Finite Group Databasebeta

← #11788858

Subgroups — #11788858

Order 1152.

865 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5804C211yesmaximal, characteristic
2#10595506C211yesmaximal, characteristic, complemented
3C2×#63661C211yesmaximal, characteristic, complemented
4C2×C3×#834C211yesmaximal, characteristic, complemented
5C2×#63580C211yesmaximal, characteristic, complemented
6#10589187C211yesmaximal, characteristic, complemented
7#10589186C211yesmaximal, characteristic, complemented
8#71848—31nomaximal
9#70034—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C22×C3×#67C2211yescharacteristic
12C2×#3757C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C3×#953C412yescomplemented
15C2×C3×#217C2211yescharacteristic
16C2×C3×#217C2211yescharacteristic
17C2×C3×#217C2211yescharacteristic
18C3×#939—22no—
19C3×#937—21no—
20C3×#935—21no—
21C3×#929C412yescomplemented
22#67⋊Dic3—22no—
23Dic3×#67—22no—
24D3×#217—21no—
25#63955—21no—
26#63661—22no—
27C3×#834—22no—
28#63580—22no—
29C3×#534—31no—
30#5804D311yescharacteristic
31#5798—31no—
32#5486—31no—
33C2×C3×#99—31no—
34C2×#834—31no—
35C2×#834—31no—
36C2×#834—31no—
37C2×#834—61no—
38C2×#834D311yescharacteristic, complemented
39C2×#806—31no—
40#4527—31no—
41#4527—31no—
42#4527—31no—
43#4526—31no—
44C24×C32C2×C411yescharacteristic, complemented
45C24×C32C2311yescharacteristic
46C23×C3×D3D411yescharacteristic
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4—21no—
52C2×C32×D4—21no—
53C22×C32×C4C2×C411yescharacteristic, complemented
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3—21no—
56C2×C3×#67—21no—
57C2×C3×#67—21no—
58C2×C3×#67—21no—
59C2×C3×#67—21no—
60C2×C3×#67—22no—
61C2×C3×#67C2×C412yes—
62C2×C3×#67D412yes—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D411yescharacteristic
67C2×D3×Dic3—22no—
68#3757—21no—
69#3757—21no—
70#3757—21no—
71#3757D412yescomplemented
72C3×#217—21no—
73C3×#217—21no—
74C3×#217—22no—
75C3×#217—21no—
76C3×#217—21no—
77C3×#217C2×C412yescomplemented
78C3×#217D412yescomplemented
79C3×(C2×D3)⋊C4—22no—
80C3×Dic3⋊C4—22no—
81Dic3⋊Dic3—22no—
82(C2×D3)⋊Dic3—22no—
83Dic32—22no—
84#1913—91noSylow
85C22×C3×D4—21no—
86C22×C3×D4—31no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C22×#67C2×D311yescharacteristic
90C3×#123—32no—
91C3×#123—61no—
92C3×#121—62no—
93C3×#120—32no—
94C3×#120—61no—
95C2×C3×C22⋊C4—31no—
96C2×C3×C22⋊C4—31no—
97C2×C3×C22⋊C4—31no—
98#953Dic312yescomplemented
99C2×#217—31no—
100C2×#217—31no—
101C2×#217—31no—
102C2×#217—31no—
103C2×#217—61no—
104C2×#217—61no—
105C2×#217—61no—
106C2×#217C2×D311yescharacteristic
107C2×#217C2×D311yescharacteristic
108C2×#217C2×D311yescharacteristic
109#939—22no—
110#937—21no—
111#935—21no—
112D4×Dic3—62no—
113D4×Dic3—62no—
114#929Dic312yescomplemented
115C4×#67—62no—
116#926—61no—
