Finite Group Databasebeta

← #11788853

Subgroups — #11788853

Order 1152.

929 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595957C211yesmaximal, characteristic, complemented
2#10595519C211yesmaximal, characteristic
3C2×C3×#806C211yesmaximal, characteristic, complemented
4C2×#63581C211yesmaximal, characteristic, complemented
5C2×#63580C211yesmaximal, characteristic, complemented
6C3×#4527C211yesmaximal, characteristic, complemented
7#10589186C211yesmaximal, characteristic, complemented
8#70034—31nomaximal
9#68964—31nomaximal
10C22×#638C2211yescharacteristic
11C22×C3×#67C2211yescharacteristic
12C2×C32×C22⋊C4C2211yescharacteristic
13C2×#3757C2211yescharacteristic
14C4×#638—22no—
15#64090—22no—
16C22⋊C4×C3⋊D3—21no—
17#64086—21no—
18C2×C3×#217C2211yescharacteristic
19C2×C3×#217C2211yescharacteristic
20C2×C3×#217C2211yescharacteristic
21#63981—21no—
22#63978—22no—
23#63977C412yescomplemented
24#63966C412yescomplemented
25#63962—21no—
26C3×#806—22no—
27#63581—22no—
28#63580—22no—
29#5804—31no—
30#5493—31no—
31#5486—31no—
32#5486—31no—
33#5486—61no—
34C2×C3×#99—31no—
35C2×#834—31no—
36C2×#806—31no—
37C2×#806—31no—
38C2×#806—31no—
39C2×#806D311yescharacteristic, complemented
40C3×#342—31no—
41#4527—31no—
42#4527D311yescharacteristic, complemented
43#4526—31no—
44C24×C32C2311yescharacteristic
45C23×C3⋊D3D411yescharacteristic
46C23×C3×D3C2×C411yescharacteristic, complemented
47C22×C32×C4—21no—
48C2×#638—21no—
49C2×#638—21no—
50C2×#638—21no—
51C2×#638—21no—
52C2×#638C2×C412yes—
53C2×#638D412yes—
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3D411yescharacteristic
56C2×C4×C3⋊D3—22no—
57C2×C3×#67—21no—
58C2×C3×#67—21no—
59C2×C3×#67—21no—
60C2×C3×#67—21no—
61C2×C3×#67—21no—
62C2×C3×#67—21no—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3C2×C411yescharacteristic, complemented
67C2×#626—22no—
68C32×C22⋊C4—21no—
69C32×C22⋊C4D412yescomplemented
70#3757—21no—
71#3757D412yescomplemented
72#3752—22no—
73#3750—22no—
74C4×C3⋊Dic3—22no—
75C3×#217—21no—
76C3×#217—21no—
77C3×#217—21no—
78C3×#217—21no—
79C3×#217—21no—
80C3×#217C2×C412yescomplemented
81Dic3⋊Dic3—22no—
82#3722—22no—
83(C2×D3)⋊Dic3—22no—
84#1913—91noSylow
85C22×C3×D4—31no—
86C22×#67—31no—
87C22×#67—31no—
88C22×#67—61no—
89C22×#67C2×D311yescharacteristic
90C2×C3×C22⋊C4—21no—
91C2×C3×C22⋊C4—31no—
92C2×C3×C22⋊C4—31no—
93C2×C3×C22⋊C4—31no—
94C2×C3×C22⋊C4C2×D311yescharacteristic
95C2×C3×C22⋊C4C2×D311yescharacteristic
96#953—32no—
97C2×#217—31no—
98C2×#217—31no—
99C2×#217—61no—
100C2×#217C2×D311yescharacteristic
101C2×#217C2×D311yescharacteristic
102C2×#217C2×D311yescharacteristic
103#939—62no—
104#937—61no—
105#935—61no—
106#930—62no—
107#929—32no—
108C4×#67—62no—
109C4×#67—62no—
110C4×#67—64no—
111#886—32no—
112#886—61no—
113#882—32no—
114#882—61no—
115#67⋊C4—64no—
116#67⋊C4—62no—
117#67⋊C4—62no—
