Finite Group Databasebeta

← #396985

Subgroups — #396985

Order 512.

1184 conjugacy classes of subgroups.

The subgroup lattice has 827 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2097C211yesmaximal, characteristic
2C2×#2056C211yesmaximal, characteristic
3C2×#1928C211yesmaximal, characteristic
4C2×#1878C211yesmaximal, characteristic
5#15241C211yesmaximal, characteristic
6#13817C211yesmaximal, characteristic
7#11256C211yesmaximal, characteristic
8#11255C211yesmaximal, characteristic
9#11190C211yesmaximal, characteristic
10#11122C211yesmaximal, characteristic
11#11024C211yesmaximal, characteristic
12#10932C211yesmaximal, characteristic
13#10908C211yesmaximal, characteristic
14#10850C211yesmaximal, characteristic
15#10789C211yesmaximal, characteristic
16C23×Q16C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C2×#391C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#382C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35#2097—24no—
36#2056—24no—
37#1928—24no—
38#1878—24no—
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51#1443—21no—
52#1443—21no—
53#1443—21no—
54#1443—21no—
55#1436—21no—
56#1436—21no—
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60#1434—21no—
61C4×#95—21no—
62C4×#95C2211yescharacteristic
63C23×Q8C2311yescharacteristic
64C23×Q8C2311yescharacteristic
65C22×Q16—22no—
66C22×Q16—22no—
67C22×Q16—22no—
68C22×Q16—22no—
69C22×Q16—22no—
70C22×Q16—41no—
71C22×Q16—41no—
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C23×C8C2311yescharacteristic
76C2×C4×Q8—22no—
77C2×C4×Q8—22no—
78C2×C4×Q8—22no—
79C2×C4×Q8—22no—
80C2×C4×Q8—41no—
81C2×C4×Q8—41no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C42—21no—
90C22×C42—21no—
91C22×C42—21no—
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C2×#107—22no—
96C2×#107—22no—
97C2×#107—41no—
98C2×#106—22no—
99C2×#106—22no—
100C2×#106—41no—
101C2×C4⋊C8—22no—
102C2×C4⋊C8—22no—
103C2×C4⋊C8—41no—
104C2×#103—22no—
105C2×#103—22no—
106C2×#103—22no—
107C2×#103—22no—
108C2×#103—22no—
109C2×#103—22no—
110C2×#103—22no—
111C2×#103—22no—
112C2×#103—22no—
113C2×#103—22no—
114C2×#103—22no—
115C2×#103—22no—
116C2×#103—22no—
117C2×#103—41no—
118C2×#103—41no—
119C2×#103—41no—
120C2×#103—41no—
121C2×#103D414yes—
122#391—22no—
123#391—22no—
124#391—22no—
125#391—22no—
126#391—22no—
127#391—22no—
128#391—22no—
129#391—41no—
130#391—41no—
131#391D414yes—
132#382—22no—
133#382—22no—
134C4×C4⋊C4—22no—
135C4×C4⋊C4—22no—
136C4×C4⋊C4—41no—
137C4×C4⋊C4—41no—
138C2×#95—21no—
139C2×#95—21no—
140C2×#95—21no—
141C2×#95—21no—
142C2×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95—21no—
148C2×#95—21no—
149C2×#95—21no—
150C2×#95—21no—
151C2×#95—21no—
152C2×#95—21no—
153C2×#95—21no—
154C2×#95—21no—
155C2×#95—21no—
156C2×#95—21no—
157C2×#95—21no—
158C2×#95D411yescharacteristic
159C2×#95D411yescharacteristic
160C2×#95D411yescharacteristic
161C2×#95D411yescharacteristic
162#340—22no—
163#340—22no—
164#340—22no—
165#340—22no—
166#340—22no—
167#340—41no—
168#340—41no—
169#336—22no—
170#336—22no—
171#336—22no—
172#336—22no—
173#336—41no—
174C22×Q8—21no—
175C22×Q8—21no—
176C22×Q8—21no—
177C22×Q8—21no—
178C22×Q8—21no—
179C22×Q8—21no—
180C22×Q8—21no—
181C22×Q8—21no—
182C22×Q8—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8—21no—
188C22×Q8—21no—
189C22×Q8—21no—
190C22×Q8—21no—
191C22×Q8—21no—
192C22×Q8—21no—
193C22×Q8—21no—
194C22×Q8—21no—
195C22×Q8—21no—
196C22×Q8—21no—
197C22×Q8—21no—
198C22×Q8C2×D412yes—
199C22×Q8C2×D412yes—
200C22×Q8#4112yes—
201C22×Q8#4112yes—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4—21no—
205C23×C4—21no—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4C2×D411yescharacteristic
211C23×C4C2×D411yescharacteristic
212C23×C4C2×D411yescharacteristic
213C23×C4C2×D411yescharacteristic
214C23×C4C2×D411yescharacteristic
215C23×C4C2×D411yescharacteristic
216C23×C4C2411yescharacteristic
217C2×Q16—28no—
218C2×Q16—44no—
219C2×Q16—44no—
220C2×Q16—44no—
221C2×Q16—44no—
222C2×Q16—44no—
223C2×Q16—44no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—21no—
