6#13116625C211yesmaximal, characteristic, complemented
7C2×#11718081C211yesmaximal, characteristic, complemented
8#13116546C211yesmaximal, characteristic, complemented
9#13116541C211yesmaximal, characteristic, complemented
10#13116450C211yesmaximal, characteristic, complemented
11C13×#2913C211yesmaximal, characteristic, complemented
12C2×C13×#131C2211yescharacteristic
13C13×#520—21no—
14#11719538—21no—
15C2×#88158C2211yescharacteristic
16C13×#428—21no—
17C13×#428—22no—
18C13×#427C2212yes—
19C13×#427C2211yescharacteristic
20C2×C13×#107C2212yes—
21C2×C13×#107C2211yescharacteristic
22#11718795—22no—
23#11718794—21no—
24#11718777C2212yes—
25#11718776C2212yes—
26C2×#88058C2211yescharacteristic
27C2×#88052C2211yescharacteristic
28C22×#6090C2211yescharacteristic
29C22⋊#6090C2212yes—
30C22⋊#6090C2212yes—
31#11718084C2211yescharacteristic
32#11718084C2212yes—
33#11718084C2211yescharacteristic
34#11718083C2211yescharacteristic
35#11718083C2212yes—
36#11718083C2211yescharacteristic
37#11718082C2212yes—
38#11718081C2212yes—
39#11718081C2212yes—
40#11718081C2212yes—
41C2×C13×#41D411yescharacteristic
42C2×#6127—21no—
43C13×#131—22no—
44C13×#131—22no—
45C2×C13×M16D411yescharacteristic
46C2×C13×M16D412yes—
47C22×C8×C13C2312yes—
48C22×C8×C13C2311yescharacteristic
49C4×Q8×C13—41no—
50C4×D4×C13—41no—
51C4×D4×C13—42no—
52C13×#117—22no—
53C13×#117—21no—
54C2×C13×C4⋊C4—22no—
55C2×C13×C4⋊C4—21no—
56#88200—41no—
57#88193—42no—
58#88192—41no—
59#88184—22no—
60C2×C4⋊Dic13—21no—
61#88178—22no—
62C2×Dic52C2311yescharacteristic
63#88158—22no—
64#88158—22no—
65C2×D104C2311yescharacteristic
66C2×#6095—21no—
67C13×#107—22no—
68C13×#107—21no—
69C13×#107C2311yescharacteristic
70C13×#107C2312yes—
71C13×#107C2311yescharacteristic
72C13×#106—22no—
73C13×#106—21no—
74#88061—22no—
75#88058—21no—
76#88058C2312yes—
77#88056—22no—
78#88052—22no—
79C2×#6090—22no—
80C2×#6090C2311yescharacteristic
81C2×#6090C2311yescharacteristic
82C2×#6090C2312yes—
83#33652—131nomaximal, Sylow
84C13×#41—22no—
85C13×#41—22no—
86C2×Q8×C13D811yescharacteristic
87C2×D4×C13D811yescharacteristic
88C2×D4×C13D812yes—
89C22×C4×C13—42no—
90C22×C4×C13—41no—
91C22×C4×C13C2×D412yes—
92C22×C4×C13C2×D411yescharacteristic
93C2×C22⋊D13—41no—
94C2×C22⋊D13—42no—
95C22×Dic13—41no—
96#6127—42no—
97#6127—42no—
98C2×D52—21no—
99C2×C4×D13—41no—
100C2×Dic26—21no—
101C13×M16—22no—
102C13×M16—24no—
103C2×C8×C13—22no—
104C2×C8×C13—22no—
105C2×C8×C13C2×D412yes—
106C2×C8×C13C2×D411yescharacteristic
107C2×C8×C13#4112yes—
108C2×C8×C13#4112yes—
109C2×C8×C13C2411yescharacteristic
110C13×C4⋊C4—21no—
111C13×C4⋊C4—22no—
112C13×C4⋊C4—21no—
113C13×C4⋊C4—42no—
114C13×C4⋊C4—41no—
115C13×C22⋊C4—42no—
116C13×C22⋊C4—41no—
117C42×C13—42no—
118C42×C13—41no—
119C22⋊Dic13—42no—
120#6103—42no—
121C4⋊Dic13—22no—
122C4⋊Dic13—41no—
123#6101—42no—
