Finite Group Databasebeta

← #11783420

Subgroups — #11783420

Order 1152.

825 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×M16C211yesmaximal, characteristic
2C2×#63841C211yesmaximal, characteristic
3C2×D3×#208C211yesmaximal, characteristic
4#10589420C211yesmaximal, characteristic, complemented
5C3×#4554C211yesmaximal, characteristic, complemented
6#10589168C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#71987—31nomaximal
9#68989—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×D3×M16—22no—
18C3×D3×M16C414yescomplemented
19C2×C3×ΓL(1,𝔽25)—21no—
20C2×C3×D3×C8—21no—
21C2×(C2×D3)⋊Dic3C412yes—
22C2×Dic32C412yes—
23#63841—21no—
24#63841—21no—
25#63841—21no—
26#63841—21no—
27C2×#3711—21no—
28D3×#208—22no—
29D3×#208C414yescomplemented
30C2×D3×C3⋊C8—21no—
31C22×C3×M16—31no—
32C2×#926—31no—
33C22×#208—31no—
34C2×D3×M16—31no—
35C2×D3×M16D311yescharacteristic
36C2×#892—31no—
37C3×#343—31no—
38#4554—31no—
39#4554—31no—
40#4554—31no—
41#4554—31no—
42#4554—31no—
43#4554—61no—
44#4554D311yescharacteristic, complemented
45#4530—31no—
46C23×C3×D3C2×C411yescharacteristic
47C22×C32×C4C2311yescharacteristic
48C22×C3⋊Dic3C2×C412yes—
49C22×C3×Dic3C2×C412yes—
50C22×C3×Dic3C2×C411yescharacteristic
51C2×C3×C4×D3C2×C412yes—
52C2×C3×C4×D3C2×C412yes—
53C2×C3×C4×D3D412yes—
54C2×C3×C4×D3D411yescharacteristic
55C2×C3×C4×D3D411yescharacteristic
56C2×C3×C4×D3D411yescharacteristic
57C2×C3×C4×D3D411yescharacteristic
58C2×C3×C4×D3Q812yes—
59C32×M16—21no—
60C32×M16C2×C412yes—
61C2×C32×C8—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4⋊(C3⋊Dic3)—21no—
64#3748—21no—
65#3748C2×C412yes—
66C2×C3⋊(C3⋊C8)—21no—
67C3×C4⋊Dic3—21no—
68C3×C4⋊Dic3—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208C2×C412yes—
72C3×#208C2×C412yes—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C3×ΓL(1,𝔽25)—24no—
76C3×D3×C8—24no—
77(C2×D3)⋊Dic3—22no—
78(C2×D3)⋊Dic3—22no—
79Dic32—22no—
80Dic32—22no—
81#3711—24no—
82D3×C3⋊C8—24no—
83#1742—91noSylow
84C23×C3×C4—31no—
85C22×C4×D3C2×D311yescharacteristic
86C2×C3×M16—21no—
87C2×C3×M16—31no—
88C2×C3×M16—31no—
89C2×C3×M16—34no—
90C2×C3×M16—61no—
91C2×C3×M16—62no—
92C2×C3×M16C2×D311yescharacteristic
93C2×C3×M16C2×D311yescharacteristic
94C22×C3×C8—61no—
95C2×C3×C4⋊C4—31no—
96C2×#217—32no—
97C2×(C2×D3)⋊C4—32no—
98#926—61no—
99#926—61no—
100#926—61no—
101#926—61no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—31no—
104C2×C4⋊Dic3—61no—
105C2×C4⋊Dic3C2×D311yescharacteristic
106C2×C4×Dic3—32no—
107C2×C4×Dic3—32no—
108C2×#208—31no—
109C2×#208—31no—
110C2×#208—34no—
111C2×#208—61no—
112C2×#208—61no—
113C2×#208—62no—
114C2×#208C2×D311yescharacteristic
115C2×#208C2×D311yescharacteristic
116C22×C3⋊C8—61no—
117D3×M16—22no—
118D3×M16—34no—
119D3×M16—62no—
120D3×M16Dic314yescomplemented
121C2×ΓL(1,𝔽25)—21no—
122C2×ΓL(1,𝔽25)—61no—
123C2×D3×C8—21no—
124C2×D3×C8—61no—
125#892—61no—
126#892—61no—
127#892—61no—
128#892—61no—
129C23×C32C22×C411yescharacteristic
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C22×C3×D3C4212yes—
133C22×C3×D3C22⋊C411yescharacteristic
