Finite Group Databasebeta

← #41×#625 #11902820

Subgroups — #41×#625 #11902820

Order 1152.

3451 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C212yesmaximal, complemented
2#41×C3⋊Dic3C211yesmaximal, characteristic, complemented
3#10595412C211yesmaximal, characteristic, complemented
4#10595409C212yesmaximal, complemented
5Q8×#625C211yesmaximal, characteristic, complemented
6#10595252C213yesmaximal, complemented
7#10595244C216yesmaximal, complemented
8D4×#625C213yesmaximal, complemented
9#10595032C213yesmaximal, complemented
10#10595022C216yesmaximal, complemented
11C2×C4×#625C213yesmaximal, complemented
12#41×#67—32nomaximal
13C2×C32×#41C2211yescharacteristic
14C3×D3×#41—216no—
15C2×C3×#239C2212yescomplemented
16C2×C3×D3×Q8C2212yescomplemented
17C2×C3×#237C2216yescomplemented
18C2×C3×D3×D4C2216yescomplemented
19C2×C3×#235C2216yescomplemented
20C22×C3×C4×D3C2216yescomplemented
21C22×#625C2213yes—
22Q8×C3⋊Dic3C2211yescharacteristic, complemented
23Q8×C3⋊Dic3C2211yescharacteristic, complemented
24D4×C3⋊Dic3C2213yescomplemented
25D4×C3⋊Dic3C2213yescomplemented
26#64135C2213yescomplemented
27C2×C4×C3⋊Dic3C2213yescomplemented
28#63980C2216yescomplemented
29#63980C2216yescomplemented
30#63976C22112yescomplemented
31C2×#3724C2213yescomplemented
32#63961C22112yescomplemented
33C2×(C2×D3)⋊Dic3C2216yescomplemented
34#63914C2213yescomplemented
35#63908C2216yescomplemented
36#63908C2216yescomplemented
37C4×#625C2213yes—
38C4×#625C2211yescharacteristic
39C4×#625C2216yescomplemented
40C4×#625C2213yescomplemented
41C4×#625C2216yescomplemented
42C4×#625C2213yescomplemented
43C4×#625C2216yescomplemented
44#63873C2213yescomplemented
45#63863C2216yescomplemented
46#63856C2216yescomplemented
47#63856C2216yescomplemented
48C22×C3×#41—32no—
49C2×D3×#41D312yescomplemented
50#5834—32no—
51#5832—36no—
52#5831—32no—
53#5829—36no—
54#5828—36no—
55Dic3×#41—32no—
56Dic3×#41—61no—
57#5824—36no—
58#5817—32no—
59Q8×#67—32no—
60#5806—36no—
61D4×#67—36no—
62#5791—36no—
63C2×C4×#67—36no—
64C23×C3×D3C2316yes—
65C32×#41D418yescomplemented
66C2×C32×Q8C2311yescharacteristic
67C2×C32×D4C2313yes—
68C22×C32×C4C2313yes—
69C22×C3⋊Dic3C2313yes—
70C22×C3⋊Dic3C2313yes—
71C2×C3×#67C23112yes—
72C22×C3×Dic3C2316yes—
73C3×#239—28no—
74C3×D3×Q8—28no—
75C3×#237—224no—
76C3×D3×D4—224no—
77C3×#235—224no—
78C2×C3×D12C2316yes—
79C2×C3×C4×D3—224no—
80C2×C3×C4×D3C2312yes—
81C2×C3×C4×D3C2316yes—
82C2×C3×C4×D3C2316yes—
83C2×C3×C4×D3C2316yes—
84C2×C3×Dic6C2316yes—
85C2×#625—212no—
86C2×#625C2316yes—
87C2×#625C2313yes—
88C2×#625C2316yes—
89C2×#625C2311yescharacteristic
90#3757C2316yes—
91C4⋊(C3⋊Dic3)C2313yes—
92C4⋊(C3⋊Dic3)C2313yes—
