Finite Group Databasebeta

← #10830662

Subgroups — #10830662

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×#5187C211yesmaximal, characteristic, complemented
3C2×#5185C211yesmaximal, characteristic, complemented
4#82777C211yesmaximal, characteristic, complemented
5C2×#5046C211yesmaximal, characteristic, complemented
6C2×#4788C211yesmaximal, characteristic, complemented
7C3×#2001C211yesmaximal, characteristic, complemented
8#71694C211yesmaximal, characteristic, complemented
9#70272C211yesmaximal, characteristic, complemented
10#70267C211yesmaximal, characteristic, complemented
11#70226C211yesmaximal, characteristic, complemented
12#69959C211yesmaximal, characteristic, complemented
13#69916C211yesmaximal, characteristic, complemented
14#68893C211yesmaximal, characteristic, complemented
15#68823C211yesmaximal, characteristic, complemented
16#24247—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic, complemented
20C2×C3×C22⋊Q8C2211yescharacteristic
21C2×C3×C22⋊Q8C2211yescharacteristic
22C2×#947C2211yescharacteristic
23C2×#946C2211yescharacteristic, complemented
24C2×Q8×Dic3C2211yescharacteristic, complemented
25C22×#215C2211yescharacteristic
26C22×#215C2211yescharacteristic
27C2×C4×#67C2211yescharacteristic
28#5630—24no—
29#5630—24no—
30C2×#895—21no—
31C2×#895C2211yescharacteristic
32C2×#894—21no—
33C2×#893C2211yescharacteristic
34C2×#882—21no—
35C2×D3×C22⋊C4—21no—
36C2×C3×#103C2211yescharacteristic, complemented
37C2×C3×#103C2211yescharacteristic, complemented
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×#835C2211yescharacteristic, complemented
40C2×#835C2211yescharacteristic, complemented
41#5212C2211yescharacteristic
42C2×#830C2211yescharacteristic
43#5187—24no—
44#5185—24no—
45C2×#821C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×#821C2211yescharacteristic
48C2×#821C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
50C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C2×Dic3⋊C8C2211yescharacteristic, complemented
52C2×C8×Dic3C2211yescharacteristic, complemented
53#5046—24no—
54#4990—21no—
55#4987C2211yescharacteristic, complemented
56#4982—21no—
57#4977C2211yescharacteristic, complemented
58C2×#809C2211yescharacteristic
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#2001D311yescharacteristic, complemented
75#2000—31no—
76#1958—31no—
77#1954—31no—
78#1804—31no—
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×Q8C2311yescharacteristic
83C22×C3×Q8C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67D411yescharacteristic
86C2×#239—22no—
87C2×#239—22no—
88C2×#239—22no—
89C2×#239—22no—
90C2×#239—41no—
91C2×#239—41no—
92C22×D12—21no—
93C22×D12—21no—
94C22×D12—21no—
95C22×D12—22no—
96C22×D12—22no—
97C22×D12—22no—
98C22×D12—22no—
99C22×D12—41no—
100C22×D12—41no—
101C22×D12C2311yescharacteristic
102C22×D12C2311yescharacteristic
103C22×C4×D3—21no—
104C22×C4×D3—21no—
105C22×C4×D3C2311yescharacteristic
106C2×C3×Q16—22no—
107C2×C3×Q16—22no—
108C2×C3×Q16—41no—
109C22×C3×C8C2311yescharacteristic
110C22×C3×C8C2311yescharacteristic
111C3×C22⋊Q8—22no—
112C3×C22⋊Q8—22no—
113C3×C22⋊Q8—22no—
114C3×C22⋊Q8—41no—
115C2×C3×C4⋊C4—21no—
116C2×C3×C4⋊C4—21no—
117C2×C3×C4⋊C4C2311yescharacteristic
118C2×C3×C4⋊C4C2311yescharacteristic
119C2×C3×C22⋊C4—21no—
120C2×C3×C22⋊C4—21no—
121C2×#217—21no—
122C2×#217D411yescharacteristic
123#947—22no—
124#947D414yes—
125#946—22no—
126#946—41no—
127Q8×Dic3—22no—
128Q8×Dic3—22no—
129C2×#215—22no—
130C2×#215—22no—
131C2×#215—22no—
132C2×#215—22no—
133C2×#215—41no—
134C2×#215D414yescomplemented
135C4×#67—22no—
136C4×#67—22no—
137C2×(C2×D3)⋊C4—21no—
138C2×(C2×D3)⋊C4—21no—
139C2×(C2×D3)⋊C4—21no—
140C2×(C2×D3)⋊C4—21no—
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×(C2×D3)⋊C4D411yescharacteristic
144C2×C4⋊Dic3—21no—
145C2×C4⋊Dic3C2311yescharacteristic
146C2×C4⋊Dic3C2311yescharacteristic
147C2×Dic3⋊C4—21no—
148C2×Dic3⋊C4D411yescharacteristic
149C2×C4×Dic3—21no—
150C2×C4×Dic3C2311yescharacteristic
151C22×C3⋊C8C2311yescharacteristic
152C22×C3⋊C8C2311yescharacteristic
153#895—28no—
154#895—22no—
155#895—22no—
156#894—28no—
157#893—22no—
158#893D414yes—
159#882—28no—
160D3×C22⋊C4—28no—
161C3×#103—22no—
162C3×#103—41no—
163C3×C22⋊C8—41no—
164#835—22no—
165#835—22no—
166C3⋊#95—21no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170#830—22no—
171#821—22no—
172#821—22no—
173#821—22no—
174#821—41no—
175(C2×D3)⋊C8—22no—
176(C2×D3)⋊C8—41no—
177Dic3⋊C8—22no—
178C8×Dic3—22no—
179#809—22no—
180#809—22no—
181#808—22no—
182C22×#41—31no—
183C23×D4—31no—
184C22×Q16C2×D311yescharacteristic, complemented
185C22×SD16—31no—
186C22×SD16—31no—
187#546—64no—
188#546—64no—
189C2×#124—31no—
190C2×#123—61no—
191C2×C22⋊Q8—31no—
192C2×C22⋊Q8C2×D311yescharacteristic
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×#106—31no—
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#380—31no—
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×Q8—21no—
248C2×C3×Q8—21no—
249C2×C3×Q8—21no—
250C2×C3×Q8—21no—
251C2×C3×Q8—21no—
252C2×C3×Q8C2×D412yes—
253C2×C3×Q8C2×D412yes—
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×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4C2411yescharacteristic
266C2×#67—22no—
