Finite Group Databasebeta

← #11868985

Subgroups — #11868985

Order 1152.

891 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5519C211yesmaximal, characteristic, complemented
2#10594996C211yesmaximal, characteristic
3#10592700C211yesmaximal, characteristic
4C3×#4998C211yesmaximal, characteristic, complemented
5#10591139C211yesmaximal, characteristic, complemented
6#10591116C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic
8#10590470C212yesmaximal, complemented
9#10590468C212yesmaximal, complemented
10#10590466C212yesmaximal, complemented
11#10590464C212yesmaximal, complemented
12#83474—31nomaximal
13#79197—31nomaximal
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C3×#926C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#890C2212yescomplemented
22C3×#888C2212yescomplemented
23C3×#878—22no—
24C3×#870—21no—
25C3×#869—21no—
26#63974—22no—
27#63894—21no—
28#63894—21no—
29#63894C2212yes—
30#63894C2212yes—
31#63636C2212yes—
32#63636C2212yes—
33C3×#808C2211yescharacteristic, complemented
34C3×#808C2211yescharacteristic, complemented
35C3×#807C2211yescharacteristic, complemented
36C3×#807C2211yescharacteristic, complemented
37#63576C2212yescomplemented
38#63574C2212yescomplemented
39Dic3⋊(C3⋊C8)C2212yescomplemented
40Dic3⋊(C3⋊C8)C2212yescomplemented
41#63564C2212yes—
42#63564C2212yes—
43C3×#544—31no—
44#5521—31no—
45#5521—31no—
46#5519D311yescharacteristic, complemented
47C3×#427—31no—
48C2×#821—31no—
49#5102—31no—
50#5087—32no—
51#5084—32no—
52#5066—32no—
53#5066—32no—
54#5001—31no—
55#5001—31no—
56#5001—61no—
57#4999—31no—
58#4998D311yescharacteristic, complemented
59#4995—31no—
60C2×#809—31no—
61#4964—31no—
62#4891—32no—
63#4890—32no—
64#4871—32no—
65#4870—32no—
66C23×C3⋊D3—21no—
67C22×C32×C4C2311yescharacteristic
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)—22no—
70C2×C4⋊(C3⋊D3)Q814yescomplemented
71C2×C4⋊(C3⋊D3)C2312yes—
72C22×C3×Dic3—21no—
73C2×C3×Dic6—22no—
74C2×#624—22no—
75C2×#624—22no—
76C32×C4⋊C4C2311yescharacteristic
77C32×C4⋊C4C2311yescharacteristic
78C32×C22⋊C4—21no—
79C32×C42—21no—
80#3748—22no—
81C2×C3⋊(C3⋊C8)C2312yes—
82C3×#217—21no—
83C3×#217D412yes—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—22no—
86C3×C4⋊Dic3D411yescharacteristic
87C3×C4⋊Dic3D411yescharacteristic
88C3×C4⋊Dic3C2312yes—
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#3722—22no—
99#3722—22no—
100#3081—91noSylow
101C22×D12—31no—
102C22×D12—31no—
103C22×D12—61no—
104C22×C3×C8—31no—
105C3×C4⋊Q8—32no—
106C3×C4⋊Q8—61no—
107C3×#125—32no—
108C3×#125—61no—
109C3×C22⋊Q8—62no—
110C3×#117—21no—
111C3×#117—31no—
112C3×#117—31no—
113C3×#117C2×D311yescharacteristic
114C3×#117C2×D311yescharacteristic
115C2×C3×C4⋊C4—31no—
116#926C2×D311yescharacteristic
117#926C2×D311yescharacteristic
118C2×C4⋊Dic3C2×D311yescharacteristic
119C2×#208—31no—
120C2×#208—31no—
121C2×#208—61no—
122C22×C3⋊C8C2×D311yescharacteristic
123#893—32no—
124#893—32no—
125#893—61no—
