Finite Group Databasebeta

← #11895769

Subgroups — #11895769

Order 1152.

862 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5543C211yesmaximal, characteristic, complemented
2#10593902C211yesmaximal, characteristic, complemented
3#10592714C211yesmaximal, characteristic, complemented
4C3×C4×#213C211yesmaximal, characteristic, complemented
5#10591481C212yesmaximal, complemented
6#10591404C212yesmaximal, complemented
7#10590550C212yesmaximal, complemented
8#10590468C212yesmaximal, complemented
9#10590281C211yesmaximal, characteristic, complemented
10#10590266C211yesmaximal, characteristic, complemented
11#10590258C211yesmaximal, characteristic, complemented
12#83638—31nomaximal
13#79570—31nomaximal
14C2×#3799—21no—
15C32×C4×D4C2211yescharacteristic
16C2×#3753C2212yes—
17#64083C2211yescharacteristic
18C3×D4×Dic3C2212yes—
19C2×C3×#213C2211yescharacteristic
20C2×C3×C4⋊Dic3—21no—
21C3×#924—21no—
22C3×#890C2212yes—
23C3×#878—22no—
24C3×C4×D12C2211yescharacteristic
25C3×#869C2211yescharacteristic
26C3×C4×Dic6C2211yescharacteristic
27#63911C2212yes—
28#63910—22no—
29#63909—21no—
30#63894C2212yes—
31#63636C2212yes—
32C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
33C3×#832C2211yescharacteristic
34C3×#809C2211yescharacteristic
35C3×#807C2211yescharacteristic
36C3×C4×C3⋊C8C2211yescharacteristic
37#63574C2212yes—
38Dic3⋊(C3⋊C8)C2212yes—
39#63564C2212yes—
40#63564C2212yes—
41#63562C2212yes—
42#63554C2212yes—
43C3×#554—31no—
44#5577—31no—
45#5553—31no—
46#5543D311yescharacteristic, complemented
47C3×C4×D8—31no—
48#5150—32no—
49#5088—31no—
50#5084—31no—
51#5067—32no—
52#5066—32no—
53#5024—31no—
54#5015—31no—
55#5015—31no—
56#5015—32no—
57#5015—61no—
58#5014—32no—
59C4×#213D311yescharacteristic, complemented
60#5008—31no—
61#4891—32no—
62#4785—32no—
63#4764—32no—
64#4694—31no—
65#4679—31no—
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)C2312yes—
71C22×C3×Dic3—22no—
72C2×C3×D12C2311yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×Dic6—21no—
75C2×C3×Dic6D411yescharacteristic
76C2×#626—22no—
77C2×#626—22no—
78C2×#624—22no—
79#3799—44no—
80C32×C4⋊C4C2311yescharacteristic
81C32×C22⋊C4—21no—
82C32×C42C2311yescharacteristic
83#3753—24no—
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×#217—22no—
86C3×#213—22no—
87C3×(C2×D3)⋊C4—21no—
88C3×C4⋊Dic3—21no—
89C3×C4⋊Dic3—22no—
90C3×C4⋊Dic3D411yescharacteristic
91C3×C4⋊Dic3C2312yes—
92C3×C4⋊Dic3C2311yescharacteristic
93C3×Dic3⋊C4—22no—
94C3×Dic3⋊C4D412yes—
95C3×C4×Dic3C2312yes—
96C2×C3×C3⋊C8C2311yescharacteristic
97C2×C3×C3⋊C8C2311yescharacteristic
98#3722—22no—
99#3366—91noSylow
100C2×#239—61no—
101C2×#235—61no—
102C2×C3×D8—31no—
103C3×C4⋊Q8—31no—
104C3×#125—32no—
105C3×C22⋊Q8—62no—
106C3×C22⋊Q8—61no—
107C3×C4×Q8—31no—
108C3×C4×D4—21no—
109C3×C4×D4—32no—
110C3×C4×D4—31no—
111C3×C4×D4C2×D311yescharacteristic
112C3×C4×D4C2×D311yescharacteristic
113C2×C3×C4⋊C4—61no—
114#940—32no—
115D4×Dic3C2×D312yes—
116C2×#213—32no—
117C2×#213—32no—
118C2×#213—62no—
119C2×#213C2×D311yescharacteristic
120#930—61no—
121C2×C4⋊Dic3—21no—
122#924—21no—
123#895—62no—
124#895—61no—