117#67⋊C4—62no—
118D3×C22⋊C4—61no—
119#877—61no—
120C3×#99—62no—
121#834—22no—
122#834—62no—
123#834—62no—
124#834—62no—
125#834—64no—
126#806—62no—
127C23×C32—21no—
128C23×C32—21no—
129C23×C32—21no—
130C23×C32—81no—
131C23×C32—81no—
132C23×C32C22×C411yescharacteristic
133C23×C32C2×D411yescharacteristic
134C23×C32C2×D411yescharacteristic
135C23×C32C2×D411yescharacteristic
136C23×C32C2×D411yescharacteristic
137C23×C32#4111yescharacteristic
138C23×C32#4111yescharacteristic
139C22×C3×D3—21no—
140C22×C3×D3—21no—
141C22×C3×D3—81no—
142C22×C3×D3C22⋊C412yes—
143C32×D4—41no—
144C32×D4—41no—
145C32×D4—41no—
146C32×D4—41no—
147C2×C32×C4—21no—
148C2×C32×C4—21no—
149C2×C32×C4—21no—
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—41no—
152C2×C3⋊Dic3—81no—
153C2×C3⋊Dic3—81no—
154C3×#67—22no—
155C3×#67—22no—
156C3×#67—22no—
157C3×#67—22no—
158C3×#67—82no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—21no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—41no—
164C2×C3×Dic3—81no—
165C2×C3×Dic3—81no—
166C2×C3×Dic3—81no—
167C2×C3×Dic3C22⋊C412yes—
168D3×Dic3—82no—
169#534—31no—
170#518—91no—
171C2×#99—31no—
172C2×#99—91no—
173C2×#99—91no—
174#342—91no—
175#342—91no—
176C24×C3—21no—
177C24×C3—21no—
178C24×C3—31no—
179C24×C3C4×D311yescharacteristic, complemented
180C24×C3C2×Dic311yescharacteristic, complemented
181C24×C3C22×D311yescharacteristic
182C24×C3C22×D311yescharacteristic
183C23×D3#6711yescharacteristic
184C2×C3×D4—22no—
185C2×C3×D4—22no—
186C2×C3×D4—21no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—21no—
193C2×C3×D4—21no—
194C2×C3×D4—21no—
195C2×C3×D4—21no—
196C2×C3×D4—21no—
197C2×C3×D4—21no—
198C2×C3×D4—32no—
199C2×C3×D4—32no—
200C2×C3×D4—41no—
201C2×C3×D4—41no—
202C2×C3×D4—41no—
203C2×C3×D4—41no—
204C2×C3×D4—61no—
205C2×C3×D4—61no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C2×C3×D4—62no—
209C22×C3×C4—21no—
210C22×C3×C4—31no—
211C22×C3×C4—61no—
212C22×C3×C4—61no—
213C22×C3×C4—61no—
214C22×C3×C4C4×D311yescharacteristic, complemented
215C22×C3×C4C2×Dic311yescharacteristic, complemented
216C2×#67—21no—
217C2×#67—21no—
218C2×#67—21no—
219C2×#67—21no—
220C2×#67—22no—
221C2×#67C2×Dic312yes—
222C2×#67#6712yes—
223C22×Dic3—21no—
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—62no—
227C22×Dic3—61no—
228C22×Dic3—61no—
229C22×Dic3—61no—
230C22×Dic3—61no—
231C22×Dic3—121no—
232C22×Dic3—121no—
233C22×Dic3#6711yescharacteristic
234C2×C4×D3—62no—
235C3×C4⋊C4—62no—
236C3×C22⋊C4—32no—
237C3×C22⋊C4—32no—
238C3×C22⋊C4—62no—
239C3×C22⋊C4—62no—
240C3×C22⋊C4—61no—
241C3×C22⋊C4—61no—
242C3×C22⋊C4—61no—
243C3×C22⋊C4—61no—
244#217—21no—
245#217—21no—
246#217—22no—
247#217—21no—
248#217—21no—
249#217—32no—
250#217—32no—
251#217—62no—
252#217—62no—
253#217—61no—
254#217—61no—
255#217—62no—
256#217—61no—
