Finite Group Databasebeta

← #10830654

Subgroups — #10830654

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×#5169C211yesmaximal, characteristic, complemented
3C2×#5166C211yesmaximal, characteristic, complemented
4#82777C211yesmaximal, characteristic, complemented
5C2×#5047C211yesmaximal, characteristic, complemented
6C2×#4788C211yesmaximal, characteristic, complemented
7C3×#2000C211yesmaximal, characteristic, complemented
8#71680C211yesmaximal, characteristic, complemented
9#70273C211yesmaximal, characteristic, complemented
10#70198C211yesmaximal, characteristic, complemented
11#70158C211yesmaximal, characteristic, complemented
12#69960C211yesmaximal, characteristic, complemented
13#69916C211yesmaximal, characteristic, complemented
14#68893C211yesmaximal, characteristic, complemented
15#68824C211yesmaximal, characteristic, complemented
16#24247—31nomaximal, Sylow
17C22×D3×D4C2211yescharacteristic
18C22×#235C2211yescharacteristic
19C22×C3×SD16C2211yescharacteristic
20C2×C3×C22⋊Q8C2211yescharacteristic, complemented
21C2×C3×#121C2211yescharacteristic
22C2×#946C2211yescharacteristic
23C2×Q8×Dic3C2211yescharacteristic, complemented
24C22×#216C2211yescharacteristic, complemented
25C22×#215C2211yescharacteristic
26C2×#938—21no—
27C2×#937—21no—
28C2×#936C2211yescharacteristic
29C2×C4×#67C2211yescharacteristic
30#5612—24no—
31#5612—24no—
32C2×#897C2211yescharacteristic
33C2×#893C2211yescharacteristic
34C2×#883—21no—
35C2×D3×C22⋊C4—21no—
36C2×C3×#103C2211yescharacteristic, complemented
37C2×C3×#102C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic, complemented
39C2×#832C2211yescharacteristic
40C2×#832C2211yescharacteristic
41#5212C2211yescharacteristic, complemented
42C2×#830C2211yescharacteristic, complemented
43#5169—24no—
44#5166—24no—
45C2×#821C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×#816C2211yescharacteristic, complemented
50C2×#816C2211yescharacteristic, complemented
51C2×Dic3⋊C8C2211yescharacteristic, complemented
52C2×C8×Dic3C2211yescharacteristic, complemented
53#5047—24no—
54#4990—21no—
55#4987C2211yescharacteristic
56#4982—21no—
57#4977C2211yescharacteristic, complemented
58C2×#810C2211yescharacteristic, complemented
59C2×#809C2211yescharacteristic
60C2×#808C2211yescharacteristic, complemented
61#4961—21no—
62#4945—21no—
63#4788—24no—
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#2034—31no—
74#2001—31no—
75#2000D311yescharacteristic, complemented
76#1958—31no—
77#1954—31no—
78#1804—31no—
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×D4—21no—
84C22×C3×D4C2311yescharacteristic
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C22×#67—21no—
88C22×#67D411yescharacteristic
89C2×D3×D4—22no—
90C2×D3×D4—22no—
91C2×D3×D4—22no—
92C2×D3×D4—22no—
93C2×D3×D4—41no—
94C2×D3×D4—41no—
95C2×#235—22no—
96C2×#235—22no—
97C2×#235—22no—
98C2×#235—22no—
99C2×#235—41no—
100C2×#235—41no—
101C22×D12C2311yescharacteristic
102C22×C4×D3—21no—
103C22×C4×D3—21no—
104C22×C4×D3C2311yescharacteristic
105C22×Dic6C2311yescharacteristic
106C2×C3×SD16—22no—
107C2×C3×SD16—22no—
108C2×C3×SD16—41no—
109C22×C3×C8C2311yescharacteristic
110C22×C3×C8C2311yescharacteristic
111C3×C22⋊Q8—22no—
112C3×C22⋊Q8—41no—
113C3×#121—22no—
114C3×#121—22no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4C2311yescharacteristic
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×#217—21no—
121C2×#217—21no—
122C2×#217—21no—
123C2×#217D411yescharacteristic
124#946—22no—
125#946—41no—
126Q8×Dic3—22no—
127Q8×Dic3—22no—
128C2×#216—22no—
129C2×#216—22no—
130C2×#216—41no—
131C2×#215—22no—
132C2×#215—22no—
133C2×#215D414yescomplemented
134#938—28no—
135#937—28no—
136#936—22no—
137#936D414yes—
138C4×#67—22no—
139C4×#67—22no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4—21no—
144C2×(C2×D3)⋊C4D411yescharacteristic
145C2×C4⋊Dic3—21no—
146C2×C4⋊Dic3—21no—
147C2×C4⋊Dic3C2311yescharacteristic
148C2×C4⋊Dic3C2311yescharacteristic
149C2×Dic3⋊C4—21no—
150C2×Dic3⋊C4D411yescharacteristic
151C2×C4×Dic3—21no—
152C2×C4×Dic3C2311yescharacteristic
153C22×C3⋊C8C2311yescharacteristic
154C22×C3⋊C8C2311yescharacteristic
