Finite Group Databasebeta

← #11895255

Subgroups — #11895255

Order 1152.

814 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
1#10596014C211yesmaximal, characteristic, complemented
2#10593863C211yesmaximal, characteristic, complemented
3C3×#5019C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic
5#10591476C212yesmaximal
6#10591445C212yesmaximal, complemented
7#10590539C212yesmaximal, complemented
8#10590494C212yesmaximal, complemented
9#10590287C211yesmaximal, characteristic, complemented
10#10590268C211yesmaximal, characteristic, complemented
11#10590254C211yesmaximal, characteristic, complemented
12#80415—31nomaximal
13#79568—31nomaximal
14C32×C4×D4C2211yescharacteristic
15D4×C3⋊Dic3C2212yes—
16C2×C4⋊(C3⋊Dic3)—21no—
17#64133—21no—
18#64099C2212yes—
19#64087—22no—
20#64078C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C2×C3×#214C2212yes—
23C2×C3×#213C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25C3×#869C2211yescharacteristic
26#63863C2212yes—
27#63858—22no—
28#63857—21no—
29#63843C2212yes—
30#63841—21no—
31C3×#832C2211yescharacteristic
32C3×#810C2212yes—
33C3×#809C2211yescharacteristic
34C3×#807C2211yescharacteristic
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2212yes—
38#63572C2212yes—
39#63566C2212yes—
40#63566C2212yes—
41#63563C2212yes—
42#63553C2212yes—
43#5732—31no—
44#5543—31no—
45#5543—31no—
46#5543—61no—
47#5542—31no—
48C3×#461—31no—
49C3×C4×D8—31no—
50#5165—32no—
51Dic3×SD16—32no—
52#5153—32no—
53#5079—31no—
54#5019D311yescharacteristic, complemented
55C4×#213D311yescharacteristic
56#5008—31no—
57#4877—32no—
58#4842—31no—
59#4830—31no—
60#4800—32no—
61#4799—32no—
62#4768—32no—
63#4758—32no—
64#4681—31no—
65C8×Dic6—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C22×C3⋊Dic3—22no—
69C2×#634—21no—
70C2×#634D411yescharacteristic
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×Dic6C2312yes—
74C32×C4⋊C4C2311yescharacteristic
75C32×C22⋊C4—21no—
76C32×C42C2311yescharacteristic
77#3757—22no—
78C4⋊(C3⋊Dic3)—21no—
79C4⋊(C3⋊Dic3)—22no—
80C4⋊(C3⋊Dic3)D411yescharacteristic
81C4⋊(C3⋊Dic3)C2312yes—
82#3750—22no—
83#3750D412yes—
84C4×C3⋊Dic3C2312yes—
85C3×#214—24no—
86C3×#213—22no—
87C3×(C2×D3)⋊C4—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2311yescharacteristic
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2312yes—
93C2×C3×C3⋊C8C2311yescharacteristic
94Dic3⋊Dic3—22no—
95(C2×D3)⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3360—91noSylow
99C2×C3×SD16—32no—
100C2×C3×D8—31no—
101C3×C4⋊Q8—31no—
102C3×C4×D4—21no—
103C3×C4×D4—31no—
104C3×C4×D4C2×D311yescharacteristic
105C3×C4×D4C2×D311yescharacteristic
106#947—32no—
107Q8×Dic3—32no—
108#936—32no—
109D4×Dic3—32no—
110D4×Dic3—32no—
111D4×Dic3—62no—
112C2×#214C2×D312yes—
113C2×#213C2×D311yescharacteristic
114#926—61no—
