Finite Group Databasebeta

← #11902601

Subgroups — #11902601

Order 1152.

3665 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#64319C211yesmaximal, characteristic, complemented
3C3×#5817C212yesmaximal, complemented
4#10595432C213yesmaximal, complemented
5#10595429C213yesmaximal, complemented
6#10595414C212yesmaximal, complemented
7Q8×#624C211yesmaximal, characteristic, complemented
8#10595362C216yesmaximal, complemented
9#10595081C213yesmaximal, complemented
10C4×#3811C213yesmaximal, complemented
11#10594918C216yesmaximal, complemented
12D3×#548—32nomaximal
13C22×C32×Q8C2211yescharacteristic, complemented
14C2×Q8×C3⋊D3—28no—
15C2×Q8×C3⋊D3C2213yes—
16C2×Q8×C3⋊D3C2211yescharacteristic
17C2×Q8×C3⋊D3C2213yescomplemented
18C2×Q8×C3⋊D3C2211yescharacteristic, complemented
19C22×C4×C3⋊D3C2213yes—
20C22×#634C2213yescomplemented
21C2×C3×#239C2212yescomplemented
22C2×#3811C2213yes—
23#64319—28no—
24C2×#3802C2213yes—
25C2×C4×D32C2213yes—
26C2×#3795C2216yescomplemented
27C3×#947C2216yescomplemented
28C3×#946C2216yescomplemented
29C3×Q8×Dic3C2212yescomplemented
30C3×#930C2216yescomplemented
31C3×C4×#67C2216yescomplemented
32#63980C2216yescomplemented
33#63974C2211yescharacteristic
34#67⋊Dic3C2216yescomplemented
35#63921C2216yes—
36#63921C2213yes—
37#63916C2216yescomplemented
38#63913C22112yescomplemented
39#63912C2216yescomplemented
40C4×#626C2216yescomplemented
41#63900C2213yes—
42#63896C22112yescomplemented
43#63883C2213yes—
44C4×#624C2213yes—
45#63881C2216yescomplemented
46#63860C2216yescomplemented
47#63857C2216yescomplemented
48#63844C2216yescomplemented
49C2×D3×#41—32no—
50C22×D3×Q8—32no—
51C22×D3×Q8—61no—
52C3×#548—32no—
53#5831—32no—
54#5817D312yescomplemented
55#5677—36no—
56D3×#124—36no—
57#5633—36no—
58D3×C22⋊Q8—36no—
59D3×#121—36no—
60#5598—36no—
61#5576—32no—
62C4×D3×Q8—32no—
63#5552—36no—
64C4×D3×D4—36no—
65C23×C3⋊D3C2311yescharacteristic
66C22×D32C2313yes—
67C2×C32×Q8—24no—
68C2×C32×Q8C2313yes—
69C2×C32×Q8C2311yescharacteristic
70C22×C32×C4C2313yes—
71C22×C3⋊Dic3C2313yes—
72Q8×C3⋊D3—24no—
73Q8×C3⋊D3—212no—
74Q8×C3⋊D3—212no—
75Q8×C3⋊D3D418yescomplemented
76C2×C4×C3⋊D3—212no—
77C2×C4×C3⋊D3C2313yes—
78C2×C4×C3⋊D3C2313yes—
79C2×C4×C3⋊D3C2313yes—
80C2×C4×C3⋊D3C2313yes—
81C2×#634—212no—
82C2×#634C2313yes—
83C2×#634C2316yes—
84C2×#634C2313yes—
85C2×C3×#67C2316yes—
86C3×#239—28no—
87C2×C3×D12C2316yes—
88C2×C3×C4×D3C2316yes—
89#3811—212no—
90C2×#626C2316yes—
91C2×#625C2316yes—
92C2×#624C2311yescharacteristic
93C2×#624C2313yes—
94C2×#624C2311yescharacteristic
95C2×D3×Dic3C2316yes—
96#3802—212no—
97C4×D32—212no—
98#3795—224no—
99C3×#217C2312yes—
100C3×(C2×D3)⋊C4C2316yes—
101C3×(C2×D3)⋊C4C23112yes—
102C3×C4⋊Dic3C2316yes—
