Finite Group Databasebeta

← #11895646

Subgroups — #11895646

Order 1152.

747 conjugacy classes of subgroups.

The subgroup lattice has 707 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5559C211yesmaximal, characteristic
2#10593851C211yesmaximal, characteristic, complemented
3#10592708C211yesmaximal, characteristic, complemented
4C3×C4×#214C211yesmaximal, characteristic, complemented
5#10591487C211yesmaximal, characteristic
6#10591478C211yesmaximal, characteristic, complemented
7#10591442C211yesmaximal, characteristic, complemented
8#10591438C211yesmaximal, characteristic
9#10590556C211yesmaximal, characteristic, complemented
10#10590545C211yesmaximal, characteristic, complemented
11#10590476C211yesmaximal, characteristic, complemented
12#10590475C211yesmaximal, characteristic, complemented
13#10590274C211yesmaximal, characteristic, complemented
14#10590267C211yesmaximal, characteristic, complemented
15C3⋊C8×Dic6C211yesmaximal, characteristic, complemented
16#83717—31nomaximal
17#79624—31nomaximal
18C32×C4×D4C2211yescharacteristic
19#64079C2211yescharacteristic
20C3×#940C2211yescharacteristic
21C3×#936C2211yescharacteristic
22C2×C3×#214C2211yescharacteristic
23C3×#929—21no—
24C3×C4×#67—21no—
25C3×#893C2211yescharacteristic
26C3×#887C2211yescharacteristic
27C3×#885—21no—
28C3×#883—21no—
29C3×#875C2211yescharacteristic
30C3×C4×Dic6C2211yescharacteristic
31C3×C4×Dic6C2211yescharacteristic
32#63918C2211yescharacteristic
33#63869C2211yescharacteristic
34#63867—21no—
35#63846—21no—
36Dic3×Dic6C2211yescharacteristic
37Dic3×Dic6C2211yescharacteristic
38#63839—21no—
39#63837—21no—
40C2×#3718C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42#63659C2211yescharacteristic
43#63659C2211yescharacteristic
44#63635C2211yescharacteristic
45#63634C2211yescharacteristic
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×C4×C3⋊C8C2211yescharacteristic
51Dic3⋊(C3⋊C8)C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63566C2211yescharacteristic
54#63566C2211yescharacteristic
55#63565C2211yescharacteristic
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59Dic3×C3⋊C8C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#559—31no—
62#5569—31no—
63#5567—31no—
64#5559D311yescharacteristic
65C3×C4×SD16—31no—
66#5166—31no—
67#5163—31no—
68#5075—31no—
69#5070—31no—
70#5056—31no—
71#5056—31no—
72#5054—31no—
73#5054—31no—
74C4×#216—31no—
75#5028—31no—
76Q8×C3⋊C8—31no—
77#5020—31no—
78C4×#214—31no—
79C4×#214D311yescharacteristic, complemented
80#5009—31no—
81#5009—31no—
82#5009—31no—
83#5009—61no—
84#4871—31no—
85#4854—31no—
86#4790—31no—
87#4788—31no—
88#4768—31no—
89#4760—31no—
90#4697—31no—
91C8×Dic6—31no—
92C2×C32×D4C2311yescharacteristic
93C22×C32×C4—21no—
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×C4×D3—21no—
98C2×C3×Dic6D411yescharacteristic
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#627—21no—
102C32×C4⋊C4C2311yescharacteristic
103C32×C22⋊C4—21no—
104C32×C42C2311yescharacteristic
