Finite Group Databasebeta

← #11901810

Subgroups — #11901810

Order 1152.

2245 conjugacy classes of subgroups.

The subgroup lattice has 607 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64081C211yesmaximal, characteristic, complemented
2C3×#5477C211yesmaximal, characteristic, complemented
3C3×#5470C211yesmaximal, characteristic, complemented
4#10595034C212yesmaximal, complemented
5#10594979C214yesmaximal, complemented
6#10594974C214yesmaximal, complemented
7#10594958C212yesmaximal, complemented
8#10593955C214yesmaximal, complemented
9#10593950C212yesmaximal, complemented
10#10593911C218yesmaximal, complemented
11#10593867C212yesmaximal, complemented
12#86273—31nomaximal
13#86236—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C2×C3×#235C2212yes—
16C2×C32×C42C2211yescharacteristic
17C2×#3752C2212yes—
18C2×#3750C2212yes—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20#64081C2212yes—
21#64081C2214yes—
22#64081C2212yes—
23C3×#930C2214yes—
24C3×#926C2212yes—
25C3×#924C2214yes—
26C3×#875C2212yescomplemented
27C3×#874C2211yescharacteristic, complemented
28C3×C4×D12C2214yescomplemented
29C3×#870C2212yescomplemented
30C3×#869C2211yescharacteristic, complemented
31C3×#869C2212yescomplemented
32C3×C4×Dic6C2214yescomplemented
33#63981C2214yes—
34#67⋊Dic3C2218yes—
35#63962C2214yes—
36#63916C2214yes—
37#63907C2218yes—
38C4×#626C2218yes—
39#63898C2214yescomplemented
40#63890C2218yes—
41#63887C2218yescomplemented
42#63886C2218yes—
43#63884C2218yescomplemented
44C4×D3×Dic3C2214yescomplemented
45#63871C2214yes—
46#63858C2218yescomplemented
47#63855C2214yescomplemented
48#63848C2218yes—
49#63846C2218yescomplemented
50#63843C2214yescomplemented
51C3×#533—31no—
52C3×#532—31no—
53#5828—32no—
54Dic3×#41—32no—
55#5733—34no—
56#5731—32no—
57#5719—32no—
58#5698—32no—
59#5697—32no—
60#5682—34no—
61#5645—34no—
62#5644—34no—
63#5617—34no—
64#5602—34no—
65#5580—38no—
66#5538—38no—
67#5524—32no—
68#5522—32no—
69#5477D311yescharacteristic, complemented
70C2×#872—31no—
71C2×#872—31no—
72C2×#872—61no—
73#5470D311yescharacteristic, complemented
74C23×C3⋊D3C2311yescharacteristic
75C22×C32×C4C2312yes—
76C22×C32×C4C2311yescharacteristic
77C22×C3⋊Dic3C2311yescharacteristic
78C22×C3⋊Dic3C2312yes—
79C2×C4×C3⋊D3—24no—
80C2×C4×C3⋊D3C2312yes—
81C2×C4×C3⋊D3C2312yes—
82C2×C3×#67C2314yes—
83C3×#235—28no—
84C2×C3×D12C2312yes—
85C2×C3×D12C2314yes—
86C2×C3×C4×D3C2314yes—
87C2×C3×Dic6C2312yes—
88C2×C3×Dic6C2314yes—
89C2×#626C2318yes—
90C2×D3×Dic3C2318yes—
91C32×C42C2312yes—
92C32×C42C2311yescharacteristic
93C32×C42C2311yescharacteristic
94#3752C2314yes—
95#3752C2314yes—
96#3750C2314yes—
97#3750C2314yes—
98C4×C3⋊Dic3C2312yes—
