Finite Group Databasebeta

← #10830664

Subgroups — #10830664

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×#5630C211yesmaximal, characteristic
2C2×#4852C211yesmaximal, characteristic, complemented
3C2×#4798C211yesmaximal, characteristic, complemented
4C2×#4808C211yesmaximal, characteristic, complemented
5C2×#4731C211yesmaximal, characteristic, complemented
6#73934C211yesmaximal, characteristic, complemented
7C3×#2035C211yesmaximal, characteristic, complemented
8#71700C211yesmaximal, characteristic, complemented
9#70581C211yesmaximal, characteristic, complemented
10#70267C211yesmaximal, characteristic, complemented
11#70226C211yesmaximal, characteristic, complemented
12#69916C211yesmaximal, characteristic, complemented
13#69521C211yesmaximal, characteristic, complemented
14#68893C211yesmaximal, characteristic, complemented
15#68887C211yesmaximal, characteristic, complemented
16#24247—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C2×C3×C22⋊Q8C2211yescharacteristic
20C2×#947C2211yescharacteristic
21C22×#216C2211yescharacteristic, complemented
22C2×C4×#67C2211yescharacteristic
23C2×#924C2211yescharacteristic
24C22×#204C2211yescharacteristic
25C22×#204C2211yescharacteristic
26#5630—24no—
27#5630—24no—
28C2×#897C2211yescharacteristic, complemented
29C2×#895—21no—
30C2×#895C2211yescharacteristic
31C2×#894—21no—
32C2×#893C2211yescharacteristic
33C2×#887C2211yescharacteristic, complemented
34C2×#882—21no—
35C2×D3×C22⋊C4—21no—
36C2×C3×#106C2211yescharacteristic, complemented
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×#103C2211yescharacteristic, complemented
39C2×C3×C22⋊C8C2211yescharacteristic
40C3×#380C2211yescharacteristic
41C2×#835C2211yescharacteristic, complemented
42C2×#830C2211yescharacteristic
43C2×#821C2211yescharacteristic
44C2×#821C2211yescharacteristic
45C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
46C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
47C2×Dic3⋊C8C2211yescharacteristic, complemented
48C2×C8×Dic3C2211yescharacteristic, complemented
49#4987C2211yescharacteristic, complemented
50#4977C2211yescharacteristic, complemented
51C2×#810C2211yescharacteristic, complemented
52C2×#809C2211yescharacteristic
53C2×#809C2211yescharacteristic
54C2×#809C2211yescharacteristic
55C2×#809C2211yescharacteristic
56#4959—21no—
57#4951—21no—
58#4852—24no—
59#4808—24no—
60#4798—24no—
61#4731—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#2035D311yescharacteristic, complemented
73#2034—31no—
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×Q8C2311yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C22×#67D411yescharacteristic
85C2×#239—22no—
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239—41no—
90C2×#239—41no—
91C22×D12—21no—
92C22×D12—21no—
93C22×D12—21no—
94C22×D12—22no—
95C22×D12—22no—
96C22×D12—22no—
97C22×D12—22no—
98C22×D12—41no—
99C22×D12—41no—
100C22×D12C2311yescharacteristic
101C22×D12C2311yescharacteristic
102C22×C4×D3—21no—
103C22×C4×D3—21no—
104C22×C4×D3C2311yescharacteristic
105C22×Dic6C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8—22no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×#217—21no—
117C2×#217D411yescharacteristic
118#947—22no—
119#947D414yes—
120C2×#216—22no—
121C2×#216—22no—
122C2×#216—41no—
123C4×#67—22no—
124C4×#67—22no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×(C2×D3)⋊C4—21no—
129C2×(C2×D3)⋊C4—21no—
130C2×(C2×D3)⋊C4—21no—
131C2×(C2×D3)⋊C4D411yescharacteristic
132C2×C4⋊Dic3—21no—
133C2×C4⋊Dic3C2311yescharacteristic
134#924—22no—
135#924—41no—
136C2×Dic3⋊C4—21no—
137C2×Dic3⋊C4—21no—
138C2×Dic3⋊C4D411yescharacteristic
139C2×C4×Dic3—21no—
