Finite Group Databasebeta

← #11868990

Subgroups — #11868990

Order 1152.

855 conjugacy classes of subgroups.

The subgroup lattice has 541 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5521C211yesmaximal, characteristic
2#10595052C211yesmaximal, characteristic, complemented
3#10592694C211yesmaximal, characteristic, complemented
4C3×#4998C211yesmaximal, characteristic, complemented
5#10591116C211yesmaximal, characteristic, complemented
6#10591085C211yesmaximal, characteristic
7C2×#63563C211yesmaximal, characteristic
8#10590558C212yesmaximal, complemented
9#10590555C212yesmaximal, complemented
10#10590545C212yesmaximal, complemented
11#10590542C212yesmaximal, complemented
12#82539—31nomaximal
13#79197—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#893C2212yes—
22C3×#893C2212yes—
23C3×D3×C22⋊C4—22no—
24C3×C4×D12—21no—
25C3×C4×D12—21no—
26#63982—22no—
27#63918—21no—
28#63918C2212yescomplemented
29#63869—21no—
30#63869C2212yescomplemented
31#63635C2212yescomplemented
32#63634C2212yescomplemented
33C3×#808C2211yescharacteristic, complemented
34C3×#808C2211yescharacteristic, complemented
35C3×#807C2211yescharacteristic, complemented
36C3×#807C2211yescharacteristic, complemented
37Dic3⋊(C3⋊C8)C2212yescomplemented
38Dic3⋊(C3⋊C8)C2212yescomplemented
39#63563C2212yes—
40#63563C2212yes—
41#63562C2212yes—
42#63562C2212yes—
43C3×#518—31no—
44#5521D311yescharacteristic
45#5519—31no—
46#5519—31no—
47C3×#427—31no—
48#5215—31no—
49C2×#832—31no—
50C2×#821—31no—
51#5102—31no—
52#5009—32no—
53#5009—32no—
54#5008—32no—
55#5007—32no—
56#5001—31no—
57#4999—31no—
58#4998D311yescharacteristic, complemented
59#4995—31no—
60#4995—31no—
61#4995—61no—
62#4891—32no—
63#4890—32no—
64#4871—32no—
65#4870—32no—
66C23×C3×D3—21no—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3—21no—
69C2×C3×D12—21no—
70C2×C3×D12—22no—
71C2×C3×D12Q814yescomplemented
72C2×C3×D12C2312yes—
73C2×C3×C4×D3—22no—
74C2×C3×C4×D3—22no—
75C2×#627—22no—
76C32×C4⋊C4C2311yescharacteristic
77C32×C4⋊C4C2311yescharacteristic
78C32×C22⋊C4—21no—
79C32×C42—21no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)C2312yes—
82#3748—22no—
83C2×C3⋊(C3⋊C8)C2312yes—
84C3×#217—21no—
85C3×#217D412yes—
86C3×(C2×D3)⋊C4—22no—
87C3×(C2×D3)⋊C4—22no—
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×C4⋊Dic3C2311yescharacteristic
92C3×C4×Dic3—21no—
93C3×C4×Dic3C2312yes—
94C2×C3×C3⋊C8—22no—
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2311yescharacteristic
97#3724—22no—
98Dic3⋊Dic3—22no—
99Dic3⋊Dic3—22no—
100#3081—91noSylow
101C22×C3×D4—31no—
102C22×D12C2×D311yescharacteristic
103C22×C3×C8—31no—
104C3×C4×D4—32no—
105C3×C4×D4—32no—
106C3×C4×D4—61no—
107C3×C4×D4—61no—
108C3×#117—21no—
109C3×#117—31no—
110C3×#117—31no—
111C3×#117C2×D311yescharacteristic
112C3×#117C2×D311yescharacteristic
113C2×C3×C22⋊C4—62no—
114#926C2×D311yescharacteristic
115#926C2×D311yescharacteristic
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—61no—
119C2×#208—31no—
120C2×#208—31no—
