Finite Group Databasebeta

← #11895264

Subgroups — #11895264

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#10596201C211yesmaximal, characteristic, complemented
2#10593863C211yesmaximal, characteristic, complemented
3C3×#5093C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5#10590540C212yesmaximal
6#10590539C212yesmaximal, complemented
7#10590495C212yesmaximal, complemented
8#10590483C212yesmaximal, complemented
9#10590379C211yesmaximal, characteristic, complemented
10C4×#3714C211yesmaximal, characteristic
11#10590254C211yesmaximal, characteristic, complemented
12#81621—31nomaximal
13#81087—31nomaximal
14C32×C4⋊Q8C2211yescharacteristic
15#64155—22no—
16#64106—21no—
17#64102C2212yes—
18C4⋊C4×C3⋊D3—21no—
19#64099C2212yes—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×#634C2211yescharacteristic
22C3×C4×D12C2211yescharacteristic
23C3×#869C2211yescharacteristic
24#63863C2212yes—
25#63858—22no—
26#63857—21no—
27#63843C2212yes—
28#63841—21no—
29C2×#3717C2212yes—
30C2×#3714C2211yescharacteristic
31C3×#810C2212yes—
32C3×#810C2212yes—
33C3×#809C2212yes—
34C3×#808C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63575C2211yescharacteristic
38#63572C2212yes—
39#63566C2212yes—
40#63564C2211yescharacteristic
41#63563C2211yescharacteristic
42#63553C2212yes—
43#5732—31no—
44#5730—31no—
45#5730—31no—
46#5730—61no—
47#5542—31no—
48C3×#487—31no—
49C3×#476—31no—
50#5093D311yescharacteristic, complemented
51#5084D311yescharacteristic, complemented
52#5083—31no—
53C4×#213—31no—
54#4857—32no—
55#4852—32no—
56#4841—31no—
57#4830—31no—
58#4819—32no—
59#4800—32no—
60#4796—32no—
61#4788—32no—
62#4787—32no—
63#4768—32no—
64C4×D24—31no—
65C8×Dic6—31no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—22no—
70C2×#634D411yescharacteristic
71C2×C3×D12C2311yescharacteristic
72C2×C3×C4×D3—21no—
73C2×C3×Dic6C2312yes—
74C32×C4⋊C4—21no—
75C32×C4⋊C4C2312yes—
76C32×C42C2311yescharacteristic
77#3752—21no—
78#3752—22no—
79C4⋊(C3⋊Dic3)—22no—
80C4⋊(C3⋊Dic3)D411yescharacteristic
81C4⋊(C3⋊Dic3)C2311yescharacteristic
82#3750—22no—
83#3750D412yes—
84C4×C3⋊Dic3C2312yes—
85C3×(C2×D3)⋊C4—21no—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2311yescharacteristic
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2312yes—
91C2×C3×C3⋊C8C2311yescharacteristic
92Dic3⋊Dic3—22no—
93(C2×D3)⋊Dic3—22no—
94(C2×D3)⋊Dic3—22no—
95Dic32—22no—
96#3717—24no—
97#3714—22no—
98#3360—91noSylow
99C3×C4⋊Q8—21no—
100C3×C4⋊Q8—31no—
101C3×C4⋊Q8C2×D311yescharacteristic
102C3×C4⋊Q8C2×D311yescharacteristic
103C3×C4×D4—31no—
104#947—32no—
105#946—62no—
106#946—62no—
107#946—64no—
108Q8×Dic3—32no—
109C2×#215—32no—
110#936—32no—
111C2×#213—31no—
112#926—61no—
