Finite Group Databasebeta

← #11904431

Subgroups — #11904431

Order 1152.

3569 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64361C211yesmaximal, characteristic, complemented
2C22×C3×#237C211yesmaximal, characteristic, complemented
3C3×#5798C211yesmaximal, characteristic, complemented
4#10595519C214yesmaximal, complemented
5C2×#63966C214yesmaximal, complemented
6#10595254C218yesmaximal, complemented
7#10595248C218yesmaximal, complemented
8#10595023C212yesmaximal, complemented
9#10594866C212yesmaximal, complemented
10#87273—31nomaximal
11#85858—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×#638C2214yes—
14#64361—28no—
15C2×#3830C2214yescomplemented
16C2×D4×C3⋊D3C2214yescomplemented
17C2×#3828C2212yes—
18C22×C3×#67C2212yescomplemented
19C23×C3×Dic3C2212yescomplemented
20C2×C3×#237—28no—
21C2×C3×#237C2218yescomplemented
22C22×C3×C4×D3C2211yescharacteristic, complemented
23C22×C3×Dic6C2211yescharacteristic, complemented
24C2×C3×#217C2214yescomplemented
25C3×D4×Dic3C2218yescomplemented
26C3×#926C2212yescomplemented
27#63981C2218yescomplemented
28#63978C22116yescomplemented
29#63977C2214yescomplemented
30#63966C2218yescomplemented
31#63966C2214yescomplemented
32#63966C22116yescomplemented
33C2×Dic3⋊Dic3C2218yescomplemented
34C2×#3722C2218yescomplemented
35#63962C2218yescomplemented
36#63909C2214yescomplemented
37C4×#626C2218yescomplemented
38#63871C2218yescomplemented
39#63866C2214yescomplemented
40#63864C2214yescomplemented
41#63857C2214yescomplemented
42C22×C3×#41—31no—
43C2×#1004—31no—
44C2×#1004—31no—
45C2×#1004—61no—
46C22×#237D311yescharacteristic, complemented
47C3×#518—31no—
48#5829—38no—
49#5824—38no—
50#5816—32no—
51#5804—34no—
52#5798D311yescharacteristic, complemented
53#5791—32no—
54C2×#929—34no—
55#5555—38no—
56#5554—38no—
57#5526—32no—
58#5524—32no—
59#5493—34no—
60C2×#886—34no—
61C24×C32C2312yes—
62C23×C3⋊D3C2314yes—
63C23×C3×D3C2311yescharacteristic
64C2×C32×D4D418yescomplemented
65C2×C32×D4C2314yes—
66C22×C32×C4C2311yescharacteristic
67C2×#638—216no—
68C2×#638C2314yes—
69C2×#638C2318yes—
70C22×C3⋊Dic3C2314yes—
71#3830—216no—
72D4×C3⋊D3—216no—
73#3828—28no—
74C2×C4⋊(C3⋊D3)C2312yes—
75C2×C4×C3⋊D3C2314yes—
76C2×#634C2312yes—
77C2×C3×#67—28no—
78C2×C3×#67C2318yes—
79C22×C3×Dic3—28no—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2311yescharacteristic
82C22×C3×Dic3C2318yes—
83C22×C3×Dic3C2318yes—
84C3×#237—232no—
85C2×C3×C4×D3—24no—
86C2×C3×C4×D3C2314yes—
87C2×C3×Dic6—24no—
88C2×C3×Dic6C2314yes—
89C2×#626C2318yes—
90C3×#217C2314yes—
91C3×#217C2318yes—
92C3×C4⋊Dic3C2314yes—
93C3×C4×Dic3C2314yes—
94Dic3⋊Dic3C2318yes—
95Dic3⋊Dic3C23116yes—
