Finite Group Databasebeta

← #11870718

Subgroups — #11870718

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
1C3×#5596C211yesmaximal, characteristic
2C2×#63844C211yesmaximal, characteristic, complemented
3#10592739C211yesmaximal, characteristic, complemented
4C3×#5034C211yesmaximal, characteristic, complemented
5#10591439C212yesmaximal, complemented
6#10591401C212yesmaximal, complemented
7#10591181C211yesmaximal, characteristic, complemented
8#10591091C211yesmaximal, characteristic, complemented
9#10591053C211yesmaximal, characteristic, complemented
10#10590487C212yesmaximal, complemented
11#10590479C212yesmaximal, complemented
12#83315—31nomaximal
13#81308—31nomaximal
14C22×#634C2211yescharacteristic
15C2×C3×#237—21no—
16C32×#121C2211yescharacteristic
17C2×#3754C2212yes—
18C3×#940C2211yescharacteristic
19C3×#939—21no—
20C3×D4×Dic3C2211yescharacteristic
21C3×#930C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C3×#893C2211yescharacteristic
25C3×#888C2211yescharacteristic
26C3×#885—21no—
27C3×#67⋊C4—21no—
28C2×#3724—21no—
29C2×Dic32—21no—
30#63844—21no—
31#63844—21no—
32#63844C2212yes—
33#63844C2212yes—
34C2×#3716C2212yes—
35#63657C2211yescharacteristic
36#63637C2212yes—
37C3×#832C2212yes—
38C3×#830C2211yescharacteristic
39C3×#808C2212yes—
40#63574C2212yes—
41Dic3⋊(C3⋊C8)C2212yes—
42#63567C2212yes—
43#63562C2212yes—
44Dic3×C3⋊C8C2212yes—
45C3×#532—31no—
46#5596D311yescharacteristic
47C2×#887—31no—
48C2×C4×Dic6—31no—
49C3×#481—31no—
50#5094—32no—
51#5075—32no—
52#5040—31no—
53#5040—31no—
54#5040—31no—
55#5040—61no—
56#5034—31no—
57#5034D311yescharacteristic, complemented
58C4×#214—32no—
59C4×#214—32no—
60#4968—31no—
61#4925—31no—
62#4854—32no—
63#4852—32no—
64#4762—32no—
65#4758—32no—
66#4738—31no—
67#4718—31no—
68C2×C32×D4—21no—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4C2311yescharacteristic
71C22×C3⋊Dic3—21no—
72C2×#634—21no—
73C2×#634—24no—
74C2×#634C2312yes—
75C2×C3×#67—21no—
76C2×C3×#67—21no—
77C2×C3×#67—21no—
78C22×C3×Dic3—21no—
79C22×C3×Dic3—21no—
80C22×C3×Dic3D411yescharacteristic
81C22×C3×Dic3D411yescharacteristic
82C3×#237—44no—
83C2×C3×D12C2311yescharacteristic
84C2×C3×C4×D3—21no—
85C2×C3×Dic6—21no—
86C32×C4⋊C4C2311yescharacteristic
87C32×C22⋊C4—21no—
88#3754—24no—
89C2×C3⋊(C3⋊C8)C2312yes—
90C3×#217—21no—
91C3×(C2×D3)⋊C4—21no—
92C3×(C2×D3)⋊C4—21no—
93C3×C4⋊Dic3—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4⋊Dic3C2312yes—
96C3×Dic3⋊C4—21no—
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3C2311yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102#3724—22no—
103#3724—22no—
104Dic32—22no—
105Dic32—22no—
106#3716—24no—
107#3103—91noSylow
108C2×C3×#41—61no—
109C2×#237—21no—
110C22×Dic6—31no—
111C22×Dic6—31no—
112C22×Dic6—61no—
113C3×C4⋊Q8—31no—
114C3×#127—31no—
115C3×#124—61no—
116C3×#121—21no—
117C3×#121—31no—
118C3×#121—61no—
119C3×#121C2×D311yescharacteristic
120C3×#121C2×D311yescharacteristic
121C3×C4×D4—31no—
122C3×C4×D4—31no—
123C3×C4×D4—61no—
124C2×C3×C4⋊C4—31no—
125C2×C3×C42—31no—
126#940C2×D311yescharacteristic
127#939—21no—
128D4×Dic3C2×D311yescharacteristic
129C2×#214—32no—
130C2×#214—32no—
131C2×#214—32no—
132C2×#214—62no—
133#930C2×D311yescharacteristic
