Finite Group Databasebeta

← #11901811

Subgroups — #11901811

Order 1152.

2191 conjugacy classes of subgroups.

The subgroup lattice has 587 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595941C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic, complemented
3C2×C3×#872C211yesmaximal, characteristic, complemented
4#10595022C212yesmaximal, complemented
5#10594977C214yesmaximal, complemented
6#10594973C214yesmaximal, complemented
7Dic3×#235C212yesmaximal, complemented
8#10593961C214yesmaximal, complemented
9#10593949C212yesmaximal, complemented
10#10593910C218yesmaximal, complemented
11#10593862C212yesmaximal, complemented
12#86236—31nomaximal
13#85738—31nomaximal
14C2×C3×#235C2212yes—
15C22×C3×C4×D3C2211yescharacteristic
16C2×C32×C42C2211yescharacteristic
17#64135C2212yes—
18#64133C2214yes—
19#64079C2212yescomplemented
20#64078C2212yescomplemented
21C4×#634C2214yescomplemented
22C3×#930C2214yes—
23C2×C3×(C2×D3)⋊C4C2212yes—
24C2×C3×Dic3⋊C4C2212yes—
25C2×C3×C4×Dic3C2211yescharacteristic
26C3×#875C2212yescomplemented
27C3×#874C2211yescharacteristic, complemented
28C3×C4×D12C2214yescomplemented
29C3×#872C2212yes—
30C3×#872C2214yes—
31C3×#872C2212yes—
32C3×#869C2211yescharacteristic, complemented
33#63976C2214yes—
34Dic3×#67C2218yes—
35#63961C2214yes—
36#63913C2218yes—
37#63908C2214yes—
38C4×#625C2218yes—
39#63896C2218yescomplemented
40Dic3×D12C2214yescomplemented
41#63891C2218yes—
42#63885C2218yes—
43#63884C2218yescomplemented
44C4×D3×Dic3C2214yescomplemented
45#63861C2218yescomplemented
46#63858C2218yes—
47#63856C2214yes—
48#63855C2214yescomplemented
49#63847C2218yescomplemented
50Dic3×Dic6C2214yescomplemented
51C3×#532—31no—
52C2×C3×#117—31no—
53#5828—32no—
54Dic3×#41—32no—
55#5791—32no—
56#5731—32no—
57#5719—32no—
58#5682—34no—
59#5617—34no—
60#5602—34no—
61#5538—38no—
62#5535—32no—
63#5534—34no—
64#5528—38no—
65#5518—32no—
66#5515—34no—
67#5494—34no—
68#5477D311yescharacteristic, complemented
69C4×#235—32no—
70C2×#872D311yescharacteristic, complemented
71#5470—31no—
72#5470—31no—
73#5470—61no—
74C23×C3×D3C2311yescharacteristic
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C2×#634C2314yes—
78C2×C3×#67C2314yes—
79C22×C3×Dic3C2311yescharacteristic
80C22×C3×Dic3C2312yes—
81C3×#235—28no—
82C2×C3×D12C2312yes—
83C2×C3×D12C2314yes—
84C2×C3×C4×D3—24no—
85C2×C3×C4×D3C2312yes—
86C2×C3×C4×D3C2312yes—
87C2×C3×C4×D3C2314yes—
88C2×C3×Dic6C2312yes—
89C2×#625C2318yes—
90C2×D3×Dic3C2318yes—
91C32×C42C2312yes—
92C32×C42C2311yescharacteristic
93C32×C42C2311yescharacteristic
94#3757C2314yes—
95C4⋊(C3⋊Dic3)C2314yes—
96C4⋊(C3⋊Dic3)C2314yes—
