Finite Group Databasebeta

← #11870727

Subgroups — #11870727

Order 1152.

935 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×Q8×Dic3C211yesmaximal, characteristic, complemented
2#10594910C211yesmaximal, characteristic
3#10592926C211yesmaximal, characteristic, complemented
4C3×#5227C211yesmaximal, characteristic, complemented
5#10591617C212yesmaximal, complemented
6Dic3×#215C212yesmaximal, complemented
7#10591544C212yesmaximal, complemented
8#10591536C212yesmaximal, complemented
9#10591125C211yesmaximal, characteristic, complemented
10#10591091C211yesmaximal, characteristic, complemented
11#10591053C211yesmaximal, characteristic, complemented
12#82442—31nomaximal
13#80028—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C2×#3804—21no—
16C2×#3755C2212yes—
17#64139C2211yescharacteristic
18C3×Q8×Dic3—21no—
19C3×Q8×Dic3—21no—
20C3×Q8×Dic3C2212yes—
21C3×Q8×Dic3C2212yes—
22C2×C3×#215C2212yes—
23C3×#930C2211yescharacteristic
24C2×C3×C4⋊Dic3—21no—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×C4×Dic3—21no—
27C2×C3×C4×Dic3C2211yescharacteristic
28#63978—21no—
29#63918C2211yescharacteristic
30#63911C2211yescharacteristic
31#63894C2211yescharacteristic
32Dic3×D12C2211yescharacteristic
33#63880—21no—
34#63852—21no—
35#63662C2212yes—
36#63657C2211yescharacteristic
37C3×#835C2212yes—
38C3×#830C2211yescharacteristic
39#63574C2212yes—
40#63573C2212yes—
41Dic3⋊(C3⋊C8)C2212yes—
42#63564C2212yes—
43#63562C2212yes—
44Dic3×C3⋊C8C2212yes—
45C2×C3×C4×Q8—31no—
46C2×Q8×Dic3D311yescharacteristic, complemented
47#5596—31no—
48#5477—31no—
49C3×#448—31no—
50#5227—31no—
51#5227—31no—
52#5227—61no—
53#5227D311yescharacteristic, complemented
54#5163—32no—
55Dic3×SD16—32no—
56#5034—31no—
57#5027—32no—
58C4×#215—32no—
59C4×#215—32no—
60#5020—32no—
61#4968—31no—
62#4968—31no—
63#4925—31no—
64#4791—32no—
65#4788—32no—
66#4735—31no—
67#4718—31no—
68C2×C32×Q8—24no—
69C2×C32×Q8—21no—
70C2×C32×Q8C2312yes—
71C22×C32×C4—21no—
72C22×C32×C4C2311yescharacteristic
73C2×#638—21no—
74C2×C4⋊(C3⋊D3)C2311yescharacteristic
75C2×C3×#67—21no—
76C22×C3×Dic3—21no—
77C22×C3×Dic3D411yescharacteristic
78C22×C3×Dic3D411yescharacteristic
79C2×C3×D12C2311yescharacteristic
80C2×#627—21no—
81C2×#626—21no—
82C2×#626—21no—
83C2×#624—21no—
84#3804—44no—
85C2×D3×Dic3—21no—
86#3755—24no—
87#3752—21no—
88C4⋊(C3⋊Dic3)C2311yescharacteristic
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#215—24no—
91C3×(C2×D3)⋊C4—21no—
92C3×C4⋊Dic3—21no—
93C3×C4⋊Dic3—22no—
94C3×C4⋊Dic3—22no—
95C3×C4⋊Dic3C2312yes—
96C3×C4⋊Dic3C2311yescharacteristic
97C3×C4×Dic3—22no—
98C3×C4×Dic3—22no—
99C3×C4×Dic3D411yescharacteristic