242C22×C8—21no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—21no—
246C22×C8—21no—
247C22×C8—21no—
248C22×C8—21no—
249C22×C8C2×D412yes—
250C22×C8#4112yes—
251C22×C8#4112yes—
252C4×Q8—44no—
253C4×Q8—44no—
254C4×Q8—44no—
255C4×Q8—44no—
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—21no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4C2×D412yes—
291C2×C4⋊C4C2×D412yes—
292C2×C4⋊C4#4112yes—
293C2×C4⋊C4#4112yes—
294C2×C4⋊C4#4112yes—
295C2×C42—21no—
296C2×C42—21no—
297C2×C42—21no—
298C2×C42—21no—
299C2×C42—24no—
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—42no—
313C2×C42—42no—
314C2×C42—42no—
315C2×C42—42no—
316C2×C42—42no—
317C2×C42—42no—
318C2×C42—81no—
319C2×C42—81no—
320C2×C42C2×D412yes—
321C2×C42#4112yes—
322#107—44no—
323#106—44no—
324C4⋊C8—44no—
325#103—28no—
326#103—44no—
327#103—44no—
328#103—44no—
329#103—44no—
330#103—44no—
331#95—24no—
332#95—24no—
333#95—24no—
334#95—24no—
335#95—22no—
336#95—22no—
337#95—41no—
338#95—41no—
339#95—42no—
340#95—42no—
341#95—42no—
342#95—42no—
343#95—42no—
344#95—42no—
345#95—42no—
346#95—42no—
347#95—42no—
348#95—42no—
349#95—42no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—42no—
354#95—81no—
355C24C22×D411yescharacteristic
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—22no—
361C2×Q8—22no—
362C2×Q8—22no—
363C2×Q8—22no—
364C2×Q8—22no—
365C2×Q8—22no—
366C2×Q8—22no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—41no—
378C2×Q8—41no—
379C2×Q8—41no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8—41no—
387C2×Q8—41no—
388C2×Q8—41no—
389C2×Q8—41no—
390C2×Q8—41no—
391C2×Q8—41no—
392C2×Q8—41no—
393C2×Q8—41no—
394C2×Q8—41no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8—41no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8—41no—
402C2×Q8—41no—
403C2×Q8—41no—
404C2×Q8—41no—
405C2×Q8—41no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8—41no—
409C2×Q8—41no—
410C2×Q8—41no—
411C2×Q8#12414yes—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—22no—
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—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
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—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—41no—
486C22×C4—41no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4—41no—
490C22×C4—41no—
491C22×C4—41no—
492C22×C4—41no—
493C22×C4—41no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498C22×C4—41no—
499C22×C4—41no—
500C22×C4—41no—
501C22×C4—41no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—41no—
505C22×C4—41no—
506C22×C4#12112yes—
507C22×C4#12112yes—
508C22×C4#13512yes—
509C22×C4#13712yes—
510C22×C4C22×D411yescharacteristic
511C22×C4C22×D411yescharacteristic
512C22×C4C2×#4111yescharacteristic
513C22×C4C2×#4111yescharacteristic
514C22×C4C2×#4111yescharacteristic
515C22×C4C2×#4111yescharacteristic
516C22×C4C2×#4111yescharacteristic
517C22×C4C2×#4111yescharacteristic
518C22×C4C2×#4111yescharacteristic
519C22×C4C2×#4111yescharacteristic
520C22×C4H(5,𝔽2)11yescharacteristic
521C22×C4H(5,𝔽2)11yescharacteristic
522C22×C4H(5,𝔽2)11yescharacteristic
523C22×C42−1+411yescharacteristic
524Q16—416no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—22no—
531C2×C8—22no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—41no—
535C2×C8—41no—
536C2×C8—41no—
537C2×C8—41no—
538C2×C8—41no—
539C2×C8—41no—
540C2×C8—41no—
541C2×C8—41no—
542C2×C8—41no—
543C2×C8—41no—
544C2×C8—41no—
545C2×C8—41no—
546C2×C8—41no—
547C2×C8—41no—
548C2×C8—41no—
549C2×C8—41no—
550C2×C8—41no—
551C2×C8—41no—
552C2×C8—41no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—48no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—41no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—41no—
567C4⋊C4—41no—
568C4⋊C4—41no—
569C4⋊C4—41no—
570C4⋊C4—41no—
571C4⋊C4—41no—
572C4⋊C4—41no—
573C4⋊C4—41no—
574C4⋊C4—41no—
575C4⋊C4—41no—
576C4⋊C4—41no—
577C4⋊C4#12314yes—
578C42—22no—
579C42—22no—
580C42—22no—
581C42—22no—
582C42—48no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—41no—
590C42—41no—
591C42—84no—
592C42—84no—
