Finite Group Databasebeta

← #10830667

Subgroups — #10830667

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×#5550C211yesmaximal, characteristic
2#82375C211yesmaximal, characteristic, complemented
3C2×#4845C211yesmaximal, characteristic, complemented
4C2×#4733C211yesmaximal, characteristic, complemented
5C2×#4731C211yesmaximal, characteristic, complemented
6C2×C4×#204C211yesmaximal, characteristic, complemented
7C3×#1954C211yesmaximal, characteristic, complemented
8#70480C211yesmaximal, characteristic, complemented
9#69964C211yesmaximal, characteristic, complemented
10#69962C211yesmaximal, characteristic, complemented
11#69960C211yesmaximal, characteristic, complemented
12#69959C211yesmaximal, characteristic, complemented
13#69936C211yesmaximal, characteristic, complemented
14#69935C211yesmaximal, characteristic, complemented
15#69773C211yesmaximal, characteristic, complemented
16#24247—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×D12C2211yescharacteristic
19C2×C3×C4×D4C2211yescharacteristic
20C2×#937—21no—
21C2×#930C2211yescharacteristic
22C2×#924C2211yescharacteristic
23C2×#924C2211yescharacteristic
24C2×#924C2211yescharacteristic, complemented
25C22×Dic12C2211yescharacteristic, complemented
26C22×#204C2211yescharacteristic
27C22×#204C2211yescharacteristic
28#5550—24no—
29#5550—24no—
30C2×#894—21no—
31C2×#884—21no—
32C2×D3×C22⋊C4—21no—
33C2×#875C2211yescharacteristic
34C2×C4×D12C2211yescharacteristic
35C2×C4×Dic6C2211yescharacteristic, complemented
36C2×C3×C4⋊C8C2211yescharacteristic, complemented
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic, complemented
40C2×C3×C22⋊C8C2211yescharacteristic, complemented
41C2×C3×C4×C8C2211yescharacteristic, complemented
42#5222—21no—
43#5212C2211yescharacteristic
44#5212C2211yescharacteristic, complemented
45C2×#821C2211yescharacteristic
46C2×#821C2211yescharacteristic
47C2×#821C2211yescharacteristic
48C2×#821C2211yescharacteristic
49C2×#821C2211yescharacteristic
50C2×#821C2211yescharacteristic
51C2×#817C2211yescharacteristic, complemented
52C2×#816C2211yescharacteristic, complemented
53C2×#816C2211yescharacteristic, complemented
54C2×#816C2211yescharacteristic, complemented
55C2×#816C2211yescharacteristic, complemented
56#4983—21no—
57#4944—21no—
58#4944—21no—
59#4936C2211yescharacteristic, complemented
60#4845—24no—
61#4733—24no—
62#4731—24no—
63C4×#204—24no—
64#4551C2211yescharacteristic, complemented
65#4551C2211yescharacteristic, 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#2000—31no—
76#1958—31no—
77#1954D311yescharacteristic, complemented
78#1804—31no—
79#1788—31no—
80#1786—31no—
81C24×D3—21no—
82C22×C3×D4D411yescharacteristic
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C22×#67—21no—
86C22×#67—21no—
87C2×#235—22no—
88C2×#235—22no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—41no—
92C2×#235—41no—
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×Dic6C2311yescharacteristic
105C22×Dic6C2311yescharacteristic
106C22×C3×C8C2311yescharacteristic
107C22×C3×C8C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C22×C3×C8C2311yescharacteristic
110C3×C4×D4—22no—
111C3×C4×D4—22no—
112C2×C3×C4⋊C4D411yescharacteristic
113C2×C3×C22⋊C4D411yescharacteristic
114C2×C3×C22⋊C4D411yescharacteristic
115C2×C3×C42C2311yescharacteristic
116C2×#217—21no—
117C2×#217—21no—
118C2×#217—21no—
119C2×#217—21no—
120C2×#217—21no—
121#937—28no—
122#930—22no—
123#930—22no—
124C2×(C2×D3)⋊C4—21no—
125C2×(C2×D3)⋊C4—21no—
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—21no—
128C2×C4⋊Dic3C2311yescharacteristic
129C2×C4⋊Dic3C2311yescharacteristic
130C2×C4⋊Dic3C2311yescharacteristic
131C2×C4⋊Dic3C2311yescharacteristic
132#924—22no—
133#924—22no—
134#924—22no—