100C3×C4×Dic3D411yescharacteristic
101C3×C4×Dic3C2311yescharacteristic
102C3×C4×Dic3C2311yescharacteristic
103C2×C3×C3⋊C8C2312yes—
104Dic3⋊Dic3—21no—
105#3722—21no—
106(C2×D3)⋊Dic3—21no—
107#3103—91noSylow
108C22×C3×Q8—21no—
109C22×C3×Q8C2×D311yescharacteristic
110C22×C3×Q8C2×D311yescharacteristic
111C2×#237—61no—
112C2×#235—61no—
113C2×C3×SD16—32no—
114C3×#121—31no—
115C3×C4×Q8—32no—
116C3×C4×Q8—32no—
117C3×C4×Q8—61no—
118C3×C4×Q8—61no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C4⋊C4—61no—
121C2×C3×C42—31no—
122C2×C3×C42—61no—
123Q8×Dic3—21no—
124Q8×Dic3—21no—
125Q8×Dic3C2×D312yes—
126Q8×Dic3C2×D312yes—
127C2×#215—32no—
128C2×#215—32no—
129C2×#215—62no—
130C2×#215C2×D312yes—
131#940—31no—
132#939—61no—
133D4×Dic3—31no—
134#930—31no—
135#930—31no—
136#930—61no—
137#930—61no—
138#930C2×D311yescharacteristic
139C2×C4⋊Dic3—21no—
140C2×C4⋊Dic3C2×D311yescharacteristic
141C2×C4×Dic3—21no—
142C2×C4×Dic3C2×D311yescharacteristic
143#893—31no—
144#888—31no—
145#885—61no—
146#67⋊C4—61no—
147#875—61no—
148#874—31no—
149C4×D12—31no—
150C4×D12—31no—
151C4×D12—61no—
152#869—31no—
153C3×#103—32no—
154C3×C22⋊C8—31no—
155#835—32no—
156#835—32no—
157#835—62no—
158#835C2×D312yes—
159#832—32no—
160#830—31no—
161#830—31no—
162#830—61no—
163#830C2×D311yescharacteristic
164#821—32no—
165#817—32no—
166Dic3⋊C8—32no—
167C8×Dic3—32no—
168#809—32no—
169#809—32no—
170#808—32no—
171#808—32no—
172#808—32no—
173C4⋊(C3⋊C8)—32no—
174C4×C3⋊C8—32no—
175C23×C32C2×D411yescharacteristic
176C22×C3⋊D3—21no—
177C22×C3×D3—21no—
178C32×Q8—24no—
179C32×Q8—22no—
180C32×Q8#4114yescomplemented
181C2×C32×C4—24no—
182C2×C32×C4—22no—
183C2×C32×C4—22no—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2411yescharacteristic
186#638—42no—
187C2×C3⋊Dic3—21no—
188C4⋊(C3⋊D3)—22no—
189C3×#67—42no—
190C2×C3×Dic3—21no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—41no—
193C2×C3×Dic3—42no—
194C2×C3×Dic3SD1614yescomplemented
195C2×C3×Dic3C2×D411yescharacteristic
196C2×C3×Dic3C2×D411yescharacteristic
197C2×C3×Dic3C2×D411yescharacteristic
198C2×C3×Dic3C2×D411yescharacteristic
199C3×D12—22no—
200#627—42no—
201#626—42no—
202#626—42no—
203#624—42no—
204D3×Dic3—42no—
205C3⋊(C3⋊C8)—22no—
206C3×C3⋊C8—22no—
207#532—91no—
208C2×C4×Q8—31no—
209#481—91no—
210#481—91no—
211#475—92no—
212#460—92no—
213#448—31no—
214#448—91no—
215C4×SD16—92no—
216C4×SD16—92no—
217#431—91no—
218C2×C3×Q8—24no—
219C2×C3×Q8—24no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—22no—
223C2×C3×Q8—41no—
224C2×C3×Q8—44no—
225C2×C3×Q8C22×D312yes—
226C2×C3×Q8C22×D312yes—
227C2×C3×D4—31no—
