Finite Group Databasebeta

← #11895725

Subgroups — #11895725

Order 1152.

1188 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596024C211yesmaximal, characteristic, complemented
2#10596010C211yesmaximal, characteristic, complemented
3C32×#442C211yesmaximal, characteristic, complemented
4#10592849C211yesmaximal, characteristic, complemented
5#10592849C211yesmaximal, characteristic, complemented
6#10592714C211yesmaximal, characteristic, complemented
7#10592708C211yesmaximal, characteristic, complemented
8#10592570C211yesmaximal, characteristic, complemented
9#10592569C211yesmaximal, characteristic, complemented
10#10592484C211yesmaximal, characteristic, complemented
11#10592463C211yesmaximal, characteristic, complemented
12#10592459C211yesmaximal, characteristic, complemented
13#10592455C211yesmaximal, characteristic, complemented
14#10592412C211yesmaximal, characteristic, complemented
15#10592400C211yesmaximal, characteristic, complemented
16#79851—34nomaximal
17C2×#3828—21no—
18C2×C32×D8C2211yescharacteristic
19C32×C4×D4C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21#64149C2211yescharacteristic
22#64149C2211yescharacteristic
23D4×C3⋊Dic3C2211yescharacteristic
24D4×C3⋊Dic3C2211yescharacteristic
25C2×#3753C2211yescharacteristic
26C2×#3753C2211yescharacteristic
27#64139—21no—
28#64133—21no—
29C2×#3750—21no—
30#64102C2211yescharacteristic
31#64102C2211yescharacteristic
32#64099C2211yescharacteristic
33#64097C2211yescharacteristic
34#64093—21no—
35#64093—21no—
36#64087—21no—
37#64087—21no—
38#64083C2211yescharacteristic
39#64079C2211yescharacteristic
40C4×#634C2211yescharacteristic
41C32×#106C2211yescharacteristic
42C32×#102C2211yescharacteristic
43C32×#102C2211yescharacteristic
44C32×#97C2211yescharacteristic
45#63659C2211yescharacteristic
46#63659C2211yescharacteristic
47#63648C2211yescharacteristic
48#63648C2211yescharacteristic
49#63648C2211yescharacteristic
50#63648C2211yescharacteristic
51#63642C2211yescharacteristic
52#63641C2211yescharacteristic
53#63641C2211yescharacteristic
54C8×C3⋊Dic3C2211yescharacteristic
55#63636C2211yescharacteristic
56#63636C2211yescharacteristic
57#63635C2211yescharacteristic
58#63634C2211yescharacteristic
59C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
60#5553—34no—
61#5539—34no—
62C3×#442D314yescomplemented
63#5150—34no—
64#5150—34no—
65#5015—34no—
66#5009—34no—
67#4871—34no—
68#4870—34no—
69#4785—34no—
70#4764—34no—
71#4760—34no—
72#4756—34no—
73#4713—34no—
74#4701—34no—
75C2×C32×D4C2311yescharacteristic
76C2×C32×D4C2311yescharacteristic
77C22×C32×C4—21no—
78C22×C32×C4—21no—
79C2×#638—21no—
80C2×#638—21no—
81C2×#638—21no—
82C2×#638—21no—
83C22×C3⋊Dic3—21no—
84C22×C3⋊Dic3—21no—
85#3828—44no—
86C2×C4⋊(C3⋊D3)—21no—
87C2×C4⋊(C3⋊D3)—21no—
88C2×C4⋊(C3⋊D3)C2311yescharacteristic
89C2×C4⋊(C3⋊D3)C2311yescharacteristic
90C2×C4×C3⋊D3—21no—
91C2×C4×C3⋊D3—21no—
92C2×#634—21no—
93C2×#634D411yescharacteristic
94C32×D8—22no—
95C2×C32×C8C2311yescharacteristic
96C2×C32×C8C2311yescharacteristic
