Finite Group Databasebeta

← #11887153

Subgroups — #11887153

Order 1152.

978 conjugacy classes of subgroups.

The subgroup lattice has 589 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594004C211yesmaximal, characteristic
2#10593960C211yesmaximal, characteristic, complemented
3#10592541C211yesmaximal, characteristic, complemented
4C3×#4848C211yesmaximal, characteristic, complemented
5C3×#4834C211yesmaximal, characteristic, complemented
6#10590942C212yesmaximal, complemented
7D3×#821C212yesmaximal, complemented
8#10590829C212yesmaximal, complemented
9#10590676C212yesmaximal, complemented
10C4×#3717C211yesmaximal, characteristic, complemented
11#10590273C211yesmaximal, characteristic, complemented
12#80395—31nomaximal
13#79439—31nomaximal
14C2×#3802—21no—
15C2×D3×D12C2212yes—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17#64078C2211yescharacteristic, complemented
18C2×C3×#204C2212yescomplemented
19C2×C3×D3×C8C2212yescomplemented
20C3×#874C2211yescharacteristic
21C3×C4×D12C2211yescharacteristic
22C3×C4×Dic6C2211yescharacteristic, complemented
23#63922—22no—
24#63916—21no—
25#63908C2212yes—
26#63896—22no—
27Dic3×D12—21no—
28D3×C4⋊Dic3C2212yescomplemented
29#63869—21no—
30#63856C2212yescomplemented
31C2×#3717C2211yescharacteristic
32C32×C4⋊C8C2211yescharacteristic, complemented
33#63648C2212yes—
34#63644C2212yescomplemented
35C3×#821C2212yescomplemented
36C3×(C2×D3)⋊C8C2212yescomplemented
37C3×C4×C3⋊C8C2211yescharacteristic, complemented
38#63573C2211yescharacteristic, complemented
39#63566C2211yescharacteristic, complemented
40#63564C2211yescharacteristic
41#63563C2212yescomplemented
42#63563C2212yescomplemented
43#5717—31no—
44#5579—31no—
45D4×D12—31no—
46#5543—31no—
47C3×#460—31no—
48C3×C8×D4—31no—
49#5171—32no—
50#5169—32no—
51#5114—32no—
52C2×#821—32no—
53#5070—31no—
54C4×#215—31no—
55#4848D311yescharacteristic, complemented
56#4842—31no—
57#4842—31no—
58#4842—61no—
59#4834D311yescharacteristic, complemented
60#4777—32no—
61D3×#102—32no—
62#4735—32no—
63#4731—32no—
64#4694—31no—
65C4×#204—31no—
66C22×D32—22no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×#634—21no—
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12D411yescharacteristic
73C2×C3×D12C2312yes—
74C2×C3×C4×D3C2312yes—
75C2×C3×Dic6C2311yescharacteristic
76C2×#626—22no—
77C2×#625—22no—
78C2×D3×Dic3—22no—
79#3802—44no—
80D3×D12—24no—
81D3×D12—42no—
82C2×C32×C8C2312yes—
83C32×C42C2311yescharacteristic
84#3752—21no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2312yes—
87C4⋊(C3⋊Dic3)C2311yescharacteristic
88C3×(C2×D3)⋊C4D412yes—
89C3×C4⋊Dic3D411yescharacteristic