118D3×C22⋊C4—61no—
119D3×C22⋊C4—61no—
120D3×C22⋊C4—62no—
121#877—61no—
122#877—61no—
123#877—62no—
124C3×#99—62no—
125#834—62no—
126#806—22no—
127#806—62no—
128#806—62no—
129#806—62no—
130C23×C32—81no—
131C23×C32C22×C411yescharacteristic
132C23×C32C2×D411yescharacteristic
133C23×C32C2×D411yescharacteristic
134C23×C32C2×D411yescharacteristic
135C23×C32C2×D411yescharacteristic
136C23×C32#4111yescharacteristic
137C23×C32#4111yescharacteristic
138C22×C3⋊D3—21no—
139C22×C3⋊D3—21no—
140C22×C3⋊D3—81no—
141C22×C3⋊D3C22⋊C412yes—
142C22×C3×D3—21no—
143C22×C3×D3—21no—
144C22×C3×D3—21no—
145C22×C3×D3—81no—
146C2×C32×C4—22no—
147C2×C32×C4—81no—
148#638—22no—
149#638—22no—
150#638—22no—
151#638—22no—
152C2×C3⋊Dic3—21no—
153C2×C3⋊Dic3—21no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—81no—
156C2×C3⋊Dic3C22⋊C412yes—
157C4×C3⋊D3—82no—
158C3×#67—41no—
159C3×#67—41no—
160C3×#67—41no—
161C3×#67—41no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—21no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—41no—
167C2×C3×Dic3—41no—
168C2×C3×Dic3—81no—
169C2×C3×Dic3—81no—
170C2×C3×Dic3—81no—
171#626—82no—
172#534—91no—
173#518—91no—
174C2×#99—31no—
175C2×#99—91no—
176C2×#99—91no—
177#342—31no—
178#342—91no—
179C24×C3—21no—
180C24×C3—31no—
181C24×C3C22×D311yescharacteristic
182C24×C3C22×D311yescharacteristic
183C23×D3—31no—
184C23×D3—31no—
185C23×D3—61no—
186C23×D3C4×D311yescharacteristic, complemented
187C2×C3×D4—61no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C2×C3×D4—61no—
191C2×C3×D4—61no—
192C2×C3×D4—61no—
193C22×C3×C4—22no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—31no—
197C22×C3×C4—61no—
198C22×C3×C4—61no—
199C22×C3×C4—61no—
200C2×#67—21no—
201C2×#67—21no—
202C2×#67—21no—
203C2×#67—21no—
204C2×#67—21no—
205C2×#67—21no—
206C2×#67—32no—
207C2×#67—32no—
208C2×#67—32no—
209C2×#67—32no—
210C2×#67—62no—
211C2×#67—62no—
212C2×#67—62no—
213C2×#67—62no—
214C2×#67—62no—
215C2×#67—62no—
216C2×#67—62no—
217C2×#67—61no—
218C2×#67—61no—
219C2×#67—61no—
220C2×#67—61no—
221C2×#67—61no—
222C2×#67—61no—
223C2×#67—61no—
224C2×#67—61no—
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—21no—
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—61no—
231C22×Dic3—62no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234C22×Dic3C4×D311yescharacteristic, complemented
235C2×D12—62no—
236C2×C4×D3—64no—
237C2×C4×D3—62no—
238C2×C4×D3—62no—
239C3×C22⋊C4—22no—
240C3×C22⋊C4—21no—
241C3×C22⋊C4—21no—
242C3×C22⋊C4—22no—
243C3×C22⋊C4—32no—
244C3×C22⋊C4—61no—
245C3×C22⋊C4—61no—
246C3×C22⋊C4—61no—
247C3×C22⋊C4—61no—
248C3×C22⋊C4—61no—
249C3×C22⋊C4D1212yescomplemented
250C3×C22⋊C4#6712yescomplemented
251#217—21no—
252#217—21no—
253#217—21no—
254#217—21no—
255#217—21no—
256#217—32no—
257#217—32no—
258#217—62no—
259#217—62no—
260#217—62no—
261#217—61no—
262#217—61no—