97C32×C4⋊C4C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C22⋊C4—21no—
100C32×C22⋊C4—21no—
101C32×C42C2311yescharacteristic
102#3757—21no—
103#3757—21no—
104#3753—22no—
105#3753—22no—
106#3752—21no—
107#3752—21no—
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)D411yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112#3750—21no—
113#3750—21no—
114#3750—21no—
115#3750—21no—
116#3750D411yescharacteristic
117#3750D411yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C4×C3⋊Dic3C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122#3366—91noSylow
123C2×#235—64no—
124C2×C3×D8C2×D314yes—
125C3×C4×D4C2×D314yes—
126C3×C4×D4C2×D314yes—
127#940—34no—
128#940—34no—
129D4×Dic3—34no—
130D4×Dic3—34no—
131C2×#213—34no—
132C2×#213—34no—
133#930—64no—
134#924—64no—
135C2×Dic3⋊C4—64no—
136#893—34no—
137#893—34no—
138#890—34no—
139#888—34no—
140#884—64no—
141#884—64no—
142#878—64no—
143#878—64no—
144#874—34no—
145#870—34no—
146C4×Dic6—34no—
147C3×#106C2×D314yes—
148C3×#102C2×D314yes—
149C3×#102C2×D314yes—
150C3×#97C2×D314yes—
151#832—34no—
152#832—34no—
153#821—34no—
154#821—34no—
155#821—34no—
156#821—34no—
157#815—34no—
158Dic3⋊C8—34no—
159Dic3⋊C8—34no—
160C8×Dic3—34no—
161#809—34no—
162#809—34no—
163#808—34no—
164#807—34no—
165C4⋊(C3⋊C8)—34no—
166C23×C32—21no—
167C23×C32—21no—
168C22×C3⋊D3—21no—
169C22×C3⋊D3—21no—
170C32×D4—21no—
171C32×D4—21no—
172C32×D4—21no—
173C32×D4#4112yescomplemented
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—42no—
177C2×C32×C4—81no—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2411yescharacteristic
181#638—42no—
182#638—42no—
183#638—81no—
184#638—81no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—42no—
188C2×C3⋊Dic3—81no—
189C2×C3⋊Dic3C2×D411yescharacteristic
190C2×C3⋊Dic3C2×D411yescharacteristic
191C2×C3⋊Dic3C2×D411yescharacteristic
192C2×C3⋊Dic3C2×D411yescharacteristic
193C4⋊(C3⋊D3)—21no—
194C4⋊(C3⋊D3)—21no—
195C4⋊(C3⋊D3)—21no—
196C4⋊(C3⋊D3)—21no—
197C4⋊(C3⋊D3)—42no—
198C4⋊(C3⋊D3)—81no—
199C4×C3⋊D3—42no—
200C4×C3⋊D3—42no—
201#634—22no—
202#634—81no—
203C32×C8—21no—
204C32×C8—21no—
205C3⋊(C3⋊C8)—21no—
206C3⋊(C3⋊C8)—21no—
207#554—91no—
208#550—91no—
209#490—91no—
210#490—91no—
211#486—91no—
212#478—91no—
213#478—91no—
214#476—91no—
215#459—91no—
216#459—91no—
217#459—91no—
218#446—91no—
219#442—91no—
220#442C3⋊D311yescharacteristic, complemented
221C4×D8—91no—
222C2×C3×D4C22×D314yes—
223C2×C3×D4C22×D314yes—
224C22×C3×C4—24no—
225C22×C3×C4—24no—
226C2×#67—64no—
227C2×#67—64no—
228C2×#67—64no—
229C2×#67—64no—
230C22×Dic3—64no—
231C22×Dic3—64no—
232#235—1216no—
233C2×D12—34no—
234C2×D12—34no—
235C2×D12—64no—
236C2×D12—64no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×Dic6—34no—
240C2×Dic6—64no—
241C3×D8—28no—
242C2×C3×C8C22×D314yes—
243C2×C3×C8C22×D314yes—
244C3×C4⋊C4C22×D314yes—
245C3×C4⋊C4C22×D314yes—
246C3×C22⋊C4—24no—
247C3×C22⋊C4—24no—
248C3×C42C22×D314yes—
249#217—64no—
250#217—64no—
251#213—68no—
252#213—68no—
253(C2×D3)⋊C4—64no—
254(C2×D3)⋊C4—64no—
255C4⋊Dic3—34no—
256C4⋊Dic3—34no—
