Finite Group Databasebeta

← #11864101

Subgroups — #11864101

Order 1152.

2418 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3830C211yesmaximal, characteristic, complemented
2C2×#64120C212yesmaximal, complemented
3C3⋊D3×#121C211yesmaximal, characteristic, complemented
4C32×#447C211yesmaximal, characteristic, complemented
5#10592916C211yesmaximal, characteristic, complemented
6#10592857C212yesmaximal, complemented
7#10592739C211yesmaximal, characteristic, complemented
8#10592480C212yesmaximal, complemented
9#10592470C212yesmaximal, complemented
10#10592437C211yesmaximal, characteristic, complemented
11#10592425C211yesmaximal, characteristic, complemented
12#80003—34nomaximal
13C22×C32×D4C2211yescharacteristic, complemented
14C22×#638—21no—
15C23×C3⋊Dic3—21no—
16C2×#3830—28no—
17C2×#3830—21no—
18C2×#3830—21no—
19C2×#3830C2212yes—
20C2×#3830C2212yescomplemented
21C2×D4×C3⋊D3—21no—
22C2×D4×C3⋊D3C2211yescharacteristic, complemented
23C22×C4×C3⋊D3C2211yescharacteristic
24C22×#634C2211yescharacteristic, complemented
25C2×C32×D8C2212yescomplemented
26C32×#121C2211yescharacteristic
27#64148—21no—
28#64147C2211yescharacteristic, complemented
29C2×#3754C2212yescomplemented
30C2×#3753C2212yescomplemented
31#64139C2211yescharacteristic
32#64120—28no—
33C2×#3744C2212yescomplemented
34C2×#3743C2212yescomplemented
35#64104C2211yescharacteristic, complemented
36C4⋊C4×C3⋊D3C2211yescharacteristic, complemented
37#64093—21no—
38C22⋊C4×C3⋊D3—21no—
39C32×#102C2212yescomplemented
40C32×C22⋊C8C2211yescharacteristic, complemented
41#63659C2212yescomplemented
42#63657C2211yescharacteristic, complemented
43#63647C2212yescomplemented
44#63643C2212yescomplemented
45#63637C2212yescomplemented
46C22×#237—34no—
47C2×#911—38no—
48D3×#121—34no—
49C3×#447D314yescomplemented
50#5217—34no—
51#5158—38no—
52#5040—34no—
53#4781—38no—
54#4771—38no—
55#4738—34no—
56#4726—34no—
57C24×C32—21no—
58C23×C3⋊D3—21no—
59C23×C3⋊D3D411yescharacteristic
60C2×C32×D4—24no—
61C2×C32×D4—21no—
62C2×C32×D4—21no—
63C2×C32×D4C2311yescharacteristic
64C2×C32×D4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C2×#638—28no—
67C2×#638—22no—
68C2×#638—22no—
69C2×#638—21no—
70C2×#638—21no—
71C2×#638—21no—
72C22×C3⋊Dic3—28no—
73C22×C3⋊Dic3—21no—
74C22×C3⋊Dic3—22no—
75C22×C3⋊Dic3—22no—
76C22×C3⋊Dic3D411yescharacteristic
77#3830—28no—
78#3830—28no—
79#3830—24no—
80#3830—24no—
81#3830—24no—
82#3830D418yescomplemented
83D4×C3⋊D3—24no—
84D4×C3⋊D3—44no—
85C2×C4⋊(C3⋊D3)—21no—
86C2×C4⋊(C3⋊D3)C2311yescharacteristic
87C2×C4×C3⋊D3—24no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3D411yescharacteristic