125#893—32no—
126#890C2×D312yes—
127#884—62no—
128#878—22no—
129#874—32no—
130#874—31no—
131#874—31no—
132#874—61no—
133C4×D12—32no—
134C4×D12C2×D311yescharacteristic
135#869C2×D311yescharacteristic
136C4×Dic6C2×D311yescharacteristic
137C3×#107—31no—
138C3×#102—31no—
139C3×#102—31no—
140C3×C4×C8—31no—
141#832—32no—
142#832C2×D311yescharacteristic
143#821—32no—
144#821—32no—
145#815—32no—
146Dic3⋊C8—32no—
147#809—32no—
148#809—32no—
149#809—32no—
150#809—32no—
151#809—32no—
152#809—62no—
153#809C2×D311yescharacteristic
154#808—32no—
155#808—32no—
156#807C2×D311yescharacteristic
157C4⋊(C3⋊C8)—31no—
158C4⋊(C3⋊C8)—31no—
159C4⋊(C3⋊C8)—32no—
160C4⋊(C3⋊C8)—61no—
161#803—32no—
162C4×C3⋊C8C2×D311yescharacteristic
163C23×C32—21no—
164C22×C3⋊D3—22no—
165C22×C3×D3—21no—
166C32×D4—21no—
167C32×D4#4112yescomplemented
168C2×C32×C4—21no—
169C2×C32×C4—42no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2411yescharacteristic
173C4⋊(C3⋊D3)—22no—
174C4⋊(C3⋊D3)—22no—
175C4⋊(C3⋊D3)—42no—
176C4⋊(C3⋊D3)—81no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—82no—
180C2×C3×Dic3C2×D412yes—
181C2×C3×Dic3C2×D412yes—
182C3×D12—21no—
183C3×D12—21no—
184C3×C4×D3—42no—
185C3×Dic6—22no—
186C3×Dic6—81no—
187#626—44no—
188#626—82no—
189#624—44no—
190C3⋊(C3⋊C8)—22no—
191C3×C3⋊C8—21no—
192C3×C3⋊C8—21no—
193#554—31no—
194#550—91no—
195#490—92no—
196#486—91no—
197#478—92no—
198#476—91no—
199#459—92no—
200#459—91no—
201#446—91no—
202#442—92no—
203C4×D8—31no—
204C2×C3×Q8—31no—
205C2×C3×Q8—61no—
206C2×C3×D4—21no—
207C2×C3×D4—31no—
208C2×C3×D4C22×D311yescharacteristic
209C2×C3×D4C22×D311yescharacteristic
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—41no—
213C22×C3×C4—62no—
214C22×C3×C4—61no—
215C2×#67—62no—
216C2×#67—62no—
217C22×Dic3—22no—
218#239—124no—
219#235—124no—
220C2×D12—32no—
221C2×D12—32no—
222C2×D12—62no—
223C2×D12—62no—
224C2×D12—61no—
225C2×D12—61no—
226C2×D12—62no—
227C2×D12—61no—
228C2×D12—61no—
229C2×D12—121no—
230C2×D12—121no—
231C2×D12C22×D311yescharacteristic
232C2×C4×D3—21no—
233C2×C4×D3—62no—
234C2×C4×D3—62no—
235C2×Dic6—21no—
236C2×Dic6#6711yescharacteristic
237C3×D8—62no—
238C2×C3×C8—31no—
239C2×C3×C8—31no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—32no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—31no—
244C3×C4⋊C4—32no—
245C3×C4⋊C4—62no—
246C3×C4⋊C4—62no—
247C3×C4⋊C4—61no—
248C3×C4⋊C4C22×D311yescharacteristic
249C3×C4⋊C4C22×D311yescharacteristic
250C3×C22⋊C4—21no—
251C3×C22⋊C4—21no—
252C3×C22⋊C4—41no—
253C3×C22⋊C4—62no—
254C3×C22⋊C4—61no—
255C3×C42—21no—
256C3×C42—32no—
257C3×C42C22×D311yescharacteristic
258C3×C42C22×D311yescharacteristic
259#217—22no—
260#213—22no—
261#213—64no—
262#213—64no—
263#213—124no—
264(C2×D3)⋊C4—21no—
265(C2×D3)⋊C4—62no—
266(C2×D3)⋊C4—62no—
267C4⋊Dic3—21no—
268C4⋊Dic3—22no—
269C4⋊Dic3#6711yescharacteristic
270C4⋊Dic3C22×D311yescharacteristic
271C4⋊Dic3C22×D312yes—
272Dic3⋊C4—22no—
273Dic3⋊C4#6712yes—
274C4×Dic3C22×D312yes—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—32no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8C22×D311yescharacteristic
