Finite Group Databasebeta

← #11869687

Subgroups — #11869687

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596262C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3C2×C3×#830C211yesmaximal, characteristic, complemented
4#10591136C212yesmaximal, complemented
5#10591135C211yesmaximal, characteristic, complemented
6#10591134C212yesmaximal, complemented
7#10591133C211yesmaximal, characteristic, complemented
8#10591125C211yesmaximal, characteristic, complemented
9#10591124C211yesmaximal, characteristic, complemented
10#10591122C212yesmaximal, complemented
11#10591105C212yesmaximal, complemented
12#82215—31nomaximal
13#78591—31nomaximal
14C23×C32×C4C2211yescharacteristic
15C2×#3828C2211yescharacteristic
16#64162—21no—
17#64139C2211yescharacteristic
18#64139C2211yescharacteristic
19#64138—21no—
20C4×#638—21no—
21C4×#638—21no—
22#64135C2211yescharacteristic
23#64133C2211yescharacteristic
24#64133C2211yescharacteristic
25C2×C3×#217—21no—
26C3×#926—21no—
27C3×#926—21no—
28C3×#926C2212yes—
29C3×#926C2212yes—
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4×Dic3—21no—
33C22×C3×C3⋊C8C2212yes—
34C3×#830C2211yescharacteristic
35C3×#830C2211yescharacteristic
36C3×#830C2212yes—
37#63575C2212yescomplemented
38#63575C2212yescomplemented
39#63573C2212yescomplemented
40#63573C2212yescomplemented
41#63567C2212yescomplemented
42#63567C2212yescomplemented
43#63564C2212yescomplemented
44#63564C2212yescomplemented
45C2×C3×#117—31no—
46#5791—31no—
47#5791—31no—
48#5791—61no—
49C2×#926D311yescharacteristic, complemented
50C2×C3×C22⋊C8—31no—
51C2×#830D311yescharacteristic, complemented
52#5113—32no—
53#5106—32no—
54#5003—32no—
55#5002—32no—
56#4998—32no—
57#4996—32no—
58#4971—31no—
59#4970—31no—
60#4968—31no—
61#4967—31no—
62#4737—32no—
63#4736—31no—
64#4735—31no—
65#4723—32no—
66#4722—31no—
67#4721—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×#638—21no—
77C2×#638—21no—
78C2×#638—21no—
79#3828—24no—
80C2×C4⋊(C3⋊D3)C2311yescharacteristic
81C2×C4×C3⋊D3—21no—
82C2×#634C2311yescharacteristic
83C22×C3×Dic3—21no—
84C22×C3×Dic3—21no—
85#3757—21no—
86#3757—21no—
87#3757—21no—
88#3752—21no—
89#3752—21no—
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92#3750—21no—
93#3750—21no—
94C4×C3⋊Dic3—21no—
95C3×#217—22no—
96C3×#217—22no—
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3—21no—
99C3×C4⋊Dic3C2312yes—
100C3×C4⋊Dic3C2312yes—
101C3×C4×Dic3—22no—
102C3×C4×Dic3—22no—
103C2×C3×C3⋊C8—24no—
104C2×C3×C3⋊C8C2312yes—
105C2×C3×C3⋊C8C2312yes—
106#3091—91noSylow
107C23×C3×C4—21no—
108C23×C3×C4C2×D311yescharacteristic
109C23×C3×C4C2×D311yescharacteristic
110C2×#235—31no—
111C2×#235—31no—
112C2×#235—61no—
113C22×C3×C8—32no—
114C3×#117—32no—
115C3×#117—32no—
116C3×#117—61no—
117C3×#117—61no—
118C2×C3×C4⋊C4—31no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C22⋊C4—61no—
121C2×C3×C42—61no—
122#953—62no—
123#953—61no—
124#953—61no—
125C2×#217—21no—
126#930—31no—
127#930—31no—
128#930—31no—
129#930—31no—
130#930—61no—
131#930—61no—
132#929—62no—
133#929—61no—
134#929—61no—
135C4×#67—62no—
136C4×#67—62no—
137C4×#67—61no—
138C4×#67—61no—
139C4×#67—61no—
140C4×#67—61no—
141#926—21no—
142#926—21no—
143#926—31no—
144#926—31no—
145#926—61no—
146#926C2×D312yes—
147#926C2×D312yes—
148C2×C4⋊Dic3C2×D311yescharacteristic
149C2×C4⋊Dic3C2×D311yescharacteristic
150#924—31no—
151#924—31no—
