Finite Group Databasebeta

← #11895777

Subgroups — #11895777

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#10596201C211yesmaximal, characteristic, complemented
2#10593906C211yesmaximal, characteristic, complemented
3C3×#5088C211yesmaximal, characteristic, complemented
4C3×#5084C211yesmaximal, characteristic, complemented
5#10590554C212yesmaximal, complemented
6#10590551C212yesmaximal, complemented
7#10590474C212yesmaximal, complemented
8#10590462C212yesmaximal, complemented
9#10590355C211yesmaximal, characteristic, complemented
10C4×#3714C211yesmaximal, characteristic, complemented
11#10590296C211yesmaximal, characteristic, complemented
12#81586—31nomaximal
13#81088—31nomaximal
14C2×#3795—21no—
15C32×C4⋊Q8C2211yescharacteristic
16#64155—22no—
17#64106—21no—
18#64102C2212yes—
19C4⋊C4×C3⋊D3—21no—
20#64099C2212yes—
21C4×C4⋊(C3⋊D3)C2211yescharacteristic
22C4×#634C2211yescharacteristic
23C3×#874C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25#63914C2212yes—
26#63908—21no—
27#63898C2212yes—
28#63885—22no—
29C2×#3714C2211yescharacteristic
30C2×#3714C2212yes—
31C3×#809C2212yes—
32C3×#809C2212yes—
33C3×#809C2212yes—
34C3×#808C2212yes—
35C3×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63575C2211yescharacteristic
38#63572C2212yes—
39#63564C2211yescharacteristic
40#63563C2212yes—
41#63563C2211yescharacteristic
42#63555C2212yes—
43#5730—31no—
44#5730—31no—
45#5730—61no—
46#5718—31no—
47#5553—31no—
48C3×#486—31no—
49C3×#476—31no—
50#5088D311yescharacteristic, complemented
51#5084D311yescharacteristic, complemented
52#5072—31no—
53C4×#213—31no—
54#4871—32no—
55#4869—32no—
56#4843—31no—
57#4831—31no—
58#4786—32no—
59#4786—32no—
60#4785—32no—
61#4766—32no—
62#4764—32no—
63#4764—32no—
64C4×D24—31no—
65#4679—31no—
66C2×C32×Q8—21no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—22no—
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⋊C4—21no—
81C32×C4⋊C4C2312yes—
82C32×C42C2311yescharacteristic
83#3752—21no—
84#3752—22no—
85C4⋊(C3⋊Dic3)—22no—
86C4⋊(C3⋊Dic3)D411yescharacteristic
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88#3750—22no—
89#3750D412yes—
90C4×C3⋊Dic3C2312yes—
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3C2311yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2312yes—
95C2×C3×C3⋊C8C2311yescharacteristic
96(C2×D3)⋊Dic3—22no—
97#3714—22no—
98#3714—24no—
99#3366—91noSylow
100C2×#237—61no—
101C2×#235—61no—
102C3×C4⋊Q8—21no—
103C3×C4⋊Q8C2×D311yescharacteristic
104C3×C4⋊Q8C2×D311yescharacteristic
105C3×#127—31no—
106C3×C4×D4—31no—
107#946—62no—
108#946—62no—
109#946—64no—
110#940—32no—
111#940—32no—
112#939—62no—
113#938—61no—
114D4×Dic3—32no—
115C2×#213—31no—
116C2×#213—32no—
117#930—61no—
118C2×D24—32no—
119C2×D24—31no—
120#897—61no—
121#897—61no—
122#897—62no—
123#893—32no—
124#893—32no—
125#893—32no—
126#893—62no—
127D3×C4⋊C4—61no—
128D3×C4⋊C4—61no—
