Finite Group Databasebeta

← #11889481

Subgroups — #11889481

Order 1152.

1140 conjugacy classes of subgroups.

The subgroup lattice has 537 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#556C211yesmaximal, characteristic, complemented
2#10596023C211yesmaximal, characteristic
3#10592790C211yesmaximal, characteristic, complemented
4#10592788C211yesmaximal, characteristic, complemented
5#10592750C211yesmaximal, characteristic, complemented
6#10592749C211yesmaximal, characteristic, complemented
7#10592748C211yesmaximal, characteristic, complemented
8#10592746C211yesmaximal, characteristic, complemented
9#10592729C211yesmaximal, characteristic, complemented
10#10592727C211yesmaximal, characteristic, complemented
11#10592710C211yesmaximal, characteristic, complemented
12#10592703C211yesmaximal, characteristic, complemented
13#10592702C211yesmaximal, characteristic, complemented
14#10592701C211yesmaximal, characteristic, complemented
15#10592695C211yesmaximal, characteristic, complemented
16#83674—34nomaximal
17C2×#3828C2211yescharacteristic
18C22×#634C2211yescharacteristic
19C32×C4⋊Q8C2211yescharacteristic
20C32×#126—21no—
21C32×#126—21no—
22C32×#124—21no—
23C32×C22⋊Q8C2211yescharacteristic
24C32×C22⋊Q8C2211yescharacteristic
25C32×C4×Q8—21no—
26C32×C4×Q8C2211yescharacteristic
27C32×C4×D4C2211yescharacteristic
28C32×#117C2211yescharacteristic
29C32×#117C2211yescharacteristic
30C2×#3756C2211yescharacteristic
31C2×#3756C2211yescharacteristic
32C2×#3755C2211yescharacteristic
33#64148—21no—
34#64139C2211yescharacteristic
35#64133C2211yescharacteristic
36C2×#3748C2211yescharacteristic
37C22×C3⋊(C3⋊C8)C2211yescharacteristic
38#64105—21no—
39#64094—21no—
40#64090—21no—
41#64084C2211yescharacteristic
42C4×#634C2211yescharacteristic
43#63662C2211yescharacteristic
44#63657C2211yescharacteristic
45#63657C2211yescharacteristic
46#63637C2211yescharacteristic
47#63637C2211yescharacteristic
48#63637C2211yescharacteristic
49#63637C2211yescharacteristic
50#63637C2211yescharacteristic
51#63637C2211yescharacteristic
52#63636C2211yescharacteristic
53#63636C2211yescharacteristic
54#63636C2211yescharacteristic
55#63635C2211yescharacteristic
56#63634C2211yescharacteristic
57#63634C2211yescharacteristic
58C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
59#63630C2211yescharacteristic
60C3×#556D314yescomplemented
61#5552—34no—
62#5091—34no—
63#5089—34no—
64#5051—34no—
65#5050—34no—
66#5049—34no—
67#5047—34no—
68#5030—34no—
69#5028—34no—
70#5011—34no—
71#5004—34no—
72#5003—34no—
73#5002—34no—
74#4996—34no—
75C2×C32×Q8—21no—
76C2×C32×Q8C2311yescharacteristic
77C2×C32×D4D411yescharacteristic
78C22×C32×C4C2311yescharacteristic
79C22×C32×C4C2311yescharacteristic
80C2×#638—21no—
81C2×#638—21no—
82C22×C3⋊Dic3—21no—
83#3828—22no—
84#3828—41no—
85C2×C4⋊(C3⋊D3)C2311yescharacteristic
86C2×C4×C3⋊D3—21no—
87C2×#634—22no—
88C2×#634—21no—
89C2×#634—41no—
90C2×#634C2311yescharacteristic
91C2×#634C2311yescharacteristic