228C2×C3×D4—61no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—31no—
233C22×C3×C4—31no—
234C22×C3×C4—41no—
235C22×C3×C4—61no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C2×#67—21no—
239C2×#67—61no—
240C2×#67—61no—
241C2×#67—61no—
242C2×#67—61no—
243C2×#67—121no—
244C22×Dic3—21no—
245C22×Dic3—61no—
246C22×Dic3#6711yescharacteristic
247C22×Dic3#6711yescharacteristic
248#237—124no—
249#235—124no—
250C2×D12—31no—
251C2×D12—31no—
252C2×D12—61no—
253C2×D12—61no—
254C2×D12—61no—
255C2×D12C22×D311yescharacteristic
256C2×C4×D3—61no—
257C2×C4×D3—61no—
258C2×C4×D3—61no—
259C2×Dic6—61no—
260C2×Dic6—61no—
261C3×SD16—64no—
262C2×C3×C8—32no—
263C3×C4⋊C4—32no—
264C3×C4⋊C4—31no—
265C3×C4⋊C4—62no—
266C3×C4⋊C4—62no—
267C3×C4⋊C4—61no—
268C3×C22⋊C4—61no—
269C3×C42—31no—
270C3×C42—31no—
271C3×C42—31no—
272C3×C42—31no—
273C3×C42—62no—
274C3×C42—62no—
275#217—61no—
276#215—24no—
277#215—64no—
278#215—64no—
279#215—124no—
280(C2×D3)⋊C4—21no—
281(C2×D3)⋊C4—61no—
282(C2×D3)⋊C4—61no—
283(C2×D3)⋊C4—61no—
284(C2×D3)⋊C4—61no—
285(C2×D3)⋊C4—61no—
286(C2×D3)⋊C4—121no—
287C4⋊Dic3—21no—
288C4⋊Dic3—22no—
289C4⋊Dic3—22no—
290C4⋊Dic3—31no—
291C4⋊Dic3—31no—
292C4⋊Dic3—61no—
293C4⋊Dic3—61no—
294C4⋊Dic3C22×D311yescharacteristic
295C4⋊Dic3C22×D312yes—
296Dic3⋊C4—61no—
297C4×Dic3—22no—
298C4×Dic3—22no—
299C4×Dic3#6711yescharacteristic
300C4×Dic3#6711yescharacteristic
301C4×Dic3C22×D311yescharacteristic
302C4×Dic3C22×D311yescharacteristic
303C2×C3⋊C8—32no—
304C2×C3⋊C8—32no—
305C2×C3⋊C8—62no—
306C2×C3⋊C8C22×D312yes—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32C2×SD1612yes—
310C22×C32C22×D411yescharacteristic
311C2×C3⋊D3—41no—
312C2×C3⋊D3—41no—
313C2×C3⋊D3—41no—
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C32×C4—24no—
318C32×C4—21no—
319C32×C4C2×#4112yes—
320C3⋊Dic3—41no—
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—41no—
324C3×Dic3—42no—
325C3×Dic3C2×SD1612yes—
326C3×Dic3C2×SD1612yes—
327C2×#41—181no—
328C22×Q8D3211yescharacteristic
329C2×SD16—32no—
330C2×SD16—92no—
331C4⋊Q8—91no—
332#127—91no—
333#124—181no—
334#121—31no—
335#121—91no—
336#121—181no—
337C4×Q8—32no—
338C4×Q8—32no—
339C4×Q8—61no—
340C4×Q8—61no—
341C4×D4—91no—
342C4×D4—91no—
343C4×D4—181no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—61no—
346C2×C42—31no—
347C2×C42—61no—
348#106—92no—
349#106—92no—
350C4⋊C8—92no—
351#103—32no—
352#103—92no—
353#102—92no—
354#102—92no—
355C22⋊C8—31no—
356C22⋊C8—91no—
357C4×C8—92no—
358C23×C3—21no—
359C23×C3—61no—
360C23×C3D3×D411yescharacteristic
361C23×C3C2×#6711yescharacteristic
362C22×D3—21no—
363C22×D3—61no—
364C22×D3—61no—
365C22×D3—121no—
366C3×Q8—24no—