155#897—22no—
156#897—22no—
157#893—22no—
158#893D414yes—
159#883—28no—
160D3×C22⋊C4—28no—
161C3×#103—22no—
162C3×#102—41no—
163C3×C22⋊C8—41no—
164#832—22no—
165#832—22no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170#830—22no—
171#821—22no—
172#821—22no—
173(C2×D3)⋊C8—22no—
174(C2×D3)⋊C8—41no—
175#816—22no—
176#816—41no—
177Dic3⋊C8—22no—
178C8×Dic3—22no—
179#810—22no—
180#809—22no—
181#808—22no—
182C22×#41—31no—
183C23×D4—31no—
184C22×Q16—31no—
185C22×SD16—31no—
186C22×SD16C2×D311yescharacteristic
187#546—64no—
188#546—64no—
189C2×#124—31no—
190C2×#123—61no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8—31no—
193C2×C22⋊Q8C2×D311yescharacteristic, complemented
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×#106—31no—
206C2×C4⋊C8—31no—
207C2×#103—31no—
208C2×#103—31no—
209C2×#103—31no—
210C2×#103C2×D311yescharacteristic, complemented
211C2×#102—31no—
212C2×#102—31no—
213C2×#102—31no—
214C2×#102—31no—
215C2×#102—31no—
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#380—31no—
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×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8—21no—
246C2×C3×Q8—21no—
247C2×C3×Q8C2×D412yes—
248C2×C3×D4—24no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4—81no—
255C2×C3×D4—81no—
256C2×C3×D4C2×D412yes—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4C2×D411yescharacteristic
267C22×C3×C4C2411yescharacteristic
268C2×#67—24no—
269C2×#67—24no—
270C2×#67—22no—
271C2×#67—22no—
272C2×#67—41no—
273C2×#67—42no—
274C2×#67—42no—
275C2×#67—42no—
276C2×#67—42no—
277C22×Dic3—21no—
278C22×Dic3—21no—
279C22×Dic3—21no—
280C22×Dic3C2×D411yescharacteristic
281C22×Dic3C2×D411yescharacteristic
282C22×Dic3C2×D411yescharacteristic
283D3×D4—44no—
284D3×D4—44no—
285D3×D4—44no—
286D3×D4—44no—
287#235—44no—
288#235—44no—
289#235—44no—
290#235—44no—
291C2×D12—21no—
292C2×D12—21no—
293C2×D12—21no—
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—
315C3×SD16—44no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—21no—
319C2×C3×C8—21no—
320C2×C3×C8—21no—
321C2×C3×C8—21no—
322C3×C4⋊C4—21no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—42no—
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#216—44no—
334#215—28no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—22no—
337(C2×D3)⋊C4—24no—
338(C2×D3)⋊C4—42no—
339(C2×D3)⋊C4—42no—
340C4⋊Dic3—24no—
341C4⋊Dic3—21no—
342C4⋊Dic3—21no—
343C4⋊Dic3—21no—
344C4⋊Dic3—21no—
345C4⋊Dic3—42no—
346Dic3⋊C4—22no—
347Dic3⋊C4—42no—
348C4×Dic3—42no—
349C4×Dic3C2×D412yes—
350C4×Dic3C2×D412yes—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8C2×D412yes—
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—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—22no—
386C2×SD16—22no—
387C2×SD16—34no—
388C2×SD16—41no—
389C2×SD16—62no—
390C2×SD16—62no—
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—41no—
400C22⋊Q8—62no—
401C22⋊Q8—62no—
402C22⋊Q8—62no—
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—21no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—61no—
419C2×C4⋊C4—61no—
420C2×C4⋊C4—61no—
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—62no—
438C4⋊C8—62no—
439#103—22no—
440#103—62no—
441#103—62no—
442#103—121no—
443#102—41no—
444#102—62no—
445#102—62no—
446#102—62no—
447#102—62no—
448#102—62no—
449C22⋊C8—41no—
450C22⋊C8—62no—
451C22⋊C8—62no—
452C22⋊C8—121no—
453C4×C8—62no—
454#95—61no—
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×Q8—22no—
495C3×Q8—22no—
496C3×Q8—41no—
497C3×Q8—41no—
498C3×D4—22no—
499C3×D4—22no—
500C3×D4—41no—
501C3×D4—41no—
502C3×D4—84no—
503C2×C3×C4—21no—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
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×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4C22×D411yescharacteristic
520C2×C3×C4C22×D411yescharacteristic
521C2×C3×C4C22×D411yescharacteristic
522C2×C3×C4C2×#4111yescharacteristic
523C2×C3×C4H(5,𝔽2)11yescharacteristic
524C2×C3×C4H(5,𝔽2)11yescharacteristic
525#67—44no—
526#67—48no—
527#67—48no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—22no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3—41no—
