Finite Group Databasebeta

← #11904432

Subgroups — #11904432

Order 1152.

3565 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3830C211yesmaximal, characteristic, complemented
2C2×C3×#1004C211yesmaximal, characteristic, complemented
3C3×#5798C211yesmaximal, characteristic, complemented
4#10595519C214yesmaximal, complemented
5C2×#63962C214yesmaximal, complemented
6#10595248C218yesmaximal, complemented
7#10595246C218yesmaximal, complemented
8#10595034C212yesmaximal, complemented
9#10594856C212yesmaximal, complemented
10#87280—31nomaximal
11#85858—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×#638C2212yescomplemented
14C23×C3⋊Dic3C2212yescomplemented
15C2×#3830—28no—
16C2×#3830C2218yescomplemented
17C22×C4×C3⋊D3C2211yescharacteristic, complemented
18C22×#634C2211yescharacteristic, complemented
19C22×C3×#67C2214yes—
20C3×#1004—28no—
21C2×C3×#237C2214yescomplemented
22C2×C3×D3×D4C2214yescomplemented
23C2×C3×#235C2212yes—
24C2×C3×#217C2214yescomplemented
25C3×D4×Dic3C2218yescomplemented
26C3×#926C2212yescomplemented
27#63981C2214yescomplemented
28#63978C22116yescomplemented
29#63977C2218yescomplemented
30#63966C2218yescomplemented
31C2×Dic3⋊Dic3C2218yescomplemented
32#63962C2218yescomplemented
33#63962C2214yescomplemented
34#63962C22116yescomplemented
35C2×(C2×D3)⋊Dic3C2218yescomplemented
36#63916C2214yescomplemented
37C4×#626C2218yescomplemented
38#63871C2214yescomplemented
39#63866C2214yescomplemented
40#63860C2214yescomplemented
41#63857C2218yescomplemented
42C2×C3×H(5,𝔽2)—31no—
43C2×#1004D311yescharacteristic, complemented
44C22×#237—31no—
45C22×#237—31no—
46C22×#237—61no—
47C3×#518—31no—
48#5828—32no—
49#5825—32no—
50#5824—38no—
51#5806—38no—
52#5804—34no—
53#5798D311yescharacteristic, complemented
54C2×#935—34no—
55#5555—38no—
56#5554—38no—
57#5526—32no—
58#5524—32no—
59#5493—34no—
60C2×#886—34no—
61C24×C32C2312yes—
62C23×C3⋊D3C2311yescharacteristic
63C23×C3×D3C2314yes—
64C2×C32×D4D418yescomplemented
65C2×C32×D4C2314yes—
66C22×C32×C4C2311yescharacteristic
67C2×#638—28no—
68C2×#638C2318yes—
69C22×C3⋊Dic3—28no—
70C22×C3⋊Dic3C2312yes—
71C22×C3⋊Dic3C2311yescharacteristic
72C22×C3⋊Dic3C2318yes—
73#3830—232no—
74C2×C4×C3⋊D3—24no—
75C2×C4×C3⋊D3C2314yes—
76C2×#634—24no—
77C2×#634C2314yes—
78C2×C3×#67—216no—
79C2×C3×#67C2314yes—
80C2×C3×#67C2318yes—
81C22×C3×Dic3C2314yes—
82C22×C3×Dic3C2318yes—
83C3×#237—216no—
84C3×D3×D4—216no—
85C3×#235—28no—
86C2×C3×D12C2312yes—
87C2×C3×C4×D3C2314yes—
88C2×C3×Dic6C2312yes—
89C2×#626C2318yes—
90C3×#217C2314yes—
91C3×#217C2318yes—
92C3×C4⋊Dic3C2314yes—
93C3×C4×Dic3C2314yes—
94Dic3⋊Dic3C23116yes—