593C23C2×#12111yescharacteristic
594C23#52511yescharacteristic
595C23#52511yescharacteristic
596C23D4211yescharacteristic
597C23#54611yescharacteristic
598C23#54711yescharacteristic
599C23#55011yescharacteristic
600C23C2×#13511yescharacteristic
601C23C2×#13711yescharacteristic
602C23#57511yescharacteristic
603C23#57511yescharacteristic
604C23#57711yescharacteristic
605C23#57811yescharacteristic
606C23#57811yescharacteristic
607C23#57811yescharacteristic
608Q8—24no—
609Q8—24no—
610Q8—42no—
611Q8—42no—
612Q8—42no—
613Q8—42no—
614Q8—42no—
615Q8—42no—
616Q8—42no—
617Q8—42no—
618Q8—42no—
619Q8—42no—
620Q8—81no—
621Q8—81no—
622Q8—81no—
623Q8—81no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
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—42no—
646C2×C4—41no—
647C2×C4—42no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
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×C4C2×#12311yescharacteristic
723C2×C4#52511yescharacteristic
724C2×C4C2×#12411yescharacteristic
725C2×C4#52911yescharacteristic
726C2×C4#52911yescharacteristic
727C2×C4#52911yescharacteristic
728C2×C4#52911yescharacteristic
729C2×C4#52911yescharacteristic
730C2×C4#53211yescharacteristic
731C2×C4#53211yescharacteristic
732C2×C4#53811yescharacteristic
733C2×C4#53811yescharacteristic
734C2×C4#53911yescharacteristic
735C2×C4#53911yescharacteristic
736C2×C4#54011yescharacteristic
737C2×C4#54211yescharacteristic
738C2×C4D4211yescharacteristic
739C2×C4#54611yescharacteristic
740C2×C4#54611yescharacteristic
741C2×C4#54611yescharacteristic
742C2×C4#54711yescharacteristic
743C2×C4#54711yescharacteristic
744C2×C4#55111yescharacteristic
745C2×C4#55111yescharacteristic
746C2×C4#55111yescharacteristic
747C2×C4#55211yescharacteristic
748C2×C4#55311yescharacteristic
749C2×C4#55911yescharacteristic
750C8—42no—
751C8—42no—
752C8—42no—
753C8—81no—
754C22#241811yescharacteristic
755C22#242511yescharacteristic
756C22#242811yescharacteristic
757C22#245511yescharacteristic
758C22#246711yescharacteristic
759C22#247911yescharacteristic
760C22#285011yescharacteristic
761C22#303511yescharacteristic
762C22#303711yescharacteristic
763C22#304411yescharacteristic
764C22#304611yescharacteristic
765C22#310211yescharacteristic
766C22#310811yescharacteristic
767C22#311111yescharacteristic
768C22#311711yescharacteristic
769C22#312011yescharacteristic
770C22#312011yescharacteristic
771C22#312711yescharacteristic
772C22#312711yescharacteristic
773C22#326911yescharacteristic
774C22#327011yescharacteristic
775C22#327511yescharacteristic
776C22#328511yescharacteristic
777C22#330011yescharacteristic
778C22#331111yescharacteristic
779C22#331511yescharacteristic
780C22#332811yescharacteristic
781C22#334211yescharacteristic
782C22#334411yescharacteristic
783C22#334911yescharacteristic
784C22#335211yescharacteristic
785C22#339411yescharacteristic
786C22#339811yescharacteristic
787C22#340211yescharacteristic
788C22#340211yescharacteristic
789C4—42no—
790C4—44no—
791C4—42no—
792C4—42no—
793C4—44no—
794C4—42no—
795C4—82no—
796C4—81no—
797C4—82no—
798C4—81no—
799C4—82no—
800C4—161no—
801C4—161no—
802C4—161no—
803C4#239511yescharacteristic
804C4#242211yescharacteristic
805C4#247211yescharacteristic
806C4#248811yescharacteristic
807C4#251611yescharacteristic
808C4#255311yescharacteristic
809C4#255711yescharacteristic
810C4#264911yescharacteristic
811C2#1474311yescharacteristic
812C2#2490211yescharacteristic
813C2#2492311yescharacteristic
814C2#2520111yescharacteristic
815C2#2522611yescharacteristic
816C2#2537411yescharacteristic
817C2#2537911yescharacteristic
818C2#2656111yescharacteristic
819C2#2657511yescharacteristic
820C2#2707411yescharacteristic
821C2#2708211yescharacteristic
822C2#2748711yescharacteristic
823C2#2751511yescharacteristic
824C2#3302911yescharacteristic
825C2#3304111yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C4×#95 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#20972
C2×#20562
C2×#19282
C2×#18782
#152412
#138172
#112562
#112552
#111902
#111222
#110242
#109322
#109082
#108502
#107892