Finite Group Databasebeta

← #11869689

Subgroups — #11869689

Order 1152.

941 conjugacy classes of subgroups.

The subgroup lattice has 633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5791C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C2×#63657C211yesmaximal, characteristic, complemented
4#10591138C212yesmaximal, complemented
5#10591132C211yesmaximal, characteristic, complemented
6#10591102C212yesmaximal, complemented
7#10591101C211yesmaximal, characteristic, complemented
8#10591091C211yesmaximal, characteristic, complemented
9#10591090C212yesmaximal, complemented
10#10591089C211yesmaximal, characteristic, complemented
11#10591083C212yesmaximal, complemented
12#82913—31nomaximal
13#82215—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2212yes—
17C3×#953—21no—
18C2×C3×#217—21no—
19C3×#930C2211yescharacteristic
20C3×#930C2211yescharacteristic
21C3×#929—21no—
22C3×C4×#67—21no—
23C3×C4×#67—21no—
24C3×#926—21no—
25C3×#926—21no—
26C3×#926C2212yes—
27C3×#926C2212yes—
28C3×#926C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C3×#924C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C2×C3×C4×Dic3—21no—
34#63657C2211yescharacteristic
35#63657C2212yes—
36#63657C2211yescharacteristic
37#63576C2212yescomplemented
38#63576C2212yescomplemented
39#63574C2212yescomplemented
40#63574C2212yescomplemented
41#63565C2212yescomplemented
42#63565C2212yescomplemented
43#63562C2212yescomplemented
44#63562C2212yescomplemented
45C3×#525—31no—
46C2×C3×#117—31no—
47#5791D311yescharacteristic
48C2×#926D311yescharacteristic, complemented
49#5233—32no—
50C2×#830—31no—
51C2×#830—31no—
52C2×#830—61no—
53#5045—32no—
54#5044—31no—
55#5043—31no—
56#5035—32no—
57#5034—31no—
58#5033—31no—
59#5003—32no—
60#5002—32no—
61#4998—32no—
62#4998—32no—
63#4996—32no—
64#4971—31no—
65#4970—31no—
66#4968—31no—
67#4967—31no—
68C24×C32D411yescharacteristic
69C22×C32×C4—24no—
70C22×C32×C4D411yescharacteristic
71C22×C32×C4D411yescharacteristic
72C22×C32×C4D411yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C2×C3×#67—21no—
77C2×C3×#67—21no—
78C2×C3×#67—21no—
79C22×C3×Dic3—21no—
80C22×C3×Dic3—21no—
81C3×#235—24no—
82C2×C3×D12C2311yescharacteristic
83C2×C3×C4×D3—21no—
84C2×C3×Dic6C2311yescharacteristic
85C2×C3⋊(C3⋊C8)—24no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#217—21no—
89C3×#217—21no—
90C3×#217—22no—
91C3×#217—22no—
92C3×#217—21no—
93C3×(C2×D3)⋊C4—21no—
94C3×(C2×D3)⋊C4—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3C2311yescharacteristic
98C3×C4⋊Dic3C2311yescharacteristic
99C3×C4⋊Dic3C2312yes—
100C3×C4⋊Dic3C2312yes—
101C3×Dic3⋊C4—21no—
102C3×Dic3⋊C4—21no—
103C3×C4×Dic3—22no—
104C3×C4×Dic3—22no—
105C3×C4×Dic3—21no—
106#3091—91noSylow
107C2×C3×#41—31no—
108C23×C3×C4—21no—
109C23×C3×C4C2×D311yescharacteristic
110C23×C3×C4C2×D311yescharacteristic
111C2×#235C2×D311yescharacteristic
112C3×#123—61no—
113C3×C22⋊Q8—31no—
114C3×C22⋊Q8—31no—
115C3×#121—31no—
116C3×#121—31no—
117C3×#120—61no—
118C3×C4×D4—61no—
119C3×C4×D4—61no—
120C3×#117—32no—
121C3×#117—31no—
122C3×#117—32no—
123C3×#117—61no—
124C3×#117—61no—
125C2×C3×C4⋊C4—31no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C22⋊C4—61no—
128C2×C3×C42—61no—
129#953—21no—
130C2×#217—21no—
131#930C2×D311yescharacteristic
132#930C2×D311yescharacteristic
