Finite Group Databasebeta

← #11904337

Subgroups — #11904337

Order 1152.

3969 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1004C211yesmaximal, characteristic, complemented
2C22×C3×D3×D4C211yesmaximal, characteristic, complemented
3#10596269C211yesmaximal, characteristic, complemented
4#10595518C214yesmaximal, complemented
5C2×#63976C214yesmaximal, complemented
6#10595244C218yesmaximal, complemented
7D4×#625C218yesmaximal, complemented
8#10595040C212yesmaximal, complemented
9#10595022C212yesmaximal, complemented
10#87284—31nomaximal
11#87239—31nomaximal
12C24×C3×D3C2212yescomplemented
13C22×C32×D4C2211yescharacteristic
14C22×C3×#67C2212yescomplemented
15C22×C3×#67C2214yescomplemented
16C3×#1004—28no—
17C2×C3×#237C2214yescomplemented
18C2×C3×D3×D4—28no—
19C2×C3×D3×D4C2218yescomplemented
20C2×C3×D3×D4C2214yescomplemented
21C2×C3×#235C2212yescomplemented
22C22×C3×D12C2211yescharacteristic, complemented
23C22×C3×C4×D3C2211yescharacteristic, complemented
24C22×#625C2218yescomplemented
25C2×#3757C2214yescomplemented
26D4×C3⋊Dic3C2218yescomplemented
27#64135C2212yescomplemented
28#63980C22116yescomplemented
29#63976C2214yescomplemented
30#63976C22116yescomplemented
31#63976C2218yescomplemented
32#63976C2218yescomplemented
33#63961C2214yescomplemented
34#63961C2218yescomplemented
35C2×(C2×D3)⋊Dic3C2218yescomplemented
36#63914C2214yescomplemented
37#63908C2214yescomplemented
38#63908C2218yescomplemented
39C4×#625C2218yescomplemented
40#63863C2214yescomplemented
41#63856C2214yescomplemented
42C2×C3×H(5,𝔽2)—31no—
43C23×C3×D4—31no—
44C2×#1004D311yescharacteristic, complemented
45C22×D3×D4D311yescharacteristic, complemented
46C2×#953—34no—
47#5830—32no—
48#5829—38no—
49#5828—32no—
50#5806—38no—
51#5805—32no—
52#5804—34no—
53#5804—34no—
54D4×#67—38no—
55D4×#67—38no—
56C2×#937—34no—
57#5798—31no—
58#5798—31no—
59#5798—61no—
60#5791—32no—
61C24×C32C2312yes—
62C23×C3×D3—28no—
63C23×C3×D3—48no—
64C23×C3×D3C2311yescharacteristic
65C23×C3×D3C2318yes—
66C23×C3×D3C2312yes—
67C23×C3×D3C2314yescomplemented
68C2×C32×D4D418yescomplemented
69C2×C32×D4C2314yes—
70C22×C32×C4C2311yescharacteristic
71C22×C3⋊Dic3C2318yescomplemented
72C2×C3×#67—28no—
73C2×C3×#67—216no—
74C2×C3×#67C2314yes—
75C2×C3×#67C2318yes—
76C2×C3×#67C2318yescomplemented
77C22×C3×Dic3C2311yescharacteristic
78C22×C3×Dic3C2314yescomplemented
79C3×#237—216no—
80C3×D3×D4—232no—
81C3×D3×D4—216no—
82C3×#235—28no—
83C2×C3×D12—24no—
84C2×C3×D12C2314yes—
85C2×C3×D12C2312yescomplemented
86C2×C3×C4×D3—24no—
