Finite Group Databasebeta

← #11878824

Subgroups — #11878824

Order 1152.

1464 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic
2#10596093C211yesmaximal, characteristic, complemented
3C32×#450C211yesmaximal, characteristic, complemented
4#10592917C211yesmaximal, characteristic, complemented
5#10592874C212yesmaximal, complemented
6#10592862C212yesmaximal, complemented
7#10592745C211yesmaximal, characteristic, complemented
8#10592461C212yesmaximal, complemented
9#10592459C212yesmaximal, complemented
10#10592430C211yesmaximal, characteristic, complemented
11#10592417C211yesmaximal, characteristic, complemented
12#80138—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C22×#638—21no—
15C22×#638—21no—
16C22×C4⋊(C3⋊D3)C2211yescharacteristic
17C2×C32×SD16C2212yescomplemented
18C32×C22⋊Q8C2211yescharacteristic
19Q8×C3⋊Dic3C2211yescharacteristic, complemented
20#64153C2211yescharacteristic, complemented
21C2×#3755C2212yescomplemented
22#64149—21no—
23#64149—21no—
24#64149C2212yes—
25#64149C2212yes—
26C2×#3754C2212yescomplemented
27#64133C2211yescharacteristic
28C2×C4×C3⋊Dic3C2211yescharacteristic
29C2×#3744C2212yescomplemented
30#64098—21no—
31#64097C2211yescharacteristic, complemented
32#64096—21no—
33#64096C2211yescharacteristic, complemented
34#64087—21no—
35#64086—21no—
36C32×#102C2212yescomplemented
37C32×C22⋊C8C2211yescharacteristic
38#63659C2212yescomplemented
39#63657C2211yescharacteristic
40#63648C2212yescomplemented
41#63641C2212yescomplemented
42C8×C3⋊Dic3C2212yescomplemented
43#63636C2212yescomplemented
44C2×#940—34no—
45#5622—34no—
46C3×#450D314yescomplemented
47#5218—34no—
48#5175—38no—
49#5163—38no—
50#5046—34no—
51#4762—38no—
52#4760—38no—
53#4731—34no—
54#4718—34no—
55C24×C32—21no—
56C23×C3⋊D3—21no—
57C2×C32×Q8C2311yescharacteristic
58C2×C32×D4—21no—
59C2×C32×D4—42no—
60C2×C32×D4C2312yes—
61C22×C32×C4C2311yescharacteristic
62C2×#638—22no—
63C2×#638—22no—
64C2×#638—22no—
65C2×#638—22no—
66C2×#638—44no—
67C2×#638—44no—
68C22×C3⋊Dic3D411yescharacteristic
69C22×C3⋊Dic3D411yescharacteristic
70C2×C4⋊(C3⋊D3)—21no—
71C2×C4⋊(C3⋊D3)—42no—
72C2×C4⋊(C3⋊D3)C2312yes—
73C2×#634—21no—
74C2×#634C2311yescharacteristic
75C32×SD16—42no—
76C2×C32×C8C2312yes—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2311yescharacteristic
79C32×C22⋊C4—21no—
80#3757—21no—
81#3755—42no—
82#3754—42no—
83C4⋊(C3⋊Dic3)—21no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85#3750—21no—
86#3750—21no—
87#3750—21no—
88#3750—21no—
89#3750—21no—
90C4×C3⋊Dic3—21no—
91C4×C3⋊Dic3—21no—
92C4×C3⋊Dic3D411yescharacteristic
93C4×C3⋊Dic3D411yescharacteristic