134C2×C4⋊Dic3C2×D311yescharacteristic
135C2×Dic3⋊C4—61no—
136C2×Dic3⋊C4—61no—
137C2×C4×Dic3—61no—
138C2×C4×Dic3—61no—
139C2×C4×Dic3C2×D311yescharacteristic
140C2×#204—32no—
141#893C2×D311yescharacteristic
142#888C2×D311yescharacteristic
143#887—32no—
144#887—32no—
145#887—61no—
146#887—61no—
147#885—21no—
148#67⋊C4—21no—
149C4×Dic6—32no—
150C4×Dic6—32no—
151C4×Dic6—61no—
152C4×Dic6—61no—
153C3×#106—32no—
154C3×#102—32no—
155C3×C22⋊C8—31no—
156#832—32no—
157#832C2×D312yes—
158#830—31no—
159#830—31no—
160#830—61no—
161#830C2×D311yescharacteristic
162#816—32no—
163Dic3⋊C8—32no—
164C8×Dic3—32no—
165#810—32no—
166#810—32no—
167#810—32no—
168#810—62no—
169#809—32no—
170#808—32no—
171#808—32no—
172#808C2×D312yes—
173C4⋊(C3⋊C8)—32no—
174C4×C3⋊C8—32no—
175C23×C32—21no—
176C23×C32C2×D411yescharacteristic
177C22×C3×D3—21no—
178C32×D4—22no—
179C32×D4—42no—
180C2×C32×C4—22no—
181C2×C32×C4—21no—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—24no—
185C2×C3⋊Dic3—22no—
186#634—24no—
187#634—22no—
188#634#4114yescomplemented
189C3×#67—42no—
190C3×#67—42no—
191C3×#67—42no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—21no—
194C2×C3×Dic3—41no—
195C2×C3×Dic3—42no—
196C2×C3×Dic3—42no—
197C2×C3×Dic3SD1614yescomplemented
198C2×C3×Dic3C2×D411yescharacteristic
199C2×C3×Dic3C2×D411yescharacteristic
200C2×C3×Dic3C2×D411yescharacteristic
201C2×C3×Dic3C2×D411yescharacteristic
202C3×D12—22no—
203C3×C4×D3—42no—
204C3×Dic6—42no—
205C3⋊(C3⋊C8)—22no—
206C3×C3⋊C8—22no—
207#532—31no—
208C2×C4×Q8—91no—
209#481—31no—
210#481—91no—
211#475—92no—
212#460—92no—
213#448—91no—
214#448—91no—
215C4×SD16—92no—
216C4×SD16—92no—
217#431—91no—
218C3×#41—124no—
219C2×C3×Q8—61no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—31no—
224C2×C3×D4—41no—
225C2×C3×D4—61no—
226C2×C3×D4—61no—
227C2×C3×D4—61no—
228C2×C3×D4C22×D311yescharacteristic
229C2×C3×D4C22×D311yescharacteristic
230C22×C3×C4—21no—
231C22×C3×C4—31no—
232C22×C3×C4—31no—
233C22×C3×C4—61no—
234C22×C3×C4—61no—
235C22×C3×C4—61no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C2×#67—21no—
239C2×#67—21no—
240C2×#67—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—61no—
244C22×Dic3—61no—
245C22×Dic3—121no—
246C22×Dic3#6711yescharacteristic
247C22×Dic3#6711yescharacteristic
248#237—44no—
249C2×D12C22×D311yescharacteristic
250C2×C4×D3—21no—
251C2×Dic6—21no—
252C2×Dic6—32no—
253C2×Dic6—32no—
254C2×Dic6—62no—
255C2×Dic6—64no—
256C2×Dic6—64no—
257C2×Dic6—61no—
258C2×Dic6—61no—
259C2×Dic6—124no—
260C2×Dic6—121no—
261C2×C3×C8—32no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—31no—
264C3×C4⋊C4—32no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4—61no—
267C3×C4⋊C4C22×D311yescharacteristic
268C3×C4⋊C4C22×D311yescharacteristic
269C3×C22⋊C4—21no—
270C3×C22⋊C4—21no—
271C3×C22⋊C4—41no—
272C3×C22⋊C4—61no—
273C3×C22⋊C4—61no—
274C3×C22⋊C4—61no—
275C3×C42—31no—
276C3×C42—31no—
277C3×C42—31no—
278C3×C42—31no—
279#217—21no—
280#214—64no—
281#214—64no—
282#214—64no—
283#214—124no—
284(C2×D3)⋊C4—21no—
285(C2×D3)⋊C4—21no—
286C4⋊Dic3—21no—
287C4⋊Dic3C22×D311yescharacteristic
288C4⋊Dic3C22×D312yes—
289Dic3⋊C4—21no—
290Dic3⋊C4—62no—
291Dic3⋊C4—62no—
292Dic3⋊C4—62no—
293Dic3⋊C4—62no—