103C3×Dic3⋊C4C2316yes—
104C3×C4×Dic3C2316yes—
105#3724C2316yes—
106Dic3⋊Dic3C2316yes—
107#3722C2312yes—
108(C2×D3)⋊Dic3C23112yes—
109(C2×D3)⋊Dic3C2316yes—
110Dic32C2316yes—
111C2×#548—91noSylow
112C2×C3×#41—32no—
113C22×C3×Q8—21no—
114C22×C3×Q8C2×D312yescomplemented
115D3×#41—616no—
116C2×#239C2×D312yescomplemented
117C2×D3×Q8—32no—
118C2×D3×Q8—36no—
119C2×D3×Q8—36no—
120C2×D3×Q8—32no—
121C2×D3×Q8—61no—
122C2×D3×Q8—63no—
123C2×D3×Q8—63no—
124C2×D3×Q8—61no—
125C2×D3×Q8—616no—
126C2×D3×Q8—616no—
127C2×#237—36no—
128C2×D3×D4—36no—
129C2×D3×D4—36no—
130C2×#235—36no—
131C22×C4×D3—36no—
132C22×C4×D3—36no—
133C22×C4×D3—63no—
134C22×Dic6—36no—
135C22×Dic6—63no—
136C3×#124—36no—
137C3×C22⋊Q8—36no—
138C3×#121—36no—
139C3×C4×Q8—32no—
140C3×C4×D4—36no—
141#947C2×D316yescomplemented
142#946C2×D316yescomplemented
143Q8×Dic3C2×D312yescomplemented
144#939—312no—
145#938—36no—
146#936—36no—
147D4×Dic3—36no—
148#930C2×D316yescomplemented
149C4×#67—36no—
150C4×#67C2×D316yescomplemented
151#924—36no—
152#897—36no—
153#896—312no—
154#895—36no—
155#893—36no—
156D3×C4⋊C4—36no—
157D3×C4⋊C4—36no—
158#887—36no—
159#885—312no—
160#885—312no—
161#884—312no—
162#67⋊C4—36no—
163#67⋊C4—36no—
164D3×C22⋊C4—32no—
165D3×C22⋊C4—36no—
166D3×C22⋊C4—312no—
167#878—312no—
168#875—36no—
169C4×D12—36no—
170C42×D3—36no—
171C4×Dic6—36no—
172C23×C32C2411yescharacteristic
173C22×C3⋊D3—22no—
174C22×C3⋊D3—22no—
175C22×C3⋊D3#4114yescomplemented
176C22×C3⋊D3C2411yescharacteristic
177C22×C3⋊D3C2411yescharacteristic
178C22×C3×D3C2416yes—
179C2×D32—26no—
180C2×D32—26no—
181C2×D32—26no—
182C32×Q8—26no—
183C32×Q8C2×D414yescomplemented
184C2×C32×C4—26no—
185C2×C32×C4C2413yes—
186C2×C32×C4C2413yes—
187C2×C3⋊Dic3—26no—
188C2×C3⋊Dic3C2413yes—
189C2×C3⋊Dic3C2413yes—
190C4×C3⋊D3—26no—
191C4×C3⋊D3—26no—
192C4×C3⋊D3—26no—
193C4×C3⋊D3C2×D4112yes—
194#634—26no—
195#634—212no—
196#634C2×D4112yescomplemented
197C3×#67—212no—
198C2×C3×Dic3C2412yes—
199C2×C3×Dic3C2416yes—
200C2×C3×Dic3C2412yes—
201C3×D12—212no—
202C3×C4×D3—212no—
203#626—212no—
204#625—212no—
205#624—22no—
206#624—26no—
207#624—22no—
208D3×Dic3—212no—
209C22×#41—91no—
210C23×Q8—91no—
211#548—32no—
212#548—96no—
213#548—92no—
214#548—96no—
215C2×#124—93no—
216C2×C22⋊Q8—93no—
217C2×#121—93no—
218C2×C4×Q8—91no—
219C2×C4×D4—93no—
220C23×D3—32no—
221C23×D3—36no—
222C23×D3—61no—
223C3×#41—68no—
224C2×C3×Q8—28no—
225C2×C3×Q8—28no—
226C2×C3×Q8—23no—
227C2×C3×Q8—21no—
228C2×C3×Q8C22×D316yes—
229C2×C3×Q8C22×D312yes—
230C2×C3×D4—36no—
231C2×C3×D4—36no—
232C22×C3×C4—23no—
233C22×C3×C4—36no—
234C22×C3×C4C22×D316yes—
235C2×#67—312no—
236C2×#67—36no—
237C2×#67C22×D316yes—
238C22×Dic3—36no—
239C22×Dic3—36no—
240C22×Dic3—63no—