152#924—31no—
153#924—31no—
154#924—61no—
155#924—61no—
156C2×C4×Dic3—21no—
157C22×C3⋊C8C2×D312yes—
158C3×C22⋊C8—31no—
159C3×C22⋊C8—31no—
160C3×C22⋊C8—32no—
161#830C2×D311yescharacteristic
162#830C2×D311yescharacteristic
163#830C2×D312yes—
164#821—32no—
165#821—32no—
166#818—32no—
167#818—32no—
168#817—32no—
169#817—32no—
170#816—32no—
171#816—32no—
172#810—32no—
173#810—32no—
174#809—32no—
175#809—32no—
176#808—32no—
177#808—32no—
178#807—32no—
179#807—32no—
180C23×C32—22no—
181C23×C32—22no—
182C23×C32—41no—
183C23×C32C2×D411yescharacteristic
184C23×C32C2×D411yescharacteristic
185C23×C32C2×D411yescharacteristic
186C22×C3⋊D3—21no—
187C2×C32×C4—22no—
188C2×C32×C4—22no—
189C2×C32×C4—22no—
190C2×C32×C4—22no—
191C2×C32×C4—22no—
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4C2×D411yescharacteristic
195C2×C32×C4#4114yes—
196C2×C32×C4C2411yescharacteristic
197#638—42no—
198#638—42no—
199#638—42no—
200C2×C3⋊Dic3—21no—
201C2×C3⋊Dic3—21no—
202C2×C3⋊Dic3—21no—
203C4⋊(C3⋊D3)—22no—
204C4×C3⋊D3—42no—
205#634—22no—
206C2×C3×Dic3—22no—
207C2×C3×Dic3—22no—
208C2×C3×Dic3—42no—
209C2×C3×Dic3—42no—
210C3×C3⋊C8—22no—
211C3×C3⋊C8—22no—
212#525—91no—
213C2×#117—31no—
214#485—92no—
215#484—91no—
216#483—91no—
217#482—92no—
218#481—91no—
219#480—91no—
220#427—92no—
221#416—92no—
222C2×C22⋊C8—31no—
223C24×C3—21no—
224C24×C3D1211yescharacteristic
225C24×C3#6711yescharacteristic
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×C4D1211yescharacteristic
238C22×C3×C4D1211yescharacteristic
239C22×C3×C4D1211yescharacteristic
240C22×C3×C4#6711yescharacteristic
241C22×C3×C4#6711yescharacteristic
242C22×C3×C4#6711yescharacteristic
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C2×#67—62no—
250C2×#67—62no—
251C2×#67—62no—
252C2×#67—61no—
253C2×#67—61no—
254C2×#67—61no—
255C2×#67—61no—
256C2×#67—61no—
257C2×#67—61no—
258C22×Dic3—21no—
259C22×Dic3—21no—
260#235—64no—
261#235—64no—
262#235—124no—
263C2×D12—31no—
264C2×D12—31no—
265C2×D12—61no—
266C2×C4×D3—62no—
267C2×C4×D3—61no—
268C2×C4×D3—61no—
269C2×Dic6—31no—
270C2×Dic6—31no—
271C2×Dic6—61no—
272C2×C3×C8—32no—
273C2×C3×C8—32no—
274C2×C3×C8—64no—
275C3×C4⋊C4—32no—
276C3×C4⋊C4—32no—
277C3×C4⋊C4—61no—
278C3×C4⋊C4—61no—
279C3×C22⋊C4—62no—
280C3×C22⋊C4—62no—
281C3×C42—62no—
282C3×C42—62no—
283#217—22no—
284#217—22no—
285#217—62no—
286#217—62no—
287#217—62no—
288#217—61no—
289#217—61no—
290#217—61no—
291#217—61no—
292#217—61no—
293#217—61no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—62no—
296(C2×D3)⋊C4—61no—
297(C2×D3)⋊C4—61no—
298(C2×D3)⋊C4—61no—
299(C2×D3)⋊C4—61no—
300C4⋊Dic3—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—31no—
303C4⋊Dic3—31no—
304C4⋊Dic3—31no—
305C4⋊Dic3—31no—
306C4⋊Dic3—61no—
307C4⋊Dic3—61no—
308C4⋊Dic3C22×D312yes—
309C4⋊Dic3C22×D312yes—
310Dic3⋊C4—62no—
311Dic3⋊C4—62no—
312Dic3⋊C4—61no—
313Dic3⋊C4—61no—
314Dic3⋊C4—61no—
315Dic3⋊C4—61no—
316C4×Dic3—22no—
317C4×Dic3—22no—
318C4×Dic3—62no—
319C4×Dic3—61no—
320C4×Dic3—61no—
321C2×C3⋊C8—24no—
322C2×C3⋊C8C22×D312yes—
323C2×C3⋊C8C22×D312yes—
324C22×C32—21no—
325C22×C32—21no—
326C22×C32—21no—
327C22×C32—21no—
328C22×C32—21no—
329C22×C32—21no—
330C22×C32—21no—
331C22×C32—44no—
332C22×C32#12312yes—
333C22×C32#13512yes—
334C22×C32C22×D411yescharacteristic
335C2×C3⋊D3—41no—
336C2×C3⋊D3—41no—
337C2×C3⋊D3—41no—
338C32×C4—21no—
339C32×C4—21no—