367C3×Q8—24no—
368C3×Q8—22no—
369C3×Q8—22no—
370C3×Q8—24no—
371C3×Q8—42no—
372C3×Q8—44no—
373C3×Q8#23514yescomplemented
374C3×Q8#23714yescomplemented
375C3×D4—62no—
376C3×D4—122no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—34no—
386C2×C3×C4—31no—
387C2×C3×C4—31no—
388C2×C3×C4—31no—
389C2×C3×C4—31no—
390C2×C3×C4—42no—
391C2×C3×C4—42no—
392C2×C3×C4—44no—
393C2×C3×C4—62no—
394C2×C3×C4—61no—
395C2×C3×C4—121no—
396C2×C3×C4—122no—
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4C2×#6711yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401#67—42no—
402#67—122no—
403#67—122no—
404#67—122no—
405#67—122no—
406#67—242no—
407C2×Dic3—21no—
408C2×Dic3—22no—
409C2×Dic3—41no—
410C2×Dic3—42no—
411C2×Dic3—61no—
412C2×Dic3—61no—
413C2×Dic3—121no—
414C2×Dic3—122no—
415C2×Dic3#21514yescomplemented
416C2×Dic3C2×#6711yescharacteristic
417C2×Dic3C2×#6711yescharacteristic
418C2×Dic3C2×#6711yescharacteristic
419C2×Dic3C2×#6711yescharacteristic
420D12—22no—
421D12—62no—
422D12—62no—
423D12—122no—
424D12—122no—
425D12—122no—
426C4×D3—122no—
427C4×D3—122no—
428C4×D3—122no—
429Dic6—122no—
430Dic6—122no—
431C3×C8—62no—
432C3⋊C8—22no—
433C3⋊C8—62no—
434C3⋊C8—62no—
435C3⋊C8—122no—
436C2×C32—22no—
437C2×C32#52511yescharacteristic
438C2×C32C22×SD1611yescharacteristic
439C2×C32#57511yescharacteristic
440C3⋊D3—81no—
441C3×D3—81no—
442#41—364no—
443C2×Q8—24no—
444C2×Q8—21no—
445C2×Q8—181no—
446C2×Q8C2×D3212yes—
447C2×D4—31no—
448C2×D4—61no—
449C2×D4—91no—
450C2×D4—181no—
451C2×D4—181no—
452C2×D4—181no—
453C22×C4—21no—
454C22×C4—31no—
455C22×C4—31no—
456C22×C4—61no—
457C22×C4—181no—
458C22×C4—181no—
459C22×C4C2×D3211yescharacteristic
460SD16—64no—
461SD16—184no—
462C2×C8—32no—
463C2×C8—92no—
464C4⋊C4—32no—
465C4⋊C4—31no—
466C4⋊C4—62no—
467C4⋊C4—62no—
468C4⋊C4—61no—
469C4⋊C4—91no—
470C4⋊C4—181no—
471C22⋊C4—61no—
472C22⋊C4—181no—
473C22⋊C4—181no—
474C22⋊C4—181no—
475C42—31no—
476C42—31no—
477C42—31no—
478C42—31no—
479C42—62no—
480C42—62no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—22no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—121no—
490C22×C3—121no—
491C22×C3—121no—
492C22×C3D3×SD1612yes—
493C22×C3C2×#21512yes—
494C22×C3C2×D3×D411yescharacteristic
495C22×C3C22×#6711yescharacteristic
496C2×D3—41no—
497C2×D3—41no—
498C2×D3—41no—
499C2×D3—121no—
500C2×D3—121no—
501C2×D3—121no—
502C2×D3—121no—
503C2×D3—121no—
504C2×D3—121no—
505C2×D3—241no—
506C2×D3—241no—
507C2×D3—241no—
508C3×C4—24no—
509C3×C4—21no—
510C3×C4—24no—
511C3×C4—21no—
512C3×C4—22no—
513C3×C4—32no—
514C3×C4—32no—
515C3×C4—41no—
516C3×C4—44no—
517C3×C4—61no—
518C3×C4—61no—
519C3×C4—122no—