115C2×C4⋊Dic3—61no—
116C2×C4⋊Dic3—61no—
117C2×C4⋊Dic3—62no—
118#924—61no—
119#924—61no—
120#924—61no—
121#924—62no—
122#898—62no—
123#897—61no—
124#892—61no—
125#890—32no—
126#890—32no—
127#890—62no—
128#887—32no—
129#879—62no—
130#878—62no—
131#878—62no—
132#878—64no—
133C4×D12C2×D311yescharacteristic
134#869—31no—
135#869—31no—
136#869—61no—
137#869C2×D311yescharacteristic
138C4×Dic6—31no—
139C4×Dic6—31no—
140C4×Dic6—61no—
141C3×#107—31no—
142C3×C4⋊C8—31no—
143C3×#103—32no—
144C3×#102—31no—
145C3×#102—31no—
146C3×C4×C8—31no—
147#835—32no—
148#835—32no—
149#832—32no—
150#832C2×D311yescharacteristic
151#821—32no—
152#817—32no—
153#816—32no—
154#816—32no—
155Dic3⋊C8—32no—
156Dic3⋊C8—32no—
157C8×Dic3—32no—
158C8×Dic3—32no—
159#810C2×D312yes—
160#809C2×D311yescharacteristic
161#808—32no—
162#807C2×D311yescharacteristic
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C23×C32—21no—
166C22×C3×D3—21no—
167C32×D4—21no—
168C32×D4#4112yes—
169C2×C32×C4—21no—
170C2×C32×C4—42no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—22no—
175C2×C3⋊Dic3—82no—
176C2×C3⋊Dic3C2×D412yes—
177C2×C3⋊Dic3C2×D412yes—
178#634—22no—
179#634—81no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—22no—
182C3×D12—21no—
183C3×D12—21no—
184C3×C4×D3—42no—
185C3×Dic6—22no—
186C3×Dic6—22no—
187C3×C3⋊C8—21no—
188C3×C3⋊C8—22no—
189C3×C3⋊C8—21no—
190#556—91no—
191#554—91no—
192#488—92no—
193#487—91no—
194#479—92no—
195#476—91no—
196#463—92no—
197#461—31no—
198C8×Q8—91no—
199C4×SD16—92no—
200C4×D8—31no—
201C2×C3×Q8—32no—
202C2×C3×D4—21no—
203C2×C3×D4—31no—
204C2×C3×D4C22×D311yescharacteristic
205C2×C3×D4C22×D311yescharacteristic
206C22×C3×C4—22no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—61no—
210C22×Dic3—62no—
211C22×Dic3—62no—
212C22×Dic3—64no—
213C2×D12C22×D311yescharacteristic
214C2×C4×D3—21no—
215C2×Dic6—31no—
216C2×Dic6—31no—
217C2×Dic6—61no—
218C2×Dic6—62no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6C22×D312yes—
222C3×SD16—64no—
223C3×D8—62no—
224C2×C3×C8—31no—
225C2×C3×C8—32no—
226C2×C3×C8—31no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—61no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4C22×D311yescharacteristic
232C3×C4⋊C4C22×D311yescharacteristic
233C3×C22⋊C4—22no—
234C3×C22⋊C4—21no—
235C3×C22⋊C4—21no—
236C3×C22⋊C4—61no—
237C3×C42—21no—
238C3×C42C22×D311yescharacteristic
239C3×C42C22×D311yescharacteristic
240#217—62no—
241#217—62no—
242#217—62no—
243#217—62no—
244#217—64no—
245#214—24no—
246#213—22no—
247(C2×D3)⋊C4—21no—
248(C2×D3)⋊C4—62no—
249(C2×D3)⋊C4—62no—
250C4⋊Dic3—21no—
251C4⋊Dic3—21no—
252C4⋊Dic3—31no—
253C4⋊Dic3—31no—
254C4⋊Dic3—32no—
255C4⋊Dic3—32no—
256C4⋊Dic3—61no—
257C4⋊Dic3—62no—
258C4⋊Dic3—62no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3—62no—
262C4⋊Dic3—64no—
263C4⋊Dic3—61no—
