Finite Group Databasebeta

← #11878638

Subgroups — #11878638

Order 1152.

1596 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#127C211yesmaximal, characteristic, complemented
2#10596019C211yesmaximal, characteristic, complemented
3C32×#459C211yesmaximal, characteristic, complemented
4#10592855C212yesmaximal, complemented
5#10592850C212yesmaximal, complemented
6#10592771C211yesmaximal, characteristic, complemented
7#10592714C211yesmaximal, characteristic, complemented
8#10592542C211yesmaximal, characteristic, complemented
9#10592532C211yesmaximal, characteristic, complemented
10#10592472C212yesmaximal, complemented
11#10592459C212yesmaximal, complemented
12#80336—34nomaximal
13C2×D4×C3⋊D3—21no—
14C2×D4×C3⋊D3—21no—
15C2×D4×C3⋊D3C2212yes—
16C2×#3828—21no—
17C2×C32×D8C2212yescomplemented
18C32×#127C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic, complemented
20#64149—21no—
21#64149—21no—
22#64149C2212yes—
23#64149C2211yescharacteristic, complemented
24#64147C2211yescharacteristic
25C2×#3753C2212yescomplemented
26C2×#3753C2212yescomplemented
27C4×#638—21no—
28C2×#3745C2212yescomplemented
29#64104C2211yescharacteristic
30#64097C2211yescharacteristic, complemented
31#64094—21no—
32#64093—21no—
33#64083C2211yescharacteristic
34C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
35C42×C3⋊D3C2211yescharacteristic
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#5548—34no—
46C3×#459D314yescomplemented
47#5156—38no—
48#5151—38no—
49#5072—34no—
50#5015—34no—
51#4843—34no—
52#4833—34no—
53#4773—38no—
54#4760—38no—
55C23×C3⋊D3—22no—
56C2×C32×D4—21no—
57C2×C32×D4—21no—
58C2×C32×D4C2312yes—
59C2×C32×D4C2311yescharacteristic
60C22×C32×C4—21no—
61C2×#638—21no—
62C2×#638—21no—
63C2×#638—21no—
64C2×#638—22no—
65C2×#638—22no—
66C2×#638—22no—
67D4×C3⋊D3—42no—
68D4×C3⋊D3—42no—
69D4×C3⋊D3—44no—
70D4×C3⋊D3—44no—
71#3828—44no—
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)—21no—
74C2×C4⋊(C3⋊D3)—21no—
75C2×C4⋊(C3⋊D3)C2311yescharacteristic
76C2×C4⋊(C3⋊D3)C2312yes—
77C2×C4×C3⋊D3—21no—
78C2×C4×C3⋊D3D411yescharacteristic
79C2×C4×C3⋊D3D411yescharacteristic
80C2×C4×C3⋊D3C2311yescharacteristic
81C2×#634—21no—
82C32×D8—42no—
83C2×C32×C8C2312yes—
84C32×C4⋊C4C2311yescharacteristic
85C32×C22⋊C4—21no—
86C32×C42C2311yescharacteristic
87#3757—21no—
88#3753—42no—
89#3753—42no—
90#3752—21no—
91#3752—21no—
92C4⋊(C3⋊Dic3)C2311yescharacteristic
93#3750—21no—
94C4×C3⋊Dic3D411yescharacteristic
95C4×C3⋊Dic3D411yescharacteristic
96C4×C3⋊Dic3C2311yescharacteristic
97C2×C3⋊(C3⋊C8)C2312yes—
98#3745—42no—
99#3205—91noSylow
100C2×D3×D4—38no—
101C2×D3×D4—64no—
102C2×D3×D4—64no—
103C2×#235—64no—
104C2×C3×D8C2×D318yescomplemented
105C3×#127C2×D314yes—
106C3×C4×D4C2×D314yescomplemented