241#239—28no—
242D3×Q8—316no—
243D3×Q8—68no—
244D3×Q8—624no—
245D3×Q8—624no—
246D3×Q8—624no—
247D3×Q8—624no—
248D3×Q8—68no—
249D3×Q8—68no—
250#237—624no—
251D3×D4—624no—
252D3×D4—624no—
253#235—624no—
254C2×D12—36no—
255C2×D12C22×D316yes—
256C2×C4×D3—36no—
257C2×C4×D3—36no—
258C2×C4×D3—36no—
259C2×C4×D3—36no—
260C2×C4×D3—36no—
261C2×C4×D3—32no—
262C2×C4×D3—36no—
263C2×C4×D3—32no—
264C2×C4×D3—63no—
265C2×C4×D3—63no—
266C2×C4×D3—63no—
267C2×C4×D3—63no—
268C2×C4×D3—624no—
269C2×C4×D3—624no—
270C2×C4×D3—624no—
271C2×C4×D3C22×D316yes—
272C2×Dic6—36no—
273C2×Dic6—36no—
274C2×Dic6—312no—
275C2×Dic6—63no—
276C2×Dic6—63no—
277C2×Dic6—66no—
278C2×Dic6—624no—
279C2×Dic6—624no—
280C3×C4⋊C4—36no—
281C3×C4⋊C4—36no—
282C3×C22⋊C4—32no—
283C3×C22⋊C4—312no—
284C3×C22⋊C4—36no—
285C3×C42—36no—
286#217—312no—
287#217—36no—
288#217C22×D312yes—
289(C2×D3)⋊C4—36no—
290(C2×D3)⋊C4—312no—
291(C2×D3)⋊C4—32no—
292(C2×D3)⋊C4—32no—
293(C2×D3)⋊C4C22×D3112yes—
294(C2×D3)⋊C4C22×D316yes—
295C4⋊Dic3—36no—
296C4⋊Dic3C22×D316yes—
297Dic3⋊C4—312no—
298Dic3⋊C4—36no—
299Dic3⋊C4C22×D316yes—
300C4×Dic3—36no—
301C4×Dic3—36no—
302C4×Dic3C22×D316yes—
303C22×C32—21no—
304C22×C32—21no—
305C22×C32C2×#4112yescomplemented
306C22×C32C2511yescharacteristic
307C2×C3⋊D3—21no—
308C2×C3⋊D3—21no—
309C2×C3⋊D3—28no—
310C2×C3⋊D3C22×D412yes—
311C2×C3⋊D3C2×#4112yes—
312C2×C3⋊D3C2×#4112yescomplemented
313C2×C3⋊D32−1+412yes—
314C2×C3×D3—26no—
315C2×C3×D3—26no—
316C2×C3×D3—26no—
317D32—412no—
318C32×C4—23no—
319C32×C4C22×D416yes—
320C3⋊Dic3—23no—
321C3⋊Dic3C22×D416yes—
322C3×Dic3—22no—
323C3×Dic3—26no—
324C3×Dic3—22no—
325C2×#41—32no—
326C2×#41—96no—
327C2×#41—188no—
328C22×Q8—91no—
329C22×Q8—93no—
330C22×Q8—93no—
331C22×Q8—91no—
332C22×Q8—93no—
333C22×Q8—188no—
334C22×Q8D3211yescharacteristic, complemented
335C22×D4—93no—
336C22×D4—93no—
337C23×C4—93no—
338C23×C4—93no—
339#124—36no—
340#124—96no—
341#124—912no—
342C22⋊Q8—36no—
343C22⋊Q8—912no—
344C22⋊Q8—96no—
345#121—36no—
346#121—96no—
347#121—96no—
348#121—96no—
349C4×Q8—32no—
350C4×Q8—96no—
351C4×D4—36no—
352C4×D4—96no—
353C4×D4—96no—
354C4×D4—96no—
355C2×C4⋊C4—93no—
356C2×C4⋊C4—93no—
357C2×C22⋊C4—91no—
358C2×C22⋊C4—93no—
359C2×C22⋊C4—96no—
360C2×C42—93no—
361C23×C3—21no—
362C23×C3—36no—
363C23×C3C23×D312yes—
364C22×D3—32no—
365C22×D3—38no—
366C22×D3—32no—
367C22×D3—64no—
368C22×D3—61no—
369C22×D3—61no—
370C22×D3—612no—
371C22×D3—612no—
372C22×D3—612no—
373C22×D3—64no—
374C22×D3—64no—
375C22×D3—64no—
376C22×D3—64no—
377C22×D3C23×D316yes—
378C3×Q8—212no—
379C3×Q8—212no—
380C3×Q8—24no—
381C3×Q8D3×D418yescomplemented
382C3×D4—612no—
383C3×D4—612no—
384C2×C3×C4—212no—
385C2×C3×C4—212no—
386C2×C3×C4—23no—
387C2×C3×C4—23no—