113#924—61no—
114C2×D24—31no—
115C2×#204—32no—
116#898—62no—
117#897—61no—
118#897—61no—
119#897—62no—
120#897—61no—
121#893—32no—
122#893—32no—
123#893—62no—
124#892—61no—
125D3×C4⋊C4—61no—
126D3×C4⋊C4—61no—
127D3×C4⋊C4—62no—
128#890—32no—
129#890—32no—
130#890—62no—
131#887—32no—
132#879—62no—
133C4×D12—31no—
134C4×D12—31no—
135C4×D12—61no—
136C4×D12C2×D311yescharacteristic
137#869C2×D311yescharacteristic
138C4×Dic6—31no—
139C4×Dic6—31no—
140C4×Dic6—61no—
141C3×#106—32no—
142C3×C4⋊C8—31no—
143C3×#103—32no—
144C3×#103—32no—
145C3×#102—32no—
146C3×C4×C8—31no—
147#835—32no—
148#832—31no—
149#821—31no—
150#821—31no—
151#818—31no—
152#816—32no—
153Dic3⋊C8—32no—
154Dic3⋊C8—32no—
155C8×Dic3—32no—
156C8×Dic3—32no—
157#810C2×D312yes—
158#810C2×D312yes—
159#809—31no—
160#809C2×D312yes—
161#808C2×D312yes—
162#807—31no—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164C4×C3⋊C8C2×D311yescharacteristic
165C22×C3⋊D3—21no—
166C22×C3×D3—21no—
167C32×Q8—81no—
168C2×C32×C4—22no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2411yescharacteristic
172C2×C3⋊Dic3—21no—
173C2×C3⋊Dic3C2×D412yes—
174C2×C3⋊Dic3C2×D412yes—
175C4⋊(C3⋊D3)—21no—
176C4⋊(C3⋊D3)#4112yes—
177C4×C3⋊D3—42no—
178C4×C3⋊D3—82no—
179#634—22no—
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—31no—
194#479—92no—
195#476—31no—
196#463—92no—
197#461—91no—
198C8×Q8—91no—
199C4×SD16—92no—
200C4×D8—91no—
201C2×C3×Q8—22no—
202C2×C3×Q8—21no—
203C2×C3×Q8—21no—
204C2×C3×Q8—32no—
205C2×C3×D4—31no—
206C22×C3×C4—61no—
207C2×D12—31no—
208C2×D12—31no—
209C2×D12—61no—
210C2×D12C22×D311yescharacteristic
211C2×C4×D3—21no—
212C2×C4×D3—62no—
213C2×C4×D3—61no—
214C2×C4×D3—61no—
215C2×C4×D3—62no—
216C2×C4×D3—62no—
217C2×C4×D3—64no—
218C2×Dic6—31no—
219C2×Dic6—31no—
220C2×Dic6—61no—
221C2×Dic6C22×D312yes—
222C2×C3×C8—31no—
223C2×C3×C8—32no—
224C2×C3×C8—31no—
225C3×C4⋊C4—22no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4—61no—
232C3×C4⋊C4C22×D312yes—
233C3×C4⋊C4C22×D312yes—
234C3×C22⋊C4—61no—
235C3×C42—21no—
236C3×C42C22×D311yescharacteristic
237C3×C42C22×D311yescharacteristic
238#217—62no—
239#217—62no—
240#215—64no—
241#213—62no—
242(C2×D3)⋊C4—21no—
243(C2×D3)⋊C4—62no—
244(C2×D3)⋊C4—62no—
245(C2×D3)⋊C4—62no—
246(C2×D3)⋊C4—62no—
247(C2×D3)⋊C4—62no—
248(C2×D3)⋊C4—64no—
249(C2×D3)⋊C4—61no—
250(C2×D3)⋊C4—61no—
251C4⋊Dic3—21no—
252C4⋊Dic3—21no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3—62no—
262C4⋊Dic3—64no—
263C4⋊Dic3C22×D311yescharacteristic
264Dic3⋊C4—32no—
265Dic3⋊C4—32no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4—62no—
270Dic3⋊C4—64no—
271C4×Dic3—32no—
272C4×Dic3—32no—
273C4×Dic3—62no—
274C4×Dic3—62no—
275C4×Dic3—62no—
276C2×C3⋊C8C22×D311yescharacteristic
