Finite Group Databasebeta

← #11805103

Subgroups — #11805103

Order 1152.

1229 conjugacy classes of subgroups.

The subgroup lattice has 551 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#926C211yesmaximal, characteristic
2C2×#63658C211yesmaximal, characteristic
3C3×#5211C211yesmaximal, characteristic
4#10591719C212yesmaximal
5#10591705C212yesmaximal
6#10591270C212yesmaximal, complemented
7#10591269C212yesmaximal, complemented
8#10591242C211yesmaximal, characteristic, complemented
9#10591239C211yesmaximal, characteristic, complemented
10#10591223C211yesmaximal, characteristic, complemented
11#10591206C211yesmaximal, characteristic, complemented
12#82237—31nomaximal
13#74059—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C23×C3⋊Dic3C2212yes—
16C2×C3×#217C2212yes—
17C2×C3×#217C2211yescharacteristic
18C2×C3×#217C2211yescharacteristic
19C3×#926C418yescomplemented
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4×Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×Dic3⋊Dic3C2212yes—
25C2×Dic3⋊Dic3C2212yes—
26C2×Dic32C2212yes—
27C2×Dic32C2212yes—
28#63658C2211yescharacteristic
29#63658C2212yes—
30#63658C2211yescharacteristic
31C3×C3⋊#95C2211yescharacteristic
32C3×C3⋊#95C2211yescharacteristic
33C3×C3⋊#95C2212yes—
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C3×#117—31no—
39C2×#926D311yescharacteristic
40C3×#381—31no—
41#5211D311yescharacteristic
42C2×C3⋊#95—31no—
43C2×C3⋊#95—31no—
44C2×C3⋊#95—61no—
45#4980—32no—
46#4980—32no—
47#4950—32no—
48#4946—32no—
49Dic3×C22⋊C4—32no—
50Dic3×C22⋊C4—32no—
51#4937—31no—
52#4936—31no—
53C4×C4⋊Dic3—31no—
54#4932—31no—
55#4654—32no—
56#4653—32no—
57#4651—31no—
58#4650—31no—
59#4649—31no—
60#4648—31no—
61C24×C32C2311yescharacteristic
62C22×C32×C4—24no—
63C22×C32×C4C2×C414yes—
64C22×C32×C4C2311yescharacteristic
65C22×C32×C4C2311yescharacteristic
66C22×C3⋊Dic3—24no—
67C22×C3⋊Dic3—24no—
68C22×C3⋊Dic3—42no—
69C22×C3⋊Dic3C2312yes—
70C22×C3⋊Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2311yescharacteristic
77C3×#217—24no—
78C3×#217C2×C414yes—
79C3×#217C2×C414yes—
80C3×C4⋊Dic3C2×C414yescomplemented
81C3×C4⋊Dic3C2×C414yescomplemented
82C3×C4×Dic3C2×C414yescomplemented
83C3×C4×Dic3C2×C414yescomplemented
84Dic3⋊Dic3—24no—
85Dic3⋊Dic3—42no—
86Dic32—24no—
87Dic32—42no—
88#2343—91noSylow
89C23×C3×C4—21no—
90C23×C3×C4C2×D311yescharacteristic
91C23×C3×C4C2×D311yescharacteristic
92C23×Dic3—32no—
93C23×Dic3—32no—
94C23×Dic3—62no—
95C3×#117—38no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C22⋊C4—31no—
99C2×C3×C22⋊C4—31no—
100C2×C3×C22⋊C4—32no—
101C2×C3×C42—31no—
102C2×C3×C42—31no—
103C2×#217C2×D312yes—
104C2×#217C2×D311yescharacteristic
105C2×#217C2×D311yescharacteristic
106#926Dic318yescomplemented
107C2×C4⋊Dic3—32no—
108C2×C4⋊Dic3—32no—
109C2×C4⋊Dic3C2×D311yescharacteristic
110C2×C4⋊Dic3C2×D311yescharacteristic
111C2×Dic3⋊C4—32no—
112C2×Dic3⋊C4—32no—
113C2×C4×Dic3—32no—
