Finite Group Databasebeta

← #11867802

Subgroups — #11867802

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
1C3×#5816C211yesmaximal, characteristic, complemented
2C2×C3×#942C211yesmaximal, characteristic, complemented
3#10595044C211yesmaximal, characteristic
4C2×#63815C211yesmaximal, characteristic, complemented
5C2×#63662C211yesmaximal, characteristic, complemented
6#10591638C212yesmaximal, complemented
7#10591635C212yesmaximal, complemented
8#10591634C212yesmaximal, complemented
9#10591587C212yesmaximal, complemented
10#10591131C211yesmaximal, characteristic, complemented
11#10591083C211yesmaximal, characteristic, complemented
12#83986—31nomaximal
13#83400—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C22×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#947—21no—
20C3×#946C2212yes—
21C3×#946C2212yes—
22C3×#944—21no—
23C2×C3×#216C2212yes—
24C3×#942—24no—
25C2×C3×#215C2212yes—
26C3×#929—22no—
27C3×#926C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic
29#63980—22no—
30#63908—21no—
31#63908C2212yes—
32#63856—21no—
33#63856C2212yes—
34C2×#3711C2212yes—
35#63815—24no—
36C2×D3×C3⋊C8C2212yes—
37#63662C2212yes—
38#63662C2212yes—
39#63575C2212yes—
40#63573C2212yes—
41#63565C2211yescharacteristic
42#63565C2211yescharacteristic
43#63562C2211yescharacteristic
44#63562C2211yescharacteristic
45C2×C3×#137—31no—
46C3×#536—31no—
47#5833—31no—
48#5833—31no—
49C2×#948—31no—
50#5816D311yescharacteristic, complemented
51C2×#942D311yescharacteristic, complemented
52C2×#907—31no—
53#5233—31no—
54C2×#835—31no—
55C2×#835—31no—
56C2×#835—61no—
57#5189—32no—
58#5188—32no—
59#5174—32no—
60#5171—32no—
61#5121—31no—
62#5052—32no—
63#5051—32no—
64#5049—32no—
65#5048—32no—
66#5002—31no—
67#4995—31no—
68C2×C32×Q8—21no—
69C2×C32×Q8—22no—
70C2×C32×Q8—22no—
71C2×C32×Q8C2312yes—
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C22×C3⋊Dic3—21no—
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—
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)C2312yes—
90C2×C3⋊(C3⋊C8)—22no—
91C2×C3⋊(C3⋊C8)C2311yescharacteristic
92C2×C3⋊(C3⋊C8)C2311yescharacteristic
93C3×#217—21no—
94C3×#216—24no—
95C3×#215—24no—
96C3×(C2×D3)⋊C4—22no—
97C3×(C2×D3)⋊C4—22no—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4⋊Dic3C2311yescharacteristic
100C3×Dic3⋊C4—22no—
101C3×Dic3⋊C4—22no—
102C3×C4×Dic3—21no—
103C3×#208D414yescomplemented
104C2×C3×C3⋊C8C2312yes—
105#3724—22no—
106(C2×D3)⋊Dic3—22no—
107(C2×D3)⋊Dic3—22no—
108#3711—24no—
109D3×C3⋊C8—24no—
110#3063—91noSylow
111C2×C3×#41—31no—
112C2×C3×#41—31no—
113C22×C3×Q8—21no—
114C22×C3×Q8C2×D311yescharacteristic
115C22×C3×Q8C2×D311yescharacteristic
116C2×#235C2×D311yescharacteristic
117C2×#235C2×D311yescharacteristic
118C3×#137—64no—
119C2×C3×Q16—32no—
120C2×C3×SD16—32no—
121C2×C3×M16—31no—
122C3×C4⋊Q8—61no—
123C3×#124—61no—
124C3×#123—62no—
125C3×C22⋊Q8—32no—
126C3×C22⋊Q8—32no—
127C3×#117—31no—
128#948—64no—