95Dic3⋊Dic3C2318yes—
96#3722C2318yes—
97(C2×D3)⋊Dic3C23116yes—
98(C2×D3)⋊Dic3C2318yes—
99#3485—91noSylow
100C3×H(5,𝔽2)—68no—
101C2×C3×#41—34no—
102C2×C3×#41—32no—
103C22×C3×D4—21no—
104C22×C3×D4—34no—
105C22×C3×D4—34no—
106C22×C3×D4C2×D311yescharacteristic
107C22×C3×D4C2×D311yescharacteristic
108C22×#67—32no—
109C22×#67—32no—
110C22×#67—62no—
111C22×#67C2×D314yes—
112C23×Dic3—32no—
113C23×Dic3—32no—
114C23×Dic3—62no—
115#1004—28no—
116C2×#237—38no—
117C2×#237—38no—
118C2×#237—68no—
119C2×#237—616no—
120C2×#237—68no—
121C2×#237—68no—
122C2×#237C2×D314yescomplemented
123C2×D3×D4C2×D314yescomplemented
124C2×#235C2×D312yes—
125C22×C4×D3—31no—
126C22×C4×D3—31no—
127C22×C4×D3—61no—
128C22×Dic6—31no—
129C22×Dic6—31no—
130C22×Dic6—61no—
131C3×C4×D4—38no—
132C3×#117—32no—
133C2×C3×C22⋊C4—34no—
134#953—38no—
135C2×#217—38no—
136C2×#217C2×D314yescomplemented
137#946—34no—
138#944—34no—
139#939—316no—
140#938—34no—
141#937—34no—
142#936—34no—
143#935—34no—
144#935—38no—
145#935—316no—
146D4×Dic3C2×D318yescomplemented
147#930—316no—
148#929—38no—
149C4×#67—38no—
150C2×(C2×D3)⋊C4—38no—
151#926C2×D312yescomplemented
152C2×C4⋊Dic3—38no—
153#924—38no—
154C2×Dic3⋊C4—38no—
155#897—38no—
156#897—34no—
157#895—34no—
158#886—34no—
159#886—38no—
160#886—316no—
161#886—38no—
162#882—38no—
163#882—34no—
164#875—34no—
165C4×D12—38no—
166#869—34no—
167C23×C32—44no—
168C23×C32C2×D418yes—
169C23×C32C2414yes—
170C23×C32C2411yescharacteristic
171C22×C3⋊D3—22no—
172C22×C3⋊D3—42no—
173C22×C3⋊D3C2412yes—
174C22×C3×D3—28no—
175C22×C3×D3—48no—
176C22×C3×D3C2414yes—
177C32×D4C2×D4116yes—
178C2×C32×C4C2×D414yes—
179C2×C32×C4C2412yes—
180#638—216no—
181C2×C3⋊Dic3—24no—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—216no—
184C2×C3⋊Dic3C2414yes—
185C2×C3⋊Dic3C2412yes—
186C4×C3⋊D3—28no—
187#634—28no—
188C3×#67—28no—
189C3×#67—216no—
190C2×C3×Dic3—28no—
191C2×C3×Dic3—48no—
192C2×C3×Dic3C2418yes—
193C2×C3×Dic3C2414yes—
194C3×D12—24no—
195C3×C4×D3—28no—
196C3×Dic6—24no—
197#626—48no—
198C2×H(5,𝔽2)—31no—
199C22×#41—91no—
200#547—98no—
201#546—98no—
202#536—92no—
203#534—94no—
204#525—92no—
205C2×#123—94no—
206#518—31no—
207C24×C3—22no—
208C24×C3—34no—
209C24×C3C22×D312yes—
210C24×C3C22×D312yes—
211C23×D3—31no—
212C23×D3—31no—
213C23×D3—61no—
214C23×D3C22×D314yes—
215C3×#41—616no—
216C3×#41—68no—
217C2×C3×Q8—32no—
218C2×C3×D4—28no—
219C2×C3×D4—24no—
220C2×C3×D4—34no—
221C2×C3×D4—38no—
222C2×C3×D4—32no—
223C2×C3×D4—616no—
224C2×C3×D4—616no—
225C2×C3×D4D1218yescomplemented
226C2×C3×D4#6718yescomplemented
227C2×C3×D4C22×D314yes—
228C2×C3×D4C22×D314yes—
229C22×C3×C4—21no—
230C22×C3×C4—34no—