97#3750C2318yes—
98C4×C3⋊Dic3C2314yes—
99C3×(C2×D3)⋊C4C2314yes—
100C3×(C2×D3)⋊C4C2314yes—
101C3×(C2×D3)⋊C4C2318yes—
102C3×C4⋊Dic3C2314yes—
103C3×Dic3⋊C4C2314yes—
104C3×Dic3⋊C4C2314yes—
105C3×C4×Dic3C2312yes—
106C3×C4×Dic3C2312yes—
107#3724C2318yes—
108Dic3⋊Dic3C2318yes—
109(C2×D3)⋊Dic3C2318yes—
110(C2×D3)⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112Dic32C2318yes—
113#3455—91noSylow
114C2×C3×#41—32no—
115C23×C3×C4—31no—
116C2×#235C2×D312yes—
117C22×C4×D3C2×D311yescharacteristic
118C3×C4⋊Q8—31no—
119C3×#127—31no—
120C3×#124—32no—
121C3×#121—34no—
122C3×C4×D4—34no—
123C3×#117—32no—
124C3×#117—34no—
125C3×#117—32no—
126C2×C3×C4⋊C4—32no—
127C2×C3×C22⋊C4—32no—
128C2×C3×C42—21no—
129C2×C3×C42—31no—
130C2×C3×C42C2×D311yescharacteristic
131C2×C3×C42C2×D311yescharacteristic
132#953—34no—
133#946—34no—
134Q8×Dic3—34no—
135#939—38no—
136#938—34no—
137#937—34no—
138#935—34no—
139#935—38no—
140D4×Dic3—38no—
141D4×Dic3—34no—
142#930—34no—
143#930C2×D314yes—
144#929—34no—
145C4×#67—38no—
146C4×#67—38no—
147C4×#67—38no—
148C2×(C2×D3)⋊C4C2×D312yes—
149#926—32no—
150#926—32no—
151#926—34no—
152#926—62no—
153#924—34no—
154#924—34no—
155#924—34no—
156#924—64no—
157C2×Dic3⋊C4C2×D312yes—
158C2×C4×Dic3—34no—
159C2×C4×Dic3C2×D311yescharacteristic
160#898—38no—
161#898—38no—
162#896—38no—
163#894—38no—
164#889—38no—
165#889—38no—
166#886—38no—
167#885—38no—
168#885—38no—
169#884—38no—
170#883—38no—
171#879—38no—
172#879—38no—
173#878—38no—
174#875C2×D312yescomplemented
175#874C2×D311yescharacteristic, complemented
176C4×D12—34no—
177C4×D12C2×D314yescomplemented
178#872—34no—
179#872C2×D312yes—
180#872C2×D312yes—
181#872C2×D314yes—
182C42×D3—34no—
183#870—32no—
184#870—32no—
185#870—62no—
186#869—32no—
187#869—32no—
188#869—62no—
189#869C2×D311yescharacteristic, complemented
190C4×Dic6—34no—
191C4×Dic6—34no—
192C4×Dic6—34no—
193C4×Dic6—64no—
194C23×C32C2411yescharacteristic
195C22×C3×D3—22no—
196C22×C3×D3—42no—
197C22×C3×D3C2412yes—
198C22×C3×D3C2414yes—
199C2×C32×C4—42no—
200C2×C32×C4#4114yes—
201C2×C32×C4C2412yes—
202C2×C32×C4C2412yes—
203C2×C32×C4C2411yescharacteristic
204C2×C32×C4C2411yescharacteristic
205C2×C3⋊Dic3C2418yes—
206#634—44no—
207C3×#67—28no—
208C2×C3×Dic3—22no—
209C2×C3×Dic3—42no—
210C2×C3×Dic3C2414yes—
211C2×C3×Dic3C2414yes—
212C2×C3×Dic3C2412yes—
213C3×D12—24no—
214C3×D12—44no—
215C3×C4×D3—24no—
216C3×C4×D3—24no—
217C3×C4×D3—28no—
218C3×Dic6—24no—
219#625—48no—
220D3×Dic3—48no—
221#542—94no—
222#541—92no—
223#540—92no—
224#539—94no—
225#538—94no—
226#533—91no—
227#532—31no—
228#529—98no—
229#525—92no—
230C4×#41—92no—
231C2×#117—31no—
