Finite Group Databasebeta

← #11885753

Subgroups — #11885753

Order 1152.

1307 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595069C212yesmaximal, complemented
2C22×#3713C211yesmaximal, characteristic, complemented
3C2×#63797C211yesmaximal, characteristic, complemented
4#10592424C211yesmaximal, characteristic, complemented
5C3×#4732C212yesmaximal, complemented
6#10591166C211yesmaximal, characteristic, complemented
7#10590945C212yesmaximal, complemented
8#10590886C211yesmaximal, characteristic, complemented
9#10590839C211yesmaximal, characteristic, complemented
10#10590749C212yesmaximal, complemented
11#10590740C211yesmaximal, characteristic, complemented
12#80024—32nomaximal
13C22×C3×D12C2212yescomplemented
14C2×D3×#67—22no—
15C2×#3802C2212yescomplemented
16C4×#638C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
18C2×C8×C3⋊D3C2211yescharacteristic, complemented
19C3×#930C2212yescomplemented
20C2×C3×D24C2212yescomplemented
21C2×C3×D24C2212yescomplemented
22#63976—22no—
23#63922—22no—
24#63916C2212yescomplemented
25#63914C2212yescomplemented
26#63898C2212yescomplemented
27#63885—22no—
28C2×#3713—24no—
29C2×#3713C2211yescharacteristic
30C2×#3713C2212yescomplemented
31C2×#3713C2211yescharacteristic, complemented
32C2×#3713C2211yescharacteristic, complemented
33#63797—24no—
34C32×C22⋊C8C2211yescharacteristic, complemented
35#63647C2211yescharacteristic, complemented
36#63641C2211yescharacteristic, complemented
37C8×C3⋊Dic3C2211yescharacteristic, complemented
38C3×#821C2212yescomplemented
39C3×#821C2212yescomplemented
40#63576C2211yescharacteristic, complemented
41#63562C2212yescomplemented
42D4×#67—32no—
43C22×#213—32no—
44C2×D3×D8—32no—
45#5609—32no—
46C3×#447—32no—
47#5156—32no—
48#5151—32no—
49#5150—32no—
50#5038—32no—
51#4786—32no—
52#4775—32no—
53#4773—32no—
54#4756—32no—
55#4732D312yescomplemented
56#67⋊C8—32no—
57#67⋊C8—61no—
58C23×C3×D3—22no—
59C22×D32—22no—
60C22×C32×C4C2311yescharacteristic
61C2×#638D411yescharacteristic
62C2×C4×C3⋊D3C2311yescharacteristic
63C2×C3×#67—22no—
64C2×C3×D12—24no—
65C2×C3×D12—22no—
66C2×C3×D12—42no—
67C2×C3×D12C2312yes—
68C2×C3×D12C2312yes—
69C2×C3×D12C2312yes—
70D3×#67—48no—
71C2×#626—22no—
72C2×#625—22no—
73C2×#625—22no—
74C2×#625—22no—
75C2×D3×Dic3—22no—
76#3802—24no—
77#3802—42no—
78C2×C32×C8C2311yescharacteristic
79C2×C32×C8C2311yescharacteristic
80#3757D411yescharacteristic
81#3752D411yescharacteristic
82#3750D411yescharacteristic
83C4×C3⋊Dic3C2311yescharacteristic
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2311yescharacteristic
87C8×C3⋊D3—22no—
88C3×(C2×D3)⋊C4—22no—
89C3×C4⋊Dic3C2312yes—
90C3×D24—24no—
