Finite Group Databasebeta

← #11863926

Subgroups — #11863926

Order 1152.

2982 conjugacy classes of subgroups.

The subgroup lattice has 573 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#64123C212yesmaximal, complemented
3#10596098C211yesmaximal, characteristic, complemented
4C32×#450C211yesmaximal, characteristic, complemented
5#10592916C211yesmaximal, characteristic, complemented
6#10592868C212yesmaximal, complemented
7#10592745C211yesmaximal, characteristic, complemented
8#10592472C212yesmaximal, complemented
9#10592469C212yesmaximal, complemented
10#10592431C211yesmaximal, characteristic, complemented
11#10592425C211yesmaximal, characteristic, complemented
12#80146—34nomaximal
13C24×C3⋊D3—21no—
14C22×C32×D4C2211yescharacteristic
15C22×#638—21no—
16C2×#3832C2211yescharacteristic, complemented
17C2×D4×C3⋊D3—28no—
18C2×D4×C3⋊D3—21no—
19C2×D4×C3⋊D3—21no—
20C2×D4×C3⋊D3C2212yes—
21C2×D4×C3⋊D3C2212yes—
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic
24C2×C32×SD16C2212yescomplemented
25C32×C22⋊Q8C2211yescharacteristic, complemented
26#64155C2211yescharacteristic, complemented
27C2×#3755C2212yescomplemented
28C2×#3753C2212yescomplemented
29#64139C2211yescharacteristic, complemented
30#64123—28no—
31C2×#3745C2212yescomplemented
32C2×#3743C2212yescomplemented
33#64104C2211yescharacteristic, complemented
34#64103—21no—
35#64102—21no—
36#64101C2211yescharacteristic, complemented
37#64091—21no—
38#64090—21no—
39C32×#102C2212yescomplemented
40C32×C22⋊C8C2211yescharacteristic, complemented
41#63659C2212yescomplemented
42#63657C2211yescharacteristic, complemented
43#63648C2212yescomplemented
44#63647C2212yescomplemented
45#63636C2212yescomplemented
46C22×D3×D4—34no—
47C2×#914—38no—
48#5627—34no—
49C3×#450D314yescomplemented
50#5217—34no—
51#5169—38no—
52#5046—34no—
53#4773—38no—
54#4770—38no—
55#4732—34no—
56#4726—34no—
57C24×C32—21no—
58C23×C3⋊D3—28no—
59C23×C3⋊D3—21no—
60C23×C3⋊D3—22no—
61C23×C3⋊D3—22no—
62C23×C3⋊D3—44no—
63C23×C3⋊D3—44no—
64C23×C3⋊D3D411yescharacteristic
65C2×C32×Q8C2311yescharacteristic, complemented
66C2×C32×D4—24no—
67C2×C32×D4—21no—
68C2×C32×D4C2312yes—
69C22×C32×C4C2311yescharacteristic
70C2×#638—28no—
71C2×#638—21no—
72C2×#638—22no—
73C2×#638—22no—
74C22×C3⋊Dic3D411yescharacteristic
75#3832—24no—
76D4×C3⋊D3—28no—
77D4×C3⋊D3—28no—
78D4×C3⋊D3—24no—
79D4×C3⋊D3—24no—
80D4×C3⋊D3—24no—
81D4×C3⋊D3D418yescomplemented
82C2×C4⋊(C3⋊D3)—21no—
83C2×C4⋊(C3⋊D3)—24no—
84C2×C4⋊(C3⋊D3)—21no—
85C2×C4⋊(C3⋊D3)—21no—
86C2×C4⋊(C3⋊D3)C2312yes—
87C2×C4⋊(C3⋊D3)C2311yescharacteristic, complemented
88C2×C4×C3⋊D3—24no—
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3D411yescharacteristic
91C2×C4×C3⋊D3D411yescharacteristic
