Finite Group Databasebeta

← #11878827

Subgroups — #11878827

Order 1152.

1464 conjugacy classes of subgroups.

The subgroup lattice has 459 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#127C211yesmaximal, characteristic
2#10596049C211yesmaximal, characteristic, complemented
3C32×#460C211yesmaximal, characteristic, complemented
4#10592874C212yesmaximal, complemented
5#10592868C212yesmaximal, complemented
6#10592774C211yesmaximal, characteristic, complemented
7#10592726C211yesmaximal, characteristic, complemented
8#10592547C211yesmaximal, characteristic, complemented
9#10592532C211yesmaximal, characteristic, complemented
10#10592475C212yesmaximal, complemented
11#10592459C212yesmaximal, complemented
12#80387—34nomaximal
13C2×D4×C3⋊D3—21no—
14C2×D4×C3⋊D3—21no—
15C2×D4×C3⋊D3C2212yes—
16C2×C32×SD16C2212yescomplemented
17C32×#127C2211yescharacteristic
18C32×C4×Q8C2211yescharacteristic, complemented
19#64155C2211yescharacteristic
20#64153C2211yescharacteristic, complemented
21C2×#3755C2212yescomplemented
22#64149—21no—
23#64149—21no—
24#64149C2212yes—
25C2×#3754C2212yescomplemented
26C2×#3744C2212yescomplemented
27#64106C2211yescharacteristic
28#64105—21no—
29#64098—21no—
30#64097C2211yescharacteristic, complemented
31#64083C2211yescharacteristic
32#64081—21no—
33C42×C3⋊D3C2211yescharacteristic
34C4×#634—21no—
35C4×#634C2211yescharacteristic, complemented
36C32×C4⋊C8C2211yescharacteristic, complemented
37C32×#102C2212yescomplemented
38#63659C2212yescomplemented
39#63648C2212yescomplemented
40#63647C2212yes—
41C8×C3⋊Dic3C2212yescomplemented
42#63636C2212yescomplemented
43C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
44D3×#127—34no—
45#5578—34no—
46C3×#460D314yescomplemented
47#5175—38no—
48#5169—38no—
49#5075—34no—
50#5027—34no—
51#4848—34no—
52#4833—34no—
53#4776—38no—
54#4760—38no—
55C23×C3⋊D3—22no—
56C2×C32×Q8C2311yescharacteristic
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4C2312yes—
60C2×#638—22no—
61C2×#638—22no—
62C2×#638—22no—
63D4×C3⋊D3—42no—
64D4×C3⋊D3—42no—
65D4×C3⋊D3—44no—
66D4×C3⋊D3—44no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C4×C3⋊D3D411yescharacteristic
71C2×C4×C3⋊D3D411yescharacteristic
72C2×C4×C3⋊D3C2311yescharacteristic
73C2×#634—21no—
74C2×#634C2311yescharacteristic
75C32×SD16—42no—
76C2×C32×C8C2312yes—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2311yescharacteristic
79C32×C42—21no—
80C32×C42C2311yescharacteristic
81#3755—42no—
82#3754—42no—
83#3752—21no—
84#3752—21no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87#3750—21no—
88#3750—21no—
89#3750—21no—
90#3750—21no—
91#3750—21no—
92C4×C3⋊Dic3—21no—
93C4×C3⋊Dic3D411yescharacteristic
94C4×C3⋊Dic3D411yescharacteristic
