Finite Group Databasebeta

← #11836032

Subgroups — #11836032

Order 1152.

2796 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic, complemented
2C2×#64146C211yesmaximal, characteristic, complemented
3C2×#64139C212yesmaximal, complemented
4C2×#64091C212yesmaximal, complemented
5C32×#386C211yesmaximal, characteristic, complemented
6#10592660C212yesmaximal, complemented
7#10592659C212yesmaximal, complemented
8#10592370C212yesmaximal, complemented
9#10592369C212yesmaximal, complemented
10#74912—34nomaximal
11C24×C3⋊D3C2211yescharacteristic
12C22×C32×D4C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic, complemented
14C22×#638C2212yes—
15C22×#638C2212yes—
16C22×#638C2212yescomplemented
17C22×C4⋊(C3⋊D3)C2212yes—
18C22×C4⋊(C3⋊D3)C2212yes—
19C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
20C2×C32×C22⋊C4C2212yes—
21C2×C32×C22⋊C4C2211yescharacteristic, complemented
22C2×#3757C2211yescharacteristic
23#64149—24no—
24#64146—24no—
25#64139—28no—
26C2×#3752C2212yes—
27C2×#3752C2212yes—
28C2×#3752C2212yes—
29C2×#3752C2212yescomplemented
30C2×#3752C2212yescomplemented
31C2×C4⋊(C3⋊Dic3)C2212yescomplemented
32C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
33#64091—28no—
34C32×#95C2212yescomplemented
35#63658C2212yescomplemented
36C2×#940—34no—
37C2×#937—34no—
38C2×#930—38no—
39C2×#882—38no—
40C3×#386D314yescomplemented
41#4961—38no—
42#4960—38no—
43#4671—38no—
44#4670—38no—
45C24×C32C2311yescharacteristic
46C24×C32C2311yescharacteristic
47C23×C3⋊D3—22no—
48C23×C3⋊D3—24no—
49C23×C3⋊D3—41no—
50C23×C3⋊D3—41no—
51C23×C3⋊D3—42no—
52C23×C3⋊D3C2312yes—
53C23×C3⋊D3C2312yes—
54C2×C32×D4—41no—
55C2×C32×D4—41no—
56C2×C32×D4D414yescomplemented
57C22×C32×C4—24no—
58C22×C32×C4—41no—
59C22×C32×C4C2312yes—
60C22×C32×C4C2312yes—
61C22×C32×C4C2311yescharacteristic
62C2×#638—24no—
63C2×#638—24no—
64C2×#638—24no—
65C2×#638—24no—
66C2×#638—24no—
67C2×#638—24no—
68C2×#638—42no—
69C2×#638—42no—
70C2×#638—42no—
71C22×C3⋊Dic3C2312yes—
72C22×C3⋊Dic3C2312yes—
73C2×C4⋊(C3⋊D3)—24no—
74C2×C4⋊(C3⋊D3)—24no—
75C2×C4⋊(C3⋊D3)—24no—
76C2×C4⋊(C3⋊D3)—22no—
77C2×C4⋊(C3⋊D3)—42no—
78C2×C4⋊(C3⋊D3)—42no—
79C2×C4⋊(C3⋊D3)—42no—
80C2×C4⋊(C3⋊D3)—41no—
81C2×C4⋊(C3⋊D3)—41no—
82C32×C22⋊C4—24no—
83C32×C22⋊C4—41no—
84#3757—22no—
85#3752—24no—
86#3752—24no—
87#3752—24no—
88#3752—42no—
89#3752D418yescomplemented
90C4⋊(C3⋊Dic3)—24no—
91C4×C3⋊Dic3—22no—
92#2669—91noSylow
93C24×D3—34no—
94C22×C3×D4C2×D314yes—
95C23×C3×C4C2×D314yescomplemented
96C22×#67—38no—
97C22×#67—38no—
98C22×#67—38no—
99C22×D12—38no—
100C22×D12—34no—
101C22×D12—38no—
102C2×C3×C22⋊C4C2×D318yes—
103C2×C3×C22⋊C4C2×D314yescomplemented
104C2×#217—34no—
105#940—616no—
106#937—616no—
107#930—632no—
108C2×(C2×D3)⋊C4—38no—
109C2×(C2×D3)⋊C4—38no—
110C2×(C2×D3)⋊C4—38no—
111C2×(C2×D3)⋊C4—38no—
112C2×(C2×D3)⋊C4—38no—
113C2×C4⋊Dic3—38no—
114C2×C4×Dic3—34no—
115#882—632no—
116C3×#95C2×D318yescomplemented
117C3⋊#95—38no—
118C23×C32—22no—