105C4⋊(C3⋊Dic3)C2311yescharacteristic
106C4⋊(C3⋊Dic3)C2311yescharacteristic
107#3750—21no—
108#3750—21no—
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#217—21no—
112C3×#217—21no—
113C3×#214—22no—
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×C4⋊Dic3D411yescharacteristic
118C3×C4⋊Dic3C2311yescharacteristic
119C3×Dic3⋊C4—21no—
120C3×Dic3⋊C4—21no—
121C3×Dic3⋊C4D411yescharacteristic
122C3×Dic3⋊C4D411yescharacteristic
123C3×C4×Dic3—21no—
124C3×C4×Dic3—21no—
125C3×C4×Dic3C2311yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129#3724—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic32—21no—
135Dic32—21no—
136#3718—22no—
137#3715—22no—
138#3365—91noSylow
139C2×C3×SD16—31no—
140C3×#127—31no—
141C3×#124—31no—
142C3×#124—31no—
143C3×#124—61no—
144C3×#123—61no—
145C3×#123—61no—
146C3×C4×Q8—31no—
147C3×C4×Q8—31no—
148C3×C4×Q8—31no—
149C3×C4×D4—21no—
150C3×C4×D4—31no—
151C3×C4×D4—61no—
152C3×C4×D4C2×D311yescharacteristic
153C3×C4×D4C2×D311yescharacteristic
154Q8×Dic3—31no—
155Q8×Dic3—31no—
156#944—61no—
157C2×#216—31no—
158C2×#216—31no—
159C2×#215—31no—
160#940C2×D311yescharacteristic
161#936C2×D311yescharacteristic
162C2×#214—31no—
163C2×#214C2×D311yescharacteristic
164#929—21no—
165C4×#67—21no—
166#893C2×D311yescharacteristic
167#890—31no—
168#890—61no—
169#889—61no—
170#889—61no—
171#888—31no—
172#888—61no—
173#887—61no—
174#887C2×D311yescharacteristic
175#885—21no—
176#883—21no—
177#875C2×D311yescharacteristic
178#870—31no—
179#870—31no—
180#870—31no—
181#870—61no—
182#870—61no—
183#869—31no—
184C4×Dic6—31no—
185C4×Dic6—31no—
186C4×Dic6—61no—
187C4×Dic6C2×D311yescharacteristic
188C4×Dic6C2×D311yescharacteristic
189C3×#106—31no—
190C3×#103—31no—
191C3×#102—31no—
192C3×C4×C8—31no—
193#835—31no—
194#835—31no—
195#835—31no—
196#832—31no—
197#832—31no—
198#832—31no—
199#832—31no—
200#832—31no—
201#832—31no—
202#832—31no—
203#832—61no—
204#832—61no—
205#832C2×D311yescharacteristic
206#821—31no—
207#821—31no—
208#816—31no—
209#816—31no—
210Dic3⋊C8—31no—
211Dic3⋊C8—31no—
212C8×Dic3—31no—
213C8×Dic3—31no—
214#810—31no—
215#810C2×D311yescharacteristic
216#809—31no—
217#808—31no—
218#808—31no—
219#808—61no—
220#808C2×D311yescharacteristic
221#807—31no—
222#807—31no—
223#807—61no—
224C4⋊(C3⋊C8)—31no—
225C4⋊(C3⋊C8)—31no—
226C4⋊(C3⋊C8)—31no—
227C4⋊(C3⋊C8)—31no—
228C4⋊(C3⋊C8)—61no—
229C4×C3⋊C8—31no—
230C4×C3⋊C8—31no—
231C4×C3⋊C8C2×D311yescharacteristic
232C23×C32—21no—
233C22×C3×D3—21no—
234C32×D4—21no—
235C32×D4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—81no—
238C2×C32×C4C2×D411yescharacteristic
239C2×C32×C4C2×D411yescharacteristic
240C2×C32×C4C2411yescharacteristic
241C2×C3⋊Dic3—21no—
242C2×C3⋊Dic3—21no—
243C3×#67—42no—
244C3×#67—81no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3C2×D411yescharacteristic
249C2×C3×Dic3C2×D411yescharacteristic
250C2×C3×Dic3C2×D411yescharacteristic
251C2×C3×Dic3C2×D411yescharacteristic
252C3×D12—21no—
253C3×D12—21no—
254C3×C4×D3—81no—
255C3×Dic6—21no—
