Finite Group Databasebeta

← #11895966

Subgroups — #11895966

Order 1152.

920 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596048C211yesmaximal, characteristic
2C3×#5567C211yesmaximal, characteristic, complemented
3C3×#5024C211yesmaximal, characteristic, complemented
4#10590367C212yesmaximal, complemented
5#10590367C211yesmaximal, characteristic, complemented
6#10590362C212yesmaximal, complemented
7C4×#3717C211yesmaximal, characteristic, complemented
8#10590313C211yesmaximal, characteristic, complemented
9#10590308C212yesmaximal, complemented
10#10590282C212yesmaximal, complemented
11#10590281C211yesmaximal, characteristic, complemented
12#83690—31nomaximal
13#79980—31nomaximal
14C2×#3832—21no—
15C32×C4×Q8C2211yescharacteristic
16#64104—21no—
17#64104—22no—
18#64083C2211yescharacteristic
19#64083C2212yes—
20C4×C4⋊(C3⋊D3)C2212yes—
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C3×#944—21no—
23C3×#889—22no—
24C3×#887—21no—
25C3×#870C2212yes—
26C3×#869C2211yescharacteristic
27C3×C4×Dic6C2211yescharacteristic
28C3×C4×Dic6C2212yes—
29C2×#3717C2211yescharacteristic
30C2×#3717C2212yes—
31C3×C4⋊(C3⋊C8)C2212yes—
32C3×C4⋊(C3⋊C8)C2211yescharacteristic
33C3×#803C2212yes—
34C3×C4×C3⋊C8C2211yescharacteristic
35#63575C2212yes—
36#63573C2211yescharacteristic
37#63566C2211yescharacteristic
38#63564C2212yes—
39#63564C2212yes—
40#63564C2211yescharacteristic
41#63564C2212yes—
42#63564C2212yes—
43C3×#557—31no—
44#5577—31no—
45#5577—31no—
46#5577—61no—
47#5567D311yescharacteristic, complemented
48C3×#446—31no—
49#5088—31no—
50#5087—31no—
51#5067—32no—
52#5066—32no—
53#5027—32no—
54#5027—31no—
55#5026—32no—
56C4×#215—31no—
57#5024D311yescharacteristic, complemented
58#4848—32no—
59#4848—31no—
60#4847—32no—
61#4846—31no—
62#4713—32no—
63#4710—32no—
64#4694—31no—
65C4×#204—31no—
66C2×C32×Q8D411yescharacteristic
67#3832—44no—
68C2×C4⋊(C3⋊D3)—22no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)—22no—
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)C2312yes—
73C2×C4⋊(C3⋊D3)C2311yescharacteristic
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—21no—
76C2×C3×Dic6—21no—
77C2×C3×Dic6C2311yescharacteristic
78C32×C4⋊C4D411yescharacteristic
79C32×C4⋊C4D412yes—
80C32×C42C2311yescharacteristic
81C32×C42C2312yes—
82#3752—22no—
83#3752—21no—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2311yescharacteristic
87C3×C4⋊Dic3C2312yes—
88C3×Dic3⋊C4—22no—
89C3×Dic3⋊C4—21no—
90C3×Dic3⋊C4—22no—
91C3×Dic3⋊C4—22no—
92C3×C4×Dic3—22no—
93C3×C4×Dic3—21no—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2311yescharacteristic
96C2×C3×C3⋊C8C2312yes—
97#3717—22no—
98#3717—24no—
99#3368—91noSylow
100C2×#239—62no—
101C2×#239—61no—
102C2×#239—61no—
103C3×C4⋊Q8—31no—
104C3×C4⋊Q8—61no—
105C3×#125—32no—
106C3×#125—62no—
107C3×C4×Q8—21no—
108C3×C4×Q8—31no—
109C3×C4×Q8—32no—
110C3×C4×Q8—61no—
111C3×C4×Q8C2×D311yescharacteristic
112C3×C4×Q8C2×D311yescharacteristic
113#944—21no—
114C2×#215—31no—
115C2×#215—32no—
116C2×#204—31no—
