Finite Group Databasebeta

← #11878635

Subgroups — #11878635

Order 1152.

1596 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic, complemented
2#10596067C211yesmaximal, characteristic, complemented
3C32×#447C211yesmaximal, characteristic, complemented
4#10592916C211yesmaximal, characteristic, complemented
5#10592850C212yesmaximal, complemented
6#10592849C212yesmaximal, complemented
7#10592735C211yesmaximal, characteristic, complemented
8#10592485C212yesmaximal, complemented
9#10592459C212yesmaximal, complemented
10#10592431C211yesmaximal, characteristic, complemented
11#10592417C211yesmaximal, characteristic, complemented
12#79994—34nomaximal
13C22×C32×D4C2211yescharacteristic
14C22×#638—21no—
15C22×#638—21no—
16C2×#3830—21no—
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C32×D8C2212yescomplemented
19C32×#121C2211yescharacteristic
20#64149—21no—
21#64149—21no—
22#64149C2212yes—
23#64149C2212yes—
24#64149C2211yescharacteristic, complemented
25#64148—21no—
26D4×C3⋊Dic3C2211yescharacteristic, complemented
27C2×#3753C2212yescomplemented
28C2×#3753C2212yescomplemented
29#64139C2211yescharacteristic
30C2×C4×C3⋊Dic3C2211yescharacteristic
31C2×#3745C2212yescomplemented
32#64102C2211yescharacteristic, complemented
33#64097C2211yescharacteristic, complemented
34#64094—21no—
35#64090—21no—
36C32×#102C2212yescomplemented
37C32×C22⋊C8C2211yescharacteristic
38#63659C2212yescomplemented
39#63657C2211yescharacteristic
40#63648C2212yescomplemented
41#63641C2212yescomplemented
42C8×C3⋊Dic3C2212yescomplemented
43#63636C2212yescomplemented
44C2×#940—34no—
45#5596—34no—
46C3×#447D314yescomplemented
47#5217—34no—
48#5151—38no—
49#5150—38no—
50#5036—34no—
51#4786—38no—
52#4760—38no—
53#4732—34no—
54#4718—34no—
55C24×C32—21no—
56C23×C3⋊D3—21no—
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4—42no—
60C2×C32×D4C2312yes—
61C2×C32×D4C2311yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C2×#638—21no—
64C2×#638—21no—
65C2×#638—21no—
66C2×#638—22no—
67C2×#638—22no—
68C2×#638—22no—
69C2×#638—22no—
70C2×#638—44no—
71C2×#638—44no—
72C22×C3⋊Dic3—21no—
73C22×C3⋊Dic3D411yescharacteristic
74C22×C3⋊Dic3D411yescharacteristic
75#3830—44no—
76C2×C4⋊(C3⋊D3)—21no—
77C2×C4⋊(C3⋊D3)—42no—
78C2×C4⋊(C3⋊D3)C2312yes—
79C2×C4⋊(C3⋊D3)C2311yescharacteristic
80C2×C4×C3⋊D3—21no—
81C2×#634—21no—
82C32×D8—42no—
83C2×C32×C8C2312yes—
84C32×C4⋊C4C2311yescharacteristic
85C32×C22⋊C4—21no—
86#3757—21no—
87#3753—42no—
88#3753—42no—
89#3752—21no—
90#3752—21no—
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92#3750—21no—
93C4×C3⋊Dic3D411yescharacteristic
94C4×C3⋊Dic3D411yescharacteristic
95C4×C3⋊Dic3C2311yescharacteristic
96C4×C3⋊Dic3C2311yescharacteristic
97C2×C3⋊(C3⋊C8)C2312yes—
98#3745—42no—
