Finite Group Databasebeta

← #11867800

Subgroups — #11867800

Order 1152.

1073 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64151C211yesmaximal, characteristic, complemented
2C3×#5816C211yesmaximal, characteristic, complemented
3#10595043C211yesmaximal, characteristic
4C2×#63814C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591598C212yesmaximal, complemented
7#10591596C212yesmaximal, complemented
8#10591589C212yesmaximal, complemented
9#10591585C212yesmaximal, complemented
10#10591139C211yesmaximal, characteristic, complemented
11#10591105C211yesmaximal, characteristic, complemented
12#83400—31nomaximal
13#78800—31nomaximal
14C22×C32×Q8C2211yescharacteristic
15C2×#3828C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17C2×#3756C2212yes—
18#64151—24no—
19C2×#3755C2212yes—
20C2×#3748C2211yescharacteristic
21C3×#947—21no—
22C3×#946C2212yes—
23C3×#946C2212yes—
24C3×#944—21no—
25C3×#929—22no—
26C3×#926C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic
29#63978—22no—
30#63916—21no—
31#63909C2212yes—
32#63871—21no—
33#63857C2212yes—
34C2×#3711C2212yes—
35#63814—24no—
36C2×D3×C3⋊C8C2212yes—
37C3×#835C2212yes—
38C3×#835C2212yes—
39#63576C2212yes—
40#63574C2212yes—
41#63567C2211yescharacteristic
42#63567C2211yescharacteristic
43#63564C2211yescharacteristic
44#63564C2211yescharacteristic
45C3×#536—31no—
46#5833—31no—
47C2×#948—31no—
48#5816D311yescharacteristic, complemented
49C2×#942—31no—
50C2×#942—31no—
51C2×#942—61no—
52C2×#901—31no—
53#5510—31no—
54C2×C3×#103—31no—
55C2×#835D311yescharacteristic, complemented
56#5113—31no—
57#5052—32no—
58#5051—32no—
59#5049—32no—
60#5048—32no—
61#5002—31no—
62#4995—31no—
63#4964—31no—
64#4816—32no—
65#4813—32no—
66#4812—32no—
67#4807—32no—
68C2×C32×Q8—21no—
69C2×C32×Q8—22no—
70C2×C32×Q8—22no—
71C2×C32×Q8C2312yes—
72C22×C32×C4—21no—
73C22×C32×C4C2311yescharacteristic
74C2×#638—21no—
75#3828—22no—
76#3828—22no—
77C2×C4⋊(C3⋊D3)C2311yescharacteristic
78C2×C4×C3⋊D3—21no—
79C2×#634C2311yescharacteristic
80C2×C3×#67D412yes—
81C22×C3×Dic3—21no—
82C3×#235—22no—
83C3×#235—22no—
84C2×C3×D12D411yescharacteristic
85C2×C3×C4×D3C2312yes—
86C2×C3×Dic6D411yescharacteristic
87C2×#626—22no—
88#3756—24no—
89#3755—24no—
90#3748D414yescomplemented
91C2×C3⋊(C3⋊C8)C2312yes—
92C3×#217—21no—
93C3×(C2×D3)⋊C4—22no—
94C3×(C2×D3)⋊C4—22no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3C2312yes—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4⋊Dic3C2311yescharacteristic
99C3×Dic3⋊C4—22no—
100C3×Dic3⋊C4—22no—
101C3×C4×Dic3—21no—
102C2×C3×C3⋊C8—22no—
103C2×C3×C3⋊C8C2311yescharacteristic