264C4⋊Dic3—61no—
265C4⋊Dic3C22×D311yescharacteristic
266Dic3⋊C4—32no—
267Dic3⋊C4—32no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—64no—
273C4×Dic3—32no—
274C4×Dic3—32no—
275C4×Dic3—62no—
276C4×Dic3—62no—
277C4×Dic3—62no—
278C2×C3⋊C8C22×D311yescharacteristic
279C2×C3⋊C8C22×D311yescharacteristic
280C2×C3⋊C8C22×D312yes—
281C22×C32—22no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32C22×D411yescharacteristic
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C32×C4—21no—
289C32×C4—41no—
290C32×C4#13512yes—
291C32×C4C2×#4111yescharacteristic
292C32×C42−1+411yescharacteristic
293C3⋊Dic3—22no—
294C3⋊Dic3—22no—
295C3⋊Dic3—42no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C2×SD16—32no—
299C2×D8—31no—
300C4⋊Q8—31no—
301C4⋊Q8—91no—
302#126—182no—
303#125—92no—
304#124—92no—
305C22⋊Q8—182no—
306C22⋊Q8—181no—
307C22⋊Q8—181no—
308C4×Q8—91no—
309C4×Q8—92no—
310C4×D4—31no—
311C4×D4—92no—
312C4×D4D3211yescharacteristic
313#117—181no—
314C2×C4⋊C4—181no—
315#107—31no—
316#106—92no—
317C4⋊C8—31no—
318C4⋊C8—92no—
319#103—32no—
320#103—92no—
321#103—92no—
322#102—31no—
323#102—31no—
324#102—92no—
325C4×C8—31no—
326C4×C8—92no—
327C23×C3—22no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—61no—
331C22×D3—21no—
332C3×Q8—62no—
333C3×Q8—62no—
334C3×D4—22no—
335C3×D4—21no—
336C3×D4—21no—
337C3×D4—22no—
338C3×D4—61no—
339C3×D4—61no—
340C3×D4#23512yes—
341C3×D4#23712yes—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—44no—
349C2×C3×C4—42no—
350C2×C3×C4—42no—
351C2×C3×C4—61no—
352C2×C3×C4—62no—
353C2×C3×C4—122no—
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4C23×D311yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×Dic3—21no—
361C2×Dic3—22no—
362C2×Dic3—32no—
363C2×Dic3—32no—
364C2×Dic3—32no—
365C2×Dic3—32no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—64no—
369C2×Dic3—62no—
370C2×Dic3—62no—
371C2×Dic3—242no—
372C2×Dic3—242no—
373C2×Dic3—244no—
374D12—21no—
375D12—21no—
376C4×D3—42no—
377Dic6—22no—
378Dic6—22no—
379Dic6—62no—
380Dic6—62no—
381Dic6—122no—
382Dic6—241no—
383Dic6—241no—
384Dic6—242no—
385C3×C8—62no—
386C3×C8—61no—
387C3×C8—61no—
388C3⋊C8—21no—
389C3⋊C8—22no—
390C3⋊C8—21no—
391C2×C32—42no—
392C2×C32#54811yescharacteristic
393C2×C32C2×#13511yescharacteristic
394C2×C32#57711yescharacteristic
395C3×D3—81no—
396C2×Q8—32no—
397C2×Q8—91no—
398C2×Q8—181no—
399C2×D4—31no—
400C2×D4C2×D3211yescharacteristic
401C22×C4—21no—
402C22×C4—61no—
403C22×C4—182no—
404SD16—64no—
405D8—62no—
406C2×C8—31no—
407C2×C8—31no—
408C2×C8—32no—
409C4⋊C4—31no—
410C4⋊C4—61no—
411C4⋊C4—61no—
412C4⋊C4—91no—
413C4⋊C4—92no—
414C4⋊C4—92no—
415C4⋊C4—182no—
416C4⋊C4—182no—
417C4⋊C4—182no—
418C4⋊C4—181no—
419C4⋊C4C2×D3211yescharacteristic
420C22⋊C4—21no—
421C22⋊C4—61no—
422C22⋊C4—182no—
423C22⋊C4—182no—
424C22⋊C4—182no—
