Finite Group Databasebeta

← #11865773

Subgroups — #11865773

Order 1152.

1062 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#237C211yesmaximal, characteristic, complemented
2C2×#63935C212yesmaximal, complemented
3#10593970C211yesmaximal, characteristic, complemented
4#10592714C211yesmaximal, characteristic, complemented
5C3×#5019C211yesmaximal, characteristic, complemented
6#10591471C212yesmaximal, complemented
7#10590610C212yesmaximal, complemented
8#10590536C212yesmaximal, complemented
9#10590384C211yesmaximal, characteristic, complemented
10#10590367C211yesmaximal, characteristic, complemented
11D3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12#82525—31nomaximal
13#80427—31nomaximal
14C2×C3×#237C2211yescharacteristic
15C2×#3799C2212yes—
16C32×C4×D4C2211yescharacteristic
17C2×#3753C2212yes—
18#64083C2211yescharacteristic
19C3×D4×Dic3C2211yescharacteristic
20C2×C3×#214C2212yes—
21C3×C4×#67—21no—
22C2×C3×C4×Dic3—21no—
23C3×#892C2211yescharacteristic
24C3×#887C2211yescharacteristic
25C3×#67⋊C4—21no—
26C3×#877—21no—
27C3×C42×D3C2211yescharacteristic
28C3×#869C2211yescharacteristic
29C3×C4×Dic6C2211yescharacteristic
30#63935—28no—
31#63909—21no—
32#63909—21no—
33#63894—21no—
34#63894—21no—
35#63864C2212yes—
36C2×#3718C2212yes—
37C2×#3717C2212yes—
38C2×D3×C3⋊C8C2212yes—
39#63636C2212yes—
40C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
41C3×#810C2212yes—
42C3×C4⋊(C3⋊C8)C2211yescharacteristic
43Dic3⋊(C3⋊C8)C2212yes—
44#63565C2212yes—
45#63564C2212yes—
46C3×C4×#41—31no—
47C2×#950—32no—
48C2×#916—32no—
49#5725—31no—
50C4×#237D311yescharacteristic, complemented
51#5477—31no—
52C3×#461—31no—
53#5165—32no—
54#5090—31no—
55#5031—31no—
56#5028—32no—
57#5027—31no—
58#5019D311yescharacteristic, complemented
59#5016—32no—
60#5015—31no—
61#5015—31no—
62#5015—61no—
63#5002—32no—
64C2×C4⋊(C3⋊C8)—31no—
65#4848—31no—
66D3×C4⋊C8—31no—
67#4804—32no—
68#4798—32no—
69C2×C32×D4C2311yescharacteristic
70C22×C32×C4—21no—
71C2×C4⋊(C3⋊D3)—21no—
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)C2312yes—
74C2×C3×#67—21no—
75C22×C3×Dic3—21no—
76C22×C3×Dic3—21no—
77C3×#237—22no—
78C3×#237D414yescomplemented
79C2×C3×C4×D3D411yescharacteristic
80C2×C3×C4×D3D411yescharacteristic
81C2×C3×C4×D3C2311yescharacteristic
82C2×C3×Dic6C2312yes—
83C2×C3×Dic6C2311yescharacteristic
84C2×#626—22no—
85C2×#624—22no—
86#3799—24no—
87#3799—24no—
88C32×C4⋊C4C2311yescharacteristic
89C32×C22⋊C4—21no—
90C32×C42C2311yescharacteristic
91#3753—24no—
92C2×C3⋊(C3⋊C8)C2312yes—
93C3×#217—21no—
94C3×#214—24no—
95C3×(C2×D3)⋊C4—21no—
96C3×C4⋊Dic3—21no—
97C3×C4⋊Dic3—21no—
98C3×C4⋊Dic3C2311yescharacteristic
99C3×Dic3⋊C4—21no—
100C3×Dic3⋊C4—21no—
101C3×C4×Dic3—21no—
102C3×C4×Dic3—21no—
103C3×C4×Dic3—21no—
104C3×C4×Dic3D411yescharacteristic
105C3×C4×Dic3D411yescharacteristic