129D3×C4⋊C4—62no—
130#890—32no—
131#890—32no—
132#890—62no—
133#884—62no—
134#874C2×D311yescharacteristic
135C4×D12—31no—
136C4×D12—31no—
137C4×D12—61no—
138C4×D12C2×D311yescharacteristic
139C4×Dic6—31no—
140C4×Dic6—31no—
141C4×Dic6—61no—
142C3×#106—32no—
143C3×C4⋊C8—31no—
144C3×#102—32no—
145C3×#102—32no—
146C3×#102—32no—
147C3×C4×C8—31no—
148#832—31no—
149#832—32no—
150#821—32no—
151#821—31no—
152#821—31no—
153#818—31no—
154#815—32no—
155#815—32no—
156Dic3⋊C8—32no—
157Dic3⋊C8—32no—
158#809—31no—
159#809C2×D312yes—
160#809C2×D312yes—
161#809C2×D312yes—
162#808C2×D312yes—
163#807—31no—
164C4⋊(C3⋊C8)C2×D311yescharacteristic
165C4×C3⋊C8C2×D311yescharacteristic
166C22×C3⋊D3—21no—
167C22×C3×D3—22no—
168C22×C3×D3—21no—
169C32×Q8—81no—
170C2×C32×C4—22no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2411yescharacteristic
174C2×C3⋊Dic3—21no—
175C2×C3⋊Dic3C2×D412yes—
176C2×C3⋊Dic3C2×D412yes—
177C4⋊(C3⋊D3)—21no—
178C4⋊(C3⋊D3)#4112yescomplemented
179C4×C3⋊D3—42no—
180C4×C3⋊D3—82no—
181#634—22no—
182C2×C3×Dic3—21no—
183C3×D12—22no—
184C3×D12—21no—
185C3×D12—21no—
186C3×D12—22no—
187C3×D12—42no—
188C3×D12—81no—
189C3×C4×D3—42no—
190#625—44no—
191#625—82no—
192D3×Dic3—44no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8—21no—
195C3×C3⋊C8—21no—
196#554—91no—
197#550—91no—
198#490—92no—
199#486—31no—
200#478—92no—
201#476—31no—
202#459—92no—
203#459—91no—
204#446—91no—
205#442—92no—
206C4×D8—91no—
207C2×C3×Q8—22no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×D4—32no—
211C2×C3×D4—31no—
212C2×C3×D4—61no—
213C2×C3×D4—61no—
214C22×C3×C4—61no—
215C2×#67—62no—
216C2×#67—62no—
217C2×#67—62no—
218C2×#67—62no—
219C22×Dic3—62no—
220#237—124no—
221#235—124no—
222C2×D12—21no—
223C2×D12—21no—
224C2×D12—31no—
225C2×D12—31no—
226C2×D12—61no—
227C2×D12C22×D311yescharacteristic
228C2×D12C22×D312yes—
229C2×C4×D3—21no—
230C2×C4×D3—62no—
231C2×C4×D3—62no—
232C2×C4×D3—61no—
233C2×C4×D3—61no—
234C2×C4×D3—62no—
235C2×C4×D3—62no—
236C2×C4×D3—64no—
237C2×Dic6—31no—
238C2×Dic6—31no—
239C2×Dic6—61no—
240C2×C3×C8—31no—
241C2×C3×C8—32no—
242C2×C3×C8—31no—
243C3×C4⋊C4—22no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—22no—
247C3×C4⋊C4—31no—
248C3×C4⋊C4C22×D312yes—
249C3×C4⋊C4C22×D312yes—
250C3×C22⋊C4—61no—
251C3×C42—21no—
252C3×C42C22×D311yescharacteristic
253C3×C42C22×D311yescharacteristic
254#217—62no—
255#213—62no—
256#213—64no—
257(C2×D3)⋊C4—21no—
258(C2×D3)⋊C4—62no—
259(C2×D3)⋊C4—62no—
260(C2×D3)⋊C4—62no—
261(C2×D3)⋊C4—62no—
262(C2×D3)⋊C4—64no—
263(C2×D3)⋊C4—61no—
264(C2×D3)⋊C4—61no—
265C4⋊Dic3—31no—
266C4⋊Dic3—31no—
267C4⋊Dic3—31no—
268C4⋊Dic3—31no—
269C4⋊Dic3—61no—
270C4⋊Dic3—61no—
271C4⋊Dic3—62no—
272C4⋊Dic3—62no—
273C4⋊Dic3—64no—
274C4⋊Dic3C22×D311yescharacteristic
275Dic3⋊C4—32no—
276Dic3⋊C4—32no—
277Dic3⋊C4—62no—
278Dic3⋊C4—62no—
279Dic3⋊C4—62no—
280Dic3⋊C4—64no—
281C4×Dic3—32no—
282C4×Dic3—32no—