96#3722C23116yes—
97#3722C2318yes—
98(C2×D3)⋊Dic3C2318yes—
99#3485—91noSylow
100C2×C3×#41—38no—
101C2×C3×#41—68no—
102C22×C3×Q8—31no—
103C22×C3×D4—21no—
104C22×C3×D4—32no—
105C22×C3×D4C2×D311yescharacteristic
106C22×C3×D4C2×D311yescharacteristic
107C23×C3×C4—32no—
108C23×C3×C4—31no—
109C22×#67—34no—
110C22×#67—34no—
111C22×#67—64no—
112C22×#67C2×D312yescomplemented
113C23×Dic3C2×D312yescomplemented
114#1004—616no—
115#1004—68no—
116#1004—68no—
117C2×#237—28no—
118C2×#237—34no—
119C2×#237—34no—
120C2×#237—64no—
121C2×#237C2×D318yescomplemented
122C2×D3×D4—34no—
123C2×D3×D4—34no—
124C2×D3×D4—64no—
125C2×#235—32no—
126C2×#235—32no—
127C2×#235—62no—
128C22×C4×D3C2×D311yescharacteristic, complemented
129C22×Dic6C2×D311yescharacteristic, complemented
130C3×C4×D4—38no—
131C3×#117—32no—
132C2×C3×C22⋊C4—34no—
133#953—34no—
134C2×#217C2×D314yescomplemented
135#947—34no—
136#946—38no—
137#944—34no—
138#939—316no—
139#937—38no—
140#935—38no—
141D4×Dic3C2×D318yescomplemented
142#930—316no—
143#930—34no—
144#929—34no—
145#929—38no—
146#929—316no—
147C4×#67—38no—
148C2×(C2×D3)⋊C4—38no—
149C2×(C2×D3)⋊C4—38no—
150#926C2×D312yescomplemented
151C2×C4⋊Dic3—38no—
152#924—34no—
153C2×Dic3⋊C4—38no—
154#897—34no—
155#897—38no—
156#895—34no—
157#886—38no—
158#886—34no—
159#886—38no—
160#886—316no—
161#882—34no—
162#882—38no—
163#875—34no—
164C4×D12—38no—
165#869—34no—
166C23×C32—44no—
167C23×C32C2×D418yes—
168C23×C32C2411yescharacteristic
169C23×C32C2414yes—
170C22×C3⋊D3—28no—
171C22×C3⋊D3—48no—
172C22×C3⋊D3C2414yes—
173C22×C3×D3—22no—
174C22×C3×D3—42no—
175C22×C3×D3C2412yes—
176C32×D4C2×D4116yes—
177C2×C32×C4C2×D414yes—
178C2×C32×C4C2412yes—
179#638—28no—
180#638—216no—
181C2×C3⋊Dic3—28no—
182C2×C3⋊Dic3C2414yes—
183C4⋊(C3⋊D3)—24no—
184C4×C3⋊D3—28no—
185#634—24no—
186C3×#67—216no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—216no—
190C2×C3×Dic3—48no—
191C2×C3×Dic3C2418yes—
192C2×C3×Dic3C2414yes—
193C2×C3×Dic3C2412yes—
194C3×C4×D3—28no—
195C3×Dic6—28no—
196#626—48no—
197C2×H(5,𝔽2)—91no—
198C22×#41—31no—
199#547—98no—
200#546—98no—
201#536—92no—
202#534—94no—
203#525—92no—
204C2×#123—94no—
205#518—31no—
206C24×C3—22no—
207C24×C3—31no—
208C24×C3C22×D312yes—
209C24×C3C22×D312yes—
210C23×D3—34no—
211C23×D3—34no—
212C23×D3—64no—
213C23×D3C22×D311yescharacteristic
214C3×#41—632no—
215C2×C3×Q8—34no—
216C2×C3×Q8—64no—
217C2×C3×D4—28no—
218C2×C3×D4—24no—
219C2×C3×D4—38no—
220C2×C3×D4—68no—
221C2×C3×D4D1218yescomplemented
222C2×C3×D4#6718yescomplemented
223C2×C3×D4C22×D314yes—
224C2×C3×D4C22×D314yes—
225C22×C3×C4—21no—
226C22×C3×C4—38no—
227C22×C3×C4—31no—
228C22×C3×C4—32no—
229C22×C3×C4—38no—
230C22×C3×C4—34no—
