Finite Group Databasebeta

← #11895765

Subgroups — #11895765

Order 1152.

906 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596050C211yesmaximal, characteristic, complemented
2C3×#5577C211yesmaximal, characteristic, complemented
3C3×#5024C211yesmaximal, characteristic, complemented
4#10590355C212yesmaximal, complemented
5#10590355C211yesmaximal, characteristic, complemented
6#10590346C212yesmaximal, complemented
7C4×#3714C211yesmaximal, characteristic, complemented
8#10590275C212yesmaximal, complemented
9#10590273C211yesmaximal, characteristic, complemented
10#10590271C212yesmaximal, complemented
11#10590268C211yesmaximal, characteristic, complemented
12#83581—31nomaximal
13#79969—31nomaximal
14C2×C3×#239—21no—
15C32×C4×Q8C2211yescharacteristic
16#64155—21no—
17#64105—22no—
18C4⋊C4×C3⋊D3—21no—
19C4×C4⋊(C3⋊D3)C2211yescharacteristic
20C4×C4⋊(C3⋊D3)C2212yes—
21#64079C2212yes—
22#64078C2211yescharacteristic
23C3×#895—21no—
24C3×#895—22no—
25C3×#874C2211yescharacteristic
26C3×#874C2212yes—
27C3×C4×D12C2211yescharacteristic
28C3×C4×D12C2212yes—
29C2×#3714C2211yescharacteristic
30C2×#3714C2212yes—
31C3×C4⋊(C3⋊C8)C2211yescharacteristic
32C3×C4⋊(C3⋊C8)C2212yes—
33C3×#803C2212yes—
34C3×C4×C3⋊C8C2211yescharacteristic
35#63575C2211yescharacteristic
36#63573C2212yes—
37#63564C2211yescharacteristic
38#63563C2212yes—
39#63563C2212yes—
40#63563C2212yes—
41#63563C2212yes—
42#63563C2211yescharacteristic
43C3×#550—31no—
44#5579—31no—
45#5579—31no—
46#5579—61no—
47#5577D311yescharacteristic, complemented
48C3×#446—31no—
49#5072—31no—
50#5072—32no—
51#5071—32no—
52#5070—31no—
53#5024D311yescharacteristic, complemented
54#5014—32no—
55C4×#213—31no—
56#5009—32no—
57#5008—31no—
58#4847—32no—
59#4843—32no—
60#4843—31no—
61#4842—31no—
62#4713—32no—
63#4711—32no—
64#4694—31no—
65C4×D24—31no—
66C2×C32×Q8D411yescharacteristic
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—22no—
70C2×#634—21no—
71C3×#239—44no—
72C2×C3×D12—22no—
73C2×C3×D12—21no—
74C2×C3×D12—22no—
75C2×C3×D12—21no—
76C2×C3×D12C2311yescharacteristic
77C2×C3×D12C2312yes—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3—21no—
80C32×C4⋊C4D411yescharacteristic
81C32×C4⋊C4D412yes—
82C32×C42C2311yescharacteristic
83C32×C42C2312yes—
84#3752—21no—
85#3752—22no—
86C4⋊(C3⋊Dic3)—21no—
87C4⋊(C3⋊Dic3)C2312yes—
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89#3750—22no—
90#3750—22no—
91C3×(C2×D3)⋊C4—22no—
92C3×(C2×D3)⋊C4—21no—
93C3×C4⋊Dic3C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97#3714—22no—
98#3714—24no—
99#3366—91noSylow
100C2×C3×#41—61no—
101C2×#239—21no—
102C3×#127—31no—
103C3×#127—32no—
104C3×#121—61no—
105C3×#121—62no—
106C3×C4×Q8—21no—
107C3×C4×Q8C2×D311yescharacteristic
108C3×C4×Q8C2×D311yescharacteristic
109C3×C4×D4—31no—
110C3×C4×D4—32no—
111#946—62no—
112#946—61no—
113#946—61no—
114C2×#213—31no—
115C2×#213—32no—
116C2×D24—31no—
117C2×D24—32no—
118#896—64no—
119#896—62no—
120#896—62no—
121#895—21no—
122#895—22no—
123D3×C4⋊C4—62no—
124D3×C4⋊C4—61no—
125D3×C4⋊C4—61no—
