Finite Group Databasebeta

← #16018114

Subgroups — #16018114

Order 3328.

546 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123713C211yesmaximal, characteristic, complemented
2#13117031C211yesmaximal, characteristic, complemented
3#13117019C211yesmaximal, characteristic, complemented
4#13116980C211yesmaximal, characteristic, complemented
5#13116975C211yesmaximal, characteristic, complemented
6#13116895C211yesmaximal, characteristic, complemented
7#13116888C211yesmaximal, characteristic, complemented
8#13116774C211yesmaximal, characteristic, complemented
9#13116757C211yesmaximal, characteristic
10#13116710C211yesmaximal, characteristic, complemented
11#13116705C211yesmaximal, characteristic, complemented
12C4×#88068C211yesmaximal, characteristic, complemented
13C4×#88067C211yesmaximal, characteristic, complemented
14#13116643C211yesmaximal, characteristic, complemented
15C13×#3175C211yesmaximal, characteristic, complemented
16C13×#542—21no—
17C2×#88158C2211yescharacteristic
18#11719228—21no—
19C13×#500C2211yescharacteristic
20C13×#495C2211yescharacteristic
21C13×#489—21no—
22C13×#468—21no—
23C13×#467C2211yescharacteristic
24C13×#466C2211yescharacteristic
25C13×#440—21no—
26C4×C13×Q16C2211yescharacteristic
27C4×C13×D8C2211yescharacteristic
28C13×#405C2211yescharacteristic
29C2×#88069C2211yescharacteristic
30C2×#88068C2211yescharacteristic
31C2×#88067C2211yescharacteristic
32C2×#88066C2211yescharacteristic
33#11718794—21no—
34C2×#88058C2211yescharacteristic
35#11718371—21no—
36#11718371—21no—
37C4×Dic52C2211yescharacteristic
38C4×Dic52C2211yescharacteristic
39C4×D104C2211yescharacteristic
40C4×D104C2211yescharacteristic
41#11718156C2211yescharacteristic
42#11718156C2211yescharacteristic
43#11718154C2211yescharacteristic
44#11718154C2211yescharacteristic
45C22⋊#6090C2211yescharacteristic
46C22⋊#6090C2211yescharacteristic
47#11718084C2211yescharacteristic
48#11718084C2211yescharacteristic
49#11718083C2211yescharacteristic
50#11718083C2211yescharacteristic
51#11718082C2211yescharacteristic
52#11718082C2211yescharacteristic
53#11718082C2211yescharacteristic
54#11718082C2211yescharacteristic
55C4⋊#6090C2211yescharacteristic
56C4⋊#6090C2211yescharacteristic
57#11718053C2211yescharacteristic
58C4×#6090C2211yescharacteristic
59C2×#6127—21no—
60C2×C13×Q16C2311yescharacteristic
61C2×C13×SD16—21no—
62C2×C13×D8C2311yescharacteristic
63C2×C13×M16D411yescharacteristic
64C22×C8×C13C2311yescharacteristic
65C13×C4⋊Q8—21no—
66C13×#126—41no—
67C13×#124—21no—
68C13×#124—41no—
69C13×#123—41no—
70C13×C22⋊Q8—21no—
71C13×C22⋊Q8—41no—
72C13×#121—21no—
73C4×Q8×C13—21no—
74C4×D4×C13—21no—
75C13×#117D411yescharacteristic
76C2×C4⋊Dic13—21no—
77C2×Dic52C2311yescharacteristic
78#88158—22no—
79#88158—22no—
80C2×D104C2311yescharacteristic
81C2×#6095—21no—
82#88146—41no—
83C4⋊C4×D13—41no—
84#88135—41no—
85#88135—41no—
86C4×D52—21no—
87C4×D52—21no—
88C4×Dic26—21no—
89C4×Dic26—21no—