134C22×C3×D3C22⋊C411yescharacteristic
135C22×C3×D3C4⋊C412yes—
136C2×C32×C4C22×C411yescharacteristic
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×Q811yescharacteristic
142C2×C3⋊Dic3—22no—
143C2×C3⋊Dic3—42no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3C4212yes—
147C2×C3×Dic3C22⋊C411yescharacteristic
148C2×C3×Dic3C22⋊C411yescharacteristic
149C2×C3×Dic3C4⋊C412yes—
150C3×C4×D3C22⋊C412yes—
151C3×C4×D3C22⋊C412yes—
152C3×C4×D3C22⋊C412yes—
153C3×C4×D3C22⋊C412yes—
154C3×C4×D3C4⋊C412yes—
155C3×C4×D3C4⋊C412yes—
156C3×C4×D3C4⋊C412yes—
157C3×C4×D3C4⋊C412yes—
158C32×C8—22no—
159C3⋊(C3⋊C8)—22no—
160C3×C3⋊C8—22no—
161C3×C3⋊C8—22no—
162C22×M16—31no—
163C22×M16—91no—
164C2×#117—91no—
165#343—31no—
166#343—91no—
167#343—91no—
168#343—91no—
169C24×C3—31no—
170C23×D3C4×D311yescharacteristic
171C22×C3×C4—21no—
172C22×C3×C4—31no—
173C22×C3×C4—32no—
174C22×C3×C4—32no—
175C22×C3×C4—31no—
176C22×C3×C4—31no—
177C22×C3×C4—32no—
178C22×C3×C4—31no—
179C22×C3×C4—31no—
180C22×C3×C4—32no—
181C22×C3×C4—32no—
182C22×C3×C4C22×D311yescharacteristic
183C22×C3×C4C22×D311yescharacteristic
184C22×Dic3—32no—
185C22×Dic3—32no—
186C22×Dic3—62no—
187C22×Dic3C4×D312yes—
188C22×Dic3C4×D311yescharacteristic
189C2×C4×D3Dic612yes—
190C2×C4×D3C4×D312yes—
191C2×C4×D3D1211yescharacteristic
192C2×C4×D3D1211yescharacteristic
193C2×C4×D3C2×Dic312yes—
194C2×C4×D3#6711yescharacteristic
195C2×C4×D3#6711yescharacteristic
196C2×C4×D3#6712yes—
197C3×M16—21no—
198C3×M16—21no—
199C3×M16—22no—
200C3×M16—32no—
201C3×M16—32no—
202C3×M16—41no—
203C3×M16—64no—
204C3×M16—61no—
205C3×M16—61no—
206C3×M16C4×D312yes—
207C3×M16C2×Dic312yes—
208C2×C3×C8—21no—
209C2×C3×C8—21no—
210C2×C3×C8—41no—
211C2×C3×C8—64no—
212C2×C3×C8—61no—
213C2×C3×C8—61no—
214C3×C4⋊C4—61no—
215C3×C4⋊C4—61no—
216#217—62no—
217#217—62no—
218(C2×D3)⋊C4—62no—
219(C2×D3)⋊C4—62no—
220C4⋊Dic3—21no—
221C4⋊Dic3—21no—
222C4⋊Dic3—61no—
223C4⋊Dic3—61no—
224C4⋊Dic3—61no—
225C4⋊Dic3—61no—
226C4⋊Dic3—121no—
227C4⋊Dic3—121no—
228C4×Dic3—62no—
229C4×Dic3—62no—
230C4×Dic3—62no—
231C4×Dic3—62no—
232#208—21no—
233#208—21no—
234#208—32no—
235#208—32no—
236#208—62no—
237#208—64no—
238#208—61no—
239#208—61no—
240#208—121no—
241#208C4×D312yes—
242#208C2×Dic312yes—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—64no—
246C2×C3⋊C8—61no—
247C2×C3⋊C8—61no—
248C2×C3⋊C8—121no—
249ΓL(1,𝔽25)—24no—
250ΓL(1,𝔽25)—64no—
251D3×C8—24no—
252D3×C8—64no—
253C22×C32—21no—
254C22×C32—21no—
255C22×C32C2×C4211yescharacteristic
256C22×C32C2×C22⋊C411yescharacteristic
257C22×C32C2×C4⋊C411yescharacteristic
258C2×C3×D3—21no—
259C2×C3×D3—21no—
260C2×C3×D3—21no—
261C2×C3×D3—21no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C2×C3×D3#9512yes—
265C2×C3×D3#9512yes—
266C32×C4C2×C22⋊C411yescharacteristic
267C32×C4C2×C22⋊C411yescharacteristic
268C32×C4C2×C4⋊C411yescharacteristic
269C32×C4C2×C4⋊C411yescharacteristic
270C3⋊Dic3—42no—
271C3×Dic3—42no—
272C3×Dic3#9512yes—
273C3×Dic3#9512yes—
274C23×C4—31no—
275C2×M16—31no—
276C2×M16—31no—
277C2×M16—34no—
278C2×M16—61no—
279C2×M16—62no—
280C2×M16—94no—
281C2×M16—91no—