542C2×Dic3—41no—
543C2×Dic3—41no—
544C2×Dic3#12012yes—
545C2×Dic3#12012yes—
546D12—22no—
547D12—22no—
548D12—22no—
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—41no—
561C3×C8—41no—
562C3⋊C8—22no—
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—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—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—44no—
650SD16—68no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—32no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C2×C8—61no—
662C2×C8—61no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—42no—
667C4⋊C4—62no—
668C4⋊C4—64no—
669C4⋊C4—61no—
670C4⋊C4—61no—
671C4⋊C4—61no—
672C4⋊C4—61no—
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—42no—
729C3×C4—81no—
730C3×C4C2×#12111yescharacteristic
731C3×C4#53511yescharacteristic
732C3×C4D4211yescharacteristic
733C3×C4#54611yescharacteristic
734Dic3—22no—
735Dic3—22no—
736Dic3—42no—
737Dic3—41no—
738Dic3—81no—
739Dic3—81no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—32no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—61no—
756C23—61no—
757C23—61no—
758C23—61no—
759C23—62no—
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—22no—
777Q8—22no—
778Q8—41no—
779Q8—41no—
780Q8—62no—
781Q8—62no—
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—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—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—62no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—128no—
823C2×C4—121no—
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×C4#100411yescharacteristic
840C2×C4#100411yescharacteristic
841C2×C4D3×#4111yescharacteristic
842C8—41no—
843C8—41no—
844C8—62no—
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—42no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—62no—
868C22—62no—
869C22—64no—
870C22—62no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—122no—
876C22—121no—
877C22—122no—
878C22—122no—
879C22—121no—
880C22—121no—
881C22—122no—
882C22—121no—
883C22—122no—
884C22—122no—
885C22—2416no—
886C22D3×#12011yescharacteristic
887C22#559011yescharacteristic
888C22#561011yescharacteristic
889C22#576211yescharacteristic
890C22D3×#13511yescharacteristic
891C22#577511yescharacteristic
892C22#577711yescharacteristic
893C4—42no—
894C4—41no—
895C4—42no—
896C4—62no—
897C4—62no—
898C4—81no—
899C4—121no—
900C4—122no—
901C4—241no—
902C4—241no—
903C4#559011yescharacteristic
904C4D3×#12111yescharacteristic
905C4#561011yescharacteristic
906C4#571511yescharacteristic
907C3#2424711yescharacteristic, complemented, Sylow
908C2—81no—
909C2—82no—
910C2—122no—
911C2—124no—
912C2#7666911yescharacteristic
913C2#8006211yescharacteristic
914C2#8012611yescharacteristic
915C2#8014811yescharacteristic
916C2#8022611yescharacteristic
917C2#8067111yescharacteristic
918C2#8082711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radicalC2×#5612C2
hypercenter#2000D3
hypocenterC3#24247
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
2. C2×#5169C2semidirect
3. C2×#5166C2semidirect
4. #82777C2semidirect
5. C2×#5047C2semidirect
6. C2×#4788C2semidirect
7. C3×#2000C2semidirect
8. #71680C2semidirect
9. #70273C2semidirect
10. #70198C2semidirect
11. #70158C2semidirect
12. #69960C2semidirect
13. #69916C2semidirect
14. #68893C2semidirect
15. #68824C2semidirect
20. C2×C3×C22⋊Q8C22semidirect
23. C2×Q8×Dic3C22semidirect
24. C22×#216C22semidirect
36. C2×C3×#103C22semidirect
38. C2×C3×C22⋊C8C22semidirect
41. #5212C22semidirect
42. C2×#830C22semidirect
49. C2×#816C22semidirect
50. C2×#816C22semidirect
51. C2×Dic3⋊C8C22semidirect
52. C2×C8×Dic3C22semidirect
57. #4977C22semidirect
58. C2×#810C22semidirect
60. C2×#808C22semidirect
64. C3×#340C22semidirect
65. #4529C22semidirect
75. #2000D3semidirect
133. C2×#215D4semidirect
193. C2×C22⋊Q8C2×D3semidirect
210. C2×#103C2×D3semidirect
220. C2×C22⋊C8C2×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×#51692
C2×#51662
#827772
C2×#50472
C2×#47882
C3×#20002
#716802
#702732
#701982
#701582
#699602
#699162
#688932
#688242
#242473