231C22×C3×C4—68no—
232C22×C3×C4—64no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—28no—
236C2×#67—34no—
237C2×#67—38no—
238C2×#67—34no—
239C2×#67—38no—
240C2×#67—38no—
241C2×#67—64no—
242C2×#67—68no—
243C2×#67—632no—
244C2×#67—616no—
245C2×#67—616no—
246C2×#67C22×D318yes—
247C22×Dic3—28no—
248C22×Dic3—34no—
249C22×Dic3—34no—
250C22×Dic3—64no—
251C22×Dic3C22×D312yes—
252C22×Dic3C22×D311yescharacteristic
253C22×Dic3C22×D318yes—
254C22×Dic3C22×D318yes—
255#237—232no—
256#237—632no—
257#237—616no—
258#237—616no—
259D3×D4—632no—
260D3×D4—616no—
261D3×D4—616no—
262#235—616no—
263#235—68no—
264#235—68no—
265C2×D12—32no—
266C2×D12—32no—
267C2×D12—38no—
268C2×D12—62no—
269C2×C4×D3—24no—
270C2×C4×D3—34no—
271C2×C4×D3—34no—
272C2×C4×D3—64no—
273C2×C4×D3C22×D314yes—
274C2×Dic6—24no—
275C2×Dic6—32no—
276C2×Dic6—32no—
277C2×Dic6—62no—
278C2×Dic6C22×D314yes—
279C3×C4⋊C4—34no—
280C3×C22⋊C4—34no—
281C3×C22⋊C4—38no—
282C3×C42—34no—
283#217—38no—
284#217C22×D314yes—
285#217C22×D318yes—
286(C2×D3)⋊C4—38no—
287(C2×D3)⋊C4—38no—
288(C2×D3)⋊C4—316no—
289(C2×D3)⋊C4—38no—
290(C2×D3)⋊C4—316no—
291C4⋊Dic3—316no—
292C4⋊Dic3—38no—
293C4⋊Dic3C22×D314yes—
294Dic3⋊C4—38no—
295Dic3⋊C4—316no—
296C4×Dic3C22×D314yes—
297C22×C32—28no—
298C22×C32—22no—
299C22×C32—48no—
300C22×C32C22×D412yes—
301C22×C32C22×D418yes—
302C22×C32C2511yescharacteristic
303C2×C3⋊D3—24no—
304C2×C3⋊D3—28no—
305C2×C3⋊D3—88no—
306C2×C3×D3—22no—
307C2×C3×D3—24no—
308C2×C3×D3—44no—
309C32×C4C22×D414yes—
310C3⋊Dic3—24no—
311C3×Dic3—24no—
312C3×Dic3—22no—
313C3×Dic3—28no—
314H(5,𝔽2)—188no—
315C2×#41—38no—
316C2×#41—68no—
317C2×#41—94no—
318C2×#41—92no—
319C22×Q8—31no—
320C22×D4—32no—
321C22×D4—94no—
322C22×D4—94no—
323C22×D4D3211yescharacteristic
324C23×C4—32no—
325C23×C4—31no—
326C4⋊Q8—94no—
327#124—94no—
328#123—94no—
329#123—98no—
330#123—916no—
331#123—98no—
332C22⋊Q8—94no—
333C22⋊Q8—98no—
334#121—94no—
335#121—916no—
336#120—98no—
337#120—94no—
338C4×D4—38no—
339C4×D4—98no—
340#117—32no—
341C2×C4⋊C4—98no—
342C2×C22⋊C4—34no—
343C2×C22⋊C4—98no—
344C23×C3—24no—
345C23×C3—21no—
346C23×C3—28no—
347C23×C3—32no—
348C23×C3—44no—
349C23×C3—44no—
350C23×C3—62no—
351C23×C3—84no—
352C23×C3—122no—
353C23×C3C2×D1218yes—
354C23×C3C2×#6718yes—
355C23×C3C23×D311yescharacteristic
356C23×C3C23×D314yes—
357C23×C3C23×D311yescharacteristic
358C23×C3C23×D314yes—
359C22×D3—22no—
360C22×D3—34no—
361C22×D3—34no—
362C22×D3—42no—
363C22×D3—64no—
364C22×D3—616no—
365C22×D3—68no—
366C22×D3—68no—
367C22×D3—128no—
368C22×D3—128no—
369C22×D3—248no—
370C22×D3C23×D312yes—
371C3×Q8—68no—
372C3×D4—216no—
373C3×D4—616no—
374C3×D4C2×D12116yes—
375C3×D4C2×#67116yes—