114C2×C4×Dic3—32no—
115C2×C4×Dic3—32no—
116C2×C4×Dic3—32no—
117C2×C4×Dic3C2×D311yescharacteristic
118C2×C4×Dic3C2×D311yescharacteristic
119C3×#95—31no—
120C3×#95—31no—
121C3×#95—32no—
122C3⋊#95—31no—
123C3⋊#95—31no—
124C3⋊#95—32no—
125C3⋊#95—31no—
126C3⋊#95—31no—
127C3⋊#95—32no—
128C3⋊#95—32no—
129C3⋊#95—32no—
130C3⋊#95—32no—
131C3⋊#95—32no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95—32no—
135C3⋊#95—32no—
136C3⋊#95—61no—
137C3⋊#95—61no—
138C3⋊#95—62no—
139C3⋊#95C2×D311yescharacteristic
140C3⋊#95C2×D311yescharacteristic
141C3⋊#95C2×D312yes—
142C23×C32—22no—
143C23×C32—21no—
144C23×C32—21no—
145C23×C32C22×C412yes—
146C23×C32#4114yes—
147C23×C32C2411yescharacteristic
148C2×C32×C4—28no—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4C22×C412yes—
152C2×C32×C4C22×C412yes—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—48no—
159C2×C3⋊Dic3#4114yes—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3C22×C412yes—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3C22×C412yes—
176C2×#117—31no—
177#387—92no—
178#387—92no—
179#385—92no—
180#383—91no—
181#382—91no—
182#381—31no—
183C4×C4⋊C4—91no—
184C4×C22⋊C4—92no—
185#376—91no—
186C2×#95—91no—
187C24×C3—21no—
188C24×C3C22×D311yescharacteristic
189C24×C3C22×D311yescharacteristic
190C22×C3×C4—24no—
191C22×C3×C4—24no—
192C22×C3×C4—24no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—31no—
196C22×C3×C4—31no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—32no—
200C22×C3×C4—32no—
201C22×C3×C4—44no—
202C22×C3×C4C4×D314yes—
203C22×C3×C4C2×Dic314yes—
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C22×Dic3—32no—
209C22×Dic3—32no—
210C22×Dic3—32no—
211C22×Dic3—32no—
212C22×Dic3—62no—
213C22×Dic3—62no—
214C22×Dic3—64no—
215C22×Dic3—64no—
216C22×Dic3—68no—
217C22×Dic3—64no—
218C22×Dic3—64no—
219C22×Dic3—124no—
220C22×Dic3—122no—
221C22×Dic3—122no—
222C22×Dic3—124no—
223C22×Dic3C22×D312yes—
224C22×Dic3C22×D312yes—
225C22×Dic3C22×D311yescharacteristic
226C22×Dic3C22×D311yescharacteristic
227C22×Dic3C22×D311yescharacteristic
228C22×Dic3C22×D311yescharacteristic
229C3×C4⋊C4—34no—
230C3×C4⋊C4—34no—
231C3×C22⋊C4—34no—
232C3×C22⋊C4—34no—
233C3×C22⋊C4—64no—
234C3×C42—34no—
235C3×C42—34no—
236#217—24no—
237#217C2×Dic314yes—
238#217C2×Dic314yes—
239C4⋊Dic3—64no—
240C4⋊Dic3—122no—
241C4⋊Dic3C2×Dic314yescomplemented
242C4⋊Dic3C2×Dic314yescomplemented
243Dic3⋊C4—64no—
244Dic3⋊C4—122no—
245C4×Dic3—64no—
246C4×Dic3—64no—
247C4×Dic3—122no—
248C4×Dic3—122no—
249C4×Dic3C2×Dic314yescomplemented
250C4×Dic3C2×Dic314yescomplemented
251C22×C32—22no—
252C22×C32—22no—
253C22×C32—24no—
254C22×C32—24no—
255C22×C32#11714yes—
256C22×C32C23×C411yescharacteristic
257C22×C32C2×#4112yes—
258C22×C32C2×#4112yes—
259C22×C32H(5,𝔽2)11yescharacteristic
260C22×C322−1+411yescharacteristic
261C32×C4—22no—
262C32×C4—22no—
263C3⋊Dic3—24no—
264C3⋊Dic3—42no—
265C3×Dic3—22no—
266C3×Dic3—22no—
267C3×Dic3—22no—