126#874C2×D311yescharacteristic
127#874C2×D312yes—
128C4×D12—31no—
129C4×D12—32no—
130C4×D12—31no—
131C4×D12—32no—
132C4×D12—61no—
133C4×D12—62no—
134C4×D12C2×D311yescharacteristic
135C4×D12C2×D312yes—
136#870—32no—
137#870—32no—
138#870—62no—
139#869—31no—
140#869—31no—
141#869—61no—
142C3×C4⋊C8—31no—
143C3×C4⋊C8—32no—
144C3×#97—32no—
145C3×C4×C8—31no—
146#832—32no—
147#832—32no—
148#832—32no—
149#832—31no—
150#832—32no—
151#821—31no—
152#821—32no—
153#821—32no—
154#821—32no—
155#821—32no—
156#821—31no—
157#818—31no—
158#817—32no—
159#809—31no—
160#808—32no—
161#807—31no—
162C4⋊(C3⋊C8)C2×D311yescharacteristic
163C4⋊(C3⋊C8)C2×D312yes—
164#803C2×D312yes—
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3⋊D3—21no—
167C22×C3×D3—22no—
168C22×C3×D3—21no—
169C32×Q8—22no—
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D412yes—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—22no—
177C4⋊(C3⋊D3)—21no—
178C4⋊(C3⋊D3)#4112yescomplemented
179C4×C3⋊D3—42no—
180C4×C3⋊D3—82no—
181#634—81no—
182C2×C3×Dic3—21no—
183C3×D12—21no—
184C3×D12—22no—
185C3×D12—21no—
186C3×D12—22no—
187C3×D12—44no—
188C3×D12—42no—
189C3×D12—81no—
190C3×D12—82no—
191C3×C4×D3—44no—
192C3×C4×D3—42no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8—21no—
195C3×C3⋊C8—21no—
196#554—91no—
197#550—31no—
198#490—92no—
199#486—91no—
200#478—92no—
201#476—91no—
202#459—92no—
203#459—91no—
204#446—31no—
205#442—92no—
206C4×D8—91no—
207C3×#41—124no—
208C2×C3×Q8—21no—
209C2×C3×Q8D1211yescharacteristic
210C2×C3×Q8#6711yescharacteristic
211C2×C3×D4—31no—
212C2×C3×D4—32no—
213C2×C3×D4—62no—
214C2×C3×D4—61no—
215C2×C3×D4—62no—
216C2×C3×D4—61no—
217C22×C3×C4—62no—
218C22×C3×C4—61no—
219#239—44no—
220C2×D12—22no—
221C2×D12—21no—
222C2×D12—22no—
223C2×D12—21no—
224C2×D12—31no—
225C2×D12—31no—
226C2×D12—61no—
227C2×D12C22×D311yescharacteristic
228C2×D12C22×D312yes—
229C2×C4×D3—22no—
230C2×C4×D3—21no—
231C2×C4×D3—62no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×C4×D3—64no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×Dic6—62no—
238C2×Dic6—61no—
239C2×Dic6—61no—
240C2×C3×C8—32no—
241C2×C3×C8—31no—
242C2×C3×C8—31no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—22no—
245C3×C4⋊C4—31no—
246C3×C4⋊C4D1211yescharacteristic
247C3×C4⋊C4D1212yes—
248C3×C4⋊C4#6711yescharacteristic
249C3×C4⋊C4#6712yes—
250C3×C22⋊C4—62no—
251C3×C22⋊C4—61no—
252C3×C42—21no—
253C3×C42—22no—
254C3×C42C22×D311yescharacteristic
255C3×C42C22×D312yes—
256C3×C42C22×D311yescharacteristic
257C3×C42C22×D312yes—
258#213—62no—
259#213—64no—
260(C2×D3)⋊C4—22no—
261(C2×D3)⋊C4—21no—
262(C2×D3)⋊C4—62no—
263(C2×D3)⋊C4—64no—
264(C2×D3)⋊C4—61no—
265(C2×D3)⋊C4—62no—
266(C2×D3)⋊C4—61no—
267(C2×D3)⋊C4—62no—
268C4⋊Dic3—31no—
269C4⋊Dic3—32no—
270C4⋊Dic3—32no—
271C4⋊Dic3—31no—
272C4⋊Dic3—62no—
273C4⋊Dic3—61no—
274C4⋊Dic3—62no—
275C4⋊Dic3—61no—
276C4⋊Dic3—61no—
277C4⋊Dic3C22×D311yescharacteristic
278Dic3⋊C4—64no—
279Dic3⋊C4—64no—
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284C2×C3⋊C8C22×D311yescharacteristic