129#947—21no—
130#946—32no—
131#946—61no—
132#946C2×D312yes—
133#946C2×D312yes—
134#944—21no—
135C2×#216C2×D312yes—
136#942—24no—
137C2×#215C2×D312yes—
138#939—62no—
139#939—62no—
140#938—32no—
141#938—61no—
142#930—32no—
143#930—61no—
144#929—22no—
145#926C2×D311yescharacteristic
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—61no—
149#924—32no—
150#924—61no—
151C2×#208—32no—
152C2×#208C2×D311yescharacteristic
153C22×C3⋊C8—31no—
154C22×C3⋊C8—31no—
155C22×C3⋊C8—32no—
156C22×C3⋊C8—61no—
157#907—64no—
158C2×ΓL(1,𝔽25)—32no—
159C2×D3×C8—32no—
160#835—32no—
161#835—32no—
162#835—32no—
163#835—32no—
164#835—31no—
165#835—31no—
166#835—62no—
167#835—62no—
168#832—31no—
169#832—31no—
170#818—32no—
171#817—32no—
172#810—31no—
173#810—31no—
174#809—31no—
175#809—31no—
176#808—32no—
177#807—32no—
178C23×C32C2×D411yescharacteristic
179C22×C3×D3—21no—
180C22×C3×D3C2×D412yes—
181C32×Q8—22no—
182C32×Q8—22no—
183C32×Q8—42no—
184C2×C32×C4—22no—
185C2×C32×C4—42no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D412yes—
188C2×C32×C4#4112yes—
189C2×C32×C4C2411yescharacteristic
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—81no—
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—
208C3⋊(C3⋊C8)—21no—
209C3⋊(C3⋊C8)—21no—
210C3×C3⋊C8C2×D414yes—
211C2×#137—31no—
212C2×#131—91no—
213#537—91no—
214#536—31no—
215#470—92no—
216#468—92no—
217#467—92no—
218#465—92no—
219#428—91no—
220#416—91no—
221C2×#103—91no—
222C3×#41—62no—
223C3×#41—62no—
224C3×#41—62no—
225C3×#41—62no—
226C2×C3×Q8—21no—
227C2×C3×Q8—21no—
228C2×C3×Q8—24no—
229C2×C3×Q8—22no—
230C2×C3×Q8—22no—
231C2×C3×Q8—22no—
232C2×C3×Q8—22no—
233C2×C3×Q8—22no—
234C2×C3×Q8—31no—
235C2×C3×Q8—31no—
236C2×C3×Q8—41no—
237C2×C3×Q8—42no—
238C2×C3×Q8C22×D312yes—
239C2×C3×Q8C22×D312yes—
240C2×C3×D4—32no—
241C2×C3×D4—31no—
242C2×C3×D4—31no—
243C2×C3×D4—61no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—32no—
248C22×C3×C4—41no—
249C22×C3×C4—61no—
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C2×#67—21no—
253C2×#67—62no—
254C2×#67—62no—
255C2×#67#6712yes—
256C22×Dic3—61no—
257C22×Dic3—61no—
258C22×Dic3—121no—
259#235—22no—
260#235—22no—
261#235—22no—
262#235—22no—
263C2×D12#6711yescharacteristic
264C2×D12C22×D311yescharacteristic
265C2×C4×D3—21no—
266C2×C4×D3C22×D312yes—
267C2×Dic6#6711yescharacteristic
268C2×Dic6C22×D311yescharacteristic
269C3×Q16—64no—
270C3×SD16—64no—
271C3×M16—34no—
272C2×C3×C8—32no—
273C3×C4⋊C4—31no—
274C3×C4⋊C4—31no—
275C3×C4⋊C4—62no—
276C3×C4⋊C4—62no—
277C3×C22⋊C4—62no—
278C3×C22⋊C4—62no—
279C3×C22⋊C4—61no—
280C3×C42—61no—
281#217—21no—
282#217—62no—
283#217—62no—
284#216—24no—
285#215—24no—
286(C2×D3)⋊C4—22no—
287(C2×D3)⋊C4—22no—
288(C2×D3)⋊C4—62no—
289(C2×D3)⋊C4—62no—
290C4⋊Dic3—32no—
291C4⋊Dic3—32no—
292C4⋊Dic3—62no—
293C4⋊Dic3—61no—
294C4⋊Dic3—61no—
295C4⋊Dic3—121no—
296C4⋊Dic3C22×D311yescharacteristic
297C4⋊Dic3C22×D311yescharacteristic
298Dic3⋊C4—22no—
