Finite Group Databasebeta

← #11895768

Subgroups — #11895768

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#10596014C211yesmaximal, characteristic, complemented
2#10593906C211yesmaximal, characteristic, complemented
3C3×#5015C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591486C212yesmaximal, complemented
6#10591436C212yesmaximal, complemented
7#10590554C212yesmaximal, complemented
8#10590473C212yesmaximal, complemented
9#10590296C211yesmaximal, characteristic, complemented
10#10590273C211yesmaximal, characteristic, complemented
11#10590268C211yesmaximal, characteristic, complemented
12#80320—31nomaximal
13#79570—31nomaximal
14C2×#3795—21no—
15C32×C4×D4C2211yescharacteristic
16D4×C3⋊Dic3C2212yes—
17C2×C4⋊(C3⋊Dic3)—21no—
18#64133—21no—
19#64099C2212yes—
20#64087—22no—
21#64078C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C2×C3×#213C2212yes—
25C3×#874C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27#63914C2212yes—
28#63908—21no—
29#63898C2212yes—
30#63885—22no—
31C3×#832C2211yescharacteristic
32C3×#809C2212yes—
33C3×#809C2211yescharacteristic
34C3×#807C2211yescharacteristic
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63573C2212yes—
38#63572C2212yes—
39#63563C2212yes—
40#63563C2212yes—
41#63563C2212yes—
42#63555C2212yes—
43#5718—31no—
44#5553—31no—
45#5543—31no—
46#5543—31no—
47#5543—61no—
48C3×#459—31no—
49C3×C4×D8—31no—
50#5152—32no—
51#5150—32no—
52#5150—32no—
53#5070—31no—
54#5015D311yescharacteristic, complemented
55C4×#213D311yescharacteristic, complemented
56#5008—31no—
57#4891—32no—
58#4842—31no—
59#4831—31no—
60#4785—32no—
61#4764—32no—
62#4764—32no—
63#4763—32no—
64#4694—31no—
65#4679—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C22×C3⋊Dic3—22no—
69C2×#634—21no—
70C2×#634D411yescharacteristic
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12C2312yes—
74C2×C3×D12C2311yescharacteristic
75C2×C3×C4×D3—21no—
76C2×#625—22no—
77C2×#625—22no—
78C2×D3×Dic3—22no—
79#3795—44no—
80C32×C4⋊C4C2311yescharacteristic
81C32×C22⋊C4—21no—
82C32×C42C2311yescharacteristic
83#3757—22no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)—22no—
86C4⋊(C3⋊Dic3)D411yescharacteristic
87C4⋊(C3⋊Dic3)C2312yes—
88#3750—22no—
89#3750D412yes—
90C4×C3⋊Dic3C2312yes—
91C3×#213—22no—
92C3×#213—24no—
93C3×(C2×D3)⋊C4—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98(C2×D3)⋊Dic3—22no—
99#3366—91noSylow
100C2×#237—61no—
101C2×#235—61no—
102C2×C3×D8—31no—
103C2×C3×D8—32no—
104C3×#127—31no—
105C3×C4×D4—21no—
106C3×C4×D4—31no—
107C3×C4×D4C2×D311yescharacteristic
108C3×C4×D4C2×D311yescharacteristic
109#940—32no—
110#940—32no—
111#939—62no—
112#938—61no—
113D4×Dic3—32no—
114D4×Dic3—32no—
115D4×Dic3—32no—
116D4×Dic3—62no—
117C2×#213C2×D311yescharacteristic
118C2×#213C2×D312yes—
119#930—61no—
120C2×C4⋊Dic3—61no—
121C2×C4⋊Dic3—61no—
122C2×C4⋊Dic3—62no—
123#924—61no—
124#924—61no—
125#924—62no—
126#893—32no—
127#890—32no—
128#890—32no—
129#890—62no—
130#884—62no—