263#217C4×D312yescomplemented
264(C2×D3)⋊C4—62no—
265(C2×D3)⋊C4—62no—
266(C2×D3)⋊C4—62no—
267(C2×D3)⋊C4—64no—
268(C2×D3)⋊C4—62no—
269(C2×D3)⋊C4—62no—
270C4⋊Dic3—62no—
271Dic3⋊C4—62no—
272Dic3⋊C4—64no—
273Dic3⋊C4—62no—
274Dic3⋊C4—62no—
275C4×Dic3—64no—
276C4×Dic3—62no—
277C4×Dic3—62no—
278C22×C32—41no—
279C22×C32—41no—
280C22×C32—41no—
281C22×C32—41no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32—41no—
285C22×C32C2×C22⋊C411yescharacteristic
286C22×C32C4×D411yescharacteristic
287C22×C32C4×D411yescharacteristic
288C22×C32#12011yescharacteristic
289C22×C32#12111yescharacteristic
290C22×C32#12111yescharacteristic
291C22×C32#12311yescharacteristic
292C2×C3⋊D3—22no—
293C2×C3⋊D3—42no—
294C2×C3⋊D3—42no—
295C2×C3⋊D3—81no—
296C2×C3×D3—42no—
297C2×C3×D3—41no—
298C2×C3×D3—81no—
299C2×C3×D3—81no—
300C32×C4—42no—
301C3⋊Dic3—22no—
302C3⋊Dic3—42no—
303C3×Dic3—42no—
304C3×Dic3—41no—
305C3×Dic3—81no—
306C3×Dic3—81no—
307C22×D4—31no—
308C22×D4—91no—
309#123—92no—
310#123—181no—
311#121—182no—
312#120—92no—
313#120—181no—
314C4×D4—182no—
315C4×D4—182no—
316#117—181no—
317C2×C22⋊C4—31no—
318C2×C22⋊C4—31no—
319C2×C22⋊C4—31no—
320C2×C22⋊C4—91no—
321C2×C22⋊C4—181no—
322C2×C22⋊C4D3211yescharacteristic
323#99—62no—
324#99—182no—
325#99—182no—
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—21no—
331C23×C3—21no—
332C23×C3—21no—
333C23×C3—61no—
334C23×C3—61no—
335C23×C3—61no—
336C23×C3—81no—
337C23×C3—81no—
338C23×C3—82no—
339C23×C3—241no—
340C23×C3C2×C4×D311yescharacteristic
341C23×C3C2×C4×D311yescharacteristic
342C23×C3C2×D1211yescharacteristic
343C23×C3#23511yescharacteristic
344C23×C3#23511yescharacteristic
345C23×C3D3×D411yescharacteristic
346C23×C3D3×D411yescharacteristic
347C23×C3D3×D411yescharacteristic
348C23×C3D3×D411yescharacteristic
349C23×C3D3×D411yescharacteristic
350C23×C3D3×D411yescharacteristic
351C23×C3#23711yescharacteristic
352C23×C3#23911yescharacteristic
353C23×C3C2×#6711yescharacteristic
354C22×D3—21no—
355C22×D3—21no—
356C22×D3—21no—
357C22×D3—32no—
358C22×D3—32no—
359C22×D3—62no—
360C22×D3—62no—
361C22×D3—61no—
362C22×D3—61no—
363C22×D3—62no—
364C22×D3—61no—
365C22×D3—61no—
366C22×D3—81no—
367C22×D3—241no—
368C22×D3—241no—
369C22×D3—242no—
370C3×D4—121no—
371C3×D4—121no—
372C3×D4—121no—
373C3×D4—121no—
374C2×C3×C4—24no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—61no—
378C2×C3×C4—61no—
379C2×C3×C4—62no—
380C2×C3×C4—61no—
381C2×C3×C4—81no—
382C2×C3×C4—81no—
383C2×C3×C4—82no—
384C2×C3×C4—121no—
385C2×C3×C4—121no—
386C2×C3×C4—241no—
387C2×C3×C4—241no—
388C2×C3×C4—241no—
389#67—41no—
390#67—41no—
391#67—41no—
392#67—41no—
393#67—64no—
394#67—64no—
395#67—64no—
396#67—64no—
397#67—62no—
398#67—62no—
399#67—62no—
400#67—62no—
401#67—62no—
402#67—62no—
403#67—62no—
404#67—62no—
405#67—242no—
406C2×Dic3—22no—
407C2×Dic3—21no—
408C2×Dic3—21no—