283C4×Dic3—62no—
284C2×C3⋊C8C22×D311yescharacteristic
285C2×C3⋊C8C22×D311yescharacteristic
286C2×C3⋊C8C22×D312yes—
287D24—64no—
288D24—62no—
289C22×C32C22×D411yescharacteristic
290C2×C3⋊D3—22no—
291C2×C3⋊D3—41no—
292C2×C3⋊D3—41no—
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—42no—
301C32×C4AGL(1,ℤ/8)12yes—
302C32×C4C2×#4111yescharacteristic
303C32×C42−1+411yescharacteristic
304C3⋊Dic3—22no—
305C3⋊Dic3—22no—
306C3⋊Dic3—41no—
307C3×Dic3—41no—
308C2×#41—181no—
309C2×D8—91no—
310C2×D8—92no—
311C4⋊Q8D3211yescharacteristic
312#127—31no—
313#127—92no—
314#125—92no—
315C22⋊Q8—181no—
316C22⋊Q8—182no—
317#121—182no—
318#121—181no—
319C4×Q8—91no—
320C4×D4—31no—
321C4×D4—92no—
322C4×D4—92no—
323C4×D4—91no—
324C2×C4⋊C4—181no—
325#107—91no—
326#106—32no—
327C4⋊C8—31no—
328C4⋊C8—92no—
329#102—32no—
330#102—32no—
331#102—32no—
332#102—91no—
333#102—91no—
334#102—92no—
335#97—92no—
336C4×C8—31no—
337C23×C3—62no—
338C23×C3—61no—
339C22×D3—21no—
340C22×D3—22no—
341C22×D3—62no—
342C22×D3—61no—
343C22×D3—61no—
344C3×Q8—81no—
345C3×Q8—81no—
346C3×Q8—82no—
347C3×D4—62no—
348C3×D4—62no—
349C3×D4—61no—
350C3×D4—61no—
351C3×D4—122no—
352C3×D4—241no—
353C2×C3×C4—24no—
354C2×C3×C4—22no—
355C2×C3×C4—22no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—61no—
360C2×C3×C4—122no—
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D411yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367#67—124no—
368#67—124no—
369#67—242no—
370#67—242no—
371C2×Dic3—21no—
372C2×Dic3—32no—
373C2×Dic3—32no—
374C2×Dic3—32no—
375C2×Dic3—32no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—61no—
380C2×Dic3—61no—
381C2×Dic3—124no—
382D12—21no—
383D12—21no—
384D12—22no—
385D12—22no—
386D12—32no—
387D12—32no—
388D12—42no—
389D12—62no—
390D12—62no—
391D12—61no—
392D12—61no—
393D12—81no—
394C4×D3—42no—
395C4×D3—124no—
396C4×D3—124no—
397C4×D3—122no—
398C4×D3—122no—
399C4×D3—242no—
400C4×D3—242no—
401C4×D3—244no—
402Dic6—62no—
403Dic6—62no—
404Dic6—122no—
405C3×C8—61no—
406C3×C8—61no—
407C3×C8—62no—
408C3⋊C8—22no—
409C3⋊C8—21no—
410C3⋊C8—21no—
411C2×C32#54811yescharacteristic
412C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
413C2×C32#57611yescharacteristic
414C3⋊D3—42no—
415C3×D3—82no—
416C3×D3—81no—
417#41—364no—
418C2×Q8—21no—
419C2×Q8—91no—
420C2×D4—31no—
421C2×D4—32no—
422C2×D4—61no—
423C2×D4—61no—
424C2×D4—91no—
425C2×D4—182no—
426C2×D4—182no—
427C22×C4—61no—
428C22×C4—182no—
429C22×C4—182no—
430C22×C4—181no—
431D8—182no—
432D8—184no—
433C2×C8—31no—
434C2×C8—31no—
435C2×C8—32no—
436C4⋊C4—21no—
437C4⋊C4—31no—
438C4⋊C4—91no—
439C4⋊C4—92no—
440C4⋊C4—91no—
441C4⋊C4—182no—
442C4⋊C4—182no—
443C4⋊C4C2×D3212yes—
444C22⋊C4—61no—
445C22⋊C4—182no—
446C22⋊C4—182no—
447C22⋊C4—181no—
448C42—92no—
449C42C2×D3211yescharacteristic
450C22×C3—21no—
451C22×C3—122no—
452C22×C3—121no—
453C22×C3—121no—
454C22×C3—122no—
455C22×C3—121no—
