Finite Group Databasebeta

← #16017720

Subgroups — #16017720

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
2C2×#11718767C211yesmaximal, characteristic, complemented
3#13117045C212yesmaximal, complemented
4#13117039C211yesmaximal, characteristic, complemented
5#13117034C211yesmaximal, characteristic, complemented
6#13117028C212yesmaximal, complemented
7#13117022C211yesmaximal, characteristic, complemented
8#13117017C211yesmaximal, characteristic, complemented
9#13116620C212yesmaximal, complemented
10#13116544C212yesmaximal, complemented
11C2×C13×C22⋊C16C211yesmaximal, characteristic, complemented
12C23×C8×C13C2211yescharacteristic
13#11719496—21no—
14C2×#88180—21no—
15C2×#88158C2211yescharacteristic
16C22×C13×C16C2212yes—
17#11718777C2211yescharacteristic
18#11718777C2211yescharacteristic
19#11718776C2211yescharacteristic
20#11718776C2211yescharacteristic
21#11718775—21no—
22#11718775—21no—
23#11718774—21no—
24#11718767—21no—
25#11718767—21no—
26#11718767C2211yescharacteristic
27#11718767C2212yes—
28#11718767C2212yes—
29C2×#88058C2211yescharacteristic
30C2×#88058C2211yescharacteristic
31C2×#88057—21no—
32C13×C22⋊C16C2211yescharacteristic
33C13×C22⋊C16C2211yescharacteristic
34C13×C22⋊C16C2212yes—
35#11718101C2212yescomplemented
36#11718101C2212yescomplemented
37#11718097C2212yescomplemented
38#11718097C2212yescomplemented
39#11718096C2212yescomplemented
40#11718096C2212yescomplemented
41#11718095C2212yescomplemented
42#11718095C2212yescomplemented
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
52#88207—41no—
53C2×C22⋊Dic13—41no—
54#88184—21no—
55#88184—21no—
56#88183—41no—
57C4×C22⋊D13—41no—
58C4×C22⋊D13—41no—
59#88180—22no—
60#88180—22no—
61#88180—21no—
62#88180—41no—
63#88180—41no—
64C2×C4⋊Dic13—21no—
65C2×C4⋊Dic13—21no—
66#88178—21no—
67#88178—21no—
68C2×C4×Dic13—41no—
69C2×Dic52C2311yescharacteristic
70#88158—24no—
71C2×D104C2311yescharacteristic
72C2×#6095—21no—
73C2×C13×C16—24no—
74C2×C13×C16C2312yes—
75C2×C13×C16C2312yes—
76#88061—21no—
77#88061—21no—
78#88058—21no—
79#88058—21no—
80#88058C2312yes—
81#88058C2312yes—
82#88058C2311yescharacteristic
83#88058C2311yescharacteristic
84#88057—22no—
85#88057—22no—
86#88057—21no—
87#88056—21no—
88#88056—21no—
89#33645—131nomaximal, Sylow
90C24×C13D811yescharacteristic
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13D811yescharacteristic
94C22×C4×C13D811yescharacteristic
95C22×C4×C13D811yescharacteristic
96C22×C4×C13C2×D411yescharacteristic
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C2×C22⋊D13—41no—
100C2×C22⋊D13—41no—
101C2×C22⋊D13—41no—
102C22×Dic13—41no—
103C22×Dic13—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
119C22⋊Dic13—41no—
120C22⋊Dic13—41no—
121C22⋊Dic13—42no—
122C22⋊Dic13—42no—
123C22⋊Dic13—41no—
124#6103—41no—
125#6103—41no—
126C4⋊Dic13—21no—
127C4⋊Dic13—21no—
128C4⋊Dic13—22no—
129C4⋊Dic13—22no—
130C4⋊Dic13—41no—
131C4⋊Dic13—41no—
132#6101—41no—
133#6101—41no—
134C4×Dic13—42no—
135C4×Dic13—42no—
136C4×Dic13—41no—
137Dic52—22no—
138D104—22no—
139#6095—42no—
140C13×C16—22no—
141C13×C16—22no—
142#3050—131no—
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⋊C16D1311yescharacteristic, complemented
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#12312yes—
168C2×C4×C13C2×D811yescharacteristic
169C2×C4×C13C2×D811yescharacteristic
170C2×C4×C13C2×D811yescharacteristic
171C2×C4×C13#13712yes—
172C2×C4×C13C22×D411yescharacteristic
173C22⋊D13—82no—
174C22⋊D13—82no—
175C22⋊D13—82no—
176C2×Dic13—42no—
177C2×Dic13—42no—
178C2×Dic13—41no—
179C2×Dic13—41no—
180C2×Dic13—41no—
181C2×Dic13—82no—
182C2×Dic13—82no—
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—261no—
196C22×C16C2×D1312yes—
197#467—131no—
198#467—131no—
199#466—131no—
200#466—131no—
201#465—261no—
202#465—261no—
203#427—132no—
204#427—132no—
205#427—131no—
206#427—261no—
207#427—261no—
208C2×#107—131no—
209C2×#107—131no—
210C2×#106—261no—
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⋊C16C2×D1311yescharacteristic
221C22⋊C16C2×D1311yescharacteristic
222C22⋊C16C2×D1312yes—