121C2×#208—61no—
122C22×C3⋊C8C2×D311yescharacteristic
123#893C2×D312yes—
124#893C2×D312yes—
125#890—32no—
126#890—61no—
127#888—32no—
128#888—61no—
129D3×C22⋊C4—22no—
130#878—62no—
131#878—62no—
132C4×D12—21no—
133C4×D12—21no—
134#870—32no—
135#870—61no—
136#869—32no—
137#869—61no—
138C3×#107—31no—
139C3×#107—31no—
140C3×#106—31no—
141C3×#106—31no—
142#832—32no—
143#832—32no—
144#832—32no—
145#832—32no—
146#821—32no—
147#821—32no—
148Dic3⋊C8—32no—
149Dic3⋊C8—32no—
150#809—32no—
151#809—32no—
152#808—32no—
153#808—32no—
154#808—62no—
155#808C2×D311yescharacteristic, complemented
156#808C2×D311yescharacteristic, complemented
157#807—32no—
158#807—32no—
159#807—62no—
160#807C2×D311yescharacteristic, complemented
161#807C2×D311yescharacteristic, complemented
162C4⋊(C3⋊C8)—32no—
163C4⋊(C3⋊C8)—32no—
164C23×C32C2×D411yescharacteristic
165C22×C3×D3—22no—
166C22×C3×D3—24no—
167C22×C3×D3—81no—
168C22×C3×D3—81no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×Q812yes—
173C2×C32×C4#4112yes—
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—81no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—21no—
179C2×C3×Dic3C2×D412yes—
180C2×C3×Dic3C2×D412yes—
181C3×D12—24no—
182C3×D12—22no—
183C3×D12C2×Q814yes—
184C3×C4×D3—82no—
185C3×C4×D3—82no—
186#627—82no—
187C3⋊(C3⋊C8)—22no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8—21no—
190#544—91no—
191#518—31no—
192#478—92no—
193#478—92no—
194#476—92no—
195#474—92no—
196#428—91no—
197#427—31no—
198#424—91no—
199#418—91no—
200C2×#102—91no—
201C24×C3—61no—
202C23×D3—21no—
203C2×C3×D4—34no—
204C2×C3×D4—32no—
205C2×C3×D4—62no—
206C2×C3×D4—61no—
207C22×C3×C4—21no—
208C22×C3×C4—62no—
209C22×C3×C4—62no—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C22×Dic3—61no—
213C22×Dic3—61no—
214C22×Dic3—121no—
215C2×D12—22no—
216C2×D12—21no—
217C2×D12Dic614yescomplemented
218C2×D12C22×D312yes—
219C2×C4×D3—22no—
220C2×C4×D3—22no—
221C2×Dic6—62no—
222C2×Dic6—62no—
223C2×C3×C8—31no—
224C2×C3×C8—31no—
225C2×C3×C8—62no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—31no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4C22×D311yescharacteristic
233C3×C4⋊C4C22×D311yescharacteristic
234C3×C4⋊C4C22×D311yescharacteristic
235C3×C4⋊C4C22×D311yescharacteristic
236C3×C22⋊C4—21no—
237C3×C22⋊C4—21no—
238C3×C22⋊C4—32no—
239C3×C22⋊C4—41no—
240C3×C22⋊C4—62no—
241C3×C22⋊C4—62no—
242C3×C22⋊C4—61no—
243C3×C42—21no—
244C3×C42—21no—
245C3×C42—32no—
246C3×C42—41no—
247C3×C42—61no—
248#217—21no—
249#217#6712yes—
250(C2×D3)⋊C4—22no—
251(C2×D3)⋊C4—22no—
252C4⋊Dic3—32no—
253C4⋊Dic3—32no—
254C4⋊Dic3—62no—
255C4⋊Dic3—62no—
256C4⋊Dic3—61no—
257C4⋊Dic3—61no—
258C4⋊Dic3—62no—
259C4⋊Dic3—121no—
260C4⋊Dic3#6711yescharacteristic
261C4⋊Dic3#6711yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263C4⋊Dic3C22×D311yescharacteristic
264Dic3⋊C4—62no—
265Dic3⋊C4—62no—
266Dic3⋊C4—62no—
267Dic3⋊C4—62no—
268C4×Dic3—21no—
269C4×Dic3C22×D312yes—
270#208—64no—
271#208—62no—
272#208—62no—