232C24×C3—31no—
233C23×D3C22×D311yescharacteristic
234C3×#41—68no—
235C2×C3×Q8—32no—
236C2×C3×D4—34no—
237C2×C3×D4—32no—
238C2×C3×D4—34no—
239C22×C3×C4—21no—
240C22×C3×C4—22no—
241C22×C3×C4—31no—
242C22×C3×C4—32no—
243C22×C3×C4—34no—
244C22×C3×C4—32no—
245C22×C3×C4—32no—
246C22×C3×C4—64no—
247C22×C3×C4C22×D312yes—
248C22×C3×C4C22×D312yes—
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C2×#67—38no—
252C2×#67—38no—
253C2×#67C22×D314yes—
254C22×Dic3—38no—
255C22×Dic3C22×D311yescharacteristic
256C22×Dic3C22×D312yes—
257#235—28no—
258C2×D12C22×D312yes—
259C2×D12C22×D314yes—
260C2×C4×D3—24no—
261C2×C4×D3—38no—
262C2×C4×D3C22×D314yes—
263C2×C4×D3C22×D312yes—
264C2×C4×D3C22×D312yes—
265C2×Dic6—34no—
266C2×Dic6—34no—
267C2×Dic6—64no—
268C2×Dic6C22×D312yes—
269C3×C4⋊C4—34no—
270C3×C4⋊C4—34no—
271C3×C4⋊C4—34no—
272C3×C22⋊C4—38no—
273C3×C22⋊C4—34no—
274C3×C22⋊C4—34no—
275C3×C42—22no—
276C3×C42—21no—
277C3×C42—21no—
278C3×C42—32no—
279C3×C42—32no—
280C3×C42C22×D312yes—
281C3×C42C22×D312yes—
282C3×C42C22×D311yescharacteristic
283C3×C42C22×D311yescharacteristic
284C3×C42C22×D311yescharacteristic
285C3×C42C22×D311yescharacteristic
286#217—34no—
287#217—34no—
288#217—38no—
289#217—38no—
290#217—38no—
291#217—64no—
292(C2×D3)⋊C4—38no—
293(C2×D3)⋊C4—38no—
294(C2×D3)⋊C4—38no—
295(C2×D3)⋊C4C22×D314yes—
296(C2×D3)⋊C4C22×D314yes—
297(C2×D3)⋊C4C22×D318yes—
298C4⋊Dic3—34no—
299C4⋊Dic3—34no—
300C4⋊Dic3—34no—
301C4⋊Dic3—34no—
302C4⋊Dic3—38no—
303C4⋊Dic3—64no—
304C4⋊Dic3—64no—
305C4⋊Dic3C22×D314yes—
306Dic3⋊C4—38no—
307Dic3⋊C4—38no—
308Dic3⋊C4—38no—
309Dic3⋊C4—38no—
310Dic3⋊C4—38no—
311Dic3⋊C4—68no—
312Dic3⋊C4C22×D314yes—
313Dic3⋊C4C22×D314yes—
314C4×Dic3—34no—
315C4×Dic3—34no—
316C4×Dic3—38no—
317C4×Dic3—38no—
318C4×Dic3—64no—
319C4×Dic3C22×D312yes—
320C4×Dic3C22×D312yes—
321C22×C32—22no—
322C22×C32C2×#4112yes—
323C22×C32C2511yescharacteristic
324C2×C3×D3—22no—
325C2×C3×D3—24no—
326C2×C3×D3—28no—
327C2×C3×D3—24no—
328C2×C3×D3—44no—
329C32×C4—22no—
330C32×C4—22no—
331C32×C4C2×#4112yes—
332C32×C4C2×#4112yes—
333C3⋊Dic3—28no—
334C3×Dic3—24no—
335C3×Dic3—22no—
336C3×Dic3—24no—
337C2×#41—32no—
338C23×C4—31no—
339C4⋊Q8—31no—
340C4⋊Q8—92no—
341#127—31no—
342#126—98no—
343#126—98no—
344#125—98no—
345#125—92no—
346#124—32no—
347#124—98no—
348#123—98no—
349#123—98no—
350#123—94no—
351C22⋊Q8—98no—
352C22⋊Q8—94no—
353C22⋊Q8—94no—
354#121—34no—
355#121—98no—
356#121—94no—
357#120—94no—
358C4×Q8—94no—
359C4×Q8—94no—
360C4×D4—34no—
361C4×D4—94no—
362C4×D4—98no—
363C4×D4—98no—
364#117—34no—
365#117—32no—
366#117—32no—
367#117—94no—
368#117—92no—
369C2×C4⋊C4—32no—