294C4×Dic3—62no—
295C4×Dic3—62no—
296C4×Dic3—62no—
297C4×Dic3—62no—
298C4×Dic3#6711yescharacteristic
299C4×Dic3#6711yescharacteristic
300C4×Dic3C22×D311yescharacteristic
301C4×Dic3C22×D311yescharacteristic
302C2×C3⋊C8—32no—
303C2×C3⋊C8—32no—
304C2×C3⋊C8—62no—
305C2×C3⋊C8C22×D312yes—
306#204—64no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32—41no—
310C22×C32—41no—
311C22×C32—41no—
312C22×C32C2×SD1612yes—
313C22×C32C22×D411yescharacteristic
314C2×C3×D3—41no—
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C32×C4—21no—
318C32×C4—41no—
319C32×C4C2×#4112yes—
320C3⋊Dic3—24no—
321C3×Dic3—21no—
322C3×Dic3—21no—
323C3×Dic3—41no—
324C3×Dic3—42no—
325C3×Dic3C2×SD1612yes—
326C3×Dic3C2×SD1612yes—
327C2×#41—61no—
328C22×Q8—91no—
329C2×SD16—92no—
330C2×SD16—92no—
331C4⋊Q8—31no—
332#127—31no—
333#124—61no—
334#121—31no—
335#121—61no—
336#121D3211yescharacteristic
337C4×Q8—92no—
338C4×Q8—92no—
339C4×Q8—181no—
340C4×Q8—181no—
341C4×D4—31no—
342C4×D4—31no—
343C4×D4—61no—
344C2×C4⋊C4—31no—
345C2×C4⋊C4—181no—
346C2×C42—31no—
347C2×C42—181no—
348#106—32no—
349#106—92no—
350C4⋊C8—92no—
351#103—92no—
352#103—92no—
353#102—32no—
354#102—92no—
355C22⋊C8—31no—
356C22⋊C8—91no—
357C4×C8—92no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—41no—
362C23×C3—61no—
363C23×C3D3×D411yescharacteristic
364C23×C3C2×#6711yescharacteristic
365C22×D3—21no—
366C3×Q8—122no—
367C3×D4—22no—
368C3×D4—22no—
369C3×D4—42no—
370C3×D4—42no—
371C3×D4—42no—
372C3×D4—62no—
373C3×D4—82no—
374C3×D4—122no—
375C3×D4—122no—
376C3×D4—122no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—34no—
384C2×C3×C4—31no—
385C2×C3×C4—31no—
386C2×C3×C4—31no—
387C2×C3×C4—31no—
388C2×C3×C4—42no—
389C2×C3×C4—41no—
390C2×C3×C4—61no—
391C2×C3×C4—62no—
392C2×C3×C4—122no—
393C2×C3×C4—122no—
394C2×C3×C4—121no—
395C2×C3×C4—122no—
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4C2×#6711yescharacteristic
398C2×C3×C4C23×D311yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400#67—42no—
401#67—42no—
402#67—42no—
403C2×Dic3—22no—
404C2×Dic3—21no—
405C2×Dic3—41no—
406C2×Dic3—42no—
407C2×Dic3—42no—
408C2×Dic3—64no—
409C2×Dic3—64no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—122no—
413C2×Dic3—124no—
414C2×Dic3#21414yescomplemented
415C2×Dic3C2×#6711yescharacteristic
416C2×Dic3C2×#6711yescharacteristic
417C2×Dic3C2×#6711yescharacteristic
418C2×Dic3C2×#6711yescharacteristic
419D12—22no—
420C4×D3—42no—
421Dic6—34no—
422Dic6—34no—
423Dic6—42no—
424Dic6—64no—
425Dic6—64no—
426Dic6—64no—
427Dic6—62no—
428Dic6—62no—
429Dic6—122no—
430Dic6—124no—
431C3×C8—62no—
432C3⋊C8—22no—
433C3⋊C8—62no—
434C3⋊C8—62no—
435C3⋊C8—122no—
436C2×C32—22no—
437C2×C32—81no—
438C2×C32#52511yescharacteristic
439C2×C32C22×SD1611yescharacteristic
440C2×C32#57511yescharacteristic
441C3×D3—81no—
442#41—124no—
443C2×Q8—61no—
444C2×Q8—92no—
445C2×Q8—184no—
446C2×Q8—181no—
447C2×D4—21no—
448C2×D4—31no—
449C2×D4—61no—
450C2×D4—61no—
451C2×D4—61no—
452C2×D4C2×D3211yescharacteristic
453C22×C4—31no—
454C22×C4—31no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4—61no—
458C22×C4—181no—
459C22×C4C2×D3211yescharacteristic
460SD16—184no—
461SD16—184no—
462C2×C8—32no—
463C2×C8—92no—
464C4⋊C4—32no—
465C4⋊C4—31no—