91C3×D24—42no—
92(C2×D3)⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94#3713—24no—
95#3713—22no—
96#3713—22no—
97#3713D414yescomplemented
98D4×D8—91noSylow
99C22×C3×D4—32no—
100C22×#67—62no—
101C2×D3×D4—32no—
102C2×D3×D4—32no—
103C2×D3×D4—62no—
104C22×D12C2×D312yescomplemented
105C2×C3×D8—32no—
106C2×C3×D8—32no—
107C3×#121—32no—
108#953—62no—
109#940—32no—
110#940—32no—
111#939—62no—
112#938—32no—
113#937—62no—
114#937—62no—
115D4×Dic3—32no—
116C2×#213—32no—
117C2×#213—32no—
118C2×#213—32no—
119C2×#213—32no—
120C2×#213—32no—
121C2×#213—68no—
122#930C2×D312yescomplemented
123C4×#67—32no—
124C4×#67—61no—
125C22×C3⋊C8—32no—
126C22×C3⋊C8—61no—
127D3×D8—68no—
128C2×D24C2×D312yescomplemented
129C2×D24C2×D312yescomplemented
130C2×D3×C8—32no—
131C2×D3×C8—61no—
132#895—32no—
133#893—32no—
134#884—62no—
135#882—62no—
136C3×#102—32no—
137C3×#102—32no—
138C3×C22⋊C8—21no—
139C3×C22⋊C8C2×D312yescomplemented
140#832—32no—
141#821C2×D312yescomplemented
142#821C2×D312yescomplemented
143(C2×D3)⋊C8—32no—
144(C2×D3)⋊C8—61no—
145Dic3⋊C8—32no—
146Dic3⋊C8—61no—
147C8×Dic3—32no—
148C8×Dic3—61no—
149#809—32no—
150#807—32no—
151C23×C32C2×D411yescharacteristic
152C22×C3⋊D3C2×D411yescharacteristic
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3—44no—
157C22×C3×D3—44no—
158C22×C3×D3—82no—
159C2×D32—44no—
160C2×D32—44no—
161C2×D32—82no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2411yescharacteristic
166#638D814yescomplemented
167C2×C3⋊Dic3C2×D411yescharacteristic
168C2×C3⋊Dic3C2×D411yescharacteristic
169C2×C3⋊Dic3C2×D411yescharacteristic
170C4×C3⋊D3—21no—
171C4×C3⋊D3—21no—
172C3×#67—44no—
173C2×C3×Dic3—22no—
174C3×D12—22no—
175C3×D12—22no—
176C3×D12—22no—
177C3×D12—22no—
178C3×D12—22no—
179C3×D12—44no—
180C3×D12C2×D414yescomplemented
181#626—44no—
182#625—44no—
183#625—44no—
184#625—82no—
185D3×Dic3—44no—
186C32×C8—21no—
187C32×C8—21no—
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)C2×D412yescomplemented
190C22×D8—91no—
191C22×D8—91no—
192D42—92no—
193#493—91no—
194#466—91no—
195#466—91no—
196#459—92no—
197#447—32no—
198#447—92no—
199C4×D8—91no—
200C8×D4—91no—
201C24×C3—62no—
202C23×D3—22no—
203C23×D3—62no—
204C23×D3—62no—
205C2×C3×D4—32no—
206C2×C3×D4—32no—
207C2×C3×D4—32no—
208C2×C3×D4—64no—
209C2×C3×D4—62no—
210C2×C3×D4—62no—
211C2×C3×D4—122no—
212C22×C3×C4—21no—
213C22×C3×C4C22×D312yes—
214C2×#67—22no—
215C2×#67—32no—
216C2×#67—61no—
217C2×#67—62no—
218C2×#67—62no—
219C2×#67—62no—
220C2×#67—62no—
221C2×#67—62no—
222C2×#67—62no—
223C2×#67—62no—
224C2×#67—128no—
225C22×Dic3—62no—
226D3×D4—64no—
227D3×D4—64no—
228D3×D4—122no—
229D3×D4—122no—
230D3×D4—128no—
231C2×D12—24no—
