Finite Group Databasebeta

← #11895764

Subgroups — #11895764

Order 1152.

948 conjugacy classes of subgroups.

The subgroup lattice has 585 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596048C211yesmaximal, characteristic, complemented
2C3×#5579C211yesmaximal, characteristic, complemented
3C3×#5024C211yesmaximal, characteristic, complemented
4#10590349C212yesmaximal, complemented
5#10590349C211yesmaximal, characteristic, complemented
6#10590346C212yesmaximal, complemented
7C4×#3714C211yesmaximal, characteristic, complemented
8#10590308C212yesmaximal, complemented
9#10590300C211yesmaximal, characteristic, complemented
10#10590282C212yesmaximal, complemented
11#10590281C211yesmaximal, characteristic, complemented
12#83638—31nomaximal
13#79969—31nomaximal
14C2×#3832—21no—
15C32×C4×Q8C2211yescharacteristic
16#64104—21no—
17#64104—22no—
18#64083C2211yescharacteristic
19#64083C2212yes—
20C4×C4⋊(C3⋊D3)C2211yescharacteristic
21C4×C4⋊(C3⋊D3)C2212yes—
22C3×#946—21no—
23C3×#896—22no—
24C3×D3×C4⋊C4—21no—
25C3×C4×D12C2211yescharacteristic
26C3×C4×D12C2212yes—
27C3×#870C2212yes—
28C3×#869C2211yescharacteristic
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#63564C2212yes—
38#63564C2212yes—
39#63564C2211yescharacteristic
40#63564C2212yes—
41#63564C2212yes—
42#63563C2211yescharacteristic
43C3×#554—31no—
44#5579D311yescharacteristic, complemented
45#5577—31no—
46#5577—31no—
47#5577—61no—
48C3×#446—31no—
49#5088—31no—
50#5084—31no—
51#5067—32no—
52#5066—32no—
53#5024D311yescharacteristic, complemented
54#5015—32no—
55#5015—31no—
56#5014—32no—
57C4×#213—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
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×D12C2311yescharacteristic
77C2×C3×C4×D3—21no—
78C2×C3×C4×D3—22no—
79C2×C3×Dic6—21no—
80C32×C4⋊C4D411yescharacteristic
81C32×C4⋊C4D412yes—
82C32×C42C2311yescharacteristic
83C32×C42C2312yes—
84#3752—22no—
85#3752—21no—
86C4⋊(C3⋊Dic3)C2311yescharacteristic
87C3×(C2×D3)⋊C4—21no—
88C3×(C2×D3)⋊C4—22no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
91C3×C4⋊Dic3C2311yescharacteristic
92C3×Dic3⋊C4—22no—
93C3×Dic3⋊C4—22no—
94C2×C3×C3⋊C8C2311yescharacteristic
95C2×C3×C3⋊C8C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97#3714—22no—
98#3714—24no—
99#3366—91noSylow
100C2×#239—62no—
101C2×#239—61no—
102C2×#239—61no—
103C3×C4⋊Q8—31no—
104C3×#125—32no—
105C3×C22⋊Q8—61no—
106C3×C22⋊Q8—62no—
107C3×C4×Q8—21no—
108C3×C4×Q8C2×D311yescharacteristic
109C3×C4×Q8C2×D311yescharacteristic
110C3×C4×D4—31no—
111C3×C4×D4—32no—
112C2×C3×C4⋊C4—61no—
113#946—21no—
114C2×#213—31no—
115C2×#213—32no—
116C2×D24—31no—
117C2×D24—32no—
118#896—22no—
119#895—62no—
120#895—64no—
121#895—61no—
122#895—62no—
123#895—61no—
124#895—62no—
125D3×C4⋊C4—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—
138C4×D12C2×D311yescharacteristic
139C4×D12C2×D312yes—
140#870C2×D312yes—
141#869C2×D311yescharacteristic
