Finite Group Databasebeta

← #450608

Subgroups — #450608

Order 512.

1202 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1925C211yesmaximal, characteristic
2C2×#1864C211yesmaximal, characteristic
3#14133C211yesmaximal, characteristic, complemented
4#13979C211yesmaximal, characteristic
5#11372C211yesmaximal, characteristic, complemented
6#11328C211yesmaximal, characteristic, complemented
7#11325C211yesmaximal, characteristic, complemented
8#11298C211yesmaximal, characteristic, complemented
9#11220C211yesmaximal, characteristic, complemented
10#11220C211yesmaximal, characteristic, complemented
11#11189C211yesmaximal, characteristic
12#11121C211yesmaximal, characteristic
13#11066C211yesmaximal, characteristic
14#10908C211yesmaximal, characteristic, complemented
15#10788C211yesmaximal, characteristic
16C22×C4×D4C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#106C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C2×#390C2211yescharacteristic
25C2×#390C2211yescharacteristic
26C2×#389C2211yescharacteristic
27C2×#389C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#387—21no—
30C2×#382C2211yescharacteristic
31C2×C4×C4⋊C4C2211yescharacteristic
32#1925—24no—
33#1864—24no—
34C2×#340C2211yescharacteristic
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49#1443—21no—
50#1442—21no—
51#1439—21no—
52#1439—21no—
53#1436—21no—
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C22⋊#95—21no—
59C22⋊#95—21no—
60C4×#95C2211yescharacteristic
61C23×D4C2311yescharacteristic
62C24×C4—21no—
63C23×C8C2311yescharacteristic
64C23×C8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C2×C4×D4—22no—
68C2×C4×D4—22no—
69C2×C4×D4—41no—
70C2×C4×D4—41no—
71C2×C4×D4—41no—
72C2×C4×D4—41no—
73C22×C4⋊C4—21no—
74C22×C4⋊C4—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4C2311yescharacteristic
77C22×C4⋊C4C2311yescharacteristic
78C22×C4⋊C4C2311yescharacteristic
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C22⋊C4—21no—
84C22×C22⋊C4—21no—
85C22×C22⋊C4—21no—
86C22×C22⋊C4—21no—
87C22×C22⋊C4—21no—
88C22×C42—21no—
89C22×C42C2311yescharacteristic
90C22×C42C2311yescharacteristic
91C22×C42C2311yescharacteristic
92C2×#107—22no—
93C2×#107—41no—
94C2×#107—41no—
95C2×#106—22no—
96C2×#106—22no—
97C2×#106—22no—
98C2×#106—22no—
99C2×#106—41no—
100C2×#106—41no—
101C2×#102—22no—
102C2×#102—22no—
103C2×#102—22no—
104C2×#102—22no—
105C2×#102—22no—
106C2×#102—22no—
107C2×#102—22no—
108C2×#102—41no—
109C2×#102—41no—
110C2×#102—41no—
111C2×#102D414yes—
112C2×#102Q814yes—
113#390—22no—
114#390—22no—
115#390—22no—
116#390—41no—
117#389—22no—
118#389—22no—
119#389—22no—
120#389—41no—
121#389—41no—
122#389—41no—
123#387—44no—
124#382—22no—
125#382—41no—
126C4×C4⋊C4—22no—
127C4×C4⋊C4—41no—
128C2×#95—21no—
129C2×#95—21no—
130C2×#95—21no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
134C2×#95—21no—
135C2×#95—21no—
136C2×#95—21no—
137C2×#95—21no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95D411yescharacteristic
143C2×#95D411yescharacteristic
144C2×#95D411yescharacteristic
145C2×#95D411yescharacteristic
146#340—22no—
147#340—22no—
148#340—22no—
149#340—22no—
150#340—41no—
151#340—41no—
152#340—41no—
153#340—41no—
154#340—41no—
155#336—22no—
156#336—22no—
157#336—22no—
158#336—22no—
159#336—41no—
160#336—41no—
161C25—21no—
162C22×D4—21no—
163C22×D4—21no—
164C22×D4—21no—
165C22×D4—21no—
166C22×D4—21no—
167C22×D4—21no—
168C22×D4—21no—
169C22×D4—21no—
170C22×D4—21no—
171C22×D4—21no—
172C22×D4—21no—
173C22×D4C2×D412yes—
174C22×D4C2×Q812yes—
175C22×D4#4112yes—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—42no—
184C23×C4—42no—
185C23×C4—42no—
186C23×C4—42no—
187C23×C4—42no—
188C23×C4—81no—
189C23×C4—81no—
190C23×C4C2×D411yescharacteristic
191C23×C4C2×D411yescharacteristic
192C23×C4C2×D411yescharacteristic
193C23×C4C2×D411yescharacteristic
194C23×C4C2×D411yescharacteristic
195C23×C4C2×D411yescharacteristic
196C23×C4C2411yescharacteristic
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—21no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C22×C8—21no—