90C3×C4⋊Dic3C2311yescharacteristic
91C3×Dic3⋊C4—21no—
92C3×C4×Dic3—21no—
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C3×#204—42no—
96C3×D3×C8—42no—
97#3724—22no—
98Dic3⋊Dic3—22no—
99(C2×D3)⋊Dic3—22no—
100(C2×D3)⋊Dic3—22no—
101#3717—22no—
102#3295—91noSylow
103C2×D3×D4—32no—
104C2×D3×D4—61no—
105C2×D3×D4—61no—
106C22×D12—32no—
107C2×C3×SD16—32no—
108C22×C3×C8—32no—
109C3×#127—31no—
110C3×C4×Q8—31no—
111C3×C4×D4—31no—
112#946—32no—
113C2×#215—31no—
114#938—32no—
115#938—61no—
116#937—62no—
117D4×Dic3—61no—
118#930—32no—
119C2×C4⋊Dic3—32no—
120#924—32no—
121C2×#204—31no—
122C2×#204C2×D312yescomplemented
123C2×D3×C8C2×D312yescomplemented
124#896—62no—
125#895—61no—
126D3×C4⋊C4—32no—
127#890—61no—
128#882—62no—
129#878—62no—
130#874C2×D311yescharacteristic
131C4×D12—31no—
132C4×D12—31no—
133C4×D12—61no—
134C4×D12—61no—
135C4×D12C2×D311yescharacteristic
136#870—61no—
137#869—31no—
138#869—31no—
139#869—61no—
140C4×Dic6C2×D311yescharacteristic, complemented
141C3×C4⋊C8—21no—
142C3×C4⋊C8C2×D311yescharacteristic, complemented
143C3×C4⋊C8C2×D311yescharacteristic, complemented
144C3×#102—32no—
145C3×C22⋊C8—32no—
146C3×C4×C8—31no—
147#835—31no—
148#832—32no—
149#832—32no—
150#821—32no—
151#821—32no—
152#821—32no—
153#821—32no—
154#821—31no—
155#821—62no—
156#821C2×D312yescomplemented
157(C2×D3)⋊C8C2×D312yescomplemented
158#817—32no—
159#817—32no—
160#817—31no—
161#817—62no—
162#816—31no—
163#809—31no—
164#808—31no—
165C4×C3⋊C8C2×D311yescharacteristic, complemented
166C22×C3⋊D3—21no—
167C22×C3×D3—22no—
168C22×C3×D3C2×D412yes—
169C2×D32—44no—
170C2×D32—44no—
171C2×D32—82no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C2×C3⋊Dic3—21no—
176C2×C3⋊Dic3—22no—
177C4⋊(C3⋊D3)—21no—
178C4⋊(C3⋊D3)#4112yes—
179C4×C3⋊D3—42no—
180#634—81no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3—21no—
183C2×C3×Dic3C2×D412yes—
184C3×D12—22no—
185C3×D12—22no—
186C3×D12—42no—
187C3×D12—81no—
188C3×D12SD1614yescomplemented
189C3×C4×D3—22no—
190C3×C4×D3—22no—
191C3×Dic6—21no—
192C3×Dic6—21no—
193#626—44no—
194#625—44no—
195D3×Dic3—82no—
196C32×C8—22no—
197C3×C3⋊C8—21no—
198C3×C3⋊C8—21no—
199#554—91no—
200D42—91no—
201#486—91no—
202#481—92no—
203#476—91no—
204#465—92no—
205#460—31no—
206#450—92no—
207C4×SD16—91no—
208C8×D4—31no—
209C2×#102—92no—
210C23×D3—62no—
211C23×D3—62no—
212C2×C3×Q8—31no—
213C2×C3×D4—31no—
214C2×C3×D4—32no—
215C2×C3×D4—61no—
216C2×C3×D4—61no—
217C22×C3×C4—32no—
218C2×#67—62no—
219C2×#67—62no—
220C2×#67—62no—
221C22×Dic3—62no—
222D3×D4—64no—
223D3×D4—122no—
224D3×D4—124no—
225D3×D4—124no—
226C2×D12—21no—
227C2×D12—21no—
228C2×D12—31no—
229C2×D12—31no—
230C2×D12—61no—