376C2×C3×C4—22no—
377C2×C3×C4—24no—
378C2×C3×C4—32no—
379C2×C3×C4—34no—
380C2×C3×C4—38no—
381C2×C3×C4—62no—
382C2×C3×C4—64no—
383C2×C3×C4—616no—
384C2×C3×C4—68no—
385C2×C3×C4—128no—
386C2×C3×C4C2×D1214yes—
387C2×C3×C4C2×#6714yes—
388C2×C3×C4C23×D312yes—
389C2×C3×C4C23×D312yes—
390#67—216no—
391#67—616no—
392#67—632no—
393#67—68no—
394#67—616no—
395#67—68no—
396#67—616no—
397#67—128no—
398C2×Dic3—24no—
399C2×Dic3—22no—
400C2×Dic3—216no—
401C2×Dic3—34no—
402C2×Dic3—34no—
403C2×Dic3—48no—
404C2×Dic3—64no—
405C2×Dic3—616no—
406C2×Dic3—68no—
407C2×Dic3—68no—
408C2×Dic3C23×D318yes—
409C2×Dic3C23×D314yes—
410C2×Dic3C23×D312yes—
411D12—68no—
412D12—64no—
413D12—64no—
414D12—128no—
415C4×D3—28no—
416C4×D3—616no—
417C4×D3—68no—
418C4×D3—68no—
419Dic6—28no—
420Dic6—68no—
421Dic6—64no—
422Dic6—64no—
423C2×C32—22no—
424C2×C32—28no—
425C2×C32C23×D411yescharacteristic
426C2×C32#58512yes—
427C3⋊D3—44no—
428C3×D3—42no—
429C24—31no—
430C24—94no—
431C24C2×D3212yes—
432#41—632no—
433#41—1816no—
434#41—188no—
435C2×Q8—34no—
436C2×Q8—64no—
437C2×Q8—92no—
438C2×D4—38no—
439C2×D4—68no—
440C2×D4—98no—
441C2×D4—94no—
442C2×D4—98no—
443C2×D4—92no—
444C2×D4—1816no—
445C2×D4—1816no—
446C2×D4#62618yescomplemented
447C2×D4C2×D3214yes—
448C22×C4—38no—
449C22×C4—31no—
450C22×C4—32no—
451C22×C4—38no—
452C22×C4—34no—
453C22×C4—68no—
454C22×C4—64no—
455C22×C4—94no—
456C22×C4—94no—
457C22×C4C2×D3211yescharacteristic
458C4⋊C4—34no—
459C4⋊C4—98no—
460C4⋊C4—916no—
461C22⋊C4—34no—
462C22⋊C4—38no—
463C22⋊C4—98no—
464C22⋊C4—916no—
465C22⋊C4—98no—
466C42—34no—
467C22×C3—28no—
468C22×C3—22no—
469C22×C3—28no—
470C22×C3—22no—
471C22×C3—28no—
472C22×C3—22no—
473C22×C3—21no—
474C22×C3—48no—
475C22×C3—42no—
476C22×C3—48no—
477C22×C3—48no—
478C22×C3—62no—
479C22×C3—64no—
480C22×C3—88no—
481C22×C3—124no—
482C22×C3C22×D1218yes—
483C22×C3C22×D1212yes—
484C22×C3C22×#6712yes—
485C22×C3C22×#6718yes—
486C22×C3C24×D311yescharacteristic
487C22×C3C24×D311yescharacteristic
488C2×D3—24no—
489C2×D3—22no—
490C2×D3—44no—
491C2×D3—68no—
492C2×D3—64no—
493C2×D3—68no—
494C2×D3—68no—
495C2×D3—64no—
496C2×D3—128no—
497C2×D3—248no—
498C2×D3—248no—
499C2×D3—2416no—
500C3×C4—24no—
501C3×C4—62no—
502C3×C4—64no—
503C3×C4—68no—
504C3×C4C22×D1214yes—
505C3×C4C22×#6714yes—
506Dic3—28no—
507Dic3—24no—
508Dic3—22no—
509Dic3—68no—
510Dic3—64no—
511Dic3—64no—
512C32#348511yescharacteristic, complemented, Sylow
513C23—32no—
514C23—44no—
515C23—62no—
516C23—94no—
517C23—122no—
518C23—188no—
519C23—368no—
520C23C2×#62618yes—
521C23C22×D3211yescharacteristic
522C23C22×D3214yes—
523Q8—68no—
524Q8—184no—
525D4—616no—
526D4—188no—
527D4—1816no—
528D4—184no—
529D4—368no—