131#878—62no—
132#878—62no—
133#878—64no—
134#874C2×D311yescharacteristic
135C4×D12C2×D311yescharacteristic
136#869—31no—
137#869—31no—
138#869—61no—
139C4×Dic6—31no—
140C4×Dic6—31no—
141C4×Dic6—61no—
142C3×#107—31no—
143C3×C4⋊C8—31no—
144C3×#102—31no—
145C3×#102—32no—
146C3×#102—31no—
147C3×C4×C8—31no—
148#832—32no—
149#832—32no—
150#832—32no—
151#832C2×D311yescharacteristic
152#821—32no—
153#821—32no—
154#821—32no—
155#817—32no—
156#815—32no—
157#815—32no—
158Dic3⋊C8—32no—
159Dic3⋊C8—32no—
160#809C2×D312yes—
161#809C2×D311yescharacteristic
162#808—32no—
163#807C2×D311yescharacteristic
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C23×C32—21no—
167C22×C3×D3—22no—
168C22×C3×D3—21no—
169C32×D4—21no—
170C32×D4#4112yescomplemented
171C2×C32×C4—21no—
172C2×C32×C4—42no—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—82no—
178C2×C3⋊Dic3C2×D412yes—
179C2×C3⋊Dic3C2×D412yes—
180#634—22no—
181#634—81no—
182C2×C3×Dic3—21no—
183C3×D12—21no—
184C3×D12—22no—
185C3×D12—22no—
186C3×D12—21no—
187C3×D12—42no—
188C3×D12—81no—
189C3×C4×D3—42no—
190#625—44no—
191#625—82no—
192D3×Dic3—44no—
193C3×C3⋊C8—21no—
194C3×C3⋊C8—22no—
195C3×C3⋊C8—21no—
196#554—91no—
197#550—91no—
198#490—92no—
199#486—91no—
200#478—92no—
201#476—91no—
202#459—31no—
203#459—92no—
204#446—91no—
205#442—92no—
206C4×D8—31no—
207C2×C3×D4—21no—
208C2×C3×D4—32no—
209C2×C3×D4—31no—
210C2×C3×D4—61no—
211C2×C3×D4—61no—
212C2×C3×D4C22×D311yescharacteristic
213C2×C3×D4C22×D311yescharacteristic
214C22×C3×C4—22no—
215C22×C3×C4—21no—
216C22×C3×C4—21no—
217C22×C3×C4—61no—
218C2×#67—62no—
219C2×#67—62no—
220C2×#67—62no—
221C2×#67—62no—
222C22×Dic3—62no—
223C22×Dic3—62no—
224C22×Dic3—62no—
225C22×Dic3—64no—
226#237—124no—
227#235—124no—
228C2×D12—21no—
229C2×D12—21no—
230C2×D12C22×D311yescharacteristic
231C2×D12C22×D312yes—
232C2×C4×D3—21no—
233C2×C4×D3—62no—
234C2×Dic6—31no—
235C2×Dic6—31no—
236C2×Dic6—61no—
237C2×Dic6—62no—
238C2×Dic6—61no—
239C2×Dic6—61no—
240C3×D8—64no—
241C3×D8—62no—
242C2×C3×C8—31no—
243C2×C3×C8—32no—
244C2×C3×C8—31no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—31no—
247C3×C4⋊C4C22×D311yescharacteristic
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C22⋊C4—22no—
250C3×C22⋊C4—21no—
251C3×C22⋊C4—21no—
252C3×C22⋊C4—61no—
253C3×C42—21no—
254C3×C42C22×D311yescharacteristic
255C3×C42C22×D311yescharacteristic
256#217—62no—
257#217—62no—
258#217—62no—
259#217—64no—
260#213—22no—
261#213—24no—
262(C2×D3)⋊C4—21no—
263(C2×D3)⋊C4—62no—
264C4⋊Dic3—31no—
265C4⋊Dic3—31no—
266C4⋊Dic3—32no—
267C4⋊Dic3—32no—
268C4⋊Dic3—61no—
269C4⋊Dic3—62no—
270C4⋊Dic3—62no—
271C4⋊Dic3—62no—
272C4⋊Dic3—62no—
273C4⋊Dic3—64no—
274C4⋊Dic3—61no—
275C4⋊Dic3—61no—
276C4⋊Dic3C22×D311yescharacteristic
277Dic3⋊C4—32no—
278Dic3⋊C4—32no—
279Dic3⋊C4—62no—
280Dic3⋊C4—62no—
281Dic3⋊C4—62no—
282Dic3⋊C4—64no—
283C4×Dic3—32no—
284C4×Dic3—32no—
285C4×Dic3—62no—
286C2×C3⋊C8C22×D311yescharacteristic
287C2×C3⋊C8C22×D311yescharacteristic
288C2×C3⋊C8C22×D312yes—