92C2×C4×C3⋊D3C2311yescharacteristic
93C2×C4×C3⋊D3C2311yescharacteristic
94C32×SD16—24no—
95C2×C32×C8C2312yescomplemented
96C32×C4⋊C4—21no—
97C32×C4⋊C4C2311yescharacteristic, complemented
98C32×C22⋊C4—21no—
99#3755—24no—
100#3753—24no—
101#3752—21no—
102#3752—21no—
103#3752—21no—
104#3752—21no—
105C4⋊(C3⋊Dic3)C2311yescharacteristic, complemented
106#3750—21no—
107C4×C3⋊Dic3—21no—
108C2×C3⋊(C3⋊C8)C2312yescomplemented
109#3745—24no—
110#3743—24no—
111#3003—91noSylow
112C24×D3—64no—
113C22×C3×D4C2×D314yes—
114C22×#67—64no—
115C2×#239—34no—
116C2×D3×D4—38no—
117C2×D3×D4—38no—
118C2×D3×D4—64no—
119C2×D3×D4—64no—
120C2×D3×D4—632no—
121C22×D12—34no—
122C22×C4×D3—34no—
123C2×C3×SD16C2×D318yescomplemented
124C3×C22⋊Q8C2×D314yescomplemented
125#946—34no—
126C2×#215—38no—
127C2×#213—38no—
128#930—34no—
129#914—632no—
130C2×D24—38no—
131C2×ΓL(1,𝔽25)—38no—
132#895—34no—
133#894—64no—
134#893—64no—
135#892—34no—
136#882—64no—
137#67⋊C4—64no—
138C3×#102C2×D318yescomplemented
139C3×C22⋊C8C2×D314yescomplemented
140#832—38no—
141#830—34no—
142#821—38no—
143(C2×D3)⋊C8—38no—
144#809—38no—
145C23×C32—24no—
146C23×C32—22no—
147C23×C32—42no—
148C23×C32—42no—
149C23×C32C2×D411yescharacteristic
150C22×C3⋊D3—22no—
151C22×C3⋊D3—22no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—24no—
154C22×C3⋊D3—28no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3—28no—
157C22×C3⋊D3—21no—
158C22×C3⋊D3—432no—
159C22×C3⋊D3—44no—
160C22×C3⋊D3—44no—
161C22×C3⋊D3—44no—
162C22×C3⋊D3—42no—
163C22×C3⋊D3—42no—
164C22×C3⋊D3—44no—
165C22×C3⋊D3C2×D411yescharacteristic
166C22×C3⋊D3C2×D411yescharacteristic
167C32×Q8—22no—
168C32×D4—24no—
169C32×D4—22no—
170C32×D4C2×D414yes—
171C2×C32×C4—22no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176#638—28no—
177#638—28no—
178#638—42no—
179C2×C3⋊Dic3—22no—
180C2×C3⋊Dic3—21no—
181C2×C3⋊Dic3C2×D411yescharacteristic
182C2×C3⋊Dic3C2×D411yescharacteristic
183C4⋊(C3⋊D3)—24no—
184C4⋊(C3⋊D3)—22no—
185C4⋊(C3⋊D3)—22no—
186C4⋊(C3⋊D3)—42no—
187C4⋊(C3⋊D3)—42no—
188C4⋊(C3⋊D3)C2×D414yes—
189C4×C3⋊D3—22no—
190C4×C3⋊D3—22no—
191C4×C3⋊D3—22no—
192C4×C3⋊D3—42no—
193C4×C3⋊D3C2×D414yes—
194C32×C8—22no—
195C3⋊(C3⋊C8)—22no—
196C23×D4—91no—
197C2×AGL(1,ℤ/8)—92no—
198#525—91no—
199#450—92no—
200#450—91no—
201#450C3⋊D311yescharacteristic, complemented
202#447—91no—
203#447—92no—
204#447—91no—
205#418—92no—
206#407—91no—
207C24×C3—24no—
208C23×D3—34no—
209C23×D3—68no—
210C23×D3—68no—
211C23×D3—632no—
212C23×D3—64no—
213C23×D3—1216no—
214C23×D3—1216no—
215C2×C3×Q8C22×D314yescomplemented
216C2×C3×D4—216no—
217C2×C3×D4—24no—
218C2×C3×D4C22×D318yes—
219C22×C3×C4C22×D314yes—
220C2×#67—68no—
221C2×#67—68no—
222C2×#67—632no—
223C2×#67—64no—
224C22×Dic3—34no—