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#48012yes—
240C4×C13C2×#12311yescharacteristic
241C4×C13C2×#13711yescharacteristic
242Dic13—81no—
243Dic13—82no—
244Dic13—81no—
245Dic13—82no—
246Dic13—81no—
247C2×#41—261no—
248C23×C4D5211yescharacteristic
249#135—264no—
250C2×Q16—131no—
251C2×SD16—261no—
252C2×D8—131no—
253C22×C8—24no—
254C22×C8D5211yescharacteristic
255C22×C8D5211yescharacteristic
256C22×C8D5211yescharacteristic
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—262no—
269#117—262no—
270#117—261no—
271#117—521no—
272#117—521no—
273C2×C4⋊C4—261no—
274C2×C4⋊C4—261no—
275C2×C22⋊C4—521no—
276C2×C42—521no—
277C2×C16—24no—
278C2×C16C22×D1312yes—
279C2×C16C22×D1312yes—
280#107—132no—
281#107—132no—
282#107—131no—
283#107—131no—
284#107—261no—
285#107—261no—
286#106—262no—
287#106—262no—
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—
300C24D10411yescharacteristic
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—521no—
311C22×C4—521no—
312C22×C4—521no—
313C22×C4D10411yescharacteristic
314C22×C4D10411yescharacteristic
315C22×C4D10411yescharacteristic
316C22×C4C2×D5211yescharacteristic
317C22×C4C2×D5211yescharacteristic
318C22×C4C2×D5211yescharacteristic
319Q16—262no—
320SD16—522no—
321D8—262no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8C2×D5211yescharacteristic
328C2×C8C2×D5211yescharacteristic
329C2×C8C2×D5211yescharacteristic
330C2×C8#612914yes—
331C2×C8C23×D1311yescharacteristic
332C4⋊C4—261no—
333C4⋊C4—261no—
334C4⋊C4—262no—
335C4⋊C4—262no—
336C4⋊C4—521no—
337C4⋊C4—521no—
338C4⋊C4—521no—
339C4⋊C4—521no—
340C22⋊C4—522no—
341C22⋊C4—522no—
342C22⋊C4—521no—
343C22⋊C4—521no—
344C22⋊C4—521no—
345C22⋊C4—521no—
346C22⋊C4—521no—
347C42—522no—
348C42—522no—
349C42—521no—
350C16—22no—
351C16—22no—
352C13#3364511yescharacteristic, complemented, Sylow
353C23—22no—
354C23—22no—
355C23—41no—
356C23—521no—
357C23C2×D10411yescharacteristic
358C23C2×D10411yescharacteristic
359C23C2×D10411yescharacteristic
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—522no—
375C2×C4—522no—
376C2×C4—521no—
377C2×C4—521no—
378C2×C4—521no—
379C2×C4—1042no—
380C2×C4—1042no—
381C2×C4—1042no—
382C2×C4#8814012yes—
383C2×C4C2×D10411yescharacteristic
384C2×C4C2×D10411yescharacteristic
385C2×C4C2×D10411yescharacteristic
386C2×C4#8816312yes—
387C2×C4C22×D5211yescharacteristic
388C8—21no—
389C8—21no—
390C8#8814012yes—
391C8C2×#612912yes—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—44no—
400C22—1041no—
401C22—1041no—
402C22—1041no—
403C22#1171839712yes—
404C22#1171856512yes—
405C22C22×D10411yescharacteristic
406C4—21no—
407C4—21no—
408C4—1042no—
409C4—1041no—
410C4—1042no—
411C4—1041no—
412C4—1041no—
413C4#1171839712yes—
414C4C2×#8814011yescharacteristic
415C4C2×#8816311yescharacteristic
416C2—22no—
417C2—22no—
418C2—41no—
419C2—2081no—
420C2C2×#1171839711yescharacteristic
421C2C2×#1171856511yescharacteristic
422C2#1312797211yescharacteristic
subgroupG/H
centerC2×C4C2×D104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC2×C13×C22⋊C16C2
socleC22×C13C22×D8
prime radical#13124417C2
hypercenterC2×C22⋊C16D13
hypocenterC13#33645
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C23×C8 ◁ C2×C22⋊C16

Complements

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

NH ≅ G/Ntype
2. C2×#11718767C2semidirect
3. #13117045C2semidirect
4. #13117039C2semidirect
5. #13117034C2semidirect
6. #13117028C2semidirect
7. #13117022C2semidirect
8. #13117017C2semidirect
9. #13116620C2semidirect
10. #13116544C2semidirect
11. C2×C13×C22⋊C16C2semidirect
35. #11718101C22semidirect
36. #11718101C22semidirect
37. #11718097C22semidirect
38. #11718097C22semidirect
39. #11718096C22semidirect
40. #11718096C22semidirect
41. #11718095C22semidirect
42. #11718095C22semidirect
152. C2×C22⋊C16D13semidirect
352. C13#33645semidirect

Maximal subgroups

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

subgroupindex
#131244172
C2×#117187672
#131170452
#131170392
#131170342
#131170282
#131170222
#131170172
#131166202
#131165442
C2×C13×C22⋊C162
#3364513