Finite Group Databasebeta

← #11867815

Subgroups — #11867815

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#901C211yesmaximal, characteristic, complemented
2#10595044C211yesmaximal, characteristic
3#10594856C211yesmaximal, characteristic, complemented
4C2×#63831C211yesmaximal, characteristic, complemented
5C2×#63643C211yesmaximal, characteristic, complemented
6C3×#5113C211yesmaximal, characteristic, complemented
7#10591131C211yesmaximal, characteristic, complemented
8#10590849C212yesmaximal, complemented
9#10590848C212yesmaximal, complemented
10#10590828C212yesmaximal, complemented
11#10590825C212yesmaximal, complemented
12#83808—31nomaximal
13#78841—31nomaximal
14C22×#634C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17C22×C32×C8C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C3×#901—24no—
22C2×C3×ΓL(1,𝔽25)C2212yes—
23C2×C3×D3×C8C2212yes—
24#63980—22no—
25#63962—22no—
26#63908—21no—
27#63908C2212yes—
28#63866—21no—
29#63860—21no—
30#63857C2212yes—
31#63857C2212yes—
32#63856—21no—
33#63856C2212yes—
34C2×#3719C2212yes—
35#63831—24no—
36C2×#3716C2212yes—
37#63643C2212yes—
38#63643C2212yes—
39C3×#821C2211yescharacteristic
40C3×#821C2211yescharacteristic
41C3×#816C2211yescharacteristic
42C3×#816C2211yescharacteristic
43#63575C2212yes—
44#63573C2212yes—
45C2×C3×#131—31no—
46#5833—31no—
47#5833—31no—
48#5825—31no—
49C2×#951—31no—
50C2×#909—31no—
51C2×#901D311yescharacteristic, complemented
52#5526—31no—
53C3×#416—31no—
54#5137—32no—
55#5134—32no—
56#5121—31no—
57#5116—32no—
58#5114—32no—
59#5113D311yescharacteristic, complemented
60C2×#816—31no—
61C2×#816—31no—
62C2×#816—61no—
63#4995—31no—
64#4816—32no—
65#4813—32no—
66#4780—32no—
67#4778—32no—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3—21no—
70C22×C3⋊Dic3—21no—
71C2×#634—22no—
72C2×#634—22no—
73C2×#634—21no—
74C2×#634C2312yes—
75C2×C3×#67—21no—
76C2×C3×#67D412yes—
77C3×#235—22no—
78C3×#235—22no—
79C3×#235—22no—
80C3×#235—22no—
81C2×C3×D12D411yescharacteristic
82C2×C3×D12C2311yescharacteristic
83C2×C3×C4×D3—21no—
84C2×C3×C4×D3C2312yes—
85C2×C3×Dic6D411yescharacteristic
86C2×C3×Dic6C2311yescharacteristic
87C2×#625—22no—
88C2×C32×C8—22no—
89C2×C32×C8C2311yescharacteristic
90C2×C32×C8C2311yescharacteristic
91C4⋊(C3⋊Dic3)—21no—
92C4⋊(C3⋊Dic3)C2312yes—
93C3×#217—21no—
94C3×C4⋊Dic3C2311yescharacteristic
95C3×C4⋊Dic3C2311yescharacteristic
96C3×C4×Dic3—21no—
97C3×#208D414yescomplemented
98C2×C3×C3⋊C8C2312yes—
99C3×ΓL(1,𝔽25)—24no—
100C3×D3×C8—24no—
101#3724—22no—
102Dic3⋊Dic3—22no—
103Dic3⋊Dic3—22no—
104(C2×D3)⋊Dic3—22no—
105(C2×D3)⋊Dic3—22no—
106(C2×D3)⋊Dic3—22no—
107(C2×D3)⋊Dic3—22no—
108#3719—24no—
109#3716—24no—
110#3063—91noSylow
111C2×C3×#41—31no—
112C2×C3×#41—31no—
113C2×#235C2×D311yescharacteristic
114C2×#235C2×D311yescharacteristic
115C22×Dic6—31no—
116C22×Dic6—31no—
117C22×Dic6—61no—
118C3×#131—64no—
119C2×C3×M16—31no—
120C2×C3×M16—32no—
121C22×C3×C8—21no—
122C22×C3×C8—32no—
123C22×C3×C8C2×D311yescharacteristic
124C22×C3×C8C2×D311yescharacteristic
125C3×#117—31no—
126#951—64no—
127#946—32no—
128#946—61no—
129#944—61no—
130C2×#216—32no—
131#939—62no—
132#939—62no—
133#938—32no—
134#938—61no—
135#936—61no—
136#935—62no—
137C2×#214—32no—
138#930—32no—
139#930—61no—