340C32×C4#12312yes—
341C32×C4C2×#4112yes—
342C3⋊Dic3—41no—
343C3⋊Dic3—41no—
344C3⋊Dic3—41no—
345C3×Dic3—42no—
346C3×Dic3—42no—
347C2×#41—91no—
348C23×C4D3211yescharacteristic
349C22×C8—32no—
350#123—181no—
351C22⋊Q8—91no—
352C22⋊Q8—91no—
353#121—91no—
354#121—91no—
355#120—181no—
356C4×D4—181no—
357C4×D4—181no—
358#117—32no—
359#117—32no—
360#117—61no—
361#117—61no—
362#117—91no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—31no—
365C2×C22⋊C4—61no—
366C2×C42—61no—
367#107—92no—
368#107—92no—
369#106—92no—
370#106—92no—
371#103—92no—
372#103—92no—
373#102—92no—
374#102—92no—
375C22⋊C8—31no—
376C22⋊C8—31no—
377C22⋊C8—32no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—42no—
386C23×C3—42no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—42no—
390C23×C3C2×D1211yescharacteristic
391C23×C3C2×D1211yescharacteristic
392C23×C3C2×D1211yescharacteristic
393C23×C3C2×#6711yescharacteristic
394C23×C3C2×#6711yescharacteristic
395C23×C3C2×#6711yescharacteristic
396C22×D3—62no—
397C22×D3—61no—
398C22×D3—61no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—24no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—42no—
415C2×C3×C4—42no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—42no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—122no—
422C2×C3×C4—122no—
423C2×C3×C4C2×D1211yescharacteristic
424C2×C3×C4C2×D1211yescharacteristic
425C2×C3×C4C2×D1211yescharacteristic
426C2×C3×C4#23514yes—
427C2×C3×C4#23714yes—
428C2×C3×C4C2×#6711yescharacteristic
429C2×C3×C4C2×#6711yescharacteristic
430C2×C3×C4C2×#6711yescharacteristic
431C2×C3×C4C23×D311yescharacteristic
432C2×C3×C4C23×D311yescharacteristic
433#67—124no—
434#67—124no—
435#67—122no—
436#67—122no—
437#67—124no—
438#67—122no—
439#67—122no—
440#67—122no—
441#67—122no—
442C2×Dic3—22no—
443C2×Dic3—22no—
444C2×Dic3—42no—
445C2×Dic3—42no—
446C2×Dic3—62no—
447C2×Dic3—62no—
448C2×Dic3—62no—
449C2×Dic3—61no—
450C2×Dic3—61no—
451C2×Dic3—61no—
452C2×Dic3—61no—
453C2×Dic3—61no—
454C2×Dic3—61no—
455D12—62no—
456D12—62no—
457D12—122no—
458C4×D3—124no—
459C4×D3—122no—
460C4×D3—122no—
461Dic6—62no—
462Dic6—62no—
463Dic6—122no—
464C3×C8—62no—
465C3×C8—62no—
466C3⋊C8—22no—
467C3⋊C8—22no—
468C2×C32—22no—
469C2×C32—22no—
470C2×C32—41no—
471C2×C32C2×#12311yescharacteristic
472C2×C32C2×#13511yescharacteristic
473C2×C32#57511yescharacteristic
474C3⋊D3—81no—
475C24#62611yescharacteristic
476#41—184no—
477C2×Q8—91no—
478C2×D4—91no—
479C2×D4—181no—
480C2×D4—181no—
481C2×D4—181no—
482C22×C4—24no—
483C22×C4—61no—
484C22×C4—61no—
485C22×C4—181no—
486C22×C4#62611yescharacteristic
487C22×C4#62611yescharacteristic
488C22×C4#62611yescharacteristic
489C22×C4C2×D3211yescharacteristic
490C22×C4C2×D3211yescharacteristic
491C22×C4C2×D3211yescharacteristic
492C2×C8—32no—
493C2×C8—32no—
494C2×C8—64no—
495C4⋊C4—32no—
496C4⋊C4—32no—
497C4⋊C4—61no—
498C4⋊C4—61no—
499C4⋊C4—91no—
500C4⋊C4—91no—
501C4⋊C4—181no—
502C4⋊C4—181no—
503C22⋊C4—62no—
504C22⋊C4—62no—
505C22⋊C4—181no—
506C22⋊C4—181no—
507C22⋊C4—181no—
508C22⋊C4—181no—
509C22⋊C4—181no—
510C42—62no—
511C42—62no—
512C42—181no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—21no—
521C22×C3—22no—
522C22×C3—21no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—21no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—41no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—41no—
