Finite Group Databasebeta

← #11805105

Subgroups — #11805105

Order 1152.

1173 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#926C211yesmaximal, characteristic
2#10592910C211yesmaximal, characteristic
3C2×C3×C3⋊#95C211yesmaximal, characteristic
4#10591718C212yesmaximal
5Dic3×#217C212yesmaximal
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#73335—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C23×C3×Dic3C2212yes—
16C2×#3757C2212yes—
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#63658C2211yescharacteristic
30#63658C2212yes—
31C3×C3⋊#95C2211yescharacteristic
32C3×C3⋊#95C2212yes—
33C3×C3⋊#95C2211yescharacteristic
34#63579C2212yes—
35#63579C2212yes—
36#63579C2212yes—
37#63579C2212yes—
38C2×C3×#117—31no—
39C2×#926D311yescharacteristic
40C2×C3×#95—31no—
41#5211—31no—
42#5211—31no—
43#5211—61no—
44#5210—32no—
45C4×#217—32no—
46C2×C3⋊#95D311yescharacteristic
47#4980—32no—
48#4980—32no—
49#4950—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⋊Dic3C2312yes—
67C22×C3⋊Dic3C2312yes—
68C22×C3×Dic3—24no—
69C22×C3×Dic3—24no—
70C22×C3×Dic3—42no—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2311yescharacteristic
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2311yescharacteristic
75C22×C3×Dic3C2311yescharacteristic
76C22×C3×Dic3C2312yes—
77#3757—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×C4—32no—
91C23×C3×C4C2×D311yescharacteristic
92C23×C3×C4C2×D311yescharacteristic
93C23×Dic3C2×D312yes—
94C3×#117—38no—
95C2×C3×C4⋊C4—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C22⋊C4—31no—
98C2×C3×C22⋊C4—31no—
99C2×C3×C42—31no—
100C2×C3×C42—31no—
101C2×#217—32no—
102C2×#217—32no—
103C2×#217—62no—
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—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—21no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—21no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—48no—
171C2×C3×Dic3C22×C412yes—
172C2×C3×Dic3C22×C412yes—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3C22×C412yes—
175C2×C3×Dic3#4114yes—
176C2×#117—31no—
177#387—92no—
178#387—92no—
179#385—92no—
180#383—91no—
181#382—91no—
182#381—91no—
183C4×C4⋊C4—91no—
184C4×C22⋊C4—92no—
185#376—91no—
186C2×#95—31no—
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×C4—64no—
203C22×C3×C4—64no—
204C22×C3×C4—122no—
205C22×C3×C4C4×D314yes—
206C22×C3×C4C2×Dic314yes—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C22×Dic3—24no—
212C22×Dic3—24no—
213C22×Dic3—32no—
214C22×Dic3—32no—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—42no—
218C22×Dic3—62no—
219C22×Dic3—62no—
220C22×Dic3C22×D312yes—
221C22×Dic3C22×D312yes—
222C22×Dic3C22×D311yescharacteristic
223C22×Dic3C22×D311yescharacteristic
224C22×Dic3C22×D311yescharacteristic
225C22×Dic3C22×D311yescharacteristic
226C3×C4⋊C4—34no—
227C3×C4⋊C4—34no—
228C3×C22⋊C4—34no—
229C3×C22⋊C4—34no—
230C3×C42—34no—
231C3×C42—34no—
232#217—64no—
233#217—64no—
234#217—124no—
235#217C2×Dic314yes—
236#217C2×Dic314yes—
237C4⋊Dic3—64no—