140#926C2×D311yescharacteristic
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—61no—
144#924—32no—
145#924—32no—
146#924—32no—
147#924—61no—
148C2×#208C2×D311yescharacteristic
149#909—64no—
150C2×Dic12—32no—
151C2×#204—32no—
152#901—24no—
153C2×ΓL(1,𝔽25)C2×D312yes—
154C2×D3×C8C2×D312yes—
155#897—32no—
156#897—32no—
157#886—62no—
158#875—61no—
159#869—61no—
160C3×#103—31no—
161C3×#103—31no—
162C3×#102—31no—
163C3×#102—31no—
164#821C2×D311yescharacteristic
165#821C2×D311yescharacteristic
166#818—32no—
167#817—32no—
168#816—32no—
169#816—32no—
170#816—32no—
171#816—32no—
172#816—62no—
173#816—62no—
174#816C2×D311yescharacteristic
175#816C2×D311yescharacteristic
176#808—32no—
177#807—32no—
178C23×C32C2×D411yescharacteristic
179C22×C3×D3—21no—
180C22×C3×D3C2×D412yes—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D412yes—
183C2×C32×C4#4112yes—
184C2×C32×C4C2411yescharacteristic
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3—42no—
188C2×C3⋊Dic3—81no—
189#634—22no—
190#634—22no—
191#634—42no—
192C3×#67—24no—
193C3×#67—42no—
194C2×C3×Dic3—21no—
195C2×C3×Dic3—21no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3C2×D412yes—
198C3×D12—22no—
199C3×D12—21no—
200C3×D12—21no—
201C3×C4×D3—22no—
202C3×C4×D3—22no—
203C3×C4×D3—42no—
204C3×Dic6—22no—
205C3×Dic6—21no—
206C3×Dic6—21no—
207#625—82no—
208C32×C8—21no—
209C32×C8—21no—
210C3×C3⋊C8C2×D414yes—
211C2×#137—91no—
212C2×#131—31no—
213#537—91no—
214#536—91no—
215#470—92no—
216#468—92no—
217#467—92no—
218#465—92no—
219#428—91no—
220#416—31no—
221C2×#103—91no—
222C3×#41—62no—
223C3×#41—62no—
224C3×#41—62no—
225C3×#41—62no—
226C2×C3×Q8—31no—
227C2×C3×Q8—31no—
228C2×C3×D4—32no—
229C2×C3×D4—31no—
230C2×C3×D4—31no—
231C2×C3×D4—61no—
232C22×C3×C4—21no—
233C22×C3×C4—32no—
234C22×C3×C4—61no—
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C2×#67—21no—
238C2×#67—62no—
239C2×#67—62no—
240C2×#67D1212yes—
241C22×Dic3—61no—
242C22×Dic3—61no—
243C22×Dic3—61no—
244C22×Dic3—61no—
245C22×Dic3—121no—
246C22×Dic3—121no—
247#235—22no—
248#235—22no—
249#235—22no—
250#235—22no—
251C2×D12D1211yescharacteristic
252C2×D12C22×D311yescharacteristic
253C2×C4×D3—21no—
254C2×C4×D3C22×D312yes—
255C2×Dic6—32no—
256C2×Dic6—32no—
257C2×Dic6—62no—
258C2×Dic6—64no—
259C2×Dic6—62no—
260C2×Dic6—62no—
261C2×Dic6—62no—
262C2×Dic6—62no—
263C2×Dic6—61no—
264C2×Dic6—61no—
265C2×Dic6—121no—
266C2×Dic6—122no—
267C2×Dic6D1211yescharacteristic
268C2×Dic6C22×D311yescharacteristic
269C3×M16—34no—
270C3×M16—64no—
271C2×C3×C8—22no—
272C2×C3×C8—22no—
273C2×C3×C8—21no—
274C2×C3×C8—21no—
275C2×C3×C8—32no—
276C2×C3×C8—42no—
277C2×C3×C8—64no—
278C2×C3×C8C22×D311yescharacteristic
279C2×C3×C8C22×D311yescharacteristic
280C2×C3×C8C22×D311yescharacteristic
281C2×C3×C8C22×D311yescharacteristic
282C3×C4⋊C4—31no—
283C3×C4⋊C4—31no—
284C3×C22⋊C4—61no—
285C3×C42—61no—
286#217—21no—
287#217—62no—
288#217—62no—
289#217—62no—
290#217—62no—
291#216—64no—
292#214—64no—
293(C2×D3)⋊C4—62no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—62no—
296(C2×D3)⋊C4—62no—
297C4⋊Dic3—32no—
298C4⋊Dic3—32no—
299C4⋊Dic3—62no—
300C4⋊Dic3—61no—
301C4⋊Dic3—61no—
302C4⋊Dic3—62no—
303C4⋊Dic3—62no—
304C4⋊Dic3—121no—
305C4⋊Dic3C22×D311yescharacteristic
306C4⋊Dic3C22×D311yescharacteristic