93C4×C3⋊Dic3C2313yes—
94C4×C3⋊Dic3C2313yes—
95C4×C3⋊Dic3C2311yescharacteristic
96C4×C3⋊Dic3C2313yes—
97#3724C2316yes—
98#3724C2316yes—
99#3724C2313yes—
100#3724C2311yescharacteristic
101(C2×D3)⋊Dic3C2316yes—
102(C2×D3)⋊Dic3C23112yes—
103(C2×D3)⋊Dic3C2316yes—
104(C2×D3)⋊Dic3C2312yes—
105(C2×D3)⋊Dic3C2316yes—
106D4×#41—91noSylow
107C2×C3×#41—21no—
108C2×C3×#41—32no—
109C2×C3×#41—36no—
110C2×C3×#41—36no—
111C2×C3×#41—616no—
112C2×C3×#41C2×D312yes—
113C22×C3×Q8—32no—
114C22×C3×D4—36no—
115C23×C3×C4—36no—
116C22×#67—36no—
117D3×#41—216no—
118C2×#239C2×D312yescomplemented
119C2×D3×Q8C2×D312yescomplemented
120C2×#237C2×D316yescomplemented
121C2×D3×D4C2×D316yescomplemented
122C2×#235C2×D316yescomplemented
123C22×C4×D3C2×D316yescomplemented
124#953—312no—
125C2×#217—36no—
126#947—36no—
127#946—36no—
128#946—36no—
129Q8×Dic3—32no—
130Q8×Dic3—32no—
131Q8×Dic3—61no—
132Q8×Dic3—61no—
133#944—36no—
134#940—36no—
135#939—312no—
136#939—312no—
137#938—36no—
138#938—36no—
139#937—312no—
140#936—36no—
141#935—312no—
142D4×Dic3—36no—
143D4×Dic3—36no—
144D4×Dic3—63no—
145D4×Dic3—63no—
146#930—36no—
147#930—36no—
148#929—312no—
149C4×#67—32no—
150C4×#67—36no—
151C4×#67—36no—
152C4×#67—36no—
153C4×#67—36no—
154C4×#67—36no—
155C4×#67—36no—
156C4×#67—36no—
157C4×#67—312no—
158C2×(C2×D3)⋊C4—36no—
159#926—36no—
160#926—63no—
161#924—36no—
162#924—36no—
163C2×Dic3⋊C4—36no—
164C2×C4×Dic3—36no—
165C2×C4×Dic3—63no—
166C23×C32C2413yes—
167C22×C3×D3—212no—
168C22×C3×D3—212no—
169C22×C3×D3—46no—
170C22×C3×D3C2416yes—
171C22×C3×D3C2412yes—
172C32×Q8C2×D414yescomplemented
173C32×D4C2×D4112yescomplemented
174C2×C32×C4C2×D4112yescomplemented
175C2×C32×C4C2411yescharacteristic
176C2×C32×C4C2413yes—
177C2×C3⋊Dic3—26no—
178C2×C3⋊Dic3—43no—
179C2×C3⋊Dic3C2411yescharacteristic
180C2×C3⋊Dic3C2413yes—
181C2×C3⋊Dic3C2413yes—
182C2×C3⋊Dic3C2411yescharacteristic
183C3×#67—224no—
184C2×C3×Dic3—212no—
185C2×C3×Dic3C2416yes—
186C2×C3×Dic3C2412yes—
187C3×D12—212no—
188C3×C4×D3—24no—
189C3×C4×D3—212no—
190C3×C4×D3—212no—
191C3×C4×D3—212no—
192C3×Dic6—212no—
193#625—212no—
194#625—26no—
195#625—46no—
196#625#4114yesdirect product factor
197C22×#41—32no—
198#550—91no—
199D4×Q8—91no—
200#548—92no—
201#547—93no—
202#546—96no—
203D42—93no—
204#532—93no—
205#525—96no—
206C4×#41—91no—
207C2×C4×D4—93no—
208C24×C3—36no—
209C23×D3C22×D316yes—
210C3×#41—28no—
211C3×#41—68no—
212C3×#41—624no—
213C3×#41—624no—
214C3×#41#67116yescomplemented
215C2×C3×Q8—21no—
216C2×C3×Q8—36no—
217C2×C3×Q8—68no—
218C2×C3×Q8C22×D312yes—
219C2×C3×D4—23no—
220C2×C3×D4—312no—
221C2×C3×D4—36no—
222C2×C3×D4—624no—
223C2×C3×D4C22×D316yes—