87C2×C3×C4×D3C2314yes—
88C2×C3×C4×D3C2314yescomplemented
89C2×C3×Dic6C2312yescomplemented
90C2×#625—416no—
91C2×#625C2318yes—
92C2×#625C23116yescomplemented
93#3757C2314yes—
94#3757C2318yescomplemented
95C4⋊(C3⋊Dic3)C2314yescomplemented
96C4×C3⋊Dic3C2314yescomplemented
97#3724C2318yescomplemented
98(C2×D3)⋊Dic3C2318yes—
99(C2×D3)⋊Dic3C23116yescomplemented
100(C2×D3)⋊Dic3C2318yescomplemented
101#3484—91noSylow
102C25×C3—32no—
103C24×D3C2×D312yescomplemented
104C3×H(5,𝔽2)—68no—
105C2×C3×#41—34no—
106C2×C3×#41—32no—
107C22×C3×D4—21no—
108C22×C3×D4—32no—
109C22×C3×D4—34no—
110C22×C3×D4—38no—
111C22×C3×D4—34no—
112C22×C3×D4—31no—
113C22×C3×D4—68no—
114C22×C3×D4C2×D311yescharacteristic
115C22×C3×D4C2×D311yescharacteristic
116C23×C3×C4—31no—
117C22×#67—38no—
118C22×#67—38no—
119C22×#67C2×D312yescomplemented
120C22×#67C2×D314yescomplemented
121#1004—28no—
122C2×#237C2×D314yescomplemented
123C2×D3×D4—28no—
124C2×D3×D4C2×D318yescomplemented
125C2×D3×D4C2×D314yescomplemented
126C2×#235C2×D312yescomplemented
127C22×D12C2×D311yescharacteristic, complemented
128C22×C4×D3C2×D311yescharacteristic, complemented
129#953—34no—
130#953—38no—
131#953—38no—
132#953—316no—
133C2×#217—34no—
134C2×#217—34no—
135C2×#217—38no—
136C2×#217—64no—
137#947—34no—
138#946—34no—
139#940—34no—
140#940—34no—
141#939—316no—
142#939—316no—
143#938—34no—
144#938—38no—
145#937—34no—
146#937—316no—
147#937—38no—
148#937—38no—
149#936—34no—
150#935—34no—
151#935—38no—
152D4×Dic3—38no—
153D4×Dic3—38no—
154D4×Dic3—68no—
155#930—38no—
156#930—34no—
157#929—34no—
158#929—38no—
159C4×#67—38no—
160C4×#67—38no—
161C2×(C2×D3)⋊C4—38no—
162#926—32no—
163#926—32no—
164#926—62no—
165#924—34no—
166C23×C32—44no—
167C23×C32C2×D418yescomplemented
168C23×C32C2411yescharacteristic
169C23×C32C2414yes—
170C22×C3×D3—22no—
171C22×C3×D3—24no—
172C22×C3×D3—24no—
173C22×C3×D3—216no—
174C22×C3×D3—28no—
175C22×C3×D3—216no—
176C22×C3×D3—48no—
177C22×C3×D3—44no—
178C22×C3×D3—48no—
179C22×C3×D3—432no—
180C22×C3×D3C2414yes—
181C22×C3×D3C2414yes—
182C22×C3×D3C2412yes—
183C32×D4C2×D4116yescomplemented
184C2×C32×C4C2×D414yescomplemented
185C2×C32×C4C2412yes—
186C2×C3⋊Dic3—48no—
187C2×C3⋊Dic3C2418yes—
188C3×#67—28no—
189C3×#67—216no—
190C3×#67—216no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—28no—
193C2×C3×Dic3C2414yes—
194C2×C3×Dic3C2412yes—
195C3×D12—28no—
196C3×D12—24no—
197C3×C4×D3—28no—
198C3×C4×D3—28no—
199C3×Dic6—24no—
200#625—216no—
201#625—416no—
202C2×H(5,𝔽2)—31no—
203C23×D4—31no—
204#546—98no—
205D42—98no—
206#535—92no—