231C22×C3×C4—38no—
232C22×C3×C4—34no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—216no—
236C2×#67—38no—
237C2×#67—38no—
238C2×#67—38no—
239C2×#67—68no—
240C2×#67—616no—
241C2×#67—68no—
242C2×#67—68no—
243C2×#67C22×D314yes—
244C2×#67C22×D318yes—
245C22×Dic3—32no—
246C22×Dic3—31no—
247C22×Dic3—38no—
248C22×Dic3—38no—
249C22×Dic3—32no—
250C22×Dic3—31no—
251C22×Dic3—62no—
252C22×Dic3—61no—
253C22×Dic3—68no—
254C22×Dic3—616no—
255C22×Dic3—68no—
256C22×Dic3—68no—
257C22×Dic3C22×D314yes—
258C22×Dic3C22×D318yes—
259#237—216no—
260#237—664no—
261#237—632no—
262#237—632no—
263D3×D4—216no—
264#235—28no—
265C2×D12—38no—
266C2×D12C22×D312yes—
267C2×C4×D3—34no—
268C2×C4×D3—34no—
269C2×C4×D3—64no—
270C2×C4×D3—68no—
271C2×C4×D3—64no—
272C2×C4×D3—64no—
273C2×C4×D3C22×D314yes—
274C2×Dic6—34no—
275C2×Dic6—34no—
276C2×Dic6—64no—
277C2×Dic6—68no—
278C2×Dic6—64no—
279C2×Dic6—64no—
280C2×Dic6C22×D312yes—
281C3×C4⋊C4—34no—
282C3×C22⋊C4—34no—
283C3×C22⋊C4—38no—
284C3×C42—34no—
285#217—316no—
286#217—38no—
287#217C22×D314yes—
288#217C22×D318yes—
289(C2×D3)⋊C4—38no—
290(C2×D3)⋊C4—316no—
291(C2×D3)⋊C4—38no—
292(C2×D3)⋊C4—38no—
293C4⋊Dic3—316no—
294C4⋊Dic3—38no—
295C4⋊Dic3C22×D314yes—
296Dic3⋊C4—38no—
297Dic3⋊C4—316no—
298C4×Dic3C22×D314yes—
299C22×C32—22no—
300C22×C32—28no—
301C22×C32—48no—
302C22×C32C22×D418yes—
303C22×C32C22×D412yes—
304C22×C32C2511yescharacteristic
305C2×C3⋊D3—22no—
306C2×C3⋊D3—24no—
307C2×C3⋊D3—44no—
308C2×C3×D3—24no—
309C2×C3×D3—28no—
310C2×C3×D3—88no—
311C32×C4C22×D414yes—
312C3⋊Dic3—24no—
313C3⋊Dic3—22no—
314C3×Dic3—24no—
315C3×Dic3—28no—
316H(5,𝔽2)—68no—
317C2×#41—34no—
318C2×#41—32no—
319C2×#41—98no—
320C2×#41—188no—
321C22×Q8—91no—
322C22×D4—34no—
323C22×D4—34no—
324C22×D4—92no—
325C22×D4D3211yescharacteristic
326C23×C4—92no—
327C23×C4—91no—
328C4⋊Q8—94no—
329#124—94no—
330#123—98no—
331#123—94no—
332#123—98no—
333#123—916no—
334C22⋊Q8—98no—
335C22⋊Q8—94no—
336#121—94no—
337#121—916no—
338#120—94no—
339#120—98no—
340C4×D4—38no—
341C4×D4—98no—
342#117—32no—
343C2×C4⋊C4—98no—
344C2×C22⋊C4—34no—
345C2×C22⋊C4—98no—
346C23×C3—21no—
347C23×C3—24no—
348C23×C3—28no—
349C23×C3—34no—
350C23×C3—44no—
351C23×C3—44no—
352C23×C3—48no—
353C23×C3—68no—
354C23×C3—128no—
355C23×C3C2×D1218yes—
356C23×C3C2×#6718yes—
357C23×C3C23×D311yescharacteristic
358C23×C3C23×D314yes—
359C23×C3C23×D311yescharacteristic
360C23×C3C23×D314yes—
361C22×D3—28no—
362C22×D3—32no—
363C22×D3—32no—
364C22×D3—48no—
365C22×D3—62no—
366C22×D3—64no—
367C22×D3—62no—
368C22×D3—62no—
369C22×D3—122no—
370C22×D3—122no—
371C22×D3—124no—
372C22×D3C23×D314yes—
373C3×Q8—64no—
374C3×D4—216no—
375C3×D4—68no—