142C3×C4⋊C8—31no—
143C3×C4⋊C8—32no—
144C3×#97—32no—
145C3×C4×C8—31no—
146#832—31no—
147#821—31no—
148#821—31no—
149#821—32no—
150#821—32no—
151#821—32no—
152#821—32no—
153#818—31no—
154#817—32no—
155#809—31no—
156#809—32no—
157#809—32no—
158#809—32no—
159#809—32no—
160#808—32no—
161#807—31no—
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—
168C22×C3×D3—21no—
169C32×Q8—22no—
170C2×C32×C4C2×D412yes—
171C2×C32×C4C2×D412yes—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—21no—
176C4⋊(C3⋊D3)—21no—
177C4⋊(C3⋊D3)—22no—
178C4⋊(C3⋊D3)—22no—
179C4⋊(C3⋊D3)—21no—
180C4⋊(C3⋊D3)—44no—
181C4⋊(C3⋊D3)—42no—
182C4⋊(C3⋊D3)—81no—
183C4⋊(C3⋊D3)—82no—
184C4×C3⋊D3—44no—
185C4×C3⋊D3—42no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C3×D12—21no—
189C3×D12#4112yescomplemented
190C3×C4×D3—42no—
191C3×C4×D3—82no—
192C3×Dic6—81no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8—21no—
195C3×C3⋊C8—21no—
196#554—31no—
197#550—91no—
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—
207C2×C3×Q8—21no—
208C2×C3×Q8—61no—
209C2×C3×Q8D1211yescharacteristic
210C2×C3×Q8#6711yescharacteristic
211C2×C3×D4—31no—
212C22×C3×C4—61no—
213C22×C3×C4—62no—
214#239—128no—
215#239—124no—
216#239—124no—
217C2×D12—31no—
218C2×D12—32no—
219C2×D12—31no—
220C2×D12—32no—
221C2×D12—61no—
222C2×D12—62no—
223C2×D12—64no—
224C2×D12—62no—
225C2×D12—62no—
226C2×D12—61no—
227C2×D12—62no—
228C2×D12—61no—
229C2×D12—62no—
230C2×D12—64no—
231C2×D12—61no—
232C2×D12—62no—
233C2×D12—62no—
234C2×D12—61no—
235C2×D12C22×D311yescharacteristic
236C2×C4×D3—21no—
237C2×C4×D3—22no—
238C2×C4×D3—64no—
239C2×C4×D3—62no—
240C2×C4×D3—62no—
241C2×C4×D3—61no—
242C2×C4×D3—62no—
243C2×C4×D3—61no—
244C2×Dic6—21no—
245C2×C3×C8—32no—
246C2×C3×C8—31no—
247C2×C3×C8—31no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—22no—
250C3×C4⋊C4—31no—
251C3×C4⋊C4—32no—
252C3×C4⋊C4—62no—
253C3×C4⋊C4—62no—
254C3×C4⋊C4—61no—
255C3×C4⋊C4D1211yescharacteristic
256C3×C4⋊C4D1212yes—
257C3×C4⋊C4#6711yescharacteristic
258C3×C4⋊C4#6712yes—
259C3×C22⋊C4—61no—
260C3×C22⋊C4—62no—
261C3×C42—21no—
262C3×C42—22no—
263C3×C42C22×D311yescharacteristic
264C3×C42C22×D312yes—
265C3×C42C22×D311yescharacteristic
266C3×C42C22×D312yes—
267#213—62no—
268#213—64no—
269(C2×D3)⋊C4—21no—
270(C2×D3)⋊C4—22no—
271(C2×D3)⋊C4—62no—
272(C2×D3)⋊C4—64no—
273(C2×D3)⋊C4—61no—
274(C2×D3)⋊C4—62no—
275(C2×D3)⋊C4—62no—
276(C2×D3)⋊C4—61no—
277C4⋊Dic3—21no—
278C4⋊Dic3—31no—
279C4⋊Dic3—31no—
280C4⋊Dic3—61no—
281C4⋊Dic3C22×D312yes—
282C4⋊Dic3C22×D311yescharacteristic
283Dic3⋊C4—22no—
284Dic3⋊C4—22no—
285C2×C3⋊C8C22×D311yescharacteristic
286C2×C3⋊C8C22×D311yescharacteristic
287C2×C3⋊C8C22×D312yes—
288D24—62no—
289D24—64no—
290C22×C32C22×D411yescharacteristic
291C2×C3⋊D3—42no—
292C2×C3⋊D3—41no—
293C2×C3⋊D3—42no—
294C2×C3⋊D3—41no—
295C2×C3⋊D3—42no—
296C2×C3⋊D3—41no—
297C2×C3×D3—22no—
298C2×C3×D3—41no—
299C2×C3×D3—41no—
300C32×C4—22no—
301C32×C4—21no—