124Dic52—21no—
125Dic52—21no—
126D104—21no—
127D104—21no—
128#6095—42no—
129#6090—21no—
130#6090—21no—
131#6090—22no—
132#3061—131no—
133#2913D1311yescharacteristic, complemented
134#2237—132no—
135#2236—132no—
136#2234—132no—
137#2232—132no—
138#2159—131no—
139C2×#366—131no—
140#2139—131no—
141#2138—131no—
142#2113—131no—
143C23×C13C2×D812yes—
144C23×C13C2×D811yescharacteristic
145C22×D13—41no—
146Q8×C13—22no—
147D4×C13—24no—
148D4×C13—22no—
149C2×C4×C13—22no—
150C2×C4×C13—22no—
151C2×C4×C13—41no—
152C2×C4×C13—42no—
153C2×C4×C13—41no—
154C2×C4×C13—161no—
155C2×C4×C13—162no—
156C2×C4×C13#12312yes—
157C2×C4×C13C2×D812yes—
158C2×C4×C13C2×D811yescharacteristic
159C2×C4×C13#13712yes—
160C2×C4×C13C22×D411yescharacteristic
161C22⋊D13—82no—
162C22⋊D13—162no—
163C2×Dic13—41no—
164C2×Dic13—42no—
165C2×Dic13—161no—
166D52—41no—
167D52—41no—
168C4×D13—82no—
169Dic26—41no—
170Dic26—41no—
171C8×C13—22no—
172C8×C13#12312yes—
173C8×C13C2×#4111yescharacteristic
174C8×C13C2×#4111yescharacteristic
175C2×#135—131no—
176C2×#131C2×D1311yescharacteristic
177#537—261no—
178#520—21no—
179C2×M32—131no—
180C22×C16—131no—
181#468—262no—
182#467—132no—
183#466—132no—
184#428—21no—
185#428—22no—
186#427C2×D1311yescharacteristic
187#427C2×D1312yes—
188C2×#107—131no—
189C2×#107C2×D1311yescharacteristic
190C2×#107C2×D1312yes—
191#417—261no—
192#367—132no—
193#366—132no—
194#366—132no—
195#366—132no—
196#358—131no—
197#358—131no—
198#358—132no—
199#357—131no—
200#357—131no—
201#357—132no—
202C22⋊C16—132no—
203C22⋊C16—132no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—22no—
207C22×C13—22no—
208C22×C13—22no—
209C22×C13#48012yes—
210C22×C13C22×D811yescharacteristic
211C2×D13—81no—
212C2×D13—81no—
213C2×D13—81no—
214C4×C13—22no—
215C4×C13—82no—
216C4×C13—81no—
217C4×C13—81no—
218C4×C13#48012yes—
219C4×C13C2×#12311yescharacteristic
220C4×C13C2×#13711yescharacteristic
221Dic13—81no—
222Dic13—82no—
223C2×#41—261no—
224C2×#41C22⋊D1311yescharacteristic
225#135—262no—
226#135—262no—
227C2×Q16—131no—
228C2×SD16—261no—
229C2×D8—131no—
230#131—22no—
231#131—22no—
232C2×M16C22⋊D1311yescharacteristic
233C2×M16C22⋊D1312yes—
234C22×C8C22×D1312yes—
235C22×C8C22×D1311yescharacteristic
236C22⋊Q8—262no—
237C22⋊Q8—521no—
238#121—262no—
239#121—521no—
240#121—522no—
241C4×Q8—41no—
242C4×D4—42no—
243C4×D4—41no—
244#117—22no—
245#117—21no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—261no—
249M32—262no—
250C2×C16—131no—
251C2×C16—131no—
252C2×C16—132no—
253C2×C16—262no—
254#107—22no—
255#107—21no—
256#107—132no—
257#107—261no—
258#107C22×D1311yescharacteristic
259#107C22×D1312yes—
260#107C22×D1311yescharacteristic
261#106—22no—
262#106—21no—
263#103—262no—
264#102—262no—
265C2×C13—22no—
266C2×C13—42no—
267C2×C13C2×#48011yescharacteristic
268C2×C13#341511yescharacteristic
269C2×C13#341711yescharacteristic