126#893—61no—
127#890C2×D312yescomplemented
128#888C2×D312yescomplemented
129D3×C22⋊C4—62no—
130D3×C22⋊C4—62no—
131#878—22no—
132C4×D12—32no—
133C4×D12—32no—
134C4×D12—61no—
135C4×D12—61no—
136#870—21no—
137#869—21no—
138C3×#107—31no—
139C3×#107—31no—
140C3×#106—31no—
141C3×#106—31no—
142#821—32no—
143#821—32no—
144Dic3⋊C8—32no—
145Dic3⋊C8—32no—
146#809—32no—
147#809—32no—
148#809—32no—
149#809—32no—
150#809—32no—
151#809—32no—
152#809—62no—
153#809—62no—
154#808—32no—
155#808—32no—
156#808C2×D311yescharacteristic, complemented
157#808C2×D311yescharacteristic, complemented
158#807—32no—
159#807—32no—
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
175C4⋊(C3⋊D3)—24no—
176C4⋊(C3⋊D3)—22no—
177C4⋊(C3⋊D3)C2×Q814yes—
178C2×C3×Dic3—21no—
179C2×C3×Dic3—21no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—81no—
182C2×C3×Dic3C2×D412yes—
183C2×C3×Dic3C2×D412yes—
184C3×Dic6—82no—
185#624—82no—
186#624—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—31no—
198#424—91no—
199#418—91no—
200C2×#102—91no—
201C23×D3—61no—
202C23×D3—61no—
203C23×D3—121no—
204C2×C3×Q8—62no—
205C22×C3×C4—21no—
206C22×C3×C4—61no—
207C22×C3×C4C22×D311yescharacteristic
208C22×C3×C4C22×D311yescharacteristic
209C22×Dic3—21no—
210C2×D12—34no—
211C2×D12—34no—
212C2×D12—32no—
213C2×D12—32no—
214C2×D12—62no—
215C2×D12—64no—
216C2×D12—62no—
217C2×D12—61no—
218C2×D12—62no—
219C2×D12—61no—
220C2×D12—122no—
221C2×D12—121no—
222C2×C4×D3—62no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×C4×D3—62no—
226C2×Dic6—22no—
227C2×C3×C8—31no—
228C2×C3×C8—31no—
229C2×C3×C8—62no—
230C3×C4⋊C4—21no—
231C3×C4⋊C4—21no—
232C3×C4⋊C4—31no—
233C3×C4⋊C4—31no—
234C3×C4⋊C4—31no—
235C3×C4⋊C4—32no—
236C3×C4⋊C4—31no—
237C3×C4⋊C4—62no—
238C3×C4⋊C4—62no—
239C3×C4⋊C4—62no—
240C3×C4⋊C4—61no—
241C3×C4⋊C4C22×D311yescharacteristic
242C3×C4⋊C4C22×D311yescharacteristic
243C3×C4⋊C4C22×D311yescharacteristic
244C3×C4⋊C4C22×D311yescharacteristic
245C3×C22⋊C4—21no—
246C3×C22⋊C4—21no—
247C3×C22⋊C4—32no—
248C3×C22⋊C4—41no—
249C3×C22⋊C4—61no—
250C3×C42—21no—
251C3×C42—21no—
252C3×C42—32no—
253C3×C42—41no—
254C3×C42—61no—
255#217—21no—
256#217#6712yes—
257(C2×D3)⋊C4—62no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—62no—
261C4⋊Dic3—21no—
262C4⋊Dic3—22no—
263C4⋊Dic3#6711yescharacteristic
264C4⋊Dic3#6711yescharacteristic
265C4⋊Dic3C22×D311yescharacteristic
266C4⋊Dic3C22×D312yes—
267C4⋊Dic3C22×D311yescharacteristic
268Dic3⋊C4—22no—
269Dic3⋊C4—22no—
270C4×Dic3—21no—
271C4×Dic3C22×D312yes—
272#208—62no—
273#208—62no—
274#208—122no—
275C2×C3⋊C8—22no—
276C2×C3⋊C8—32no—
277C2×C3⋊C8—32no—
278C2×C3⋊C8—62no—
279C2×C3⋊C8C22×D311yescharacteristic
280C2×C3⋊C8C22×D311yescharacteristic
281C22×C32—21no—
282C22×C32—21no—
283C22×C32C22⋊Q812yes—
284C22×C32C22×D411yescharacteristic
285C2×C3⋊D3—24no—
286C2×C3⋊D3—42no—
287C2×C3⋊D3—42no—
288C2×C3⋊D3—84no—
289C32×C4—41no—
290C32×C4—41no—
291C32×C4C22⋊Q812yes—
292C32×C4C22×Q811yescharacteristic