277C2×C3⋊C8C22×D311yescharacteristic
278C2×C3⋊C8C22×D312yes—
279D24—62no—
280#204—64no—
281C22×C32C22×D411yescharacteristic
282C2×C3⋊D3—22no—
283C2×C3⋊D3—41no—
284C2×C3⋊D3—41no—
285C2×C3×D3—41no—
286C2×C3×D3—41no—
287C2×C3×D3—41no—
288C32×C4—21no—
289C32×C4—42no—
290C32×C4#13512yes—
291C32×C4C2×#4111yescharacteristic
292C32×C42−1+411yescharacteristic
293C3⋊Dic3—22no—
294C3⋊Dic3—22no—
295C3⋊Dic3—41no—
296C3×Dic3—42no—
297C3×Dic3—41no—
298C2×SD16—92no—
299C2×D8—91no—
300C4⋊Q8—31no—
301C4⋊Q8D3211yescharacteristic
302#126—182no—
303#125—92no—
304#124—92no—
305C22⋊Q8—181no—
306C22⋊Q8—181no—
307C22⋊Q8—182no—
308C4×Q8—91no—
309C4×Q8—92no—
310C4×D4—31no—
311C4×D4—92no—
312C4×D4—91no—
313#117—181no—
314C2×C4⋊C4—181no—
315#107—91no—
316#106—32no—
317C4⋊C8—31no—
318C4⋊C8—92no—
319#103—32no—
320#103—32no—
321#103—92no—
322#102—32no—
323#102—91no—
324#102—91no—
325C4×C8—31no—
326C4×C8—92no—
327C23×C3—61no—
328C22×D3—21no—
329C22×D3—62no—
330C22×D3—61no—
331C22×D3—61no—
332C3×Q8—62no—
333C3×Q8—62no—
334C3×Q8—81no—
335C3×Q8—81no—
336C3×Q8—82no—
337C3×D4—61no—
338C3×D4—61no—
339C2×C3×C4—24no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—61no—
346C2×C3×C4—62no—
347C2×C3×C4—122no—
348C2×C3×C4D3×D411yescharacteristic
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D411yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×Dic3—21no—
355C2×Dic3—22no—
356C2×Dic3—32no—
357C2×Dic3—32no—
358C2×Dic3—32no—
359C2×Dic3—32no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—61no—
364C2×Dic3—61no—
365D12—21no—
366D12—21no—
367D12—32no—
368D12—32no—
369D12—62no—
370D12—62no—
371D12—61no—
372D12—61no—
373C4×D3—42no—
374C4×D3—124no—
375C4×D3—122no—
376C4×D3—122no—
377C4×D3—242no—
378C4×D3—242no—
379C4×D3—244no—
380Dic6—22no—
381Dic6—22no—
382Dic6—62no—
383Dic6—62no—
384Dic6—122no—
385C3×C8—61no—
386C3×C8—62no—
387C3×C8—61no—
388C3⋊C8—21no—
389C3⋊C8—22no—
390C3⋊C8—21no—
391C2×C32#54811yescharacteristic
392C2×C32C2×#13511yescharacteristic
393C2×C32#57711yescharacteristic
394C3⋊D3—42no—
395C3×D3—81no—
396C2×Q8—21no—
397C2×Q8—32no—
398C2×Q8—91no—
399C2×D4—31no—
400C2×D4—91no—
401C22×C4—61no—
402C22×C4—182no—
403C22×C4—181no—
404SD16—184no—
405D8—182no—
406C2×C8—31no—
407C2×C8—31no—
408C2×C8—32no—
409C4⋊C4—21no—
410C4⋊C4—31no—
411C4⋊C4—61no—
412C4⋊C4—61no—
413C4⋊C4—91no—
414C4⋊C4—92no—
415C4⋊C4—91no—
416C4⋊C4—182no—
417C4⋊C4—182no—
418C4⋊C4—182no—
419C4⋊C4C2×D3212yes—
420C22⋊C4—61no—
421C22⋊C4—182no—
422C22⋊C4—182no—
423C22⋊C4—182no—
424C22⋊C4—181no—
425C42—92no—
426C42—182no—
427C42C2×D3211yescharacteristic
428C22×C3—21no—
429C22×C3—121no—
430C22×C3—121no—
431C22×C3—121no—
432C22×C3C2×D3×D411yescharacteristic
433C22×C3C2×D3×D411yescharacteristic