270D13—161no—
271#41—22no—
272#41—22no—
273#41—522no—
274#41—522no—
275C2×Q8—261no—
276C2×Q8#610411yescharacteristic
277C2×D4—261no—
278C2×D4—521no—
279C2×D4—522no—
280C2×D4#610412yes—
281C2×D4#610411yescharacteristic
282C22×C4—42no—
283C22×C4—41no—
284C22×C4—521no—
285C22×C4—521no—
286C22×C4C2×C22⋊D1312yes—
287C22×C4C2×C22⋊D1311yescharacteristic
288Q16—261no—
289Q16—261no—
290SD16—522no—
291D8—261no—
292D8—261no—
293M16—22no—
294M16—24no—
295C2×C8—22no—
296C2×C8—22no—
297C2×C8#612712yes—
298C2×C8#612712yes—
299C2×C8C2×C22⋊D1312yes—
300C2×C8C2×C22⋊D1311yescharacteristic
301C2×C8C23×D1311yescharacteristic
302C4⋊C4—21no—
303C4⋊C4—22no—
304C4⋊C4—21no—
305C4⋊C4—42no—
306C4⋊C4—41no—
307C4⋊C4—262no—
308C4⋊C4—521no—
309C4⋊C4—522no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—522no—
313C22⋊C4—522no—
314C42—42no—
315C42—41no—
316C16—261no—
317C16—261no—
318C16—262no—
319C13#3365211yescharacteristic, complemented, Sylow
320C23—521no—
321C23C2×#610412yes—
322C23C2×#610411yescharacteristic
323Q8—22no—
324Q8—521no—
325Q8—521no—
326D4—24no—
327D4—22no—
328D4—521no—
329D4—521no—
330D4—1042no—
331D4—2082no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—161no—
338C2×C4—162no—
339C2×C4—522no—
340C2×C4—521no—
341C2×C4—1042no—
342C2×C4—2081no—
343C2×C4#8818312yes—
344C2×C4C2×#610412yes—
345C2×C4C2×#610411yescharacteristic
346C2×C4#8819612yes—
347C2×C4C22×C22⋊D1311yescharacteristic
348C8—22no—
349C8#8818312yes—
350C8C2×#612711yescharacteristic
351C8C2×#612711yescharacteristic
352C22—21no—
353C22—21no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—1041no—
358C22—1041no—
359C22—1041no—
360C22#1171862812yes—
361C22C22×#610411yescharacteristic
362C4—22no—
363C4—82no—
364C4—81no—
365C4—81no—
366C4—1042no—
367C4—1041no—
368C4#1171862812yes—
369C4C2×#8818311yescharacteristic
370C4C2×#8819611yescharacteristic
371C2—22no—
372C2—42no—
373C2—2081no—
374C2C2×#1171862811yescharacteristic
375C2#1312797511yescharacteristic
376C2#1312798711yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#2913C2
socleC22×C13C22×D8
prime radical#13124506C2
hypercenter#2913D13
hypocenterC13#33652
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×#131 ◁ #2913

Complements

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

NH ≅ G/Ntype
2. #13117044C2semidirect
3. #13117038C2semidirect
4. #13117027C2semidirect
5. #13117016C2semidirect
6. #13116625C2semidirect
7. C2×#11718081C2semidirect
8. #13116546C2semidirect
9. #13116541C2semidirect
10. #13116450C2semidirect
11. C13×#2913C2semidirect
133. #2913D13semidirect
319. C13#33652semidirect

Maximal subgroups

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

subgroupindex
#131245062
#131170442
#131170382
#131170272
#131170162
#131166252
C2×#117180812
#131165462
#131165412
#131164502
C13×#29132
#3365213