94C4×C3⋊Dic3C2311yescharacteristic
95C4×C3⋊Dic3C2311yescharacteristic
96C2×C3⋊(C3⋊C8)C2312yes—
97#3744—42no—
98#3208—91noSylow
99C22×C3×D4C2×D314yes—
100C22×#67—64no—
101C22×#67—64no—
102C22×D12—34no—
103C2×C3×SD16C2×D318yescomplemented
104C3×C22⋊Q8C2×D314yes—
105Q8×Dic3—34no—
106#944—34no—
107C2×#215—38no—
108#940—38no—
109#940—38no—
110#940—64no—
111#940—64no—
112C2×#214—38no—
113#924—34no—
114C2×C4×Dic3—34no—
115C2×#204—38no—
116#889—64no—
117#888—34no—
118#887—34no—
119#887—64no—
120#878—64no—
121#877—64no—
122C3×#102C2×D318yescomplemented
123C3×C22⋊C8C2×D314yes—
124#832—38no—
125#830—34no—
126#821—38no—
127Dic3⋊C8—38no—
128C8×Dic3—38no—
129#809—38no—
130C23×C32—22no—
131C23×C32—42no—
132C23×C32—42no—
133C23×C32—42no—
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—22no—
136C22×C3⋊D3—42no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C32×Q8—22no—
140C32×D4—22no—
141C32×D4—22no—
142C32×D4—42no—
143C2×C32×C4—22no—
144C2×C32×C4—21no—
145C2×C32×C4—21no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2411yescharacteristic
148#638—44no—
149#638—44no—
150#638—44no—
151#638—44no—
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3—21no—
155C2×C3⋊Dic3SD1614yescomplemented
156C2×C3⋊Dic3C2×D411yescharacteristic
157C2×C3⋊Dic3C2×D411yescharacteristic
158C2×C3⋊Dic3C2×D411yescharacteristic
159C2×C3⋊Dic3C2×D411yescharacteristic
160C4⋊(C3⋊D3)—22no—
161C4⋊(C3⋊D3)—22no—
162C4⋊(C3⋊D3)—42no—
163#634—22no—
164#634—42no—
165C32×C8—22no—
166C3⋊(C3⋊C8)—22no—
167#533—91no—
168C2×#127—91no—
169#492—92no—
170#486—92no—
171#460—92no—
172#460—92no—
173#450—91no—
174#450—91no—
175#450—91no—
176#450C3⋊D311yescharacteristic, complemented
177#431—91no—
178C24×C3—24no—
179C23×D3—64no—
180C2×C3×Q8C22×D314yes—
181C2×C3×D4—24no—
182C2×C3×D4—48no—
183C2×C3×D4C22×D318yes—
184C22×C3×C4C22×D314yes—
185C2×#67—68no—
186C2×#67—68no—
187C2×#67—68no—
188C2×#67—68no—
189C2×#67—1216no—
190C2×#67—1216no—
191C22×Dic3—34no—
192C22×Dic3—34no—
193C2×D12—38no—
194C2×D12—64no—
195C2×D12—128no—
196C2×Dic6—34no—
197C2×Dic6—64no—
198C3×SD16—48no—
199C2×C3×C8C22×D318yes—
200C3×C4⋊C4—24no—
201C3×C4⋊C4C22×D314yes—
202C3×C22⋊C4—24no—
203#217—64no—
204#215—128no—
205#214—128no—
206C4⋊Dic3—34no—
207C4⋊Dic3—64no—
208Dic3⋊C4—64no—
209Dic3⋊C4—64no—
210Dic3⋊C4—64no—
211Dic3⋊C4—64no—
212Dic3⋊C4—64no—
213C4×Dic3—34no—
214C4×Dic3—34no—
215C4×Dic3—34no—
216C4×Dic3—34no—
217C4×Dic3—64no—
218C4×Dic3—64no—
219C2×C3⋊C8—38no—
220#204—128no—
221C22×C32—21no—
222C22×C32—21no—
223C22×C32—42no—
224C22×C32—42no—
225C22×C32—42no—
226C22×C32—84no—
227C22×C32C2×SD1612yes—
228C22×C32C22×D411yescharacteristic
