Finite Group Databasebeta

← #10830656

Subgroups — #10830656

Order 768.

1564 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5612C211yesmaximal, characteristic
2C2×#4852C211yesmaximal, characteristic, complemented
3C2×#4767C211yesmaximal, characteristic, complemented
4C2×#4776C211yesmaximal, characteristic, complemented
5C2×#4733C211yesmaximal, characteristic, complemented
6#73934C211yesmaximal, characteristic, complemented
7C3×#2034C211yesmaximal, characteristic, complemented
8#71685C211yesmaximal, characteristic, complemented
9#70582C211yesmaximal, characteristic, complemented
10#70198C211yesmaximal, characteristic, complemented
11#70158C211yesmaximal, characteristic, complemented
12#69916C211yesmaximal, characteristic, complemented
13#69522C211yesmaximal, characteristic, complemented
14#68893C211yesmaximal, characteristic, complemented
15#68888C211yesmaximal, characteristic, complemented
16#24247—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×#938—21no—
21C2×#937—21no—
22C2×#936C2211yescharacteristic
23C22×#214C2211yescharacteristic
24C2×C4×#67C2211yescharacteristic
25C2×#924C2211yescharacteristic, complemented
26C22×Dic12C2211yescharacteristic, complemented
27C22×#204C2211yescharacteristic
28#5612—24no—
29#5612—24no—
30C2×#897C2211yescharacteristic
31C2×#897C2211yescharacteristic
32C2×#893C2211yescharacteristic
33C2×#887C2211yescharacteristic, complemented
34C2×#883—21no—
35C2×D3×C22⋊C4—21no—
36C2×C3×#106C2211yescharacteristic, complemented
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic, complemented
40C3×#380C2211yescharacteristic, complemented
41C2×#832C2211yescharacteristic
42C2×#830C2211yescharacteristic, complemented
43C2×#821C2211yescharacteristic
44C2×(C2×D3)⋊C8C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×#816C2211yescharacteristic, complemented
47C2×Dic3⋊C8C2211yescharacteristic, complemented
48C2×C8×Dic3C2211yescharacteristic, complemented
49#4987C2211yescharacteristic
50#4977C2211yescharacteristic, complemented
51C2×#810C2211yescharacteristic, complemented
52C2×#810C2211yescharacteristic, complemented
53C2×#810C2211yescharacteristic, complemented
54C2×#809C2211yescharacteristic
55C2×#809C2211yescharacteristic
56#4959—21no—
57#4951—21no—
58#4852—24no—
59#4776—24no—
60#4767—24no—
61#4733—24no—
62#4669—21no—
63#4657—21no—
64C3×#340C2211yescharacteristic, complemented
65#4529C2211yescharacteristic, complemented
66C2×#546—31no—
67C2×#464—31no—
68C2×#452—31no—
69C2×#450—31no—
70C2×C4×SD16—31no—
71#2536—31no—
72#2035—31no—
73#2034D311yescharacteristic, complemented
74#2001—31no—
75#2000—31no—
76#1958—31no—
77#1954—31no—
78#1804—31no—
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×D4—21no—
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×#67—21no—
87C22×#67D411yescharacteristic
88C2×D3×D4—22no—
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4—22no—
92C2×D3×D4—41no—
93C2×D3×D4—41no—
94C2×#235—22no—
95C2×#235—22no—
96C2×#235—22no—
97C2×#235—22no—
98C2×#235—41no—
99C2×#235—41no—
100C22×D12C2311yescharacteristic
101C22×C4×D3—21no—
102C22×C4×D3—21no—
103C22×C4×D3C2311yescharacteristic
104C22×Dic6C2311yescharacteristic
105C22×Dic6C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C3×#121—22no—
109C3×#121—22no—
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×#217—21no—
116C2×#217—21no—
117C2×#217—21no—
118C2×#217D411yescharacteristic
119#938—28no—
120#937—28no—
121#936—22no—
122#936D414yes—
123C2×#214—22no—
124C2×#214—22no—
125C2×#214—41no—
126C4×#67—22no—
127C4×#67—22no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4—21no—
132C2×(C2×D3)⋊C4D411yescharacteristic
133C2×C4⋊Dic3—21no—
134C2×C4⋊Dic3—21no—
135C2×C4⋊Dic3C2311yescharacteristic
136#924—22no—
137#924—41no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4D411yescharacteristic
141C2×C4×Dic3—21no—
142C2×C4×Dic3C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144C22×C3⋊C8C2311yescharacteristic
145C2×Dic12—22no—
146C2×Dic12—22no—
147C2×Dic12—41no—
148C2×#204—22no—
149C2×#204—22no—
150C2×#204D414yescomplemented
151#897—22no—
152#897—22no—
153#897—22no—
154#897—41no—