92C32×C4⋊C4—21no—
93C32×C4⋊C4—21no—
94C32×C4⋊C4—21no—
95C32×C4⋊C4—21no—
96C32×C4⋊C4D411yescharacteristic
97C32×C4⋊C4C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C4⋊C4C2311yescharacteristic
100C32×C22⋊C4—21no—
101C32×C22⋊C4—21no—
102C32×C22⋊C4—21no—
103C32×C22⋊C4—21no—
104C32×C22⋊C4D411yescharacteristic
105C32×C22⋊C4D411yescharacteristic
106C32×C42—21no—
107C32×C42—21no—
108C32×C42—21no—
109C32×C42C2311yescharacteristic
110#3757—21no—
111#3756—22no—
112#3756—41no—
113#3755—41no—
114#3752—21no—
115#3752—21no—
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3750—21no—
120C4×C3⋊Dic3—21no—
121#3748—41no—
122C2×C3⋊(C3⋊C8)—41no—
123C2×C3⋊(C3⋊C8)C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126C2×C3⋊(C3⋊C8)C2311yescharacteristic
127#3313—91noSylow
128C2×#235—34no—
129C22×Dic6—34no—
130C3×C4⋊Q8C2×D314yes—
131C3×#126—24no—
132C3×#126—24no—
133C3×#124—24no—
134C3×C22⋊Q8C2×D314yes—
135C3×C22⋊Q8C2×D314yes—
136C3×C4×Q8—24no—
137C3×C4×Q8C2×D314yes—
138C3×C4×D4C2×D314yes—
139C3×#117C2×D314yes—
140C3×#117C2×D314yes—
141C2×#216—34no—
142C2×#216—34no—
143C2×#215—34no—
144#939—64no—
145#930—34no—
146#924—34no—
147C2×#208—34no—
148C22×C3⋊C8—34no—
149#896—64no—
150#885—64no—
151#67⋊C4—64no—
152#875—34no—
153C4×Dic6—34no—
154#835—34no—
155#830—34no—
156#830—34no—
157#810—34no—
158#810—34no—
159#810—34no—
160#810—34no—
161#810—34no—
162#810—34no—
163#809—34no—
164#809—34no—
165#809—34no—
166#808—34no—
167#807—34no—
168#807—34no—
169C4⋊(C3⋊C8)—34no—
170#803—34no—
171C23×C32C2×D411yescharacteristic
172C23×C32C2×D411yescharacteristic
173C22×C3⋊D3—21no—
174C32×Q8—21no—
175C32×Q8—21no—
176C32×Q8—42no—
177C32×D4—41no—
178C2×C32×C4—21no—
179C2×C32×C4—21no—
180C2×C32×C4—21no—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4—21no—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2411yescharacteristic
191#638—42no—
192#638—42no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—42no—
197C4⋊(C3⋊D3)—21no—
198C4⋊(C3⋊D3)—21no—
199C4×C3⋊D3—42no—
200#634—21no—
201#634—21no—
202#634—21no—
203#634—42no—
204#634#4112yes—
205C3⋊(C3⋊C8)—21no—
206C3⋊(C3⋊C8)—21no—
207C3⋊(C3⋊C8)—21no—
208C3⋊(C3⋊C8)—21no—
209#556C3⋊D311yescharacteristic, complemented
210#548—91no—
211#489—91no—
212#485—91no—
213#482—91no—
214#477—91no—
215#468—91no—
216#467—91no—
217#464—91no—
218#452—91no—
219#451—91no—
220#441—91no—
221#435—91no—
222#419—91no—
223#416—91no—
224C2×C3×Q8—24no—
225C2×C3×Q8C22×D314yes—
226C2×C3×D4#6714yes—
227C22×C3×C4C22×D314yes—
228C22×C3×C4C22×D314yes—
229C2×#67—64no—
230C2×#67—64no—
231C22×Dic3—64no—
232#235—68no—
233#235—124no—
234C2×D12—34no—
235C2×C4×D3—64no—
236C2×Dic6—34no—
237C2×Dic6—34no—
238C2×Dic6—68no—
239C2×Dic6—64no—
240C2×Dic6—124no—
241C3×C4⋊C4—24no—
242C3×C4⋊C4—24no—
243C3×C4⋊C4—24no—
244C3×C4⋊C4—24no—
245C3×C4⋊C4#6714yes—
246C3×C4⋊C4C22×D314yes—
247C3×C4⋊C4C22×D314yes—
248C3×C4⋊C4C22×D314yes—
249C3×C22⋊C4—24no—
250C3×C22⋊C4—24no—
251C3×C22⋊C4—24no—