299Dic3⋊C4—22no—
300Dic3⋊C4—62no—
301Dic3⋊C4—62no—
302C4×Dic3—21no—
303#208—64no—
304#208#6714yescomplemented
305C2×C3⋊C8—31no—
306C2×C3⋊C8—31no—
307C2×C3⋊C8—31no—
308C2×C3⋊C8—31no—
309C2×C3⋊C8—61no—
310C2×C3⋊C8—61no—
311C2×C3⋊C8—62no—
312C2×C3⋊C8—62no—
313C2×C3⋊C8—64no—
314C2×C3⋊C8—122no—
315C2×C3⋊C8C22×D312yes—
316ΓL(1,𝔽25)—64no—
317D3×C8—64no—
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—42no—
329C32×C4#12112yes—
330C32×C4C22×D411yescharacteristic
331C32×C4C2×#4111yescharacteristic
332C3⋊Dic3—42no—
333C3×Dic3—22no—
334C3×Dic3—41no—
335C3×Dic3—41no—
336C3×Dic3—41no—
337C2×#41—31no—
338C2×#41—31no—
339C22×Q8D3211yescharacteristic
340#137—64no—
341C2×Q16—32no—
342C2×SD16—32no—
343#131—184no—
344C2×M16—31no—
345C2×M16—92no—
346C22×C8—92no—
347C22×C8—91no—
348C4⋊Q8—61no—
349#124—61no—
350#123—62no—
351C22⋊Q8—32no—
352C22⋊Q8—32no—
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—91no—
363#103—91no—
364#103—92no—
365#103—92no—
366#102—91no—
367#102—91no—
368C23×C3—21no—
369C23×C3—32no—
370C23×C3—61no—
371C23×C3D3×D411yescharacteristic
372C23×C3C2×#6711yescharacteristic
373C22×D3—21no—
374C22×D3C2×#6712yes—
375C3×Q8—24no—
376C3×Q8—22no—
377C3×Q8—22no—
378C3×Q8—22no—
379C3×Q8—22no—
380C3×Q8—42no—
381C3×Q8—44no—
382C3×Q8—42no—
383C3×Q8—42no—
384C3×Q8—62no—
385C3×Q8—61no—
386C3×Q8—61no—
387C3×D4—64no—
388C3×D4—62no—
389C3×D4—61no—
390C3×D4—61no—
391C3×D4—122no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—21no—
398C2×C3×C4—32no—
399C2×C3×C4—42no—
400C2×C3×C4—44no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—62no—
404C2×C3×C4—62no—
405C2×C3×C4—61no—
406C2×C3×C4—61no—
407C2×C3×C4—61no—
408C2×C3×C4—122no—
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D412yes—
411C2×C3×C4#23712yes—
412C2×C3×C4#23712yes—
413C2×C3×C4C2×#6712yes—
414C2×C3×C4C2×#6711yescharacteristic
415C2×C3×C4C23×D311yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417#67—24no—
418#67—42no—
419#67—242no—
420#67—242no—
421C2×Dic3—21no—
422C2×Dic3—21no—
423C2×Dic3—21no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426C2×Dic3—122no—
427C2×Dic3—241no—
428C2×Dic3—241no—
429C2×Dic3—242no—
430C2×Dic3C2×#6712yes—
431D12—22no—
432D12—21no—
433D12—21no—
434C4×D3—22no—
435C4×D3—22no—
436C4×D3—42no—
437Dic6—22no—
438Dic6—21no—
439Dic6—21no—
440C3×C8—34no—
441C3⋊C8—61no—
442C3⋊C8—61no—
443C3⋊C8—61no—
444C3⋊C8—61no—
445C3⋊C8—121no—
446C3⋊C8—121no—
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—21no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—31no—
462C2×Q8—31no—
463C2×Q8C2×D3212yes—
464C2×D4—32no—
465C2×D4—31no—
466C2×D4—31no—
467C2×D4—61no—
468C2×D4—182no—
469C22×C4—21no—
470C22×C4—32no—
471C22×C4—61no—
472C22×C4—181no—
473C22×C4C2×D3211yescharacteristic
474Q16—64no—
475SD16—64no—
476M16—34no—
477M16—184no—
478C2×C8—32no—
479C2×C8—91no—
480C2×C8—91no—
481C2×C8—184no—
482C2×C8—182no—
483C4⋊C4—31no—
484C4⋊C4—31no—
485C4⋊C4—62no—
486C4⋊C4—62no—