225#239—616no—
226D3×D4—332no—
227D3×D4—616no—
228D3×D4—616no—
229D3×D4—632no—
230D3×D4—632no—
231D3×D4—616no—
232C2×D12—38no—
233C2×D12—34no—
234C2×D12—616no—
235C2×D12—64no—
236C2×D12—64no—
237C2×D12—64no—
238C2×C4×D3—34no—
239C2×C4×D3—34no—
240C2×C4×D3—34no—
241C2×C4×D3—34no—
242C2×C4×D3—616no—
243C2×C4×D3—64no—
244C3×SD16—216no—
245C2×C3×C8C22×D318yescomplemented
246C3×C4⋊C4—24no—
247C3×C4⋊C4C22×D314yescomplemented
248C3×C22⋊C4—24no—
249#215—616no—
250#213—616no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—64no—
255C4⋊Dic3—34no—
256Dic3⋊C4—64no—
257C4×Dic3—64no—
258C2×C3⋊C8—38no—
259D24—616no—
260ΓL(1,𝔽25)—616no—
261C22×C32—21no—
262C22×C32—21no—
263C22×C32—24no—
264C22×C32—48no—
265C22×C32—42no—
266C22×C32—42no—
267C22×C32AGL(1,ℤ/8)12yescomplemented
268C22×C32C22×D411yescharacteristic
269C2×C3⋊D3—28no—
270C2×C3⋊D3—21no—
271C2×C3⋊D3—21no—
272C2×C3⋊D3—21no—
273C2×C3⋊D3—21no—
274C2×C3⋊D3—24no—
275C2×C3⋊D3—416no—
276C2×C3⋊D3—416no—
277C2×C3⋊D3—48no—
278C2×C3⋊D3—42no—
279C2×C3⋊D3—42no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3#12012yes—
284C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
285C32×C4—21no—
286C32×C4—41no—
287C32×C4—41no—
288C32×C4C22×D412yes—
289C3⋊Dic3—21no—
290C3⋊Dic3—41no—
291C3⋊Dic3#12012yes—
292C25—181no—
293C2×#41—91no—
294C22×D4—92no—
295C22×D4—92no—
296C22×D4—91no—
297C22×D4—181no—
298C22×D4—181no—
299C22×D4—181no—
300C22×D4—188no—
301C22×D4C2×C3⋊D311yescharacteristic
302C23×C4—91no—
303AGL(1,ℤ/8)—188no—
304C2×SD16—92no—
305C2×SD16C2×C3⋊D312yescomplemented
306C2×D8—92no—
307C2×D8—92no—
308C2×M16—92no—
309#123—181no—
310C22⋊Q8—91no—
311C22⋊Q8C2×C3⋊D311yescharacteristic, complemented
312#121—91no—
313#121—91no—
314#120—181no—
315C4×D4—181no—
316C4×D4—181no—
317#117—91no—
318#102—92no—
319#102—92no—
320#102—92no—
321#102C2×C3⋊D312yescomplemented
322C22⋊C8—91no—
323C22⋊C8—92no—
324C22⋊C8C2×C3⋊D311yescharacteristic, complemented
325C23×C3—216no—
326C23×C3—28no—
327C23×C3—48no—
328C23×C3—48no—
329C23×C3D3×D414yes—
330C22×D3—34no—
331C22×D3—34no—
332C22×D3—68no—
333C22×D3—68no—
334C22×D3—632no—
335C22×D3—68no—
336C22×D3—616no—
337C22×D3—632no—
338C22×D3—68no—
339C22×D3—64no—
340C22×D3—1216no—
341C22×D3—12128no—
342C22×D3—1216no—
343C22×D3—1216no—
344C22×D3—1216no—
345C22×D3—128no—
346C22×D3—128no—
347C3×Q8—28no—
348C3×D4—216no—
349C3×D4—28no—
350C3×D4D3×D4116yes—
351C2×C3×C4—28no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4D3×D414yes—
355C2×C3×C4C23×D314yes—
356#67—632no—
357#67—632no—
358#67—128no—
359C2×Dic3—34no—
360C2×Dic3—34no—
361C2×Dic3—68no—
362C2×Dic3—64no—
363D12—316no—
364D12—616no—
365D12—68no—
366D12—68no—
367D12—128no—
368D12—128no—
369C4×D3—316no—
370C4×D3—68no—