293C32×C4C2×#4111yescharacteristic
294C3×Dic3—22no—
295C3×Dic3—22no—
296C3×Dic3—41no—
297C3×Dic3—42no—
298C3×Dic3—41no—
299C22×D4—91no—
300C2×M16—91no—
301C22×C8—31no—
302C4⋊Q8—32no—
303C4⋊Q8—61no—
304#125—32no—
305#125—61no—
306C22⋊Q8—62no—
307C4×D4—92no—
308C4×D4—92no—
309C4×D4—181no—
310C4×D4—181no—
311#117—31no—
312#117—31no—
313#117D3211yescharacteristic
314C2×C4⋊C4—31no—
315C2×C22⋊C4—182no—
316#107—31no—
317#107—31no—
318#107—92no—
319#106—31no—
320#106—31no—
321#106—92no—
322C4⋊C8—92no—
323C4⋊C8—92no—
324#102—92no—
325#102—92no—
326#102—92no—
327#102—92no—
328C23×C3—21no—
329C23×C3D3×D411yescharacteristic
330C23×C3C2×#6711yescharacteristic
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—64no—
334C22×D3—64no—
335C22×D3—122no—
336C22×D3—124no—
337C22×D3—241no—
338C22×D3—241no—
339C22×D3—241no—
340C22×D3—241no—
341C22×D3—242no—
342C22×D3—242no—
343C3×Q8—242no—
344C2×C3×C4—21no—
345C2×C3×C4—21no—
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—32no—
353C2×C3×C4—32no—
354C2×C3×C4—41no—
355C2×C3×C4—41no—
356C2×C3×C4—62no—
357C2×C3×C4—61no—
358C2×C3×C4—61no—
359C2×C3×C4—241no—
360C2×C3×C4#23512yes—
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×Q812yes—
363C2×C3×C4D3×Q812yes—
364C2×C3×C4#23912yes—
365C2×C3×C4C2×#6711yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367C2×C3×C4C23×D311yescharacteristic
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—22no—
371C2×Dic3—81no—
372C2×Dic3C2×#6712yes—
373C2×Dic3C2×#6712yes—
374D12—34no—
375D12—34no—
376D12—64no—
377D12—64no—
378D12—64no—
379D12—62no—
380D12—62no—
381D12—122no—
382D12—124no—
383C4×D3—242no—
384C4×D3—242no—
385C4×D3—242no—
386C4×D3—242no—
387Dic6—82no—
388C3×C8—61no—
389C3×C8—61no—
390C3⋊C8—21no—
391C3⋊C8—21no—
392C3⋊C8—62no—
393C3⋊C8—62no—
394C3⋊C8—122no—
395C2×C32—22no—
396C2×C32C2×C22⋊Q811yescharacteristic
397C2×C32#57611yescharacteristic
398C2×C32#57711yescharacteristic
399C3⋊D3—44no—
400C24—181no—
401C2×Q8—62no—
402C2×D4—92no—
403C2×D4—94no—
404C2×D4—182no—
405C2×D4—181no—
406C22×C4—61no—
407C22×C4—182no—
408C22×C4—182no—
409C22×C4C2×D3211yescharacteristic
410M16—182no—
411C2×C8—31no—
412C2×C8—31no—
413C2×C8—62no—
414C2×C8—92no—
415C4⋊C4—31no—
416C4⋊C4—31no—
417C4⋊C4—32no—
418C4⋊C4—31no—
419C4⋊C4—31no—
420C4⋊C4—62no—
421C4⋊C4—62no—
422C4⋊C4—62no—
423C4⋊C4—61no—
424C4⋊C4C2×D3211yescharacteristic
425C4⋊C4C2×D3211yescharacteristic
426C22⋊C4—21no—
427C22⋊C4—32no—
428C22⋊C4—61no—
429C22⋊C4—182no—
430C22⋊C4—182no—
431C42—21no—
432C42—32no—
433C42—61no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—22no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3#89612yes—
443C22×C3#94612yes—
444C22×C3C2×D3×D411yescharacteristic
445C22×C3C22×#6711yescharacteristic
446C2×D3—64no—
447C2×D3—64no—
448C2×D3—124no—
449C2×D3—122no—
450C2×D3—122no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—242no—
454C2×D3—242no—
455C2×D3—244no—
456C2×D3—244no—