99#3205—91noSylow
100C22×C3×D4C2×D314yes—
101C22×#67—64no—
102C22×#67—64no—
103C2×#237—64no—
104C22×D12—34no—
105C2×C3×D8C2×D318yescomplemented
106C3×#121C2×D314yes—
107#940—38no—
108#940—34no—
109#940—38no—
110#940—64no—
111#940—64no—
112#939—64no—
113D4×Dic3—34no—
114C2×#213—38no—
115C2×#213—38no—
116#930—34no—
117C2×C4×Dic3—34no—
118C2×D24—38no—
119#893—34no—
120#888—34no—
121#885—64no—
122#67⋊C4—64no—
123C3×#102C2×D318yescomplemented
124C3×C22⋊C8C2×D314yes—
125#832—38no—
126#830—34no—
127#821—38no—
128Dic3⋊C8—38no—
129C8×Dic3—38no—
130#809—38no—
131C23×C32—22no—
132C23×C32—21no—
133C23×C32—42no—
134C23×C32—42no—
135C23×C32—42no—
136C23×C32C2×D411yescharacteristic
137C22×C3⋊D3—22no—
138C22×C3⋊D3—21no—
139C22×C3⋊D3—42no—
140C22×C3⋊D3—42no—
141C22×C3⋊D3—42no—
142C32×D4—22no—
143C32×D4—22no—
144C32×D4—22no—
145C32×D4—42no—
146C32×D4—42no—
147C2×C32×C4—22no—
148C2×C32×C4—21no—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4C2411yescharacteristic
151#638—44no—
152#638—42no—
153#638—42no—
154#638—44no—
155#638—44no—
156#638—42no—
157#638—44no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—21no—
160C2×C3⋊Dic3—42no—
161C2×C3⋊Dic3D814yescomplemented
162C2×C3⋊Dic3C2×D411yescharacteristic
163C2×C3⋊Dic3C2×D411yescharacteristic
164C2×C3⋊Dic3C2×D411yescharacteristic
165C2×C3⋊Dic3C2×D411yescharacteristic
166C4⋊(C3⋊D3)—22no—
167C4⋊(C3⋊D3)—22no—
168C4⋊(C3⋊D3)—22no—
169C4⋊(C3⋊D3)—42no—
170C4×C3⋊D3—42no—
171#634—42no—
172C32×C8—22no—
173C3⋊(C3⋊C8)—22no—
174#532—91no—
175C2×#127—91no—
176#493—92no—
177#486—92no—
178#459—92no—
179#459—92no—
180#447—91no—
181#447—91no—
182#447—91no—
183#447C3⋊D311yescharacteristic, complemented
184#431—91no—
185C24×C3—24no—
186C23×D3—64no—
187C2×C3×D4—24no—
188C2×C3×D4—24no—
189C2×C3×D4—48no—
190C2×C3×D4C22×D318yes—
191C2×C3×D4C22×D314yes—
192C22×C3×C4C22×D314yes—
193C2×#67—64no—
194C2×#67—64no—
195C2×#67—68no—
196C2×#67—68no—
197C2×#67—68no—
198C2×#67—68no—
199C2×#67—64no—
200C2×#67—1216no—
201C2×#67—1216no—
202C22×Dic3—34no—
203C22×Dic3—34no—
204C22×Dic3—64no—
205#237—1216no—
206C2×D12—38no—
207C2×D12—34no—
208C2×D12—64no—
209C2×D12—128no—
210C2×C4×D3—64no—
211C2×Dic6—64no—
212C3×D8—48no—
213C2×C3×C8C22×D318yes—
214C3×C4⋊C4C22×D314yes—
215C3×C22⋊C4—24no—
216#217—64no—
217#213—128no—
218#213—128no—
219(C2×D3)⋊C4—64no—
220(C2×D3)⋊C4—64no—
221C4⋊Dic3—34no—
222Dic3⋊C4—64no—
223C4×Dic3—34no—
224C4×Dic3—34no—
225C4×Dic3—34no—
226C4×Dic3—34no—
227C2×C3⋊C8—38no—
228D24—128no—
229C22×C32—21no—
230C22×C32—21no—
231C22×C32—42no—
232C22×C32—41no—
233C22×C32—41no—
234C22×C32—42no—
235C22×C32—42no—
236C22×C32—41no—
237C22×C32—84no—
238C22×C32C2×D812yes—
239C22×C32C22×D411yescharacteristic
240C2×C3⋊D3—42no—
241C2×C3⋊D3—41no—
242C2×C3⋊D3—41no—
243C2×C3⋊D3—42no—