252C3×C22⋊C4—24no—
253C3×C22⋊C4#6714yes—
254C3×C22⋊C4#6714yes—
255C3×C42—24no—
256C3×C42—24no—
257C3×C42—24no—
258C3×C42C22×D314yes—
259#217—64no—
260#216—68no—
261#216—124no—
262#215—124no—
263(C2×D3)⋊C4—64no—
264(C2×D3)⋊C4—64no—
265(C2×D3)⋊C4—64no—
266C4⋊Dic3—34no—
267Dic3⋊C4—64no—
268Dic3⋊C4—64no—
269C4×Dic3—64no—
270#208—124no—
271C2×C3⋊C8—34no—
272C2×C3⋊C8—34no—
273C2×C3⋊C8—34no—
274C2×C3⋊C8—34no—
275C2×C3⋊C8—124no—
276C22×C32—21no—
277C22×C32—21no—
278C22×C32—21no—
279C22×C32—21no—
280C22×C32—21no—
281C22×C32—21no—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3⋊D3—41no—
286C32×C4—21no—
287C32×C4—21no—
288C32×C4—21no—
289C32×C4—21no—
290C32×C4—41no—
291C32×C4—41no—
292C32×C4—41no—
293C32×C4—41no—
294C32×C4C2×#4111yescharacteristic
295C32×C4H(5,𝔽2)11yescharacteristic
296C3⋊Dic3—22no—
297C3⋊Dic3—41no—
298C3⋊Dic3—41no—
299C2×#41—91no—
300C22×Q8—91no—
301C2×Q16—91no—
302C2×Q16—91no—
303C2×SD16—91no—
304C2×M16—91no—
305C22×C8—91no—
306C4⋊Q8C2×C3⋊D311yescharacteristic
307#126—21no—
308#126—21no—
309#124—21no—
310#124—91no—
311#124—181no—
312C22⋊Q8—91no—
313C22⋊Q8—181no—
314C22⋊Q8C2×C3⋊D311yescharacteristic
315C22⋊Q8C2×C3⋊D311yescharacteristic
316#121—91no—
317#121—181no—
318C4×Q8—21no—
319C4×Q8—91no—
320C4×Q8C2×C3⋊D311yescharacteristic
321C4×D4—181no—
322C4×D4C2×C3⋊D311yescharacteristic
323#117C2×C3⋊D311yescharacteristic
324#117C2×C3⋊D311yescharacteristic
325#107—91no—
326#107—91no—
327#106—91no—
328C4⋊C8—91no—
329#103—91no—
330#103—91no—
331#103—91no—
332#103—91no—
333#103—91no—
334#103—91no—
335#103—91no—
336#102—91no—
337#102—91no—
338#102—91no—
339C22⋊C8—91no—
340C22⋊C8—91no—
341#97—91no—
342C23×C3C2×#6714yes—
343C23×C3C2×#6714yes—
344C22×D3—64no—
345C3×Q8—24no—
346C3×Q8—24no—
347C3×Q8—48no—
348C3×D4—44no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4—24no—
356C2×C3×C4—24no—
357C2×C3×C4C2×#6714yes—
358C2×C3×C4C2×#6714yes—
359C2×C3×C4C2×#6714yes—
360C2×C3×C4C2×#6714yes—
361C2×C3×C4C23×D314yes—
362#67—128no—
363#67—128no—
364C2×Dic3—64no—
365C2×Dic3—64no—
366C2×Dic3—64no—
367C2×Dic3—128no—
368D12—64no—
369D12—64no—
370C4×D3—128no—
371Dic6—38no—
372Dic6—64no—
373Dic6—64no—
374Dic6—64no—
375Dic6—128no—
376C3⋊C8—64no—
377C3⋊C8—64no—
378C3⋊C8—64no—
379C3⋊C8—64no—
380C2×C32—41no—
381C2×C32—41no—
382C2×C32#54611yescharacteristic
383C2×C32#57511yescharacteristic
384C2×C32#57811yescharacteristic
385C3⋊D3—81no—
386#41—182no—
387#41—361no—
388C2×Q8—21no—
389C2×Q8—91no—
390C2×Q8—91no—
391C2×Q8—182no—
392C2×Q8—181no—
393C2×Q8—361no—
394C2×Q8C22×C3⋊D311yescharacteristic
395C2×D4—91no—
396C2×D4—181no—
397C2×D4—181no—
398C2×D4#63811yescharacteristic
399C22×C4—181no—
400C22×C4—181no—
401C22×C4C22×C3⋊D311yescharacteristic
402C22×C4C22×C3⋊D311yescharacteristic
403Q16—182no—
404Q16—361no—
405SD16—361no—
406M16—361no—
407C2×C8—91no—
408C2×C8—91no—
409C2×C8—91no—
410C2×C8—91no—
411C2×C8—361no—
412C4⋊C4—21no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—91no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4#63811yescharacteristic