107#940—34no—
108#940—38no—
109#940—64no—
110#940—64no—
111#938—34no—
112C2×#213—38no—
113C2×#213—38no—
114C4×#67—64no—
115C2×D24—38no—
116#895—34no—
117#888—34no—
118#885—64no—
119#884—64no—
120#874—34no—
121C4×D12—34no—
122C42×D3—34no—
123C3×C4⋊C8C2×D314yescomplemented
124C3×#102C2×D318yescomplemented
125#832—38no—
126#821—38no—
127(C2×D3)⋊C8—38no—
128C8×Dic3—38no—
129#809—38no—
130C4⋊(C3⋊C8)—34no—
131C23×C32—22no—
132C23×C32—21no—
133C22×C3⋊D3—22no—
134C22×C3⋊D3—21no—
135C22×C3⋊D3—44no—
136C22×C3⋊D3—44no—
137C22×C3⋊D3—44no—
138C22×C3⋊D3C2×D411yescharacteristic
139C32×D4—21no—
140C32×D4—22no—
141C32×D4—21no—
142C32×D4—22no—
143C32×D4—42no—
144C32×D4—42no—
145C2×C32×C4—21no—
146C2×C32×C4—42no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2411yescharacteristic
150#638—44no—
151#638—42no—
152#638—42no—
153#638—44no—
154#638—44no—
155#638—42no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3C2×D411yescharacteristic
158C2×C3⋊Dic3C2×D411yescharacteristic
159C2×C3⋊Dic3C2×D411yescharacteristic
160C4⋊(C3⋊D3)—21no—
161C4⋊(C3⋊D3)—22no—
162C4⋊(C3⋊D3)—21no—
163C4⋊(C3⋊D3)—22no—
164C4⋊(C3⋊D3)—42no—
165C4⋊(C3⋊D3)—42no—
166C4⋊(C3⋊D3)—42no—
167C4×C3⋊D3—21no—
168C4×C3⋊D3—21no—
169C4×C3⋊D3—22no—
170C4×C3⋊D3—42no—
171C4×C3⋊D3D814yescomplemented
172#634—42no—
173C32×C8—22no—
174C3⋊(C3⋊C8)—22no—
175#532—91no—
176C2×#127—91no—
177#493—92no—
178#486—92no—
179#459—91no—
180#459—91no—
181#459—91no—
182#459C3⋊D311yescharacteristic, complemented
183#447—92no—
184#447—92no—
185#431—91no—
186C23×D3—68no—
187C2×C3×D4—24no—
188C2×C3×D4—24no—
189C2×C3×D4C22×D318yes—
190C2×C3×D4C22×D314yes—
191C22×C3×C4—24no—
192C2×#67—64no—
193C2×#67—64no—
194C2×#67—68no—
195C2×#67—68no—
196C2×#67—68no—
197C2×#67—64no—
198D3×D4—1216no—
199D3×D4—128no—
200D3×D4—128no—
201D3×D4—1216no—
202#235—1216no—
203C2×D12—38no—
204C2×D12—34no—
205C2×D12—64no—
206C2×D12—64no—
207C2×D12—64no—
208C2×C4×D3—34no—
209C2×C4×D3—34no—
210C2×C4×D3—34no—
211C2×C4×D3—64no—
212C2×Dic6—64no—
213C3×D8—48no—
214C2×C3×C8C22×D318yes—
215C3×C4⋊C4C22×D314yes—
216C3×C22⋊C4—24no—
217C3×C42C22×D314yes—
218#217—64no—
219#213—128no—
220#213—128no—
221(C2×D3)⋊C4—64no—
222(C2×D3)⋊C4—64no—
223C4⋊Dic3—34no—
224Dic3⋊C4—64no—
225C4×Dic3—34no—
226C4×Dic3—34no—
227C4×Dic3—34no—
228C2×C3⋊C8—38no—
229D24—128no—
230C22×C32—42no—
231C22×C32—41no—
232C22×C32—41no—
233C22×C32—42no—
234C22×C32—42no—
235C22×C32—41no—
236C22×C32C22×D411yescharacteristic
237C2×C3⋊D3—21no—
238C2×C3⋊D3—21no—
239C2×C3⋊D3—42no—
240C2×C3⋊D3—41no—
241C2×C3⋊D3—41no—
242C2×C3⋊D3—42no—
243C2×C3⋊D3—42no—
244C2×C3⋊D3—41no—
245C2×C3⋊D3—88no—
246C2×C3⋊D3C2×D812yes—
247C32×C4—21no—
248C32×C4—41no—
249C32×C4C2×D812yes—
250C32×C4H(5,𝔽2)11yescharacteristic
251C32×C4H(5,𝔽2)11yescharacteristic