95C4×C3⋊Dic3C2311yescharacteristic
96C2×C3⋊(C3⋊C8)C2312yes—
97#3744—42no—
98#3208—91noSylow
99C2×D3×D4—38no—
100C2×D3×D4—64no—
101C2×D3×D4—64no—
102C2×C3×SD16C2×D318yescomplemented
103C3×#127C2×D314yes—
104C3×C4×Q8C2×D314yescomplemented
105#946—34no—
106#944—34no—
107C2×#215—38no—
108#940—38no—
109#940—64no—
110#940—64no—
111C2×#214—38no—
112C2×#204—38no—
113#897—34no—
114#896—64no—
115#889—64no—
116#888—34no—
117#874—34no—
118#872—64no—
119C42×D3—34no—
120C4×Dic6—34no—
121C4×Dic6—64no—
122C3×C4⋊C8C2×D314yescomplemented
123C3×#102C2×D318yescomplemented
124#832—38no—
125#821—38no—
126(C2×D3)⋊C8—38no—
127C8×Dic3—38no—
128#809—38no—
129C4⋊(C3⋊C8)—34no—
130C23×C32—22no—
131C22×C3⋊D3—22no—
132C22×C3⋊D3—44no—
133C22×C3⋊D3—44no—
134C22×C3⋊D3—44no—
135C22×C3⋊D3C2×D411yescharacteristic
136C32×Q8—21no—
137C32×Q8—21no—
138C32×D4—22no—
139C32×D4—22no—
140C32×D4—42no—
141C32×D4—42no—
142C2×C32×C4—21no—
143C2×C32×C4—21no—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2411yescharacteristic
147#638—44no—
148#638—44no—
149#638—44no—
150C2×C3⋊Dic3—21no—
151C2×C3⋊Dic3—21no—
152C2×C3⋊Dic3C2×D411yescharacteristic
153C2×C3⋊Dic3C2×D411yescharacteristic
154C2×C3⋊Dic3C2×D411yescharacteristic
155C4⋊(C3⋊D3)—22no—
156C4⋊(C3⋊D3)—22no—
157C4⋊(C3⋊D3)—42no—
158C4⋊(C3⋊D3)—42no—
159C4×C3⋊D3—21no—
160C4×C3⋊D3—21no—
161C4×C3⋊D3—22no—
162C4×C3⋊D3SD1614yescomplemented
163#634—21no—
164#634—21no—
165#634—42no—
166C32×C8—22no—
167C3⋊(C3⋊C8)—22no—
168#533—91no—
169C2×#127—91no—
170#492—92no—
171#486—92no—
172#460—91no—
173#460—91no—
174#460—91no—
175#460C3⋊D311yescharacteristic, complemented
176#450—92no—
177#450—92no—
178#431—91no—
179C23×D3—68no—
180C2×C3×Q8C22×D314yes—
181C2×C3×D4—24no—
182C2×C3×D4—24no—
183C2×C3×D4C22×D318yes—
184C2×#67—68no—
185C2×#67—68no—
186C2×#67—68no—
187D3×D4—1216no—
188D3×D4—128no—
189D3×D4—128no—
190D3×D4—1216no—
191C2×D12—38no—
192C2×D12—64no—
193C2×D12—64no—
194C2×C4×D3—34no—
195C2×C4×D3—34no—
196C2×C4×D3—34no—
197C2×Dic6—34no—
198C2×Dic6—64no—
199C3×SD16—48no—
200C2×C3×C8C22×D318yes—
201C3×C4⋊C4—24no—
202C3×C4⋊C4C22×D314yes—
203C3×C42—24no—
204C3×C42C22×D314yes—
205#215—128no—
206#214—128no—
207(C2×D3)⋊C4—64no—
208(C2×D3)⋊C4—64no—
209C4⋊Dic3—34no—
210C4⋊Dic3—64no—
211Dic3⋊C4—64no—
212Dic3⋊C4—64no—
213Dic3⋊C4—64no—
214Dic3⋊C4—64no—
215Dic3⋊C4—64no—
216C4×Dic3—34no—
217C4×Dic3—34no—
218C4×Dic3—34no—
219C4×Dic3—64no—
220C2×C3⋊C8—38no—
221#204—128no—
222C22×C32—42no—
223C22×C32—42no—
224C22×C32—42no—
225C22×C32C22×D411yescharacteristic
226C2×C3⋊D3—21no—
227C2×C3⋊D3—21no—
228C2×C3⋊D3—42no—
229C2×C3⋊D3—42no—
230C2×C3⋊D3—42no—
231C2×C3⋊D3—88no—
232C2×C3⋊D3C2×SD1612yes—
233C32×C4—21no—
234C32×C4—41no—
235C32×C4—41no—