155#893—22no—
156#893D414yes—
157#887—22no—
158#887—22no—
159#883—28no—
160D3×C22⋊C4—28no—
161C3×#106—22no—
162C3×#102—22no—
163C3×#102—22no—
164C3×C22⋊C8—22no—
165C3×#95—21no—
166#832—41no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170#830—41no—
171#821—22no—
172(C2×D3)⋊C8—22no—
173(C2×D3)⋊C8—41no—
174#816—22no—
175Dic3⋊C8—22no—
176C8×Dic3—22no—
177#810—22no—
178#810—22no—
179#810—41no—
180#809—22no—
181#809—22no—
182C22×#41—31no—
183C23×D4—31no—
184C22×Q16—31no—
185C22×SD16—31no—
186C22×SD16—31no—
187#546—64no—
188#546—64no—
189C2×#124—31no—
190C2×#123—61no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8—31no—
193C2×C22⋊Q8—31no—
194C2×#121—61no—
195C2×#121C2×D311yescharacteristic
196C2×#120—61no—
197C2×C4×Q8—31no—
198C2×C4×D4—31no—
199C2×C4×D4—31no—
200C22×C22⋊C4—61no—
201#464—64no—
202#452—64no—
203#450—64no—
204C4×SD16—64no—
205C2×#106C2×D311yescharacteristic, complemented
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103—31no—
209C2×#103—31no—
210C2×#103—31no—
211C2×#102—31no—
212C2×#102—31no—
213C2×#102—31no—
214C2×#102—31no—
215C2×#102C2×D311yescharacteristic
216C2×#102C2×D311yescharacteristic
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8C2×D311yescharacteristic, complemented
221C2×C4×C8—31no—
222#398—61no—
223#394—61no—
224#388—61no—
225#388—61no—
226#382—31no—
227#380—31no—
228#380C2×D311yescharacteristic, complemented
229#340—31no—
230#340C2×D311yescharacteristic, complemented
231C24×C3—21no—
232C24×C3C2×D411yescharacteristic
233C23×D3—21no—
234C23×D3—24no—
235C23×D3—42no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—42no—
239C23×D3—81no—
240C23×D3—81no—
241C23×D3C2×D411yescharacteristic
242C2×C3×D4—24no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4—21no—
246C2×C3×D4—21no—
247C2×C3×D4—21no—
248C2×C3×D4—81no—
249C2×C3×D4—81no—
250C2×C3×D4C2×D412yes—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2411yescharacteristic
262C2×#67—24no—
263C2×#67—24no—
264C2×#67—22no—
265C2×#67—22no—
266C2×#67—41no—
267C2×#67—42no—
268C2×#67—42no—
269C2×#67—42no—
270C2×#67—42no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274C22×Dic3C2×D411yescharacteristic
275C22×Dic3C2×D411yescharacteristic
276C22×Dic3C2×D411yescharacteristic
277D3×D4—44no—
278D3×D4—44no—
279D3×D4—44no—
280D3×D4—44no—
281#235—44no—
282#235—44no—
283#235—44no—
284#235—44no—
285C2×D12—21no—
286C2×D12—21no—
287C2×D12—21no—
288C2×D12C2×D412yes—
289C2×D12C2×D412yes—
290C2×D12#4112yes—
291C2×C4×D3—24no—
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—24no—
299C2×C4×D3—42no—
300C2×C4×D3—42no—
301C2×C4×D3—81no—
302C2×C4×D3—81no—
303C2×Dic6—21no—
304C2×Dic6—21no—
305C2×Dic6—21no—
306C2×Dic6—21no—
307C2×Dic6—21no—
308C2×Dic6—21no—
309C2×Dic6—21no—
310C2×Dic6—21no—
311C2×Dic6—21no—
312C2×Dic6—21no—
313C2×Dic6C2×D412yes—
314C2×Dic6C2×D412yes—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8C2×D412yes—
321C3×C4⋊C4—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4C2×D412yes—
327C3×C22⋊C4—24no—
328C3×C22⋊C4—42no—
329#217—24no—
330#217—24no—
331#217—22no—
332#217—42no—
333#214—44no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—22no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—42no—
338(C2×D3)⋊C4—42no—
339C4⋊Dic3—24no—
340C4⋊Dic3—21no—
341C4⋊Dic3—21no—
342C4⋊Dic3—42no—
343Dic3⋊C4—22no—
344Dic3⋊C4—42no—
345Dic3⋊C4—42no—
346C4×Dic3—42no—
347C4×Dic3C2×D412yes—
348C4×Dic3C2×D412yes—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355Dic12—44no—
356#204—28no—
357C25—61no—
358C2×#41—62no—
359C2×#41—62no—
360C2×#41—62no—
361C2×#41—62no—
362C2×#41—121no—
363C2×#41—121no—
364C22×Q8—31no—
365C22×Q8—31no—
366C22×D4—21no—
367C22×D4—31no—
368C22×D4—31no—
369C22×D4—61no—
370C22×D4—62no—
371C22×D4—62no—
372C22×D4—62no—
373C22×D4—61no—
374C22×D4—62no—
375C22×D4—121no—
376C22×D4—121no—
377C22×D4C22×D311yescharacteristic
378C23×C4—31no—
379C23×C4—61no—
380C23×C4—61no—
381C23×C4C22×D311yescharacteristic
382C2×Q16—62no—
383C2×Q16—62no—
384C2×Q16—121no—
385C2×SD16—34no—
386C2×SD16—62no—
387C2×SD16—62no—
388C2×SD16—62no—
389C2×SD16—62no—
390C2×SD16—121no—
391C22×C8—31no—
392C22×C8—31no—