535C22×C3—41no—
536C22×C3—41no—
537C22×C3—44no—
538C22×C3—44no—
539C22×C3—48no—
540C22×C3#88612yes—
541C22×C3#90412yes—
542C22×C3#92912yes—
543C22×C3#95012yes—
544C22×C3C22×D1211yescharacteristic
545C22×C3C22×#6711yescharacteristic
546C2×D3—122no—
547C2×D3—122no—
548C2×D3—122no—
549C2×D3—121no—
550C2×D3—121no—
551C2×D3—121no—
552C2×D3—121no—
553C2×D3—121no—
554C2×D3—121no—
555C3×C4—21no—
556C3×C4—21no—
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—22no—
560C3×C4—22no—
561C3×C4—41no—
562C3×C4—41no—
563C3×C4—122no—
564C3×C4—122no—
565C3×C4#88612yes—
566C3×C4#92912yes—
567C3×C4C2×#23512yes—
568C3×C4C2×#23712yes—
569Dic3—42no—
570Dic3—42no—
571Dic3—122no—
572Dic3—122no—
573Dic3—122no—
574Dic3—121no—
575Dic3—121no—
576Dic3—121no—
577Dic3—121no—
578Dic3—121no—
579Dic3—121no—
580C32#309111yescharacteristic, complemented, Sylow
581C23—22no—
582C23—22no—
583C23—41no—
584C23—181no—
585C23C2×#62611yescharacteristic
586C23C2×#62611yescharacteristic
587C23C2×#62611yescharacteristic
588Q8—182no—
589D4—182no—
590D4—362no—
591D4—362no—
592D4—362no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—62no—
599C2×C4—62no—
600C2×C4—122no—
601C2×C4—122no—
602C2×C4—181no—
603C2×C4—181no—
604C2×C4—181no—
605C2×C4—362no—
606C2×C4#380414yes—
607C2×C4C2×#62611yescharacteristic
608C2×C4C2×#62611yescharacteristic
609C2×C4C2×#62611yescharacteristic
610C2×C4C22×D3211yescharacteristic
611C8—62no—
612C8—62no—
613C2×C3—22no—
614C2×C3—22no—
615C2×C3—22no—
616C2×C3—22no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—42no—
621C2×C3—42no—
622C2×C3—42no—
623C2×C3—41no—
624C2×C3—41no—
625C2×C3C2×#88611yescharacteristic
626C2×C3C2×#90411yescharacteristic
627C2×C3#574811yescharacteristic
628C2×C3C2×#92911yescharacteristic
629C2×C3C2×#95011yescharacteristic
630C2×C3#582211yescharacteristic
631D3—242no—
632D3—241no—
633D3—241no—
634C22—21no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—21no—
639C22—21no—
640C22—21no—
641C22—44no—
642C22—361no—
643C22—361no—
644C22—361no—
645C22#6382912yes—
646C22#6396612yes—
647C22C22×#62611yescharacteristic
648C4—21no—
649C4—21no—
650C4—122no—
651C4—122no—
652C4—361no—
653C4—361no—
654C4—361no—
655C4#6396612yes—
656C4C2×#380412yes—
657C3—21no—
658C3#7859111yescharacteristic, complemented
659C3#8221511yescharacteristic, complemented
660C2—22no—
661C2—22no—
662C2—41no—
663C2—721no—
664C2C2×#6382911yescharacteristic
665C2#1059479511yescharacteristic
666C2C2×#6396611yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC22×C32C22×D4
prime radical#10596262C2
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×C3×#830C2semidirect
4. #10591136C2semidirect
5. #10591135C2semidirect
6. #10591134C2semidirect
7. #10591133C2semidirect
8. #10591125C2semidirect
9. #10591124C2semidirect
10. #10591122C2semidirect
11. #10591105C2semidirect
37. #63575C22semidirect
38. #63575C22semidirect
39. #63573C22semidirect
40. #63573C22semidirect
41. #63567C22semidirect
42. #63567C22semidirect
43. #63564C22semidirect
44. #63564C22semidirect
49. C2×#926D3semidirect
51. C2×#830D3semidirect
580. C32#3091semidirect
658. C3#78591semidirect
659. C3#82215semidirect

Maximal subgroups

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

subgroupindex
#105962622
C2×C3×#9262
C2×C3×#8302
#105911362
#105911352
#105911342
#105911332
#105911252
#105911242
#105911222
#105911052
#822153
#785913