106C3×C4×Dic3C2311yescharacteristic
107C2×C3×C3⋊C8C2312yes—
108#3722—22no—
109#3722—22no—
110#3718—24no—
111#3717—24no—
112D3×C3⋊C8—24no—
113#3035—91noSylow
114C2×C3×#41—31no—
115C2×#239—32no—
116C2×#237C2×D311yescharacteristic
117C2×#235—32no—
118C2×C3×SD16—32no—
119C3×C4⋊Q8—31no—
120C3×C4×Q8—31no—
121C3×C4×Q8—31no—
122C3×C4×D4—21no—
123C3×C4×D4—31no—
124C3×C4×D4—61no—
125C3×C4×D4—61no—
126C3×C4×D4C2×D311yescharacteristic
127C3×C4×D4C2×D311yescharacteristic
128C3×#117—31no—
129C3×#117—61no—
130C2×C3×C42—31no—
131C2×C3×C42—61no—
132#950—68no—
133#947—32no—
134C2×#216—32no—
135C2×#216—32no—
136C2×#215—32no—
137D4×Dic3C2×D311yescharacteristic
138C2×#214C2×D312yes—
139C2×#213—32no—
140C2×#213—32no—
141C2×#213—62no—
142#930—61no—
143#930—61no—
144C4×#67—21no—
145C2×C4×Dic3—21no—
146C22×C3⋊C8—32no—
147#916—68no—
148C2×#204—32no—
149C2×D3×C8—32no—
150#895—61no—
151#895—61no—
152#893—61no—
153#893—61no—
154#892C2×D311yescharacteristic
155#887C2×D311yescharacteristic
156#67⋊C4—21no—
157#877—21no—
158#875—32no—
159#874—31no—
160#874—31no—
161#874—61no—
162C4×D12—61no—
163C4×D12—61no—
164C42×D3C2×D311yescharacteristic
165#869C2×D311yescharacteristic
166C4×Dic6C2×D311yescharacteristic
167C3×C4⋊C8—31no—
168C3×#103—32no—
169#835—32no—
170#821—32no—
171Dic3⋊C8—32no—
172#810—32no—
173#810C2×D312yes—
174#809—32no—
175#809—32no—
176#809—32no—
177#809—62no—
178C4⋊(C3⋊C8)—31no—
179C4⋊(C3⋊C8)—31no—
180C4⋊(C3⋊C8)—32no—
181C4⋊(C3⋊C8)—61no—
182C4⋊(C3⋊C8)C2×D311yescharacteristic
183C23×C32—21no—
184C22×C3⋊D3—22no—
185C22×C3×D3C2×D411yescharacteristic
186C32×D4—21no—
187C32×D4C2×D412yes—
188C2×C32×C4—21no—
189C2×C32×C4—42no—
190C2×C32×C4C2×D411yescharacteristic
191C2×C32×C4C2×D411yescharacteristic
192C2×C32×C4C2411yescharacteristic
193C4⋊(C3⋊D3)—22no—
194C4⋊(C3⋊D3)—22no—
195C4⋊(C3⋊D3)—42no—
196C4⋊(C3⋊D3)—42no—
197C3×#67—24no—
198C2×C3×Dic3—21no—
199C2×C3×Dic3—24no—
200C2×C3×Dic3—22no—
201C2×C3×Dic3—21no—
202C2×C3×Dic3—42no—
203C2×C3×Dic3C2×D411yescharacteristic
204C2×C3×Dic3C2×D411yescharacteristic
205C2×C3×Dic3C2×D411yescharacteristic
206C3×C4×D3—22no—
207C3×C4×D3—41no—
208C3×C4×D3C2×D412yes—
209C3×C4×D3#4112yes—
210C3×Dic6—21no—
211C3×Dic6—22no—
212C3×Dic6—22no—
213C3×Dic6C2×D412yes—
214#626—44no—
215#624—44no—
216C3⋊(C3⋊C8)—22no—
217C3×C3⋊C8—22no—
218C2×#135—92no—
219#532—91no—
220C4×#41—31no—
221#464—92no—
222#463—92no—
223#462—91no—
224#461—31no—
225#460—91no—
226#459—91no—
227C2×C4⋊C8—91no—
228#416—92no—
229C3×#41—34no—
230C3×#41—62no—
231C2×C3×Q8—31no—
232C2×C3×Q8—32no—
233C2×C3×D4—21no—
234C2×C3×D4—61no—
235C2×C3×D4C22×D311yescharacteristic
236C2×C3×D4C22×D311yescharacteristic
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—31no—
240C22×C3×C4—31no—
241C22×C3×C4—31no—
242C22×C3×C4—41no—
243C22×C3×C4—61no—
244C22×C3×C4—61no—
245C2×#67—21no—