420C4⋊C4C22×C3⋊D311yescharacteristic
421C4⋊C4C22×C3⋊D311yescharacteristic
422C4⋊C4C22×C3⋊D311yescharacteristic
423C22⋊C4—21no—
424C22⋊C4—21no—
425C22⋊C4—21no—
426C22⋊C4—21no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22⋊C4—181no—
431C22⋊C4#63811yescharacteristic
432C22⋊C4#63811yescharacteristic
433C42—21no—
434C42—21no—
435C42—21no—
436C42—181no—
437C42C22×C3⋊D311yescharacteristic
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3—24no—
442C22×C3—24no—
443C22×C3—24no—
444C22×C3C22×#6714yes—
445C2×D3—124no—
446C2×D3—124no—
447C2×D3—124no—
448C3×C4—24no—
449C3×C4—24no—
450C3×C4—24no—
451C3×C4—24no—
452C3×C4—44no—
453C3×C4—44no—
454C3×C4—44no—
455C3×C4—44no—
456C3×C4D3×#4114yes—
457C3×C4#100914yes—
458Dic3—68no—
459Dic3—124no—
460Dic3—124no—
461C32#331311yescharacteristic, complemented, Sylow
462C23—181no—
463C23C2×#63811yescharacteristic
464C23C2×#63811yescharacteristic
465Q8—21no—
466Q8—21no—
467Q8—42no—
468Q8—92no—
469Q8—181no—
470Q8—181no—
471Q8—181no—
472Q8—362no—
473D4—41no—
474D4—181no—
475D4—181no—
476D4—362no—
477D4—362no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—181no—
489C2×C4—362no—
490C2×C4—362no—
491C2×C4C2×#63811yescharacteristic
492C2×C4C2×#63811yescharacteristic
493C2×C4C2×#63811yescharacteristic
494C2×C4C2×#63811yescharacteristic
495C2×C4C23×C3⋊D311yescharacteristic
496C8—181no—
497C8—181no—
498C8—181no—
499C8—181no—
500C2×C3—44no—
501C2×C3—44no—
502C2×C3#582214yes—
503C2×C3#582914yes—
504C2×C3#583814yes—
505D3—244no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—361no—
513C22—361no—
514C22—361no—
515C22C22×#63811yescharacteristic
516C4—21no—
517C4—21no—
518C4—21no—
519C4—21no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—41no—
524C4—182no—
525C4—361no—
526C4—361no—
527C4#41×C3⋊D311yescharacteristic
528C4#6436611yescharacteristic
529C3#8367414yescomplemented
530C2—41no—
531C2—41no—
532C2—721no—
533C2#1059629311yescharacteristic
534C2#1059630011yescharacteristic
535C2#1059630911yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#556C2
socleC22×C32C22×D4
prime radical#10596023C2
hypercenter#556C3⋊D3
hypocenterC32#3313
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C32×#556C2semidirect
3. #10592790C2semidirect
4. #10592788C2semidirect
5. #10592750C2semidirect
6. #10592749C2semidirect
7. #10592748C2semidirect
8. #10592746C2semidirect
9. #10592729C2semidirect
10. #10592727C2semidirect
11. #10592710C2semidirect
12. #10592703C2semidirect
13. #10592702C2semidirect
14. #10592701C2semidirect
15. #10592695C2semidirect
60. C3×#556D3semidirect
209. #556C3⋊D3semidirect
461. C32#3313semidirect
529. C3#83674semidirect

Maximal subgroups

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

subgroupindex
C32×#5562
#105960232
#105927902
#105927882
#105927502
#105927492
#105927482
#105927462
#105927292
#105927272
#105927102
#105927032
#105927022
#105927012
#105926952
#836743