117C2×#204—32no—
118#895—62no—
119#895—64no—
120#895—61no—
121#895—62no—
122#895—61no—
123#895—62no—
124#889—22no—
125#887—21no—
126#874—31no—
127#874—32no—
128#874—32no—
129#874—31no—
130#874—61no—
131#874—62no—
132C4×D12—31no—
133C4×D12—32no—
134C4×D12—31no—
135C4×D12—32no—
136C4×D12—61no—
137C4×D12—62no—
138#870C2×D312yes—
139#869C2×D311yescharacteristic
140C4×Dic6C2×D311yescharacteristic
141C4×Dic6C2×D312yes—
142C3×C4⋊C8—31no—
143C3×C4⋊C8—32no—
144C3×#97—32no—
145C3×C4×C8—31no—
146#835—31no—
147#821—31no—
148#821—32no—
149#821—32no—
150#821—32no—
151#821—32no—
152#818—32no—
153#817—31no—
154#816—31no—
155#809—31no—
156#809—32no—
157#809—32no—
158#809—32no—
159#809—32no—
160#808—31no—
161#807—32no—
162C4⋊(C3⋊C8)C2×D312yes—
163C4⋊(C3⋊C8)C2×D311yescharacteristic
164#803C2×D312yes—
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3⋊D3—22no—
167C22×C3⋊D3—21no—
168C32×Q8—22no—
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—21no—
175C4⋊(C3⋊D3)—21no—
176C4⋊(C3⋊D3)—22no—
177C4⋊(C3⋊D3)—22no—
178C4⋊(C3⋊D3)—21no—
179C4⋊(C3⋊D3)—44no—
180C4⋊(C3⋊D3)—42no—
181C4⋊(C3⋊D3)—82no—
182C4⋊(C3⋊D3)—81no—
183C4×C3⋊D3—44no—
184C4×C3⋊D3—42no—
185C2×C3×Dic3—21no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C3×Dic6—21no—
189C3×Dic6—42no—
190C3×Dic6#4112yescomplemented
191C3×C3⋊C8—21no—
192C3×C3⋊C8—22no—
193C3×C3⋊C8—21no—
194#557—31no—
195#550—91no—
196#490—92no—
197#486—91no—
198#478—92no—
199#474—91no—
200#460—92no—
201#460—91no—
202#446—31no—
203#440—92no—
204C4×SD16—91no—
205C2×C3×Q8—21no—
206C2×C3×Q8—31no—
207C2×C3×Q8—61no—
208C2×C3×Q8D1211yescharacteristic
209C2×C3×Q8#6711yescharacteristic
210#239—128no—
211#239—124no—
212#239—124no—
213C2×D12—31no—
214C2×D12—32no—
215C2×D12—31no—
216C2×D12—32no—
217C2×D12—61no—
218C2×D12—62no—
219C2×D12—64no—
220C2×D12—62no—
221C2×D12—62no—
222C2×D12—61no—
223C2×D12—62no—
224C2×D12—61no—
225C2×D12—64no—
226C2×D12—62no—
227C2×D12—62no—
228C2×D12—61no—
229C2×D12—62no—
230C2×D12—61no—
231C2×C4×D3—64no—
232C2×C4×D3—62no—
233C2×C4×D3—62no—
234C2×C4×D3—61no—
235C2×C4×D3—62no—
236C2×C4×D3—61no—
237C2×Dic6—21no—
238C2×Dic6C22×D311yescharacteristic
239C2×C3×C8—31no—
240C2×C3×C8—31no—
241C2×C3×C8—32no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—22no—
244C3×C4⋊C4—32no—
245C3×C4⋊C4—31no—
246C3×C4⋊C4—61no—
247C3×C4⋊C4—62no—
248C3×C4⋊C4—62no—
249C3×C4⋊C4—62no—
250C3×C4⋊C4—61no—
251C3×C4⋊C4D1211yescharacteristic
252C3×C4⋊C4D1212yes—
253C3×C4⋊C4#6711yescharacteristic
254C3×C4⋊C4#6712yes—
255C3×C42—21no—
256C3×C42—22no—
257C3×C42—62no—
258C3×C42—61no—
259C3×C42C22×D311yescharacteristic
260C3×C42C22×D312yes—
261C3×C42C22×D311yescharacteristic
262C3×C42C22×D312yes—
263#215—62no—
264#215—64no—
265(C2×D3)⋊C4—64no—
266(C2×D3)⋊C4—62no—
267(C2×D3)⋊C4—62no—
268(C2×D3)⋊C4—61no—
269(C2×D3)⋊C4—62no—
270(C2×D3)⋊C4—61no—
271C4⋊Dic3—21no—
272C4⋊Dic3—31no—
273C4⋊Dic3—31no—
274C4⋊Dic3—61no—
275C4⋊Dic3C22×D311yescharacteristic
276C4⋊Dic3C22×D312yes—
277Dic3⋊C4—21no—
278Dic3⋊C4—22no—
279Dic3⋊C4—22no—
280Dic3⋊C4—22no—