487C4⋊C4—92no—
488C4⋊C4—182no—
489C4⋊C4—181no—
490C22⋊C4—62no—
491C22⋊C4—62no—
492C22⋊C4—61no—
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#93812yes—
511C22×C3#93912yes—
512C22×C3C2×D3×D411yescharacteristic
513C22×C3C22×#6711yescharacteristic
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—44no—
524C3×C4—42no—
525C3×C4—42no—
526C3×C4—62no—
527C3×C4—121no—
528C3×C4—121no—
529C3×C4—121no—
530C3×C4#93812yes—
531C3×C4#93912yes—
532C3×C4C2×D3×D411yescharacteristic
533C3×C4C2×#23711yescharacteristic
534C3×C4C2×#23711yescharacteristic
535C3×C4C22×#6711yescharacteristic
536Dic3—22no—
537Dic3—41no—
538Dic3—41no—
539Dic3—41no—
540Dic3—122no—
541Dic3—122no—
542Dic3—242no—
543C32#306311yescharacteristic, complemented, Sylow
544C23—32no—
545C23—61no—
546C23D3×#6711yescharacteristic
547Q8—22no—
548Q8—22no—
549Q8—42no—
550Q8—62no—
551Q8—61no—
552Q8—61no—
553D4—64no—
554D4—61no—
555D4—61no—
556D4—62no—
557D4—122no—
558D4—722no—
559C2×C4—22no—
560C2×C4—32no—
561C2×C4—42no—
562C2×C4—62no—
563C2×C4—62no—
564C2×C4—61no—
565C2×C4—61no—
566C2×C4—61no—
567C2×C4—122no—
568C2×C4—182no—
569C2×C4—721no—
570C2×C4#380512yes—
571C2×C4D3×#6712yes—
572C2×C4D3×#6711yescharacteristic
573C2×C4C22×D3211yescharacteristic
574C8—34no—
575C8—181no—
576C8—181no—
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×C3#577811yescharacteristic
586C2×C3#577911yescharacteristic
587C2×C3C2×#93811yescharacteristic
588C2×C3C2×#93911yescharacteristic
589C2×C3#583711yescharacteristic
590C2×C3#583811yescharacteristic
591D3—42no—
592D3—81no—
593C22—21no—
594C22—21no—
595C22—62no—
596C22—62no—
597C22—62no—
598C22—121no—
599C22—121no—
600C22—121no—
601C22#6397012yes—
602C22C2×D3×#6711yescharacteristic
603C4—42no—
604C4—62no—
605C4—121no—
606C4—121no—
607C4—121no—
608C4—362no—
609C4#6397012yes—
610C4C2×#380511yescharacteristic
611C4C2×D3×#6711yescharacteristic
612C3—21no—
613C3#8340011yescharacteristic, complemented
614C3#8398611yescharacteristic, complemented
615C2—22no—
616C2—122no—
617C2—241no—
618C2#1059531911yescharacteristic
619C2#1059532811yescharacteristic
620C2C2×#6397011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radical#10595044C2
hypercenterC22×Q8D32
hypocenterC32#3063
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. C3×#5816C2semidirect
2. C2×C3×#942C2semidirect
4. C2×#63815C2semidirect
5. C2×#63662C2semidirect
6. #10591638C2semidirect
7. #10591635C2semidirect
8. #10591634C2semidirect
9. #10591587C2semidirect
10. #10591131C2semidirect
11. #10591083C2semidirect
50. #5816D3semidirect
51. C2×#942D3semidirect
103. C3×#208D4semidirect
304. #208#67semidirect
543. C32#3063semidirect
613. C3#83400semidirect
614. C3#83986semidirect

Maximal subgroups

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

subgroupindex
C3×#58162
C2×C3×#9422
#105950442
C2×#638152
C2×#636622
#105916382
#105916352
#105916342
#105915872
#105911312
#105910832
#839863
#834003