90C13×#107—21no—
91C13×#107C2311yescharacteristic
92C13×#107C2311yescharacteristic
93C13×#103—21no—
94C13×#103—21no—
95C13×#102—21no—
96C13×#102—21no—
97C13×#97D411yescharacteristic
98C13×#97D411yescharacteristic
99C4×C8×C13C2311yescharacteristic
100C4×C8×C13C2311yescharacteristic
101#88069—22no—
102#88068—22no—
103#88067—22no—
104#88066—22no—
105#88061—21no—
106#88061—21no—
107#88058—21no—
108#88058C2311yescharacteristic
109#88058C2311yescharacteristic
110#88056—21no—
111#88056—21no—
112C2×#6090C2311yescharacteristic
113C2×#6090C2311yescharacteristic
114C2×#6090C2311yescharacteristic
115C2×#6090C2311yescharacteristic
116#33685—131nomaximal, Sylow
117C2×Q8×C13—21no—
118C2×Q8×C13—41no—
119C2×D4×C13—21no—
120C2×D4×C13—41no—
121C22×C4×C13—41no—
122C22×C4×C13C2×D411yescharacteristic
123C2×C22⋊D13—41no—
124C22×Dic13—41no—
125#6127—24no—
126#6127—42no—
127C2×D52—21no—
128C2×C4×D13—41no—
129C2×C4×D13—41no—
130C2×C4×D13—41no—
131C2×Dic26—21no—
132C13×Q16—21no—
133C13×Q16—21no—
134C13×SD16—42no—
135C13×D8—21no—
136C13×D8—21no—
137C13×M16—41no—
138C2×C8×C13—21no—
139C2×C8×C13—21no—
140C2×C8×C13C2×D411yescharacteristic
141C2×C8×C13C2×D411yescharacteristic
142C2×C8×C13C2×D411yescharacteristic
143C2×C8×C13C2411yescharacteristic
144C13×C4⋊C4—21no—
145C13×C4⋊C4—21no—
146C13×C4⋊C4—41no—
147C13×C4⋊C4—41no—
148C13×C4⋊C4—41no—
149C13×C4⋊C4D811yescharacteristic
150C13×C4⋊C4D811yescharacteristic
151C13×C22⋊C4—41no—
152C13×C22⋊C4—41no—
153C13×C22⋊C4—41no—
154C13×C22⋊C4—41no—
155C13×C22⋊C4—41no—
156C13×C22⋊C4D811yescharacteristic
157C13×C22⋊C4D811yescharacteristic
158C42×C13—41no—
159C42×C13C2×D411yescharacteristic
160C42×C13C2×D411yescharacteristic
161#6103—41no—
162#6103—41no—
163C4⋊Dic13—21no—
164C4⋊Dic13—21no—
165C4⋊Dic13—41no—
166#6101—41no—
167#6101—41no—
168C4×Dic13—41no—
169C4×Dic13—41no—
170Dic52—21no—
171Dic52#4112yes—
172D104—21no—
173D104#4112yes—
174#6095—24no—
175#6090—21no—
176#6090—21no—
177#6090—21no—
178#6090—21no—
179#3175D1311yescharacteristic, complemented
180#2951—131no—
181#2235—131no—
182#2233—131no—
183#2226—131no—
184#2225—131no—
185#2211—131no—
186#2210—131no—
187#2189—131no—
188#2186—131no—
189#2177—131no—
190#2176—131no—
191C4×SD32—131no—
192C4×SD32—131no—
193#2164—131no—
194C23×C13—41no—
195C23×C13C2×D811yescharacteristic
196C22×D13—41no—
197Q8×C13—41no—
198Q8×C13—41no—
199Q8×C13—161no—
200D4×C13—41no—
201D4×C13—41no—
202D4×C13—161no—
203C2×C4×C13—21no—
204C2×C4×C13—21no—
205C2×C4×C13—41no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
208C2×C4×C13—161no—
209C2×C4×C13C2×D811yescharacteristic
210C2×C4×C13C2×D811yescharacteristic
211C2×C4×C13C2×D811yescharacteristic
212C2×C4×C13C2×D811yescharacteristic
213C2×C4×C13C2×D811yescharacteristic
214C2×C4×C13C22×D411yescharacteristic
215C22⋊D13—44no—
216C2×Dic13—41no—
217C2×Dic13—41no—
218C2×Dic13—41no—
219C2×Dic13—161no—
220D52—22no—
221D52—41no—
222C4×D13—44no—
223C4×D13—161no—
224C4×D13—161no—
225Dic26—22no—