207#534—94no—
208#525—92no—
209C2×#120—94no—
210#518—91no—
211C24×C3—22no—
212C24×C3—31no—
213C24×C3—38no—
214C24×C3—32no—
215C24×C3—34no—
216C24×C3—68no—
217C24×C3—128no—
218C24×C3C22×D312yes—
219C24×C3C22×D312yes—
220C23×D3—28no—
221C23×D3—48no—
222C23×D3C22×D311yescharacteristic
223C23×D3C22×D318yes—
224C23×D3C22×D312yes—
225C23×D3C22×D314yescomplemented
226C3×#41—616no—
227C3×#41—68no—
228C2×C3×Q8—32no—
229C2×C3×D4—28no—
230C2×C3×D4—24no—
231C2×C3×D4—34no—
232C2×C3×D4—38no—
233C2×C3×D4—38no—
234C2×C3×D4—34no—
235C2×C3×D4—32no—
236C2×C3×D4—68no—
237C2×C3×D4—616no—
238C2×C3×D4—632no—
239C2×C3×D4—616no—
240C2×C3×D4—64no—
241C2×C3×D4#6718yescomplemented
242C2×C3×D4#6718yescomplemented
243C2×C3×D4C22×D314yes—
244C2×C3×D4C22×D314yes—
245C22×C3×C4—21no—
246C22×C3×C4—34no—
247C22×C3×C4—31no—
248C22×C3×C4—34no—
249C22×C3×C4—34no—
250C22×C3×C4—64no—
251C22×C3×C4C22×D311yescharacteristic
252C22×C3×C4C22×D311yescharacteristic
253C2×#67—28no—
254C2×#67—216no—
255C2×#67—38no—
256C2×#67—38no—
257C2×#67—316no—
258C2×#67—316no—
259C2×#67—1216no—
260C2×#67—1216no—
261C2×#67C22×D318yes—
262C2×#67C22×D314yes—
263C2×#67C22×D318yescomplemented
264C22×Dic3—38no—
265C22×Dic3—38no—
266C22×Dic3—68no—
267C22×Dic3C22×D311yescharacteristic
268C22×Dic3C22×D314yescomplemented
269#237—216no—
270D3×D4—232no—
271D3×D4—216no—
272#235—28no—
273C2×D12—24no—
274C2×D12C22×D314yes—
275C2×D12C22×D312yescomplemented
276C2×C4×D3—24no—
277C2×C4×D3C22×D314yes—
278C2×C4×D3C22×D314yescomplemented
279C2×Dic6C22×D312yescomplemented
280#217—34no—
281#217—34no—
282#217—38no—
283#217—38no—
284#217—38no—
285#217—38no—
286#217—316no—
287#217—64no—
288#217—68no—
289(C2×D3)⋊C4—38no—
290(C2×D3)⋊C4—316no—
291(C2×D3)⋊C4—38no—
292C4⋊Dic3—34no—
293C4⋊Dic3—34no—
294C4⋊Dic3—64no—
295Dic3⋊C4—38no—
296Dic3⋊C4—38no—
297C4×Dic3—34no—
298C4×Dic3—34no—
299C4×Dic3—64no—
300C22×C32—28no—
301C22×C32—22no—
302C22×C32—48no—
303C22×C32C22×D412yes—
304C22×C32C22×D418yes—
305C22×C32C2511yescharacteristic
306C2×C3×D3—28no—
307C2×C3×D3—22no—
308C2×C3×D3—22no—
309C2×C3×D3—24no—
310C2×C3×D3—24no—
311C2×C3×D3—28no—
312C2×C3×D3—28no—
313C2×C3×D3—432no—
314C2×C3×D3—48no—
315C2×C3×D3—88no—
316C2×C3×D3H(5,𝔽2)14yescomplemented
317C32×C4C22×D414yes—
318C3⋊Dic3—28no—
319C3×Dic3—24no—
320C3×Dic3—22no—
321C25—32no—
322H(5,𝔽2)—68no—
323C2×#41—34no—
324C2×#41—32no—
325C22×D4—34no—
326C22×D4—32no—
327C22×D4—34no—
328C22×D4—38no—
329C22×D4—31no—
330C22×D4—68no—
331C22×D4—98no—
332C22×D4D3211yescharacteristic
333C23×C4—31no—
334#127—94no—
335#124—94no—