279C2×C3⋊C8C22×D311yescharacteristic
280C22×C32—22no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32C22×D411yescharacteristic
284C2×C3⋊D3—42no—
285C2×C3⋊D3—42no—
286C2×C3⋊D3—42no—
287C2×C3×D3—41no—
288C2×C3×D3—41no—
289C2×C3×D3—41no—
290C32×C4—21no—
291C32×C4—41no—
292C32×C4AGL(1,ℤ/8)12yes—
293C32×C4C2×#4111yescharacteristic
294C32×C42−1+411yescharacteristic
295C3×Dic3—22no—
296C3×Dic3—22no—
297C3×Dic3—41no—
298C3×Dic3—42no—
299C2×#41—181no—
300C2×D8—31no—
301C2×D8—92no—
302C4⋊Q8—31no—
303#127—92no—
304#127—91no—
305#125—32no—
306C22⋊Q8—62no—
307C22⋊Q8—61no—
308#121—182no—
309#121—181no—
310C4×Q8—31no—
311C4×D4—32no—
312C4×D4—31no—
313C4×D4—92no—
314C4×D4D3211yescharacteristic
315C2×C4⋊C4—61no—
316#107—31no—
317#106—92no—
318C4⋊C8—92no—
319C4⋊C8—91no—
320#102—31no—
321#102—31no—
322#102—92no—
323#102—92no—
324#102—92no—
325#102—92no—
326#97—92no—
327C4×C8—31no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—41no—
331C23×C3—61no—
332C22×D3—21no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—122no—
336C3×Q8—62no—
337C3×Q8—241no—
338C3×D4—21no—
339C3×D4—21no—
340C3×D4—22no—
341C3×D4—41no—
342C3×D4—61no—
343C3×D4—61no—
344C3×D4#23512yescomplemented
345C3×D4#23912yescomplemented
346C2×C3×C4—21no—
347C2×C3×C4—21no—
348C2×C3×C4—21no—
349C2×C3×C4—21no—
350C2×C3×C4—21no—
351C2×C3×C4—32no—
352C2×C3×C4—32no—
353C2×C3×C4—41no—
354C2×C3×C4—42no—
355C2×C3×C4—42no—
356C2×C3×C4—62no—
357C2×C3×C4—61no—
358C2×C3×C4—82no—
359C2×C3×C4—122no—
360C2×C3×C4—242no—
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4D3×D411yescharacteristic
363C2×C3×C4C2×#6711yescharacteristic
364C2×C3×C4C2×#6711yescharacteristic
365C2×C3×C4C23×D311yescharacteristic
366C2×C3×C4C23×D311yescharacteristic
367#67—124no—
368#67—242no—
369C2×Dic3—21no—
370C2×Dic3—22no—
371C2×Dic3—82no—
372C2×Dic3C2×#6712yes—
373C2×Dic3C2×#6712yes—
374D12—21no—
375D12—21no—
376D12—62no—
377D12—62no—
378D12—62no—
379D12—62no—
380D12—122no—
381D12—122no—
382D12—124no—
383D12—122no—
384D12—122no—
385D12—242no—
386D12—241no—
387D12—241no—
388D12—242no—
389D12—242no—
390C4×D3—42no—
391C4×D3—124no—
392C4×D3—124no—
393Dic6—22no—
394Dic6—81no—
395C3×C8—61no—
396C3×C8—61no—
397C3⋊C8—21no—
398C3⋊C8—21no—
399C3⋊C8—62no—
400C3⋊C8—62no—
401C3⋊C8—122no—
402C2×C32—42no—
403C2×C32#54811yescharacteristic
404C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
405C2×C32#57611yescharacteristic
406C3⋊D3—82no—
407C3×D3—81no—
408#41—364no—
409C2×Q8—31no—
410C2×Q8—61no—
411C2×D4—31no—
412C2×D4—92no—
413C2×D4—182no—
414C2×D4—182no—
415C2×D4—181no—
416C2×D4—181no—
417C2×D4C2×D3211yescharacteristic
418C22×C4—21no—
419C22×C4—62no—
420C22×C4—61no—
421C22×C4—182no—
422D8—62no—
423D8—184no—
424C2×C8—31no—
425C2×C8—31no—
426C2×C8—92no—
427C4⋊C4—31no—
428C4⋊C4—32no—
429C4⋊C4—31no—
430C4⋊C4—32no—
431C4⋊C4—62no—
432C4⋊C4—62no—
433C4⋊C4—61no—
434C4⋊C4C2×D3211yescharacteristic
435C22⋊C4—21no—
436C22⋊C4—62no—
437C22⋊C4—61no—
438C22⋊C4—182no—
439C42—32no—
440C42C2×D3211yescharacteristic
441C22×C3—22no—
442C22×C3—22no—
443C22×C3—21no—
444C22×C3—42no—
445C22×C3—41no—
446C22×C3—41no—
447C22×C3—41no—