307Dic3⋊C4—62no—
308Dic3⋊C4—62no—
309Dic3⋊C4—62no—
310Dic3⋊C4—62no—
311C4×Dic3—21no—
312#208#6714yescomplemented
313C2×C3⋊C8C22×D312yes—
314Dic12—64no—
315#204—64no—
316ΓL(1,𝔽25)—24no—
317D3×C8—24no—
318C22×C32—21no—
319C22×C32—21no—
320C22×C32#12112yes—
321C22×C32C22×D411yescharacteristic
322C2×C3×D3—22no—
323C2×C3×D3—22no—
324C2×C3×D3—22no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C2×C3×D3—41no—
328C32×C4#12112yes—
329C32×C4C22×D411yescharacteristic
330C32×C4C2×#4111yescharacteristic
331C3⋊Dic3—42no—
332C3⋊Dic3—42no—
333C3×Dic3—22no—
334C3×Dic3—41no—
335C3×Dic3—41no—
336C3×Dic3—41no—
337C2×#41—31no—
338C2×#41—31no—
339C22×Q8—91no—
340#137—184no—
341C2×Q16—92no—
342C2×SD16—92no—
343#131—64no—
344C2×M16—31no—
345C2×M16—32no—
346C22×C8—32no—
347C22×C8D3211yescharacteristic
348C4⋊Q8—181no—
349#124—181no—
350#123—182no—
351C22⋊Q8—92no—
352C22⋊Q8—92no—
353C22⋊Q8—92no—
354C22⋊Q8—181no—
355#121—92no—
356#121—181no—
357#121—182no—
358#117—31no—
359C2×C4⋊C4—91no—
360#107—92no—
361#106—92no—
362#103—31no—
363#103—31no—
364#103—92no—
365#103—92no—
366#102—31no—
367#102—31no—
368C23×C3—21no—
369C23×C3—32no—
370C23×C3—61no—
371C23×C3C2×D1211yescharacteristic
372C23×C3D3×D411yescharacteristic
373C22×D3—21no—
374C22×D3C2×D1212yes—
375C3×Q8—62no—
376C3×Q8—61no—
377C3×Q8—61no—
378C3×D4—64no—
379C3×D4—62no—
380C3×D4—61no—
381C3×D4—61no—
382C3×D4—122no—
383C2×C3×C4—21no—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—32no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—61no—
391C2×C3×C4—61no—
392C2×C3×C4—61no—
393C2×C3×C4—122no—
394C2×C3×C4C2×D1211yescharacteristic
395C2×C3×C4#23512yes—
396C2×C3×C4#23512yes—
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4D3×D412yes—
399C2×C3×C4C2×#6712yes—
400C2×C3×C4C23×D311yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402#67—24no—
403#67—42no—
404#67—242no—
405#67—242no—
406C2×Dic3—21no—
407C2×Dic3—21no—
408C2×Dic3—21no—
409C2×Dic3—62no—
410C2×Dic3—62no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—122no—
414C2×Dic3—122no—
415C2×Dic3—124no—
416C2×Dic3—122no—
417C2×Dic3—122no—
418C2×Dic3—241no—
419C2×Dic3—241no—
420C2×Dic3—242no—
421C2×Dic3C2×D1212yes—
422D12—22no—
423D12—21no—
424D12—21no—
425C4×D3—22no—
426C4×D3—22no—
427C4×D3—42no—
428Dic6—22no—
429Dic6—21no—
430Dic6—21no—
431Dic6—64no—
432Dic6—62no—
433Dic6—62no—
434Dic6—62no—
435Dic6—62no—
436Dic6—122no—
437Dic6—124no—
438Dic6—122no—
439Dic6—122no—
440C3×C8—21no—
441C3×C8—21no—
442C3×C8—21no—
443C3×C8—21no—
444C3×C8—34no—
445C3×C8—41no—
446C3×C8—41no—
447C3⋊C8C2×#6714yes—
448C2×C32—22no—
449C2×C32C2×#12111yescharacteristic
450C2×C32#57711yescharacteristic
451C2×C32#57811yescharacteristic
452C3×D3—42no—
453C3×D3—81no—
454#41—62no—
455#41—62no—
456#41—62no—
457#41—62no—
458C2×Q8—31no—
459C2×Q8—31no—
460C2×Q8—92no—
461C2×Q8—181no—
462C2×Q8—182no—
463C2×Q8—182no—
464C2×D4—32no—
465C2×D4—31no—
466C2×D4—31no—
467C2×D4—61no—
468C2×D4—182no—
469C22×C4—32no—
470C22×C4—61no—
471C22×C4—181no—
472C22×C4—181no—
473C22×C4C2×D3211yescharacteristic
474Q16—184no—
475SD16—184no—
476M16—34no—
477M16—64no—
478C2×C8—22no—
479C2×C8—32no—
480C2×C8—64no—
481C2×C8C2×D3211yescharacteristic
482C2×C8C2×D3211yescharacteristic
483C4⋊C4—31no—