267C2×#67—22no—
268C2×#67—41no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3C2×D411yescharacteristic
272C22×Dic3C2×D411yescharacteristic
273C22×Dic3C2×D411yescharacteristic
274#239—44no—
275#239—44no—
276#239—44no—
277#239—44no—
278C2×D12—21no—
279C2×D12—21no—
280C2×D12—21no—
281C2×D12—21no—
282C2×D12—21no—
283C2×D12—21no—
284C2×D12—21no—
285C2×D12—24no—
286C2×D12—24no—
287C2×D12—21no—
288C2×D12—24no—
289C2×D12—44no—
290C2×D12—44no—
291C2×D12—44no—
292C2×D12—42no—
293C2×D12—42no—
294C2×D12—42no—
295C2×D12—42no—
296C2×D12—44no—
297C2×D12—81no—
298C2×D12—81no—
299C2×D12C2×D412yes—
300C2×D12C2×D412yes—
301C2×D12C2×D412yes—
302C2×D12#4112yes—
303C2×C4×D3—24no—
304C2×C4×D3—21no—
305C2×C4×D3—21no—
306C2×C4×D3—21no—
307C2×C4×D3—21no—
308C2×C4×D3—21no—
309C2×C4×D3—21no—
310C2×C4×D3—24no—
311C2×C4×D3—42no—
312C2×C4×D3—42no—
313C2×C4×D3—81no—
314C2×C4×D3—81no—
315C3×Q16—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—24no—
323C3×C4⋊C4—21no—
324C3×C4⋊C4—21no—
325C3×C4⋊C4—21no—
326C3×C4⋊C4—42no—
327C3×C4⋊C4C2×D412yes—
328C3×C22⋊C4—24no—
329C3×C22⋊C4—42no—
330#217—22no—
331#217—42no—
332#215—28no—
333#215—44no—
334(C2×D3)⋊C4—24no—
335(C2×D3)⋊C4—24no—
336(C2×D3)⋊C4—24no—
337(C2×D3)⋊C4—24no—
338(C2×D3)⋊C4—22no—
339(C2×D3)⋊C4—42no—
340(C2×D3)⋊C4—42no—
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×Q8C22×D311yescharacteristic
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—22no—
383C2×Q16—22no—
384C2×Q16—41no—
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—22no—
401C22⋊Q8—41no—
402C22⋊Q8—62no—
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—21no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—31no—
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—41no—
441#103—62no—
442#103—62no—
443#102—62no—
444#102—62no—
445#102—62no—
446#102—62no—
447#102—62no—
448#102—121no—
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—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—22no—
497C3×Q8—22no—
498C3×Q8—41no—
499C3×Q8—41no—
500C3×Q8—41no—
501C3×Q8—41no—
502C2×C3×C4—21no—
503C2×C3×C4—22no—
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×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4C22×D411yescharacteristic
522C2×C3×C4C22×D411yescharacteristic
523C2×C3×C4C22×D411yescharacteristic
524C2×C3×C4C2×#4111yescharacteristic
525C2×C3×C4H(5,𝔽2)11yescharacteristic
526C2×C3×C4H(5,𝔽2)11yescharacteristic
527#67—44no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541C2×Dic3#12012yes—
542C2×Dic3#12012yes—
543D12—22no—
544D12—22no—
545D12—22no—
546D12—22no—
547D12—22no—
548D12—48no—
549D12—48no—
550D12—41no—
551D12—41no—
552D12—84no—
553D12#12114yes—
554C4×D3—48no—
555C4×D3—41no—
556C4×D3—41no—
557C4×D3—41no—
558C4×D3—41no—
559C4×D3—84no—
560C3×C8—41no—
561C3×C8—41no—
562C3⋊C8—22no—
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—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—21no—
589C2×Q8D3×D412yes—
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—44no—
649SD16—68no—
650SD16—124no—
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—24no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—42no—
668C4⋊C4—62no—
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—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—42no—
730C3×C4—81no—
731C3×C4C2×#12111yescharacteristic
732C3×C4#53511yescharacteristic
733C3×C4D4211yescharacteristic
734C3×C4#54611yescharacteristic
735Dic3—22no—
736Dic3—22no—
737Dic3—41no—
738Dic3—81no—
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—62no—
754C23—61no—
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#91912yes—
775C23C2×D3×D411yescharacteristic
776Q8—22no—
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
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—22no—
797C2×C4—22no—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—32no—
803C2×C4—32no—
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—61no—
824C2×C4—128no—
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—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—122no—
874C22—121no—
875C22—121no—
876C22—122no—
877C22—121no—
878C22—122no—
879C22—121no—
880C22—121no—
881C22—2416no—
882C22—241no—
883C22—241no—
884C22—241no—
885C22—241no—
886C22D3×#12011yescharacteristic
887C22#559011yescharacteristic
888C22#561011yescharacteristic
889C22C2×#91911yescharacteristic
890C22#577011yescharacteristic
891C22#577711yescharacteristic
892C22#577811yescharacteristic
893C4—42no—
894C4—41no—
895C4—42no—
896C4—42no—
897C4—62no—
898C4—62no—
899C4—81no—
900C4—121no—
901C4—241no—
902C4—241no—
903C4#559011yescharacteristic
904C4D3×#12111yescharacteristic
905C4#561011yescharacteristic
906C4#571511yescharacteristic
907C3#2424711yescharacteristic, complemented, Sylow
908C2—42no—
909C2—124no—
910C2—241no—
911C2—242no—
912C2#7666911yescharacteristic
913C2#8018211yescharacteristic
914C2#8020711yescharacteristic
915C2#8022911yescharacteristic
916C2#8026811yescharacteristic
917C2#8077511yescharacteristic
918C2#8092411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2001C2
socleC23×C3C22×D4
prime radicalC2×#5630C2
hypercenter#2001D3
hypocenterC3#24247
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2001