281C4×Dic3—22no—
282C4×Dic3—21no—
283C2×C3⋊C8C22×D311yescharacteristic
284C2×C3⋊C8C22×D311yescharacteristic
285C2×C3⋊C8C22×D312yes—
286#204—62no—
287#204—64no—
288C22×C32C22×D411yescharacteristic
289C2×C3⋊D3—42no—
290C2×C3⋊D3—41no—
291C2×C3⋊D3—42no—
292C2×C3⋊D3—41no—
293C2×C3⋊D3—42no—
294C2×C3⋊D3—41no—
295C32×C4—22no—
296C32×C4—22no—
297C32×C4—21no—
298C32×C4AGL(1,ℤ/8)12yes—
299C32×C4C2×#4111yescharacteristic
300C32×C42−1+411yescharacteristic
301C3⋊Dic3—41no—
302C3×Dic3—22no—
303C3×Dic3—42no—
304C3×Dic3—41no—
305C2×#41—181no—
306C2×SD16—91no—
307C2×SD16—92no—
308C4⋊Q8—31no—
309C4⋊Q8—61no—
310#127—91no—
311#127—92no—
312#125—32no—
313#125—62no—
314#121—181no—
315#121—182no—
316C4×Q8—31no—
317C4×Q8—32no—
318C4×Q8—61no—
319C4×Q8D3211yescharacteristic
320C4×D4—91no—
321C4×D4—92no—
322#107—92no—
323#106—91no—
324C4⋊C8—31no—
325C4⋊C8—32no—
326#103—91no—
327#102—91no—
328#102—92no—
329#102—92no—
330#102—92no—
331#102—92no—
332#97—32no—
333C4×C8—31no—
334C22×D3—64no—
335C22×D3—62no—
336C22×D3—62no—
337C22×D3—61no—
338C22×D3—62no—
339C22×D3—61no—
340C3×Q8—24no—
341C3×Q8—22no—
342C3×Q8—22no—
343C3×Q8—32no—
344C3×Q8—61no—
345C3×Q8—122no—
346C2×C3×C4—21no—
347C2×C3×C4—22no—
348C2×C3×C4—21no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—61no—
352C2×C3×C4—61no—
353C2×C3×C4—62no—
354C2×C3×C4C2×D1212yes—
355C2×C3×C4C2×D1211yescharacteristic
356C2×C3×C4C2×D1212yes—
357C2×C3×C4C2×D1211yescharacteristic
358C2×C3×C4C2×#6712yes—
359C2×C3×C4C2×#6712yes—
360C2×C3×C4C2×#6711yescharacteristic
361C2×C3×C4C2×#6711yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363C2×C3×C4C23×D311yescharacteristic
364C2×Dic3—21no—
365C2×Dic3—21no—
366C2×Dic3—22no—
367C2×Dic3—62no—
368C2×Dic3—61no—
369C2×Dic3—61no—
370D12—61no—
371D12—62no—
372D12—61no—
373D12—62no—
374D12—61no—
375D12—62no—
376D12—61no—
377D12—62no—
378D12—121no—
379D12—122no—
380D12—121no—
381D12—122no—
382D12—128no—
383D12—124no—
384D12—124no—
385D12—124no—
386D12—122no—
387D12—122no—
388D12—242no—
389D12—241no—
390D12—242no—
391D12—241no—
392D12—244no—
393D12—242no—
394C4×D3—128no—
395C4×D3—124no—
396C4×D3—124no—
397C4×D3—124no—
398C4×D3—122no—
399C4×D3—122no—
400Dic6—21no—
401Dic6—42no—
402Dic6#23912yescomplemented
403C3×C8—61no—
404C3×C8—62no—
405C3×C8—61no—
406C3⋊C8—21no—
407C3⋊C8—21no—
408C3⋊C8—22no—
409C2×C32#54811yescharacteristic
410C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
411C2×C32#57711yescharacteristic
412C3⋊D3—82no—
413C3⋊D3—81no—
414#41—364no—
415C2×Q8—31no—
416C2×Q8—61no—
417C2×Q8#62611yescharacteristic
418C2×D4—91no—
419C2×D4—92no—
420C2×D4—182no—
421C2×D4—181no—
422C2×D4—182no—
423C2×D4—181no—
424C22×C4—182no—
425C22×C4—181no—
426SD16—182no—
427SD16—184no—
428C2×C8—31no—
429C2×C8—31no—
430C2×C8—32no—
431C4⋊C4—31no—
432C4⋊C4—32no—
433C4⋊C4—61no—
434C4⋊C4—62no—
435C4⋊C4—62no—
436C4⋊C4—62no—
437C4⋊C4—61no—
438C4⋊C4—91no—
439C4⋊C4#62611yescharacteristic
440C4⋊C4#62612yes—
441C22⋊C4—182no—
442C22⋊C4—181no—
443C42—62no—
444C42—61no—