231C2×D12—64no—
232C2×D12—62no—
233C2×D12—122no—
234C2×D12D1211yescharacteristic
235C2×D12C22×D312yes—
236C2×C4×D3—61no—
237C2×C4×D3—61no—
238C2×C4×D3—62no—
239C2×C4×D3—121no—
240C2×C4×D3C22×D312yes—
241C2×Dic6—61no—
242C2×Dic6—61no—
243C2×Dic6—121no—
244C2×Dic6C22×D311yescharacteristic
245C3×SD16—122no—
246C2×C3×C8—22no—
247C2×C3×C8—31no—
248C2×C3×C8—31no—
249C2×C3×C8—122no—
250C2×C3×C8C22×D312yes—
251C2×C3×C8C22×D312yes—
252C3×C4⋊C4—31no—
253C3×C4⋊C4—31no—
254C3×C4⋊C4—61no—
255C3×C22⋊C4—32no—
256C3×C42—21no—
257C3×C42—61no—
258C3×C42C22×D311yescharacteristic
259C3×C42C22×D311yescharacteristic
260#217—62no—
261#217—62no—
262#215—62no—
263(C2×D3)⋊C4—62no—
264(C2×D3)⋊C4—62no—
265(C2×D3)⋊C4—61no—
266(C2×D3)⋊C4—61no—
267(C2×D3)⋊C4—121no—
268(C2×D3)⋊C4D1212yes—
269C4⋊Dic3—31no—
270C4⋊Dic3—31no—
271C4⋊Dic3—32no—
272C4⋊Dic3—32no—
273C4⋊Dic3—61no—
274C4⋊Dic3—62no—
275C4⋊Dic3—62no—
276C4⋊Dic3—61no—
277C4⋊Dic3—61no—
278C4⋊Dic3—121no—
279C4⋊Dic3D1211yescharacteristic
280C4⋊Dic3C22×D311yescharacteristic
281Dic3⋊C4—21no—
282Dic3⋊C4—62no—
283Dic3⋊C4—62no—
284Dic3⋊C4—62no—
285C4×Dic3—21no—
286C2×C3⋊C8C22×D311yescharacteristic
287C2×C3⋊C8C22×D311yescharacteristic
288#204—42no—
289#204—62no—
290D3×C8—42no—
291C22×C32C22×D411yescharacteristic
292C2×C3⋊D3—22no—
293C2×C3⋊D3—41no—
294C2×C3⋊D3—41no—
295C2×C3×D3—22no—
296C2×C3×D3—22no—
297C2×C3×D3—42no—
298C2×C3×D3—42no—
299C2×C3×D3—42no—
300C2×C3×D3C2×SD1614yes—
301D32—88no—
302C32×C4—21no—
303C32×C4C2×SD1612yes—
304C32×C4C2×#4111yescharacteristic
305C32×C4H(5,𝔽2)11yescharacteristic
306C3⋊Dic3—41no—
307C3⋊Dic3—42no—
308C3×Dic3—22no—
309C3×Dic3—41no—
310C3×Dic3—41no—
311C22×D4—92no—
312C22×D4—181no—
313C2×SD16—32no—
314C2×SD16—91no—
315C22×C8—32no—
316C4⋊Q8—91no—
317#127—31no—
318#125—181no—
319C22⋊Q8—92no—
320C22⋊Q8—182no—
321#121—92no—
322#121—181no—
323#120—182no—
324C4×Q8—31no—
325C4×D4—31no—
326C4×D4—91no—
327C4×D4—181no—
328C2×C4⋊C4—92no—
329#106—91no—
330#106—92no—
331C4⋊C8D3211yescharacteristic, complemented
332#103—91no—
333#102—32no—
334#102—91no—
335#102—92no—
336#102—92no—
337#102—92no—
338C22⋊C8—32no—
339C4×C8—31no—
340C23×C3—32no—
341C23×C3—62no—
342C22×D3—22no—
343C22×D3—61no—
344C22×D3—61no—
345C22×D3—121no—
346C22×D3—124no—
347C22×D3—124no—
348C22×D3—124no—
349C22×D3—124no—
350C22×D3—242no—
351C22×D3—242no—
352C22×D3C2×D1212yes—
353C3×Q8—61no—
354C3×Q8—61no—
355C3×D4—34no—
356C3×D4—62no—
357C3×D4—62no—
358C3×D4—122no—
359C3×D4—241no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—32no—
364C2×C3×C4—62no—
365C2×C3×C4—62no—
366C2×C3×C4—61no—
367C2×C3×C4—61no—
368C2×C3×C4C2×D1211yescharacteristic