257#217—61no—
258#217—61no—
259#217—61no—
260#217—121no—
261#217—121no—
262#217C2×Dic312yescomplemented
263#217#6712yescomplemented
264(C2×D3)⋊C4—22no—
265(C2×D3)⋊C4—62no—
266C4⋊Dic3—62no—
267Dic3⋊C4—22no—
268Dic3⋊C4—62no—
269C4×Dic3—62no—
270C4×Dic3—62no—
271C22×C32—41no—
272C22×C32—41no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32—41no—
276C22×C32—41no—
277C22×C32—41no—
278C22×C32—41no—
279C22×C32—42no—
280C22×C32—81no—
281C22×C32—81no—
282C22×C32C2×C22⋊C411yescharacteristic
283C22×C32C4×D411yescharacteristic
284C22×C32C4×D411yescharacteristic
285C22×C32#12011yescharacteristic
286C22×C32#12111yescharacteristic
287C22×C32#12111yescharacteristic
288C22×C32#12311yescharacteristic
289C2×C3×D3—22no—
290C2×C3×D3—42no—
291C2×C3×D3—42no—
292C2×C3×D3—81no—
293C32×C4—41no—
294C3⋊Dic3—42no—
295C3⋊Dic3—81no—
296C3×Dic3—22no—
297C3×Dic3—42no—
298C3×Dic3—42no—
299C3×Dic3—81no—
300C22×D4—31no—
301C22×D4D3211yescharacteristic
302#123—32no—
303#123—61no—
304#121—62no—
305#120—32no—
306#120—61no—
307C4×D4—182no—
308C4×D4—182no—
309#117—181no—
310C2×C22⋊C4—31no—
311C2×C22⋊C4—31no—
312C2×C22⋊C4—31no—
313C2×C22⋊C4—91no—
314C2×C22⋊C4—91no—
315C2×C22⋊C4—181no—
316#99—62no—
317#99—182no—
318#99—182no—
319C23×C3—22no—
320C23×C3—21no—
321C23×C3—21no—
322C23×C3—21no—
323C23×C3—21no—
324C23×C3—21no—
325C23×C3—21no—
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—21no—
331C23×C3—21no—
332C23×C3—21no—
333C23×C3—32no—
334C23×C3—41no—
335C23×C3—41no—
336C23×C3—61no—
337C23×C3—61no—
338C23×C3—81no—
339C23×C3—81no—
340C23×C3—81no—
341C23×C3—81no—
342C23×C3—82no—
343C23×C3—82no—
344C23×C3—241no—
345C23×C3C2×C4×D311yescharacteristic
346C23×C3#23511yescharacteristic
347C23×C3D3×D411yescharacteristic
348C23×C3D3×D411yescharacteristic
349C23×C3D3×D411yescharacteristic
350C23×C3D3×D411yescharacteristic
351C23×C3D3×D411yescharacteristic
352C23×C3#23711yescharacteristic
353C23×C3#23711yescharacteristic
354C23×C3#23711yescharacteristic
355C23×C3C22×Dic311yescharacteristic
356C23×C3C2×#6711yescharacteristic
357C23×C3C2×#6711yescharacteristic
358C23×C3C2×#6711yescharacteristic
359C22×D3—21no—
360C22×D3—21no—
361C22×D3—81no—
362C22×D3#21712yes—
363C3×D4—42no—
364C3×D4—42no—
365C3×D4—42no—
366C3×D4—42no—
367C3×D4—41no—
368C3×D4—41no—
369C3×D4—41no—
370C3×D4—41no—
371C3×D4—41no—
372C3×D4—41no—
373C3×D4—41no—
374C3×D4—41no—
375C3×D4—62no—
376C3×D4—62no—
377C3×D4—62no—
378C3×D4—62no—
379C3×D4—242no—
380C2×C3×C4—22no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—32no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—61no—
391C2×C3×C4—61no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—121no—
395C2×C3×C4—241no—
396C2×C3×C4—241no—
397C2×C3×C4—241no—
398#67—22no—
399#67—22no—
400#67—22no—
401#67—22no—
402#67—82no—