238C4⋊Dic3—122no—
239C4⋊Dic3C2×Dic314yescomplemented
240C4⋊Dic3C2×Dic314yescomplemented
241Dic3⋊C4—64no—
242Dic3⋊C4—122no—
243C4×Dic3—64no—
244C4×Dic3—64no—
245C4×Dic3—122no—
246C4×Dic3—122no—
247C4×Dic3C2×Dic314yescomplemented
248C4×Dic3C2×Dic314yescomplemented
249C22×C32—22no—
250C22×C32—22no—
251C22×C32—24no—
252C22×C32—24no—
253C22×C32#11714yes—
254C22×C32C23×C411yescharacteristic
255C22×C32C2×#4112yes—
256C22×C32C2×#4112yes—
257C22×C32H(5,𝔽2)11yescharacteristic
258C22×C322−1+411yescharacteristic
259C32×C4—22no—
260C32×C4—22no—
261C3⋊Dic3—42no—
262C3⋊Dic3—42no—
263C3×Dic3—22no—
264C3×Dic3—22no—
265C3×Dic3—22no—
266C3×Dic3—22no—
267C3×Dic3—24no—
268C3×Dic3—42no—
269C23×C4—32no—
270C23×C4D3211yescharacteristic
271#117—38no—
272C2×C4⋊C4—31no—
273C2×C4⋊C4—31no—
274C2×C4⋊C4—92no—
275C2×C4⋊C4—92no—
276C2×C22⋊C4—31no—
277C2×C22⋊C4—31no—
278C2×C22⋊C4—92no—
279C2×C42—31no—
280C2×C42—31no—
281C2×C42—92no—
282C2×C42—92no—
283#95—31no—
284#95—31no—
285#95—32no—
286#95—92no—
287#95—92no—
288#95—92no—
289#95—92no—
290#95—91no—
291#95—91no—
292#95—92no—
293C23×C3—22no—
294C23×C3—21no—
295C23×C3—21no—
296C23×C3—22no—
297C23×C3—21no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—22no—
301C23×C3—24no—
302C23×C3—41no—
303C23×C3—42no—
304C23×C3—41no—
305C23×C3C2×C4×D312yes—
306C23×C3#23514yes—
307C23×C3#23714yes—
308C23×C3C22×Dic312yes—
309C23×C3C23×D311yescharacteristic
310C23×C3C23×D311yescharacteristic
311C2×C3×C4—28no—
312C2×C3×C4—28no—
313C2×C3×C4—22no—
314C2×C3×C4—22no—
315C2×C3×C4—22no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—32no—
320C2×C3×C4—32no—
321C2×C3×C4—32no—
322C2×C3×C4—32no—
323C2×C3×C4—34no—
324C2×C3×C4—42no—
325C2×C3×C4—42no—
326C2×C3×C4—48no—
327C2×C3×C4—62no—
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—128no—
339C2×C3×C4C2×C4×D312yes—
340C2×C3×C4C2×C4×D312yes—
341C2×C3×C4C22×Dic312yes—
342C2×C3×C4C22×Dic312yes—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—21no—
348C2×Dic3—21no—
349C2×Dic3—21no—
350C2×Dic3—21no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—48no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—122no—
368C2×Dic3—122no—
369C2×Dic3—122no—
370C2×Dic3—122no—
371C2×Dic3—122no—
372C2×Dic3—122no—
373C2×Dic3#23514yes—
374C2×Dic3C22×Dic312yes—
375C2×Dic3C22×Dic312yes—
376C2×Dic3C22×Dic312yes—
377C2×Dic3C22×Dic312yes—
378C2×C32—24no—
379C2×C32C2×#11711yescharacteristic
380C2×C32C4×#4111yescharacteristic
381C2×C32#52011yescharacteristic
382C2×C32#55112yes—
383C2×C32#55212yes—
384C24C2×D3211yescharacteristic
385C22×C4—24no—
386C22×C4—32no—
387C22×C4—31no—
388C22×C4—31no—
389C22×C4—31no—
390C22×C4—31no—
391C22×C4—32no—
392C22×C4—64no—
393C22×C4—64no—
394C22×C4—92no—
395C22×C4—92no—
396C22×C4—122no—
397C22×C4D3×Dic314yes—
398C22×C4C2×D3211yescharacteristic
399C22×C4C2×D3211yescharacteristic
400C4⋊C4—34no—
401C4⋊C4—34no—
402C4⋊C4—184no—
403C4⋊C4—362no—
404C22⋊C4—34no—
405C22⋊C4—34no—
406C22⋊C4—184no—
407C42—34no—
408C42—34no—
409C42—184no—
410C42—362no—
411C22×C3—22no—