256C3×Dic6—22no—
257C3×Dic6—21no—
258C3×Dic6—21no—
259C3×Dic6#4112yes—
260#627—42no—
261C3⋊(C3⋊C8)—21no—
262C3⋊(C3⋊C8)—21no—
263C3×C3⋊C8—21no—
264C3×C3⋊C8—21no—
265#559—31no—
266#557—91no—
267#488—91no—
268#488—91no—
269#486—91no—
270#478—91no—
271#478—91no—
272#475—91no—
273#464—91no—
274#464—91no—
275#460—91no—
276C8×Q8—91no—
277C4×Q16—91no—
278C4×SD16—31no—
279C4×SD16—91no—
280C2×C3×Q8—31no—
281C2×C3×Q8—31no—
282C2×C3×Q8—31no—
283C2×C3×D4—21no—
284C2×C3×D4—31no—
285C2×C3×D4—61no—
286C2×C3×D4—61no—
287C2×C3×D4C22×D311yescharacteristic
288C2×C3×D4C22×D311yescharacteristic
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—41no—
292C22×C3×C4—61no—
293C2×#67—21no—
294C2×#67—21no—
295C2×D12C22×D311yescharacteristic
296C2×C4×D3—21no—
297C2×Dic6—61no—
298C2×Dic6—61no—
299C2×Dic6#6711yescharacteristic
300C2×Dic6C22×D311yescharacteristic
301C2×Dic6C22×D311yescharacteristic
302C3×SD16—62no—
303C2×C3×C8—31no—
304C2×C3×C8—31no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C4⋊C4C22×D311yescharacteristic
313C3×C4⋊C4C22×D311yescharacteristic
314C3×C22⋊C4—21no—
315C3×C22⋊C4—21no—
316C3×C22⋊C4—41no—
317C3×C22⋊C4—61no—
318C3×C22⋊C4—61no—
319C3×C22⋊C4—61no—
320C3×C22⋊C4—61no—
321C3×C22⋊C4—61no—
322C3×C42—21no—
323C3×C42—31no—
324C3×C42—31no—
325C3×C42—61no—
326C3×C42—61no—
327C3×C42C22×D311yescharacteristic
328C3×C42C22×D311yescharacteristic
329#217—21no—
330#217—21no—
331#216—62no—
332#216—62no—
333#215—62no—
334#214—22no—
335#214—62no—
336(C2×D3)⋊C4—21no—
337(C2×D3)⋊C4—21no—
338(C2×D3)⋊C4—21no—
339C4⋊Dic3—31no—
340C4⋊Dic3—31no—
341C4⋊Dic3—31no—
342C4⋊Dic3—31no—
343C4⋊Dic3—61no—
344C4⋊Dic3—61no—
345C4⋊Dic3—61no—
346C4⋊Dic3—61no—
347C4⋊Dic3—61no—
348C4⋊Dic3—61no—
349C4⋊Dic3#6711yescharacteristic
350C4⋊Dic3C22×D311yescharacteristic
351Dic3⋊C4—21no—
352Dic3⋊C4—21no—
353Dic3⋊C4—61no—
354Dic3⋊C4—61no—
355Dic3⋊C4—61no—
356Dic3⋊C4—61no—
357Dic3⋊C4—61no—
358Dic3⋊C4—61no—
359Dic3⋊C4—61no—
360Dic3⋊C4—61no—
361Dic3⋊C4—61no—
362Dic3⋊C4—61no—
363Dic3⋊C4—121no—
364Dic3⋊C4—121no—
365Dic3⋊C4#6711yescharacteristic
366Dic3⋊C4#6711yescharacteristic
367C4×Dic3—21no—
368C4×Dic3—21no—
369C4×Dic3—61no—
370C4×Dic3—61no—
371C4×Dic3—61no—
372C4×Dic3—61no—
373C4×Dic3C22×D311yescharacteristic
374C4×Dic3C22×D311yescharacteristic
375C2×C3⋊C8—31no—
376C2×C3⋊C8—31no—
377C2×C3⋊C8—31no—
378C2×C3⋊C8—31no—
379C2×C3⋊C8—61no—
380C2×C3⋊C8—61no—
381C2×C3⋊C8C22×D311yescharacteristic
382C2×C3⋊C8C22×D311yescharacteristic
383C22×C32—41no—
384C22×C32—41no—
385C22×C32—41no—
386C22×C32C22×D411yescharacteristic
387C2×C3×D3—41no—
388C2×C3×D3—41no—
389C2×C3×D3—41no—
390C32×C4—21no—
391C32×C4—21no—
392C32×C4—41no—
393C32×C4C2×#4111yescharacteristic
394C32×C42−1+411yescharacteristic
395C3⋊Dic3—41no—
396C3⋊Dic3—41no—
397C3×Dic3—22no—
398C3×Dic3—21no—
399C3×Dic3—21no—
400C3×Dic3—21no—
401C3×Dic3—41no—
402C3×Dic3—41no—
403C3×Dic3#13512yes—
404C2×Q16—91no—
405C2×SD16—31no—
406C2×SD16—91no—
407C4⋊Q8—91no—
408C4⋊Q8—181no—
409#127—31no—
410#125—91no—
411#125—91no—
412#125—181no—