388C2×C3×C4—32no—
389C2×C3×C4—36no—
390C2×C3×C4—32no—
391C2×C3×C4—612no—
392C2×C3×C4C23×D316yes—
393C2×C3×C4C23×D316yes—
394#67—212no—
395#67—612no—
396#67—624no—
397C2×Dic3—36no—
398C2×Dic3—36no—
399C2×Dic3—63no—
400C2×Dic3—63no—
401C2×Dic3—612no—
402C2×Dic3—612no—
403C2×Dic3—612no—
404C2×Dic3C23×D312yes—
405C2×Dic3C23×D316yes—
406C2×Dic3C23×D312yes—
407D12—212no—
408D12—612no—
409C4×D3—212no—
410C4×D3—324no—
411C4×D3—612no—
412C4×D3—64no—
413C4×D3—64no—
414C4×D3—612no—
415C4×D3—612no—
416C4×D3—612no—
417C4×D3—612no—
418C4×D3—612no—
419C4×D3—612no—
420C4×D3—612no—
421C4×D3—612no—
422Dic6—324no—
423Dic6—612no—
424Dic6—624no—
425Dic6—624no—
426Dic6—612no—
427Dic6—612no—
428C2×C32—22no—
429C2×C32C23×D411yescharacteristic
430C2×C32C22×#4111yescharacteristic
431C2×C32C2×2−1+411yescharacteristic
432C3⋊D3—22no—
433C3⋊D3#54814yescomplemented
434C3×D3—46no—
435C24—93no—
436C24—91no—
437#41—68no—
438#41—1824no—
439C2×Q8—24no—
440C2×Q8—98no—
441C2×Q8—93no—
442C2×Q8—96no—
443C2×Q8—93no—
444C2×Q8—1812no—
445C2×Q8—1812no—
446C2×Q8—1812no—
447C2×Q8—184no—
448C2×Q8C2×D3213yes—
449C2×Q8C2×D3211yescharacteristic
450C2×D4—36no—
451C2×D4—36no—
452C2×D4—96no—
453C2×D4—96no—
454C2×D4—1812no—
455C2×D4—1812no—
456C22×C4—36no—
457C22×C4—91no—
458C22×C4—93no—
459C22×C4—91no—
460C22×C4—96no—
461C22×C4—93no—
462C22×C4—93no—
463C22×C4—93no—
464C22×C4—93no—
465C22×C4—93no—
466C22×C4—1812no—
467C22×C4—1812no—
468C22×C4C2×D3213yes—
469C4⋊C4—36no—
470C4⋊C4—36no—
471C4⋊C4—96no—
472C4⋊C4—96no—
473C22⋊C4—32no—
474C22⋊C4—36no—
475C22⋊C4—312no—
476C22⋊C4—92no—
477C22⋊C4—96no—
478C22⋊C4—912no—
479C42—36no—
480C42—96no—
481C22×C3—22no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—21no—
487C22×C3—66no—
488C22×C3—66no—
489C22×C3—66no—
490C22×C3D3×#4114yescomplemented
491C22×C3C24×D312yes—
492C2×D3—26no—
493C2×D3—26no—
494C2×D3—26no—
495C2×D3—34no—
496C2×D3—34no—
497C2×D3—34no—
498C2×D3—34no—
499C2×D3—62no—
500C2×D3—62no—
501C2×D3—62no—
502C2×D3—62no—
503C2×D3—616no—
504C2×D3—62no—
505C2×D3—616no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—62no—
509C2×D3—1224no—
510C3×C4—26no—
511C3×C4—26no—
512C3×C4—26no—
513C3×C4—62no—
514C3×C4—66no—
515C3×C4—62no—
516C3×C4C2×D3×D4112yes—
517Dic3—22no—
518Dic3—26no—
519Dic3—22no—
520Dic3—312no—
521Dic3—66no—
522Dic3—66no—
523Dic3—66no—
524C32C2×#54811yescharacteristic, complemented, Sylow
525C23—36no—
526C23—91no—
527C23—94no—
528C23—91no—
529C23—182no—
530C23—182no—
531C23—186no—
532C23—186no—
533C23—186no—
534C23C22×D3211yescharacteristic
535Q8—26no—
536Q8—912no—
537Q8—1812no—
538Q8—186no—
539Q8#381114yescomplemented
540D4—612no—
541D4—612no—
542D4—1812no—
543D4—1812no—
544C2×C4—26no—
545C2×C4—32no—
546C2×C4—36no—