285C2×C3⋊C8C22×D311yescharacteristic
286C2×C3⋊C8C22×D312yes—
287D24—62no—
288D24—64no—
289C22×C32C22×D411yescharacteristic
290C2×C3⋊D3—22no—
291C2×C3⋊D3—41no—
292C2×C3⋊D3—41no—
293C2×C3×D3—42no—
294C2×C3×D3—41no—
295C2×C3×D3—42no—
296C2×C3×D3—41no—
297C2×C3×D3—42no—
298C2×C3×D3—41no—
299C32×C4—22no—
300C32×C4—21no—
301C32×C4—22no—
302C32×C4AGL(1,ℤ/8)12yes—
303C32×C4C2×#4111yescharacteristic
304C32×C42−1+411yescharacteristic
305C3⋊Dic3—41no—
306C3⋊Dic3—42no—
307C3×Dic3—41no—
308C2×#41—61no—
309C2×D8—91no—
310C2×D8—92no—
311C4⋊Q8—91no—
312#127—31no—
313#127—32no—
314#125—92no—
315C22⋊Q8—181no—
316C22⋊Q8—182no—
317#121—61no—
318#121—62no—
319C4×Q8D3211yescharacteristic
320C4×D4—31no—
321C4×D4—32no—
322C4×D4—91no—
323C4×D4—92no—
324C2×C4⋊C4—181no—
325#107—91no—
326#106—92no—
327C4⋊C8—31no—
328C4⋊C8—32no—
329#102—91no—
330#102—91no—
331#102—92no—
332#102—92no—
333#102—92no—
334#102—92no—
335#97—32no—
336C4×C8—31no—
337C23×C3—62no—
338C23×C3—61no—
339C22×D3—22no—
340C22×D3—21no—
341C22×D3—62no—
342C22×D3—61no—
343C22×D3—61no—
344C3×Q8—22no—
345C3×Q8—22no—
346C3×Q8—42no—
347C3×D4—61no—
348C3×D4—62no—
349C3×D4—61no—
350C3×D4—62no—
351C3×D4—124no—
352C3×D4—122no—
353C3×D4—241no—
354C3×D4—242no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—21no—
360C2×C3×C4—61no—
361C2×C3×C4—124no—
362C2×C3×C4—122no—
363C2×C3×C4C2×D1212yes—
364C2×C3×C4C2×D1212yes—
365C2×C3×C4C2×D1211yescharacteristic
366C2×C3×C4C2×D1211yescharacteristic
367C2×C3×C4C2×#6712yes—
368C2×C3×C4C2×#6712yes—
369C2×C3×C4C2×#6711yescharacteristic
370C2×C3×C4C2×#6711yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373C2×Dic3—21no—
374C2×Dic3—62no—
375C2×Dic3—64no—
376C2×Dic3—61no—
377C2×Dic3—62no—
378C2×Dic3—61no—
379C2×Dic3—62no—
380D12—21no—
381D12—22no—
382D12—21no—
383D12—22no—
384D12—32no—
385D12—32no—
386D12—44no—
387D12—42no—
388D12—62no—
389D12—62no—
390D12—61no—
391D12—61no—
392D12—81no—
393D12—82no—
394C4×D3—44no—
395C4×D3—42no—
396C4×D3—124no—
397C4×D3—122no—
398C4×D3—122no—
399C4×D3—242no—
400C4×D3—242no—
401C4×D3—244no—
402Dic6—241no—
403Dic6—241no—
404Dic6—242no—
405C3×C8—62no—
406C3×C8—61no—
407C3×C8—61no—
408C3⋊C8—21no—
409C3⋊C8—21no—
410C3⋊C8—22no—
411C2×C32#54811yescharacteristic
412C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
413C2×C32#57611yescharacteristic
414C3⋊D3—42no—
415C3×D3—82no—
416C3×D3—81no—
417#41—124no—
418C2×Q8—181no—
419C2×Q8#62611yescharacteristic
420C2×D4—31no—
421C2×D4—32no—
422C2×D4—62no—
423C2×D4—61no—
424C2×D4—61no—
425C2×D4—62no—
426C2×D4—91no—
427C22×C4—62no—
428C22×C4—61no—
429C22×C4—181no—
430C22×C4—182no—
431D8—182no—
432D8—184no—
433C2×C8—31no—
434C2×C8—31no—
435C2×C8—32no—
436C4⋊C4—31no—
437C4⋊C4—92no—
438C4⋊C4—91no—
439C4⋊C4—182no—
440C4⋊C4—181no—
441C4⋊C4—182no—
442C4⋊C4#62611yescharacteristic
443C4⋊C4#62612yes—
444C22⋊C4—61no—
445C22⋊C4—62no—
446C22⋊C4—181no—
447C22⋊C4—182no—
448C42C2×D3211yescharacteristic
449C42C2×D3212yes—
450C22×C3—21no—
451C22×C3—122no—
452C22×C3—121no—
453C22×C3—122no—
454C22×C3—121no—
455C22×C3—122no—