229C2×C3⋊D3—42no—
230C2×C3⋊D3—42no—
231C2×C3⋊D3—42no—
232C2×C3⋊D3—84no—
233C32×C4—21no—
234C32×C4—41no—
235C32×C4—41no—
236C32×C4H(5,𝔽2)12yes—
237C3⋊Dic3—21no—
238C3⋊Dic3—41no—
239C3⋊Dic3—41no—
240C3⋊Dic3C2×SD1612yes—
241C3⋊Dic3C2×SD1612yes—
242C3⋊Dic3AGL(1,ℤ/8)12yes—
243C22×D4—91no—
244C22×D4—181no—
245C22×D4—181no—
246C22×D4C2×C3⋊D311yescharacteristic
247C2×SD16—92no—
248C2×SD16—92no—
249C2×SD16—92no—
250C2×SD16C2×C3⋊D312yescomplemented
251C4⋊Q8—91no—
252C4⋊Q8—91no—
253#127—92no—
254#127—92no—
255#127—181no—
256#127—181no—
257#125—181no—
258C22⋊Q8—91no—
259C22⋊Q8—181no—
260C22⋊Q8C2×C3⋊D311yescharacteristic
261C4×Q8—91no—
262C4×Q8—91no—
263C4×Q8—181no—
264#117—181no—
265C2×C42—91no—
266C4⋊C8—92no—
267#102—92no—
268#102—92no—
269#102—92no—
270#102C2×C3⋊D312yescomplemented
271C22⋊C8—91no—
272C22⋊C8C2×C3⋊D311yescharacteristic
273C4×C8—92no—
274C23×C3—28no—
275C23×C3—48no—
276C23×C3—48no—
277C23×C3—48no—
278C23×C3D3×D414yes—
279C22×D3—68no—
280C22×D3—128no—
281C22×D3—128no—
282C22×D3—128no—
283C3×Q8—28no—
284C3×D4—28no—
285C3×D4—28no—
286C3×D4—48no—
287C2×C3×C4—28no—
288C2×C3×C4—24no—
289C2×C3×C4—24no—
290C2×C3×C4D3×D414yes—
291C2×C3×C4C23×D314yes—
292#67—1216no—
293#67—1216no—
294#67—1216no—
295#67—1216no—
296C2×Dic3—316no—
297C2×Dic3—34no—
298C2×Dic3—34no—
299C2×Dic3—34no—
300C2×Dic3—34no—
301C2×Dic3—68no—
302C2×Dic3—64no—
303C2×Dic3—64no—
304D12—68no—
305D12—68no—
306D12—128no—
307Dic6—68no—
308Dic6—128no—
309C3×C8—28no—
310C3⋊C8—68no—
311C2×C32—22no—
312C2×C32—82no—
313C2×C32#53511yescharacteristic
314C2×C32C22×SD1611yescharacteristic
315C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
316C3⋊D3—82no—
317C24—21no—
318C24—181no—
319C2×Q8—91no—
320C2×Q8—181no—
321C2×Q8C22×C3⋊D311yescharacteristic
322C2×D4—21no—
323C2×D4—42no—
324C2×D4—92no—
325C2×D4—182no—
326C2×D4—182no—
327C2×D4—182no—
328C2×D4—182no—
329C2×D4—181no—
330C2×D4—362no—
331C2×D4—364no—
332C2×D4—364no—
333C2×D4C22×C3⋊D312yes—
334C22×C4—91no—
335C22×C4—91no—
336C22×C4C22×C3⋊D311yescharacteristic
337SD16—42no—
338SD16—362no—
339SD16—362no—
340SD16—362no—
341C2×C8—92no—
342C2×C8C22×C3⋊D312yes—
343C4⋊C4—21no—
344C4⋊C4—91no—
345C4⋊C4—181no—
346C4⋊C4—181no—
347C4⋊C4—181no—
348C4⋊C4—181no—
349C4⋊C4—181no—
350C4⋊C4—181no—
351C4⋊C4C22×C3⋊D311yescharacteristic
352C22⋊C4—21no—
353C22⋊C4—181no—
354C42—91no—
355C42—91no—
356C42—91no—
357C42—91no—
358C42—181no—
359C42—181no—
360C22×C3—24no—
361C22×C3—24no—
362C22×C3—48no—
363C22×C3—48no—
364C22×C3—48no—
365C22×C3—816no—
366C22×C3D3×SD1618yes—
367C22×C3C2×D3×D414yes—
368C2×D3—128no—
369C2×D3—128no—
370C2×D3—128no—