246C2×#67—62no—
247C22×Dic3—21no—
248C22×Dic3—21no—
249#239—64no—
250#239—64no—
251#237—22no—
252#237D1214yescomplemented
253#235—64no—
254#235—64no—
255C2×D12—32no—
256C2×D12—32no—
257C2×D12—62no—
258C2×D12—62no—
259C2×D12—61no—
260C2×D12—61no—
261C2×D12—61no—
262C2×D12—61no—
263C2×D12—121no—
264C2×D12—121no—
265C2×C4×D3—62no—
266C2×C4×D3—62no—
267C2×C4×D3#6711yescharacteristic
268C2×C4×D3#6711yescharacteristic
269C2×C4×D3C22×D311yescharacteristic
270C2×Dic6C22×D312yes—
271C2×Dic6C22×D311yescharacteristic
272C3×SD16—64no—
273C2×C3×C8—32no—
274C3×C4⋊C4—21no—
275C3×C4⋊C4—31no—
276C3×C4⋊C4—61no—
277C3×C4⋊C4—61no—
278C3×C4⋊C4—61no—
279C3×C4⋊C4—61no—
280C3×C4⋊C4C22×D311yescharacteristic
281C3×C4⋊C4C22×D311yescharacteristic
282C3×C22⋊C4—21no—
283C3×C22⋊C4—21no—
284C3×C22⋊C4—41no—
285C3×C22⋊C4—61no—
286C3×C22⋊C4—61no—
287C3×C42—21no—
288C3×C42—31no—
289C3×C42—31no—
290C3×C42—31no—
291C3×C42—61no—
292C3×C42—61no—
293C3×C42—61no—
294C3×C42C22×D311yescharacteristic
295C3×C42C22×D311yescharacteristic
296#217—21no—
297#216—64no—
298#216—64no—
299#215—64no—
300#214—24no—
301#213—64no—
302#213—64no—
303#213—124no—
304(C2×D3)⋊C4—21no—
305(C2×D3)⋊C4—62no—
306(C2×D3)⋊C4—62no—
307(C2×D3)⋊C4—62no—
308(C2×D3)⋊C4—62no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4⋊Dic3C22×D311yescharacteristic
312Dic3⋊C4—21no—
313Dic3⋊C4—21no—
314C4×Dic3—21no—
315C4×Dic3—21no—
316C4×Dic3—21no—
317C4×Dic3#6711yescharacteristic
318C4×Dic3#6711yescharacteristic
319C4×Dic3C22×D311yescharacteristic
320C2×C3⋊C8—32no—
321C2×C3⋊C8—32no—
322C2×C3⋊C8—62no—
323C2×C3⋊C8—64no—
324C2×C3⋊C8C22×D312yes—
325#204—64no—
326D3×C8—64no—
327C22×C32—22no—
328C22×C32—41no—
329C22×C32—41no—
330C22×C32C22×D411yescharacteristic
331C2×C3⋊D3—42no—
332C2×C3⋊D3—42no—
333C2×C3⋊D3—42no—
334C2×C3×D3—21no—
335C2×C3×D3—21no—
336C2×C3×D3#12112yes—
337C32×C4—21no—
338C32×C4—41no—
339C32×C4#13512yescomplemented
340C32×C4C22×D411yescharacteristic
341C32×C4C2×#4111yescharacteristic
342C3×Dic3—22no—
343C3×Dic3—21no—
344C3×Dic3—21no—
345C3×Dic3—42no—
346C3×Dic3—41no—
347C3×Dic3#12112yes—
348C2×#41—31no—
349C2×#41—92no—
350#135—188no—
351C2×Q16—92no—
352C2×SD16—32no—
353C2×SD16—92no—
354C2×D8—92no—
355C22×C8—92no—
356C4⋊Q8—31no—
357#127—91no—
358#124—92no—
359#121—181no—
360#121—181no—
361C4×Q8—31no—
362C4×Q8—31no—
363C4×D4—31no—
364C4×D4—61no—
365C4×D4—61no—
366C4×D4—181no—
367C4×D4—181no—
368C4×D4D3211yescharacteristic
369#117—31no—
370#117—61no—
371C2×C42—31no—
372C2×C42—61no—
373C4⋊C8—31no—
374C4⋊C8—92no—
375C4⋊C8—91no—
376#103—32no—
377#103—92no—
378#102—92no—
379#102—92no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—31no—
383C23×C3—41no—
384C22×D3—62no—
385C22×D3—62no—
386C22×D3—122no—
387C22×D3C2×#6711yescharacteristic
388C3×Q8—32no—
389C3×Q8—61no—
390C3×Q8—62no—
391C3×Q8—62no—