369C2×C3×C4C2×D1211yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374#67—124no—
375#67—124no—
376#67—124no—
377C2×Dic3—21no—
378C2×Dic3—21no—
379C2×Dic3—62no—
380C2×Dic3—61no—
381C2×Dic3—62no—
382C2×Dic3—61no—
383C2×Dic3—122no—
384C2×Dic3—121no—
385C2×Dic3—242no—
386C2×Dic3C2×D1212yes—
387D12—22no—
388D12—22no—
389D12—32no—
390D12—32no—
391D12—42no—
392D12—62no—
393D12—61no—
394D12—61no—
395D12—81no—
396D12—121no—
397D12—124no—
398D12#20414yescomplemented
399C4×D3—22no—
400C4×D3—22no—
401C4×D3—122no—
402C4×D3—122no—
403C4×D3—242no—
404C4×D3—242no—
405Dic6—21no—
406Dic6—21no—
407Dic6—241no—
408Dic6—241no—
409Dic6—242no—
410C3×C8—22no—
411C3×C8—22no—
412C3×C8—42no—
413C3×C8—61no—
414C3×C8—61no—
415C3⋊C8—21no—
416C3⋊C8—21no—
417C2×C32#54611yescharacteristic
418C2×C32C22×SD1611yescharacteristic
419C2×C32#57611yescharacteristic
420C3⋊D3—42no—
421C3×D3—24no—
422C3×D3—82no—
423C24—182no—
424C2×Q8—31no—
425C2×Q8—181no—
426C2×D4—32no—
427C2×D4—31no—
428C2×D4—61no—
429C2×D4—61no—
430C2×D4—91no—
431C2×D4—182no—
432C2×D4—184no—
433C2×D4—182no—
434C2×D4—362no—
435C2×D4—364no—
436C22×C4—32no—
437C22×C4—182no—
438C22×C4—181no—
439SD16—122no—
440SD16—182no—
441C2×C8—31no—
442C2×C8—31no—
443C2×C8—122no—
444C2×C8C2×D3212yes—
445C4⋊C4—31no—
446C4⋊C4—31no—
447C4⋊C4—61no—
448C4⋊C4—92no—
449C4⋊C4—91no—
450C4⋊C4—182no—
451C4⋊C4—182no—
452C4⋊C4—181no—
453C22⋊C4—32no—
454C22⋊C4—182no—
455C22⋊C4—182no—
456C22⋊C4—181no—
457C42—61no—
458C42C2×D3211yescharacteristic
459C22×C3—21no—
460C22×C3—34no—
461C22×C3—62no—
462C22×C3—62no—
463C22×C3—122no—
464C22×C3—122no—
465C22×C3—122no—
466C22×C3C22×D1211yescharacteristic
467C22×C3C2×D3×D411yescharacteristic
468C2×D3—22no—
469C2×D3—22no—
470C2×D3—42no—
471C2×D3—42no—
472C2×D3—42no—
473C2×D3—62no—
474C2×D3—62no—
475C2×D3—122no—
476C2×D3—121no—
477C2×D3—121no—
478C2×D3—121no—
479C2×D3—121no—
480C2×D3—241no—
481C2×D3—241no—
482C2×D3—248no—
483C2×D3—248no—
484C2×D3C2×#20414yes—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—41no—
491C3×C4—62no—
492C3×C4—121no—
493C3×C4—121no—
494C3×C4C2×#20412yes—
495C3×C4D3×SD1612yes—
496C3×C4#100411yescharacteristic
497C3×C4#100411yescharacteristic
498C3×C4D3×#4111yescharacteristic
499C3×C4D3×#4111yescharacteristic
500Dic3—22no—
501Dic3—41no—
502Dic3—41no—
503Dic3—121no—
504Dic3—122no—
505Dic3—121no—
506Dic3—122no—
507Dic3—242no—
508Dic3—241no—
509C32#329511yescharacteristic, complemented, Sylow
510C23—32no—
511C23—62no—
512C23—181no—
513C23—364no—
514C23—364no—
515C23—722no—
516Q8—61no—
517Q8—61no—
518Q8—721no—
519D4—34no—
520D4—62no—
521D4—62no—
522D4—92no—
523D4—122no—
524D4—181no—
525D4—241no—
526D4—364no—
527D4—364no—