302C32×C4—22no—
303C32×C4AGL(1,ℤ/8)12yes—
304C32×C4C2×#4111yescharacteristic
305C32×C42−1+411yescharacteristic
306C3⋊Dic3—41no—
307C3×Dic3—41no—
308C3×Dic3—42no—
309C2×#41—181no—
310C2×D8—91no—
311C2×D8—92no—
312C4⋊Q8—31no—
313#127—91no—
314#127—92no—
315#125—32no—
316C22⋊Q8—61no—
317C22⋊Q8—62no—
318#121—181no—
319#121—182no—
320C4×Q8D3211yescharacteristic
321C4×D4—31no—
322C4×D4—32no—
323C4×D4—91no—
324C4×D4—92no—
325C2×C4⋊C4—61no—
326#107—91no—
327#106—92no—
328C4⋊C8—31no—
329C4⋊C8—32no—
330#102—91no—
331#102—92no—
332#102—92no—
333#102—92no—
334#102—92no—
335#102—91no—
336#97—32no—
337C4×C8—31no—
338C23×C3—61no—
339C22×D3—21no—
340C22×D3—64no—
341C22×D3—62no—
342C22×D3—62no—
343C22×D3—61no—
344C22×D3—62no—
345C22×D3—61no—
346C3×Q8—24no—
347C3×Q8—22no—
348C3×Q8—22no—
349C3×Q8—241no—
350C3×D4—32no—
351C3×D4—61no—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—22no—
357C2×C3×C4—61no—
358C2×C3×C4—62no—
359C2×C3×C4—122no—
360C2×C3×C4—242no—
361C2×C3×C4C2×D1211yescharacteristic
362C2×C3×C4C2×D1212yes—
363C2×C3×C4C2×D1212yes—
364C2×C3×C4C2×D1211yescharacteristic
365C2×C3×C4C2×#6712yes—
366C2×C3×C4C2×#6712yes—
367C2×C3×C4C2×#6711yescharacteristic
368C2×C3×C4C2×#6711yescharacteristic
369C2×C3×C4C23×D311yescharacteristic
370C2×C3×C4C23×D311yescharacteristic
371C2×Dic3—21no—
372C2×Dic3—22no—
373C2×Dic3—62no—
374C2×Dic3—61no—
375C2×Dic3—61no—
376D12—21no—
377D12—61no—
378D12—62no—
379D12—61no—
380D12—62no—
381D12—61no—
382D12—62no—
383D12—61no—
384D12—62no—
385D12—121no—
386D12—122no—
387D12—121no—
388D12—122no—
389D12—128no—
390D12—124no—
391D12—124no—
392D12—124no—
393D12—122no—
394D12—122no—
395D12—242no—
396D12—241no—
397D12—241no—
398D12—242no—
399D12—244no—
400D12—242no—
401D12#23912yescomplemented
402C4×D3—42no—
403C4×D3—82no—
404C4×D3—128no—
405C4×D3—124no—
406C4×D3—124no—
407C4×D3—124no—
408C4×D3—122no—
409C4×D3—122no—
410Dic6—81no—
411C3×C8—62no—
412C3×C8—61no—
413C3×C8—61no—
414C3⋊C8—21no—
415C3⋊C8—21no—
416C3⋊C8—22no—
417C2×C32#54811yescharacteristic
418C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
419C2×C32#57611yescharacteristic
420C3⋊D3—82no—
421C3⋊D3—81no—
422C3×D3—42no—
423#41—364no—
424C2×Q8—61no—
425C2×Q8#62611yescharacteristic
426C2×D4—31no—
427C2×D4—91no—
428C2×D4—92no—
429C2×D4—182no—
430C2×D4—181no—
431C2×D4—181no—
432C2×D4—182no—
433C22×C4—61no—
434C22×C4—62no—
435C22×C4—182no—
436C22×C4—181no—
437D8—182no—
438D8—184no—
439C2×C8—31no—
440C2×C8—31no—
441C2×C8—32no—
442C4⋊C4—32no—
443C4⋊C4—31no—
444C4⋊C4—62no—
445C4⋊C4—61no—
446C4⋊C4—62no—
447C4⋊C4—91no—
448C4⋊C4#62611yescharacteristic
449C4⋊C4#62612yes—
450C22⋊C4—61no—
451C22⋊C4—62no—
452C22⋊C4—181no—
453C22⋊C4—182no—
454C42C2×D3211yescharacteristic
455C42C2×D3212yes—
456C22×C3—21no—
457C22×C3—62no—
458C22×C3—121no—
459C22×C3—121no—
460C22×C3C22×D1211yescharacteristic
461C22×C3C22×#6711yescharacteristic
462C2×D3—22no—
463C2×D3—41no—
464C2×D3—41no—
465C2×D3—124no—