456C22×C3—122no—
457C22×C3C2×D3×D411yescharacteristic
458C22×C3C2×D3×D411yescharacteristic
459C2×D3—41no—
460C2×D3—42no—
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—21no—
475C3×C4—21no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—22no—
479C3×C4—41no—
480C3×C4—44no—
481C3×C4—42no—
482C3×C4—42no—
483C3×C4—121no—
484C3×C4#91412yes—
485C3×C4#91412yes—
486C3×C4#100711yescharacteristic
487C3×C4D3×#4111yescharacteristic
488C3×C4D3×#4111yescharacteristic
489C3×C4#101011yescharacteristic
490Dic3—41no—
491Dic3—62no—
492Dic3—62no—
493Dic3—62no—
494Dic3—62no—
495Dic3—122no—
496Dic3—122no—
497Dic3—122no—
498Dic3—121no—
499Dic3—121no—
500C32#336611yescharacteristic, complemented, Sylow
501C23—61no—
502C23—62no—
503C23—181no—
504Q8—81no—
505Q8—182no—
506D4—61no—
507D4—62no—
508D4—61no—
509D4—62no—
510D4—92no—
511D4—122no—
512D4—181no—
513D4—241no—
514D4—364no—
515D4—722no—
516C2×C4—22no—
517C2×C4—61no—
518C2×C4—92no—
519C2×C4—92no—
520C2×C4—122no—
521C2×C4—181no—
522C2×C4—364no—
523C2×C4—362no—
524C2×C4—722no—
525C2×C4#381111yescharacteristic
526C2×C4#381111yescharacteristic
527C2×C4C22×D3211yescharacteristic
528C8—61no—
529C8—61no—
530C8—62no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—241no—
535C2×C3—242no—
536C2×C3#563311yescharacteristic
537C2×C3#567711yescharacteristic
538C2×C3#575711yescharacteristic
539C2×C3C2×#91411yescharacteristic
540C2×C3C2×#91411yescharacteristic
541C2×C3#577411yescharacteristic
542D3—82no—
543D3—81no—
544D3—124no—
545D3—122no—
546D3—122no—
547C22—122no—
548C22—121no—
549C22—121no—
550C22—122no—
551C22—121no—
552C22—122no—
553C22—182no—
554C22—361no—
555C22—361no—
556C22C2×#381111yescharacteristic
557C4—21no—
558C4—42no—
559C4—121no—
560C4—182no—
561C4—182no—
562C4—361no—
563C4#6394112yes—
564C4#6431511yescharacteristic
565C4#6431911yescharacteristic
566C3—21no—
567C3#8108811yescharacteristic, complemented
568C3#8158611yescharacteristic, complemented
569C2—242no—
570C2—241no—
571C2—362no—
572C2#1059510211yescharacteristic
573C2C2×#6394111yescharacteristic
574C2#1059536211yescharacteristic
subgroupG/H
centerC22C2×#3811
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 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596201C2semidirect
2. #10593906C2semidirect
3. C3×#5088C2semidirect
4. C3×#5084C2semidirect
5. #10590554C2semidirect
6. #10590551C2semidirect
7. #10590474C2semidirect
8. #10590462C2semidirect
9. #10590355C2semidirect
10. C4×#3714C2semidirect
11. #10590296C2semidirect
50. #5088D3semidirect
51. #5084D3semidirect
178. C4⋊(C3⋊D3)#41semidirect
500. C32#3366semidirect
567. C3#81088semidirect
568. C3#81586semidirect

Maximal subgroups

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

subgroupindex
#105962012
#105939062
C3×#50882
C3×#50842
#105905542
#105905512
#105904742
#105904622
#105903552
C4×#37142
#105902962
#815863
#810883