370C2×C22⋊C4—32no—
371C2×C42—31no—
372C2×C42—94no—
373C2×C42D3211yescharacteristic
374C23×C3—21no—
375C23×C3—32no—
376C23×C3—34no—
377C23×C3—62no—
378C23×C3—122no—
379C23×C3C23×D311yescharacteristic
380C23×C3C23×D311yescharacteristic
381C22×D3—22no—
382C22×D3—42no—
383C22×D3C23×D312yes—
384C22×D3C23×D314yes—
385C3×Q8—64no—
386C3×D4—68no—
387C3×D4—64no—
388C3×D4—124no—
389C2×C3×C4—21no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—21no—
393C2×C3×C4—24no—
394C2×C3×C4—34no—
395C2×C3×C4—34no—
396C2×C3×C4—32no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—44no—
400C2×C3×C4—62no—
401C2×C3×C4—68no—
402C2×C3×C4—64no—
403C2×C3×C4—64no—
404C2×C3×C4—122no—
405C2×C3×C4#23514yes—
406C2×C3×C4#23714yes—
407C2×C3×C4C23×D312yes—
408C2×C3×C4C23×D312yes—
409C2×C3×C4C23×D312yes—
410C2×C3×C4C23×D312yes—
411C2×C3×C4C23×D311yescharacteristic
412C2×C3×C4C23×D311yescharacteristic
413C2×C3×C4C23×D311yescharacteristic
414C2×C3×C4C23×D311yescharacteristic
415#67—28no—
416#67—128no—
417#67—128no—
418C2×Dic3—22no—
419C2×Dic3—38no—
420C2×Dic3—38no—
421C2×Dic3—42no—
422C2×Dic3—68no—
423C2×Dic3—128no—
424C2×Dic3C23×D314yes—
425C2×Dic3C23×D314yes—
426C2×Dic3C23×D312yes—
427D12—24no—
428D12—44no—
429C4×D3—24no—
430C4×D3—24no—
431C4×D3—28no—
432C4×D3—128no—
433Dic6—24no—
434Dic6—124no—
435Dic6—124no—
436Dic6—128no—
437C2×C32—22no—
438C2×C32C22×#4111yescharacteristic
439C2×C32#58512yes—
440C3×D3—44no—
441C3×D3—42no—
442C24—31no—
443#41—68no—
444C2×Q8—32no—
445C2×Q8—94no—
446C2×D4—34no—
447C2×D4—32no—
448C2×D4—34no—
449C2×D4—98no—
450C22×C4—31no—
451C22×C4—32no—
452C22×C4—32no—
453C22×C4—34no—
454C22×C4—32no—
455C22×C4—64no—
456C22×C4—98no—
457C22×C4C2×D3212yes—
458C22×C4C2×D3211yescharacteristic
459C4⋊C4—34no—
460C4⋊C4—34no—
461C4⋊C4—34no—
462C4⋊C4—98no—
463C4⋊C4—98no—
464C4⋊C4—94no—
465C4⋊C4—98no—
466C4⋊C4—94no—
467C22⋊C4—34no—
468C22⋊C4—34no—
469C22⋊C4—38no—
470C22⋊C4—98no—
471C22⋊C4—98no—
472C22⋊C4—98no—
473C22⋊C4—94no—
474C42—32no—
475C42—32no—
476C42—98no—
477C42—94no—
478C42C2×D3211yescharacteristic
479C42C2×D3211yescharacteristic
480C42C2×D3212yes—
481C22×C3—22no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—21no—
485C22×C3—42no—
486C22×C3—64no—
487C22×C3—62no—
488C22×C3—68no—
489C22×C3—64no—
490C22×C3—124no—
491C22×C3C2×#23512yes—
492C22×C3C2×#23712yes—
493C22×C3C24×D311yescharacteristic
494C22×C3C24×D311yescharacteristic
495C2×D3—22no—
496C2×D3—24no—
497C2×D3—28no—
498C2×D3—24no—
499C2×D3—44no—
500C3×C4—24no—
501C3×C4—22no—
502C3×C4—22no—
503C3×C4—22no—
504C3×C4—22no—
505C3×C4—22no—
506C3×C4—22no—
507C3×C4—42no—
508C3×C4—64no—
509C3×C4—62no—
510C3×C4—64no—