244C2×C3⋊D3—42no—
245C2×C3⋊D3—41no—
246C2×C3⋊D3—84no—
247C32×C4—21no—
248C32×C4—41no—
249C32×C4H(5,𝔽2)12yes—
250C3⋊Dic3—21no—
251C3⋊Dic3—41no—
252C3⋊Dic3C2×D812yes—
253C3⋊Dic3C2×D812yes—
254C3⋊Dic3AGL(1,ℤ/8)12yes—
255C2×#41—181no—
256C22×D4—91no—
257C22×D4—181no—
258C22×D4—181no—
259C22×D4C2×C3⋊D311yescharacteristic
260C2×D8—92no—
261C2×D8—92no—
262C2×D8—92no—
263C2×D8C2×C3⋊D312yescomplemented
264C4⋊Q8—91no—
265#127—92no—
266#127—92no—
267#127—91no—
268#127—181no—
269#127—181no—
270#124—181no—
271#121—91no—
272#121—181no—
273#121C2×C3⋊D311yescharacteristic
274C4×D4—91no—
275C4×D4—91no—
276C4×D4—181no—
277C2×C42—91no—
278C4⋊C8—92no—
279#102—92no—
280#102—92no—
281#102—92no—
282#102C2×C3⋊D312yescomplemented
283C22⋊C8—91no—
284C22⋊C8C2×C3⋊D311yescharacteristic
285C4×C8—92no—
286C23×C3—24no—
287C23×C3—28no—
288C23×C3—48no—
289C23×C3—48no—
290C23×C3—48no—
291C23×C3D3×D414yes—
292C22×D3—64no—
293C22×D3—68no—
294C22×D3—128no—
295C22×D3—128no—
296C22×D3—128no—
297C3×D4—28no—
298C3×D4—28no—
299C3×D4—28no—
300C3×D4—48no—
301C3×D4—48no—
302C2×C3×C4—28no—
303C2×C3×C4—24no—
304C2×C3×C4D3×D414yes—
305C2×C3×C4C23×D314yes—
306#67—128no—
307#67—128no—
308#67—1216no—
309#67—1216no—
310#67—1216no—
311#67—1216no—
312#67—128no—
313C2×Dic3—316no—
314C2×Dic3—34no—
315C2×Dic3—34no—
316C2×Dic3—34no—
317C2×Dic3—34no—
318C2×Dic3—68no—
319C2×Dic3—64no—
320C2×Dic3—128no—
321D12—68no—
322D12—68no—
323D12—68no—
324D12—128no—
325C4×D3—128no—
326Dic6—128no—
327C3×C8—28no—
328C3⋊C8—68no—
329C2×C32—22no—
330C2×C32—81no—
331C2×C32—82no—
332C2×C32#53511yescharacteristic
333C2×C32C22×D811yescharacteristic
334C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
335C3⋊D3—81no—
336C3⋊D3—82no—
337C24—21no—
338C24—181no—
339#41—364no—
340C2×Q8—181no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—42no—
344C2×D4—92no—
345C2×D4—91no—
346C2×D4—181no—
347C2×D4—181no—
348C2×D4—182no—
349C2×D4—182no—
350C2×D4—182no—
351C2×D4—182no—
352C2×D4—181no—
353C2×D4—181no—
354C2×D4—362no—
355C2×D4—364no—
356C2×D4—364no—
357C2×D4C22×C3⋊D312yes—
358C2×D4C22×C3⋊D311yescharacteristic
359C22×C4—91no—
360C22×C4—91no—
361C22×C4—181no—
362C22×C4—181no—
363C22×C4C22×C3⋊D311yescharacteristic
364D8—42no—
365D8—362no—
366D8—362no—
367D8—362no—
368C2×C8—92no—
369C2×C8C22×C3⋊D312yes—
370C4⋊C4—91no—
371C4⋊C4—181no—
372C4⋊C4C22×C3⋊D311yescharacteristic
373C22⋊C4—21no—
374C22⋊C4—181no—
375C22⋊C4—181no—
376C22⋊C4—181no—
377C42—91no—
378C42—91no—
379C42—91no—
380C42—91no—
381C22×C3—24no—
382C22×C3—24no—
383C22×C3—44no—
384C22×C3—48no—
385C22×C3—48no—
386C22×C3—44no—
387C22×C3—48no—
388C22×C3—44no—
389C22×C3—816no—
390C22×C3D3×D818yes—
391C22×C3C2×D3×D414yes—
392C2×D3—124no—
393C2×D3—128no—
394C2×D3—128no—
395C2×D3—124no—
396C2×D3—128no—