119C23×C32—22no—
120C23×C32—22no—
121C23×C32—21no—
122C23×C32—21no—
123C23×C32—21no—
124C23×C32—22no—
125C23×C32—21no—
126C23×C32C2×D412yes—
127C23×C32C2×D412yes—
128C23×C32C2411yescharacteristic
129C22×C3⋊D3—22no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3—22no—
132C22×C3⋊D3—22no—
133C22×C3⋊D3—22no—
134C22×C3⋊D3—22no—
135C22×C3⋊D3—22no—
136C22×C3⋊D3—22no—
137C22×C3⋊D3—22no—
138C22×C3⋊D3—22no—
139C22×C3⋊D3—22no—
140C22×C3⋊D3—22no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—44no—
143C22×C3⋊D3—48no—
144C22×C3⋊D3—48no—
145C22×C3⋊D3—44no—
146C22×C3⋊D3—44no—
147C22×C3⋊D3C2×D414yes—
148C32×D4—44no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4—22no—
154C2×C32×C4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—44no—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2×D414yes—
159#638—48no—
160#638—48no—
161#638—48no—
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—22no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3—22no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3C2×D414yes—
168C4⋊(C3⋊D3)—48no—
169C4⋊(C3⋊D3)—44no—
170C4⋊(C3⋊D3)—48no—
171C2×#127—91no—
172C2×#121—92no—
173C2×#120—91no—
174C2×#120—92no—
175#394—92no—
176#392—92no—
177#392—92no—
178#388—92no—
179#386C3⋊D311yescharacteristic, complemented
180C24×C3C22×D314yes—
181C24×C3C22×D314yes—
182C23×D3—38no—
183C23×D3—38no—
184C23×D3—616no—
185C23×D3—68no—
186C23×D3—124no—
187C23×D3—124no—
188C23×D3—128no—
189C2×C3×D4—44no—
190C2×C3×D4—44no—
191C2×C3×D4D12116yescomplemented
192C22×C3×C4—216no—
193C22×C3×C4—44no—
194C22×C3×C4C22×D318yes—
195C22×C3×C4C22×D314yes—
196C22×C3×C4C22×D318yes—
197C2×#67—616no—
198C2×#67—616no—
199C2×#67—616no—
200C2×#67—616no—
201C2×#67—616no—
202C2×#67—616no—
203C2×#67—128no—
204C2×#67—128no—
205C2×#67—128no—
206C22×Dic3—38no—
207C22×Dic3—38no—
208C2×D12—616no—
209C2×D12—616no—
210C2×D12—68no—
211C2×D12—616no—
212C2×D12—128no—
213C2×D12—124no—
214C2×D12—124no—
215C2×D12—128no—
216C2×D12—128no—
217C3×C22⋊C4—216no—
218C3×C22⋊C4—44no—
219#217—68no—
220(C2×D3)⋊C4—332no—
221(C2×D3)⋊C4—616no—
222(C2×D3)⋊C4—616no—
223(C2×D3)⋊C4—616no—
224(C2×D3)⋊C4—128no—
225C4⋊Dic3—616no—
226C4×Dic3—68no—
227C22×C32—22no—
228C22×C32—22no—
229C22×C32—24no—
230C22×C32—24no—
231C22×C32—42no—
232C22×C32—42no—
233C22×C32—41no—
234C22×C32—41no—
235C22×C32—41no—
236C22×C32—41no—
237C22×C32C22×D411yescharacteristic
238C22×C32C22×D412yes—
239C22×C32H(5,𝔽2)11yescharacteristic
240C22×C32H(5,𝔽2)11yescharacteristic
241C22×C32H(5,𝔽2)12yes—
242C2×C3⋊D3—24no—
243C2×C3⋊D3—24no—
244C2×C3⋊D3—24no—
245C2×C3⋊D3—416no—
246C2×C3⋊D3—42no—
247C2×C3⋊D3—42no—
248C2×C3⋊D3—42no—
249C2×C3⋊D3—42no—
250C2×C3⋊D3—42no—
251C2×C3⋊D3—42no—
252C2×C3⋊D3—42no—
253C2×C3⋊D3—42no—
254C2×C3⋊D3—42no—
255C2×C3⋊D3—42no—
256C2×C3⋊D3—42no—
257C32×C4—22no—
258C32×C4—24no—
259C32×C4—42no—
260C3⋊Dic3—24no—
261C3⋊Dic3—42no—
262C25—91no—
263C22×D4—92no—
264C22×D4—92no—
265C22×D4—92no—
266C22×D4—92no—
267C22×D4—92no—