511C3×C4C2×#23512yes—
512C3×C4C2×#23512yes—
513C3×C4C2×#23712yes—
514C3×C4C2×#23712yes—
515Dic3—22no—
516Dic3—24no—
517Dic3—24no—
518Dic3—68no—
519Dic3—68no—
520Dic3—128no—
521C32#345511yescharacteristic, complemented, Sylow
522C23—32no—
523C23—34no—
524C23—62no—
525C23—122no—
526C23C22×D3211yescharacteristic
527Q8—64no—
528Q8—364no—
529D4—68no—
530D4—64no—
531D4—124no—
532D4—368no—
533C2×C4—34no—
534C2×C4—34no—
535C2×C4—32no—
536C2×C4—42no—
537C2×C4—62no—
538C2×C4—64no—
539C2×C4—64no—
540C2×C4—68no—
541C2×C4—98no—
542C2×C4—122no—
543C2×C4—368no—
544C2×C4#379514yes—
545C2×C4C22×D3212yes—
546C2×C4C22×D3212yes—
547C2×C4C22×D3211yescharacteristic
548C2×C4C22×D3211yescharacteristic
549C2×C3—22no—
550C2×C3—22no—
551C2×C3—21no—
552C2×C3—22no—
553C2×C3—42no—
554C2×C3—122no—
555C2×C3—124no—
556C2×C3C22×#23511yescharacteristic
557C2×C3C22×#23711yescharacteristic
558C2×C3#596412yes—
559C2×C3#596412yes—
560D3—44no—
561D3—42no—
562C22—22no—
563C22—62no—
564C22—64no—
565C22—68no—
566C22—64no—
567C22—124no—
568C22C2×#379512yes—
569C22C23×D3211yescharacteristic
570C4—22no—
571C4—22no—
572C4—62no—
573C4—64no—
574C4—64no—
575C4—188no—
576C4C2×#379512yes—
577C4C2×#379512yes—
578C3—21no—
579C3#8573811yescharacteristic, complemented
580C3#8623611yescharacteristic, complemented
581C2—22no—
582C2—122no—
583C2—124no—
584C2C22×#379511yescharacteristic
585C2#1059666912yes—
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3455
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. #10595941C2semidirect
2. C3×#5477C2semidirect
3. C2×C3×#872C2semidirect
4. #10595022C2semidirect
5. #10594977C2semidirect
6. #10594973C2semidirect
7. Dic3×#235C2semidirect
8. #10593961C2semidirect
9. #10593949C2semidirect
10. #10593910C2semidirect
11. #10593862C2semidirect
19. #64079C22semidirect
20. #64078C22semidirect
21. C4×#634C22semidirect
26. C3×#875C22semidirect
27. C3×#874C22semidirect
28. C3×C4×D12C22semidirect
32. C3×#869C22semidirect
39. #63896C22semidirect
40. Dic3×D12C22semidirect
43. #63884C22semidirect
44. C4×D3×Dic3C22semidirect
45. #63861C22semidirect
48. #63855C22semidirect
49. #63847C22semidirect
50. Dic3×Dic6C22semidirect
68. #5477D3semidirect
70. C2×#872D3semidirect
174. #875C2×D3semidirect
175. #874C2×D3semidirect
177. C4×D12C2×D3semidirect
189. #869C2×D3semidirect
521. C32#3455semidirect
579. C3#85738semidirect
580. C3#86236semidirect

Maximal subgroups

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

subgroupindex
#105959412
C3×#54772
C2×C3×#8722
#105950222
#105949772
#105949732
Dic3×#2352
#105939612
#105939492
#105939102
#105938622
#862363
#857383