226Dic26—41no—
227C8×C13—21no—
228C8×C13—21no—
229C8×C13—21no—
230C8×C13C2×#4111yescharacteristic
231C8×C13C2×#4111yescharacteristic
232C2×#135—131no—
233#542—21no—
234#520—261no—
235C2×Q32—131no—
236C2×SD32—131no—
237C2×SD32—131no—
238C2×D16—131no—
239#500C2×D1311yescharacteristic
240#495C2×D1311yescharacteristic
241#489—21no—
242#468—21no—
243#467C2×D1311yescharacteristic
244#466C2×D1311yescharacteristic
245#440—21no—
246#440—261no—
247#440—261no—
248C4×Q16—131no—
249C4×Q16—131no—
250C4×Q16C2×D1311yescharacteristic
251C4×D8—131no—
252C4×D8—131no—
253C4×D8C2×D1311yescharacteristic
254C2×#107—131no—
255#417—261no—
256#405C2×D1311yescharacteristic
257#367—131no—
258#367—131no—
259#367—131no—
260#367—131no—
261C4⋊C16—131no—
262C4⋊C16—131no—
263#358—131no—
264#358—131no—
265#358—131no—
266#358—131no—
267#357—131no—
268#357—131no—
269#357—131no—
270#357—131no—
271C22⋊C16—131no—
272C22⋊C16—131no—
273#346—131no—
274C4×C16—131no—
275C22×C13—21no—
276C22×C13—21no—
277C22×C13—21no—
278C22×C13—81no—
279C22×C13—81no—
280C22×C13—81no—
281C22×C13C22×D811yescharacteristic
282C2×D13—42no—
283C2×D13—81no—
284C2×D13—81no—
285C4×C13—21no—
286C4×C13—21no—
287C4×C13—21no—
288C4×C13—21no—
289C4×C13—21no—
290C4×C13—81no—
291C4×C13—81no—
292C4×C13—81no—
293C4×C13#52511yescharacteristic
294C4×C13#57511yescharacteristic
295Dic13—42no—
296Dic13—81no—
297Dic13—81no—
298C2×#41—261no—
299#135—262no—
300#135—262no—
301C2×Q16—131no—
302C2×Q16C22×D1311yescharacteristic
303C2×SD16—21no—
304C2×SD16—261no—
305C2×D8—131no—
306C2×D8C22×D1311yescharacteristic
307C2×M16C22⋊D1311yescharacteristic
308C22×C8C22×D1311yescharacteristic
309C4⋊Q8—21no—
310#126—41no—
311#124—21no—
312#124—41no—
313#123—41no—
314C22⋊Q8—21no—
315C22⋊Q8—41no—
316#121—21no—
317C4×Q8—21no—
318C4×Q8—261no—
319C4×Q8—261no—
320C4×D4—21no—
321C4×D4—261no—
322C4×D4—261no—
323C4×D4—521no—
324C4×D4—521no—
325#117—521no—
326#117C22⋊D1311yescharacteristic
327C2×C4⋊C4—261no—
328C2×C4⋊C4—521no—
329Q32—262no—
330SD32—262no—
331SD32—262no—
332D16—262no—
333C2×C16—131no—
334C2×C16—131no—
335C2×C16—131no—
336C2×C16—131no—
337#107—21no—
338#107—131no—
339#107—131no—
340#107—261no—
341#107C22×D1311yescharacteristic
342#107C22×D1311yescharacteristic
343#103—21no—
344#103—21no—
345#103—261no—
346#103—261no—
347#102—21no—
348#102—21no—
349#102—261no—
350#102—261no—
351#97C22⋊D1311yescharacteristic
352#97C22⋊D1311yescharacteristic
353C4×C8C22×D1311yescharacteristic
354C4×C8C22×D1311yescharacteristic
355C2×C13—41no—
356C2×C13—161no—
357C2×C13#310011yescharacteristic
358C2×C13#341611yescharacteristic
359C2×C13#341611yescharacteristic
360D13—82no—
361#41—264no—
362#41—522no—
363C2×Q8—21no—
364C2×Q8—41no—
365C2×Q8—261no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4—261no—
369C2×D4—521no—
370C22×C4—41no—
371C22×C4—521no—
372C22×C4—521no—
373C22×C4—521no—
374C22×C4—521no—
375C22×C4C2×C22⋊D1311yescharacteristic
376Q16—21no—
377Q16—21no—