268C22×D4—91no—
269C22×D4C2×C3⋊D311yescharacteristic
270C23×C4C2×C3⋊D311yescharacteristic, complemented
271#127—184no—
272#121—188no—
273#120—188no—
274#120—184no—
275C2×C4⋊C4—92no—
276C2×C22⋊C4—92no—
277C2×C22⋊C4—91no—
278C2×C22⋊C4—92no—
279C2×C22⋊C4—92no—
280C2×C22⋊C4—92no—
281C2×C22⋊C4—92no—
282C2×C22⋊C4C2×C3⋊D312yes—
283C2×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
284C2×C42—91no—
285#95—92no—
286#95C2×C3⋊D312yescomplemented
287C23×C3—28no—
288C23×C3—28no—
289C23×C3—24no—
290C23×C3—24no—
291C23×C3—24no—
292C23×C3—24no—
293C23×C3—28no—
294C23×C3—28no—
295C23×C3C2×D1218yes—
296C23×C3C2×D1218yes—
297C23×C3C23×D314yes—
298C22×D3—316no—
299C22×D3—68no—
300C22×D3—68no—
301C22×D3—68no—
302C22×D3—68no—
303C22×D3—68no—
304C22×D3—68no—
305C22×D3—68no—
306C22×D3—68no—
307C22×D3—68no—
308C22×D3—68no—
309C22×D3—68no—
310C22×D3—68no—
311C22×D3—68no—
312C22×D3—1216no—
313C22×D3—1232no—
314C22×D3—1232no—
315C22×D3—1216no—
316C22×D3—1216no—
317C3×D4—416no—
318C2×C3×C4—28no—
319C2×C3×C4—28no—
320C2×C3×C4—24no—
321C2×C3×C4—24no—
322C2×C3×C4—28no—
323C2×C3×C4—28no—
324C2×C3×C4—28no—
325C2×C3×C4—416no—
326C2×C3×C4C2×D1218yes—
327C2×C3×C4D3×D4116yes—
328#67—1232no—
329#67—1232no—
330#67—1232no—
331C2×Dic3—316no—
332C2×Dic3—68no—
333C2×Dic3—68no—
334C2×Dic3—68no—
335C2×Dic3—68no—
336C2×Dic3—68no—
337D12—1232no—
338D12—1216no—
339D12—1232no—
340C2×C32—42no—
341C2×C32—42no—
342C2×C32#53411yescharacteristic
343C2×C32#53512yes—
344C2×C32D4212yes—
345C2×C32D4211yescharacteristic
346C2×C32#56011yescharacteristic
347C3⋊D3—44no—
348C3⋊D3—82no—
349C24—92no—
350C24—92no—
351C24—184no—
352C24—182no—
353C24—361no—
354C24—361no—
355C24—362no—
356C24C22×C3⋊D311yescharacteristic
357C24C22×C3⋊D311yescharacteristic
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—184no—
361C2×D4—184no—
362C2×D4—184no—
363C2×D4—184no—
364C2×D4—184no—
365C2×D4—184no—
366C2×D4—184no—
367C2×D4—184no—
368C2×D4—182no—
369C2×D4—184no—
370C2×D4—362no—
371C2×D4—361no—
372C2×D4—361no—
373C2×D4—362no—
374C2×D4—362no—
375C2×D4—362no—
376C2×D4—362no—
377C2×D4—362no—
378C2×D4C4⋊(C3⋊D3)14yescomplemented
379C22×C4—24no—
380C22×C4—41no—
381C22×C4—92no—
382C22×C4—92no—
383C22×C4C22×C3⋊D312yes—
384C22×C4C22×C3⋊D311yescharacteristic
385C22×C4C22×C3⋊D312yes—
386C4⋊C4—184no—
387C22⋊C4—24no—
388C22⋊C4—41no—
389C22⋊C4—98no—
390C22⋊C4—184no—
391C22⋊C4—182no—
392C22⋊C4—184no—
393C22⋊C4—184no—
394C22⋊C4—362no—
395C42—182no—
396C22×C3—28no—
397C22×C3—28no—
398C22×C3—216no—
399C22×C3—216no—
400C22×C3—44no—
401C22×C3—44no—
402C22×C3—44no—
403C22×C3—44no—
404C22×C3—48no—
405C22×C3—48no—
406C22×C3C22×D1214yes—
407C22×C3C2×D3×D418yes—
408C22×C3#100414yes—
409C22×C3#100414yes—
410C22×C3#100918yes—
411C2×D3—616no—
412C2×D3—616no—
413C2×D3—616no—
414C2×D3—1264no—
415C2×D3—128no—
416C2×D3—128no—
417C2×D3—128no—
418C2×D3—128no—
419C2×D3—128no—
420C2×D3—128no—
421C2×D3—128no—
422C2×D3—128no—
423C2×D3—128no—
424C2×D3—128no—