445C42C2×D3211yescharacteristic
446C42C2×D3212yes—
447C22×C3—21no—
448C22×C3C22×D1211yescharacteristic
449C22×C3C22×#6711yescharacteristic
450C2×D3—124no—
451C2×D3—122no—
452C2×D3—124no—
453C2×D3—122no—
454C2×D3—124no—
455C2×D3—122no—
456C2×D3—122no—
457C2×D3—121no—
458C2×D3—122no—
459C2×D3—121no—
460C2×D3—122no—
461C2×D3—121no—
462C2×D3—122no—
463C2×D3—121no—
464C2×D3—122no—
465C2×D3—121no—
466C2×D3—122no—
467C2×D3—121no—
468C3×C4—24no—
469C3×C4—22no—
470C3×C4—22no—
471C3×C4—21no—
472C3×C4—22no—
473C3×C4—22no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—22no—
478C3×C4—42no—
479C3×C4—41no—
480C3×C4—62no—
481C3×C4—122no—
482C3×C4—121no—
483C3×C4#90812yes—
484C3×C4#94912yes—
485C3×C4C2×#23911yescharacteristic
486C3×C4#100711yescharacteristic
487C3×C4#100711yescharacteristic
488C3×C4D3×#4111yescharacteristic
489Dic3—22no—
490Dic3—42no—
491Dic3—41no—
492Dic3—122no—
493Dic3—121no—
494Dic3—121no—
495C32#336811yescharacteristic, complemented, Sylow
496C23—182no—
497C23—181no—
498Q8—22no—
499Q8—32no—
500Q8—61no—
501Q8—122no—
502D4—181no—
503D4—182no—
504D4—181no—
505D4—182no—
506D4—364no—
507D4—362no—
508D4—722no—
509D4—721no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—62no—
513C2×C4—181no—
514C2×C4—364no—
515C2×C4—362no—
516C2×C4C2×#62612yes—
517C2×C4C2×#62611yescharacteristic
518C2×C4C2×#62612yes—
519C2×C4C2×#62611yescharacteristic
520C2×C4C22×D3211yescharacteristic
521C8—61no—
522C8—61no—
523C8—62no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3#557611yescharacteristic
528C2×C3C2×#90811yescharacteristic
529C2×C3#575111yescharacteristic
530C2×C3#581711yescharacteristic
531C2×C3C2×#94911yescharacteristic
532C2×C3#583711yescharacteristic
533D3—244no—
534D3—242no—
535D3—242no—
536D3—241no—
537D3—242no—
538D3—241no—
539C22—362no—
540C22—361no—
541C22—362no—
542C22—361no—
543C22—362no—
544C22—361no—
545C22C22×#62611yescharacteristic
546C4—22no—
547C4—21no—
548C4—22no—
549C4—62no—
550C4—121no—
551C4—122no—
552C4—361no—
553C4#6382512yes—
554C4#6431611yescharacteristic
555C4D3×#23911yescharacteristic
556C3—21no—
557C3#7998011yescharacteristic, complemented
558C3#8369011yescharacteristic, complemented
559C2—722no—
560C2—721no—
561C2C2×#6382511yescharacteristic
562C2#1059534211yescharacteristic
563C2#1059544811yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10596048C2
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. C3×#5024C2semidirect
4. #10590367C2semidirect
5. #10590367C2semidirect
6. #10590362C2semidirect
7. C4×#3717C2semidirect
8. #10590313C2semidirect
9. #10590308C2semidirect
10. #10590282C2semidirect
11. #10590281C2semidirect
47. #5567D3semidirect
57. #5024D3semidirect
190. C3×Dic6#41semidirect
402. Dic6#239semidirect
495. C32#3368semidirect
557. C3#79980semidirect
558. C3#83690semidirect

Maximal subgroups

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

subgroupindex
#105960482
C3×#55672
C3×#50242
#105903672
#105903622
C4×#37172
#105903132
#105903082
#105902822
#105902812
#836903
#799803