133#929—21no—
134C4×#67—21no—
135C4×#67—21no—
136#926—21no—
137#926—21no—
138#926C2×D312yes—
139#926C2×D311yescharacteristic
140#926C2×D312yes—
141C2×C4⋊Dic3C2×D311yescharacteristic
142C2×C4⋊Dic3C2×D311yescharacteristic
143#924C2×D311yescharacteristic
144#924C2×D311yescharacteristic
145C2×C4×Dic3—21no—
146C22×C3⋊C8—32no—
147C22×C3⋊C8—32no—
148C22×C3⋊C8—62no—
149#835—32no—
150#835—32no—
151#832—32no—
152#832—32no—
153#830—31no—
154#830—31no—
155#830—32no—
156#830—31no—
157#830—31no—
158#830—32no—
159#830—61no—
160#830—61no—
161#830—62no—
162#810—32no—
163#810—32no—
164#809—32no—
165#809—32no—
166#808—32no—
167#808—32no—
168#808—32no—
169#808—32no—
170#807—32no—
171#807—32no—
172#807—32no—
173#807—32no—
174C23×C32—22no—
175C23×C32—22no—
176C23×C32—41no—
177C23×C32C2×D411yescharacteristic
178C23×C32C2×D411yescharacteristic
179C23×C32C2×D411yescharacteristic
180C22×C3×D3—21no—
181C2×C32×C4—22no—
182C2×C32×C4—22no—
183C2×C32×C4—22no—
184C2×C32×C4—22no—
185C2×C32×C4—22no—
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4C2×D411yescharacteristic
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4#4114yes—
190C2×C32×C4C2411yescharacteristic
191C3×#67—42no—
192C3×#67—42no—
193C3×#67—42no—
194C2×C3×Dic3—22no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—21no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—42no—
200C2×C3×Dic3—42no—
201C3×D12—22no—
202C3×C4×D3—42no—
203C3×Dic6—22no—
204C3⋊(C3⋊C8)—22no—
205C3⋊(C3⋊C8)—22no—
206#525—31no—
207C2×#117—31no—
208#485—92no—
209#484—91no—
210#483—91no—
211#482—92no—
212#481—91no—
213#480—91no—
214#427—92no—
215#416—92no—
216C2×C22⋊C8—91no—
217C24×C3—21no—
218C24×C3#6711yescharacteristic
219C24×C3#6711yescharacteristic
220C3×#41—64no—
221C2×C3×Q8—31no—
222C2×C3×D4—31no—
223C2×C3×D4—61no—
224C2×C3×D4—61no—
225C2×C3×D4—61no—
226C22×C3×C4—24no—
227C22×C3×C4—24no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—44no—
235C22×C3×C4—61no—
236C22×C3×C4—61no—
237C22×C3×C4—61no—
238C22×C3×C4#6711yescharacteristic
239C22×C3×C4#6711yescharacteristic
240C22×C3×C4#6711yescharacteristic
241C22×C3×C4#6711yescharacteristic
242C22×C3×C4#6711yescharacteristic
243C22×C3×C4#6711yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C2×#67—21no—
251C2×#67—21no—
252C2×#67—21no—
253C22×Dic3—21no—
254C22×Dic3—21no—
255#235—24no—
256C2×D12C22×D311yescharacteristic
257C2×C4×D3—21no—
258C2×Dic6C22×D311yescharacteristic
259C3×C4⋊C4—31no—
260C3×C4⋊C4—31no—
261C3×C4⋊C4—32no—
262C3×C4⋊C4—32no—
263C3×C4⋊C4—61no—
264C3×C4⋊C4—61no—
265C3×C4⋊C4—61no—
266C3×C4⋊C4—61no—
267C3×C22⋊C4—62no—
268C3×C22⋊C4—62no—
269C3×C22⋊C4—61no—
270C3×C22⋊C4—61no—
271C3×C22⋊C4—61no—
272C3×C22⋊C4—61no—
273C3×C22⋊C4—61no—
274C3×C42—62no—
275C3×C42—62no—
276C3×C42—61no—
277#217—21no—
278#217—21no—
279#217—22no—
280#217—22no—
281#217—21no—
282(C2×D3)⋊C4—21no—
283(C2×D3)⋊C4—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3—21no—
286C4⋊Dic3C22×D311yescharacteristic
287C4⋊Dic3C22×D311yescharacteristic
288C4⋊Dic3C22×D312yes—
289C4⋊Dic3C22×D312yes—
290Dic3⋊C4—21no—
291Dic3⋊C4—21no—
292C4×Dic3—22no—
293C4×Dic3—22no—
294C4×Dic3—21no—
295C2×C3⋊C8—32no—
296C2×C3⋊C8—32no—
297C2×C3⋊C8—32no—
298C2×C3⋊C8—32no—
299C2×C3⋊C8—62no—
300C2×C3⋊C8—62no—
301C2×C3⋊C8—64no—
302C2×C3⋊C8—64no—
