Finite Group Databasebeta

← #11895968

Subgroups — #11895968

Order 1152.

811 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5577C211yesmaximal, characteristic
2C3×#5567C211yesmaximal, characteristic, complemented
3#10592723C211yesmaximal, characteristic, complemented
4#10590364C212yesmaximal, complemented
5#10590364C211yesmaximal, characteristic, complemented
6#10590358C212yesmaximal, complemented
7C4×#3715C211yesmaximal, characteristic, complemented
8#10590279C212yesmaximal, complemented
9#10590277C211yesmaximal, characteristic, complemented
10#10590270C212yesmaximal, complemented
11#10590269C211yesmaximal, characteristic, complemented
12#83690—31nomaximal
13#83587—31nomaximal
14C2×C3×#239—21no—
15C32×C4×Q8C2211yescharacteristic
16C3×#944—21no—
17C3×#895—21no—
18C3×#895—22no—
19C3×#889—22no—
20C3×#887—21no—
21C3×#874C2211yescharacteristic
22C3×#874C2212yes—
23C3×C4×D12C2211yescharacteristic
24C3×C4×D12C2212yes—
25C3×#870C2212yes—
26C3×#869C2211yescharacteristic
27C3×C4×Dic6C2211yescharacteristic
28C3×C4×Dic6C2212yes—
29C2×#3715C2211yescharacteristic
30C2×#3715C2212yes—
31C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
32C4⋊(C3⋊(C3⋊C8))C2212yes—
33#63630C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35#63576C2212yes—
36#63574C2211yescharacteristic
37#63565C2211yescharacteristic
38#63562C2212yes—
39#63562C2212yes—
40#63562C2212yes—
41#63562C2212yes—
42#63562C2211yescharacteristic
43C3×#557—31no—
44C3×#550—31no—
45#5577D311yescharacteristic
46#5567D311yescharacteristic, complemented
47#5088—31no—
48#5087—31no—
49#5075—31no—
50#5075—32no—
51#5071—32no—
52#5070—31no—
53#5067—32no—
54#5066—32no—
55#5027—32no—
56#5027—31no—
57#5026—32no—
58C4×#215—31no—
59#5024—31no—
60#5024—31no—
61#5024—61no—
62#5018—32no—
63C4×#214—31no—
64#5009—32no—
65#5007—31no—
66C2×C32×Q8D411yescharacteristic
67C3×#239—44no—
68C2×C3×D12—22no—
69C2×C3×D12—21no—
70C2×C3×D12—22no—
71C2×C3×D12—21no—
72C2×C3×D12C2311yescharacteristic
73C2×C3×D12C2312yes—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—21no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6C2311yescharacteristic
78C32×C4⋊C4D411yescharacteristic
79C32×C4⋊C4D412yes—
80C32×C42C2311yescharacteristic
81C32×C42C2312yes—
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×(C2×D3)⋊C4—22no—
86C3×(C2×D3)⋊C4—21no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2311yescharacteristic
89C3×C4⋊Dic3C2312yes—
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—22no—
92C3×Dic3⋊C4—21no—
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4—22no—
95C3×C4×Dic3—22no—
96C3×C4×Dic3—21no—
97#3715—22no—
98#3715—24no—
99#3368—91noSylow
100C2×C3×#41—61no—
101C2×#239—21no—
102C3×C4⋊Q8—31no—
103C3×C4⋊Q8—61no—
104C3×#127—31no—
105C3×#127—32no—
106C3×#125—32no—
107C3×#125—62no—
108C3×#121—61no—
109C3×#121—62no—
110C3×C4×Q8—21no—
111C3×C4×Q8—31no—
112C3×C4×Q8—32no—