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—41no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—81no—
411C2×Dic3—81no—
412C2×Dic3—81no—
413C2×Dic3—122no—
414C2×Dic3—122no—
415C2×Dic3—121no—
416C2×Dic3—121no—
417C2×Dic3—242no—
418C2×Dic3—241no—
419C2×Dic3—241no—
420C2×Dic3—242no—
421C2×Dic3—242no—
422C2×Dic3—241no—
423C2×Dic3—241no—
424C2×Dic3#21712yes—
425C4×D3—242no—
426C2×C32—21no—
427C2×C32—21no—
428C2×C32—21no—
429C2×C32—21no—
430C2×C32—21no—
431C2×C32—21no—
432C2×C32—21no—
433C2×C32—81no—
434C2×C32#38611yescharacteristic
435C3×D3—42no—
436C24—31no—
437C24D3×Dic311yescharacteristic, complemented
438C24C2×D3211yescharacteristic
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—32no—
446C2×D4—32no—
447C2×D4—61no—
448C2×D4—61no—
449C2×D4—61no—
450C2×D4—61no—
451C2×D4—62no—
452C22×C4—31no—
453C22×C4—61no—
454C22×C4—61no—
455C22×C4—61no—
456C22×C4—182no—
457C22×C4—181no—
458C22×C4—181no—
459C22×C4D3×Dic311yescharacteristic, complemented
460C4⋊C4—62no—
461C4⋊C4—182no—
462C22⋊C4—32no—
463C22⋊C4—32no—
464C22⋊C4—62no—
465C22⋊C4—62no—
466C22⋊C4—61no—
467C22⋊C4—61no—
468C22⋊C4—61no—
469C22⋊C4—61no—
470C22⋊C4—92no—
471C22⋊C4—182no—
472C22⋊C4—181no—
473C22⋊C4—181no—
474C22⋊C4—181no—
475C42—182no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—21no—
482C22×C3—21no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—41no—
488C22×C3—41no—
489C22×C3—41no—
490C22×C3—41no—
491C22×C3—41no—
492C22×C3—41no—
493C22×C3—41no—
494C22×C3—41no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3—42no—
500C22×C3—42no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3—41no—
504C22×C3—41no—
505C22×C3—62no—
506C22×C3—81no—
507C22×C3—81no—
508C22×C3—81no—
509C22×C3—81no—
510C22×C3—82no—
511C22×C3—81no—
512C22×C3—81no—
513C22×C3—81no—
514C22×C3—81no—
515C22×C3—82no—
516C22×C3—82no—
517C22×C3—122no—
518C22×C3—122no—
519C22×C3—241no—
520C22×C3D3×C22⋊C411yescharacteristic
521C22×C3#67⋊C411yescharacteristic
522C22×C3#88311yescharacteristic
523C22×C3#88411yescharacteristic
524C22×C3C4×#6711yescharacteristic
525C22×C3D4×Dic311yescharacteristic
526C22×C3D4×Dic311yescharacteristic
527C22×C3#93511yescharacteristic
528C22×C3#93711yescharacteristic
529C22×C3#93711yescharacteristic
530C22×C3#93811yescharacteristic
531C22×C3#93911yescharacteristic
532C22×C3#93911yescharacteristic
533C22×C3C2×#21711yescharacteristic
534C2×D3—22no—
535C2×D3—42no—
536C2×D3—42no—
537C2×D3—81no—
538C3×C4—42no—
539C3×C4—41no—
540C3×C4—41no—
541C3×C4—62no—
542C3×C4—122no—
543C3×C4—122no—
544C3×C4—241no—
545Dic3—22no—
546Dic3—42no—
547Dic3—42no—
548Dic3—81no—
549Dic3—122no—
550Dic3—122no—
551Dic3—242no—
552Dic3—241no—
553Dic3—241no—
554Dic3—242no—
555C32#191311yescharacteristic, complemented, Sylow
556C23—21no—
557C23—21no—
558C23—21no—
559C23—32no—
560C23—61no—
561C23—61no—