376C3×D4—616no—
377C3×D4—64no—
378C3×D4C2×D12116yes—
379C3×D4C2×#67116yes—
380C2×C3×C4—22no—
381C2×C3×C4—24no—
382C2×C3×C4—34no—
383C2×C3×C4—38no—
384C2×C3×C4—68no—
385C2×C3×C4—68no—
386C2×C3×C4—128no—
387C2×C3×C4C2×D1214yes—
388C2×C3×C4C2×#6714yes—
389C2×C3×C4C23×D312yes—
390C2×C3×C4C23×D312yes—
391#67—28no—
392#67—216no—
393#67—632no—
394#67—616no—
395#67—616no—
396#67—128no—
397C2×Dic3—28no—
398C2×Dic3—34no—
399C2×Dic3—32no—
400C2×Dic3—34no—
401C2×Dic3—32no—
402C2×Dic3—48no—
403C2×Dic3—64no—
404C2×Dic3—62no—
405C2×Dic3—68no—
406C2×Dic3—64no—
407C2×Dic3—632no—
408C2×Dic3—64no—
409C2×Dic3—62no—
410C2×Dic3—616no—
411C2×Dic3—64no—
412C2×Dic3—62no—
413C2×Dic3—616no—
414C2×Dic3C23×D318yes—
415C2×Dic3C23×D314yes—
416D12—24no—
417D12—128no—
418C4×D3—28no—
419C4×D3—616no—
420C4×D3—68no—
421C4×D3—68no—
422Dic6—24no—
423Dic6—616no—
424Dic6—68no—
425Dic6—68no—
426C2×C32—22no—
427C2×C32—28no—
428C2×C32C23×D411yescharacteristic
429C2×C32#58512yes—
430C3⋊D3—42no—
431C3×D3—44no—
432C24—34no—
433C24—91no—
434C24C2×D3212yes—
435#41—616no—
436#41—68no—
437#41—1832no—
438C2×Q8—32no—
439C2×Q8—94no—
440C2×Q8—184no—
441C2×D4—34no—
442C2×D4—38no—
443C2×D4—32no—
444C2×D4—616no—
445C2×D4—616no—
446C2×D4—98no—
447C2×D4—98no—
448C2×D4—188no—
449C2×D4#62618yescomplemented
450C2×D4C2×D3214yes—
451C22×C4—34no—
452C22×C4—38no—
453C22×C4—34no—
454C22×C4—98no—
455C22×C4—91no—
456C22×C4—92no—
457C22×C4—94no—
458C22×C4—188no—
459C22×C4—184no—
460C22×C4C2×D3211yescharacteristic
461C4⋊C4—34no—
462C4⋊C4—98no—
463C4⋊C4—916no—
464C22⋊C4—34no—
465C22⋊C4—38no—
466C22⋊C4—98no—
467C22⋊C4—98no—
468C22⋊C4—916no—
469C42—34no—
470C22×C3—24no—
471C22×C3—28no—
472C22×C3—28no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—28no—
477C22×C3—21no—
478C22×C3—48no—
479C22×C3—48no—
480C22×C3—48no—
481C22×C3—416no—
482C22×C3—64no—
483C22×C3—68no—
484C22×C3—248no—
485C22×C3C22×D1212yes—
486C22×C3C22×D1218yes—
487C22×C3C22×#6718yes—
488C22×C3C22×#6712yes—
489C22×C3C24×D311yescharacteristic
490C22×C3C24×D311yescharacteristic
491C2×D3—28no—
492C2×D3—24no—
493C2×D3—64no—
494C2×D3—62no—
495C2×D3—64no—
496C2×D3—64no—
497C2×D3—62no—
498C2×D3—88no—
499C2×D3—124no—
500C2×D3—128no—
501C2×D3—124no—
502C2×D3—124no—
503C3×C4—24no—
504C3×C4—64no—
505C3×C4—68no—
506C3×C4C22×D1214yes—
507C3×C4C22×#6714yes—
508Dic3—28no—
509Dic3—24no—
510Dic3—68no—
511Dic3—64no—
512Dic3—64no—
513Dic3—62no—
514Dic3—64no—
515Dic3—62no—
516C32#348511yescharacteristic, complemented, Sylow
517C23—34no—
518C23—44no—
519C23—68no—
520C23—92no—
521C23—128no—
522C23—182no—
523C23—362no—
524C23C2×#62618yes—
525C23C22×D3211yescharacteristic