99C4×C3⋊Dic3C2312yes—
100C3×#217C2314yes—
101C3×(C2×D3)⋊C4C2318yes—
102C3×C4⋊Dic3C2314yes—
103C3×C4⋊Dic3C2314yes—
104C3×C4⋊Dic3C2314yes—
105C3×Dic3⋊C4C2318yes—
106C3×C4×Dic3C2314yes—
107Dic3⋊Dic3C2318yes—
108Dic3⋊Dic3C2318yes—
109#3722C2318yes—
110(C2×D3)⋊Dic3C2318yes—
111(C2×D3)⋊Dic3C2318yes—
112Dic32C2318yes—
113#3455—91noSylow
114C2×C3×#41—32no—
115C2×#235C2×D312yes—
116C22×C4×D3—31no—
117C22×C4×D3—31no—
118C22×C4×D3—61no—
119C3×C4⋊Q8—31no—
120C3×C4⋊Q8—32no—
121C3×#127—31no—
122C3×#125—32no—
123C3×#124—32no—
124C3×C22⋊Q8—34no—
125C3×#121—34no—
126C3×C4×Q8—34no—
127C3×C4×D4—34no—
128C3×#117—32no—
129C2×C3×C42—21no—
130C2×C3×C42C2×D311yescharacteristic
131C2×C3×C42C2×D311yescharacteristic
132#947—38no—
133#946—38no—
134#946—34no—
135Q8×Dic3—34no—
136#939—38no—
137#938—34no—
138#937—34no—
139#935—34no—
140#935—38no—
141D4×Dic3—38no—
142D4×Dic3—34no—
143#930C2×D314yes—
144C4×#67—38no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—62no—
148#926—34no—
149#926C2×D312yes—
150#924C2×D314yes—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—32no—
153C2×Dic3⋊C4—62no—
154C2×C4×Dic3—31no—
155C2×C4×Dic3—31no—
156C2×C4×Dic3—34no—
157C2×C4×Dic3—61no—
158#898—38no—
159#898—38no—
160#898—38no—
161#897—34no—
162#895—38no—
163#895—34no—
164#894—38no—
165#894—38no—
166#893—34no—
167#890—38no—
168#889—38no—
169#887—34no—
170#886—34no—
171#886—38no—
172#885—38no—
173#882—34no—
174#67⋊C4—38no—
175#879—38no—
176#878—38no—
177#875C2×D312yescomplemented
178#874C2×D311yescharacteristic, complemented
179C4×D12—38no—
180C4×D12C2×D314yescomplemented
181#872—34no—
182#872—32no—
183#872—32no—
184#872—32no—
185#872—32no—
186#872—34no—
187#872—34no—
188#872—64no—
189#872—62no—
190#872—62no—
191C42×D3—34no—
192#870C2×D312yescomplemented
193#869C2×D312yescomplemented
194#869C2×D311yescharacteristic, complemented
195C4×Dic6C2×D314yescomplemented
196C23×C32C2411yescharacteristic
197C22×C3⋊D3—22no—
198C22×C3⋊D3—42no—
199C22×C3⋊D3C2412yes—
200C22×C3×D3C2414yes—
201C2×C32×C4—42no—
202C2×C32×C4#4114yes—
203C2×C32×C4C2412yes—
204C2×C32×C4C2412yes—
205C2×C32×C4C2411yescharacteristic
206C2×C32×C4C2411yescharacteristic
207C2×C3⋊Dic3—22no—
208C2×C3⋊Dic3—42no—
209C2×C3⋊Dic3C2414yes—
210C2×C3⋊Dic3C2412yes—
211C4×C3⋊D3—24no—
212C4×C3⋊D3—24no—
213C3×#67—28no—
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2418yes—
216C3×D12—24no—
217C3×D12—44no—
218C3×C4×D3—28no—
219C3×Dic6—24no—
220C3×Dic6—44no—
221#626—48no—
222D3×Dic3—48no—
223#542—94no—
224#541—92no—
225#540—92no—
226#539—94no—
227#538—94no—
228#533—31no—
229#532—31no—
230#529—98no—
231#525—92no—
232C4×#41—92no—
233C2×#117—91no—
234C23×D3—31no—
235C23×D3—31no—