289C22×C32—22no—
290C22×C32—41no—
291C22×C32—41no—
292C22×C32C22×D411yescharacteristic
293C2×C3×D3—41no—
294C2×C3×D3—42no—
295C2×C3×D3—42no—
296C2×C3×D3—41no—
297C2×C3×D3—41no—
298C2×C3×D3—42no—
299C32×C4—21no—
300C32×C4—41no—
301C32×C4AGL(1,ℤ/8)12yes—
302C32×C4C2×#4111yescharacteristic
303C32×C42−1+411yescharacteristic
304C3⋊Dic3—22no—
305C3⋊Dic3—22no—
306C3⋊Dic3—42no—
307C3×Dic3—41no—
308C2×#41—181no—
309C2×D8—31no—
310C2×D8—32no—
311C4⋊Q8—91no—
312#127—31no—
313#127—92no—
314#125—92no—
315C22⋊Q8—182no—
316C22⋊Q8—181no—
317#121—182no—
318#121—181no—
319C4×Q8—91no—
320C4×D4—31no—
321C4×D4—92no—
322C4×D4—92no—
323C4×D4D3211yescharacteristic
324C2×C4⋊C4—181no—
325#107—31no—
326#106—92no—
327C4⋊C8—31no—
328C4⋊C8—92no—
329#102—31no—
330#102—31no—
331#102—32no—
332#102—92no—
333#102—92no—
334#102—92no—
335#97—92no—
336C4×C8—31no—
337C23×C3—22no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—62no—
341C23×C3—61no—
342C22×D3—21no—
343C22×D3—22no—
344C3×D4—22no—
345C3×D4—21no—
346C3×D4—21no—
347C3×D4—22no—
348C3×D4—62no—
349C3×D4—61no—
350C3×D4—62no—
351C3×D4—61no—
352C3×D4—122no—
353C3×D4—241no—
354C3×D4#23512yescomplemented
355C3×D4#23712yescomplemented
356C2×C3×C4—22no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—44no—
363C2×C3×C4—42no—
364C2×C3×C4—42no—
365C2×C3×C4—61no—
366C2×C3×C4—122no—
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4C23×D311yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373#67—124no—
374#67—124no—
375#67—242no—
376#67—242no—
377C2×Dic3—21no—
378C2×Dic3—32no—
379C2×Dic3—32no—
380C2×Dic3—32no—
381C2×Dic3—32no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—64no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—124no—
388C2×Dic3—242no—
389C2×Dic3—242no—
390C2×Dic3—244no—
391D12—21no—
392D12—22no—
393D12—21no—
394D12—22no—
395D12—42no—
396D12—81no—
397C4×D3—42no—
398C4×D3—124no—
399Dic6—62no—
400Dic6—62no—
401Dic6—122no—
402Dic6—241no—
403Dic6—241no—
404Dic6—242no—
405C3×C8—62no—
406C3×C8—61no—
407C3×C8—61no—
408C3⋊C8—21no—
409C3⋊C8—22no—
410C3⋊C8—21no—
411C2×C32—42no—
412C2×C32#54811yescharacteristic
413C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
414C2×C32#57611yescharacteristic
415C3×D3—82no—
416C3×D3—81no—
417#41—364no—
418C2×Q8—91no—
419C2×Q8—181no—
420C2×D4—31no—
421C2×D4—32no—
422C2×D4—61no—
423C2×D4—61no—
424C2×D4—182no—
425C2×D4—182no—
426C2×D4C2×D3211yescharacteristic
427C22×C4—21no—
428C22×C4—61no—
429C22×C4—182no—
430C22×C4—182no—
431D8—62no—
432D8—64no—
433C2×C8—31no—
434C2×C8—31no—
435C2×C8—32no—
436C4⋊C4—31no—
437C4⋊C4—91no—
438C4⋊C4—92no—
439C4⋊C4—92no—
440C4⋊C4—182no—
441C4⋊C4—182no—
442C4⋊C4—181no—
443C4⋊C4C2×D3211yescharacteristic
444C22⋊C4—21no—
445C22⋊C4—61no—
446C22⋊C4—182no—
447C22⋊C4—182no—
448C42—92no—
449C42C2×D3211yescharacteristic
450C22×C3—24no—
451C22×C3—22no—
452C22×C3—22no—
453C22×C3—21no—
454C22×C3—42no—
455C22×C3—42no—
456C22×C3—41no—
457C22×C3—41no—
458C22×C3—41no—
459C22×C3—41no—
460C22×C3—122no—