Complements

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

NH ≅ G/Ntype
2. C2×#5187C2semidirect
3. C2×#5185C2semidirect
4. #82777C2semidirect
5. C2×#5046C2semidirect
6. C2×#4788C2semidirect
7. C3×#2001C2semidirect
8. #71694C2semidirect
9. #70272C2semidirect
10. #70267C2semidirect
11. #70226C2semidirect
12. #69959C2semidirect
13. #69916C2semidirect
14. #68893C2semidirect
15. #68823C2semidirect
19. C22×C3×Q16C22semidirect
23. C2×#946C22semidirect
24. C2×Q8×Dic3C22semidirect
36. C2×C3×#103C22semidirect
37. C2×C3×#103C22semidirect
39. C2×#835C22semidirect
40. C2×#835C22semidirect
49. C2×(C2×D3)⋊C8C22semidirect
50. C2×(C2×D3)⋊C8C22semidirect
51. C2×Dic3⋊C8C22semidirect
52. C2×C8×Dic3C22semidirect
55. #4987C22semidirect
57. #4977C22semidirect
60. C2×#808C22semidirect
64. C3×#340C22semidirect
65. #4529C22semidirect
74. #2001D3semidirect
134. C2×#215D4semidirect
184. C22×Q16C2×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×#51872
C2×#51852
#827772
C2×#50462
C2×#47882
C3×#20012
#716942
#702722
#702672
#702262
#699592
#699162
#688932
#688232
#242473