236C23×D3—61no—
237C3×#41—68no—
238C2×C3×Q8—32no—
239C2×C3×Q8—34no—
240C2×C3×D4—34no—
241C2×C3×D4—32no—
242C2×C3×D4—34no—
243C22×C3×C4—21no—
244C22×C3×C4—22no—
245C22×C3×C4—34no—
246C22×C3×C4C22×D312yes—
247C22×C3×C4C22×D312yes—
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C2×#67—38no—
251C2×#67C22×D314yes—
252C22×Dic3—31no—
253C22×Dic3—31no—
254C22×Dic3—32no—
255C22×Dic3—32no—
256C22×Dic3—38no—
257C22×Dic3—61no—
258C22×Dic3—62no—
259#235—28no—
260C2×D12—38no—
261C2×D12C22×D312yes—
262C2×D12C22×D314yes—
263C2×C4×D3—32no—
264C2×C4×D3—32no—
265C2×C4×D3—32no—
266C2×C4×D3—32no—
267C2×C4×D3—38no—
268C2×C4×D3—62no—
269C2×C4×D3—62no—
270C2×C4×D3—68no—
271C2×C4×D3—64no—
272C2×C4×D3—64no—
273C2×C4×D3C22×D314yes—
274C2×Dic6C22×D312yes—
275C2×Dic6C22×D314yes—
276C3×C4⋊C4—34no—
277C3×C4⋊C4—34no—
278C3×C4⋊C4—38no—
279C3×C4⋊C4—34no—
280C3×C22⋊C4—34no—
281C3×C22⋊C4—38no—
282C3×C42—21no—
283C3×C42—21no—
284C3×C42—22no—
285C3×C42—34no—
286C3×C42C22×D312yes—
287C3×C42C22×D311yescharacteristic
288C3×C42C22×D311yescharacteristic
289C3×C42C22×D311yescharacteristic
290C3×C42C22×D312yes—
291C3×C42C22×D311yescharacteristic
292#217—38no—
293#217—38no—
294#217C22×D314yes—
295(C2×D3)⋊C4—38no—
296(C2×D3)⋊C4—38no—
297(C2×D3)⋊C4—34no—
298(C2×D3)⋊C4—34no—
299(C2×D3)⋊C4—34no—
300(C2×D3)⋊C4—34no—
301(C2×D3)⋊C4—38no—
302(C2×D3)⋊C4—38no—
303(C2×D3)⋊C4—64no—
304(C2×D3)⋊C4—64no—
305(C2×D3)⋊C4C22×D318yes—
306C4⋊Dic3—38no—
307C4⋊Dic3—38no—
308C4⋊Dic3C22×D314yes—
309C4⋊Dic3C22×D314yes—
310C4⋊Dic3C22×D314yes—
311Dic3⋊C4—34no—
312Dic3⋊C4—34no—
313Dic3⋊C4—34no—
314Dic3⋊C4—34no—
315Dic3⋊C4—38no—
316Dic3⋊C4—38no—
317Dic3⋊C4—64no—
318Dic3⋊C4—64no—
319Dic3⋊C4C22×D318yes—
320C4×Dic3—32no—
321C4×Dic3—32no—
322C4×Dic3—32no—
323C4×Dic3—32no—
324C4×Dic3—38no—
325C4×Dic3—38no—
326C4×Dic3—62no—
327C4×Dic3—62no—
328C4×Dic3C22×D314yes—
329C22×C32—22no—
330C22×C32C2×#4112yes—
331C22×C32C2511yescharacteristic
332C2×C3⋊D3—22no—
333C2×C3⋊D3—24no—
334C2×C3⋊D3—44no—
335C2×C3×D3—24no—
336C2×C3×D3—28no—
337C32×C4—22no—
338C32×C4—22no—
339C32×C4C2×#4112yes—
340C32×C4C2×#4112yes—
341C3⋊Dic3—22no—
342C3⋊Dic3—24no—
343C3×Dic3—24no—
344C3×Dic3—28no—
345C2×#41—32no—
346C23×C4—91no—
347C4⋊Q8—31no—
348C4⋊Q8—32no—
349#127—31no—
350#126—98no—
351#126—98no—
352#125—32no—
353#125—98no—
354#124—32no—
355#124—98no—
356#123—98no—
357#123—94no—
358#123—98no—
359C22⋊Q8—34no—
360C22⋊Q8—98no—
361C22⋊Q8—94no—
362#121—34no—
363#121—94no—
364#121—98no—
365#120—94no—
366C4×Q8—34no—
367C4×Q8—94no—
368C4×D4—34no—
369C4×D4—98no—
370C4×D4—98no—
371C4×D4—94no—
372#117—32no—
373#117—94no—
374#117—94no—
375#117—92no—
376#117—92no—
377C2×C4⋊C4—92no—
378C2×C22⋊C4—92no—
379C2×C42—94no—