90C2×C4×C3⋊D3D411yescharacteristic
91C2×C4×C3⋊D3C2311yescharacteristic
92C2×C4×C3⋊D3C2311yescharacteristic
93C2×#634—21no—
94C2×#634—24no—
95C2×#634C2312yes—
96C32×D8—24no—
97C2×C32×C8C2312yes—
98C32×C4⋊C4C2311yescharacteristic
99C32×C22⋊C4—21no—
100#3757—21no—
101#3754—24no—
102#3753—24no—
103#3752—21no—
104#3752—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106#3750—21no—
107C2×C3⋊(C3⋊C8)C2312yes—
108#3744—24no—
109#3743—24no—
110#3006—91noSylow
111C22×C3×D4C2×D314yescomplemented
112C22×#67—64no—
113C23×Dic3—64no—
114C2×#237—38no—
115C2×#237—38no—
116C2×#237—64no—
117C2×#237—64no—
118C2×#237—632no—
119C2×D3×D4—34no—
120C2×D3×D4—64no—
121C22×C4×D3—34no—
122C22×Dic6—34no—
123C2×C3×D8C2×D318yescomplemented
124C3×#121C2×D314yes—
125#939—64no—
126#938—34no—
127C2×#214—38no—
128C2×#213—38no—
129#930—34no—
130#911—632no—
131C2×#204—38no—
132C2×ΓL(1,𝔽25)—38no—
133#895—34no—
134D3×C4⋊C4—34no—
135#884—64no—
136D3×C22⋊C4—64no—
137C3×#102C2×D318yescomplemented
138C3×C22⋊C8C2×D314yescomplemented
139#832—38no—
140#830—34no—
141(C2×D3)⋊C8—38no—
142#816—38no—
143#810—38no—
144C23×C32—24no—
145C23×C32—22no—
146C23×C32—21no—
147C23×C32—42no—
148C23×C32—42no—
149C23×C32C2×D411yescharacteristic
150C22×C3⋊D3—22no—
151C22×C3⋊D3—22no—
152C22×C3⋊D3—21no—
153C22×C3⋊D3—41no—
154C22×C3⋊D3—42no—
155C22×C3⋊D3—42no—
156C22×C3⋊D3—42no—
157C22×C3⋊D3C2×D411yescharacteristic
158C22×C3⋊D3C2×D411yescharacteristic
159C32×D4—24no—
160C32×D4—22no—
161C32×D4—22no—
162C32×D4—42no—
163C32×D4C2×D414yescomplemented
164C2×C32×C4—22no—
165C2×C32×C4—21no—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168#638—28no—
169#638—28no—
170#638—42no—
171#638—42no—
172#638—42no—
173C2×C3⋊Dic3—24no—
174C2×C3⋊Dic3—28no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—28no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3C2×D411yescharacteristic
180C2×C3⋊Dic3C2×D411yescharacteristic
181C4⋊(C3⋊D3)—22no—
182C4⋊(C3⋊D3)—42no—
183C4×C3⋊D3—22no—
184C4×C3⋊D3—22no—
185C4×C3⋊D3—22no—
186C4×C3⋊D3—42no—
187C4×C3⋊D3C2×D414yes—
188#634—24no—
189#634—22no—
190#634C2×D414yescomplemented
191C32×C8—22no—
192C3⋊(C3⋊C8)—22no—
193C22×#41—91no—
194C2×AGL(1,ℤ/8)—92no—
195C2×#121—91no—
196#449—92no—
197#449—92no—
198#448—91no—
199#448—91no—
200#447—91no—
201#447C3⋊D311yescharacteristic, complemented
202#417—92no—
203#407—91no—
204C24×C3—24no—
205C23×D3—34no—
206C23×D3—64no—
207C2×C3×D4—216no—
208C2×C3×D4—24no—
209C2×C3×D4—24no—
210C2×C3×D4C22×D314yes—
211C2×C3×D4C22×D318yes—
212C22×C3×C4C22×D314yes—
213C2×#67—64no—
214C2×#67—68no—