224C22×C3×C4—23no—
225C22×C3×C4—36no—
226C22×C3×C4—36no—
227C22×C3×C4—36no—
228C22×C3×C4—32no—
229C22×C3×C4—36no—
230C22×C3×C4—624no—
231C22×C3×C4C22×D316yes—
232C2×#67—32no—
233C2×#67—36no—
234C2×#67—36no—
235C2×#67—36no—
236C2×#67—312no—
237C2×#67—624no—
238C2×#67C22×D3112yes—
239C22×Dic3—36no—
240C22×Dic3—36no—
241C22×Dic3—63no—
242C22×Dic3—63no—
243C22×Dic3C22×D316yes—
244#239—28no—
245D3×Q8—28no—
246#237—224no—
247D3×D4—224no—
248#235—224no—
249C2×D12C22×D316yes—
250C2×C4×D3—224no—
251C2×C4×D3C22×D312yes—
252C2×C4×D3C22×D316yes—
253C2×C4×D3C22×D316yes—
254C2×C4×D3C22×D316yes—
255C2×Dic6C22×D316yes—
256#217—312no—
257#217—36no—
258#217—312no—
259#217—32no—
260#217—36no—
261#217—36no—
262#217—66no—
263(C2×D3)⋊C4—32no—
264(C2×D3)⋊C4—36no—
265(C2×D3)⋊C4—36no—
266(C2×D3)⋊C4—36no—
267(C2×D3)⋊C4—312no—
268C4⋊Dic3—36no—
269C4⋊Dic3—36no—
270C4⋊Dic3—63no—
271C4⋊Dic3—63no—
272Dic3⋊C4—32no—
273Dic3⋊C4—36no—
274Dic3⋊C4—36no—
275Dic3⋊C4—36no—
276Dic3⋊C4—312no—
277C4×Dic3—32no—
278C4×Dic3—36no—
279C4×Dic3—36no—
280C4×Dic3—36no—
281C4×Dic3—61no—
282C4×Dic3—63no—
283C4×Dic3—63no—
284C4×Dic3—63no—
285C22×C32—23no—
286C22×C32—23no—
287C22×C32C22×D416yes—
288C22×C32C2511yescharacteristic
289C2×C3×D3—22no—
290C2×C3×D3—22no—
291C2×C3×D3—26no—
292C2×C3×D3—26no—
293C2×C3×D3—26no—
294C2×C3×D3—424no—
295C2×C3×D3C2×#4114yescomplemented
296C32×C4C22×D416yes—
297C32×C4C22×D412yes—
298C3⋊Dic3—21no—
299C3⋊Dic3—23no—
300C3⋊Dic3—23no—
301C3⋊Dic3C2×#4112yescomplemented
302C3×Dic3—26no—
303C3×Dic3—22no—
304C2×#41—32no—
305C2×#41—36no—
306C2×#41—36no—
307C2×#41—616no—
308C2×#41D3211yescharacteristic
309C22×Q8—32no—
310C22×D4—36no—
311C22×D4—93no—
312C23×C4—36no—
313C4⋊Q8—93no—
314#127—93no—
315#124—96no—
316#123—912no—
317C22⋊Q8—96no—
318C22⋊Q8—96no—
319#121—96no—
320#121—96no—
321#121—96no—
322#121—96no—
323#120—912no—
324C4×Q8—91no—
325C4×Q8—91no—
326C4×D4—91no—
327C4×D4—96no—
328C4×D4—93no—
329C4×D4—93no—
330C4×D4—96no—
331C4×D4—93no—
332C4×D4—96no—
333C4×D4—93no—
334C4×D4—93no—
335#117—93no—
336C2×C4⋊C4—93no—
337C2×C22⋊C4—96no—
338C2×C42—93no—
339C23×C3—23no—
340C23×C3—32no—
341C23×C3—36no—
342C23×C3—612no—
343C23×C3—612no—
344C23×C3—126no—
345C23×C3C23×D316yes—
346C22×D3—212no—
347C22×D3—212no—
348C22×D3—46no—
349C22×D3C23×D316yes—
350C22×D3C23×D312yes—
351C3×Q8—24no—
352C3×Q8—612no—
353C3×Q8C2×#6718yescomplemented
354C3×D4—212no—
355C3×D4—624no—
356C3×D4—612no—
357C3×D4C2×#67124yescomplemented
358C2×C3×C4—23no—
359C2×C3×C4—21no—
360C2×C3×C4—212no—
361C2×C3×C4—32no—
362C2×C3×C4—36no—
363C2×C3×C4—612no—
364C2×C3×C4—64no—
365C2×C3×C4—612no—
366C2×C3×C4—612no—
367C2×C3×C4—612no—
368C2×C3×C4C2×#67124yescomplemented