425C2×D3—128no—
426C3×C4—28no—
427C3×C4—216no—
428C3×C4—48no—
429Dic3—616no—
430Dic3—128no—
431C32#266911yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—22no—
439C23—22no—
440C23—94no—
441C23—182no—
442C23—182no—
443C23—182no—
444C23—182no—
445C23—182no—
446C23—182no—
447C23—182no—
448C23—182no—
449C23—182no—
450C23—182no—
451C23—182no—
452C23—182no—
453C23—182no—
454C23—368no—
455C23—364no—
456C23—364no—
457C23—368no—
458C23—364no—
459C23C2×C4⋊(C3⋊D3)12yes—
460C23C2×C4⋊(C3⋊D3)12yes—
461C23C23×C3⋊D311yescharacteristic
462D4—44no—
463D4—368no—
464D4—364no—
465D4—368no—
466D4—368no—
467D4—368no—
468D4—368no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—44no—
477C2×C4—94no—
478C2×C4—182no—
479C2×C4—182no—
480C2×C4—182no—
481C2×C4—182no—
482C2×C4—182no—
483C2×C4C2×C4⋊(C3⋊D3)12yes—
484C2×C4D4×C3⋊D314yes—
485C2×C3—48no—
486C2×C3—48no—
487C2×C3#549314yes—
488C2×C3D4×D1218yes—
489C2×C3#559014yes—
490C2×C3#560718yes—
491C2×C3#566614yes—
492D3—1216no—
493D3—248no—
494C22—22no—
495C22—22no—
496C22—24no—
497C22—24no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—42no—
503C22—42no—
504C22—184no—
505C22—184no—
506C22—184no—
507C22—3616no—
508C22—362no—
509C22—362no—
510C22—362no—
511C22—362no—
512C22—362no—
513C22—362no—
514C22—362no—
515C22—362no—
516C22—362no—
517C22—362no—
518C22—362no—
519C22C22×C4⋊(C3⋊D3)11yescharacteristic
520C22C2×D4×C3⋊D312yes—
521C22#6436111yescharacteristic
522C22#6436111yescharacteristic
523C22#6436612yes—
524C4—22no—
525C4—24no—
526C4—42no—
527C4—184no—
528C4—362no—
529C3#7491214yescomplemented
530C2—42no—
531C2—42no—
532C2—364no—
533C2—722no—
534C2#1059596411yescharacteristic
535C2D4×C4⋊(C3⋊D3)12yes—
536C2#1059606111yescharacteristic
537C2#1059607812yes—
538C2#1059613711yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#386C2
hypercenter#386C3⋊D3
hypocenterC32#2669
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#64149C2semidirect
2. C2×#64146C2semidirect
3. C2×#64139C2semidirect
4. C2×#64091C2semidirect
5. C32×#386C2semidirect
6. #10592660C2semidirect
7. #10592659C2semidirect
8. #10592370C2semidirect
9. #10592369C2semidirect
13. C23×C32×C4C22semidirect
16. C22×#638C22semidirect
19. C22×C4⋊(C3⋊D3)C22semidirect
21. C2×C32×C22⋊C4C22semidirect
29. C2×#3752C22semidirect
30. C2×#3752C22semidirect
31. C2×C4⋊(C3⋊Dic3)C22semidirect
32. C2×C4×C3⋊Dic3C22semidirect
34. C32×#95C22semidirect
35. #63658C22semidirect
40. C3×#386D3semidirect
56. C2×C32×D4D4semidirect
89. #3752D4semidirect
95. C23×C3×C4C2×D3semidirect
103. C2×C3×C22⋊C4C2×D3semidirect
116. C3×#95C2×D3semidirect
179. #386C3⋊D3semidirect
191. C2×C3×D4D12semidirect
270. C23×C4C2×C3⋊D3semidirect
283. C2×C22⋊C4C2×C3⋊D3semidirect
286. #95C2×C3⋊D3semidirect
378. C2×D4C4⋊(C3⋊D3)semidirect
431. C32#2669semidirect
529. C3#74912semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
C2×#641462
C2×#641392
C2×#640912
C32×#3862
#105926602
#105926592
#105923702
#105923692
#749123