378Q16—132no—
379Q16—261no—
380SD16—42no—
381SD16—264no—
382D8—21no—
383D8—21no—
384D8—132no—
385D8—261no—
386M16—41no—
387C2×C8—21no—
388C2×C8—21no—
389C2×C8C2×C22⋊D1311yescharacteristic
390C2×C8C2×C22⋊D1311yescharacteristic
391C2×C8C2×C22⋊D1311yescharacteristic
392C2×C8C23×D1311yescharacteristic
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—261no—
399C4⋊C4—261no—
400C4⋊C4—521no—
401C4⋊C4—521no—
402C4⋊C4—521no—
403C4⋊C4#610411yescharacteristic
404C4⋊C4#610411yescharacteristic
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—521no—
411C22⋊C4—521no—
412C22⋊C4#610411yescharacteristic
413C22⋊C4#610411yescharacteristic
414C42—41no—
415C42—521no—
416C42—521no—
417C42C2×C22⋊D1311yescharacteristic
418C42C2×C22⋊D1311yescharacteristic
419C16—261no—
420C16—261no—
421C16—261no—
422C16—261no—
423C13#3368511yescharacteristic, complemented, Sylow
424C23—41no—
425C23—521no—
426C23C2×#610411yescharacteristic
427Q8—41no—
428Q8—41no—
429Q8—161no—
430Q8—262no—
431Q8—521no—
432D4—41no—
433D4—41no—
434D4—161no—
435D4—262no—
436D4—524no—
437D4—521no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—161no—
444C2×C4—524no—
445C2×C4—521no—
446C2×C4—521no—
447C2×C4—521no—
448C2×C4—2081no—
449C2×C4—2081no—
450C2×C4—2081no—
451C2×C4C2×#610411yescharacteristic
452C2×C4C2×#610411yescharacteristic
453C2×C4C2×#610411yescharacteristic
454C2×C4C2×#610411yescharacteristic
455C2×C4C2×#610411yescharacteristic
456C2×C4C22×C22⋊D1311yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8#41×D1311yescharacteristic
461C8#41×D1311yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22—522no—
469C22—1041no—
470C22—1041no—
471C22C22×#610411yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—81no—
478C4—81no—
479C4—81no—
480C4—522no—
481C4—1041no—
482C4—1041no—
483C4#1171952711yescharacteristic
484C4#1171953311yescharacteristic
485C2—41no—
486C2—161no—
487C2—1042no—
488C2#1312483211yescharacteristic
489C2#1312798011yescharacteristic
490C2#1312798311yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3175C2
socleC22×C13C22×D8
prime radical#13116757C2
hypercenter#3175D13
hypocenterC13#33685
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3175

Complements

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

NH ≅ G/Ntype
1. #13123713C2semidirect
2. #13117031C2semidirect
3. #13117019C2semidirect
4. #13116980C2semidirect
5. #13116975C2semidirect
6. #13116895C2semidirect
7. #13116888C2semidirect
8. #13116774C2semidirect
10. #13116710C2semidirect
11. #13116705C2semidirect
12. C4×#88068C2semidirect
13. C4×#88067C2semidirect
14. #13116643C2semidirect
15. C13×#3175C2semidirect
179. #3175D13semidirect
423. C13#33685semidirect

Maximal subgroups

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

subgroupindex
#131237132
#131170312
#131170192
#131169802
#131169752
#131168952
#131168882
#131167742
#131167572
#131167102
#131167052
C4×#880682
C4×#880672
#131166432
C13×#31752
#3368513