268C3×Dic3—22no—
269C3×Dic3—42no—
270C3×Dic3—42no—
271C23×C4—92no—
272C23×C4D3211yescharacteristic
273#117—38no—
274C2×C4⋊C4—31no—
275C2×C4⋊C4—31no—
276C2×C4⋊C4—92no—
277C2×C4⋊C4—92no—
278C2×C22⋊C4—31no—
279C2×C22⋊C4—31no—
280C2×C22⋊C4—32no—
281C2×C42—31no—
282C2×C42—31no—
283C2×C42—92no—
284C2×C42—92no—
285#95—31no—
286#95—31no—
287#95—32no—
288#95—92no—
289#95—92no—
290#95—92no—
291#95—92no—
292#95—91no—
293#95—91no—
294#95—92no—
295C23×C3—24no—
296C23×C3—22no—
297C23×C3—22no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—21no—
301C23×C3—21no—
302C23×C3—21no—
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—22no—
306C23×C3—24no—
307C23×C3C2×C4×D312yes—
308C23×C3#23514yes—
309C23×C3#23714yes—
310C23×C3C22×Dic312yes—
311C23×C3C23×D311yescharacteristic
312C23×C3C23×D311yescharacteristic
313C2×C3×C4—28no—
314C2×C3×C4—28no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—32no—
322C2×C3×C4—32no—
323C2×C3×C4—32no—
324C2×C3×C4—32no—
325C2×C3×C4—42no—
326C2×C3×C4—42no—
327C2×C3×C4—48no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
330C2×C3×C4—61no—
331C2×C3×C4—61no—
332C2×C3×C4—61no—
333C2×C3×C4—61no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4C2×C4×D312yes—
341C2×C3×C4C2×C4×D312yes—
342C2×C3×C4C22×Dic312yes—
343C2×C3×C4C22×Dic312yes—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—21no—
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—34no—
357C2×Dic3—34no—
358C2×Dic3—64no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—64no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—122no—
371C2×Dic3—122no—
372C2×Dic3—122no—
373C2×Dic3—122no—
374C2×Dic3—128no—
375C2×Dic3—128no—
376C2×Dic3—1216no—
377C2×Dic3C22×Dic312yes—
378C2×Dic3C22×Dic312yes—
379C2×Dic3C22×Dic312yes—
380C2×Dic3C22×Dic312yes—
381C2×C32—24no—
382C2×C32C2×#11711yescharacteristic
383C2×C32C4×#4111yescharacteristic
384C2×C32#52011yescharacteristic
385C2×C32#55112yes—
386C2×C32#55212yes—
387C24C2×D3211yescharacteristic
388C22×C4—24no—
389C22×C4—31no—
390C22×C4—31no—
391C22×C4—31no—
392C22×C4—31no—
393C22×C4—32no—
394C22×C4—32no—
395C22×C4—92no—
396C22×C4—92no—
397C22×C4—184no—
398C22×C4—184no—
399C22×C4—362no—
400C22×C4D3×Dic314yes—
401C22×C4C2×D3211yescharacteristic
402C22×C4C2×D3211yescharacteristic
403C4⋊C4—34no—
404C4⋊C4—34no—
405C4⋊C4—184no—
406C4⋊C4—362no—
407C22⋊C4—34no—
408C22⋊C4—34no—
409C22⋊C4—64no—
410C42—34no—
411C42—34no—
412C42—184no—
413C42—362no—
414C22×C3—28no—
415C22×C3—24no—
416C22×C3—28no—
417C22×C3—24no—
418C22×C3—24no—
419C22×C3—24no—
420C22×C3—22no—
421C22×C3—22no—
422C22×C3—24no—
423C22×C3—24no—
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—21no—
427C22×C3—22no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—22no—
431C22×C3—24no—
432C22×C3#87714yes—
433C22×C3#92614yes—
434C22×C3C22×C4×D311yescharacteristic
435C22×C3C2×#23512yes—
436C22×C3C2×#23712yes—
437C22×C3D3×#4112yes—
438C22×C3D3×#4112yes—