212C22×C8—21no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8C2×D412yes—
223C22×C8C2×Q812yes—
224C22×C8#4112yes—
225C4×D4—44no—
226C4×D4—44no—
227C4×D4—44no—
228C4×D4—44no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—42no—
268C2×C4⋊C4—42no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—42no—
271C2×C4⋊C4—81no—
272C2×C4⋊C4—81no—
273C2×C4⋊C4—81no—
274C2×C4⋊C4C2×D412yes—
275C2×C4⋊C4C2×Q812yes—
276C2×C4⋊C4#4112yes—
277C2×C4⋊C4#4112yes—
278C2×C4⋊C4#4112yes—
279C2×C4⋊C4#4112yes—
280C2×C22⋊C4—24no—
281C2×C22⋊C4—24no—
282C2×C22⋊C4—42no—
283C2×C22⋊C4—42no—
284C2×C22⋊C4—42no—
285C2×C22⋊C4—42no—
286C2×C22⋊C4—42no—
287C2×C22⋊C4—42no—
288C2×C22⋊C4—42no—
289C2×C22⋊C4—81no—
290C2×C22⋊C4—81no—
291C2×C22⋊C4—81no—
292C2×C22⋊C4—81no—
293C2×C22⋊C4—81no—
294C2×C22⋊C4—81no—
295C2×C42—21no—
296C2×C42—21no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—21no—
303C2×C42—21no—
304C2×C42—21no—
305C2×C42—21no—
306C2×C42—21no—
307C2×C42—21no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—42no—
314C2×C42—42no—
315C2×C42—81no—
316#107—44no—
317#106—44no—
318#106—44no—
319#102—28no—
320#102—28no—
321#102—44no—
322#102—44no—
323#95—24no—
324#95—22no—
325#95—22no—
326#95—41no—
327#95—41no—
328#95—42no—
329#95—42no—
330#95—42no—
331#95—42no—
332#95—42no—
333#95—42no—
334#95—42no—
335#95—42no—
336#95—42no—
337#95—42no—
338#95—81no—
339#95—81no—
340#95—81no—
341C24—22no—
342C24—22no—
343C24—22no—
344C24—41no—
345C24—41no—
346C24—41no—
347C24—41no—
348C24—41no—
349C24—41no—
350C24—41no—
351C24—41no—
352C24—41no—
353C24—41no—
354C24—41no—
355C24—41no—
356C24C22×D411yescharacteristic
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—22no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—22no—
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4C22⋊Q814yes—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—48no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463C22×C4—41no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—84no—
476C22×C4—84no—
477C22×C4—84no—
478C22×C4—84no—
479C22×C4—84no—
480C22×C4—84no—
481C22×C4#13512yes—
482C22×C4AGL(1,ℤ/8)12yes—
483C22×C4C22×D411yescharacteristic
484C22×C4C22×Q811yescharacteristic
485C22×C4C2×#4111yescharacteristic
486C22×C4C2×#4111yescharacteristic
487C22×C4C2×#4111yescharacteristic
488C22×C4C2×#4111yescharacteristic
489C22×C4C2×#4111yescharacteristic
490C22×C4C2×#4111yescharacteristic
491C22×C4H(5,𝔽2)11yescharacteristic
492C22×C4H(5,𝔽2)11yescharacteristic
493C22×C4H(5,𝔽2)11yescharacteristic
494C22×C4H(5,𝔽2)11yescharacteristic
495C22×C42−1+411yescharacteristic
496C22×C42−1+411yescharacteristic
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—22no—
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C2×C8—41no—
512C2×C8—41no—
513C2×C8—41no—
514C2×C8—41no—
515C2×C8—41no—
516C2×C8—41no—
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—48no—
538C4⋊C4—41no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—41no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—41no—
554C4⋊C4—84no—
555C4⋊C4—84no—
556C22⋊C4—48no—
557C22⋊C4—84no—
558C22⋊C4—84no—
559C22⋊C4—84no—
560C22⋊C4—84no—
561C42—41no—
562C42—41no—
563C42—41no—
564C42—41no—
565C42—41no—
566C42—41no—
567C42—41no—
568C42—41no—
569C42—41no—
570C42—41no—
571C42—41no—
572C42—41no—
573C42—84no—
574C23—24no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—42no—
581C23—42no—
582C23—42no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—81no—
594C23—81no—
595C23—81no—
596C23—81no—
597C23—81no—
598C23—81no—
599C23—81no—
600C23—81no—
601C23—81no—
602C23—81no—
603C23—81no—
604C23—81no—
605C23—81no—
606C23—81no—
607C23—81no—
608C23—81no—
609C23#52511yescharacteristic
610C23#52511yescharacteristic
611C23#53511yescharacteristic
612C23D4211yescharacteristic
613C23#54611yescharacteristic
614C23#54711yescharacteristic
615C23D4×Q811yescharacteristic
616C23C2×#13511yescharacteristic
617C23C2×AGL(1,ℤ/8)11yescharacteristic
618C23#57511yescharacteristic