520C3×C4—121no—
521C3×C4C2×#23512yes—
522C3×C4C2×#23712yes—
523Dic3—21no—
524Dic3—21no—
525Dic3—41no—
526Dic3—42no—
527Dic3—121no—
528Dic3—121no—
529Dic3—241no—
530Dic3C2×#21512yes—
531Dic3C2×#21512yes—
532C32#310311yescharacteristic, complemented, Sylow
533C23—61no—
534C23—181no—
535C23D3×#6711yescharacteristic
536Q8—24no—
537Q8—22no—
538Q8—362no—
539Q8#380414yescomplemented
540D4—62no—
541D4—122no—
542D4—182no—
543D4—362no—
544D4—362no—
545D4—362no—
546C2×C4—24no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—31no—
550C2×C4—31no—
551C2×C4—34no—
552C2×C4—31no—
553C2×C4—31no—
554C2×C4—62no—
555C2×C4—61no—
556C2×C4—121no—
557C2×C4—122no—
558C2×C4—181no—
559C2×C4—362no—
560C2×C4—362no—
561C2×C4D3×#6711yescharacteristic
562C2×C4C22×D3211yescharacteristic
563C8—62no—
564C8—182no—
565C2×C3—22no—
566C2×C3—22no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—42no—
571C2×C3—241no—
572C2×C3#558611yescharacteristic
573C2×C3C2×D3×SD1611yescharacteristic
574C2×C3#577711yescharacteristic
575C2×C3#579111yescharacteristic
576C2×C3C22×#21511yescharacteristic
577C2×C3#582211yescharacteristic
578D3—81no—
579D3—241no—
580D3—241no—
581D3—481no—
582C22—21no—
583C22—21no—
584C22—121no—
585C22—121no—
586C22—121no—
587C22—361no—
588C22—361no—
589C22—361no—
590C22D3×#21512yes—
591C22C2×D3×#6711yescharacteristic
592C4—24no—
593C4—21no—
594C4—32no—
595C4—32no—
596C4—61no—
597C4—61no—
598C4—121no—
599C4—122no—
600C4—361no—
601C4C2×#380412yes—
602C3—21no—
603C3#8002811yescharacteristic, complemented
604C3#8244211yescharacteristic, complemented
605C2—22no—
606C2—241no—
607C2—721no—
608C2C2×D3×#21511yescharacteristic
609C2#1059531711yescharacteristic
610C2#1059549811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radical#10594910C2
hypercenterC22×Q8D32
hypocenterC32#3103
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×Q8×Dic3C2semidirect
3. #10592926C2semidirect
4. C3×#5227C2semidirect
5. #10591617C2semidirect
6. Dic3×#215C2semidirect
7. #10591544C2semidirect
8. #10591536C2semidirect
9. #10591125C2semidirect
10. #10591091C2semidirect
11. #10591053C2semidirect
46. C2×Q8×Dic3D3semidirect
53. #5227D3semidirect
180. C32×Q8#41semidirect
194. C2×C3×Dic3SD16semidirect
373. C3×Q8#235semidirect
374. C3×Q8#237semidirect
415. C2×Dic3#215semidirect
532. C32#3103semidirect
539. Q8#3804semidirect
603. C3#80028semidirect
604. C3#82442semidirect

Maximal subgroups

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

subgroupindex
C2×C3×Q8×Dic32
#105949102
#105929262
C3×#52272
#105916172
Dic3×#2152
#105915442
#105915362
#105911252
#105910912
#105910532
#824423
#800283