448C22×C3—41no—
449C22×C3—81no—
450C22×C3—81no—
451C22×C3—121no—
452C22×C3—121no—
453C22×C3—121no—
454C22×C3C2×D3×D411yescharacteristic
455C22×C3C22×#6711yescharacteristic
456C2×D3—41no—
457C2×D3—41no—
458C2×D3—41no—
459C2×D3—122no—
460C2×D3—122no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—122no—
464C2×D3—122no—
465C2×D3—242no—
466C2×D3—242no—
467C2×D3—242no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—21no—
471C3×C4—21no—
472C3×C4—22no—
473C3×C4—41no—
474C3×C4—41no—
475C3×C4—41no—
476C3×C4—62no—
477C3×C4—62no—
478C3×C4—81no—
479C3×C4—122no—
480C3×C4—121no—
481C3×C4#91112yes—
482C3×C4#94912yes—
483C3×C4C2×#23511yescharacteristic
484C3×C4C2×#23911yescharacteristic
485C3×C4#100711yescharacteristic
486C3×C4#101011yescharacteristic
487Dic3—22no—
488Dic3—22no—
489Dic3—41no—
490Dic3—42no—
491C32#336611yescharacteristic, complemented, Sylow
492C23—21no—
493C23—61no—
494C23—182no—
495Q8—62no—
496Q8—241no—
497D4—21no—
498D4—61no—
499D4—61no—
500D4—182no—
501D4—182no—
502D4—364no—
503D4—362no—
504D4—721no—
505D4—722no—
506D4#379912yescomplemented
507C2×C4—21no—
508C2×C4—32no—
509C2×C4—32no—
510C2×C4—42no—
511C2×C4—61no—
512C2×C4—62no—
513C2×C4—122no—
514C2×C4—242no—
515C2×C4—364no—
516C2×C4D3×#6711yescharacteristic
517C2×C4D3×#6711yescharacteristic
518C2×C4C22×D3211yescharacteristic
519C8—61no—
520C8—61no—
521C8—182no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—42no—
526C2×C3—42no—
527C2×C3—82no—
528C2×C3—241no—
529C2×C3#555211yescharacteristic
530C2×C3C2×#91111yescharacteristic
531C2×C3#576911yescharacteristic
532C2×C3#581711yescharacteristic
533C2×C3C2×#94911yescharacteristic
534C2×C3#583511yescharacteristic
535D3—81no—
536D3—242no—
537D3—242no—
538D3—482no—
539C22—22no—
540C22—41no—
541C22—41no—
542C22—121no—
543C22—121no—
544C22—121no—
545C22—362no—
546C22—362no—
547C22—362no—
548C22C2×D3×#6711yescharacteristic
549C4—21no—
550C4—41no—
551C4—62no—
552C4—62no—
553C4—121no—
554C4—122no—
555C4#6392512yes—
556C4#6429711yescharacteristic
557C4C2×#379911yescharacteristic
558C3—21no—
559C3#7957011yescharacteristic, complemented
560C3#8363811yescharacteristic, complemented
561C2—42no—
562C2—241no—
563C2—722no—
564C2#1059490211yescharacteristic
565C2C2×#6392511yescharacteristic
566C2#1059545611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
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. C3×#5543C2semidirect
2. #10593902C2semidirect
3. #10592714C2semidirect
4. C3×C4×#213C2semidirect
5. #10591481C2semidirect
6. #10591404C2semidirect
7. #10590550C2semidirect
8. #10590468C2semidirect
9. #10590281C2semidirect
10. #10590266C2semidirect
11. #10590258C2semidirect
46. #5543D3semidirect
59. C4×#213D3semidirect
167. C32×D4#41semidirect
344. C3×D4#235semidirect
345. C3×D4#239semidirect
491. C32#3366semidirect
506. D4#3799semidirect
559. C3#79570semidirect
560. C3#83638semidirect

Maximal subgroups

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

subgroupindex
C3×#55432
#105939022
#105927142
C3×C4×#2132
#105914812
#105914042
#105905502
#105904682
#105902812
#105902662
#105902582
#836383
#795703