257C4⋊Dic3—34no—
258C4⋊Dic3—64no—
259Dic3⋊C4—34no—
260Dic3⋊C4—34no—
261Dic3⋊C4—64no—
262Dic3⋊C4—64no—
263Dic3⋊C4—64no—
264Dic3⋊C4—64no—
265C4×Dic3—34no—
266C4×Dic3—34no—
267C2×C3⋊C8—34no—
268C2×C3⋊C8—34no—
269C22×C32—22no—
270C22×C32—41no—
271C22×C32—41no—
272C22×C32—41no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32C22×D411yescharacteristic
276C2×C3⋊D3—41no—
277C2×C3⋊D3—41no—
278C2×C3⋊D3—41no—
279C2×C3⋊D3—41no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C32×C4—21no—
283C32×C4—21no—
284C32×C4—41no—
285C32×C4—41no—
286C32×C4C2×#4111yescharacteristic
287C32×C42−1+411yescharacteristic
288C3⋊Dic3—21no—
289C3⋊Dic3—21no—
290C3⋊Dic3—21no—
291C3⋊Dic3—41no—
292C3⋊Dic3—41no—
293C3⋊Dic3AGL(1,ℤ/8)12yes—
294C2×#41—181no—
295C2×D8—91no—
296C2×D8—91no—
297C2×D8C2×C3⋊D311yescharacteristic
298C4⋊Q8—91no—
299#127—91no—
300#127—91no—
301#127—91no—
302#125—91no—
303#125—91no—
304C22⋊Q8—181no—
305C22⋊Q8—181no—
306C22⋊Q8—181no—
307#121—181no—
308#121—181no—
309#121—181no—
310C4×Q8—91no—
311C4×D4—91no—
312C4×D4—91no—
313C4×D4—91no—
314C4×D4—91no—
315C4×D4C2×C3⋊D311yescharacteristic
316C4×D4C2×C3⋊D311yescharacteristic
317C2×C4⋊C4—181no—
318#107—91no—
319#106—91no—
320#106C2×C3⋊D311yescharacteristic
321C4⋊C8—91no—
322C4⋊C8—91no—
323C4⋊C8—91no—
324#102—91no—
325#102—91no—
326#102—91no—
327#102—91no—
328#102—91no—
329#102—91no—
330#102—91no—
331#102—91no—
332#102C2×C3⋊D311yescharacteristic
333#102C2×C3⋊D311yescharacteristic
334#97—91no—
335#97C2×C3⋊D311yescharacteristic
336C4×C8—91no—
337C23×C3—24no—
338C23×C3—24no—
339C22×D3—64no—
340C22×D3—64no—
341C3×D4—24no—
342C3×D4—24no—
343C3×D4—24no—
344C3×D4#23518yescomplemented
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—48no—
348C2×C3×C4—84no—
349C2×C3×C4D3×D414yes—
350C2×C3×C4D3×D414yes—
351C2×C3×C4C23×D314yes—
352#67—128no—
353#67—128no—
354#67—244no—
355#67—244no—
356C2×Dic3—34no—
357C2×Dic3—34no—
358C2×Dic3—34no—
359C2×Dic3—34no—
360C2×Dic3—64no—
361C2×Dic3—64no—
362C2×Dic3—128no—
363C2×Dic3—244no—
364D12—64no—
365D12—64no—
366D12—64no—
367D12—64no—
368D12—128no—
369D12—244no—
370C4×D3—128no—
371C4×D3—128no—
372Dic6—68no—
373Dic6—244no—
374C3×C8—24no—
375C3×C8—24no—
376C3⋊C8—64no—
377C3⋊C8—64no—
378C2×C32—42no—
379C2×C32—81no—
380C2×C32#54811yescharacteristic
381C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
382C2×C32#57611yescharacteristic
383C3⋊D3—81no—
384C3⋊D3—81no—
385#41—364no—
386C2×Q8—91no—
387C2×Q8—181no—
388C2×D4—91no—
389C2×D4—91no—
390C2×D4—181no—
391C2×D4—181no—
392C2×D4—181no—
393C2×D4—181no—
394C2×D4—181no—
395C2×D4—181no—
396C2×D4C22×C3⋊D311yescharacteristic
397C2×D4C22×C3⋊D311yescharacteristic
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4—181no—
403C22×C4—181no—
404D8—22no—
405D8—182no—
406D8—182no—
407C2×C8—91no—
408C2×C8—91no—
409C2×C8C22×C3⋊D311yescharacteristic
410C2×C8C22×C3⋊D311yescharacteristic
411C4⋊C4—91no—
412C4⋊C4—91no—
413C4⋊C4—91no—
414C4⋊C4—91no—
415C4⋊C4—91no—
416C4⋊C4—181no—
417C4⋊C4—181no—
418C4⋊C4—181no—
419C4⋊C4—181no—
420C4⋊C4—181no—