412C22×C3—24no—
413C22×C3—22no—
414C22×C3—24no—
415C22×C3—24no—
416C22×C3—24no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—21no—
420C22×C3—22no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—22no—
424C22×C3—24no—
425C22×C3—44no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—44no—
429C22×C3#87714yes—
430C22×C3#92614yes—
431C22×C3C22×C4×D311yescharacteristic
432C22×C3C2×#23512yes—
433C22×C3C2×#23512yes—
434C22×C3C2×#23712yes—
435C22×C3#100411yescharacteristic
436C22×C3#100711yescharacteristic
437C22×C3D3×#4112yes—
438C22×C3#100911yescharacteristic
439C22×C3#101011yescharacteristic
440C22×C3C23×Dic311yescharacteristic
441C3×C4—22no—
442C3×C4—22no—
443C3×C4—22no—
444C3×C4—22no—
445C3×C4—42no—
446C3×C4—42no—
447C3×C4—62no—
448C3×C4—62no—
449C3×C4—62no—
450C3×C4—62no—
451C3×C4—64no—
452C3×C4—122no—
453Dic3—24no—
454Dic3—22no—
455Dic3—22no—
456Dic3—22no—
457Dic3—22no—
458Dic3—42no—
459Dic3—122no—
460Dic3—122no—
461Dic3—122no—
462Dic3—122no—
463Dic3—242no—
464Dic3—242no—
465C32#234311yescharacteristic, complemented, Sylow
466C23—21no—
467C23—22no—
468C23—21no—
469C23C2×D3×Dic312yes—
470C23#380414yes—
471C23C22×D3211yescharacteristic
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—28no—
475C2×C4—34no—
476C2×C4—32no—
477C2×C4—32no—
478C2×C4—32no—
479C2×C4—32no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—61no—
485C2×C4—62no—
486C2×C4—61no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—128no—
492C2×C4—182no—
493C2×C4—182no—
494C2×C4—182no—
495C2×C4—182no—
496C2×C4—182no—
497C2×C4—182no—
498C2×C4C2×D3×Dic312yes—
499C2×C4C2×D3×Dic312yes—
500C2×C3—24no—
501C2×C3—24no—
502C2×C3—22no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—22no—
507C2×C3—44no—
508C2×C3C4×#23511yescharacteristic
509C2×C3C2×#87711yescharacteristic
510C2×C3#549512yes—
511C2×C3#550411yescharacteristic
512C2×C3#551312yes—
513C2×C3#552712yes—
514C2×C3#553112yes—
515C2×C3C2×#92611yescharacteristic
516C2×C3Dic3×#4111yescharacteristic
517C2×C3#582711yescharacteristic
518C22—24no—
519C22—22no—
520C22—22no—
521C22—24no—
522C22#6395514yes—
523C22#6429711yescharacteristic
524C22D3×#23512yes—
525C22#6430711yescharacteristic
526C22C22×D3×Dic311yescharacteristic
527C22C2×#380412yes—
528C4—22no—
529C4—22no—
530C4—64no—
531C4—62no—
532C4—62no—
533C4—62no—
534C4—62no—
535C4—122no—
536C4—362no—
537C4—362no—
538C3—21no—
539C3#7333511yescharacteristic, complemented
540C3#8223711yescharacteristic, complemented
541C2—24no—
542C2#1059480712yes—
543C2#1059493712yes—
544C2Dic3×#23511yescharacteristic
545C2#1059498611yescharacteristic
546C2C2×#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
239. C4⋊Dic3C2×Dic3semidirect
240. C4⋊Dic3C2×Dic3semidirect
247. C4×Dic3C2×Dic3semidirect
248. C4×Dic3C2×Dic3semidirect
465. C32#2343semidirect
539. C3#73335semidirect
540. 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
#105929102
C2×C3×C3⋊#952
#105917182
Dic3×#2172
#105912702
#105912692
#105912422
#105912392
#105912232
#105912062
#822373
#733353