104C2×C3×C3⋊C8C2311yescharacteristic
105Dic3⋊Dic3—22no—
106#3722—22no—
107(C2×D3)⋊Dic3—22no—
108#3711—24no—
109D3×C3⋊C8—24no—
110#3063—91noSylow
111C2×C3×#41—31no—
112C22×C3×Q8—21no—
113C22×C3×Q8C2×D311yescharacteristic
114C22×C3×Q8C2×D311yescharacteristic
115C2×#235—31no—
116C2×#235—31no—
117C2×#235—61no—
118C2×#235C2×D311yescharacteristic
119C22×C3×C8—31no—
120C3×C4⋊Q8—61no—
121C3×#124—61no—
122C3×#123—62no—
123C3×C22⋊Q8—32no—
124C3×C22⋊Q8—32no—
125C3×#117—31no—
126C2×C3×C4⋊C4—31no—
127#948—64no—
128#947—21no—
129#946—61no—
130#946C2×D312yes—
131#946C2×D312yes—
132#944—21no—
133C2×#216—32no—
134C2×#216—32no—
135C2×#216—62no—
136#942—64no—
137#942—64no—
138#942—68no—
139C2×#215—32no—
140C2×#215—32no—
141C2×#215—62no—
142#939—62no—
143#938—61no—
144#930—32no—
145#930—62no—
146#929—22no—
147#926C2×D311yescharacteristic
148C2×C4⋊Dic3C2×D311yescharacteristic
149#924—32no—
150C2×#208—31no—
151C2×#208—31no—
152C2×#208—32no—
153C2×#208—61no—
154C22×C3⋊C8—32no—
155C22×C3⋊C8C2×D311yescharacteristic
156#901—64no—
157C2×ΓL(1,𝔽25)—32no—
158C2×D3×C8—32no—
159#897—32no—
160#897—61no—
161#895—32no—
162#895—61no—
163C3×#103—32no—
164C3×#103—32no—
165#835C2×D312yes—
166#835C2×D312yes—
167#821—31no—
168#821—31no—
169#816—31no—
170#816—31no—
171#810—31no—
172#810—31no—
173#809—31no—
174#809—31no—
175#808—32no—
176#808—32no—
177#807—32no—
178#807—32no—
179C23×C32C2×D411yescharacteristic
180C22×C3⋊D3—21no—
181C22×C3×D3C2×D412yes—
182C32×Q8—22no—
183C32×Q8—22no—
184C32×Q8—42no—
185C2×C32×C4—22no—
186C2×C32×C4—42no—
187C2×C32×C4C2×D412yes—
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4#4112yes—
190C2×C32×C4C2411yescharacteristic
191#638—42no—
192C2×C3⋊Dic3—21no—
193C4⋊(C3⋊D3)—21no—
194C4⋊(C3⋊D3)—21no—
195C4×C3⋊D3—42no—
196#634—21no—
197#634—21no—
198C3×#67—24no—
199C2×C3×Dic3—22no—
200C2×C3×Dic3—21no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—81no—
203C2×C3×Dic3C2×D412yes—
204C3×D12—22no—
205C3×C4×D3—22no—
206C3×C4×D3—22no—
207C3×Dic6—22no—
208#626—82no—
209C3⋊(C3⋊C8)C2×D414yes—
210C3×C3⋊C8—21no—
211C3×C3⋊C8—21no—
212C2×#137—91no—
213C2×#131—91no—
214#537—91no—
215#536—31no—
216#470—92no—
217#468—92no—
218#467—92no—
219#465—92no—
220#428—91no—
221#416—91no—
222C2×#103—31no—
223C3×#41—62no—
224C3×#41—62no—
225C2×C3×Q8—21no—
226C2×C3×Q8—21no—
227C2×C3×Q8—24no—
228C2×C3×Q8—22no—
229C2×C3×Q8—22no—
230C2×C3×Q8—22no—
231C2×C3×Q8—22no—
232C2×C3×Q8—22no—
233C2×C3×Q8—31no—
234C2×C3×Q8—41no—
235C2×C3×Q8—42no—
236C2×C3×Q8C22×D312yes—
237C2×C3×Q8C22×D312yes—
238C2×C3×D4—32no—
239C2×C3×D4—31no—
240C22×C3×C4—21no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—32no—