413#125—181no—
414#124—31no—
415#124—31no—
416#124—61no—
417#123—61no—
418#123—61no—
419C4×Q8—31no—
420C4×Q8—31no—
421C4×Q8—31no—
422C4×Q8—91no—
423C4×Q8—91no—
424C4×Q8—181no—
425C4×D4—31no—
426C4×D4—61no—
427C4×D4D3211yescharacteristic
428#107—91no—
429#106—31no—
430#106—91no—
431C4⋊C8—91no—
432C4⋊C8—91no—
433C4⋊C8—91no—
434#103—31no—
435#103—91no—
436#103—91no—
437#103—91no—
438#102—31no—
439#102—91no—
440#102—91no—
441#102—91no—
442#102—91no—
443#102—91no—
444C4×C8—31no—
445C4×C8—91no—
446C4×C8—91no—
447C23×C3—21no—
448C23×C3—21no—
449C23×C3—41no—
450C23×C3—61no—
451C22×D3—21no—
452C3×Q8—32no—
453C3×Q8—62no—
454C3×Q8—61no—
455C3×Q8—61no—
456C3×Q8—61no—
457C3×D4—22no—
458C3×D4—21no—
459C3×D4—21no—
460C3×D4—21no—
461C3×D4—21no—
462C3×D4—41no—
463C3×D4—61no—
464C3×D4—61no—
465C3×D4—122no—
466C3×D4—241no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—31no—
473C2×C3×C4—31no—
474C2×C3×C4—31no—
475C2×C3×C4—31no—
476C2×C3×C4—41no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—81no—
481C2×C3×C4—81no—
482C2×C3×C4—82no—
483C2×C3×C4—241no—
484C2×C3×C4D3×D411yescharacteristic
485C2×C3×C4D3×D411yescharacteristic
486C2×C3×C4C2×#6711yescharacteristic
487C2×C3×C4C2×#6711yescharacteristic
488C2×C3×C4C23×D311yescharacteristic
489C2×C3×C4C23×D311yescharacteristic
490#67—42no—
491#67—81no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—61no—
496C2×Dic3—61no—
497C2×Dic3—61no—
498C2×Dic3—61no—
499C2×Dic3—121no—
500C2×Dic3—121no—
501C2×Dic3C2×#6711yescharacteristic
502C2×Dic3C2×#6711yescharacteristic
503C2×Dic3C2×#6711yescharacteristic
504C2×Dic3C2×#6711yescharacteristic
505D12—21no—
506D12—21no—
507C4×D3—81no—
508Dic6—21no—
509Dic6—22no—
510Dic6—21no—
511Dic6—21no—
512Dic6—122no—
513Dic6—122no—
514Dic6#23512yes—
515C3×C8—61no—
516C3×C8—61no—
517C3⋊C8—21no—
518C3⋊C8—21no—
519C3⋊C8—61no—
520C3⋊C8—61no—
521C3⋊C8—61no—
522C3⋊C8—61no—
523C3⋊C8—121no—
524C3⋊C8—121no—
525C2×C32—81no—
526C2×C32#54811yescharacteristic
527C2×C32C2×#13511yescharacteristic
528C2×C32#57711yescharacteristic
529C3×D3—81no—
530C2×Q8—31no—
531C2×Q8—31no—
532C2×Q8—31no—
533C2×Q8—181no—
534C2×D4—31no—
535C2×D4—61no—
536C2×D4—61no—
537C2×D4C2×D3211yescharacteristic
538C22×C4—21no—
539C22×C4—61no—
540Q16—182no—
541SD16—62no—
542SD16—182no—
543C2×C8—31no—
544C2×C8—31no—
545C2×C8—91no—
546C2×C8—91no—
547C4⋊C4—31no—
548C4⋊C4—31no—
549C4⋊C4—31no—
550C4⋊C4—31no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—91no—
554C4⋊C4—91no—
555C4⋊C4—181no—
556C4⋊C4—181no—
557C4⋊C4—181no—
558C4⋊C4—181no—
559C4⋊C4—181no—
560C4⋊C4—181no—
561C4⋊C4—181no—
562C4⋊C4C2×D3211yescharacteristic
563C22⋊C4—21no—
564C22⋊C4—61no—
565C22⋊C4—61no—
566C22⋊C4—61no—
567C22⋊C4—61no—
568C22⋊C4—61no—
569C42—31no—
570C42—31no—
571C42—61no—
572C42—61no—
573C42—181no—
574C42—181no—
575C42C2×D3211yescharacteristic
576C22×C3—21no—
577C22×C3—42no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—81no—
585C22×C3—81no—
586C22×C3—121no—
587C22×C3—121no—
588C22×C3—121no—