369C2×C3×C4C23×D316yes—
370C2×C3×C4C23×D312yes—
371#67—224no—
372#67—38no—
373#67—612no—
374#67—612no—
375#67—612no—
376#67—1212no—
377C2×Dic3—212no—
378C2×Dic3—32no—
379C2×Dic3—32no—
380C2×Dic3—36no—
381C2×Dic3—36no—
382C2×Dic3—61no—
383C2×Dic3—61no—
384C2×Dic3—63no—
385C2×Dic3—63no—
386C2×Dic3—612no—
387C2×Dic3—126no—
388C2×Dic3—126no—
389C2×Dic3—126no—
390C2×Dic3C23×D316yes—
391C2×Dic3C23×D312yes—
392D12—212no—
393C4×D3—24no—
394C4×D3—212no—
395C4×D3—212no—
396C4×D3—212no—
397Dic6—212no—
398C2×C32—26no—
399C2×C32C23×D411yescharacteristic
400C2×C32C22×#4111yescharacteristic
401C2×C32#58511yescharacteristic
402C3×D3—24no—
403C3×D3—46no—
404C24—36no—
405#41—68no—
406#41—624no—
407#41—624no—
408#41#62518yesdirect product factor
409C2×Q8—36no—
410C2×Q8—68no—
411C2×Q8C2×D3211yescharacteristic
412C2×D4—312no—
413C2×D4—36no—
414C2×D4—624no—
415C2×D4—91no—
416C2×D4—96no—
417C2×D4—93no—
418C2×D4—96no—
419C2×D4—1812no—
420C2×D4C2×D3213yes—
421C22×C4—36no—
422C22×C4—36no—
423C22×C4—36no—
424C22×C4—32no—
425C22×C4—36no—
426C22×C4—624no—
427C22×C4—93no—
428C22×C4—93no—
429C22×C4C2×D3213yes—
430C4⋊C4—91no—
431C4⋊C4—93no—
432C4⋊C4—96no—
433C4⋊C4—96no—
434C4⋊C4—93no—
435C4⋊C4—93no—
436C22⋊C4—92no—
437C22⋊C4—96no—
438C22⋊C4—96no—
439C22⋊C4—96no—
440C22⋊C4—912no—
441C22⋊C4—96no—
442C42—93no—
443C42—93no—
444C42—91no—
445C42—93no—
446C22×C3—26no—
447C22×C3—26no—
448C22×C3—26no—
449C22×C3—21no—
450C22×C3—34no—
451C22×C3—43no—
452C22×C3—43no—
453C22×C3—62no—
454C22×C3—62no—
455C22×C3—66no—
456C22×C3—66no—
457C22×C3—66no—
458C22×C3—1224no—
459C22×C3C22×#67112yes—
460C22×C3C24×D312yes—
461C2×D3—22no—
462C2×D3—22no—
463C2×D3—26no—
464C2×D3—26no—
465C2×D3—26no—
466C2×D3—424no—
467C2×D3D3×#4114yescomplemented
468C3×C4—22no—
469C3×C4—26no—
470C3×C4—62no—
471C3×C4—66no—
472C3×C4C22×#67112yes—
473C3×C4C22×#6714yes—
474Dic3—26no—
475Dic3—22no—
476Dic3—34no—
477Dic3—62no—
478Dic3—62no—
479Dic3—66no—
480Dic3—62no—
481Dic3—66no—
482Dic3—123no—
483Dic3—123no—
484C32D4×#4111yescharacteristic, complemented, Sylow
485C23—32no—
486C23—36no—
487C23—612no—
488C23—612no—
489C23—126no—
490C23C22×D3213yes—
491Q8—612no—
492Q8C2×#62514yescomplemented
493D4—624no—
494D4—612no—
495D4—94no—
496D4—186no—
497D4—1812no—
498D4—366no—
499D4C2×#625112yescomplemented
500C2×C4—32no—
501C2×C4—36no—
502C2×C4—612no—
503C2×C4—64no—
504C2×C4—612no—
505C2×C4—612no—
506C2×C4—612no—
507C2×C4—91no—
508C2×C4—91no—
509C2×C4—93no—
510C2×C4—93no—
511C2×C4—186no—
512C2×C4—363no—
513C2×C4C2×#625112yescomplemented
514C2×C4C22×D3213yes—
515C2×C4C22×D3211yescharacteristic
516C2×C3—212no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—46no—