282C2×M16—181no—
283C2×M16—182no—
284C2×M16D3211yescharacteristic
285C22×C8—61no—
286C22×C8—181no—
287#117—181no—
288#117—181no—
289#117—181no—
290#117—181no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4—91no—
293C2×C22⋊C4—92no—
294C2×C42—92no—
295C23×C3—21no—
296C23×C3—31no—
297C23×C3—31no—
298C23×C3—32no—
299C23×C3—32no—
300C23×C3—121no—
301C23×C3—121no—
302C23×C3C2×C4×D311yescharacteristic
303C23×C3C2×C4×D311yescharacteristic
304C22×D3—41no—
305C22×D3—41no—
306C22×D3C4×Dic312yes—
307C22×D3Dic3⋊C412yes—
308C22×D3(C2×D3)⋊C411yescharacteristic
309C22×D3(C2×D3)⋊C411yescharacteristic
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—32no—
317C2×C3×C4—31no—
318C2×C3×C4—31no—
319C2×C3×C4—32no—
320C2×C3×C4—32no—
321C2×C3×C4—32no—
322C2×C3×C4—32no—
323C2×C3×C4—32no—
324C2×C3×C4—32no—
325C2×C3×C4—32no—
326C2×C3×C4—32no—
327C2×C3×C4—32no—
328C2×C3×C4—62no—
329C2×C3×C4—122no—
330C2×C3×C4C2×Dic611yescharacteristic
331C2×C3×C4C2×C4×D311yescharacteristic
332C2×C3×C4C2×C4×D311yescharacteristic
333C2×C3×C4C2×C4×D311yescharacteristic
334C2×C3×C4C2×D1211yescharacteristic
335C2×C3×C4D3×D411yescharacteristic
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4D3×D411yescharacteristic
338C2×C3×C4D3×Q811yescharacteristic
339C2×C3×C4C22×Dic311yescharacteristic
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C2×#6711yescharacteristic
342C2×Dic3—22no—
343C2×Dic3—42no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—122no—
347C2×Dic3—122no—
348C2×Dic3—122no—
349C2×Dic3—242no—
350C2×Dic3C4×Dic312yes—
351C2×Dic3Dic3⋊C412yes—
352C2×Dic3(C2×D3)⋊C411yescharacteristic
353C2×Dic3(C2×D3)⋊C411yescharacteristic
354C4×D3Dic3⋊C412yes—
355C4×D3Dic3⋊C412yes—
356C4×D3C4⋊Dic312yes—
357C4×D3C4⋊Dic312yes—
358C4×D3(C2×D3)⋊C412yes—
359C4×D3(C2×D3)⋊C412yes—
360C4×D3#21712yes—
361C4×D3#21712yes—
362C3×C8—22no—
363C3×C8—22no—
364C3×C8—42no—
365C3×C8—62no—
366C3×C8—62no—
367C3⋊C8—22no—
368C3⋊C8—22no—
369C3⋊C8—62no—
370C3⋊C8—62no—
371C3⋊C8—122no—
372C2×C32—21no—
373C2×C32—21no—
374C2×C32C2×#9511yescharacteristic
375C2×C32#41311yescharacteristic
376C2×C32#41311yescharacteristic
377C3×D3—22no—
378C3×D3—22no—
379C24—31no—
380C22×C4—31no—
381C22×C4—32no—
382C22×C4—32no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—32no—
386C22×C4—31no—
387C22×C4—31no—
388C22×C4—32no—
389C22×C4—32no—
390C22×C4—92no—
391C22×C4C2×D3211yescharacteristic
392M16—21no—
393M16—32no—
394M16—32no—
395M16—64no—
396M16—61no—
397M16—61no—
398M16—92no—
399M16—184no—
400M16—181no—
401M16D3×Dic312yes—
402C2×C8—21no—
403C2×C8—64no—
404C2×C8—61no—
405C2×C8—61no—
406C2×C8—184no—
407C2×C8—181no—
408C4⋊C4—61no—
409C4⋊C4—61no—
410C4⋊C4—181no—
411C4⋊C4—181no—
412C22⋊C4—182no—
413C22⋊C4—182no—
414C42—182no—
415C42—182no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—32no—
424C22×C3—32no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—61no—
428C22×C3—61no—
429C22×C3—61no—
430C22×C3—61no—
431C22×C3—122no—
432C22×C3—122no—
433C22×C3C42×D311yescharacteristic
434C22×C3D3×C22⋊C411yescharacteristic
435C22×C3D3×C4⋊C411yescharacteristic