273C2×C3⋊C8—22no—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8C22×D311yescharacteristic
278C2×C3⋊C8C22×D311yescharacteristic
279C22×C32—21no—
280C22×C32—21no—
281C22×C32C22⋊Q812yes—
282C22×C32C22×D411yescharacteristic
283C2×C3×D3—24no—
284C2×C3×D3—42no—
285C2×C3×D3—42no—
286C2×C3×D3—84no—
287C32×C4—41no—
288C32×C4—41no—
289C32×C4C22⋊Q812yes—
290C32×C4C22×Q811yescharacteristic
291C32×C4C2×#4111yescharacteristic
292C3⋊Dic3—42no—
293C3×Dic3—22no—
294C3×Dic3—22no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C22×D4—31no—
298C2×M16—91no—
299C22×C8—31no—
300C4⋊Q8—92no—
301C4⋊Q8—181no—
302#125—92no—
303#125—181no—
304C22⋊Q8—182no—
305C4×D4—32no—
306C4×D4—32no—
307C4×D4—61no—
308C4×D4—61no—
309#117—31no—
310#117—31no—
311#117D3211yescharacteristic
312C2×C4⋊C4—91no—
313C2×C22⋊C4—62no—
314#107—31no—
315#107—31no—
316#107—92no—
317#106—31no—
318#106—31no—
319#106—92no—
320C4⋊C8—92no—
321C4⋊C8—92no—
322#102—92no—
323#102—92no—
324#102—92no—
325#102—92no—
326C23×C3—21no—
327C23×C3—62no—
328C23×C3—64no—
329C23×C3—241no—
330C23×C3—241no—
331C23×C3D3×D411yescharacteristic
332C23×C3C2×#6711yescharacteristic
333C22×D3—22no—
334C22×D3—24no—
335C22×D3—81no—
336C22×D3—81no—
337C3×D4—34no—
338C3×D4—64no—
339C3×D4—62no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—21no—
344C2×C3×C4—21no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—41no—
351C2×C3×C4—41no—
352C2×C3×C4—61no—
353C2×C3×C4—61no—
354C2×C3×C4—242no—
355C2×C3×C4—242no—
356C2×C3×C4C2×Dic612yes—
357C2×C3×C4#23512yes—
358C2×C3×C4#23512yes—
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4D3×Q812yes—
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363C2×C3×C4C23×D311yescharacteristic
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—122no—
369C2×Dic3—241no—
370C2×Dic3—241no—
371C2×Dic3—242no—
372C2×Dic3C2×#6712yes—
373C2×Dic3C2×#6712yes—
374D12—24no—
375D12—22no—
376D12C2×Dic614yes—
377C4×D3—82no—
378C4×D3—82no—
379Dic6—242no—
380Dic6—242no—
381C3×C8—61no—
382C3×C8—61no—
383C3⋊C8—21no—
384C3⋊C8—21no—
385C3⋊C8—64no—
386C3⋊C8—62no—
387C3⋊C8—62no—
388C2×C32—22no—
389C2×C32C2×C22⋊Q811yescharacteristic
390C2×C32#57611yescharacteristic
391C2×C32#57711yescharacteristic
392C3×D3—44no—
393C24—61no—
394C2×Q8—182no—
395C2×D4—32no—
396C2×D4—34no—
397C2×D4—62no—
398C2×D4—61no—
399C22×C4—62no—
400C22×C4—62no—
401C22×C4—181no—
402C22×C4C2×D3211yescharacteristic
403M16—182no—
404C2×C8—31no—
405C2×C8—31no—
406C2×C8—62no—
407C2×C8—92no—
408C4⋊C4—31no—
409C4⋊C4—31no—
410C4⋊C4—31no—
411C4⋊C4—31no—
412C4⋊C4—92no—
413C4⋊C4—182no—
414C4⋊C4—182no—
415C4⋊C4—182no—
416C4⋊C4—181no—
417C4⋊C4C2×D3211yescharacteristic
418C4⋊C4C2×D3211yescharacteristic
419C22⋊C4—21no—
420C22⋊C4—32no—
421C22⋊C4—62no—
422C22⋊C4—62no—
423C22⋊C4—61no—
424C42—21no—
425C42—32no—
426C42—61no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—22no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—64no—
436C22×C3—122no—
437C22×C3—122no—
438C22×C3—244no—
439C22×C3#89612yes—
440C22×C3#92412yes—
441C22×C3C2×D3×D411yescharacteristic