456C22×C3—121no—
457C22×C3C22×D1211yescharacteristic
458C22×C3C22×#6711yescharacteristic
459C2×D3—42no—
460C2×D3—41no—
461C2×D3—42no—
462C2×D3—41no—
463C2×D3—42no—
464C2×D3—41no—
465C2×D3—64no—
466C2×D3—62no—
467C2×D3—62no—
468C2×D3—122no—
469C2×D3—122no—
470C2×D3—121no—
471C2×D3—121no—
472C2×D3—121no—
473C2×D3—121no—
474C3×C4—22no—
475C3×C4—21no—
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—21no—
479C3×C4—22no—
480C3×C4—21no—
481C3×C4—21no—
482C3×C4—22no—
483C3×C4—41no—
484C3×C4—42no—
485C3×C4—42no—
486C3×C4—121no—
487C3×C4#90812yes—
488C3×C4#93212yes—
489C3×C4#100711yescharacteristic
490C3×C4D3×#4111yescharacteristic
491C3×C4D3×#4111yescharacteristic
492C3×C4#101011yescharacteristic
493Dic3—41no—
494Dic3—124no—
495Dic3—122no—
496Dic3—121no—
497Dic3—122no—
498Dic3—121no—
499Dic3—122no—
500C32#336611yescharacteristic, complemented, Sylow
501C23—62no—
502C23—61no—
503C23—181no—
504Q8—22no—
505Q8—721no—
506D4—61no—
507D4—62no—
508D4—61no—
509D4—62no—
510D4—92no—
511D4—124no—
512D4—122no—
513D4—181no—
514D4—242no—
515D4—241no—
516C2×C4—61no—
517C2×C4—124no—
518C2×C4—122no—
519C2×C4—181no—
520C2×C4—182no—
521C2×C4—362no—
522C2×C4—722no—
523C2×C4C2×#62611yescharacteristic
524C2×C4C2×#62612yes—
525C2×C4C2×#62612yes—
526C2×C4C2×#62611yescharacteristic
527C2×C4C22×D3211yescharacteristic
528C8—61no—
529C8—61no—
530C8—62no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—242no—
535C2×C3—241no—
536C2×C3#557611yescharacteristic
537C2×C3C2×#90811yescharacteristic
538C2×C3#575211yescharacteristic
539C2×C3C2×#93211yescharacteristic
540C2×C3#583111yescharacteristic
541C2×C3#583511yescharacteristic
542D3—82no—
543D3—81no—
544D3—124no—
545D3—122no—
546D3—122no—
547C22—122no—
548C22—121no—
549C22—121no—
550C22—122no—
551C22—122no—
552C22—121no—
553C22—182no—
554C22—361no—
555C22—361no—
556C22C22×#62611yescharacteristic
557C4—22no—
558C4—21no—
559C4—22no—
560C4—121no—
561C4—362no—
562C4—361no—
563C4#6383012yes—
564C4#6431511yescharacteristic
565C4#6431911yescharacteristic
566C3—21no—
567C3#7996911yescharacteristic, complemented
568C3#8358111yescharacteristic, complemented
569C2—242no—
570C2—241no—
571C2—362no—
572C2C2×#6383011yescharacteristic
573C2#1059541411yescharacteristic
574C2#1059544911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
hypercenterC4×Q8D32
hypocenterC32#3366
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
1. #10596050C2semidirect
2. C3×#5577C2semidirect
3. C3×#5024C2semidirect
4. #10590355C2semidirect
5. #10590355C2semidirect
6. #10590346C2semidirect
7. C4×#3714C2semidirect
8. #10590275C2semidirect
9. #10590273C2semidirect
10. #10590271C2semidirect
11. #10590268C2semidirect
47. #5577D3semidirect
53. #5024D3semidirect
178. C4⋊(C3⋊D3)#41semidirect
500. C32#3366semidirect
567. C3#79969semidirect
568. C3#83581semidirect

Maximal subgroups

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

subgroupindex
#105960502
C3×#55772
C3×#50242
#105903552
#105903462
C4×#37142
#105902752
#105902732
#105902712
#105902682
#835813
#799693