232C2×D12—22no—
233C2×D12—42no—
234C2×D12—62no—
235C2×D12C22×D312yes—
236C2×D12C22×D312yes—
237C2×D12C22×D312yes—
238C2×C4×D3—32no—
239C2×C4×D3—61no—
240C2×C4×D3—62no—
241C3×D8—64no—
242C3×D8—122no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8C22×D312yes—
246C2×C3×C8C22×D312yes—
247C3×C4⋊C4—32no—
248C3×C22⋊C4—62no—
249#217—32no—
250#217—61no—
251#217—62no—
252#217—62no—
253#213—38no—
254#213—64no—
255#213—64no—
256#213—64no—
257#213—64no—
258(C2×D3)⋊C4—22no—
259(C2×D3)⋊C4—32no—
260(C2×D3)⋊C4—61no—
261(C2×D3)⋊C4—62no—
262(C2×D3)⋊C4—62no—
263C4⋊Dic3C22×D312yes—
264Dic3⋊C4—32no—
265Dic3⋊C4—61no—
266C4×Dic3—32no—
267C4×Dic3—61no—
268C2×C3⋊C8—32no—
269C2×C3⋊C8—32no—
270C2×C3⋊C8—61no—
271C2×C3⋊C8—61no—
272C2×C3⋊C8—64no—
273C2×C3⋊C8—122no—
274D24—24no—
275D24—42no—
276D3×C8—64no—
277D3×C8—122no—
278C22×C32—21no—
279C22×C32—21no—
280C22×C32C2×D812yescomplemented
281C22×C32C22×D411yescharacteristic
282C2×C3⋊D3—21no—
283C2×C3⋊D3—21no—
284C2×C3⋊D3C2×D812yescomplemented
285C2×C3×D3—24no—
286C2×C3×D3—42no—
287C2×C3×D3—42no—
288C2×C3×D3—42no—
289C2×C3×D3—42no—
290C2×C3×D3—42no—
291C2×C3×D3—42no—
292C2×C3×D3—42no—
293C2×C3×D3—42no—
294C2×C3×D3—88no—
295D32—88no—
296C32×C4—21no—
297C32×C4C22×D411yescharacteristic
298C32×C4H(5,𝔽2)11yescharacteristic
299C3⋊Dic3—21no—
300C3⋊Dic3—21no—
301C3⋊Dic3C2×D812yescomplemented
302C3×Dic3—42no—
303C22×D4—32no—
304C22×D4—92no—
305C22×D4—182no—
306C2×D8—32no—
307C2×D8—32no—
308C2×D8—91no—
309C2×D8—92no—
310C2×D8—91no—
311C2×D8—91no—
312C2×D8—184no—
313C2×D8—184no—
314C22×C8—91no—
315C22×C8—91no—
316#127—92no—
317#121—32no—
318#121—92no—
319#121—182no—
320#120—182no—
321#120—182no—
322C4×D4—91no—
323C4×D4—92no—
324#107—91no—
325C4⋊C8—91no—
326#102—32no—
327#102—32no—
328#102—92no—
329C22⋊C8—91no—
330C22⋊C8D3211yescharacteristic, complemented
331C4×C8—91no—
332C23×C3—21no—
333C23×C3—62no—
334C23×C3—62no—
335C23×C3—62no—
336C23×C3—124no—
337C23×C3—124no—
338C23×C3—242no—
339C23×C3D3×D412yes—
340C22×D3—22no—
341C22×D3—22no—
342C22×D3—22no—
343C22×D3—32no—
344C22×D3—44no—
345C22×D3—44no—
346C22×D3—61no—
347C22×D3—82no—
348C22×D3—124no—
349C22×D3—124no—
350C22×D3—124no—
351C22×D3—124no—
352C22×D3—242no—
353C22×D3—242no—
354C3×D4—34no—
355C3×D4—62no—
356C3×D4—62no—
357C3×D4—62no—
358C3×D4—62no—
359C3×D4—62no—
360C3×D4—124no—
361C3×D4—124no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—41no—
367C2×C3×C4—41no—
368C2×C3×C4—62no—
369C2×C3×C4D3×D412yes—
370C2×C3×C4C23×D312yes—
371#67—38no—
372#67—44no—
373#67—64no—
374#67—124no—
375#67—124no—
376#67—124no—
377#67—124no—
378#67—124no—
379#67—242no—
380#67—242no—
381C2×Dic3—22no—
382C2×Dic3—32no—