526C23C22×D3214yes—
527Q8—64no—
528Q8—188no—
529D4—616no—
530D4—68no—
531D4—64no—
532D4—1816no—
533D4—368no—
534D4C2×#626116yes—
535C2×C4—38no—
536C2×C4—34no—
537C2×C4—68no—
538C2×C4—68no—
539C2×C4—92no—
540C2×C4—94no—
541C2×C4—128no—
542C2×C4—182no—
543C2×C4—184no—
544C2×C4—1816no—
545C2×C4—188no—
546C2×C4C2×#62614yes—
547C2×C4C22×D3212yes—
548C2×C3—24no—
549C2×C3—22no—
550C2×C3—28no—
551C2×C3—28no—
552C2×C3—22no—
553C2×C3—22no—
554C2×C3—21no—
555C2×C3—48no—
556C2×C3—124no—
557C2×C3C23×D1211yescharacteristic
558C2×C3#596612yes—
559C2×C3#596612yes—
560C2×C3C23×#6711yescharacteristic
561D3—44no—
562D3—124no—
563D3—122no—
564D3—122no—
565C22—28no—
566C22—22no—
567C22—48no—
568C22—68no—
569C22—64no—
570C22—184no—
571C22—182no—
572C22—248no—
573C22—364no—
574C22C22×#62618yes—
575C22C22×#62612yes—
576C22C23×D3211yescharacteristic
577C4—68no—
578C4—64no—
579C4—182no—
580C4—184no—
581C4C22×#62614yes—
582C3—21no—
583C3#8585811yescharacteristic, complemented
584C3#8728011yescharacteristic, complemented
585C2—22no—
586C2—28no—
587C2—124no—
588C2—362no—
589C2#1059667912yes—
590C2C23×#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. C22×#3830C2semidirect
2. C2×C3×#1004C2semidirect
3. C3×#5798C2semidirect
4. #10595519C2semidirect
5. C2×#63962C2semidirect
6. #10595248C2semidirect
7. #10595246C2semidirect
8. #10595034C2semidirect
9. #10594856C2semidirect
13. C22×#638C22semidirect
14. C23×C3⋊Dic3C22semidirect
16. C2×#3830C22semidirect
17. C22×C4×C3⋊D3C22semidirect
18. C22×#634C22semidirect
21. C2×C3×#237C22semidirect
22. C2×C3×D3×D4C22semidirect
24. C2×C3×#217C22semidirect
25. C3×D4×Dic3C22semidirect
26. C3×#926C22semidirect
27. #63981C22semidirect
28. #63978C22semidirect
29. #63977C22semidirect
30. #63966C22semidirect
31. C2×Dic3⋊Dic3C22semidirect
32. #63962C22semidirect
33. #63962C22semidirect
34. #63962C22semidirect
35. C2×(C2×D3)⋊Dic3C22semidirect
36. #63916C22semidirect
37. C4×#626C22semidirect
38. #63871C22semidirect
39. #63866C22semidirect
40. #63860C22semidirect
41. #63857C22semidirect
43. C2×#1004D3semidirect
53. #5798D3semidirect
64. C2×C32×D4D4semidirect
122. C2×#237C2×D3semidirect
123. C2×D3×D4C2×D3semidirect
136. C2×#217C2×D3semidirect
146. D4×Dic3C2×D3semidirect
151. #926C2×D3semidirect
225. C2×C3×D4D12semidirect
226. C2×C3×D4#67semidirect
449. C2×D4#626semidirect
516. C32#3485semidirect
583. C3#85858semidirect
584. C3#87280semidirect

Maximal subgroups

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

subgroupindex
C22×#38302
C2×C3×#10042
C3×#57982
#105955192
C2×#639622
#105952482
#105952462
#105950342
#105948562
#872803
#858583