421C4⋊C4C22×C3⋊D311yescharacteristic
422C4⋊C4C22×C3⋊D311yescharacteristic
423C22⋊C4—21no—
424C22⋊C4—21no—
425C22⋊C4—181no—
426C22⋊C4—181no—
427C22⋊C4—181no—
428C22⋊C4—181no—
429C42—91no—
430C42—91no—
431C42C22×C3⋊D311yescharacteristic
432C22×C3—28no—
433C22×C3—44no—
434C22×C3—44no—
435C22×C3—44no—
436C22×C3—44no—
437C22×C3—44no—
438C22×C3C2×D3×D414yes—
439C2×D3—124no—
440C2×D3—124no—
441C2×D3—124no—
442C2×D3—124no—
443C2×D3—124no—
444C2×D3—124no—
445C3×C4—24no—
446C3×C4—24no—
447C3×C4—44no—
448C3×C4—44no—
449C3×C4C2×#23514yes—
450C3×C4#101014yes—
451Dic3—38no—
452Dic3—64no—
453Dic3—64no—
454Dic3—64no—
455Dic3—124no—
456Dic3—124no—
457C32#336611yescharacteristic, complemented, Sylow
458C23—21no—
459C23—21no—
460C23—181no—
461C23—181no—
462Q8—182no—
463Q8—721no—
464D4—21no—
465D4—21no—
466D4—21no—
467D4—181no—
468D4—181no—
469D4—181no—
470D4—181no—
471D4—362no—
472D4—362no—
473D4—362no—
474D4—721no—
475D4—721no—
476D4—721no—
477D4#382812yescomplemented
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—42no—
481C2×C4—81no—
482C2×C4—91no—
483C2×C4—91no—
484C2×C4—91no—
485C2×C4—91no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4—362no—
489C2×C4—362no—
490C2×C4—362no—
491C2×C4—721no—
492C2×C4D4×C3⋊D311yescharacteristic
493C2×C4D4×C3⋊D311yescharacteristic
494C2×C4C23×C3⋊D311yescharacteristic
495C8—21no—
496C8—21no—
497C8—181no—
498C8—181no—
499C2×C3—48no—
500C2×C3—84no—
501C2×C3#555214yes—
502C2×C3D3×AGL(1,ℤ/8)14yes—
503C2×C3#577414yes—
504D3—244no—
505D3—244no—
506C22—22no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—361no—
513C22—361no—
514C22—361no—
515C22—361no—
516C22—361no—
517C22—361no—
518C22C2×D4×C3⋊D311yescharacteristic
519C4—21no—
520C4—21no—
521C4—41no—
522C4—41no—
523C4—92no—
524C4—181no—
525C4—181no—
526C4—181no—
527C4—361no—
528C4—361no—
529C4C2×#382811yescharacteristic
530C4#6436711yescharacteristic
531C3#7985114yescomplemented
532C2—42no—
533C2—81no—
534C2—721no—
535C2—721no—
536C2#1059602311yescharacteristic
537C2C3⋊D3×AGL(1,ℤ/8)11yescharacteristic
538C2#1059624511yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#442C2
socleC22×C32C22×D4
hypercenter#442C3⋊D3
hypocenterC32#3366
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #10596024C2semidirect
2. #10596010C2semidirect
3. C32×#442C2semidirect
4. #10592849C2semidirect
5. #10592849C2semidirect
6. #10592714C2semidirect
7. #10592708C2semidirect
8. #10592570C2semidirect
9. #10592569C2semidirect
10. #10592484C2semidirect
11. #10592463C2semidirect
12. #10592459C2semidirect
13. #10592455C2semidirect
14. #10592412C2semidirect
15. #10592400C2semidirect
62. C3×#442D3semidirect
173. C32×D4#41semidirect
220. #442C3⋊D3semidirect
344. C3×D4#235semidirect
457. C32#3366semidirect
477. D4#3828semidirect
531. C3#79851semidirect

Maximal subgroups

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

subgroupindex
#105960242
#105960102
C32×#4422
#105928492
#105927142
#105927082
#105925702
#105925692
#105924842
#105924632
#105924592
#105924552
#105924122
#105924002
#798513