436C22×C3C2×C4×Dic311yescharacteristic
437C22×C3C2×Dic3⋊C411yescharacteristic
438C22×C3C2×(C2×D3)⋊C411yescharacteristic
439C2×D3—21no—
440C2×D3—21no—
441C2×D3—21no—
442C2×D3—21no—
443C2×D3—42no—
444C2×D3—42no—
445C2×D3C3⋊#9512yes—
446C2×D3C3⋊#9512yes—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—32no—
452C3×C4—32no—
453C3×C4—122no—
454C3×C4D3×C22⋊C411yescharacteristic
455C3×C4D3×C22⋊C411yescharacteristic
456C3×C4D3×C4⋊C411yescharacteristic
457C3×C4D3×C4⋊C411yescharacteristic
458C3×C4C2×Dic3⋊C411yescharacteristic
459C3×C4C2×C4⋊Dic311yescharacteristic
460C3×C4C2×(C2×D3)⋊C411yescharacteristic
461C3×C4C2×#21711yescharacteristic
462Dic3—42no—
463Dic3—122no—
464Dic3—122no—
465Dic3—242no—
466Dic3C3⋊#9512yes—
467Dic3C3⋊#9512yes—
468C32#174211yescharacteristic, complemented, Sylow
469C23—31no—
470C23—31no—
471C23—32no—
472C23—32no—
473C23—121no—
474C23—121no—
475C23C4×D3211yescharacteristic
476C2×C4—32no—
477C2×C4—32no—
478C2×C4—31no—
479C2×C4—31no—
480C2×C4—32no—
481C2×C4—32no—
482C2×C4—32no—
483C2×C4—32no—
484C2×C4—32no—
485C2×C4—32no—
486C2×C4—32no—
487C2×C4—32no—
488C2×C4—62no—
489C2×C4—122no—
490C2×C4—182no—
491C2×C4—362no—
492C2×C4D3×Dic611yescharacteristic
493C2×C4C4×D3211yescharacteristic
494C2×C4D3×D1211yescharacteristic
495C2×C4C2×D3×Dic311yescharacteristic
496C2×C4D3×#6711yescharacteristic
497C2×C4D3×#6711yescharacteristic
498C8—22no—
499C8—62no—
500C8—62no—
501C8—182no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—41no—
510C2×C3—41no—
511C2×C3—62no—
512C2×C3—62no—
513C2×C3D3×#9511yescharacteristic
514C2×C3#474511yescharacteristic
515C2×C3#475111yescharacteristic
516C2×C3#513211yescharacteristic
517C2×C3#513211yescharacteristic
518C2×C3C2×C3⋊#9511yescharacteristic
519D3—22no—
520D3—22no—
521C22—21no—
522C22—21no—
523C22—32no—
524C22—32no—
525C22—61no—
526C22—61no—
527C22—61no—
528C22—61no—
529C22—122no—
530C22—122no—
531C22C4×D3×Dic311yescharacteristic
532C22D3×Dic3⋊C411yescharacteristic
533C22D3×(C2×D3)⋊C411yescharacteristic
534C4—32no—
535C4—32no—
536C4—122no—
537C4—362no—
538C4D3×Dic3⋊C411yescharacteristic
539C4D3×C4⋊Dic311yescharacteristic
540C4D3×(C2×D3)⋊C411yescharacteristic
541C4D3×#21711yescharacteristic
542C3—21no—
543C3#6898911yescharacteristic, complemented
544C3#7198711yescharacteristic, complemented
545C2—21no—
546C2—21no—
547C2—62no—
548C2—62no—
549C2#1059100611yescharacteristic
550C2#1059100711yescharacteristic
551C2D3×C3⋊#9511yescharacteristic
subgroupG/H
centerC22D3×(C2×D3)⋊C4
commutatorC22×C32C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C2×C22⋊C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1742
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #10589420C2semidirect
5. C3×#4554C2semidirect
6. #10589168C2semidirect
7. #10589167C2semidirect
18. C3×D3×M16C4semidirect
29. D3×#208C4semidirect
44. #4554D3semidirect
120. D3×M16Dic3semidirect
468. C32#1742semidirect
543. C3#68989semidirect
544. C3#71987semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×M162
C2×#638412
C2×D3×#2082
#105894202
C3×#45542
#105891682
#105891672
#719873
#689893