461C22×C3—121no—
462C22×C3—122no—
463C22×C3—121no—
464C22×C3—122no—
465C22×C3—121no—
466C22×C3C2×D3×D411yescharacteristic
467C22×C3C2×D3×D411yescharacteristic
468C2×D3—41no—
469C2×D3—42no—
470C2×D3—41no—
471C2×D3—42no—
472C2×D3—41no—
473C2×D3—42no—
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—22no—
479C3×C4—41no—
480C3×C4—42no—
481C3×C4—41no—
482C3×C4—41no—
483C3×C4—121no—
484C3×C4#91112yes—
485C3×C4#91112yes—
486C3×C4C2×#23511yescharacteristic
487C3×C4C2×#23711yescharacteristic
488C3×C4#101011yescharacteristic
489C3×C4#101011yescharacteristic
490Dic3—41no—
491Dic3—62no—
492Dic3—62no—
493Dic3—62no—
494Dic3—62no—
495Dic3—122no—
496Dic3—122no—
497Dic3—124no—
498Dic3—122no—
499Dic3—122no—
500C32#336611yescharacteristic, complemented, Sylow
501C23—21no—
502C23—61no—
503C23—62no—
504Q8—182no—
505Q8—721no—
506D4—21no—
507D4—61no—
508D4—62no—
509D4—61no—
510D4—62no—
511D4—122no—
512D4—241no—
513D4—364no—
514D4—722no—
515D4#379512yescomplemented
516C2×C4—21no—
517C2×C4—42no—
518C2×C4—61no—
519C2×C4—92no—
520C2×C4—92no—
521C2×C4—122no—
522C2×C4—182no—
523C2×C4—364no—
524C2×C4—722no—
525C2×C4#381111yescharacteristic
526C2×C4#381111yescharacteristic
527C2×C4C22×D3211yescharacteristic
528C8—61no—
529C8—62no—
530C8—61no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—44no—
535C2×C3—42no—
536C2×C3—42no—
537C2×C3—241no—
538C2×C3—242no—
539C2×C3#555211yescharacteristic
540C2×C3#559811yescharacteristic
541C2×C3C2×#91111yescharacteristic
542C2×C3C2×#91111yescharacteristic
543C2×C3#576911yescharacteristic
544C2×C3#577411yescharacteristic
545D3—82no—
546D3—81no—
547C22—22no—
548C22—41no—
549C22—41no—
550C22—121no—
551C22—122no—
552C22—121no—
553C22—122no—
554C22—122no—
555C22—121no—
556C22C2×#381111yescharacteristic
557C4—21no—
558C4—41no—
559C4—121no—
560C4—182no—
561C4—182no—
562C4—362no—
563C4#6392712yes—
564C4C2×#379511yescharacteristic
565C4#6429811yescharacteristic
566C3—21no—
567C3#7957011yescharacteristic, complemented
568C3#8032011yescharacteristic, complemented
569C2—42no—
570C2—241no—
571C2—242no—
572C2#1059491811yescharacteristic
573C2C2×#6392711yescharacteristic
574C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3366
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10596014C2semidirect
2. #10593906C2semidirect
3. C3×#5015C2semidirect
4. C3×C4×#213C2semidirect
5. #10591486C2semidirect
6. #10591436C2semidirect
7. #10590554C2semidirect
8. #10590473C2semidirect
9. #10590296C2semidirect
10. #10590273C2semidirect
11. #10590268C2semidirect
54. #5015D3semidirect
55. C4×#213D3semidirect
170. C32×D4#41semidirect
354. C3×D4#235semidirect
355. C3×D4#237semidirect
500. C32#3366semidirect
515. D4#3795semidirect
567. C3#79570semidirect
568. C3#80320semidirect

Maximal subgroups

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

subgroupindex
#105960142
#105939062
C3×#50152
C3×C4×#2132
#105914862
#105914362
#105905542
#105904732
#105902962
#105902732
#105902682
#803203
#795703