393C22×C8C22×D311yescharacteristic
394C22×C8C22×D311yescharacteristic
395#124—34no—
396#124—62no—
397#123—68no—
398C22⋊Q8—62no—
399C22⋊Q8—62no—
400C22⋊Q8—62no—
401C22⋊Q8—62no—
402C22⋊Q8—121no—
403C22⋊Q8—121no—
404#121—22no—
405#121—22no—
406#121—68no—
407#120—68no—
408C4×Q8—62no—
409C4×Q8—62no—
410C4×D4—34no—
411C4×D4—62no—
412C4×D4—62no—
413C4×D4—62no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—61no—
417C2×C4⋊C4—61no—
418C2×C4⋊C4—61no—
419C2×C4⋊C4—61no—
420C2×C4⋊C4C22×D311yescharacteristic
421C2×C4⋊C4C22×D311yescharacteristic
422C2×C4⋊C4C22×D311yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—31no—
426C2×C22⋊C4—31no—
427C2×C22⋊C4—68no—
428C2×C22⋊C4—61no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4—61no—
434C2×C22⋊C4—61no—
435C2×C42—31no—
436C2×C42—61no—
437#106—22no—
438C4⋊C8—62no—
439#103—62no—
440#103—62no—
441#103—62no—
442#103—121no—
443#102—22no—
444#102—22no—
445#102—62no—
446#102—62no—
447#102—62no—
448#102—121no—
449C22⋊C8—22no—
450C22⋊C8—62no—
451C22⋊C8—121no—
452C22⋊C8—121no—
453C4×C8—62no—
454#95—21no—
455#95—61no—
456#95—61no—
457#95—61no—
458C23×C3—22no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3—41no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3C22×D411yescharacteristic
473C22×D3—21no—
474C22×D3—22no—
475C22×D3—21no—
476C22×D3—22no—
477C22×D3—21no—
478C22×D3—22no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—48no—
483C22×D3—48no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—84no—
489C22×D3—84no—
490C22×D3—84no—
491C22×D3—84no—
492C22×D3—84no—
493C22×D3#13512yes—
494C3×D4—22no—
495C3×D4—22no—
496C3×D4—41no—
497C3×D4—41no—
498C3×D4—84no—
499C2×C3×C4—21no—
500C2×C3×C4—22no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4C22×D411yescharacteristic
516C2×C3×C4C22×D411yescharacteristic
517C2×C3×C4C22×D411yescharacteristic
518C2×C3×C4C2×#4111yescharacteristic
519C2×C3×C4H(5,𝔽2)11yescharacteristic
520C2×C3×C4H(5,𝔽2)11yescharacteristic
521#67—44no—
522#67—48no—
523#67—48no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—22no—
530C2×Dic3—22no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3#12012yes—
541C2×Dic3#12012yes—
542D12—22no—
543D12—22no—
544D12—22no—
545D12#12114yes—
546C4×D3—48no—
547C4×D3—41no—
548C4×D3—41no—
549C4×D3—41no—
550C4×D3—41no—
551C4×D3—84no—
552Dic6—22no—
553Dic6—22no—
554Dic6—22no—
555Dic6—22no—
556Dic6—41no—
557Dic6—41no—
558Dic6—41no—
559Dic6—41no—
560C3×C8—22no—
561C3×C8—41no—
562C3⋊C8—41no—
563C3⋊C8—41no—
564C24—21no—
565C24—31no—
566C24—64no—
567C24—61no—
568C24—122no—
569C24—122no—
570C24—122no—
571C24—122no—
572C24—241no—
573C24—241no—
574C24D3×D411yescharacteristic
575#41—124no—
576#41—124no—
577#41—124no—
578#41—124no—
579C2×Q8—32no—
580C2×Q8—32no—
581C2×Q8—61no—
582C2×Q8—61no—
583C2×Q8—61no—
584C2×Q8—61no—
585C2×Q8—61no—
586C2×Q8—61no—
587C2×Q8—61no—
588C2×Q8—61no—
589C2×Q8—61no—
590C2×Q8—61no—
591C2×D4—24no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—32no—
598C2×D4—32no—
599C2×D4—32no—
600C2×D4—62no—
601C2×D4—62no—
602C2×D4—64no—
603C2×D4—64no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—81no—
608C2×D4—81no—
609C2×D4—121no—
610C2×D4—122no—
611C2×D4—122no—
612C2×D4—124no—
613C2×D4—124no—
614C2×D4—124no—
615C2×D4—124no—
616C2×D4—122no—
617C2×D4—122no—
618C2×D4D3×D412yes—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—31no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—64no—
632C22×C4—64no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—61no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—61no—
640C22×C4—61no—
641C22×C4—61no—
642C22×C4—122no—
643C22×C4—122no—
644C22×C4—241no—
645C22×C4—241no—
646C22×C4D3×D411yescharacteristic
647C22×C4C23×D311yescharacteristic
648Q16—124no—
649SD16—68no—
650SD16—124no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C2×C8—61no—
662C2×C8D3×D412yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—62no—
669C4⋊C4—64no—
670C4⋊C4—61no—
671C4⋊C4—61no—
672C4⋊C4—122no—
673C4⋊C4—122no—
674C4⋊C4—122no—
675C4⋊C4D3×D412yes—
676C22⋊C4—24no—
677C22⋊C4—42no—
678C22⋊C4—62no—
679C22⋊C4—64no—
680C22⋊C4—64no—
681C22⋊C4—62no—