135#924—22no—
136#924—41no—
137#924—41no—
138C2×Dic3⋊C4—21no—
139C2×Dic3⋊C4—21no—
140C2×Dic3⋊C4—21no—
141C2×Dic3⋊C4—21no—
142C2×C4×Dic3—21no—
143C2×Dic12—22no—
144C2×Dic12—22no—
145C2×Dic12—41no—
146C2×#204—22no—
147C2×#204—22no—
148C2×#204—22no—
149C2×#204—22no—
150C2×#204—41no—
151C2×#204D414yescomplemented
152#894—28no—
153#884—28no—
154D3×C22⋊C4—28no—
155#875—22no—
156#875D414yes—
157C4×D12—22no—
158C4×D12D414yes—
159C4×Dic6—22no—
160C4×Dic6—22no—
161C3×C4⋊C8—22no—
162C3×C22⋊C8—22no—
163C3×C22⋊C8—22no—
164C3×C22⋊C8—41no—
165C3×C22⋊C8—41no—
166C3×C4×C8—22no—
167C3⋊#95—21no—
168C3⋊#95—21no—
169C3⋊#95—21no—
170C3⋊#95—21no—
171#821—22no—
172#821—22no—
173#821—22no—
174#821—22no—
175#821—22no—
176#821—41no—
177#817—22no—
178#816—22no—
179#816—22no—
180#816—22no—
181#816—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⋊Q8—31no—
194C2×#121—31no—
195C2×#121—61no—
196C2×#120—61no—
197C2×C4×Q8—31no—
198C2×C4×D4—31no—
199C2×C4×D4C2×D311yescharacteristic
200C22×C22⋊C4—61no—
201#464—64no—
202#452—64no—
203#450—64no—
204C4×SD16—64no—
205C2×#106—31no—
206C2×C4⋊C8C2×D311yescharacteristic, complemented
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×#102—31no—
216C2×#102—31no—
217C2×C22⋊C8C2×D311yescharacteristic
218C2×C22⋊C8C2×D311yescharacteristic
219C2×C22⋊C8C2×D311yescharacteristic, complemented
220C2×C22⋊C8C2×D311yescharacteristic, complemented
221C2×C4×C8C2×D311yescharacteristic, complemented
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#340—31no—
231C24×C3C2×D411yescharacteristic
232C24×C3C2×D411yescharacteristic
233C23×D3—21no—
234C23×D3—21no—
235C23×D3—24no—
236C23×D3—42no—
237C23×D3—42no—
238C23×D3—42no—
239C23×D3—42no—
240C23×D3—81no—
241C23×D3—81no—
242C2×C3×D4—22no—
243C2×C3×D4—22no—
244C2×C3×D4—41no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
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×C4C2×D411yescharacteristic
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2411yescharacteristic
262C2×#67—24no—
263C2×#67—24no—
264C2×#67—42no—
265C2×#67—42no—
266C2×#67—81no—
267C2×#67—81no—
268C22×Dic3—21no—
269C22×Dic3—21no—
270C22×Dic3—21no—
271C22×Dic3—21no—
272C22×Dic3—21no—
273C22×Dic3—21no—
274#235—44no—
275#235—44no—
276#235—44no—
277#235—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—21no—
287C2×D12—44no—
288C2×D12—44no—
289C2×D12—44no—
290C2×D12—42no—
291C2×D12—42no—
292C2×D12—44no—
293C2×D12C2×D412yes—
294C2×D12C2×D412yes—
295C2×D12C2×D412yes—
296C2×D12#4112yes—
297C2×C4×D3—24no—
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×C8—21no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8C2×D412yes—
327C3×C4⋊C4—22no—
328C3×C22⋊C4—22no—
329C3×C22⋊C4—22no—
330C3×C42C2×D412yes—
331C3×C42C2×D412yes—
332#217—24no—
333#217—42no—
334#217—42no—
335#217—42no—
336#217—42no—
337(C2×D3)⋊C4—24no—
338(C2×D3)⋊C4—24no—
339(C2×D3)⋊C4—24no—
340(C2×D3)⋊C4—24no—
341C4⋊Dic3—21no—
342C4⋊Dic3—21no—
343C4⋊Dic3—21no—
344C4⋊Dic3—21no—
345C4⋊Dic3—21no—
346C4⋊Dic3—21no—
347C4⋊Dic3—21no—
348C4⋊Dic3C2×D412yes—
349Dic3⋊C4—24no—
350Dic3⋊C4—42no—
351Dic3⋊C4—42no—
352Dic3⋊C4—42no—
353C4×Dic3—42no—
354Dic12—44no—
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×Q8—31no—
366C22×D4—31no—
367C22×D4—31no—
368C22×D4—62no—
369C22×D4—62no—
370C22×D4—62no—
371C22×D4—62no—
372C22×D4—61no—
373C22×D4—61no—
374C22×D4—61no—
375C22×D4—121no—
376C22×D4—121no—
377C22×D4D1211yescharacteristic
378C23×C4—61no—
379C23×C4—61no—
380C23×C4C22×D311yescharacteristic
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×C8C22×D311yescharacteristic
392C22×C8C22×D311yescharacteristic
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—68no—
405#121—62no—
406#121—62no—
407#120—68no—
408C4×Q8—62no—
409C4×Q8—62no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4—34no—