521C2×C3—64no—
522C2×C3—126no—
523C2×C3C2×D3×#4112yes—
524C2×C3#596412yes—
525C2×C3C23×#6712yes—
526D3—24no—
527D3—46no—
528C22—23no—
529C22—23no—
530C22—34no—
531C22—62no—
532C22—62no—
533C22—66no—
534C22—66no—
535C22—66no—
536C22—1224no—
537C22C22×#62516yes—
538C22C23×D3211yescharacteristic
539C4—62no—
540C4—66no—
541C4—92no—
542C4—183no—
543C4—181no—
544C4—183no—
545C4C22×#62512yes—
546C4C22×#62516yes—
547C3—21no—
548C3#41×#6712yescomplemented
549C2—26no—
550C2—64no—
551C2—126no—
552C2D32×#4111yescharacteristic
553C2#1059669511yescharacteristic
554C2C23×#62511yescharacteristic
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32D4×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×#41C2semidirect
2. #41×C3⋊Dic3C2semidirect
3. #10595412C2semidirect
4. #10595409C2semidirect
5. Q8×#625C2semidirect
6. #10595252C2semidirect
7. #10595244C2semidirect
8. D4×#625C2semidirect
9. #10595032C2semidirect
10. #10595022C2semidirect
11. C2×C4×#625C2semidirect
15. C2×C3×#239C22semidirect
16. C2×C3×D3×Q8C22semidirect
17. C2×C3×#237C22semidirect
18. C2×C3×D3×D4C22semidirect
19. C2×C3×#235C22semidirect
20. C22×C3×C4×D3C22semidirect
22. Q8×C3⋊Dic3C22semidirect
23. Q8×C3⋊Dic3C22semidirect
24. D4×C3⋊Dic3C22semidirect
25. D4×C3⋊Dic3C22semidirect
26. #64135C22semidirect
27. C2×C4×C3⋊Dic3C22semidirect
28. #63980C22semidirect
29. #63980C22semidirect
30. #63976C22semidirect
31. C2×#3724C22semidirect
32. #63961C22semidirect
33. C2×(C2×D3)⋊Dic3C22semidirect
34. #63914C22semidirect
35. #63908C22semidirect
36. #63908C22semidirect
39. C4×#625C22semidirect
40. C4×#625C22semidirect
41. C4×#625C22semidirect
42. C4×#625C22semidirect
43. C4×#625C22semidirect
44. #63873C22semidirect
45. #63863C22semidirect
46. #63856C22semidirect
47. #63856C22semidirect
49. C2×D3×#41D3semidirect
65. C32×#41D4semidirect
118. C2×#239C2×D3semidirect
119. C2×D3×Q8C2×D3semidirect
120. C2×#237C2×D3semidirect
121. C2×D3×D4C2×D3semidirect
122. C2×#235C2×D3semidirect
123. C22×C4×D3C2×D3semidirect
172. C32×Q8C2×D4semidirect
173. C32×D4C2×D4semidirect
174. C2×C32×C4C2×D4semidirect
196. #625#41direct (N × H)
214. C3×#41#67semidirect
295. C2×C3×D3C2×#41semidirect
301. C3⋊Dic3C2×#41semidirect
353. C3×Q8C2×#67semidirect
357. C3×D4C2×#67semidirect
368. C2×C3×C4C2×#67semidirect
408. #41#625direct (N × H)
467. C2×D3D3×#41semidirect
484. C32D4×#41semidirect
492. Q8C2×#625semidirect
499. D4C2×#625semidirect
513. C2×C4C2×#625semidirect
548. C3#41×#67semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
#41×C3⋊Dic32
#105954122
#105954092
Q8×#6252
#105952522
#105952442
D4×#6252
#105950322
#105950222
C2×C4×#6252
#41×#673