380C2×C42—91no—
381C2×C42D3211yescharacteristic
382C23×C3—21no—
383C23×C3—34no—
384C23×C3C23×D311yescharacteristic
385C23×C3C23×D311yescharacteristic
386C22×D3—32no—
387C22×D3—32no—
388C22×D3—62no—
389C22×D3—64no—
390C22×D3—62no—
391C22×D3—62no—
392C22×D3—122no—
393C22×D3—122no—
394C22×D3—124no—
395C22×D3C23×D314yes—
396C3×Q8—64no—
397C3×Q8—124no—
398C3×D4—68no—
399C3×D4—64no—
400C3×D4—124no—
401C2×C3×C4—21no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—24no—
406C2×C3×C4—34no—
407C2×C3×C4—38no—
408C2×C3×C4—42no—
409C2×C3×C4—42no—
410C2×C3×C4—44no—
411C2×C3×C4—68no—
412C2×C3×C4#23714yes—
413C2×C3×C4#23914yes—
414C2×C3×C4C23×D312yes—
415C2×C3×C4C23×D312yes—
416C2×C3×C4C23×D312yes—
417C2×C3×C4C23×D312yes—
418C2×C3×C4C23×D311yescharacteristic
419C2×C3×C4C23×D311yescharacteristic
420C2×C3×C4C23×D311yescharacteristic
421C2×C3×C4C23×D311yescharacteristic
422#67—28no—
423#67—128no—
424C2×Dic3—34no—
425C2×Dic3—34no—
426C2×Dic3—32no—
427C2×Dic3—32no—
428C2×Dic3—62no—
429C2×Dic3—64no—
430C2×Dic3—64no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—128no—
434C2×Dic3—122no—
435C2×Dic3—122no—
436C2×Dic3—124no—
437C2×Dic3C23×D314yes—
438C2×Dic3C23×D318yes—
439D12—24no—
440D12—44no—
441D12—128no—
442C4×D3—28no—
443C4×D3—68no—
444C4×D3—68no—
445C4×D3—64no—
446C4×D3—64no—
447C4×D3—64no—
448C4×D3—64no—
449C4×D3—128no—
450Dic6—24no—
451Dic6—44no—
452C2×C32—22no—
453C2×C32C22×#4111yescharacteristic
454C2×C32#58512yes—
455C3⋊D3—42no—
456C3×D3—44no—
457C24—91no—
458#41—68no—
459C2×Q8—32no—
460C2×Q8—34no—
461C2×D4—34no—
462C2×D4—32no—
463C2×D4—34no—
464C2×D4—98no—
465C22×C4—34no—
466C22×C4—98no—
467C22×C4—91no—
468C22×C4—92no—
469C22×C4—92no—
470C22×C4—92no—
471C22×C4—184no—
472C22×C4C2×D3212yes—
473C22×C4C2×D3211yescharacteristic
474C4⋊C4—34no—
475C4⋊C4—34no—
476C4⋊C4—38no—
477C4⋊C4—34no—
478C4⋊C4—98no—
479C4⋊C4—98no—
480C4⋊C4—94no—
481C4⋊C4—94no—
482C22⋊C4—34no—
483C22⋊C4—38no—
484C22⋊C4—98no—
485C22⋊C4—98no—
486C22⋊C4—98no—
487C22⋊C4—94no—
488C22⋊C4—94no—
489C42—34no—
490C42—98no—
491C42—92no—
492C42—92no—
493C42C2×D3211yescharacteristic
494C42C2×D3211yescharacteristic
495C42C2×D3212yes—
496C22×C3—24no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—21no—
501C22×C3—64no—
502C22×C3—68no—
503C22×C3C2×#23712yes—
504C22×C3C2×#23912yes—
505C22×C3C24×D311yescharacteristic
506C22×C3C24×D311yescharacteristic
507C2×D3—24no—
508C2×D3—28no—
509C2×D3—64no—
510C2×D3—62no—
511C2×D3—62no—
512C2×D3—64no—
513C2×D3—64no—
514C2×D3—124no—
515C2×D3—128no—
516C2×D3—124no—
517C2×D3—124no—
518C3×C4—22no—
519C3×C4—22no—
520C3×C4—22no—
521C3×C4—22no—
522C3×C4—22no—
523C3×C4—22no—
524C3×C4—42no—
525C3×C4—42no—
526C3×C4—64no—