244C22×C3×C4—41no—
245C22×C3×C4—61no—
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C2×#67—62no—
249C2×#67—61no—
250C2×#67—61no—
251C2×#67—121no—
252C2×#67#6712yes—
253C22×Dic3—21no—
254#235—22no—
255#235—22no—
256#235—64no—
257#235—62no—
258#235—62no—
259#235—62no—
260#235—62no—
261#235—122no—
262C2×D12—31no—
263C2×D12—31no—
264C2×D12—61no—
265C2×D12—62no—
266C2×D12#6711yescharacteristic
267C2×C4×D3—61no—
268C2×C4×D3—61no—
269C2×C4×D3—121no—
270C2×C4×D3C22×D312yes—
271C2×Dic6—31no—
272C2×Dic6—31no—
273C2×Dic6—61no—
274C2×Dic6#6711yescharacteristic
275C2×C3×C8—31no—
276C2×C3×C8—31no—
277C2×C3×C8—62no—
278C3×C4⋊C4—31no—
279C3×C4⋊C4—32no—
280C3×C4⋊C4—31no—
281C3×C4⋊C4—62no—
282C3×C4⋊C4—62no—
283C3×C4⋊C4—61no—
284C3×C22⋊C4—62no—
285C3×C22⋊C4—62no—
286C3×C22⋊C4—61no—
287C3×C42—61no—
288#217—21no—
289#217—62no—
290#216—64no—
291#216—64no—
292#216—68no—
293#215—64no—
294#215—64no—
295#215—68no—
296(C2×D3)⋊C4—22no—
297(C2×D3)⋊C4—22no—
298(C2×D3)⋊C4—62no—
299(C2×D3)⋊C4—62no—
300(C2×D3)⋊C4—62no—
301C4⋊Dic3—21no—
302C4⋊Dic3—62no—
303C4⋊Dic3C22×D311yescharacteristic
304C4⋊Dic3C22×D312yes—
305C4⋊Dic3C22×D311yescharacteristic
306Dic3⋊C4—22no—
307Dic3⋊C4—22no—
308Dic3⋊C4—62no—
309C4×Dic3—21no—
310#208—34no—
311#208—34no—
312#208—64no—
313#208—64no—
314C2×C3⋊C8—22no—
315C2×C3⋊C8—32no—
316C2×C3⋊C8—32no—
317C2×C3⋊C8—62no—
318C2×C3⋊C8—64no—
319C2×C3⋊C8C22×D311yescharacteristic
320C2×C3⋊C8C22×D311yescharacteristic
321ΓL(1,𝔽25)—64no—
322D3×C8—64no—
323C22×C32—21no—
324C22×C32—21no—
325C22×C32#12112yes—
326C22×C32C22×D411yescharacteristic
327C2×C3⋊D3—41no—
328C2×C3⋊D3—41no—
329C2×C3⋊D3—41no—
330C2×C3×D3—22no—
331C2×C3×D3—22no—
332C2×C3×D3—22no—
333C32×C4—42no—
334C32×C4#12112yes—
335C32×C4C22×D411yescharacteristic
336C32×C4C2×#4111yescharacteristic
337C3⋊Dic3—41no—
338C3×Dic3—22no—
339C3×Dic3—42no—
340C3×Dic3—41no—
341C3×Dic3—41no—
342C2×#41—31no—
343C2×#41—91no—
344C22×Q8D3211yescharacteristic
345#137—184no—
346C2×Q16—92no—
347C2×SD16—92no—
348#131—184no—
349C2×M16—92no—
350C2×M16—91no—
351C22×C8—31no—
352C22×C8—92no—
353C4⋊Q8—61no—
354#124—61no—
355#123—62no—
356C22⋊Q8—32no—
357C22⋊Q8—32no—
358C22⋊Q8—92no—
359C22⋊Q8—181no—
360#121—92no—
361#121—181no—
362#121—182no—
363#117—31no—
364C2×C4⋊C4—31no—
365#107—92no—
366#106—92no—
367#103—32no—
368#103—32no—
369#103—91no—
370#103—91no—
371#102—91no—
372#102—91no—
373C23×C3—21no—
374C23×C3—32no—
375C23×C3D3×D411yescharacteristic
376C23×C3C2×#6711yescharacteristic
377C22×D3—61no—
378C22×D3—61no—
379C22×D3—121no—
380C22×D3C2×#6712yes—
381C3×Q8—24no—
382C3×Q8—22no—
383C3×Q8—22no—
384C3×Q8—22no—