530D4C2×#626116yes—
531C2×C4—38no—
532C2×C4—32no—
533C2×C4—34no—
534C2×C4—62no—
535C2×C4—64no—
536C2×C4—616no—
537C2×C4—68no—
538C2×C4—94no—
539C2×C4—128no—
540C2×C4—188no—
541C2×C4—188no—
542C2×C4C2×#62614yes—
543C2×C4C22×D3212yes—
544C2×C3—28no—
545C2×C3—22no—
546C2×C3—22no—
547C2×C3—28no—
548C2×C3—22no—
549C2×C3—21no—
550C2×C3—48no—
551C2×C3—42no—
552C2×C3—122no—
553C2×C3C23×D1211yescharacteristic
554C2×C3#596412yes—
555C2×C3#596612yes—
556C2×C3C23×#6711yescharacteristic
557D3—42no—
558D3—128no—
559D3—124no—
560D3—124no—
561C22—28no—
562C22—22no—
563C22—48no—
564C22—64no—
565C22—62no—
566C22—124no—
567C22—188no—
568C22—184no—
569C22—728no—
570C22C22×#62612yes—
571C22C22×#62618yes—
572C22C23×D3211yescharacteristic
573C4—68no—
574C4—62no—
575C4—64no—
576C4—184no—
577C4C22×#62614yes—
578C3—21no—
579C3#8585811yescharacteristic, complemented
580C3#8727311yescharacteristic, complemented
581C2—22no—
582C2—28no—
583C2—122no—
584C2—364no—
585C2#1059667812yes—
586C2C23×#62611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#3485
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64361C2semidirect
2. C22×C3×#237C2semidirect
3. C3×#5798C2semidirect
4. #10595519C2semidirect
5. C2×#63966C2semidirect
6. #10595254C2semidirect
7. #10595248C2semidirect
8. #10595023C2semidirect
9. #10594866C2semidirect
15. C2×#3830C22semidirect
16. C2×D4×C3⋊D3C22semidirect
18. C22×C3×#67C22semidirect
19. C23×C3×Dic3C22semidirect
21. C2×C3×#237C22semidirect
22. C22×C3×C4×D3C22semidirect
23. C22×C3×Dic6C22semidirect
24. C2×C3×#217C22semidirect
25. C3×D4×Dic3C22semidirect
26. C3×#926C22semidirect
27. #63981C22semidirect
28. #63978C22semidirect
29. #63977C22semidirect
30. #63966C22semidirect
31. #63966C22semidirect
32. #63966C22semidirect
33. C2×Dic3⋊Dic3C22semidirect
34. C2×#3722C22semidirect
35. #63962C22semidirect
36. #63909C22semidirect
37. C4×#626C22semidirect
38. #63871C22semidirect
39. #63866C22semidirect
40. #63864C22semidirect
41. #63857C22semidirect
46. C22×#237D3semidirect
52. #5798D3semidirect
64. C2×C32×D4D4semidirect
112. C22×#67C2×D3semidirect
113. C23×Dic3C2×D3semidirect
121. C2×#237C2×D3semidirect
128. C22×C4×D3C2×D3semidirect
129. C22×Dic6C2×D3semidirect
134. C2×#217C2×D3semidirect
141. D4×Dic3C2×D3semidirect
150. #926C2×D3semidirect
221. C2×C3×D4D12semidirect
222. C2×C3×D4#67semidirect
446. C2×D4#626semidirect
512. C32#3485semidirect
579. C3#85858semidirect
580. C3#87273semidirect

Maximal subgroups

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

subgroupindex
C2×#643612
C22×C3×#2372
C3×#57982
#105955192
C2×#639662
#105952542
#105952482
#105950232
#105948662
#872733
#858583