Finite Group Databasebeta

← #11868977

Subgroups — #11868977

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×#5500C211yesmaximal, characteristic, complemented
2#10594982C211yesmaximal, characteristic
3#10592663C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic
5#10591122C211yesmaximal, characteristic, complemented
6#10591116C211yesmaximal, characteristic, complemented
7#10591085C211yesmaximal, characteristic
8#10590469C212yesmaximal, complemented
9#10590467C212yesmaximal, complemented
10#10590465C212yesmaximal, complemented
11#10590463C212yesmaximal, complemented
12#83474—31nomaximal
13#78731—31nomaximal
14C22×C3×D12C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16#64135C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C3×#924—22no—
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#890—21no—
23C3×#890C2212yescomplemented
24C3×#888—21no—
25C3×#888C2212yescomplemented
26D3×#217—22no—
27#63898—21no—
28#63898—21no—
29Dic3×D12C2212yes—
30Dic3×D12C2212yes—
31#63635C2212yescomplemented
32#63634C2212yescomplemented
33C3×#809C2212yes—
34C3×#809C2212yes—
35#63575C2211yescharacteristic, complemented
36#63575C2211yescharacteristic, complemented
37#63573C2211yescharacteristic, complemented
38#63573C2211yescharacteristic, complemented
39Dic3⋊(C3⋊C8)C2212yescomplemented
40Dic3⋊(C3⋊C8)C2212yescomplemented
41#63562C2212yes—
42#63562C2212yes—
43C3×#544—31no—
44#5798—31no—
45#5521—31no—
46#5500D311yescharacteristic, complemented
47C2×C3×#102—31no—
48#5215—31no—
49#5106—31no—
50#5102—31no—
51#5087—32no—
52#5084—32no—
53#5066—32no—
54#5066—32no—
55#5001—31no—
56#4999—31no—
57#4998—31no—
58C2×#809D311yescharacteristic
59#4964—31no—
60#4964—31no—
61#4964—61no—
62#4766—32no—
63#4763—32no—
64#4761—32no—
65#4759—32no—
66C23×C3×D3—21no—
67C22×C32×C4—21no—
68C22×C32×C4C2311yescharacteristic
69C2×C3×D12—21no—
70C2×C3×D12—22no—
71C2×C3×D12Q814yescomplemented
72C2×C3×D12C2312yes—
73C2×C3×Dic6—22no—
74C2×D3×Dic3—22no—
75C2×D3×Dic3—22no—
76C32×C4⋊C4—21no—
77C32×C4⋊C4C2312yes—
78#3757—21no—
79C4⋊(C3⋊Dic3)C2311yescharacteristic
80C4⋊(C3⋊Dic3)C2311yescharacteristic
81C4×C3⋊Dic3—21no—
82#3748—22no—
83C2×C3⋊(C3⋊C8)C2312yes—
84C3×#217—21no—
85C3×#217D412yes—
86C3×C4⋊Dic3—22no—
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3D411yescharacteristic
89C3×C4⋊Dic3C2311yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—22no—
93C3×C4×Dic3—21no—
94C3×C4×Dic3C2312yes—
95C2×C3×C3⋊C8—22no—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98(C2×D3)⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100#3081—91noSylow
101C22×C3×D4—31no—
102C22×D12C2×D311yescharacteristic
103C22×C3×C8—31no—
104C3×C4⋊Q8—32no—
105C3×C4⋊Q8—61no—
106C3×#125—32no—
107C3×#125—61no—
108C3×C22⋊Q8—62no—
109C3×#117—31no—
110C3×#117—31no—
111C2×C3×C4⋊C4—21no—
112C2×C3×C4⋊C4C2×D311yescharacteristic
113C2×C3×C4⋊C4C2×D311yescharacteristic
114C2×#217—62no—
115D4×Dic3—32no—
116D4×Dic3—32no—
117D4×Dic3—61no—
118D4×Dic3—61no—
119#926—31no—
120#926—31no—
121#926—61no—
122#926C2×D311yescharacteristic
123#926C2×D311yescharacteristic
124#924—22no—
125C2×#208—31no—
126C2×#208—31no—
127C2×#208—61no—
128C22×C3⋊C8C2×D311yescharacteristic
129#893—61no—
130#893—61no—
131#890—21no—
132#890C2×D312yescomplemented
133#888—21no—
134#888C2×D312yescomplemented
135D3×C22⋊C4—62no—
136C4×D12—32no—
137C4×D12—32no—
138C3×#102—32no—
139C3×#102—32no—
140#832—32no—
141#832—32no—
142#818—31no—
143#818—31no—
144#817—31no—
145#817—31no—
146Dic3⋊C8—32no—
147Dic3⋊C8—32no—