425C42—92no—
426C42—182no—
427C42C2×D3211yescharacteristic
428C22×C3—24no—
429C22×C3—22no—
430C22×C3—22no—
431C22×C3—21no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—121no—
439C22×C3—121no—
440C22×C3—121no—
441C22×C3C2×D3×D411yescharacteristic
442C22×C3C2×D3×D411yescharacteristic
443C2×D3—41no—
444C2×D3—41no—
445C2×D3—41no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—22no—
451C3×C4—41no—
452C3×C4—42no—
453C3×C4—41no—
454C3×C4—41no—
455C3×C4—121no—
456C3×C4—122no—
457C3×C4#91212yes—
458C3×C4#91612yes—
459C3×C4C2×#23511yescharacteristic
460C3×C4C2×#23711yescharacteristic
461C3×C4#101011yescharacteristic
462C3×C4#101011yescharacteristic
463Dic3—41no—
464Dic3—42no—
465Dic3—62no—
466Dic3—62no—
467Dic3—62no—
468Dic3—62no—
469Dic3—122no—
470Dic3—122no—
471Dic3—124no—
472Dic3—122no—
473Dic3—122no—
474C32#336011yescharacteristic, complemented, Sylow
475C23—21no—
476C23—61no—
477Q8—62no—
478Q8—62no—
479Q8—182no—
480Q8—721no—
481D4—21no—
482D4—61no—
483D4—61no—
484D4#379512yes—
485C2×C4—21no—
486C2×C4—42no—
487C2×C4—61no—
488C2×C4—62no—
489C2×C4—92no—
490C2×C4—92no—
491C2×C4—122no—
492C2×C4—182no—
493C2×C4—722no—
494C2×C4#381111yescharacteristic
495C2×C4#381111yescharacteristic
496C2×C4C22×D3211yescharacteristic
497C8—61no—
498C8—62no—
499C8—61no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—44no—
504C2×C3—42no—
505C2×C3—42no—
506C2×C3—241no—
507C2×C3#555211yescharacteristic
508C2×C3#559811yescharacteristic
509C2×C3C2×#91211yescharacteristic
510C2×C3C2×#91611yescharacteristic
511C2×C3#577011yescharacteristic
512C2×C3#577811yescharacteristic
513D3—81no—
514C22—22no—
515C22—41no—
516C22—41no—
517C22—121no—
518C22—121no—
519C22—121no—
520C22C2×#381111yescharacteristic
521C4—21no—
522C4—41no—
523C4—121no—
524C4—122no—
525C4—182no—
526C4—182no—
527C4—362no—
528C4#6393612yes—
529C4C2×#379511yescharacteristic
530C4#6429811yescharacteristic
531C3—21no—
532C3#7956811yescharacteristic, complemented
533C3#8041511yescharacteristic, complemented
534C2—42no—
535C2—241no—
536C2#1059491811yescharacteristic
537C2C2×#6393611yescharacteristic
538C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#213C22
hypercenterC4×D4D32
hypocenterC32#3360
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596014C2semidirect
2. #10593863C2semidirect
3. C3×#5019C2semidirect
6. #10591445C2semidirect
7. #10590539C2semidirect
8. #10590494C2semidirect
9. #10590287C2semidirect
10. #10590268C2semidirect
11. #10590254C2semidirect
54. #5019D3semidirect
474. C32#3360semidirect
532. C3#79568semidirect
533. C3#80415semidirect

Maximal subgroups

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

subgroupindex
#105960142
#105938632
C3×#50192
C3×C4×#2132
#105914762
#105914452
#105905392
#105904942
#105902872
#105902682
#105902542
#804153
#795683