371C2×D3—2416no—
372C3×C4—24no—
373C3×C4—44no—
374C3×C4—44no—
375C3×C4#100418yes—
376Dic3—38no—
377Dic3—38no—
378Dic3—38no—
379Dic3—64no—
380Dic3—124no—
381Dic3—124no—
382C32#320811yescharacteristic, complemented, Sylow
383C23—22no—
384C23—42no—
385C23—42no—
386C23—42no—
387C23—182no—
388C23—362no—
389C23—362no—
390C23—362no—
391C23D4×C3⋊D311yescharacteristic
392Q8—22no—
393Q8—182no—
394Q8—362no—
395D4—22no—
396D4—22no—
397D4—42no—
398D4—182no—
399D4—182no—
400D4—362no—
401D4—364no—
402D4—364no—
403D4—364no—
404D4—364no—
405C2×C4—22no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—91no—
409C2×C4—91no—
410C2×C4—91no—
411C2×C4—94no—
412C2×C4—91no—
413C2×C4—182no—
414C2×C4—181no—
415C2×C4—181no—
416C2×C4D4×C3⋊D311yescharacteristic
417C2×C4C23×C3⋊D311yescharacteristic
418C8—22no—
419C8—182no—
420C2×C3—28no—
421C2×C3—88no—
422C2×C3#559214yes—
423C2×C3C2×D3×SD1614yes—
424C2×C3D3×AGL(1,ℤ/8)14yes—
425D3—248no—
426C22—21no—
427C22—21no—
428C22—42no—
429C22—42no—
430C22—42no—
431C22—84no—
432C22—362no—
433C22—362no—
434C22—362no—
435C22—724no—
436C22SD16×C3⋊D312yes—
437C22C2×D4×C3⋊D311yescharacteristic
438C4—21no—
439C4—41no—
440C4—41no—
441C4—92no—
442C4—92no—
443C4—92no—
444C4—181no—
445C4—361no—
446C4—361no—
447C4#6436112yes—
448C3#8013814yescomplemented
449C2—22no—
450C2—82no—
451C2—722no—
452C2#1059606311yescharacteristic
453C2C2×SD16×C3⋊D311yescharacteristic
454C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#450C2
socleC22×C32C22×D4
prime radicalC2×#64149C2
hypercenter#450C3⋊D3
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
2. #10596093C2semidirect
3. C32×#450C2semidirect
4. #10592917C2semidirect
5. #10592874C2semidirect
6. #10592862C2semidirect
7. #10592745C2semidirect
8. #10592461C2semidirect
9. #10592459C2semidirect
10. #10592430C2semidirect
11. #10592417C2semidirect
17. C2×C32×SD16C22semidirect
19. Q8×C3⋊Dic3C22semidirect
20. #64153C22semidirect
21. C2×#3755C22semidirect
26. C2×#3754C22semidirect
29. C2×#3744C22semidirect
31. #64097C22semidirect
33. #64096C22semidirect
36. C32×#102C22semidirect
38. #63659C22semidirect
40. #63648C22semidirect
41. #63641C22semidirect
42. C8×C3⋊Dic3C22semidirect
43. #63636C22semidirect
46. C3×#450D3semidirect
103. C2×C3×SD16C2×D3semidirect
122. C3×#102C2×D3semidirect
155. C2×C3⋊Dic3SD16semidirect
176. #450C3⋊D3semidirect
250. C2×SD16C2×C3⋊D3semidirect
270. #102C2×C3⋊D3semidirect
382. C32#3208semidirect
448. C3#80138semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
#105960932
C32×#4502
#105929172
#105928742
#105928622
#105927452
#105924612
#105924592
#105924302
#105924172
#801383