336#123—94no—
337#123—98no—
338C22⋊Q8—94no—
339#121—94no—
340#121—98no—
341#121—916no—
342#120—94no—
343#120—98no—
344#120—916no—
345#120—98no—
346C4×D4—98no—
347C4×D4—98no—
348#117—92no—
349C2×C22⋊C4—98no—
350C2×C22⋊C4—94no—
351C23×C3—21no—
352C23×C3—24no—
353C23×C3—28no—
354C23×C3—32no—
355C23×C3—34no—
356C23×C3—34no—
357C23×C3—44no—
358C23×C3—44no—
359C23×C3—64no—
360C23×C3—616no—
361C23×C3—62no—
362C23×C3—616no—
363C23×C3—64no—
364C23×C3—68no—
365C23×C3—84no—
366C23×C3—128no—
367C23×C3—124no—
368C23×C3—128no—
369C23×C3—1232no—
370C23×C3C2×#6718yescomplemented
371C23×C3C2×#6718yescomplemented
372C23×C3C23×D311yescharacteristic
373C23×C3C23×D311yescharacteristic
374C23×C3C23×D314yes—
375C23×C3C23×D314yes—
376C22×D3—22no—
377C22×D3—24no—
378C22×D3—24no—
379C22×D3—216no—
380C22×D3—28no—
381C22×D3—216no—
382C22×D3—48no—
383C22×D3—44no—
384C22×D3—48no—
385C22×D3—432no—
386C22×D3C23×D314yes—
387C22×D3C23×D314yes—
388C22×D3C23×D312yes—
389C3×Q8—64no—
390C3×D4—216no—
391C3×D4—616no—
392C3×D4—68no—
393C3×D4—616no—
394C3×D4—68no—
395C3×D4—64no—
396C3×D4C2×#67116yescomplemented
397C3×D4C2×#67116yescomplemented
398C2×C3×C4—22no—
399C2×C3×C4—24no—
400C2×C3×C4—32no—
401C2×C3×C4—34no—
402C2×C3×C4—62no—
403C2×C3×C4—68no—
404C2×C3×C4—68no—
405C2×C3×C4—68no—
406C2×C3×C4C2×#6714yescomplemented
407C2×C3×C4C2×#6714yescomplemented
408C2×C3×C4C23×D312yes—
409C2×C3×C4C23×D312yes—
410#67—28no—
411#67—216no—
412#67—216no—
413#67—616no—
414#67—616no—
415#67—1216no—
416#67—1216no—
417C2×Dic3—22no—
418C2×Dic3—28no—
419C2×Dic3—38no—
420C2×Dic3—38no—
421C2×Dic3—68no—
422C2×Dic3—128no—
423C2×Dic3—128no—
424C2×Dic3—248no—
425C2×Dic3C23×D312yes—
426C2×Dic3C23×D314yes—
427D12—28no—
428D12—24no—
429C4×D3—28no—
430C4×D3—28no—
431Dic6—24no—
432C2×C32—22no—
433C2×C32—28no—
434C2×C32C23×D411yescharacteristic
435C2×C32C2×H(5,𝔽2)12yes—
436C3×D3—24no—
437C3×D3—44no—
438C3×D3—44no—
439C24—31no—
440C24—38no—
441C24—32no—
442C24—34no—
443C24—68no—
444C24—128no—
445C24C2×D3212yes—
446#41—616no—
447#41—68no—
448C2×Q8—32no—
449C2×D4—34no—
450C2×D4—38no—
451C2×D4—38no—
452C2×D4—34no—
453C2×D4—32no—
454C2×D4—68no—
455C2×D4—616no—
456C2×D4—632no—
457C2×D4—616no—
458C2×D4—64no—
459C2×D4—98no—
460C2×D4—916no—
461C2×D4—3616no—
462C2×D4#62518yescomplemented
463C2×D4C2×D3214yes—
464C22×C4—34no—
465C22×C4—31no—
466C22×C4—34no—
467C22×C4—34no—
468C22×C4—64no—
469C22×C4—98no—
470C22×C4C2×D3211yescharacteristic
471C4⋊C4—98no—
472C4⋊C4—94no—
473C22⋊C4—98no—
474C22⋊C4—916no—
475C22⋊C4—98no—
476C22⋊C4—94no—