589C22×C3C2×D3×D411yescharacteristic
590C22×C3C22×#6711yescharacteristic
591C2×D3—41no—
592C2×D3—41no—
593C2×D3—41no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—21no—
598C3×C4—21no—
599C3×C4—21no—
600C3×C4—32no—
601C3×C4—41no—
602C3×C4—41no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—61no—
606C3×C4—61no—
607C3×C4—61no—
608C3×C4—62no—
609C3×C4—81no—
610C3×C4—121no—
611C3×C4—121no—
612C3×C4C2×#23511yescharacteristic
613C3×C4D3×#4111yescharacteristic
614C3×C4#101011yescharacteristic
615C3×C4#101011yescharacteristic
616Dic3—22no—
617Dic3—21no—
618Dic3—21no—
619Dic3—21no—
620Dic3—41no—
621Dic3—41no—
622Dic3—121no—
623Dic3—121no—
624Dic3—121no—
625Dic3—121no—
626Dic3—241no—
627Dic3—241no—
628Dic3#95012yes—
629C32#336511yescharacteristic, complemented, Sylow
630C23—21no—
631C23—61no—
632Q8—32no—
633Q8—62no—
634Q8—61no—
635Q8—61no—
636Q8—61no—
637Q8—362no—
638D4—21no—
639D4—21no—
640D4—61no—
641D4—61no—
642D4—122no—
643D4—241no—
644C2×C4—21no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—61no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—81no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4—241no—
656C2×C4D3×#6711yescharacteristic
657C2×C4D3×#6711yescharacteristic
658C2×C4C22×D3211yescharacteristic
659C8—61no—
660C8—61no—
661C8—181no—
662C8—181no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—82no—
667C2×C3—81no—
668C2×C3—81no—
669C2×C3—241no—
670C2×C3#555211yescharacteristic
671C2×C3#576211yescharacteristic
672C2×C3D3×#13511yescharacteristic
673C2×C3C2×#95011yescharacteristic
674C2×C3#583111yescharacteristic
675C2×C3#583611yescharacteristic
676D3—81no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—121no—
681C22—121no—
682C22—121no—
683C22C2×D3×#6711yescharacteristic
684C4—21no—
685C4—21no—
686C4—32no—
687C4—41no—
688C4—61no—
689C4—61no—
690C4—62no—
691C4—61no—
692C4—121no—
693C4—121no—
694C4—361no—
695C4—361no—
696C4#6429811yescharacteristic
697C4D3×#23511yescharacteristic
698C3—21no—
699C3#7962411yescharacteristic, complemented
700C3#8371711yescharacteristic, complemented
701C2—81no—
702C2—241no—
703C2#1059489911yescharacteristic
704C2#1059510511yescharacteristic
705C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC3×#940C22
hypercenterC4×D4D32
hypocenterC32#3365
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593851C2semidirect
3. #10592708C2semidirect
4. C3×C4×#214C2semidirect
6. #10591478C2semidirect
7. #10591442C2semidirect
9. #10590556C2semidirect
10. #10590545C2semidirect
11. #10590476C2semidirect
12. #10590475C2semidirect
13. #10590274C2semidirect
14. #10590267C2semidirect
15. C3⋊C8×Dic6C2semidirect
79. C4×#214D3semidirect
629. C32#3365semidirect
699. C3#79624semidirect
700. C3#83717semidirect

Maximal subgroups

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

subgroupindex
C3×#55592
#105938512
#105927082
C3×C4×#2142
#105914872
#105914782
#105914422
#105914382
#105905562
#105905452
#105904762
#105904752
#105902742
#105902672
C3⋊C8×Dic62
#837173
#796243