371C4×D3—68no—
372C4×D3—68no—
373C4×D3—128no—
374C3×C8—28no—
375C3⋊C8—68no—
376C2×C32—22no—
377C2×C32—44no—
378C2×C32C2×#12011yescharacteristic
379C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
380C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
381C3⋊D3—22no—
382C3⋊D3—22no—
383C3⋊D3—44no—
384C3⋊D3—81no—
385C24—21no—
386C24—91no—
387C24—182no—
388C24—182no—
389C24—188no—
390C24—181no—
391C24—364no—
392C24—364no—
393#41—184no—
394C2×Q8C22×C3⋊D311yescharacteristic, complemented
395C2×D4—24no—
396C2×D4—21no—
397C2×D4—98no—
398C2×D4—92no—
399C2×D4—91no—
400C2×D4—184no—
401C2×D4—181no—
402C2×D4—181no—
403C2×D4—184no—
404C2×D4—182no—
405C2×D4—182no—
406C2×D4—184no—
407C2×D4—188no—
408C2×D4—188no—
409C2×D4—188no—
410C2×D4—184no—
411C2×D4—181no—
412C2×D4—181no—
413C2×D4C22×C3⋊D312yes—
414C22×C4—91no—
415C22×C4—91no—
416C22×C4—91no—
417C22×C4—91no—
418C22×C4—91no—
419C22×C4—184no—
420C22×C4—181no—
421C22×C4C22×C3⋊D311yescharacteristic
422SD16—24no—
423SD16—184no—
424D8—184no—
425D8—184no—
426M16—184no—
427C2×C8—92no—
428C2×C8C22×C3⋊D312yescomplemented
429C4⋊C4—21no—
430C4⋊C4—91no—
431C4⋊C4—181no—
432C4⋊C4C22×C3⋊D311yescharacteristic, complemented
433C22⋊C4—21no—
434C22⋊C4—181no—
435C22⋊C4—181no—
436C22⋊C4—181no—
437C22⋊C4—181no—
438C42—181no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3—216no—
442C22×C3—432no—
443C22×C3—48no—
444C22×C3—48no—
445C22×C3#91418yescomplemented
446C22×C3C2×D3×D414yes—
447C2×D3—38no—
448C2×D3—38no—
449C2×D3—632no—
450C2×D3—64no—
451C2×D3—64no—
452C2×D3—64no—
453C2×D3—64no—
454C2×D3—616no—
455C2×D3—1264no—
456C2×D3—1264no—
457C2×D3—1232no—
458C2×D3—128no—
459C2×D3—128no—
460C2×D3—124no—
461C2×D3—124no—
462C2×D3—124no—
463C3×C4—24no—
464C3×C4—44no—
465C3×C4—44no—
466C3×C4C2×D3×D418yes—
467Dic3—38no—
468Dic3—64no—
469Dic3—124no—
470C32#300311yescharacteristic, complemented, Sylow
471C23—24no—
472C23—22no—
473C23—42no—
474C23—42no—
475C23—91no—
476C23—91no—
477C23—182no—
478C23—182no—
479C23—188no—
480C23—184no—
481C23—188no—
482C23—182no—
483C23—182no—
484C23—181no—
485C23—362no—
486C23—364no—
487C23—3632no—
488C23—364no—
489C23—364no—
490C23—364no—
491C23—362no—
492C23D4×C3⋊D311yescharacteristic
493Q8—22no—
494D4—24no—
495D4—22no—
496D4—94no—
497D4—184no—
498D4—188no—
499D4—188no—
500D4—182no—
501D4—182no—
502D4—362no—
503D4—362no—
504D4—362no—
505D4D4×C3⋊D314yes—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—91no—
510C2×C4—94no—
511C2×C4—91no—
512C2×C4—182no—
513C2×C4—182no—
514C2×C4—182no—
515C2×C4—182no—
516C2×C4—181no—
517C2×C4—362no—
518C2×C4D4×C3⋊D311yescharacteristic
519C2×C4C23×C3⋊D311yescharacteristic
520C8—22no—
521C8—182no—
522C2×C3—28no—
523C2×C3—416no—
524C2×C3D3×#12014yes—