215C2×#67—68no—
216C2×#67—632no—
217C2×#67—64no—
218C2×#67—64no—
219C22×Dic3—34no—
220C22×Dic3—68no—
221C22×Dic3—68no—
222C22×Dic3—632no—
223C22×Dic3—64no—
224#237—332no—
225#237—616no—
226#237—616no—
227#237—632no—
228#237—632no—
229#237—616no—
230D3×D4—616no—
231D3×D4—1216no—
232C2×D12—34no—
233C2×D12—64no—
234C2×C4×D3—34no—
235C2×C4×D3—34no—
236C2×C4×D3—34no—
237C2×C4×D3—34no—
238C2×C4×D3—616no—
239C2×C4×D3—64no—
240C2×Dic6—38no—
241C2×Dic6—616no—
242C2×Dic6—64no—
243C3×D8—216no—
244C2×C3×C8C22×D318yes—
245C3×C4⋊C4C22×D314yes—
246C3×C22⋊C4—24no—
247#217—64no—
248#214—616no—
249#213—616no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252C4⋊Dic3—34no—
253Dic3⋊C4—64no—
254C2×C3⋊C8—38no—
255#204—616no—
256ΓL(1,𝔽25)—616no—
257C22×C32—21no—
258C22×C32—21no—
259C22×C32—24no—
260C22×C32—48no—
261C22×C32—42no—
262C22×C32—42no—
263C22×C32—41no—
264C22×C32—41no—
265C22×C32—41no—
266C22×C32AGL(1,ℤ/8)12yescomplemented
267C22×C32C22×D411yescharacteristic
268C2×C3⋊D3—21no—
269C2×C3⋊D3—21no—
270C2×C3⋊D3—21no—
271C2×C3⋊D3—21no—
272C2×C3⋊D3—21no—
273C2×C3⋊D3—44no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C2×C3⋊D3—41no—
277C2×C3⋊D3—84no—
278C2×C3⋊D3#12012yes—
279C32×C4—21no—
280C32×C4—41no—
281C32×C4C22×D412yes—
282C3⋊Dic3—24no—
283C3⋊Dic3—21no—
284C3⋊Dic3—41no—
285C3⋊Dic3#12012yes—
286C2×#41—92no—
287C2×#41—92no—
288C2×#41—181no—
289C2×#41—181no—
290C2×#41—188no—
291C22×Q8—91no—
292C22×D4—91no—
293C22×D4—181no—
294C22×D4—181no—
295C22×D4C2×C3⋊D311yescharacteristic, complemented
296C23×C4—91no—
297C23×C4—181no—
298AGL(1,ℤ/8)—188no—
299C2×SD16—92no—
300C2×SD16—92no—
301C2×D8—92no—
302C2×D8C2×C3⋊D312yescomplemented
303C2×M16—92no—
304#121—91no—
305#121—91no—
306#121—91no—
307#121—181no—
308#121—181no—
309#121C2×C3⋊D311yescharacteristic
310C2×C4⋊C4—91no—
311C2×C22⋊C4—181no—
312#103—92no—
313#103—92no—
314#102—92no—
315#102C2×C3⋊D312yescomplemented
316C22⋊C8—91no—
317C22⋊C8—92no—
318C22⋊C8C2×C3⋊D311yescharacteristic, complemented
319C23×C3—216no—
320C23×C3—28no—
321C23×C3—24no—
322C23×C3—48no—
323C23×C3—48no—
324C23×C3D3×D414yes—
325C22×D3—34no—
326C22×D3—34no—
327C22×D3—68no—
328C22×D3—68no—
329C22×D3—64no—
330C22×D3—128no—
331C22×D3—124no—
332C22×D3—128no—
333C22×D3—128no—
334C3×D4—216no—
335C3×D4—28no—
336C3×D4—28no—
337C3×D4—48no—
338C3×D4D3×D4116yescomplemented
339C2×C3×C4—28no—
340C2×C3×C4—24no—
341C2×C3×C4D3×D414yes—
342C2×C3×C4C23×D314yes—
343#67—632no—
344#67—632no—
345#67—128no—
346#67—128no—
347#67—128no—
348C2×Dic3—34no—
349C2×Dic3—34no—
350C2×Dic3—68no—
351C2×Dic3—632no—
352C2×Dic3—616no—
353C2×Dic3—632no—