457C2×D3—248no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4—22no—
461C3×C4—41no—
462C3×C4—41no—
463C3×C4—41no—
464C3×C4—41no—
465C3×C4—62no—
466C3×C4—62no—
467C3×C4—81no—
468C3×C4—81no—
469C3×C4—122no—
470C3×C4—121no—
471C3×C4—121no—
472C3×C4#89612yes—
473C3×C4#94612yes—
474C3×C4C2×#23511yescharacteristic
475C3×C4C2×D3×Q811yescharacteristic
476C3×C4C2×D3×Q811yescharacteristic
477C3×C4C2×#23911yescharacteristic
478Dic3—22no—
479Dic3—22no—
480Dic3—41no—
481Dic3—41no—
482Dic3—42no—
483C32#308111yescharacteristic, complemented, Sylow
484C23—182no—
485C23—184no—
486C23—721no—
487C23—721no—
488C23D3×#6711yescharacteristic
489Q8—242no—
490D4—94no—
491D4—182no—
492D4—184no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—32no—
496C2×C4—32no—
497C2×C4—61no—
498C2×C4—61no—
499C2×C4—62no—
500C2×C4—241no—
501C2×C4—722no—
502C2×C4—722no—
503C2×C4#379712yes—
504C2×C4#379912yes—
505C2×C4D3×#6711yescharacteristic
506C2×C4C22×D3211yescharacteristic
507C8—61no—
508C8—61no—
509C8—182no—
510C2×C3—22no—
511C2×C3—22no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—42no—
516C2×C3C2×#89611yescharacteristic
517C2×C3#576911yescharacteristic
518C2×C3#577011yescharacteristic
519C2×C3C2×#94611yescharacteristic
520C2×C3#583511yescharacteristic
521C2×C3#583711yescharacteristic
522D3—124no—
523D3—124no—
524D3—244no—
525C22—21no—
526C22—21no—
527C22—184no—
528C22—362no—
529C22—362no—
530C22—724no—
531C22#6388812yes—
532C22C2×D3×#6711yescharacteristic
533C4—41no—
534C4—41no—
535C4—62no—
536C4—62no—
537C4—122no—
538C4—121no—
539C4—121no—
540C4#6388812yes—
541C4C2×#379711yescharacteristic
542C4C2×#379911yescharacteristic
543C3—21no—
544C3#7919711yescharacteristic, complemented
545C3#8347411yescharacteristic, complemented
546C2—22no—
547C2—364no—
548C2C2×#6388811yescharacteristic
549C2#1059545611yescharacteristic
550C2#1059545711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
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
1. C3×#5519C2semidirect
4. C3×#4998C2semidirect
5. #10591139C2semidirect
6. #10591116C2semidirect
8. #10590470C2semidirect
9. #10590468C2semidirect
10. #10590466C2semidirect
11. #10590464C2semidirect
21. C3×#890C22semidirect
22. C3×#888C22semidirect
33. C3×#808C22semidirect
34. C3×#808C22semidirect
35. C3×#807C22semidirect
36. C3×#807C22semidirect
37. #63576C22semidirect
38. #63574C22semidirect
39. Dic3⋊(C3⋊C8)C22semidirect
40. Dic3⋊(C3⋊C8)C22semidirect
46. #5519D3semidirect
58. #4998D3semidirect
70. C2×C4⋊(C3⋊D3)Q8semidirect
127. #890C2×D3semidirect
128. #888C2×D3semidirect
156. #808C2×D3semidirect
157. #808C2×D3semidirect
160. #807C2×D3semidirect
161. #807C2×D3semidirect
483. C32#3081semidirect
544. C3#79197semidirect
545. C3#83474semidirect

Maximal subgroups

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

subgroupindex
C3×#55192
#105949962
#105927002
C3×#49982
#105911392
#105911162
C2×#635642
#105904702
#105904682
#105904662
#105904642
#834743
#791973