525C2×C3C2×#91414yes—
526C2×C3D3×AGL(1,ℤ/8)14yes—
527D3—68no—
528D3—68no—
529D3—1216no—
530D3—244no—
531C22—21no—
532C22—21no—
533C22—24no—
534C22—48no—
535C22—42no—
536C22—42no—
537C22—92no—
538C22—92no—
539C22—188no—
540C22—181no—
541C22—181no—
542C22—181no—
543C22—181no—
544C22—184no—
545C22—368no—
546C22—3616no—
547C22—3616no—
548C22—362no—
549C22—362no—
550C22—361no—
551C22—361no—
552C22—361no—
553C22#6412312yescomplemented
554C22C2×D4×C3⋊D311yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—92no—
559C4—181no—
560C4—361no—
561C4C2×D4×C3⋊D312yes—
562C3#8014614yescomplemented
563C2—22no—
564C2—44no—
565C2—182no—
566C2—182no—
567C2—364no—
568C2—721no—
569C2C3⋊D3×#12011yescharacteristic
570C2C2×#6412311yescharacteristic
571C2C3⋊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
hypercenter#450C3⋊D3
hypocenterC32#3003
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
1. C22×D4×C3⋊D3C2semidirect
2. C2×#64123C2semidirect
3. #10596098C2semidirect
4. C32×#450C2semidirect
5. #10592916C2semidirect
6. #10592868C2semidirect
7. #10592745C2semidirect
8. #10592472C2semidirect
9. #10592469C2semidirect
10. #10592431C2semidirect
11. #10592425C2semidirect
16. C2×#3832C22semidirect
24. C2×C32×SD16C22semidirect
25. C32×C22⋊Q8C22semidirect
26. #64155C22semidirect
27. C2×#3755C22semidirect
28. C2×#3753C22semidirect
29. #64139C22semidirect
31. C2×#3745C22semidirect
32. C2×#3743C22semidirect
33. #64104C22semidirect
36. #64101C22semidirect
39. C32×#102C22semidirect
40. C32×C22⋊C8C22semidirect
41. #63659C22semidirect
42. #63657C22semidirect
43. #63648C22semidirect
44. #63647C22semidirect
45. #63636C22semidirect
49. C3×#450D3semidirect
65. C2×C32×Q8C23semidirect
81. D4×C3⋊D3D4semidirect
87. C2×C4⋊(C3⋊D3)C23semidirect
95. C2×C32×C8C23semidirect
97. C32×C4⋊C4C23semidirect
105. C4⋊(C3⋊Dic3)C23semidirect
108. C2×C3⋊(C3⋊C8)C23semidirect
123. C2×C3×SD16C2×D3semidirect
124. C3×C22⋊Q8C2×D3semidirect
138. C3×#102C2×D3semidirect
139. C3×C22⋊C8C2×D3semidirect
201. #450C3⋊D3semidirect
215. C2×C3×Q8C22×D3semidirect
245. C2×C3×C8C22×D3semidirect
247. C3×C4⋊C4C22×D3semidirect
267. C22×C32AGL(1,ℤ/8)semidirect
284. C2×C3⋊D3AGL(1,ℤ/8)semidirect
305. C2×SD16C2×C3⋊D3semidirect
311. C22⋊Q8C2×C3⋊D3semidirect
321. #102C2×C3⋊D3semidirect
324. C22⋊C8C2×C3⋊D3semidirect
394. C2×Q8C22×C3⋊D3semidirect
428. C2×C8C22×C3⋊D3semidirect
432. C4⋊C4C22×C3⋊D3semidirect
445. C22×C3#914semidirect
470. C32#3003semidirect
553. C22#64123semidirect
562. C3#80146semidirect

Maximal subgroups

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

subgroupindex
C22×D4×C3⋊D32
C2×#641232
#105960982
C32×#4502
#105929162
#105928682
#105927452
#105924722
#105924692
#105924312
#105924252
#801463