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C2×#204—22no—
144C2×#204—22no—
145C2×#204—22no—
146C2×#204—22no—
147C2×#204—41no—
148C2×#204D414yescomplemented
149#897—22no—
150#897—41no—
151#895—28no—
152#895—22no—
153#895—22no—
154#894—28no—
155#893—22no—
156#893D414yes—
157#887—22no—
158#887—22no—
159#882—28no—
160D3×C22⋊C4—28no—
161C3×#106—22no—
162C3×#103—22no—
163C3×#103—22no—
164C3×C22⋊C8—22no—
165C3×#95—21no—
166#835—41no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170#830—41no—
171#821—22no—
172#821—22no—
173(C2×D3)⋊C8—22no—
174(C2×D3)⋊C8—41no—
175Dic3⋊C8—22no—
176C8×Dic3—22no—
177#810—22no—
178#809—22no—
179#809—22no—
180#809—22no—
181#809—41no—
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⋊Q8C2×D311yescharacteristic
194C2×#121—31no—
195C2×#121—61no—
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×#103C2×D311yescharacteristic, complemented
210C2×#103C2×D311yescharacteristic, complemented
211C2×#102—31no—
212C2×#102—31no—
213C2×#102—31no—
214C2×#102—31no—
215C2×#102—31no—
216C2×#102—31no—
217C2×C22⋊C8—31no—
218C2×C22⋊C8—31no—
219C2×C22⋊C8—31no—
220C2×C22⋊C8C2×D311yescharacteristic
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
229#340—31no—
230#340C2×D311yescharacteristic, complemented
231C24×C3C2×D411yescharacteristic
232C23×D3—21no—
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×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8C2×D412yes—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
259C22×C3×C4C2411yescharacteristic
260C2×#67—22no—
261C2×#67—22no—
262C2×#67—41no—
263C22×Dic3—21no—
264C22×Dic3—21no—
265C22×Dic3C2×D411yescharacteristic
266C22×Dic3C2×D411yescharacteristic
267C22×Dic3C2×D411yescharacteristic
268#239—44no—
269#239—44no—
270#239—44no—
271#239—44no—
272C2×D12—21no—
273C2×D12—21no—
274C2×D12—21no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12—21no—
279C2×D12—24no—
280C2×D12—24no—
281C2×D12—21no—
282C2×D12—24no—
283C2×D12—44no—
284C2×D12—44no—
285C2×D12—44no—
286C2×D12—42no—
287C2×D12—42no—
288C2×D12—42no—
289C2×D12—42no—
290C2×D12—44no—
291C2×D12—81no—
292C2×D12—81no—
293C2×D12C2×D412yes—
294C2×D12C2×D412yes—
295C2×D12C2×D412yes—
296C2×D12#4112yes—
297C2×C4×D3—24no—
298C2×C4×D3—21no—
299C2×C4×D3—21no—
300C2×C4×D3—21no—
301C2×C4×D3—21no—
302C2×C4×D3—21no—
303C2×C4×D3—21no—
304C2×C4×D3—24no—
305C2×C4×D3—42no—
306C2×C4×D3—42no—
307C2×C4×D3—81no—
308C2×C4×D3—81no—
309C2×Dic6—21no—
310C2×Dic6—21no—
311C2×Dic6—21no—
312C2×Dic6—21no—
313C2×Dic6—21no—
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—24no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—21no—
327C3×C4⋊C4C2×D412yes—
328C3×C22⋊C4—24no—
329C3×C22⋊C4—42no—
330#217—22no—
331#217—42no—
332#216—44no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—22no—
338(C2×D3)⋊C4—42no—
339(C2×D3)⋊C4—42no—
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—
355#204—28no—
356#204—44no—
357C25—61no—
358C2×#41—62no—
359C2×#41—62no—
360C2×#41—62no—
361C2×#41—62no—
362C2×#41—121no—
363C2×#41—121no—
364C22×Q8—31no—
365C22×Q8C22×D311yescharacteristic
366C22×D4—31no—
367C22×D4—31no—
368C22×D4—31no—
369C22×D4—62no—
370C22×D4—62no—
371C22×D4—62no—
372C22×D4—62no—
373C22×D4—61no—
374C22×D4—61no—
375C22×D4—61no—
376C22×D4—121no—
377C22×D4—121no—
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—22no—
399C22⋊Q8—22no—
400C22⋊Q8—62no—
401C22⋊Q8—62no—
402C22⋊Q8—121no—
403C22⋊Q8—121no—
404#121—62no—
405#121—68no—
406#121—62no—
407#120—68no—
408C4×Q8—62no—
409C4×Q8—62no—
410C4×D4—34no—
411C4×D4—62no—
412C4×D4—62no—
413C4×D4—62no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
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—22no—