477C22⋊C4—98no—
478C42—94no—
479C22×C3—28no—
480C22×C3—22no—
481C22×C3—28no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—28no—
485C22×C3—21no—
486C22×C3—34no—
487C22×C3—48no—
488C22×C3—42no—
489C22×C3—48no—
490C22×C3—48no—
491C22×C3—68no—
492C22×C3—62no—
493C22×C3—62no—
494C22×C3—68no—
495C22×C3—68no—
496C22×C3—64no—
497C22×C3—64no—
498C22×C3—88no—
499C22×C3—1232no—
500C22×C3—128no—
501C22×C3—248no—
502C22×C3C22×#6718yes—
503C22×C3C22×#6712yes—
504C22×C3C22×#6712yes—
505C22×C3C22×#6718yes—
506C22×C3C24×D311yescharacteristic
507C22×C3C24×D311yescharacteristic
508C2×D3—28no—
509C2×D3—22no—
510C2×D3—22no—
511C2×D3—28no—
512C2×D3—28no—
513C2×D3—24no—
514C2×D3—24no—
515C2×D3—432no—
516C2×D3—48no—
517C2×D3—88no—
518C2×D3#100414yescomplemented
519C3×C4—24no—
520C3×C4—62no—
521C3×C4—64no—
522C3×C4C22×#6714yes—
523C3×C4C22×#6714yes—
524Dic3—24no—
525Dic3—22no—
526Dic3—68no—
527Dic3—68no—
528Dic3—128no—
529C32#348411yescharacteristic, complemented, Sylow
530C23—32no—
531C23—34no—
532C23—34no—
533C23—44no—
534C23—64no—
535C23—616no—
536C23—62no—
537C23—616no—
538C23—64no—
539C23—68no—
540C23—128no—
541C23—124no—
542C23—128no—
543C23—1232no—
544C23C2×#62518yescomplemented
545C23C22×D3211yescharacteristic
546C23C22×D3214yes—
547Q8—64no—
548D4—616no—
549D4—68no—
550D4—616no—
551D4—68no—
552D4—64no—
553D4—1816no—
554D4—3616no—
555D4C2×#625116yescomplemented
556C2×C4—34no—
557C2×C4—32no—
558C2×C4—62no—
559C2×C4—68no—
560C2×C4—68no—
561C2×C4—68no—
562C2×C4—98no—
563C2×C4—368no—
564C2×C4C2×#62514yescomplemented
565C2×C4C22×D3212yes—
566C2×C3—22no—
567C2×C3—28no—
568C2×C3—28no—
569C2×C3—22no—
570C2×C3—22no—
571C2×C3—21no—
572C2×C3—42no—
573C2×C3—48no—
574C2×C3—64no—
575C2×C3—124no—
576C2×C3—124no—
577C2×C3C2×#100412yes—
578C2×C3D3×H(5,𝔽2)12yes—
579C2×C3C23×#6711yescharacteristic
580C2×C3C23×#6711yescharacteristic
581D3—24no—
582D3—44no—
583D3—44no—
584C22—28no—
585C22—22no—
586C22—34no—
587C22—48no—
588C22—68no—
589C22—62no—
590C22—62no—
591C22—68no—
592C22—68no—
593C22—64no—
594C22—64no—
595C22—1232no—
596C22—128no—
597C22—248no—
598C22C22×#62512yes—
599C22C22×#62518yes—
600C22C23×D3211yescharacteristic
601C4—62no—
602C4—64no—
603C4—188no—
604C4C22×#62514yes—
605C3—21no—
606C3#8723911yescharacteristic, complemented
607C3#8728411yescharacteristic, complemented
608C2—22no—
609C2—28no—
610C2—64no—
611C2—124no—
612C2—124no—
613C2D3×#100412yes—
614C2C23×#62511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#3484
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1004C2semidirect