148#809—32no—
149#809—32no—
150#809C2×D312yes—
151#809C2×D312yes—
152#808—32no—
153#808—32no—
154#808—31no—
155#808—31no—
156#808—62no—
157#807—32no—
158#807—32no—
159#807—31no—
160#807—31no—
161#807—62no—
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—22no—
170C2×C32×C4—81no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×Q812yes—
173C2×C32×C4#4112yes—
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—21no—
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×Dic6—82no—
185D3×Dic3—82no—
186D3×Dic3—82no—
187C3⋊(C3⋊C8)—22no—
188C3×C3⋊C8—21no—
189C3×C3⋊C8—21no—
190#544—31no—
191#518—91no—
192#478—92no—
193#478—92no—
194#476—92no—
195#474—92no—
196#428—91no—
197#427—91no—
198#424—91no—
199#418—91no—
200C2×#102—31no—
201C24×C3—61no—
202C23×D3—21no—
203C2×C3×Q8—62no—
204C2×C3×D4—34no—
205C2×C3×D4—32no—
206C2×C3×D4—62no—
207C2×C3×D4—61no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—41no—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C22×Dic3—62no—
215C22×Dic3—62no—
216C2×D12—21no—
217C2×D12—22no—
218C2×D12Dic614yescomplemented
219C2×D12C22×D312yes—
220C2×C4×D3—62no—
221C2×C4×D3—62no—
222C2×Dic6—22no—
223C2×C3×C8—31no—
224C2×C3×C8—31no—
225C2×C3×C8—62no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—21no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—31no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—41no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—62no—
237C3×C4⋊C4C22×D312yes—
238C3×C4⋊C4C22×D312yes—
239C3×C22⋊C4—32no—
240C3×C22⋊C4—61no—
241C3×C42—32no—
242C3×C42—61no—
243#217—21no—
244#217—61no—
245#217—61no—
246#217—62no—
247#217—62no—
248#217—121no—
249#217#6712yes—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252C4⋊Dic3—22no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—31no—
256C4⋊Dic3—31no—
257C4⋊Dic3—61no—
258C4⋊Dic3—61no—
259C4⋊Dic3#6711yescharacteristic
260C4⋊Dic3#6711yescharacteristic
261C4⋊Dic3C22×D311yescharacteristic
262C4⋊Dic3C22×D311yescharacteristic
263Dic3⋊C4—22no—
264Dic3⋊C4—22no—
265C4×Dic3—21no—
266C4×Dic3—61no—
267C4×Dic3—61no—
268C4×Dic3—121no—
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—42no—
288C32×C4C22⋊Q812yes—
289C32×C4C22×Q811yescharacteristic
290C32×C4C2×#4111yescharacteristic
291C3⋊Dic3—41no—
292C3⋊Dic3—41no—
293C3×Dic3—22no—
294C3×Dic3—22no—
295C3×Dic3—41no—
296C3×Dic3—41no—
297C22×D4—31no—
298C2×M16—91no—
299C22×C8—31no—
300C4⋊Q8—32no—
301C4⋊Q8—61no—
302#125—32no—
303#125—61no—
304C22⋊Q8—62no—
305C4×D4—92no—
306C4×D4—92no—
307C4×D4—181no—
308C4×D4—181no—
309#117—31no—
310#117—31no—
311#117—91no—
312C2×C4⋊C4D3211yescharacteristic
313C2×C22⋊C4—182no—
314#107—91no—
315#107—91no—
316#107—92no—
317#106—91no—
318#106—91no—
319#106—92no—
320C4⋊C8—92no—
321C4⋊C8—92no—
322#102—32no—
323#102—32no—
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×Q8—242no—
338C3×D4—34no—
339C3×D4—64no—
340C3×D4—62no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—21no—
347C2×C3×C4—32no—
348C2×C3×C4—32no—
349C2×C3×C4—42no—
350C2×C3×C4—61no—
351C2×C3×C4—61no—
352C2×C3×C4—81no—
353C2×C3×C4—81no—
354C2×C3×C4—82no—
355C2×C3×C4C2×Dic612yes—
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4#23712yes—
358C2×C3×C4D3×Q812yes—
359C2×C3×C4#23912yes—
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C23×D311yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—61no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368C2×Dic3—61no—
369C2×Dic3—121no—
370C2×Dic3—121no—
371C2×Dic3—242no—
372C2×Dic3—242no—