236C32×C4C2×SD1612yes—
237C32×C4H(5,𝔽2)11yescharacteristic
238C32×C4H(5,𝔽2)11yescharacteristic
239C3⋊Dic3—21no—
240C3⋊Dic3—41no—
241C3⋊Dic3—41no—
242C3⋊Dic3C2×SD1612yes—
243C3⋊Dic3AGL(1,ℤ/8)12yes—
244C22×D4—92no—
245C22×D4—181no—
246C22×D4—181no—
247C2×SD16—92no—
248C2×SD16—92no—
249C2×SD16—92no—
250C2×SD16C2×C3⋊D312yescomplemented
251C4⋊Q8—91no—
252C4⋊Q8—91no—
253#127—92no—
254#127—91no—
255#127—181no—
256#127—181no—
257#127C2×C3⋊D311yescharacteristic
258#125—181no—
259C22⋊Q8—91no—
260C22⋊Q8—91no—
261C22⋊Q8—181no—
262C4×Q8—91no—
263C4×Q8—181no—
264C4×Q8C2×C3⋊D311yescharacteristic, complemented
265#117—181no—
266C2×C42—91no—
267C4⋊C8—91no—
268C4⋊C8C2×C3⋊D311yescharacteristic, complemented
269#102—92no—
270#102—92no—
271#102—92no—
272#102C2×C3⋊D312yescomplemented
273C22⋊C8—92no—
274C4×C8—92no—
275C23×C3—28no—
276C22×D3—34no—
277C22×D3—68no—
278C22×D3—1216no—
279C22×D3—1216no—
280C22×D3—1216no—
281C3×Q8—24no—
282C3×Q8—24no—
283C3×D4—28no—
284C3×D4—28no—
285C3×D4—48no—
286C3×D4—48no—
287C2×C3×C4—24no—
288C2×C3×C4—24no—
289C2×C3×C4D3×D414yes—
290C2×C3×C4D3×D414yes—
291C2×C3×C4C23×D314yes—
292#67—1216no—
293#67—1216no—
294#67—1216no—
295C2×Dic3—34no—
296C2×Dic3—34no—
297C2×Dic3—34no—
298C2×Dic3—64no—
299C2×Dic3—64no—
300D12—68no—
301D12—68no—
302D12—128no—
303D12—128no—
304C4×D3—316no—
305C4×D3—68no—
306C4×D3—64no—
307C4×D3—64no—
308Dic6—64no—
309Dic6—64no—
310Dic6—128no—
311C3×C8—28no—
312C3⋊C8—68no—
313C2×C32—82no—
314C2×C32#53511yescharacteristic
315C2×C32C22×SD1611yescharacteristic
316C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
317C3⋊D3—22no—
318C3⋊D3—82no—
319C24—182no—
320C2×Q8—91no—
321C2×Q8—181no—
322C2×Q8C22×C3⋊D311yescharacteristic
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—92no—
326C2×D4—182no—
327C2×D4—182no—
328C2×D4—182no—
329C2×D4—181no—
330C2×D4—181no—
331C2×D4—364no—
332C2×D4—362no—
333C2×D4—362no—
334C2×D4—364no—
335C2×D4C22×C3⋊D312yes—
336C22×C4—91no—
337C22×C4—91no—
338C22×C4—91no—
339SD16—42no—
340SD16—362no—
341SD16—362no—
342SD16—362no—
343C2×C8—92no—
344C2×C8C22×C3⋊D312yes—
345C4⋊C4—21no—
346C4⋊C4—91no—
347C4⋊C4—181no—
348C4⋊C4—181no—
349C4⋊C4—181no—
350C4⋊C4—181no—
351C4⋊C4—181no—
352C4⋊C4—181no—
353C4⋊C4C22×C3⋊D311yescharacteristic
354C22⋊C4—181no—
355C22⋊C4—181no—
356C42—21no—
357C42—91no—
358C42—91no—
359C42—91no—
360C42—181no—
361C42C22×C3⋊D311yescharacteristic
362C22×C3—48no—
363C22×C3—48no—
364C22×C3—48no—
365C22×C3C2×D3×D414yes—
366C2×D3—38no—
367C2×D3—64no—
368C2×D3—64no—
369C2×D3—128no—
370C2×D3—128no—
371C2×D3—128no—
372C2×D3—2432no—
373C3×C4—24no—
374C3×C4—44no—
375C3×C4—44no—
376C3×C4D3×SD1618yes—
377C3×C4#100414yes—
378C3×C4#100914yes—
379Dic3—38no—
380Dic3—38no—