409C2×Dic3—21no—
410C2×Dic3—32no—
411C2×Dic3—32no—
412C2×Dic3—41no—
413C2×Dic3—41no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—61no—
420C2×Dic3—61no—
421C2×Dic3—64no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—81no—
425C2×Dic3—81no—
426C2×Dic3—81no—
427C2×Dic3—241no—
428C2×Dic3—241no—
429C2×Dic3—242no—
430D12—242no—
431C4×D3—244no—
432C4×D3—242no—
433C4×D3—242no—
434C2×C32—21no—
435C2×C32—21no—
436C2×C32—21no—
437C2×C32—21no—
438C2×C32—21no—
439C2×C32—21no—
440C2×C32—21no—
441C2×C32#38611yescharacteristic
442C3⋊D3—42no—
443C3×D3—81no—
444C24—31no—
445C24—91no—
446C24C2×D3211yescharacteristic
447C2×D4—61no—
448C2×D4—61no—
449C2×D4—61no—
450C2×D4—61no—
451C2×D4—61no—
452C2×D4—61no—
453C2×D4—92no—
454C2×D4—92no—
455C2×D4—182no—
456C2×D4—181no—
457C2×D4—181no—
458C2×D4—181no—
459C2×D4—181no—
460C22×C4—21no—
461C22×C4—31no—
462C22×C4—61no—
463C22×C4—61no—
464C22×C4—61no—
465C22×C4—91no—
466C22×C4—182no—
467C22×C4—181no—
468C4⋊C4—182no—
469C4⋊C4—182no—
470C22⋊C4—21no—
471C22⋊C4—32no—
472C22⋊C4—61no—
473C22⋊C4—61no—
474C22⋊C4—61no—
475C22⋊C4—61no—
476C22⋊C4—61no—
477C22⋊C4—92no—
478C22⋊C4—182no—
479C22⋊C4—182no—
480C22⋊C4—182no—
481C22⋊C4—181no—
482C22⋊C4#62612yescomplemented
483C42—182no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—41no—
492C22×C3—41no—
493C22×C3—41no—
494C22×C3—41no—
495C22×C3—41no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3—41no—
499C22×C3—41no—
500C22×C3—41no—
501C22×C3—41no—
502C22×C3—41no—
503C22×C3—41no—
504C22×C3—41no—
505C22×C3—42no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—81no—
509C22×C3—81no—
510C22×C3—81no—
511C22×C3—81no—
512C22×C3—122no—
513C22×C3—121no—
514C22×C3—241no—
515C22×C3—241no—
516C22×C3C4×D1211yescharacteristic
517C22×C3D3×C22⋊C411yescharacteristic
518C22×C3D3×C22⋊C411yescharacteristic
519C22×C3#67⋊C411yescharacteristic
520C22×C3#88211yescharacteristic
521C22×C3#88311yescharacteristic
522C22×C3#88411yescharacteristic
523C22×C3#88411yescharacteristic
524C22×C3#89311yescharacteristic
525C22×C3#89411yescharacteristic
526C22×C3#89511yescharacteristic
527C22×C3C4×#6711yescharacteristic
528C22×C3#93711yescharacteristic
529C22×C3#93811yescharacteristic
530C2×D3—42no—
531C2×D3—41no—
532C2×D3—64no—
533C2×D3—62no—
534C2×D3—62no—
535C2×D3—81no—
536C2×D3—81no—
537C2×D3—124no—
538C2×D3—122no—
539C2×D3—122no—
540C2×D3—122no—
541C2×D3—122no—
542C2×D3—242no—
543C2×D3—241no—
544C2×D3—241no—
545C2×D3—242no—
546C3×C4—44no—
547C3×C4—42no—
548C3×C4—42no—
549C3×C4—122no—
550C3×C4—121no—
551C3×C4—241no—
552C3×C4—241no—
553Dic3—42no—
554Dic3—41no—
555Dic3—64no—
556Dic3—62no—
557Dic3—62no—
558Dic3—81no—
559Dic3—81no—
560Dic3—124no—
561Dic3—122no—
562Dic3—122no—
563C32#191311yescharacteristic, complemented, Sylow
564C23—61no—
565C23—61no—
566C23—61no—
567C23—81no—
568C23—92no—
569C23—181no—