373C2×Dic3C2×#6712yes—
374C2×Dic3C2×#6712yes—
375D12—24no—
376D12—22no—
377D12C2×Dic614yes—
378C4×D3—242no—
379C4×D3—242no—
380Dic6—82no—
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—62no—
395C2×D4—32no—
396C2×D4—34no—
397C2×D4—62no—
398C2×D4—61no—
399C22×C4—21no—
400C22×C4—182no—
401C22×C4—182no—
402C22×C4C2×D3211yescharacteristic
403M16—182no—
404C2×C8—31no—
405C2×C8—31no—
406C2×C8—62no—
407C2×C8—92no—
408C4⋊C4—21no—
409C4⋊C4—31no—
410C4⋊C4—31no—
411C4⋊C4—31no—
412C4⋊C4—31no—
413C4⋊C4—62no—
414C4⋊C4—62no—
415C4⋊C4—62no—
416C4⋊C4—91no—
417C4⋊C4—91no—
418C4⋊C4C2×D3212yes—
419C22⋊C4—32no—
420C22⋊C4—61no—
421C22⋊C4—182no—
422C22⋊C4—182no—
423C22⋊C4—181no—
424C42—32no—
425C42—61no—
426C42—181no—
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#87812yes—
440C22×C3#94612yes—
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—42no—
451C3×C4—42no—
452C3×C4—62no—
453C3×C4—62no—
454C3×C4—82no—
455C3×C4—121no—
456C3×C4—121no—
457C3×C4#87812yes—
458C3×C4#94612yes—
459C3×C4C22×Dic611yescharacteristic
460C3×C4C2×#23711yescharacteristic
461C3×C4C2×D3×Q811yescharacteristic
462C3×C4C2×#23911yescharacteristic
463Dic3—22no—
464Dic3—22no—
465Dic3—41no—
466Dic3—41no—
467Dic3—121no—
468Dic3—121no—
469Dic3—121no—
470Dic3—121no—
471Dic3—241no—
472Dic3—241no—
473C32#308111yescharacteristic, complemented, Sylow
474C23—62no—
475C23—64no—
476C23—241no—
477C23—241no—
478C23D3×#6711yescharacteristic
479Q8—242no—
480D4—34no—
481D4—62no—
482D4—64no—
483C2×C4—22no—
484C2×C4—32no—
485C2×C4—32no—
486C2×C4—61no—
487C2×C4—61no—
488C2×C4—81no—
489C2×C4—181no—
490C2×C4—181no—
491C2×C4—722no—
492C2×C4—722no—
493C2×C4D3×Dic612yes—
494C2×C4#379612yes—
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×#87811yescharacteristic
508C2×C3#575711yescharacteristic
509C2×C3#576211yescharacteristic
510C2×C3C2×#94611yescharacteristic
511C2×C3#583511yescharacteristic
512C2×C3#583711yescharacteristic
513D3—44no—
514C22—21no—
515C22—21no—
516C22—64no—
517C22—122no—
518C22—122no—
519C22—244no—
520C22#6388712yes—
521C22C2×D3×#6711yescharacteristic
522C4—42no—
523C4—62no—
524C4—62no—
525C4—121no—
526C4—121no—
527C4—361no—
528C4—361no—
529C4#6388712yes—
530C4C2×D3×Dic611yescharacteristic
531C4C2×#379611yescharacteristic
532C3—21no—
533C3#7873111yescharacteristic, complemented
534C3#8347411yescharacteristic, complemented
535C2—22no—
536C2—124no—
537C2C2×#6388711yescharacteristic
538C2#1059509611yescharacteristic
539C2#1059531811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC22×C3×D12C22
hypercenterC2×C4⋊C4D32
hypocenterC32#3081
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5500C2semidirect
3. #10592663C2semidirect
5. #10591122C2semidirect
6. #10591116C2semidirect
8. #10590469C2semidirect
9. #10590467C2semidirect
10. #10590465C2semidirect
11. #10590463C2semidirect
23. C3×#890C22semidirect
25. C3×#888C22semidirect
31. #63635C22semidirect
32. #63634C22semidirect
35. #63575C22semidirect
36. #63575C22semidirect
37. #63573C22semidirect
38. #63573C22semidirect
39. Dic3⋊(C3⋊C8)C22semidirect
40. Dic3⋊(C3⋊C8)C22semidirect
46. #5500D3semidirect
71. C2×C3×D12Q8semidirect
132. #890C2×D3semidirect
134. #888C2×D3semidirect
218. C2×D12Dic6semidirect
473. C32#3081semidirect
533. C3#78731semidirect
534. C3#83474semidirect

Maximal subgroups

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

subgroupindex
C3×#55002
#105949822
#105926632
C2×C3×#8092
#105911222
#105911162
#105910852
#105904692
#105904672
#105904652
#105904632
#834743
#787313