354C2×Dic3—68no—
355C2×Dic3—64no—
356D12—68no—
357D12—128no—
358C4×D3—316no—
359C4×D3—68no—
360C4×D3—68no—
361C4×D3—68no—
362C4×D3—128no—
363Dic6—316no—
364Dic6—616no—
365Dic6—68no—
366C3×C8—28no—
367C3⋊C8—68no—
368C2×C32—22no—
369C2×C32—44no—
370C2×C32—81no—
371C2×C32C2×#12011yescharacteristic
372C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
373C2×C32#57511yescharacteristic
374C3⋊D3—22no—
375C3⋊D3—41no—
376C3⋊D3—81no—
377C24—21no—
378C24—91no—
379C24—181no—
380#41—98no—
381#41—184no—
382#41—184no—
383#41—188no—
384#41—188no—
385#41—184no—
386C2×Q8—92no—
387C2×Q8—184no—
388C2×Q8—181no—
389C2×D4—24no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—91no—
393C2×D4—181no—
394C2×D4—184no—
395C2×D4—181no—
396C2×D4—182no—
397C2×D4—182no—
398C2×D4—188no—
399C2×D4—181no—
400C2×D4—181no—
401C2×D4—364no—
402C2×D4C22×C3⋊D311yescharacteristic
403C2×D4C22×C3⋊D312yes—
404C22×C4—91no—
405C22×C4—91no—
406C22×C4—91no—
407C22×C4—91no—
408C22×C4—91no—
409C22×C4—184no—
410C22×C4—181no—
411C22×C4—182no—
412C22×C4—182no—
413C22×C4—188no—
414C22×C4—181no—
415C22×C4C22×C3⋊D311yescharacteristic
416SD16—184no—
417SD16—184no—
418D8—24no—
419D8—184no—
420M16—184no—
421C2×C8—92no—
422C2×C8C22×C3⋊D312yes—
423C4⋊C4—91no—
424C4⋊C4—181no—
425C4⋊C4C22×C3⋊D311yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C22⋊C4—181no—
430C22×C3—24no—
431C22×C3—24no—
432C22×C3—216no—
433C22×C3—432no—
434C22×C3—48no—
435C22×C3—48no—
436C22×C3—44no—
437C22×C3—44no—
438C22×C3—44no—
439C22×C3#91118yescomplemented
440C22×C3C2×D3×D414yes—
441C2×D3—38no—
442C2×D3—64no—
443C2×D3—64no—
444C2×D3—64no—
445C2×D3—64no—
446C2×D3—64no—
447C2×D3—1216no—
448C2×D3—124no—
449C2×D3—124no—
450C2×D3—124no—
451C2×D3—2416no—
452C3×C4—24no—
453C3×C4—44no—
454C3×C4C2×D3×D418yes—
455Dic3—38no—
456Dic3—616no—
457Dic3—64no—
458Dic3—124no—
459C32#300611yescharacteristic, complemented, Sylow
460C23—24no—
461C23—22no—
462C23—21no—
463C23—42no—
464C23—42no—
465C23—91no—
466C23—91no—
467C23—182no—
468C23—182no—
469C23—181no—
470C23—361no—
471C23—362no—
472C23—362no—
473C23—362no—
474C23D4×C3⋊D311yescharacteristic
475Q8—94no—
476Q8—184no—
477Q8—182no—
478D4—24no—
479D4—22no—
480D4—22no—
481D4—42no—
482D4—188no—
483D4—188no—
484D4—182no—
485D4—362no—
486D4—362no—
487D4—362no—
488D4—362no—
489D4D4×C3⋊D314yescomplemented
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—91no—
493C2×C4—94no—
494C2×C4—91no—
495C2×C4—182no—
496C2×C4—182no—
497C2×C4—182no—
498C2×C4—188no—
499C2×C4—184no—
500C2×C4—188no—
501C2×C4—182no—
502C2×C4—182no—
503C2×C4—181no—
504C2×C4—362no—