385C3×Q8—22no—
386C3×Q8—42no—
387C3×Q8—44no—
388C3×Q8—42no—
389C3×Q8—42no—
390C3×Q8—62no—
391C3×D4—64no—
392C3×D4—62no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—21no—
396C2×C3×C4—22no—
397C2×C3×C4—21no—
398C2×C3×C4—22no—
399C2×C3×C4—32no—
400C2×C3×C4—42no—
401C2×C3×C4—44no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—61no—
407C2×C3×C4—61no—
408C2×C3×C4—62no—
409C2×C3×C4—241no—
410C2×C3×C4#23512yes—
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4D3×D412yes—
413C2×C3×C4D3×D412yes—
414C2×C3×C4#23712yes—
415C2×C3×C4C2×#6711yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417C2×C3×C4C23×D311yescharacteristic
418#67—24no—
419#67—124no—
420#67—122no—
421#67—122no—
422#67—242no—
423C2×Dic3—22no—
424C2×Dic3—21no—
425C2×Dic3—21no—
426C2×Dic3—61no—
427C2×Dic3—61no—
428C2×Dic3—81no—
429C2×Dic3—121no—
430C2×Dic3C2×#6712yes—
431D12—22no—
432D12—62no—
433D12—61no—
434D12—61no—
435D12—61no—
436D12—61no—
437D12—121no—
438D12—242no—
439C4×D3—22no—
440C4×D3—22no—
441C4×D3—124no—
442C4×D3—122no—
443C4×D3—122no—
444Dic6—22no—
445Dic6—62no—
446Dic6—61no—
447Dic6—61no—
448Dic6—61no—
449Dic6—61no—
450Dic6—121no—
451C3×C8—61no—
452C3×C8—61no—
453C3⋊C8—21no—
454C3⋊C8—21no—
455C3⋊C8—34no—
456C3⋊C8—34no—
457C3⋊C8—64no—
458C2×C32—22no—
459C2×C32C2×#12111yescharacteristic
460C2×C32#57711yescharacteristic
461C2×C32#57811yescharacteristic
462C3⋊D3—81no—
463C3×D3—42no—
464#41—62no—
465#41—62no—
466#41—182no—
467#41—182no—
468C2×Q8—21no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—31no—
472C2×Q8—91no—
473C2×Q8C2×D3212yes—
474C2×D4—32no—
475C2×D4—31no—
476C2×D4—91no—
477C2×D4—182no—
478C2×D4—181no—
479C22×C4—21no—
480C22×C4—32no—
481C22×C4—61no—
482C22×C4—181no—
483C22×C4C2×D3211yescharacteristic
484Q16—184no—
485SD16—184no—
486M16—94no—
487M16—184no—
488C2×C8—31no—
489C2×C8—31no—
490C2×C8—62no—
491C2×C8—92no—
492C2×C8—184no—
493C4⋊C4—31no—
494C4⋊C4—31no—
495C4⋊C4—32no—
496C4⋊C4—62no—
497C4⋊C4—62no—
498C4⋊C4—61no—
499C4⋊C4—182no—
500C22⋊C4—62no—
501C22⋊C4—62no—
502C22⋊C4—61no—
503C22⋊C4—182no—
504C22⋊C4—182no—
505C42—61no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—22no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—62no—
515C22×C3—62no—
516C22×C3—62no—
517C22×C3#88412yes—
518C22×C3#93912yes—
519C22×C3C2×D3×D411yescharacteristic
520C22×C3C22×#6711yescharacteristic
521C2×D3—22no—
522C2×D3—22no—
523C2×D3—22no—
524C2×D3—122no—
525C2×D3—121no—
526C2×D3—121no—
527C2×D3—121no—
528C2×D3—121no—
529C2×D3—121no—
530C2×D3—121no—
531C2×D3—241no—
532C2×D3—241no—
533C3×C4—21no—
534C3×C4—21no—
535C3×C4—22no—
536C3×C4—44no—
537C3×C4—42no—