2. C22×C3×D3×D4C2semidirect
3. #10596269C2semidirect
4. #10595518C2semidirect
5. C2×#63976C2semidirect
6. #10595244C2semidirect
7. D4×#625C2semidirect
8. #10595040C2semidirect
9. #10595022C2semidirect
12. C24×C3×D3C22semidirect
14. C22×C3×#67C22semidirect
15. C22×C3×#67C22semidirect
17. C2×C3×#237C22semidirect
19. C2×C3×D3×D4C22semidirect
20. C2×C3×D3×D4C22semidirect
21. C2×C3×#235C22semidirect
22. C22×C3×D12C22semidirect
23. C22×C3×C4×D3C22semidirect
24. C22×#625C22semidirect
25. C2×#3757C22semidirect
26. D4×C3⋊Dic3C22semidirect
27. #64135C22semidirect
28. #63980C22semidirect
29. #63976C22semidirect
30. #63976C22semidirect
31. #63976C22semidirect
32. #63976C22semidirect
33. #63961C22semidirect
34. #63961C22semidirect
35. C2×(C2×D3)⋊Dic3C22semidirect
36. #63914C22semidirect
37. #63908C22semidirect
38. #63908C22semidirect
39. C4×#625C22semidirect
40. #63863C22semidirect
41. #63856C22semidirect
44. C2×#1004D3semidirect
45. C22×D3×D4D3semidirect
67. C23×C3×D3C23semidirect
68. C2×C32×D4D4semidirect
71. C22×C3⋊Dic3C23semidirect
76. C2×C3×#67C23semidirect
78. C22×C3×Dic3C23semidirect
85. C2×C3×D12C23semidirect
88. C2×C3×C4×D3C23semidirect
89. C2×C3×Dic6C23semidirect
92. C2×#625C23semidirect
94. #3757C23semidirect
95. C4⋊(C3⋊Dic3)C23semidirect
96. C4×C3⋊Dic3C23semidirect
97. #3724C23semidirect
99. (C2×D3)⋊Dic3C23semidirect
100. (C2×D3)⋊Dic3C23semidirect
103. C24×D3C2×D3semidirect
119. C22×#67C2×D3semidirect
120. C22×#67C2×D3semidirect
122. C2×#237C2×D3semidirect
124. C2×D3×D4C2×D3semidirect
125. C2×D3×D4C2×D3semidirect
126. C2×#235C2×D3semidirect
127. C22×D12C2×D3semidirect
128. C22×C4×D3C2×D3semidirect
167. C23×C32C2×D4semidirect
183. C32×D4C2×D4semidirect
184. C2×C32×C4C2×D4semidirect
225. C23×D3C22×D3semidirect
241. C2×C3×D4#67semidirect
242. C2×C3×D4#67semidirect
263. C2×#67C22×D3semidirect
268. C22×Dic3C22×D3semidirect
275. C2×D12C22×D3semidirect
278. C2×C4×D3C22×D3semidirect
279. C2×Dic6C22×D3semidirect
316. C2×C3×D3H(5,𝔽2)semidirect
370. C23×C3C2×#67semidirect
371. C23×C3C2×#67semidirect
396. C3×D4C2×#67semidirect
397. C3×D4C2×#67semidirect
406. C2×C3×C4C2×#67semidirect
407. C2×C3×C4C2×#67semidirect
462. C2×D4#625semidirect
518. C2×D3#1004semidirect
529. C32#3484semidirect
544. C23C2×#625semidirect
555. D4C2×#625semidirect
564. C2×C4C2×#625semidirect
606. C3#87239semidirect
607. C3#87284semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10042
C22×C3×D3×D42
#105962692
#105955182
C2×#639762
#105952442
D4×#6252
#105950402
#105950222
#872843
#872393