682C22⋊C4—64no—
683C22⋊C4—64no—
684C22⋊C4—122no—
685C22⋊C4—122no—
686C22⋊C4—122no—
687C42—32no—
688C42—32no—
689C42—122no—
690C22×C3—41no—
691C22×C3—42no—
692C22×C3—41no—
693C22×C3—42no—
694C22×C3—41no—
695C22×C3—42no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—81no—
701C22×C3—81no—
702C22×C3—81no—
703C22×C3—81no—
704C22×C3C2×#12011yescharacteristic
705C22×C3D4211yescharacteristic
706C22×C3#54611yescharacteristic
707C22×C3C2×#13511yescharacteristic
708C22×C3#57511yescharacteristic
709C22×C3#57711yescharacteristic
710C22×C3#57711yescharacteristic
711C2×D3—24no—
712C2×D3—22no—
713C2×D3—22no—
714C2×D3—22no—
715C2×D3—41no—
716C2×D3—42no—
717C2×D3—42no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—42no—
721C2×D3—42no—
722C2×D3—42no—
723C2×D3—41no—
724C2×D3—42no—
725C2×D3—816no—
726C3×C4—41no—
727C3×C4—42no—
728C3×C4—81no—
729C3×C4—81no—
730C3×C4C2×#12111yescharacteristic
731C3×C4#53511yescharacteristic
732C3×C4D4211yescharacteristic
733C3×C4#54611yescharacteristic
734Dic3—22no—
735Dic3—22no—
736Dic3—42no—
737Dic3—42no—
738Dic3—41no—
739Dic3—81no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—22no—
746C23—21no—
747C23—21no—
748C23—32no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—61no—
756C23—62no—
757C23—61no—
758C23—61no—
759C23—61no—
760C23—61no—
761C23—62no—
762C23—61no—
763C23—62no—
764C23—128no—
765C23—128no—
766C23—121no—
767C23—121no—
768C23—121no—
769C23—121no—
770C23—244no—
771C23—244no—
772C23—244no—
773C23—244no—
774C23—244no—
775C23C2×D3×D411yescharacteristic
776Q8—62no—
777Q8—62no—
778Q8—62no—
779Q8—62no—
780Q8—121no—
781Q8—121no—
782Q8—121no—
783Q8—121no—
784D4—22no—
785D4—22no—
786D4—34no—
787D4—41no—
788D4—41no—
789D4—62no—
790D4—62no—
791D4—62no—
792D4—84no—
793D4—124no—
794D4—128no—
795D4—128no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—21no—
800C2×C4—32no—
801C2×C4—32no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—62no—
820C2×C4—61no—
821C2×C4—62no—
822C2×C4—61no—
823C2×C4—128no—
824C2×C4—121no—
825C2×C4—121no—
826C2×C4—121no—
827C2×C4—121no—
828C2×C4—121no—
829C2×C4—121no—
830C2×C4—121no—
831C2×C4—121no—
832C2×C4—121no—
833C2×C4—121no—
834C2×C4—121no—
835C2×C4—244no—
836C2×C4C2×D3×D411yescharacteristic
837C2×C4C2×D3×D411yescharacteristic
838C2×C4C2×D3×D411yescharacteristic
839C2×C4D3×#4111yescharacteristic
840C2×C4#100911yescharacteristic
841C2×C4#100911yescharacteristic
842C8—22no—
843C8—41no—
844C8—121no—
845C8—121no—
846C2×C3—82no—
847C2×C3—81no—
848C2×C3#240811yescharacteristic
849C2×C3#300211yescharacteristic
850C2×C3#300911yescharacteristic
851C2×C3#327511yescharacteristic
852C2×C3#328211yescharacteristic
853C2×C3#329611yescharacteristic
854C2×C3#332311yescharacteristic
855D3—42no—
856D3—44no—
857C22—41no—
858C22—42no—
859C22—41no—
860C22—41no—
861C22—42no—
862C22—41no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—41no—
867C22—62no—
868C22—64no—
869C22—62no—
870C22—62no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—122no—
876C22—121no—
877C22—122no—
878C22—121no—
879C22—121no—
880C22—122no—
881C22—122no—
882C22—122no—
883C22—121no—
884C22—122no—
885C22—2416no—
886C22D3×#12011yescharacteristic
887C22#560911yescharacteristic
888C22#565411yescharacteristic
889C22#576211yescharacteristic
890C22D3×#13511yescharacteristic
891C22#577311yescharacteristic
892C22#577511yescharacteristic
893C4—42no—
894C4—41no—
895C4—62no—
896C4—62no—
897C4—81no—
898C4—81no—
899C4—121no—
900C4—122no—
901C4—122no—
902C4—241no—
903C4D3×#12111yescharacteristic
904C4#560911yescharacteristic
905C4#565411yescharacteristic
906C4#567411yescharacteristic
907C3#2424711yescharacteristic, complemented, Sylow
908C2—81no—
909C2—82no—
910C2—122no—
911C2—124no—
912C2#7689511yescharacteristic
913C2#8008211yescharacteristic
914C2#8014811yescharacteristic
915C2#8067811yescharacteristic
916C2#8088311yescharacteristic
917C2#8133311yescharacteristic
918C2#8138111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2034C2
socleC23×C3C22×D4
prime radicalC2×#5612C2
hypercenter#2034D3
hypocenterC3#24247
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