303C2×C3⋊C8—124no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32—21no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32—21no—
310C22×C32—21no—
311C22×C32—44no—
312C22×C32#12312yes—
313C22×C32#13512yes—
314C22×C32C22×D411yescharacteristic
315C2×C3×D3—41no—
316C2×C3×D3—41no—
317C2×C3×D3—41no—
318C32×C4—21no—
319C32×C4—21no—
320C32×C4#12312yes—
321C32×C4C2×#4112yes—
322C3×Dic3—41no—
323C3×Dic3—42no—
324C3×Dic3—41no—
325C3×Dic3—42no—
326C3×Dic3—41no—
327C2×#41—31no—
328C23×C4D3211yescharacteristic
329C22×C8—92no—
330#123—61no—
331C22⋊Q8—31no—
332C22⋊Q8—31no—
333#121—31no—
334#121—31no—
335#120—61no—
336C4×D4—61no—
337C4×D4—61no—
338#117—32no—
339#117—32no—
340#117—31no—
341#117—61no—
342#117—61no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—31no—
345C2×C22⋊C4—61no—
346C2×C42—61no—
347#107—92no—
348#107—92no—
349#106—92no—
350#106—92no—
351#103—92no—
352#103—92no—
353#102—92no—
354#102—92no—
355C22⋊C8—91no—
356C22⋊C8—91no—
357C22⋊C8—92no—
358C23×C3—24no—
359C23×C3—22no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—22no—
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—42no—
367C23×C3—41no—
368C23×C3—41no—
369C23×C3—42no—
370C23×C3—61no—
371C23×C3C2×#6711yescharacteristic
372C23×C3C2×#6711yescharacteristic
373C23×C3C2×#6711yescharacteristic
374C23×C3C2×#6711yescharacteristic
375C23×C3C2×#6711yescharacteristic
376C23×C3C2×#6711yescharacteristic
377C22×D3—21no—
378C3×Q8—62no—
379C3×D4—62no—
380C3×D4—122no—
381C3×D4—122no—
382C3×D4—122no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—21no—
394C2×C3×C4—24no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
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×C4—122no—
410C2×C3×C4—122no—
411C2×C3×C4#23514yes—
412C2×C3×C4#23714yes—
413C2×C3×C4C2×#6711yescharacteristic
414C2×C3×C4C2×#6711yescharacteristic
415C2×C3×C4C2×#6711yescharacteristic
416C2×C3×C4C2×#6711yescharacteristic
417C2×C3×C4C2×#6711yescharacteristic
418C2×C3×C4C2×#6711yescharacteristic
419C2×C3×C4C23×D311yescharacteristic
420C2×C3×C4C23×D311yescharacteristic
421#67—42no—
422#67—42no—
423#67—42no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—21no—
427C2×Dic3—21no—
428C2×Dic3—21no—
429C2×Dic3—42no—
430C2×Dic3—42no—
431D12—22no—
432C4×D3—42no—
433Dic6—22no—
434C3⋊C8—62no—
435C3⋊C8—62no—
436C3⋊C8—62no—
437C3⋊C8—62no—
438C3⋊C8—122no—
439C3⋊C8—122no—
440C2×C32—22no—
441C2×C32—22no—
442C2×C32—41no—
443C2×C32C2×#12311yescharacteristic
444C2×C32C2×#13511yescharacteristic
445C2×C32#57511yescharacteristic
446C3×D3—81no—
447C24#62511yescharacteristic
448#41—64no—
449C2×Q8—31no—
450C2×D4—31no—
451C2×D4—61no—
452C2×D4—61no—
453C2×D4—61no—
454C22×C4—24no—
455C22×C4—61no—
456C22×C4—61no—
457C22×C4—61no—
458C22×C4#62511yescharacteristic
459C22×C4#62511yescharacteristic
460C22×C4#62511yescharacteristic
461C22×C4C2×D3211yescharacteristic
462C22×C4C2×D3211yescharacteristic
463C22×C4C2×D3211yescharacteristic
464C2×C8—92no—
465C2×C8—92no—
466C2×C8—184no—
467C4⋊C4—32no—
468C4⋊C4—32no—
469C4⋊C4—31no—
470C4⋊C4—31no—
471C4⋊C4—61no—
472C4⋊C4—61no—
473C4⋊C4—61no—
474C4⋊C4—61no—
475C22⋊C4—62no—
476C22⋊C4—62no—
477C22⋊C4—61no—
478C22⋊C4—61no—
479C22⋊C4—61no—
480C22⋊C4—61no—
481C22⋊C4—61no—
482C42—62no—
483C42—62no—