113C3×C4×Q8—61no—
114C3×C4×Q8C2×D311yescharacteristic
115C3×C4×Q8C2×D311yescharacteristic
116C3×C4×D4—31no—
117C3×C4×D4—32no—
118#944—21no—
119C2×#215—31no—
120C2×#215—32no—
121C2×#214—31no—
122C2×#214—32no—
123#895—21no—
124#895—22no—
125#889—22no—
126#887—21no—
127#874C2×D312yes—
128#874C2×D311yescharacteristic
129C4×D12C2×D311yescharacteristic
130C4×D12C2×D312yes—
131#870C2×D312yes—
132#869C2×D311yescharacteristic
133C4×Dic6C2×D311yescharacteristic
134C4×Dic6C2×D312yes—
135#835—31no—
136#832—32no—
137#832—32no—
138#832—32no—
139#832—31no—
140#832—32no—
141#810—31no—
142#809—31no—
143#809—32no—
144#809—32no—
145#809—32no—
146#809—32no—
147#808—31no—
148#808—31no—
149#807—32no—
150#807—32no—
151C4⋊(C3⋊C8)—31no—
152C4⋊(C3⋊C8)—32no—
153C4⋊(C3⋊C8)—32no—
154C4⋊(C3⋊C8)—31no—
155C4⋊(C3⋊C8)—61no—
156C4⋊(C3⋊C8)—62no—
157#803—32no—
158#803—32no—
159#803—62no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—31no—
162C4×C3⋊C8—61no—
163C22×C3×D3—22no—
164C22×C3×D3—21no—
165C32×Q8—22no—
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2×D412yes—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C3×D12—21no—
176C3×D12—22no—
177C3×D12—21no—
178C3×D12—22no—
179C3×D12—44no—
180C3×D12—42no—
181C3×D12—82no—
182C3×D12—81no—
183C3×C4×D3—44no—
184C3×C4×D3—42no—
185C3×Dic6—21no—
186C3×Dic6—42no—
187C3×Dic6#4112yescomplemented
188C3⋊(C3⋊C8)—21no—
189C3⋊(C3⋊C8)—21no—
190C3⋊(C3⋊C8)—22no—
191#557—31no—
192#550—31no—
193#490—92no—
194#486—91no—
195#478—92no—
196#474—91no—
197#460—92no—
198#460—91no—
199#446—91no—
200#440—92no—
201C4×SD16—91no—
202C3×#41—124no—
203C2×C3×Q8—21no—
204C2×C3×Q8—31no—
205C2×C3×Q8—61no—
206C2×C3×Q8#6711yescharacteristic
207C2×C3×Q8#6711yescharacteristic
208C2×C3×D4—31no—
209C2×C3×D4—32no—
210C2×C3×D4—62no—
211C2×C3×D4—61no—
212C2×C3×D4—62no—
213C2×C3×D4—61no—
214C22×C3×C4—62no—
215C22×C3×C4—61no—
216#239—44no—
217C2×D12—22no—
218C2×D12—21no—
219C2×D12—22no—
220C2×D12—21no—
221C2×D12C22×D311yescharacteristic
222C2×D12C22×D312yes—
223C2×C4×D3—22no—
224C2×C4×D3—21no—
225C2×Dic6—21no—
226C2×Dic6C22×D311yescharacteristic
227C3×C4⋊C4—21no—
228C3×C4⋊C4—22no—
229C3×C4⋊C4—31no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—31no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4—62no—
234C3×C4⋊C4—62no—
235C3×C4⋊C4—62no—
236C3×C4⋊C4—61no—
237C3×C4⋊C4#6711yescharacteristic
238C3×C4⋊C4#6712yes—
239C3×C4⋊C4#6711yescharacteristic
240C3×C4⋊C4#6712yes—
241C3×C22⋊C4—62no—
242C3×C22⋊C4—61no—
243C3×C42—21no—
244C3×C42—22no—
245C3×C42—62no—
246C3×C42—61no—
247C3×C42C22×D311yescharacteristic
248C3×C42C22×D311yescharacteristic
249C3×C42C22×D312yes—
250C3×C42C22×D312yes—
251#215—62no—
252#215—64no—
253#214—62no—
254#214—64no—
255(C2×D3)⋊C4—22no—
256(C2×D3)⋊C4—21no—
257C4⋊Dic3—21no—
258C4⋊Dic3C22×D311yescharacteristic
259C4⋊Dic3C22×D312yes—
260C4⋊Dic3C22×D311yescharacteristic
261Dic3⋊C4—21no—
262Dic3⋊C4—22no—