619C23#57511yescharacteristic
620C23#57611yescharacteristic
621C23#57711yescharacteristic
622C23#57711yescharacteristic
623C23#57711yescharacteristic
624D4—24no—
625D4—24no—
626D4—42no—
627D4—42no—
628D4—42no—
629D4—42no—
630D4—42no—
631D4—42no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—816no—
693C2×C4—81no—
694C2×C4—81no—
695C2×C4—81no—
696C2×C4—81no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—81no—
700C2×C4—81no—
701C2×C4—81no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4—81no—
708C2×C4—81no—
709C2×C4—81no—
710C2×C4—81no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—81no—
724C2×C4C2×C22⋊Q811yescharacteristic
725C2×C4#52511yescharacteristic
726C2×C4#52911yescharacteristic
727C2×C4#53311yescharacteristic
728C2×C4#53411yescharacteristic
729C2×C4#53811yescharacteristic
730C2×C4#53911yescharacteristic
731C2×C4#53911yescharacteristic
732C2×C4#53911yescharacteristic
733C2×C4#54211yescharacteristic
734C2×C4#54211yescharacteristic
735C2×C4#54411yescharacteristic
736C2×C4#54611yescharacteristic
737C2×C4#54711yescharacteristic
738C2×C4#54711yescharacteristic
739C2×C4#55111yescharacteristic
740C2×C4#55111yescharacteristic
741C2×C4#55211yescharacteristic
742C2×C4#55311yescharacteristic
743C2×C4#55311yescharacteristic
744C2×C4#55311yescharacteristic
745C2×C4#55411yescharacteristic
746C2×C4#55411yescharacteristic
747C2×C4#55411yescharacteristic
748C2×C4#55611yescharacteristic
749C2×C4#55911yescharacteristic
750C2×C4#56011yescharacteristic
751C2×C4#56311yescharacteristic
752C8—42no—
753C8—42no—
754C8—42no—
755C8—81no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22#244911yescharacteristic
772C22#245511yescharacteristic
773C22#246511yescharacteristic
774C22#246811yescharacteristic
775C22#259811yescharacteristic
776C22#267811yescharacteristic
777C22#272011yescharacteristic
778C22#310211yescharacteristic
779C22#310611yescharacteristic
780C22#311111yescharacteristic
781C22#311411yescharacteristic
782C22#311811yescharacteristic
783C22#311911yescharacteristic
784C22#312311yescharacteristic
785C22#312611yescharacteristic
786C22#321111yescharacteristic
787C22#321411yescharacteristic
788C22#322211yescharacteristic
789C22#322411yescharacteristic
790C22#326411yescharacteristic
791C22#326711yescharacteristic
792C22#327511yescharacteristic
793C22#328211yescharacteristic
794C22#329611yescharacteristic
795C22#330911yescharacteristic
796C22#331111yescharacteristic
797C22#333211yescharacteristic
798C22#334011yescharacteristic
799C22#334511yescharacteristic
800C22#334711yescharacteristic
801C22#335111yescharacteristic
802C22#338011yescharacteristic
803C22#338411yescharacteristic
804C22#338811yescharacteristic
805C22#338811yescharacteristic
806C4—42no—
807C4—42no—
808C4—82no—
809C4—82no—
810C4—81no—
811C4—82no—
812C4—81no—
813C4—82no—
814C4—82no—
815C4—82no—
816C4—81no—
817C4—81no—
818C4—161no—
819C4#243811yescharacteristic
820C4#246611yescharacteristic
821C4#257911yescharacteristic
822C4#258911yescharacteristic
823C4#271711yescharacteristic
824C4#278711yescharacteristic
825C4#279011yescharacteristic
826C4#279611yescharacteristic
827C2—84no—
828C2#1597311yescharacteristic
829C2#2638011yescharacteristic
830C2#2638611yescharacteristic
831C2#2655311yescharacteristic
832C2#2656211yescharacteristic
833C2#2700611yescharacteristic
834C2#2701411yescharacteristic
835C2#2710711yescharacteristic
836C2#2712511yescharacteristic
837C2#2937311yescharacteristic
838C2#2937711yescharacteristic
839C2#3099611yescharacteristic
840C2#3101111yescharacteristic
841C2#3235111yescharacteristic
842C2#3236811yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #14133C2semidirect
5. #11372C2semidirect
6. #11328C2semidirect
7. #11325C2semidirect
8. #11298C2semidirect
9. #11220C2semidirect
10. #11220C2semidirect
14. #10908C2semidirect

Maximal subgroups

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

subgroupindex
C2×#19252
C2×#18642
#141332
#139792
#113722
#113282
#113252
#112982
#112202
#111892
#111212
#110662
#109082
#107882