397C2×D3—124no—
398C2×D3—2416no—
399C3×C4—24no—
400C3×C4—44no—
401C3×C4#100418yes—
402Dic3—38no—
403Dic3—38no—
404Dic3—38no—
405Dic3—64no—
406Dic3—124no—
407C32#320511yescharacteristic, complemented, Sylow
408C23—21no—
409C23—22no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—181no—
414C23—182no—
415C23—362no—
416C23—362no—
417C23—362no—
418C23D4×C3⋊D311yescharacteristic
419Q8—362no—
420D4—22no—
421D4—22no—
422D4—22no—
423D4—42no—
424D4—42no—
425D4—182no—
426D4—182no—
427D4—182no—
428D4—362no—
429D4—364no—
430D4—364no—
431D4—364no—
432D4—362no—
433D4—362no—
434D4—364no—
435D4—362no—
436C2×C4—22no—
437C2×C4—21no—
438C2×C4—91no—
439C2×C4—91no—
440C2×C4—91no—
441C2×C4—94no—
442C2×C4—91no—
443C2×C4—182no—
444C2×C4—181no—
445C2×C4—362no—
446C2×C4—362no—
447C2×C4D4×C3⋊D311yescharacteristic
448C2×C4C23×C3⋊D311yescharacteristic
449C8—22no—
450C8—182no—
451C2×C3—28no—
452C2×C3—88no—
453C2×C3—84no—
454C2×C3#559214yes—
455C2×C3C2×D3×D814yes—
456C2×C3D3×AGL(1,ℤ/8)14yes—
457D3—248no—
458D3—244no—
459C22—21no—
460C22—21no—
461C22—41no—
462C22—42no—
463C22—42no—
464C22—41no—
465C22—42no—
466C22—41no—
467C22—84no—
468C22—361no—
469C22—362no—
470C22—362no—
471C22—361no—
472C22—362no—
473C22—361no—
474C22—724no—
475C22D8×C3⋊D312yes—
476C22C2×D4×C3⋊D311yescharacteristic
477C4—21no—
478C4—41no—
479C4—92no—
480C4—92no—
481C4—92no—
482C4—181no—
483C4—361no—
484C4#6436112yes—
485C3#7999414yescomplemented
486C2—22no—
487C2—82no—
488C2—81no—
489C2—722no—
490C2—721no—
491C2#1059606311yescharacteristic
492C2C2×D8×C3⋊D311yescharacteristic
493C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#447C2
socleC22×C32C22×D4
hypercenter#447C3⋊D3
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#64149C2semidirect
2. #10596067C2semidirect
3. C32×#447C2semidirect
4. #10592916C2semidirect
5. #10592850C2semidirect
6. #10592849C2semidirect
7. #10592735C2semidirect
8. #10592485C2semidirect
9. #10592459C2semidirect
10. #10592431C2semidirect
11. #10592417C2semidirect
18. C2×C32×D8C22semidirect
24. #64149C22semidirect
26. D4×C3⋊Dic3C22semidirect
27. C2×#3753C22semidirect
28. C2×#3753C22semidirect
31. C2×#3745C22semidirect
32. #64102C22semidirect
33. #64097C22semidirect
36. C32×#102C22semidirect
38. #63659C22semidirect
40. #63648C22semidirect
41. #63641C22semidirect
42. C8×C3⋊Dic3C22semidirect
43. #63636C22semidirect
46. C3×#447D3semidirect
105. C2×C3×D8C2×D3semidirect
123. C3×#102C2×D3semidirect
161. C2×C3⋊Dic3D8semidirect
183. #447C3⋊D3semidirect
263. C2×D8C2×C3⋊D3semidirect
282. #102C2×C3⋊D3semidirect
407. C32#3205semidirect
485. C3#79994semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
#105960672
C32×#4472
#105929162
#105928502
#105928492
#105927352
#105924852
#105924592
#105924312
#105924172
#799943