570C23—181no—
571C23—241no—
572C23—721no—
573C23#379611yescharacteristic
574C23#379811yescharacteristic
575C23C4×D3211yescharacteristic
576C23#380211yescharacteristic
577C23C2×#62611yescharacteristic
578C23#381111yescharacteristic
579C23#381111yescharacteristic
580D4—121no—
581D4—121no—
582D4—121no—
583D4—121no—
584D4—182no—
585D4—182no—
586D4—182no—
587D4—182no—
588D4—722no—
589C2×C4—22no—
590C2×C4—61no—
591C2×C4—61no—
592C2×C4—62no—
593C2×C4—61no—
594C2×C4—81no—
595C2×C4—92no—
596C2×C4—121no—
597C2×C4—121no—
598C2×C4—181no—
599C2×C4—181no—
600C2×C4—182no—
601C2×C4—241no—
602C2×C4—241no—
603C2×C4—241no—
604C2×C4—722no—
605C2×C4—721no—
606C2×C3—22no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—21no—
615C2×C3—21no—
616C2×C3—21no—
617C2×C3—21no—
618C2×C3—21no—
619C2×C3—21no—
620C2×C3—21no—
621C2×C3—21no—
622C2×C3—41no—
623C2×C3—41no—
624C2×C3—41no—
625C2×C3—41no—
626C2×C3—41no—
627C2×C3—41no—
628C2×C3—241no—
629C2×C3#466511yescharacteristic
630C2×C3#495611yescharacteristic
631D3—81no—
632D3—124no—
633D3—122no—
634D3—122no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—122no—
643C22—121no—
644C22—182no—
645C22—241no—
646C22—241no—
647C22—362no—
648C22—362no—
649C22—721no—
650C22#6385311yescharacteristic
651C22#6388111yescharacteristic
652C22C4×#62611yescharacteristic
653C22#6391211yescharacteristic
654C22#6391611yescharacteristic
655C22#6392111yescharacteristic
656C22#6398111yescharacteristic
657C4—42no—
658C4—122no—
659C4—121no—
660C4—182no—
661C4—241no—
662C4—241no—
663C4—362no—
664C3—21no—
665C3#6896411yescharacteristic, complemented
666C3#7003411yescharacteristic, complemented
667C2—21no—
668C2—21no—
669C2—21no—
670C2—21no—
671C2—21no—
672C2—21no—
673C2—21no—
674C2—241no—
675C2—362no—
676C2#1059138711yescharacteristic
subgroupG/H
centerC2#10591387
commutatorC23×C32C22×C4
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC2×C32#386
prime radical#10595519C2
cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1913
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #10595957C2semidirect
3. C2×C3×#806C2semidirect
4. C2×#63581C2semidirect
5. C2×#63580C2semidirect
6. C3×#4527C2semidirect
7. #10589186C2semidirect
23. #63977C4semidirect
24. #63966C4semidirect
39. C2×#806D3semidirect
42. #4527D3semidirect
46. C23×C3×D3C2×C4semidirect
66. C22×C3×Dic3C2×C4semidirect
69. C32×C22⋊C4D4semidirect
71. #3757D4semidirect
80. C3×#217C2×C4semidirect
186. C23×D3C4×D3semidirect
234. C22×Dic3C4×D3semidirect
249. C3×C22⋊C4D12semidirect
250. C3×C22⋊C4#67semidirect
263. #217C4×D3semidirect
482. C22⋊C4#626semidirect
563. C32#1913semidirect
665. C3#68964semidirect
666. C3#70034semidirect

Maximal subgroups

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

subgroupindex
#105959572
#105955192
C2×C3×#8062
C2×#635812
C2×#635802
C3×#45272
#105891862
#700343
#689643