562C23—81no—
563C23—81no—
564C23—241no—
565C23C2×D3×Dic311yescharacteristic
566C23#380411yescharacteristic
567C23#380511yescharacteristic
568C23D3×#6711yescharacteristic
569C23D3×#6711yescharacteristic
570C23D3×#6711yescharacteristic
571C23#381111yescharacteristic
572D4—41no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—62no—
577D4—62no—
578D4—62no—
579D4—62no—
580D4—242no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—32no—
585C2×C4—61no—
586C2×C4—61no—
587C2×C4—62no—
588C2×C4—62no—
589C2×C4—121no—
590C2×C4—182no—
591C2×C4—241no—
592C2×C4—241no—
593C2×C4—241no—
594C2×C4—361no—
595C2×C4—722no—
596C2×C4—721no—
597C2×C4—721no—
598C2×C3—22no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—41no—
615C2×C3—41no—
616C2×C3—41no—
617C2×C3—41no—
618C2×C3—41no—
619C2×C3—41no—
620C2×C3—82no—
621C2×C3—81no—
622C2×C3—81no—
623C2×C3—122no—
624C2×C3#495611yescharacteristic
625C2×C3#522011yescharacteristic
626D3—42no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—42no—
635C22—41no—
636C22—62no—
637C22—81no—
638C22—81no—
639C22—122no—
640C22—122no—
641C22—241no—
642C22D3×#21711yescharacteristic
643C22#6396911yescharacteristic
644C22#6397011yescharacteristic
645C22#6397111yescharacteristic
646C22Dic3×#6711yescharacteristic
647C22#67⋊Dic311yescharacteristic
648C22#6398311yescharacteristic
649C4—41no—
650C4—62no—
651C4—122no—
652C4—122no—
653C4—241no—
654C4—362no—
655C4—721no—
656C3—21no—
657C3#7003411yescharacteristic, complemented
658C3#7184811yescharacteristic, complemented
659C2—21no—
660C2—21no—
661C2—21no—
662C2—21no—
663C2—21no—
664C2—21no—
665C2—21no—
666C2—81no—
667C2—122no—
668C2#1059172111yescharacteristic
subgroupG/H
centerC2#10591721
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC22×C32×D4C22
socleC2×C32#386
prime radicalC3×#5804C2
cosocleC24×C32C23
hypercenterC22×D4D32
hypocenterC32#1913
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10595506C2semidirect
3. C2×#63661C2semidirect
4. C2×C3×#834C2semidirect
5. C2×#63580C2semidirect
6. #10589187C2semidirect
7. #10589186C2semidirect
14. C3×#953C4semidirect
21. C3×#929C4semidirect
38. C2×#834D3semidirect
44. C24×C32C2×C4semidirect
53. C22×C32×C4C2×C4semidirect
71. #3757D4semidirect
77. C3×#217C2×C4semidirect
78. C3×#217D4semidirect
98. #953Dic3semidirect
114. #929Dic3semidirect
179. C24×C3C4×D3semidirect
180. C24×C3C2×Dic3semidirect
214. C22×C3×C4C4×D3semidirect
215. C22×C3×C4C2×Dic3semidirect
262. #217C2×Dic3semidirect
263. #217#67semidirect
437. C24D3×Dic3semidirect
459. C22×C4D3×Dic3semidirect
555. C32#1913semidirect
657. C3#70034semidirect
658. C3#71848semidirect

Maximal subgroups

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

subgroupindex
C3×#58042
#105955062
C2×#636612
C2×C3×#8342
C2×#635802
#105891872
#105891862
#718483
#700343