440#103—22no—
441#103—62no—
442#103—121no—
443#102—62no—
444#102—62no—
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—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—21no—
464C23×C3#13512yes—
465C23×C3C22×D411yescharacteristic
466C22×D3—22no—
467C22×D3—22no—
468C22×D3—22no—
469C22×D3—22no—
470C22×D3—21no—
471C22×D3—21no—
472C22×D3—21no—
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—48no—
478C22×D3—41no—
479C22×D3—41no—
480C22×D3—41no—
481C22×D3—41no—
482C22×D3—48no—
483C22×D3—41no—
484C22×D3—41no—
485C22×D3—41no—
486C22×D3—41no—
487C22×D3—41no—
488C22×D3—41no—
489C22×D3—84no—
490C22×D3—84no—
491C22×D3—84no—
492C22×D3—84no—
493C22×D3—84no—
494C3×Q8—22no—
495C3×Q8—22no—
496C3×Q8—41no—
497C3×Q8—41no—
498C2×C3×C4—21no—
499C2×C3×C4—22no—
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×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4C22×D411yescharacteristic
518C2×C3×C4C22×D411yescharacteristic
519C2×C3×C4C22×D411yescharacteristic
520C2×C3×C4C2×#4111yescharacteristic
521C2×C3×C4H(5,𝔽2)11yescharacteristic
522C2×C3×C4H(5,𝔽2)11yescharacteristic
523#67—44no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—22no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3#12012yes—
538C2×Dic3#12012yes—
539D12—22no—
540D12—22no—
541D12—22no—
542D12—22no—
543D12—22no—
544D12—48no—
545D12—48no—
546D12—41no—
547D12—41no—
548D12—84no—
549D12#12114yes—
550C4×D3—48no—
551C4×D3—41no—
552C4×D3—41no—
553C4×D3—41no—
554C4×D3—41no—
555C4×D3—84no—
556Dic6—22no—
557Dic6—22no—
558Dic6—41no—
559Dic6—41no—
560C3×C8—22no—
561C3×C8—41no—
562C3⋊C8—41no—
563C3⋊C8—41no—
564C24—31no—
565C24—64no—
566C24—61no—
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—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—32no—
585C2×Q8—61no—
586C2×Q8—61no—
587C2×Q8—61no—
588C2×Q8—61no—
589C2×Q8—61no—
590C2×Q8D3×D412yes—
591C2×D4—32no—
592C2×D4—32no—
593C2×D4—32no—
594C2×D4—32no—
595C2×D4—64no—
596C2×D4—64no—
597C2×D4—64no—
598C2×D4—62no—
599C2×D4—62no—
600C2×D4—61no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—122no—
609C2×D4—122no—
610C2×D4—124no—
611C2×D4—124no—
612C2×D4—124no—
613C2×D4—124no—
614C2×D4—122no—
615C2×D4—122no—
616C2×D4—121no—
617C2×D4—241no—
618C2×D4—241no—
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—21no—
629C22×C4—31no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—64no—
633C22×C4—64no—
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—24no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—62no—
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—64no—
682C22⋊C4—64no—
683C22⋊C4—62no—
684C22⋊C4—122no—
685C22⋊C4—122no—
686C22⋊C4—122no—
687C42—32no—
688C42—32no—
689C42—122no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3C2×#12011yescharacteristic
698C22×C3D4211yescharacteristic
699C22×C3#54611yescharacteristic
700C22×C3C2×#13511yescharacteristic
701C22×C3#57511yescharacteristic
702C22×C3#57711yescharacteristic
703C22×C3#57711yescharacteristic
704C2×D3—24no—
705C2×D3—42no—
706C2×D3—42no—
707C2×D3—42no—
708C2×D3—42no—
709C2×D3—42no—
710C2×D3—42no—
711C2×D3—41no—
712C2×D3—42no—
713C2×D3—41no—
714C2×D3—42no—
715C2×D3—41no—
716C2×D3—42no—
717C2×D3—41no—
718C2×D3—41no—
719C2×D3—41no—
720C2×D3—41no—
721C2×D3—816no—
722C2×D3—81no—
723C2×D3—81no—
724C2×D3—81no—
725C2×D3—81no—
726C3×C4—42no—
727C3×C4—41no—
728C3×C4—42no—
729C3×C4—81no—
730C3×C4—81no—
731C3×C4C2×#12111yescharacteristic
732C3×C4#53511yescharacteristic
733C3×C4D4211yescharacteristic
734C3×C4#54611yescharacteristic
735Dic3—22no—
736Dic3—22no—
737Dic3—42no—
738Dic3—41no—
739Dic3—81no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—62no—