263Dic3⋊C4—22no—
264Dic3⋊C4—22no—
265C4×Dic3—22no—
266C4×Dic3—21no—
267C2×C3⋊C8—31no—
268C2×C3⋊C8—31no—
269C2×C3⋊C8—31no—
270C2×C3⋊C8—31no—
271C2×C3⋊C8—32no—
272C2×C3⋊C8—32no—
273C2×C3⋊C8—61no—
274C2×C3⋊C8—61no—
275C2×C3⋊C8—62no—
276C22×C32C22×D411yescharacteristic
277C2×C3×D3—42no—
278C2×C3×D3—41no—
279C2×C3×D3—42no—
280C2×C3×D3—41no—
281C2×C3×D3—42no—
282C2×C3×D3—41no—
283C32×C4—22no—
284C32×C4—22no—
285C32×C4—21no—
286C32×C4AGL(1,ℤ/8)12yes—
287C32×C4C2×#4111yescharacteristic
288C32×C42−1+411yescharacteristic
289C3×Dic3—22no—
290C3×Dic3—42no—
291C3×Dic3—41no—
292C3×Dic3—41no—
293C2×#41—61no—
294C2×SD16—91no—
295C2×SD16—92no—
296C4⋊Q8—31no—
297C4⋊Q8—61no—
298#127—31no—
299#127—32no—
300#125—32no—
301#125—62no—
302#121—61no—
303#121—62no—
304C4×Q8—31no—
305C4×Q8—32no—
306C4×Q8—61no—
307C4×Q8D3211yescharacteristic
308C4×D4—31no—
309C4×D4—32no—
310#107—92no—
311#106—91no—
312C4⋊C8—91no—
313C4⋊C8—92no—
314#103—91no—
315#102—91no—
316#102—92no—
317#102—92no—
318#102—92no—
319#102—92no—
320#97—92no—
321C4×C8—91no—
322C23×C3—62no—
323C23×C3—61no—
324C22×D3—22no—
325C22×D3—21no—
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—32no—
329C3×Q8—42no—
330C3×Q8—61no—
331C3×Q8—122no—
332C3×D4—61no—
333C3×D4—62no—
334C3×D4—61no—
335C3×D4—62no—
336C3×D4—124no—
337C3×D4—122no—
338C3×D4—242no—
339C3×D4—241no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—22no—
345C2×C3×C4—61no—
346C2×C3×C4—61no—
347C2×C3×C4—62no—
348C2×C3×C4—61no—
349C2×C3×C4—124no—
350C2×C3×C4—122no—
351C2×C3×C4C2×#6712yes—
352C2×C3×C4C2×#6712yes—
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C2×#6712yes—
355C2×C3×C4C2×#6711yescharacteristic
356C2×C3×C4C2×#6712yes—
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359C2×C3×C4C23×D311yescharacteristic
360C2×C3×C4C23×D311yescharacteristic
361C2×Dic3—21no—
362C2×Dic3—21no—
363C2×Dic3—22no—
364C2×Dic3—21no—
365D12—21no—
366D12—22no—
367D12—21no—
368D12—22no—
369D12—44no—
370D12—42no—
371D12—82no—
372D12—81no—
373C4×D3—44no—
374C4×D3—42no—
375Dic6—21no—
376Dic6—42no—
377Dic6#23912yescomplemented
378C3⋊C8—62no—
379C3⋊C8—61no—
380C3⋊C8—62no—
381C3⋊C8—61no—
382C3⋊C8—61no—
383C3⋊C8—62no—
384C3⋊C8—61no—
385C3⋊C8—121no—
386C3⋊C8—122no—
387C2×C32#54811yescharacteristic
388C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
389C2×C32#57711yescharacteristic
390C3×D3—82no—
391C3×D3—81no—
392#41—124no—
393C2×Q8—31no—
394C2×Q8—61no—
395C2×Q8#62511yescharacteristic
396C2×D4—31no—
397C2×D4—32no—
398C2×D4—62no—
399C2×D4—61no—
400C2×D4—62no—
401C2×D4—61no—
402C22×C4—62no—
403C22×C4—61no—
404SD16—182no—
405SD16—184no—
406C2×C8—91no—
407C2×C8—91no—
408C2×C8—92no—
409C4⋊C4—31no—
410C4⋊C4—32no—
411C4⋊C4—31no—
412C4⋊C4—61no—
413C4⋊C4—62no—
414C4⋊C4—62no—
415C4⋊C4—62no—
416C4⋊C4—61no—
417C4⋊C4#62511yescharacteristic
418C4⋊C4#62512yes—
419C22⋊C4—62no—
420C22⋊C4—61no—
421C42—62no—
422C42—61no—
423C42C2×D3211yescharacteristic