442C22×C3C22×#6711yescharacteristic
443C2×D3—24no—
444C2×D3—42no—
445C2×D3—42no—
446C2×D3—84no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—41no—
451C3×C4—41no—
452C3×C4—41no—
453C3×C4—41no—
454C3×C4—62no—
455C3×C4—62no—
456C3×C4—81no—
457C3×C4—81no—
458C3×C4—121no—
459C3×C4—121no—
460C3×C4#89612yes—
461C3×C4#92412yes—
462C3×C4C22×Dic611yescharacteristic
463C3×C4C2×#23511yescharacteristic
464C3×C4C2×#23511yescharacteristic
465C3×C4C2×D3×Q811yescharacteristic
466Dic3—22no—
467Dic3—22no—
468Dic3—41no—
469Dic3—41no—
470Dic3—122no—
471Dic3—122no—
472Dic3—242no—
473C32#308111yescharacteristic, complemented, Sylow
474C23—62no—
475C23—64no—
476C23—241no—
477C23—241no—
478C23D3×#6711yescharacteristic
479Q8—722no—
480D4—34no—
481D4—62no—
482D4—64no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—32no—
486C2×C4—32no—
487C2×C4—61no—
488C2×C4—61no—
489C2×C4—182no—
490C2×C4—242no—
491C2×C4—242no—
492C2×C4—721no—
493C2×C4D3×Dic612yes—
494C2×C4#379812yes—
495C2×C4D3×#6711yescharacteristic
496C2×C4C22×D3211yescharacteristic
497C8—61no—
498C8—61no—
499C8—182no—
500C2×C3—22no—
501C2×C3—22no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—42no—
506C2×C3—124no—
507C2×C3C2×#89611yescharacteristic
508C2×C3#576911yescharacteristic
509C2×C3#577011yescharacteristic
510C2×C3C2×#92411yescharacteristic
511C2×C3#583511yescharacteristic
512C2×C3#583611yescharacteristic
513D3—44no—
514C22—21no—
515C22—21no—
516C22—64no—
517C22—122no—
518C22—122no—
519C22—244no—
520C22#6385112yes—
521C22C2×D3×#6711yescharacteristic
522C4—41no—
523C4—41no—
524C4—62no—
525C4—62no—
526C4—121no—
527C4—121no—
528C4—362no—
529C4#6385112yes—
530C4C2×D3×Dic611yescharacteristic
531C4C2×#379811yescharacteristic
532C3—21no—
533C3#7919711yescharacteristic, complemented
534C3#8253911yescharacteristic, complemented
535C2—22no—
536C2—124no—
537C2C2×#6385111yescharacteristic
538C2#1059545611yescharacteristic
539C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenter#117D32
hypocenterC32#3081
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10595052C2semidirect
3. #10592694C2semidirect
4. C3×#4998C2semidirect
5. #10591116C2semidirect
8. #10590558C2semidirect
9. #10590555C2semidirect
10. #10590545C2semidirect
11. #10590542C2semidirect
28. #63918C22semidirect
30. #63869C22semidirect
31. #63635C22semidirect
32. #63634C22semidirect
33. C3×#808C22semidirect
34. C3×#808C22semidirect
35. C3×#807C22semidirect
36. C3×#807C22semidirect
37. Dic3⋊(C3⋊C8)C22semidirect
38. Dic3⋊(C3⋊C8)C22semidirect
58. #4998D3semidirect
71. C2×C3×D12Q8semidirect
155. #808C2×D3semidirect
156. #808C2×D3semidirect
160. #807C2×D3semidirect
161. #807C2×D3semidirect
217. C2×D12Dic6semidirect
473. C32#3081semidirect
533. C3#79197semidirect
534. C3#82539semidirect

Maximal subgroups

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

subgroupindex
C3×#55212
#105950522
#105926942
C3×#49982
#105911162
#105910852
C2×#635632
#105905582
#105905552
#105905452
#105905422
#825393
#791973