383C2×Dic3—32no—
384C2×Dic3—32no—
385C2×Dic3—61no—
386C2×Dic3—61no—
387C2×Dic3—61no—
388C2×Dic3—124no—
389D12—22no—
390D12—22no—
391D12—22no—
392D12—22no—
393D12—22no—
394D12—44no—
395D12—124no—
396D12D3×D414yescomplemented
397C4×D3—62no—
398C4×D3—62no—
399C4×D3—121no—
400C4×D3—121no—
401C4×D3—124no—
402C3×C8—22no—
403C3×C8—22no—
404C3×C8—41no—
405C3×C8—41no—
406C3⋊C8—34no—
407C3⋊C8—62no—
408C3⋊C8—62no—
409C3⋊C8—121no—
410C2×C32—22no—
411C2×C32D4211yescharacteristic
412C2×C32C22×D811yescharacteristic
413C2×C32#57611yescharacteristic
414C3⋊D3—22no—
415C3×D3—44no—
416C3×D3—82no—
417C3×D3—82no—
418C24—62no—
419C24—182no—
420C2×D4—32no—
421C2×D4—32no—
422C2×D4—32no—
423C2×D4—64no—
424C2×D4—62no—
425C2×D4—62no—
426C2×D4—91no—
427C2×D4—122no—
428C2×D4—182no—
429C2×D4—182no—
430C2×D4—182no—
431C2×D4—182no—
432C2×D4—184no—
433C2×D4—362no—
434C2×D4—368no—
435C22×C4—91no—
436C22×C4—182no—
437C22×C4C2×D3211yescharacteristic
438D8—64no—
439D8—94no—
440D8—122no—
441D8—182no—
442D8—182no—
443D8—184no—
444C2×C8—91no—
445C2×C8—91no—
446C2×C8—182no—
447C2×C8—182no—
448C2×C8C2×D3211yescharacteristic
449C2×C8C2×D3211yescharacteristic
450C4⋊C4—32no—
451C4⋊C4—91no—
452C22⋊C4—62no—
453C22⋊C4—91no—
454C22⋊C4—91no—
455C22⋊C4—182no—
456C22⋊C4—182no—
457C42—91no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—21no—
461C22×C3—22no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3—64no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3—122no—
468C22×C3—122no—
469C22×C3—122no—
470C22×C3—122no—
471C22×C3—122no—
472C22×C3—122no—
473C22×C3—248no—
474C22×C3D3×D814yescomplemented
475C22×C3C2×D3×D412yes—
476C2×D3—24no—
477C2×D3—34no—
478C2×D3—42no—
479C2×D3—42no—
480C2×D3—42no—
481C2×D3—42no—
482C2×D3—42no—
483C2×D3—42no—
484C2×D3—42no—
485C2×D3—42no—
486C2×D3—62no—
487C2×D3—62no—
488C2×D3—62no—
489C2×D3—88no—
490C2×D3—121no—
491C2×D3—121no—
492C2×D3—248no—
493C2×D3—248no—
494C3×C4—22no—
495C3×C4—21no—
496C3×C4—21no—
497C3×C4—41no—
498C3×C4—122no—
499C3×C4C2×D3×D412yes—
500C3×C4#100412yes—
501Dic3—34no—
502Dic3—42no—
503Dic3—62no—
504Dic3—62no—
505Dic3—62no—
506Dic3—121no—
507Dic3—121no—
508C32D4×D811yescharacteristic, complemented, Sylow
509C23—62no—
510C23—62no—
511C23—62no—
512C23—91no—
513C23—124no—
514C23—124no—
515C23—242no—
516C23—364no—
517C23—364no—
518C23—722no—
519C23#380211yescharacteristic
520D4—34no—
521D4—62no—
522D4—62no—
523D4—62no—
524D4—62no—
525D4—62no—
526D4—94no—
527D4—124no—
528D4—124no—
529D4—364no—
530D4—364no—
531D4—364no—
532D4—722no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—62no—
536C2×C4—91no—
537C2×C4—91no—
538C2×C4—91no—
539C2×C4—181no—
540C2×C4—181no—