484C42—61no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—22no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—21no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3—41no—
508C22×C3—41no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—48no—
512C22×C3—121no—
513C22×C3—121no—
514C22×C3—121no—
515C22×C3#92912yes—
516C22×C3#93512yes—
517C22×C3#95012yes—
518C22×C3#95012yes—
519C22×C3C22×#6711yescharacteristic
520C22×C3C22×#6711yescharacteristic
521C2×D3—41no—
522C2×D3—41no—
523C2×D3—41no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—22no—
529C3×C4—22no—
530C3×C4—41no—
531C3×C4—41no—
532C3×C4—121no—
533C3×C4—122no—
534C3×C4—121no—
535C3×C4—122no—
536C3×C4—121no—
537C3×C4#92912yes—
538C3×C4#93512yes—
539C3×C4C2×#23512yes—
540C3×C4C2×#23712yes—
541Dic3—41no—
542Dic3—42no—
543Dic3—41no—
544Dic3—42no—
545Dic3—41no—
546C32#309111yescharacteristic, complemented, Sylow
547C23—22no—
548C23—22no—
549C23—41no—
550C23—61no—
551C23C2×#62511yescharacteristic
552C23C2×#62511yescharacteristic
553C23C2×#62511yescharacteristic
554Q8—62no—
555D4—62no—
556D4—122no—
557D4—122no—
558D4—122no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—61no—
567C2×C4—61no—
568C2×C4—61no—
569C2×C4—122no—
570C2×C4—122no—
571C2×C4—122no—
572C2×C4#380414yes—
573C2×C4C2×#62511yescharacteristic
574C2×C4C2×#62511yescharacteristic
575C2×C4C2×#62511yescharacteristic
576C2×C4C22×D3211yescharacteristic
577C8—182no—
578C8—182no—
579C2×C3—24no—
580C2×C3—22no—
581C2×C3—22no—
582C2×C3—22no—
583C2×C3—22no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—42no—
588C2×C3—42no—
589C2×C3—41no—
590C2×C3—41no—
591C2×C3—241no—
592C2×C3C2×#92911yescharacteristic
593C2×C3C2×#93511yescharacteristic
594C2×C3C2×#95011yescharacteristic
595C2×C3C2×#95011yescharacteristic
596C2×C3#582211yescharacteristic
597C2×C3#582211yescharacteristic
598D3—81no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—44no—
607C22—121no—
608C22—121no—
609C22—121no—
610C22#6382212yes—
611C22#6396112yes—
612C22C22×#62511yescharacteristic
613C4—21no—
614C4—21no—
615C4—121no—
616C4—122no—
617C4—121no—
618C4—122no—
619C4—121no—
620C4#6396112yes—
621C4C2×#380412yes—
622C3—21no—
623C3#8221511yescharacteristic, complemented
624C3#8291311yescharacteristic, complemented
625C2—22no—
626C2—22no—
627C2—41no—
628C2—241no—
629C2C2×#6382211yescharacteristic
630C2#1059478611yescharacteristic
631C2C2×#6396111yescharacteristic
subgroupG/H
centerC2×C4C2×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC22×C32C22×D4
prime radicalC3×#5791C2
hypercenterC23×C4D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. C2×#63657C2semidirect
4. #10591138C2semidirect
5. #10591132C2semidirect
6. #10591102C2semidirect
7. #10591101C2semidirect
8. #10591091C2semidirect
9. #10591090C2semidirect
10. #10591089C2semidirect
11. #10591083C2semidirect
37. #63576C22semidirect
38. #63576C22semidirect
39. #63574C22semidirect
40. #63574C22semidirect
41. #63565C22semidirect
42. #63565C22semidirect
43. #63562C22semidirect
44. #63562C22semidirect
48. C2×#926D3semidirect
546. C32#3091semidirect
623. C3#82215semidirect
624. C3#82913semidirect

Maximal subgroups

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

subgroupindex
C3×#57912
C2×C3×#9262
C2×#636572
#105911382
#105911322
#105911022
#105911012
#105910912
#105910902
#105910892
#105910832
#829133
#822153