538C3×C4—42no—
539C3×C4—62no—
540C3×C4—121no—
541C3×C4—121no—
542C3×C4—122no—
543C3×C4#88412yes—
544C3×C4#93912yes—
545C3×C4C2×#23511yescharacteristic
546C3×C4C2×D3×D411yescharacteristic
547C3×C4C2×D3×D411yescharacteristic
548C3×C4C2×#23711yescharacteristic
549Dic3—22no—
550Dic3—42no—
551Dic3—41no—
552Dic3—41no—
553Dic3—122no—
554Dic3—121no—
555Dic3—121no—
556C32#306311yescharacteristic, complemented, Sylow
557C23—32no—
558C23—181no—
559C23D3×#6711yescharacteristic
560Q8—22no—
561Q8—22no—
562Q8—42no—
563Q8—62no—
564Q8—181no—
565Q8—181no—
566D4—64no—
567D4—62no—
568D4—181no—
569D4—181no—
570D4—362no—
571D4—722no—
572C2×C4—22no—
573C2×C4—32no—
574C2×C4—42no—
575C2×C4—62no—
576C2×C4—62no—
577C2×C4—61no—
578C2×C4—61no—
579C2×C4—62no—
580C2×C4—181no—
581C2×C4—241no—
582C2×C4—362no—
583C2×C4#380412yes—
584C2×C4D3×#6711yescharacteristic
585C2×C4#381112yes—
586C2×C4C22×D3211yescharacteristic
587C8—61no—
588C8—61no—
589C8—94no—
590C2×C3—22no—
591C2×C3—22no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—42no—
596C2×C3—122no—
597C2×C3C2×#88411yescharacteristic
598C2×C3#576211yescharacteristic
599C2×C3#576611yescharacteristic
600C2×C3C2×#93911yescharacteristic
601C2×C3#583711yescharacteristic
602C2×C3#583811yescharacteristic
603D3—42no—
604D3—242no—
605D3—241no—
606D3—241no—
607C22—21no—
608C22—21no—
609C22—62no—
610C22—62no—
611C22—62no—
612C22—361no—
613C22—361no—
614C22—361no—
615C22#6397112yes—
616C22C2×D3×#6711yescharacteristic
617C4—42no—
618C4—62no—
619C4—122no—
620C4—121no—
621C4—121no—
622C4—361no—
623C4#6397112yes—
624C4C2×#380411yescharacteristic
625C4C2×#381111yescharacteristic
626C3—21no—
627C3#7880011yescharacteristic, complemented
628C3#8340011yescharacteristic, complemented
629C2—22no—
630C2—122no—
631C2—721no—
632C2#1059531811yescharacteristic
633C2#1059532711yescharacteristic
634C2C2×#6397111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radical#10595043C2
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. C2×#64151C2semidirect
2. C3×#5816C2semidirect
4. C2×#63814C2semidirect
5. C2×C3×#835C2semidirect
6. #10591598C2semidirect
7. #10591596C2semidirect
8. #10591589C2semidirect
9. #10591585C2semidirect
10. #10591139C2semidirect
11. #10591105C2semidirect
48. #5816D3semidirect
55. C2×#835D3semidirect
90. #3748D4semidirect
556. C32#3063semidirect
627. C3#78800semidirect
628. C3#83400semidirect

Maximal subgroups

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

subgroupindex
C2×#641512
C3×#58162
#105950432
C2×#638142
C2×C3×#8352
#105915982
#105915962
#105915892
#105915852
#105911392
#105911052
#834003
#788003