466C2×D3—122no—
467C2×D3—124no—
468C2×D3—122no—
469C2×D3—122no—
470C2×D3—124no—
471C2×D3—122no—
472C2×D3—121no—
473C2×D3—121no—
474C2×D3—122no—
475C2×D3—122no—
476C2×D3—121no—
477C2×D3—122no—
478C2×D3—121no—
479C2×D3—122no—
480C2×D3—121no—
481C2×D3—122no—
482C2×D3—121no—
483C3×C4—24no—
484C3×C4—22no—
485C3×C4—22no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—21no—
489C3×C4—22no—
490C3×C4—21no—
491C3×C4—21no—
492C3×C4—22no—
493C3×C4—42no—
494C3×C4—41no—
495C3×C4—121no—
496C3×C4—122no—
497C3×C4#90812yes—
498C3×C4#94912yes—
499C3×C4C2×#23911yescharacteristic
500C3×C4#100711yescharacteristic
501C3×C4#100711yescharacteristic
502C3×C4D3×#4111yescharacteristic
503Dic3—41no—
504Dic3—42no—
505Dic3—122no—
506Dic3—121no—
507Dic3—121no—
508C32#336611yescharacteristic, complemented, Sylow
509C23—61no—
510C23—182no—
511C23—181no—
512Q8—22no—
513Q8—241no—
514D4—32no—
515D4—61no—
516D4—181no—
517D4—182no—
518D4—181no—
519D4—182no—
520D4—364no—
521D4—362no—
522D4—722no—
523D4—721no—
524C2×C4—61no—
525C2×C4—62no—
526C2×C4—122no—
527C2×C4—181no—
528C2×C4—242no—
529C2×C4—364no—
530C2×C4—362no—
531C2×C4C2×#62611yescharacteristic
532C2×C4C2×#62612yes—
533C2×C4C2×#62612yes—
534C2×C4C2×#62611yescharacteristic
535C2×C4C22×D3211yescharacteristic
536C8—61no—
537C8—61no—
538C8—62no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—21no—
542C2×C3—122no—
543C2×C3#557611yescharacteristic
544C2×C3C2×#90811yescharacteristic
545C2×C3#575211yescharacteristic
546C2×C3#581711yescharacteristic
547C2×C3C2×#94911yescharacteristic
548C2×C3#583511yescharacteristic
549D3—42no—
550D3—244no—
551D3—242no—
552D3—242no—
553D3—241no—
554D3—242no—
555D3—241no—
556C22—62no—
557C22—121no—
558C22—121no—
559C22—362no—
560C22—361no—
561C22—361no—
562C22—362no—
563C22—362no—
564C22—361no—
565C22C22×#62611yescharacteristic
566C4—22no—
567C4—21no—
568C4—22no—
569C4—122no—
570C4—121no—
571C4—361no—
572C4#6382512yes—
573C4#6431611yescharacteristic
574C4D3×#23911yescharacteristic
575C3—21no—
576C3#7996911yescharacteristic, complemented
577C3#8363811yescharacteristic, complemented
578C2—122no—
579C2—722no—
580C2—721no—
581C2C2×#6382511yescharacteristic
582C2#1059534211yescharacteristic
583C2#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. #10596048C2semidirect
2. C3×#5579C2semidirect
3. C3×#5024C2semidirect
4. #10590349C2semidirect
5. #10590349C2semidirect
6. #10590346C2semidirect
7. C4×#3714C2semidirect
8. #10590308C2semidirect
9. #10590300C2semidirect
10. #10590282C2semidirect
11. #10590281C2semidirect
44. #5579D3semidirect
53. #5024D3semidirect
189. C3×D12#41semidirect
401. D12#239semidirect
508. C32#3366semidirect
576. C3#79969semidirect
577. C3#83638semidirect

Maximal subgroups

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

subgroupindex
#105960482
C3×#55792
C3×#50242
#105903492
#105903462
C4×#37142
#105903082
#105903002
#105902822
#105902812
#836383
#799693