528C2×C4—32no—
529C2×C4—62no—
530C2×C4—62no—
531C2×C4—61no—
532C2×C4—61no—
533C2×C4—181no—
534C2×C4—182no—
535C2×C4—362no—
536C2×C4—722no—
537C2×C4D3×D1211yescharacteristic
538C2×C4D3×D1211yescharacteristic
539C2×C4C22×D3211yescharacteristic
540C8—22no—
541C8—61no—
542C8—61no—
543C2×C3—21no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—64no—
547C2×C3—242no—
548C2×C3#555411yescharacteristic
549C2×C3#561211yescharacteristic
550C2×C3C22×#20411yescharacteristic
551C2×C3#575211yescharacteristic
552C2×C3C2×D3×SD1611yescharacteristic
553C2×C3#577411yescharacteristic
554D3—24no—
555D3—82no—
556D3—122no—
557D3—122no—
558D3—242no—
559C22—34no—
560C22—62no—
561C22—62no—
562C22—122no—
563C22—122no—
564C22—122no—
565C22—182no—
566C22—361no—
567C22—361no—
568C22—728no—
569C22C2×D3×D1211yescharacteristic
570C4—21no—
571C4—62no—
572C4—121no—
573C4—121no—
574C4—361no—
575C4—362no—
576C4D3×#20412yes—
577C4#6431311yescharacteristic
578C4#6431911yescharacteristic
579C3—21no—
580C3#7943911yescharacteristic, complemented
581C3#8039511yescharacteristic, complemented
582C2—64no—
583C2—242no—
584C2—362no—
585C2#1059463011yescharacteristic
586C2C2×D3×#20411yescharacteristic
587C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10594004C2
hypercenterC4⋊C8D32
hypocenterC32#3295
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593960C2semidirect
3. #10592541C2semidirect
4. C3×#4848C2semidirect
5. C3×#4834C2semidirect
6. #10590942C2semidirect
7. D3×#821C2semidirect
8. #10590829C2semidirect
9. #10590676C2semidirect
10. C4×#3717C2semidirect
11. #10590273C2semidirect
17. #64078C22semidirect
18. C2×C3×#204C22semidirect
19. C2×C3×D3×C8C22semidirect
22. C3×C4×Dic6C22semidirect
28. D3×C4⋊Dic3C22semidirect
30. #63856C22semidirect
32. C32×C4⋊C8C22semidirect
34. #63644C22semidirect
35. C3×#821C22semidirect
36. C3×(C2×D3)⋊C8C22semidirect
37. C3×C4×C3⋊C8C22semidirect
38. #63573C22semidirect
39. #63566C22semidirect
41. #63563C22semidirect
42. #63563C22semidirect
55. #4848D3semidirect
59. #4834D3semidirect
122. C2×#204C2×D3semidirect
123. C2×D3×C8C2×D3semidirect
140. C4×Dic6C2×D3semidirect
142. C3×C4⋊C8C2×D3semidirect
143. C3×C4⋊C8C2×D3semidirect
156. #821C2×D3semidirect
157. (C2×D3)⋊C8C2×D3semidirect
165. C4×C3⋊C8C2×D3semidirect
188. C3×D12SD16semidirect
331. C4⋊C8D32semidirect
398. D12#204semidirect
509. C32#3295semidirect
580. C3#79439semidirect
581. C3#80395semidirect

Maximal subgroups

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

subgroupindex
#105940042
#105939602
#105925412
C3×#48482
C3×#48342
#105909422
D3×#8212
#105908292
#105906762
C4×#37172
#105902732
#803953
#794393