413C4×D4—62no—
414C2×C4⋊C4—31no—
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⋊C4—61no—
422C2×C4⋊C4D1211yescharacteristic
423C2×C22⋊C4—68no—
424C2×C22⋊C4—61no—
425C2×C22⋊C4—61no—
426C2×C22⋊C4—61no—
427C2×C22⋊C4—61no—
428C2×C22⋊C4—61no—
429C2×C22⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C22⋊C4—61no—
432C2×C22⋊C4—61no—
433C2×C22⋊C4D1211yescharacteristic
434C2×C22⋊C4D1211yescharacteristic
435C2×C42—61no—
436C2×C42C22×D311yescharacteristic
437#106—62no—
438C4⋊C8—22no—
439#103—62no—
440#103—62no—
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—22no—
451C22⋊C8—41no—
452C22⋊C8—41no—
453C4×C8—22no—
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—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3#13512yes—
472C23×C3C22×D411yescharacteristic
473C22×D3—22no—
474C22×D3—22no—
475C22×D3—22no—
476C22×D3—22no—
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×D4—44no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
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#12012yes—
514C2×C3×C4#12012yes—
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—48no—
522#67—84no—
523C2×Dic3—22no—
524C2×Dic3—22no—
525C2×Dic3—22no—
526C2×Dic3—41no—
527C2×Dic3—41no—
528C2×Dic3—41no—
529C2×Dic3—41no—
530C2×Dic3—41no—
531C2×Dic3—41no—
532C2×Dic3—41no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540C2×Dic3—41no—
541D12—22no—
542D12—22no—
543D12—22no—
544D12—22no—
545D12—22no—
546D12—48no—
547D12—41no—
548D12—41no—
549D12#12114yes—
550C4×D3—48no—
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—64no—
565C24—61no—
566C24—61no—
567C24—122no—
568C24—122no—
569C24—122no—
570C24—122no—
571C24—241no—
572C24—241no—
573C24C2×D1211yescharacteristic
574C24C2×D1211yescharacteristic
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—22no—
592C2×D4—22no—
593C2×D4—32no—
594C2×D4—32no—
595C2×D4—32no—
596C2×D4—32no—
597C2×D4—41no—
598C2×D4—64no—
599C2×D4—64no—
600C2×D4—64no—
601C2×D4—61no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—61no—
609C2×D4—122no—
610C2×D4—122no—
611C2×D4—124no—
612C2×D4—124no—
613C2×D4—124no—
614C2×D4—124no—
615C2×D4—122no—
616C2×D4—122no—
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—21no—
630C22×C4—21no—
631C22×C4—64no—
632C22×C4—61no—
633C22×C4—61no—
634C22×C4—61no—
635C22×C4—64no—
636C22×C4—61no—
637C22×C4—61no—
638C22×C4—61no—
639C22×C4—122no—
640C22×C4—122no—
641C22×C4—241no—
642C22×C4—241no—
643C22×C4C2×D1211yescharacteristic
644C22×C4C2×D1211yescharacteristic
645C22×C4C2×D1211yescharacteristic
646C22×C4C2×D1211yescharacteristic
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—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8D3×D412yes—
663C4⋊C4—22no—
664C4⋊C4—32no—
665C4⋊C4—64no—
666C4⋊C4—61no—
667C4⋊C4—61no—
668C4⋊C4—61no—
669C4⋊C4—61no—
670C4⋊C4—61no—
671C4⋊C4—61no—
672C4⋊C4—61no—
673C4⋊C4—122no—
674C4⋊C4—122no—
675C4⋊C4—122no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—64no—
679C22⋊C4—64no—
680C22⋊C4—64no—
681C22⋊C4—64no—
682C22⋊C4—64no—
683C22⋊C4—122no—
684C22⋊C4—122no—
685C22⋊C4—122no—
686C22⋊C4—122no—
687C42—122no—
688C42D3×D412yes—
689C42D3×D412yes—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—22no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—41no—
697C22×C3—41no—
698C22×C3—41no—
699C22×C3—41no—
700C22×C3—41no—
701C22×C3—41no—
702C22×C3—41no—
703C22×C3—41no—
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—42no—
713C2×D3—42no—
714C2×D3—42no—
715C2×D3—42no—
716C2×D3—42no—
717C2×D3—42no—
718C2×D3—42no—
719C2×D3—42no—
720C2×D3—42no—
721C2×D3—816no—
722C2×D3—81no—
723C2×D3—81no—
724C2×D3—81no—
725C2×D3—81no—
726C3×C4—22no—
727C3×C4—22no—
728C3×C4—41no—
729C3×C4—41no—
730C3×C4C2×#12111yescharacteristic