439C22×C3#100911yescharacteristic
440C22×C3#100911yescharacteristic
441C22×C3#101011yescharacteristic
442C22×C3#101011yescharacteristic
443C22×C3C23×Dic311yescharacteristic
444C3×C4—22no—
445C3×C4—22no—
446C3×C4—22no—
447C3×C4—22no—
448C3×C4—42no—
449C3×C4—42no—
450C3×C4—62no—
451C3×C4—62no—
452C3×C4—62no—
453C3×C4—62no—
454C3×C4—122no—
455C3×C4—122no—
456Dic3—22no—
457Dic3—22no—
458Dic3—22no—
459Dic3—22no—
460Dic3—42no—
461Dic3—42no—
462Dic3—64no—
463Dic3—64no—
464Dic3—124no—
465Dic3—124no—
466Dic3—122no—
467Dic3—122no—
468C32#234311yescharacteristic, complemented, Sylow
469C23—21no—
470C23—22no—
471C23—21no—
472C23C2×D3×Dic312yes—
473C23#380414yes—
474C23C22×D3211yescharacteristic
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—28no—
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—32no—
481C2×C4—32no—
482C2×C4—61no—
483C2×C4—61no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—94no—
495C2×C4—182no—
496C2×C4—182no—
497C2×C4—182no—
498C2×C4—182no—
499C2×C4—182no—
500C2×C4—368no—
501C2×C4C2×D3×Dic312yes—
502C2×C4C2×D3×Dic312yes—
503C2×C3—28no—
504C2×C3—24no—
505C2×C3—24no—
506C2×C3—21no—
507C2×C3—22no—
508C2×C3—22no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3C2×#87711yescharacteristic
512C2×C3#552211yescharacteristic
513C2×C3#552311yescharacteristic
514C2×C3#552712yes—
515C2×C3#553112yes—
516C2×C3#565012yes—
517C2×C3#565812yes—
518C2×C3C2×#92611yescharacteristic
519C2×C3Dic3×#4111yescharacteristic
520C2×C3#582711yescharacteristic
521C22—22no—
522C22—24no—
523C22—24no—
524C22—22no—
525C22#6395514yes—
526C22#6429811yescharacteristic
527C22#6430612yes—
528C22#6430811yescharacteristic
529C22C22×D3×Dic311yescharacteristic
530C22C2×#380412yes—
531C4—22no—
532C4—22no—
533C4—62no—
534C4—62no—
535C4—62no—
536C4—62no—
537C4—122no—
538C4—122no—
539C4—184no—
540C4—362no—
541C3—21no—
542C3#7405911yescharacteristic, complemented
543C3#8223711yescharacteristic, complemented
544C2—24no—
545C2#1059495811yescharacteristic
546C2#1059496012yes—
547C2#1059496612yes—
548C2#1059499211yescharacteristic
549C2C2×#6395511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC23×C4D32
hypocenterC32#2343
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. #10591270C2semidirect
7. #10591269C2semidirect
8. #10591242C2semidirect
9. #10591239C2semidirect
10. #10591223C2semidirect
11. #10591206C2semidirect
19. C3×#926C4semidirect
80. C3×C4⋊Dic3C2×C4semidirect
81. C3×C4⋊Dic3C2×C4semidirect
82. C3×C4×Dic3C2×C4semidirect
83. C3×C4×Dic3C2×C4semidirect
106. #926Dic3semidirect
241. C4⋊Dic3C2×Dic3semidirect
242. C4⋊Dic3C2×Dic3semidirect
249. C4×Dic3C2×Dic3semidirect
250. C4×Dic3C2×Dic3semidirect
468. C32#2343semidirect
542. C3#74059semidirect
543. C3#82237semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9262
C2×#636582
C3×#52112
#105917192
#105917052
#105912702
#105912692
#105912422
#105912392
#105912232
#105912062
#822373
#740593