252C3⋊Dic3—21no—
253C3⋊Dic3—41no—
254C3⋊Dic3C2×D812yes—
255C3⋊Dic3AGL(1,ℤ/8)12yes—
256C2×#41—181no—
257C22×D4—92no—
258C22×D4—181no—
259C22×D4—181no—
260C2×D8—92no—
261C2×D8—92no—
262C2×D8—92no—
263C2×D8C2×C3⋊D312yescomplemented
264C4⋊Q8—91no—
265#127—92no—
266#127—91no—
267#127—91no—
268#127—181no—
269#127—181no—
270#127C2×C3⋊D311yescharacteristic
271#124—181no—
272#121—91no—
273#121—91no—
274#121—181no—
275C4×D4—91no—
276C4×D4—181no—
277C4×D4C2×C3⋊D311yescharacteristic, complemented
278C2×C42—91no—
279C4⋊C8—91no—
280C4⋊C8C2×C3⋊D311yescharacteristic, complemented
281#102—92no—
282#102—92no—
283#102—92no—
284#102C2×C3⋊D312yescomplemented
285C22⋊C8—92no—
286C4×C8—92no—
287C23×C3—24no—
288C23×C3—28no—
289C22×D3—34no—
290C22×D3—64no—
291C22×D3—68no—
292C22×D3—1216no—
293C22×D3—1216no—
294C22×D3—1216no—
295C3×D4—24no—
296C3×D4—28no—
297C3×D4—24no—
298C3×D4—28no—
299C3×D4—48no—
300C3×D4—48no—
301C2×C3×C4—24no—
302C2×C3×C4—48no—
303C2×C3×C4D3×D414yes—
304C2×C3×C4D3×D414yes—
305C2×C3×C4C23×D314yes—
306#67—128no—
307#67—1216no—
308#67—1216no—
309#67—128no—
310#67—1216no—
311#67—128no—
312C2×Dic3—34no—
313C2×Dic3—34no—
314C2×Dic3—34no—
315C2×Dic3—64no—
316D12—64no—
317D12—68no—
318D12—64no—
319D12—68no—
320D12—128no—
321D12—128no—
322D12—128no—
323C4×D3—316no—
324C4×D3—68no—
325C4×D3—64no—
326C4×D3—64no—
327C4×D3—128no—
328Dic6—128no—
329C3×C8—28no—
330C3⋊C8—68no—
331C2×C32—82no—
332C2×C32—81no—
333C2×C32#53511yescharacteristic
334C2×C32C22×D811yescharacteristic
335C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
336C3⋊D3—22no—
337C3⋊D3—81no—
338C3⋊D3—82no—
339C24—182no—
340#41—364no—
341C2×Q8—181no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—92no—
345C2×D4—91no—
346C2×D4—181no—
347C2×D4—181no—
348C2×D4—181no—
349C2×D4—182no—
350C2×D4—182no—
351C2×D4—182no—
352C2×D4—181no—
353C2×D4—181no—
354C2×D4—181no—
355C2×D4—364no—
356C2×D4—362no—
357C2×D4—362no—
358C2×D4—364no—
359C2×D4C22×C3⋊D312yes—
360C2×D4C22×C3⋊D311yescharacteristic
361C22×C4—21no—
362C22×C4—91no—
363C22×C4—91no—
364C22×C4—91no—
365C22×C4—181no—
366D8—42no—
367D8—362no—
368D8—362no—
369D8—362no—
370C2×C8—92no—
371C2×C8C22×C3⋊D312yes—
372C4⋊C4—91no—
373C4⋊C4—181no—
374C4⋊C4C22×C3⋊D311yescharacteristic
375C22⋊C4—21no—
376C22⋊C4—181no—
377C22⋊C4—181no—
378C22⋊C4—181no—
379C42—91no—
380C42—91no—
381C42—91no—
382C42C22×C3⋊D311yescharacteristic
383C22×C3—44no—
384C22×C3—48no—
385C22×C3—48no—
386C22×C3—44no—
387C22×C3—48no—
388C22×C3—44no—
389C22×C3C2×D3×D414yes—
390C2×D3—38no—
391C2×D3—64no—
392C2×D3—64no—
393C2×D3—124no—
394C2×D3—128no—
395C2×D3—128no—
396C2×D3—124no—
397C2×D3—128no—
398C2×D3—124no—
399C2×D3—2432no—
400C3×C4—24no—
401C3×C4—44no—
402C3×C4D3×D818yes—
403C3×C4#100414yes—