527C3×C4—68no—
528C3×C4C2×#23712yes—
529C3×C4C2×#23712yes—
530C3×C4C2×#23912yes—
531C3×C4C2×#23912yes—
532Dic3—24no—
533Dic3—28no—
534Dic3—64no—
535Dic3—62no—
536Dic3—62no—
537Dic3—64no—
538Dic3—64no—
539Dic3—124no—
540C32#345511yescharacteristic, complemented, Sylow
541C23—34no—
542C23—92no—
543C23—182no—
544C23—362no—
545C23C22×D3211yescharacteristic
546Q8—64no—
547Q8—124no—
548D4—68no—
549D4—64no—
550D4—124no—
551D4—368no—
552C2×C4—38no—
553C2×C4—34no—
554C2×C4—42no—
555C2×C4—68no—
556C2×C4—94no—
557C2×C4—92no—
558C2×C4—182no—
559C2×C4—184no—
560C2×C4—184no—
561C2×C4—368no—
562C2×C4—362no—
563C2×C4#379614yes—
564C2×C4C22×D3212yes—
565C2×C4C22×D3212yes—
566C2×C4C22×D3211yescharacteristic
567C2×C4C22×D3211yescharacteristic
568C2×C3—24no—
569C2×C3—22no—
570C2×C3—22no—
571C2×C3—21no—
572C2×C3—22no—
573C2×C3—124no—
574C2×C3C22×#23711yescharacteristic
575C2×C3C22×#23911yescharacteristic
576C2×C3#596412yes—
577C2×C3#596412yes—
578D3—44no—
579D3—124no—
580D3—122no—
581D3—122no—
582C22—22no—
583C22—64no—
584C22—68no—
585C22—182no—
586C22—184no—
587C22—364no—
588C22C2×#379612yes—
589C22C23×D3211yescharacteristic
590C4—22no—
591C4—22no—
592C4—64no—
593C4—68no—
594C4—182no—
595C4—184no—
596C4C2×#379612yes—
597C4C2×#379612yes—
598C3—21no—
599C3#8623611yescharacteristic, complemented
600C3#8627311yescharacteristic, complemented
601C2—22no—
602C2—124no—
603C2—362no—
604C2C22×#379611yescharacteristic
605C2#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. C2×#64081C2semidirect
2. C3×#5477C2semidirect
3. C3×#5470C2semidirect
4. #10595034C2semidirect
5. #10594979C2semidirect
6. #10594974C2semidirect
7. #10594958C2semidirect
8. #10593955C2semidirect
9. #10593950C2semidirect
10. #10593911C2semidirect
11. #10593867C2semidirect
26. C3×#875C22semidirect
27. C3×#874C22semidirect
28. C3×C4×D12C22semidirect
29. C3×#870C22semidirect
30. C3×#869C22semidirect
31. C3×#869C22semidirect
32. C3×C4×Dic6C22semidirect
39. #63898C22semidirect
41. #63887C22semidirect
43. #63884C22semidirect
44. C4×D3×Dic3C22semidirect
46. #63858C22semidirect
47. #63855C22semidirect
49. #63846C22semidirect
50. #63843C22semidirect
69. #5477D3semidirect
73. #5470D3semidirect
177. #875C2×D3semidirect
178. #874C2×D3semidirect
180. C4×D12C2×D3semidirect
192. #870C2×D3semidirect
193. #869C2×D3semidirect
194. #869C2×D3semidirect
195. C4×Dic6C2×D3semidirect
540. C32#3455semidirect
599. C3#86236semidirect
600. C3#86273semidirect

Maximal subgroups

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

subgroupindex
C2×#640812
C3×#54772
C3×#54702
#105950342
#105949792
#105949742
#105949582
#105939552
#105939502
#105939112
#105938672
#862733
#862363