424C42C2×D3212yes—
425C22×C3—21no—
426C22×C3—122no—
427C22×C3—121no—
428C22×C3—122no—
429C22×C3—121no—
430C22×C3—122no—
431C22×C3—121no—
432C22×C3C22×#6711yescharacteristic
433C22×C3C22×#6711yescharacteristic
434C2×D3—42no—
435C2×D3—41no—
436C2×D3—42no—
437C2×D3—41no—
438C2×D3—42no—
439C2×D3—41no—
440C3×C4—22no—
441C3×C4—22no—
442C3×C4—22no—
443C3×C4—21no—
444C3×C4—22no—
445C3×C4—21no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—22no—
449C3×C4—42no—
450C3×C4—42no—
451C3×C4—41no—
452C3×C4—62no—
453C3×C4—122no—
454C3×C4—121no—
455C3×C4—121no—
456C3×C4#93212yes—
457C3×C4#94912yes—
458C3×C4C2×#23911yescharacteristic
459C3×C4#100711yescharacteristic
460C3×C4D3×#4111yescharacteristic
461C3×C4#101011yescharacteristic
462Dic3—22no—
463Dic3—41no—
464Dic3—42no—
465Dic3—41no—
466C32#336811yescharacteristic, complemented, Sylow
467C23—62no—
468C23—61no—
469Q8—22no—
470Q8—32no—
471Q8—61no—
472Q8—122no—
473D4—61no—
474D4—62no—
475D4—61no—
476D4—62no—
477D4—124no—
478D4—122no—
479D4—242no—
480D4—241no—
481C2×C4—61no—
482C2×C4—61no—
483C2×C4—62no—
484C2×C4—61no—
485C2×C4—124no—
486C2×C4—122no—
487C2×C4C2×#62512yes—
488C2×C4C2×#62511yescharacteristic
489C2×C4C2×#62512yes—
490C2×C4C2×#62511yescharacteristic
491C2×C4C22×D3211yescharacteristic
492C8—181no—
493C8—181no—
494C8—182no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—242no—
499C2×C3—241no—
500C2×C3C2×#93211yescharacteristic
501C2×C3#581711yescharacteristic
502C2×C3C2×#94911yescharacteristic
503C2×C3#583111yescharacteristic
504C2×C3#583611yescharacteristic
505C2×C3#583711yescharacteristic
506D3—82no—
507D3—81no—
508C22—122no—
509C22—121no—
510C22—122no—
511C22—121no—
512C22—122no—
513C22—121no—
514C22C22×#62511yescharacteristic
515C4—22no—
516C4—21no—
517C4—22no—
518C4—62no—
519C4—121no—
520C4—121no—
521C4—122no—
522C4#6382312yes—
523C4#6431511yescharacteristic
524C4D3×#23911yescharacteristic
525C3—21no—
526C3#8358711yescharacteristic, complemented
527C3#8369011yescharacteristic, complemented
528C2—242no—
529C2—241no—
530C2C2×#6382311yescharacteristic
531C2#1059540911yescharacteristic
532C2#1059544611yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC3×#5577C2
hypercenterC4×Q8D32
hypocenterC32#3368
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5567C2semidirect
3. #10592723C2semidirect
4. #10590364C2semidirect
5. #10590364C2semidirect
6. #10590358C2semidirect
7. C4×#3715C2semidirect
8. #10590279C2semidirect
9. #10590277C2semidirect
10. #10590270C2semidirect
11. #10590269C2semidirect
46. #5567D3semidirect
187. C3×Dic6#41semidirect
377. Dic6#239semidirect
466. C32#3368semidirect
526. C3#83587semidirect
527. C3#83690semidirect

Maximal subgroups

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

subgroupindex
C3×#55772
C3×#55672
#105927232
#105903642
#105903582
C4×#37152
#105902792
#105902772
#105902702
#105902692
#836903
#835873