381Dic3—64no—
382Dic3—124no—
383Dic3—124no—
384C32#320811yescharacteristic, complemented, Sylow
385C23—22no—
386C23—91no—
387C23—182no—
388C23—364no—
389C23—364no—
390C23—364no—
391Q8—21no—
392Q8—21no—
393Q8—181no—
394Q8—181no—
395Q8—362no—
396D4—22no—
397D4—22no—
398D4—42no—
399D4—42no—
400D4—182no—
401D4—182no—
402D4—362no—
403D4—364no—
404D4—364no—
405D4—364no—
406D4—362no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—91no—
410C2×C4—91no—
411C2×C4—94no—
412C2×C4—91no—
413C2×C4—182no—
414C2×C4—181no—
415C2×C4—181no—
416C2×C4—181no—
417C2×C4—181no—
418C2×C4D4×C3⋊D311yescharacteristic
419C2×C4D4×C3⋊D311yescharacteristic
420C2×C4C23×C3⋊D311yescharacteristic
421C8—22no—
422C8—182no—
423C2×C3—88no—
424C2×C3#560714yes—
425C2×C3C2×D3×SD1614yes—
426C2×C3D3×AGL(1,ℤ/8)14yes—
427D3—68no—
428D3—248no—
429C22—42no—
430C22—42no—
431C22—42no—
432C22—92no—
433C22—181no—
434C22—181no—
435C22—362no—
436C22—362no—
437C22—362no—
438C22—728no—
439C22C2×D4×C3⋊D311yescharacteristic
440C4—21no—
441C4—41no—
442C4—41no—
443C4—92no—
444C4—92no—
445C4—181no—
446C4—361no—
447C4—361no—
448C4SD16×C3⋊D312yes—
449C4#6436111yescharacteristic
450C4#6436611yescharacteristic
451C3#8038714yescomplemented
452C2—82no—
453C2—182no—
454C2—722no—
455C2#1059607811yescharacteristic
456C2C2×SD16×C3⋊D311yescharacteristic
457C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#460C2
socleC22×C32C22×D4
prime radicalC3⋊D3×#127C2
hypercenter#460C3⋊D3
hypocenterC32#3208
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. #10596049C2semidirect
3. C32×#460C2semidirect
4. #10592874C2semidirect
5. #10592868C2semidirect
6. #10592774C2semidirect
7. #10592726C2semidirect
8. #10592547C2semidirect
9. #10592532C2semidirect
10. #10592475C2semidirect
11. #10592459C2semidirect
16. C2×C32×SD16C22semidirect
18. C32×C4×Q8C22semidirect
20. #64153C22semidirect
21. C2×#3755C22semidirect
25. C2×#3754C22semidirect
26. C2×#3744C22semidirect
30. #64097C22semidirect
35. C4×#634C22semidirect
36. C32×C4⋊C8C22semidirect
37. C32×#102C22semidirect
38. #63659C22semidirect
39. #63648C22semidirect
41. C8×C3⋊Dic3C22semidirect
42. #63636C22semidirect
43. C4⋊(C3⋊(C3⋊C8))C22semidirect
46. C3×#460D3semidirect
102. C2×C3×SD16C2×D3semidirect
104. C3×C4×Q8C2×D3semidirect
122. C3×C4⋊C8C2×D3semidirect
123. C3×#102C2×D3semidirect
162. C4×C3⋊D3SD16semidirect
175. #460C3⋊D3semidirect
250. C2×SD16C2×C3⋊D3semidirect
264. C4×Q8C2×C3⋊D3semidirect
268. C4⋊C8C2×C3⋊D3semidirect
272. #102C2×C3⋊D3semidirect
384. C32#3208semidirect
451. C3#80387semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1272
#105960492
C32×#4602
#105928742
#105928682
#105927742
#105927262
#105925472
#105925322
#105924752
#105924592
#803873