747C23—62no—
748C23—62no—
749C23—61no—
750C23—61no—
751C23—61no—
752C23—61no—
753C23—61no—
754C23—62no—
755C23—61no—
756C23—61no—
757C23—128no—
758C23—128no—
759C23—121no—
760C23—121no—
761C23—121no—
762C23—121no—
763C23—121no—
764C23—121no—
765C23—121no—
766C23—121no—
767C23—121no—
768C23—121no—
769C23—244no—
770C23—244no—
771C23—244no—
772C23—244no—
773C23—244no—
774C23#91612yes—
775C23C2×D3×D411yescharacteristic
776Q8—22no—
777Q8—22no—
778Q8—41no—
779Q8—41no—
780Q8—62no—
781Q8—62no—
782Q8—121no—
783Q8—121no—
784D4—34no—
785D4—62no—
786D4—62no—
787D4—62no—
788D4—62no—
789D4—62no—
790D4—128no—
791D4—128no—
792D4—124no—
793D4—121no—
794D4—121no—
795D4—244no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—32no—
802C2×C4—32no—
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—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—62no—
824C2×C4—61no—
825C2×C4—128no—
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—42no—
847C2×C3#240811yescharacteristic
848C2×C3#300211yescharacteristic
849C2×C3#300911yescharacteristic
850C2×C3#327511yescharacteristic
851C2×C3#328211yescharacteristic
852C2×C3#329611yescharacteristic
853C2×C3#332311yescharacteristic
854D3—44no—
855D3—81no—
856D3—82no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—64no—
865C22—122no—
866C22—122no—
867C22—122no—
868C22—122no—
869C22—122no—
870C22—122no—
871C22—121no—
872C22—121no—
873C22—121no—
874C22—121no—
875C22—122no—
876C22—121no—
877C22—122no—
878C22—121no—
879C22—121no—
880C22—122no—
881C22—2416no—
882C22—241no—
883C22—241no—
884C22—241no—
885C22—241no—
886C22D3×#12011yescharacteristic
887C22#560911yescharacteristic
888C22#565411yescharacteristic
889C22C2×#91611yescharacteristic
890C22#577011yescharacteristic
891C22#577711yescharacteristic
892C22#577811yescharacteristic
893C4—41no—
894C4—42no—
895C4—42no—
896C4—62no—
897C4—62no—
898C4—81no—
899C4—81no—
900C4—121no—
901C4—122no—
902C4—241no—
903C4D3×#12111yescharacteristic
904C4#560911yescharacteristic
905C4#565411yescharacteristic
906C4#567411yescharacteristic
907C3#2424711yescharacteristic, complemented, Sylow
908C2—42no—
909C2—124no—
910C2—241no—
911C2—242no—
912C2#7689511yescharacteristic
913C2#8003811yescharacteristic
914C2#8022911yescharacteristic
915C2#8067711yescharacteristic
916C2#8092211yescharacteristic
917C2#8144511yescharacteristic
918C2#8154911yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2035C2
socleC23×C3C22×D4
prime radicalC2×#5630C2
hypercenter#2035D3
hypocenterC3#24247
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
2. C2×#4852C2semidirect
3. C2×#4798C2semidirect
4. C2×#4808C2semidirect
5. C2×#4731C2semidirect
6. #73934C2semidirect
7. C3×#2035C2semidirect
8. #71700C2semidirect
9. #70581C2semidirect
10. #70267C2semidirect
11. #70226C2semidirect
12. #69916C2semidirect
13. #69521C2semidirect
14. #68893C2semidirect
15. #68887C2semidirect
21. C22×#216C22semidirect
28. C2×#897C22semidirect
33. C2×#887C22semidirect
36. C2×C3×#106C22semidirect
37. C2×C3×#103C22semidirect
38. C2×C3×#103C22semidirect
41. C2×#835C22semidirect
45. C2×(C2×D3)⋊C8C22semidirect
46. C2×(C2×D3)⋊C8C22semidirect
47. C2×Dic3⋊C8C22semidirect
48. C2×C8×Dic3C22semidirect
49. #4987C22semidirect
50. #4977C22semidirect
51. C2×#810C22semidirect
64. C3×#340C22semidirect
65. #4529C22semidirect
72. #2035D3semidirect
148. C2×#204D4semidirect
205. C2×#106C2×D3semidirect
209. C2×#103C2×D3semidirect
210. C2×#103C2×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×#56302
C2×#48522
C2×#47982
C2×#48082
C2×#47312
#739342
C3×#20352
#717002
#705812
#702672
#702262
#699162
#695212
#688932
#688872
#242473