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

NH ≅ G/Ntype
2. C2×#4852C2semidirect
3. C2×#4767C2semidirect
4. C2×#4776C2semidirect
5. C2×#4733C2semidirect
6. #73934C2semidirect
7. C3×#2034C2semidirect
8. #71685C2semidirect
9. #70582C2semidirect
10. #70198C2semidirect
11. #70158C2semidirect
12. #69916C2semidirect
13. #69522C2semidirect
14. #68893C2semidirect
15. #68888C2semidirect
25. C2×#924C22semidirect
26. C22×Dic12C22semidirect
33. C2×#887C22semidirect
36. C2×C3×#106C22semidirect
39. C2×C3×C22⋊C8C22semidirect
40. C3×#380C22semidirect
42. C2×#830C22semidirect
46. C2×#816C22semidirect
47. C2×Dic3⋊C8C22semidirect
48. C2×C8×Dic3C22semidirect
50. #4977C22semidirect
51. C2×#810C22semidirect
52. C2×#810C22semidirect
53. C2×#810C22semidirect
64. C3×#340C22semidirect
65. #4529C22semidirect
73. #2034D3semidirect
150. C2×#204D4semidirect
205. C2×#106C2×D3semidirect
220. C2×C22⋊C8C2×D3semidirect
228. #380C2×D3semidirect
230. #340C2×D3semidirect
907. C3#24247semidirect

Maximal subgroups

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

subgroupindex
C2×#56122
C2×#48522
C2×#47672
C2×#47762
C2×#47332
#739342
C3×#20342
#716852
#705822
#701982
#701582
#699162
#695222
#688932
#688882
#242473