392C3×D4—21no—
393C3×D4—21no—
394C3×D4—22no—
395C3×D4—41no—
396C3×D4—64no—
397C3×D4C2×D1212yes—
398C3×D4D3×D412yes—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—31no—
405C2×C3×C4—32no—
406C2×C3×C4—32no—
407C2×C3×C4—31no—
408C2×C3×C4—31no—
409C2×C3×C4—41no—
410C2×C3×C4—42no—
411C2×C3×C4—42no—
412C2×C3×C4—64no—
413C2×C3×C4—61no—
414C2×C3×C4—62no—
415C2×C3×C4—61no—
416C2×C3×C4—62no—
417C2×C3×C4—82no—
418C2×C3×C4—121no—
419C2×C3×C4—122no—
420C2×C3×C4D3×D411yescharacteristic
421C2×C3×C4D3×D411yescharacteristic
422C2×C3×C4C2×#6711yescharacteristic
423C2×C3×C4C2×#6711yescharacteristic
424C2×C3×C4C23×D311yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426#67—24no—
427#67—124no—
428C2×Dic3—21no—
429C2×Dic3—24no—
430C2×Dic3—22no—
431C2×Dic3—21no—
432C2×Dic3—42no—
433C2×Dic3C2×#6711yescharacteristic
434C2×Dic3C2×#6711yescharacteristic
435C2×Dic3C2×#6711yescharacteristic
436D12—62no—
437D12—62no—
438D12—62no—
439D12—62no—
440D12—122no—
441D12—122no—
442D12—122no—
443D12—122no—
444D12—124no—
445D12—122no—
446D12—122no—
447D12—242no—
448D12—242no—
449C4×D3—22no—
450C4×D3—41no—
451C4×D3—124no—
452C4×D3—124no—
453C4×D3C2×D1212yes—
454C4×D3#23512yes—
455Dic6—21no—
456Dic6—22no—
457Dic6—22no—
458Dic6C2×D1212yes—
459C3×C8—62no—
460C3⋊C8—22no—
461C3⋊C8—62no—
462C3⋊C8—62no—
463C3⋊C8—122no—
464C2×C32—42no—
465C2×C32C2×#12111yescharacteristic
466C2×C32C2×#13511yescharacteristic
467C2×C32#57511yescharacteristic
468C3⋊D3—82no—
469C3×D3—22no—
470#41—34no—
471#41—62no—
472#41—184no—
473#41—184no—
474C2×Q8—31no—
475C2×Q8—32no—
476C2×D4—61no—
477C2×D4—92no—
478C2×D4—182no—
479C2×D4—181no—
480C2×D4—181no—
481C2×D4C2×D3211yescharacteristic
482C22×C4—21no—
483C22×C4—31no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—61no—
487C22×C4—61no—
488C22×C4—182no—
489Q16—184no—
490SD16—64no—
491SD16—184no—
492D8—184no—
493C2×C8—32no—
494C2×C8—92no—
495C2×C8—184no—
496C4⋊C4—31no—
497C4⋊C4—61no—
498C4⋊C4—61no—
499C4⋊C4—61no—
500C4⋊C4—61no—
501C4⋊C4C2×D3211yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—61no—
504C22⋊C4—61no—
505C22⋊C4—182no—
506C22⋊C4—182no—
507C42—31no—
508C42—31no—
509C42—31no—
510C42—61no—
511C42—61no—
512C42—61no—
513C42C2×D3211yescharacteristic
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—21no—
517C22×C3—32no—
518C22×C3—42no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—61no—
524C22×C3—61no—
525C22×C3—81no—
526C22×C3—81no—
527C22×C3C2×D3×D411yescharacteristic
528C22×C3C22×#6711yescharacteristic
529C2×D3—21no—
530C2×D3—21no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—122no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—122no—
537C2×D3—242no—
538C2×D3—242no—
539C2×D3—242no—
540C2×D3#93012yes—
541C3×C4—21no—
542C3×C4—21no—
543C3×C4—21no—
544C3×C4—21no—
545C3×C4—22no—
546C3×C4—32no—
547C3×C4—41no—