505C2×C4D4×C3⋊D311yescharacteristic
506C2×C4C23×C3⋊D311yescharacteristic
507C8—22no—
508C8—182no—
509C2×C3—28no—
510C2×C3—416no—
511C2×C3—84no—
512C2×C3D3×#12014yes—
513C2×C3C2×#91114yes—
514C2×C3#577314yes—
515D3—68no—
516D3—124no—
517D3—244no—
518C22—21no—
519C22—21no—
520C22—24no—
521C22—48no—
522C22—42no—
523C22—42no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—92no—
528C22—181no—
529C22—181no—
530C22—181no—
531C22—181no—
532C22—181no—
533C22—364no—
534C22—361no—
535C22—361no—
536C22—361no—
537C22—724no—
538C22#6412012yescomplemented
539C22C2×D4×C3⋊D311yescharacteristic
540C4—21no—
541C4—41no—
542C4—92no—
543C4—181no—
544C4—184no—
545C4—361no—
546C4C2×D4×C3⋊D312yes—
547C3#8000314yescomplemented
548C2—22no—
549C2—44no—
550C2—81no—
551C2—182no—
552C2—361no—
553C2—721no—
554C2C3⋊D3×#12011yescharacteristic
555C2C2×#6412011yescharacteristic
556C2#1059624411yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#447C2
socleC22×C32C22×D4
hypercenter#447C3⋊D3
hypocenterC32#3006
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. C22×#3830C2semidirect
2. C2×#64120C2semidirect
3. C3⋊D3×#121C2semidirect
4. C32×#447C2semidirect
5. #10592916C2semidirect
6. #10592857C2semidirect
7. #10592739C2semidirect
8. #10592480C2semidirect
9. #10592470C2semidirect
10. #10592437C2semidirect
11. #10592425C2semidirect
13. C22×C32×D4C22semidirect
20. C2×#3830C22semidirect
22. C2×D4×C3⋊D3C22semidirect
24. C22×#634C22semidirect
25. C2×C32×D8C22semidirect
28. #64147C22semidirect
29. C2×#3754C22semidirect
30. C2×#3753C22semidirect
33. C2×#3744C22semidirect
34. C2×#3743C22semidirect
35. #64104C22semidirect
36. C4⋊C4×C3⋊D3C22semidirect
39. C32×#102C22semidirect
40. C32×C22⋊C8C22semidirect
41. #63659C22semidirect
42. #63657C22semidirect
43. #63647C22semidirect
44. #63643C22semidirect
45. #63637C22semidirect
49. C3×#447D3semidirect
82. #3830D4semidirect
111. C22×C3×D4C2×D3semidirect
123. C2×C3×D8C2×D3semidirect
137. C3×#102C2×D3semidirect
138. C3×C22⋊C8C2×D3semidirect
163. C32×D4C2×D4semidirect
190. #634C2×D4semidirect
201. #447C3⋊D3semidirect
266. C22×C32AGL(1,ℤ/8)semidirect
295. C22×D4C2×C3⋊D3semidirect
302. C2×D8C2×C3⋊D3semidirect
315. #102C2×C3⋊D3semidirect
318. C22⋊C8C2×C3⋊D3semidirect
338. C3×D4D3×D4semidirect
439. C22×C3#911semidirect
459. C32#3006semidirect
489. D4D4×C3⋊D3semidirect
538. C22#64120semidirect
547. C3#80003semidirect

Maximal subgroups

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

subgroupindex
C22×#38302
C2×#641202
C3⋊D3×#1212
C32×#4472
#105929162
#105928572
#105927392
#105924802
#105924702
#105924372
#105924252
#800033