466C4⋊C4—61no—
467C4⋊C4—61no—
468C4⋊C4—182no—
469C4⋊C4—182no—
470C4⋊C4C2×D3211yescharacteristic
471C22⋊C4—21no—
472C22⋊C4—61no—
473C22⋊C4—61no—
474C22⋊C4—61no—
475C42—31no—
476C42—31no—
477C42—31no—
478C42—31no—
479C42—182no—
480C42—182no—
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—41no—
490C22×C3—41no—
491C22×C3—41no—
492C22×C3—41no—
493C22×C3—41no—
494C22×C3—41no—
495C22×C3—81no—
496C22×C3—81no—
497C22×C3—81no—
498C22×C3—121no—
499C22×C3—121no—
500C22×C3—121no—
501C22×C3D3×SD1612yes—
502C22×C3C2×#21412yes—
503C22×C3C2×D3×D411yescharacteristic
504C22×C3C22×#6711yescharacteristic
505C2×D3—41no—
506C2×D3—41no—
507C2×D3—41no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—22no—
511C3×C4—32no—
512C3×C4—32no—
513C3×C4—41no—
514C3×C4—41no—
515C3×C4—41no—
516C3×C4—61no—
517C3×C4—61no—
518C3×C4—81no—
519C3×C4—121no—
520C3×C4—122no—
521C3×C4D3×#4112yes—
522C3×C4D3×#4112yes—
523Dic3—21no—
524Dic3—21no—
525Dic3—42no—
526Dic3—41no—
527Dic3—64no—
528Dic3—64no—
529Dic3—124no—
530Dic3C2×#21412yes—
531Dic3C2×#21412yes—
532C32#310311yescharacteristic, complemented, Sylow
533C23—21no—
534C23—61no—
535C23D3×#6711yescharacteristic
536Q8—94no—
537Q8—122no—
538Q8—184no—
539Q8—182no—
540D4—22no—
541D4—42no—
542D4—62no—
543D4—122no—
544D4—122no—
545D4—122no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—31no—
549C2×C4—31no—
550C2×C4—34no—
551C2×C4—31no—
552C2×C4—31no—
553C2×C4—62no—
554C2×C4—61no—
555C2×C4—122no—
556C2×C4—122no—
557C2×C4—121no—
558C2×C4—122no—
559C2×C4—184no—
560C2×C4—182no—
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—81no—
572C2×C3—81no—
573C2×C3—161no—
574C2×C3—241no—
575C2×C3#565611yescharacteristic
576C2×C3C2×D3×SD1611yescharacteristic
577C2×C3#577311yescharacteristic
578C2×C3C22×#21411yescharacteristic
579C2×C3#582211yescharacteristic
580C2×C3#582811yescharacteristic
581D3—81no—
582C22—21no—
583C22—21no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—121no—
588C22—121no—
589C22—121no—
590C22D3×#21412yes—
591C22C2×D3×#6711yescharacteristic
592C4—21no—
593C4—32no—
594C4—32no—
595C4—41no—
596C4—61no—
597C4—61no—
598C4—121no—
599C4—122no—
600C4—184no—
601C4#6431212yes—
602C3—21no—
603C3#8130811yescharacteristic, complemented
604C3#8331511yescharacteristic, complemented
605C2—22no—
606C2—81no—
607C2—241no—
608C2C2×D3×#21411yescharacteristic
609C2#1059515911yescharacteristic
610C2#1059546911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×#5596C2
hypercenter#121D32
hypocenterC32#3103
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. C2×#63844C2semidirect
3. #10592739C2semidirect
4. C3×#5034C2semidirect
5. #10591439C2semidirect
6. #10591401C2semidirect
7. #10591181C2semidirect
8. #10591091C2semidirect
9. #10591053C2semidirect
10. #10590487C2semidirect
11. #10590479C2semidirect
57. #5034D3semidirect
188. #634#41semidirect
197. C2×C3×Dic3SD16semidirect
414. C2×Dic3#214semidirect
532. C32#3103semidirect
603. C3#81308semidirect
604. C3#83315semidirect

Maximal subgroups

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

subgroupindex
C3×#55962
C2×#638442
#105927392
C3×#50342
#105914392
#105914012
#105911812
#105910912
#105910532
#105904872
#105904792
#833153
#813083