547C2×C4—32no—
548C2×C4—612no—
549C2×C4—93no—
550C2×C4—912no—
551C2×C4—93no—
552C2×C4—186no—
553C2×C4—186no—
554C2×C4—182no—
555C2×C4—186no—
556C2×C4—182no—
557C2×C4—1812no—
558C2×C4—186no—
559C2×C4—186no—
560C2×C4C22×D3213yes—
561C2×C4C22×D3213yes—
562C2×C3—24no—
563C2×C3—24no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—126no—
568C2×C3C22×D3×D412yes—
569C2×C3C2×D3×#4112yes—
570C2×C3D3×2−1+412yes—
571D3—38no—
572D3—46no—
573D3—64no—
574D3—64no—
575D3—64no—
576C22—21no—
577C22—21no—
578C22—66no—
579C22—66no—
580C22—66no—
581C22—92no—
582C22—92no—
583C22—92no—
584C22—92no—
585C22—188no—
586C22—181no—
587C22—181no—
588C22—3612no—
589C22#6431912yescomplemented
590C22C23×D3211yescharacteristic
591C4—23no—
592C4—66no—
593C4—62no—
594C4—62no—
595C4—96no—
596C4—183no—
597C4C2×#381116yes—
598C3—21no—
599C3D3×#54812yescomplemented
600C2—22no—
601C2—94no—
602C2—126no—
603C2—182no—
604C2C2×#6431911yescharacteristic
605C2#1059668711yescharacteristic
606C2C22×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32C2×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×Q8×C3⋊D3C2semidirect
2. C2×#64319C2semidirect
3. C3×#5817C2semidirect
4. #10595432C2semidirect
5. #10595429C2semidirect
6. #10595414C2semidirect
7. Q8×#624C2semidirect
8. #10595362C2semidirect
9. #10595081C2semidirect
10. C4×#3811C2semidirect
11. #10594918C2semidirect
13. C22×C32×Q8C22semidirect
17. C2×Q8×C3⋊D3C22semidirect
18. C2×Q8×C3⋊D3C22semidirect
20. C22×#634C22semidirect
21. C2×C3×#239C22semidirect
26. C2×#3795C22semidirect
27. C3×#947C22semidirect
28. C3×#946C22semidirect
29. C3×Q8×Dic3C22semidirect
30. C3×#930C22semidirect
31. C3×C4×#67C22semidirect
32. #63980C22semidirect
34. #67⋊Dic3C22semidirect
37. #63916C22semidirect
38. #63913C22semidirect
39. #63912C22semidirect
40. C4×#626C22semidirect
42. #63896C22semidirect
45. #63881C22semidirect
46. #63860C22semidirect
47. #63857C22semidirect
48. #63844C22semidirect
54. #5817D3semidirect
75. Q8×C3⋊D3D4semidirect
114. C22×C3×Q8C2×D3semidirect
116. C2×#239C2×D3semidirect
141. #947C2×D3semidirect
142. #946C2×D3semidirect
143. Q8×Dic3C2×D3semidirect
148. #930C2×D3semidirect
150. C4×#67C2×D3semidirect
175. C22×C3⋊D3#41semidirect
183. C32×Q8C2×D4semidirect
196. #634C2×D4semidirect
305. C22×C32C2×#41semidirect
312. C2×C3⋊D3C2×#41semidirect
334. C22×Q8D32semidirect
381. C3×Q8D3×D4semidirect
433. C3⋊D3#548semidirect
490. C22×C3D3×#41semidirect
524. C32C2×#548semidirect
539. Q8#3811semidirect
589. C22#64319semidirect
599. C3D3×#548semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×C3⋊D32
C2×#643192
C3×#58172
#105954322
#105954292
#105954142
Q8×#6242
#105953622
#105950812
C4×#38112
#105949182
D3×#5483