404C3×C4#100914yes—
405Dic3—38no—
406Dic3—38no—
407Dic3—64no—
408Dic3—124no—
409C32#320511yescharacteristic, complemented, Sylow
410C23—21no—
411C23—22no—
412C23—91no—
413C23—181no—
414C23—182no—
415C23—364no—
416C23—364no—
417C23—364no—
418Q8—362no—
419D4—21no—
420D4—22no—
421D4—21no—
422D4—22no—
423D4—42no—
424D4—42no—
425D4—181no—
426D4—182no—
427D4—181no—
428D4—182no—
429D4—362no—
430D4—362no—
431D4—364no—
432D4—364no—
433D4—362no—
434D4—362no—
435D4—364no—
436D4—362no—
437D4—362no—
438C2×C4—21no—
439C2×C4—42no—
440C2×C4—91no—
441C2×C4—91no—
442C2×C4—94no—
443C2×C4—91no—
444C2×C4—182no—
445C2×C4—181no—
446C2×C4—181no—
447C2×C4—181no—
448C2×C4—362no—
449C2×C4D4×C3⋊D311yescharacteristic
450C2×C4D4×C3⋊D311yescharacteristic
451C2×C4C23×C3⋊D311yescharacteristic
452C8—22no—
453C8—182no—
454C2×C3—88no—
455C2×C3—84no—
456C2×C3#560714yes—
457C2×C3C2×D3×D814yes—
458C2×C3D3×AGL(1,ℤ/8)14yes—
459D3—68no—
460D3—248no—
461D3—244no—
462C22—41no—
463C22—42no—
464C22—42no—
465C22—41no—
466C22—42no—
467C22—41no—
468C22—92no—
469C22—181no—
470C22—181no—
471C22—361no—
472C22—362no—
473C22—362no—
474C22—361no—
475C22—362no—
476C22—361no—
477C22—728no—
478C22C2×D4×C3⋊D311yescharacteristic
479C4—21no—
480C4—41no—
481C4—92no—
482C4—92no—
483C4—181no—
484C4—361no—
485C4D8×C3⋊D312yes—
486C4#6436111yescharacteristic
487C4#6436611yescharacteristic
488C3#8033614yescomplemented
489C2—82no—
490C2—81no—
491C2—182no—
492C2—722no—
493C2—721no—
494C2#1059607811yescharacteristic
495C2C2×D8×C3⋊D311yescharacteristic
496C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#459C2
socleC22×C32C22×D4
hypercenter#459C3⋊D3
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C3⋊D3×#127C2semidirect
2. #10596019C2semidirect
3. C32×#459C2semidirect
4. #10592855C2semidirect
5. #10592850C2semidirect
6. #10592771C2semidirect
7. #10592714C2semidirect
8. #10592542C2semidirect
9. #10592532C2semidirect
10. #10592472C2semidirect
11. #10592459C2semidirect
17. C2×C32×D8C22semidirect
19. C32×C4×D4C22semidirect
23. #64149C22semidirect
25. C2×#3753C22semidirect
26. C2×#3753C22semidirect
28. C2×#3745C22semidirect
30. #64097C22semidirect
34. C4×C4⋊(C3⋊D3)C22semidirect
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×#459D3semidirect
104. C2×C3×D8C2×D3semidirect
106. C3×C4×D4C2×D3semidirect
123. C3×C4⋊C8C2×D3semidirect
124. C3×#102C2×D3semidirect
171. C4×C3⋊D3D8semidirect
182. #459C3⋊D3semidirect
263. C2×D8C2×C3⋊D3semidirect
277. C4×D4C2×C3⋊D3semidirect
280. C4⋊C8C2×C3⋊D3semidirect
284. #102C2×C3⋊D3semidirect
409. C32#3205semidirect
488. C3#80336semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1272
#105960192
C32×#4592
#105928552
#105928502
#105927712
#105927142
#105925422
#105925322
#105924722
#105924592
#803363