484C4⋊C4—31no—
485C4⋊C4—92no—
486C4⋊C4—182no—
487C4⋊C4—182no—
488C4⋊C4—182no—
489C4⋊C4—181no—
490C22⋊C4—61no—
491C22⋊C4—182no—
492C22⋊C4—182no—
493C22⋊C4—182no—
494C22⋊C4—182no—
495C42—61no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—22no—
504C22×C3—62no—
505C22×C3—62no—
506C22×C3—62no—
507C22×C3—121no—
508C22×C3—121no—
509C22×C3—121no—
510C22×C3#88412yes—
511C22×C3#93012yes—
512C22×C3C22×D1211yescharacteristic
513C22×C3C2×D3×D411yescharacteristic
514C2×D3—22no—
515C2×D3—22no—
516C2×D3—22no—
517C2×D3—41no—
518C2×D3—41no—
519C2×D3—41no—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—22no—
523C3×C4—62no—
524C3×C4—121no—
525C3×C4—121no—
526C3×C4—121no—
527C3×C4#88412yes—
528C3×C4#93012yes—
529C3×C4C2×#23511yescharacteristic
530C3×C4C2×#23511yescharacteristic
531C3×C4C2×D3×D411yescharacteristic
532C3×C4C22×#6711yescharacteristic
533Dic3—22no—
534Dic3—41no—
535Dic3—41no—
536Dic3—41no—
537Dic3—124no—
538Dic3—122no—
539Dic3—122no—
540Dic3—122no—
541Dic3—122no—
542Dic3—242no—
543C32#306311yescharacteristic, complemented, Sylow
544C23—32no—
545C23—61no—
546C23D3×D1211yescharacteristic
547Q8—62no—
548Q8—61no—
549Q8—61no—
550Q8—182no—
551Q8—182no—
552Q8—362no—
553D4—64no—
554D4—61no—
555D4—61no—
556D4—62no—
557D4—122no—
558D4—722no—
559C2×C4—32no—
560C2×C4—62no—
561C2×C4—62no—
562C2×C4—61no—
563C2×C4—61no—
564C2×C4—61no—
565C2×C4—122no—
566C2×C4—182no—
567C2×C4—182no—
568C2×C4—362no—
569C2×C4—721no—
570C2×C4#379812yes—
571C2×C4D3×D1211yescharacteristic
572C2×C4D3×#6712yes—
573C2×C4C22×D3211yescharacteristic
574C8—21no—
575C8—21no—
576C8—34no—
577C2×C3—24no—
578C2×C3—22no—
579C2×C3—22no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—122no—
584C2×C3—241no—
585C2×C3C2×#88411yescharacteristic
586C2×C3#575111yescharacteristic
587C2×C3#575311yescharacteristic
588C2×C3#577011yescharacteristic
589C2×C3#577111yescharacteristic
590C2×C3C2×#93011yescharacteristic
591D3—42no—
592D3—81no—
593C22—21no—
594C22—21no—
595C22—62no—
596C22—62no—
597C22—62no—
598C22—121no—
599C22—121no—
600C22—121no—
601C22#6390612yes—
602C22C2×D3×D1211yescharacteristic
603C4—62no—
604C4—121no—
605C4—121no—
606C4—121no—
607C4—362no—
608C4—362no—
609C4#6390612yes—
610C4C2×#379811yescharacteristic
611C4C2×D3×#6711yescharacteristic
612C3—21no—
613C3#7884111yescharacteristic, complemented
614C3#8380811yescharacteristic, complemented
615C2—22no—
616C2—122no—
617C2—241no—
618C2#1059467911yescharacteristic
619C2#1059469211yescharacteristic
620C2C2×#6390611yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10595044C2
hypercenterC22×C8D32
hypocenterC32#3063
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#901C2semidirect
3. #10594856C2semidirect
4. C2×#63831C2semidirect
5. C2×#63643C2semidirect
6. C3×#5113C2semidirect
7. #10591131C2semidirect
8. #10590849C2semidirect
9. #10590848C2semidirect
10. #10590828C2semidirect
11. #10590825C2semidirect
51. C2×#901D3semidirect
59. #5113D3semidirect
97. C3×#208D4semidirect
312. #208#67semidirect
543. C32#3063semidirect
613. C3#78841semidirect
614. C3#83808semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9012
#105950442
#105948562
C2×#638312
C2×#636432
C3×#51132
#105911312
#105908492
#105908482
#105908282
#105908252
#838083
#788413