548C3×C4—41no—
549C3×C4—41no—
550C3×C4—61no—
551C3×C4—61no—
552C3×C4—62no—
553C3×C4—81no—
554C3×C4—121no—
555C3×C4—122no—
556C3×C4#91612yescomplemented
557C3×C4#95012yescomplemented
558C3×C4C22×D1211yescharacteristic
559C3×C4C2×#23511yescharacteristic
560C3×C4C2×D3×D411yescharacteristic
561C3×C4D3×#4111yescharacteristic
562Dic3—22no—
563Dic3—21no—
564Dic3—21no—
565Dic3—41no—
566Dic3—42no—
567Dic3#93012yes—
568C32#303511yescharacteristic, complemented, Sylow
569C23—21no—
570C23—31no—
571C23—182no—
572Q8—32no—
573Q8—61no—
574Q8—62no—
575Q8—62no—
576D4—21no—
577D4—64no—
578D4—182no—
579D4—182no—
580D4—362no—
581D4—364no—
582D4—362no—
583D4D3×D1212yes—
584C2×C4—21no—
585C2×C4—31no—
586C2×C4—32no—
587C2×C4—32no—
588C2×C4—31no—
589C2×C4—31no—
590C2×C4—42no—
591C2×C4—64no—
592C2×C4—61no—
593C2×C4—62no—
594C2×C4—61no—
595C2×C4—62no—
596C2×C4—121no—
597C2×C4—122no—
598C2×C4—364no—
599C2×C4D3×#6711yescharacteristic
600C2×C4D3×#6711yescharacteristic
601C2×C4C22×D3211yescharacteristic
602C8—62no—
603C8—182no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—42no—
608C2×C3—42no—
609C2×C3—62no—
610C2×C3—82no—
611C2×C3D3×#12111yescharacteristic
612C2×C3C2×#91611yescharacteristic
613C2×C3#577711yescharacteristic
614C2×C3C2×#93011yescharacteristic
615C2×C3C2×#95011yescharacteristic
616C2×C3#582211yescharacteristic
617D3—22no—
618D3—242no—
619D3—242no—
620D3—482no—
621C22—22no—
622C22—32no—
623C22—41no—
624C22—41no—
625C22—61no—
626C22—61no—
627C22—362no—
628C22—362no—
629C22—362no—
630C22C2×D3×#6711yescharacteristic
631C4—21no—
632C4—32no—
633C4—41no—
634C4—61no—
635C4—61no—
636C4—62no—
637C4—121no—
638C4—122no—
639C4#6393512yescomplemented
640C4C2×D3×D1211yescharacteristic
641C4D3×#23511yescharacteristic
642C3—21no—
643C3#8042711yescharacteristic, complemented
644C3#8252511yescharacteristic, complemented
645C2—42no—
646C2—62no—
647C2—722no—
648C2D3×#93011yescharacteristic
649C2C2×#6393511yescharacteristic
650C2#1059547011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3035
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
1. C3×C4×#237C2semidirect
2. C2×#63935C2semidirect
3. #10593970C2semidirect
4. #10592714C2semidirect
5. C3×#5019C2semidirect
6. #10591471C2semidirect
7. #10590610C2semidirect
8. #10590536C2semidirect
9. #10590384C2semidirect
10. #10590367C2semidirect
11. D3×C4⋊(C3⋊C8)C2semidirect
50. C4×#237D3semidirect
58. #5019D3semidirect
78. C3×#237D4semidirect
252. #237D12semidirect
339. C32×C4#135semidirect
556. C3×C4#916semidirect
557. C3×C4#950semidirect
568. C32#3035semidirect
639. C4#63935semidirect
643. C3#80427semidirect
644. C3#82525semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2372
C2×#639352
#105939702
#105927142
C3×#50192
#105914712
#105906102
#105905362
#105903842
#105903672
D3×C4⋊(C3⋊C8)2
#825253
#804273