731C3×C4#53511yescharacteristic
732C3×C4D4211yescharacteristic
733C3×C4#54611yescharacteristic
734Dic3—42no—
735Dic3—42no—
736Dic3—42no—
737Dic3—81no—
738Dic3—81no—
739Dic3—81no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—62no—
754C23—62no—
755C23—62no—
756C23—62no—
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#90412yes—
775C23C22×D1211yescharacteristic
776Q8—62no—
777Q8—62no—
778Q8—62no—
779Q8—62no—
780Q8—121no—
781Q8—121no—
782Q8—121no—
783Q8—121no—
784D4—34no—
785D4—44no—
786D4—62no—
787D4—62no—
788D4—62no—
789D4—62no—
790D4—62no—
791D4—128no—
792D4—128no—
793D4—121no—
794D4—121no—
795D4—244no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
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—62no—
815C2×C4—62no—
816C2×C4—62no—
817C2×C4—128no—
818C2×C4—121no—
819C2×C4—121no—
820C2×C4—121no—
821C2×C4—121no—
822C2×C4—121no—
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—244no—
834C2×C4#88212yes—
835C2×C4#88212yes—
836C2×C4C2×D3×D411yescharacteristic
837C2×C4C2×D3×D411yescharacteristic
838C2×C4C2×D3×D411yescharacteristic
839C2×C4#100411yescharacteristic
840C2×C4D3×#4111yescharacteristic
841C2×C4#100911yescharacteristic
842C8—22no—
843C8—41no—
844C8—41no—
845C8—41no—
846C2×C3—42no—
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—44no—
856D3—82no—
857C22—22no—
858C22—22no—
859C22—22no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—64no—
872C22—122no—
873C22—122no—
874C22—122no—
875C22—122no—
876C22—122no—
877C22—122no—
878C22—122no—
879C22—122no—
880C22—122no—
881C22—2416no—
882C22—241no—
883C22—241no—
884C22—241no—
885C22—241no—
886C22C2×#88211yescharacteristic
887C22D4×D1211yescharacteristic
888C22#555411yescharacteristic
889C22C2×#90411yescharacteristic
890C22#574811yescharacteristic
891C22#575111yescharacteristic
892C22#575111yescharacteristic
893C4—22no—
894C4—22no—
895C4—41no—
896C4—41no—
897C4—122no—
898C4—122no—
899C4—122no—
900C4—241no—
901C4—241no—
902C4—241no—
903C4D3×#12111yescharacteristic
904C4#560711yescharacteristic
905C4#567611yescharacteristic
906C4#571711yescharacteristic
907C3#2424711yescharacteristic, complemented, Sylow
908C2—42no—
909C2—81no—
910C2—124no—
911C2—242no—
912C2#7643611yescharacteristic
913C2#7861011yescharacteristic
914C2#7867111yescharacteristic
915C2#7943511yescharacteristic
916C2#7944011yescharacteristic
917C2#7955111yescharacteristic
918C2#7955411yescharacteristic
subgroupG/H
centerC23C22×D12
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1954C2
socleC23×C3C22×D4
prime radicalC2×#5550C2
hypercenter#1954D3
hypocenterC3#24247
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. #82375C2semidirect
3. C2×#4845C2semidirect
4. C2×#4733C2semidirect
5. C2×#4731C2semidirect
6. C2×C4×#204C2semidirect
7. C3×#1954C2semidirect
8. #70480C2semidirect
9. #69964C2semidirect
10. #69962C2semidirect
11. #69960C2semidirect
12. #69959C2semidirect
13. #69936C2semidirect
14. #69935C2semidirect
15. #69773C2semidirect
24. C2×#924C22semidirect
25. C22×Dic12C22semidirect
35. C2×C4×Dic6C22semidirect
36. C2×C3×C4⋊C8C22semidirect
39. C2×C3×C22⋊C8C22semidirect
40. C2×C3×C22⋊C8C22semidirect
41. C2×C3×C4×C8C22semidirect
44. #5212C22semidirect
51. C2×#817C22semidirect
52. C2×#816C22semidirect
53. C2×#816C22semidirect
54. C2×#816C22semidirect
55. C2×#816C22semidirect
59. #4936C22semidirect
64. #4551C22semidirect
65. #4551C22semidirect
77. #1954D3semidirect
151. C2×#204D4semidirect
206. C2×C4⋊C8C2×D3semidirect
219. C2×C22⋊C8C2×D3semidirect
220. C2×C22⋊C8C2×D3semidirect
221. C2×C4×C8C2×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×#55502
#823752
C2×#48452
C2×#47332
C2×#47312
C2×C4×#2042
C3×#19542
#704802
#699642
#699622
#699602
#699592
#699362
#699352
#697732
#242473