434C2×D3—41no—
435C2×D3—41no—
436C2×D3—41no—
437C2×D3—64no—
438C2×D3—62no—
439C2×D3—62no—
440C2×D3—122no—
441C2×D3—122no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—121no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—21no—
450C3×C4—22no—
451C3×C4—41no—
452C3×C4—44no—
453C3×C4—42no—
454C3×C4—42no—
455C3×C4—122no—
456C3×C4—121no—
457C3×C4#91612yes—
458C3×C4#91912yes—
459C3×C4#100711yescharacteristic
460C3×C4D3×#4111yescharacteristic
461C3×C4D3×#4111yescharacteristic
462C3×C4#101011yescharacteristic
463Dic3—42no—
464Dic3—41no—
465Dic3—62no—
466Dic3—62no—
467Dic3—62no—
468Dic3—62no—
469Dic3—122no—
470Dic3—122no—
471Dic3—122no—
472Dic3—121no—
473Dic3—121no—
474C32#336011yescharacteristic, complemented, Sylow
475C23—61no—
476C23—181no—
477Q8—62no—
478Q8—62no—
479Q8—81no—
480Q8—182no—
481D4—61no—
482D4—61no—
483D4—92no—
484D4—181no—
485C2×C4—22no—
486C2×C4—61no—
487C2×C4—62no—
488C2×C4—92no—
489C2×C4—92no—
490C2×C4—122no—
491C2×C4—181no—
492C2×C4—362no—
493C2×C4—722no—
494C2×C4#381111yescharacteristic
495C2×C4#381111yescharacteristic
496C2×C4C22×D3211yescharacteristic
497C8—61no—
498C8—61no—
499C8—62no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—241no—
504C2×C3#563311yescharacteristic
505C2×C3#567711yescharacteristic
506C2×C3C2×#91611yescharacteristic
507C2×C3#576211yescharacteristic
508C2×C3C2×#91911yescharacteristic
509C2×C3#577511yescharacteristic
510D3—81no—
511D3—124no—
512D3—122no—
513D3—122no—
514C22—121no—
515C22—121no—
516C22—121no—
517C22—182no—
518C22—361no—
519C22—361no—
520C22C2×#381111yescharacteristic
521C4—21no—
522C4—42no—
523C4—121no—
524C4—122no—
525C4—182no—
526C4—182no—
527C4—361no—
528C4#6395012yes—
529C4#6431511yescharacteristic
530C4#6431911yescharacteristic
531C3—21no—
532C3#8108711yescharacteristic, complemented
533C3#8162111yescharacteristic, complemented
534C2—241no—
535C2—362no—
536C2#1059511511yescharacteristic
537C2C2×#6395011yescharacteristic
538C2#1059536211yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×#3714C22
hypercenterC4⋊Q8D32
hypocenterC32#3360
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596201C2semidirect
2. #10593863C2semidirect
3. C3×#5093C2semidirect
4. C3×#5084C2semidirect
6. #10590539C2semidirect
7. #10590495C2semidirect
8. #10590483C2semidirect
9. #10590379C2semidirect
11. #10590254C2semidirect
50. #5093D3semidirect
51. #5084D3semidirect
474. C32#3360semidirect
532. C3#81087semidirect
533. C3#81621semidirect

Maximal subgroups

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

subgroupindex
#105962012
#105938632
C3×#50932
C3×#50842
#105905402
#105905392
#105904952
#105904832
#105903792
C4×#37142
#105902542
#816213
#810873