541C2×C4—364no—
542C2×C4#380211yescharacteristic
543C2×C4C22×D3211yescharacteristic
544C8—21no—
545C8—21no—
546C8—92no—
547C8—181no—
548C2×C3—24no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—21no—
552C2×C3—42no—
553C2×C3—124no—
554C2×C3—242no—
555C2×C3—242no—
556C2×C3#559012yes—
557C2×C3C2×D3×D812yes—
558C2×C3#577412yes—
559D3—44no—
560D3—64no—
561D3—82no—
562D3—82no—
563D3—122no—
564C22—21no—
565C22—21no—
566C22—64no—
567C22—92no—
568C22—122no—
569C22—122no—
570C22—122no—
571C22—122no—
572C22—122no—
573C22—122no—
574C22—122no—
575C22—122no—
576C22—181no—
577C22—181no—
578C22—248no—
579C22—728no—
580C22#6379712yescomplemented
581C22C2×#380211yescharacteristic
582C4—21no—
583C4—92no—
584C4—122no—
585C4—181no—
586C4—181no—
587C4D32×D411yescharacteristic
588C4#6431311yescharacteristic
589C3—21no—
590C3#8002412yescomplemented
591C2—22no—
592C2—124no—
593C2—182no—
594C2—242no—
595C2—242no—
596C2#1059427111yescharacteristic
597C2C2×#6379711yescharacteristic
598C2#1059472011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10595069C2semidirect
2. C22×#3713C2semidirect
3. C2×#63797C2semidirect
4. #10592424C2semidirect
5. C3×#4732C2semidirect
6. #10591166C2semidirect
7. #10590945C2semidirect
8. #10590886C2semidirect
9. #10590839C2semidirect
10. #10590749C2semidirect
11. #10590740C2semidirect
13. C22×C3×D12C22semidirect
15. C2×#3802C22semidirect
17. C22×C3⋊(C3⋊C8)C22semidirect
18. C2×C8×C3⋊D3C22semidirect
19. C3×#930C22semidirect
20. C2×C3×D24C22semidirect
21. C2×C3×D24C22semidirect
24. #63916C22semidirect
25. #63914C22semidirect
26. #63898C22semidirect
30. C2×#3713C22semidirect
31. C2×#3713C22semidirect
32. C2×#3713C22semidirect
34. C32×C22⋊C8C22semidirect
35. #63647C22semidirect
36. #63641C22semidirect
37. C8×C3⋊Dic3C22semidirect
38. C3×#821C22semidirect
39. C3×#821C22semidirect
40. #63576C22semidirect
41. #63562C22semidirect
55. #4732D3semidirect
97. #3713D4semidirect
104. C22×D12C2×D3semidirect
122. #930C2×D3semidirect
128. C2×D24C2×D3semidirect
129. C2×D24C2×D3semidirect
139. C3×C22⋊C8C2×D3semidirect
141. #821C2×D3semidirect
142. #821C2×D3semidirect
166. #638D8semidirect
180. C3×D12C2×D4semidirect
189. C3⋊(C3⋊C8)C2×D4semidirect
280. C22×C32C2×D8semidirect
284. C2×C3⋊D3C2×D8semidirect
301. C3⋊Dic3C2×D8semidirect
330. C22⋊C8D32semidirect
396. D12D3×D4semidirect
474. C22×C3D3×D8semidirect
508. C32D4×D8semidirect
580. C22#63797semidirect
590. C3#80024semidirect

Maximal subgroups

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

subgroupindex
#105950692
C22×#37132
C2×#637972
#105924242
C3×#47322
#105911662
#105909452
#105908862
#105908392
#105907492
#105907402
#800243