Finite Group Databasebeta

← #396758

Subgroups — #396758

Order 512.

1442 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1862C211yesmaximal, characteristic
2C2×#1862C211yesmaximal, characteristic
3#15187C211yesmaximal, characteristic, complemented
4D4×#95C211yesmaximal, characteristic
5#11377C211yesmaximal, characteristic, complemented
6#11315C211yesmaximal, characteristic, complemented
7#11298C211yesmaximal, characteristic, complemented
8#11293C211yesmaximal, characteristic, complemented
9#11256C211yesmaximal, characteristic, complemented
10#11256C211yesmaximal, characteristic, complemented
11#11219C211yesmaximal, characteristic, complemented
12#10788C211yesmaximal, characteristic
13#10788C211yesmaximal, characteristic
14#10788C211yesmaximal, characteristic
15#10788C211yesmaximal, characteristic
16C22×C4×D4C2211yescharacteristic
17C22×C4×D4C2211yescharacteristic
18C22×C4×D4C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#107C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C2×#389C2211yescharacteristic
26C2×#389C2211yescharacteristic
27C22×#95—21no—
28#1862—24no—
29#1862—24no—
30C2×#340C2211yescharacteristic
31C2×#340C2211yescharacteristic
32C2×#340C2211yescharacteristic
33C2×#340C2211yescharacteristic
34C2×#340C2211yescharacteristic
35C2×#340C2211yescharacteristic
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#336C2211yescharacteristic
41C2×#336C2211yescharacteristic
42C2×#336C2211yescharacteristic
43C2×#336C2211yescharacteristic
44C2×#336C2211yescharacteristic
45C2×#336C2211yescharacteristic
46#1445—21no—
47#1443—21no—
48#1442—21no—
49#1441—21no—
50C4⋊#95C2211yescharacteristic
51C4⋊#95C2211yescharacteristic
52C4⋊#95C2211yescharacteristic
53C4⋊#95C2211yescharacteristic
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C22⋊#95—21no—
58C22⋊#95—21no—
59C22⋊#95—21no—
60C4×#95C2211yescharacteristic
61C23×D4C2311yescharacteristic
62C24×C4—21no—
63C24×C4—21no—
64C24×C4—21no—
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C2×C4×D4—22no—
70C2×C4×D4—22no—
71C2×C4×D4—22no—
72C2×C4×D4—22no—
73C2×C4×D4—22no—
74C2×C4×D4—22no—
75C2×C4×D4—22no—
76C2×C4×D4—22no—
77C2×C4×D4—22no—
78C2×C4×D4—22no—
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4—41no—
82C2×C4×D4—41no—
83C2×C4×D4—41no—
84C2×C4×D4—41no—
85C2×C4×D4—41no—
86C2×C4×D4—41no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4—21no—
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C22⋊C4—21no—
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101C22×C42C2311yescharacteristic
102C2×#107—22no—
103C2×#107—22no—
104C2×#107—22no—
105C2×#107—22no—
106C2×#107—41no—
107C2×#107—41no—
108C2×#102—22no—
109C2×#102—22no—
110C2×#102—22no—
111C2×#102—22no—
112C2×#102—22no—
113C2×#102—22no—
114C2×#102—22no—
115C2×#102—22no—
116C2×#102—22no—
117C2×#102—22no—
118C2×#102D414yes—
119C2×#102Q814yes—
120#389—22no—
121#389—22no—
122#389—41no—
123#389—41no—
124C2×#95—21no—
125C2×#95—21no—
126C2×#95—21no—
127C2×#95—21no—
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—44no—
141C2×#95D411yescharacteristic
142C2×#95D411yescharacteristic
143C2×#95D411yescharacteristic
144C2×#95D411yescharacteristic
145#340—22no—
146#340—22no—
147#340—22no—
148#340—22no—
149#340—22no—
150#340—22no—
151#340—41no—
152#340—41no—
153#340—41no—
154#340—41no—
155#336—22no—
156#336—22no—
157#336—41no—
158#336—41no—
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×D4C2×D412yes—
170C22×D4C2×Q812yes—
171C22×D4#4112yes—
172C22×D4#4112yes—
173C22×D4#4112yes—
174C22×D4#4112yes—
175C22×D4#4112yes—
176C23×C4—21no—
177C23×C4—21no—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—21no—
181C23×C4—24no—
182C23×C4—24no—
183C23×C4—24no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—42no—
187C23×C4—42no—
188C23×C4—42no—
189C23×C4—42no—
190C23×C4—42no—
191C23×C4—42no—
192C23×C4—42no—
193C23×C4—42no—
194C23×C4—42no—
195C23×C4—42no—
196C23×C4—42no—
197C23×C4—42no—
198C23×C4—81no—
199C23×C4—81no—
200C23×C4—81no—
201C23×C4—81no—
202C23×C4—81no—
203C23×C4—81no—
204C23×C4C2×D411yescharacteristic
205C23×C4C2×D411yescharacteristic
206C23×C4C2×D411yescharacteristic
207C23×C4C2×D411yescharacteristic
208C23×C4C2×D411yescharacteristic
209C23×C4C2×D411yescharacteristic
210C23×C4C2411yescharacteristic
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×C8—21no—
223C22×C8—21no—
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×C8C2×D412yes—
238C22×C8C2×Q812yes—
239C4×D4—44no—
240C4×D4—44no—
241C4×D4—44no—
242C4×D4—44no—
243C4×D4—44no—
244C4×D4—44no—
245C4×D4—44no—
246C4×D4—44no—
247C4×D4—44no—
248C4×D4—44no—
249C4×D4—44no—
250C4×D4—44no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
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—21no—
267C2×C4⋊C4—21no—
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⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—81no—
293C2×C4⋊C4—81no—
294C2×C4⋊C4C2×D412yes—
295C2×C4⋊C4C2×Q812yes—
296C2×C4⋊C4#4112yes—
297C2×C4⋊C4#4112yes—
298C2×C4⋊C4#4112yes—
299C2×C22⋊C4—24no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—42no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4—42no—
305C2×C22⋊C4—42no—
306C2×C22⋊C4—42no—
307C2×C22⋊C4—42no—
308C2×C42—21no—
309C2×C42—21no—
310C2×C42—21no—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—21no—
316C2×C42—21no—
317C2×C42—21no—
318C2×C42—21no—
319C2×C42—21no—
320C2×C42—21no—
321C2×C42—21no—
322C2×C42—21no—
323C2×C42—21no—
324C2×C42—21no—
325C2×C42—21no—
326#107—44no—
327#107—44no—
328#102—28no—
329#102—28no—
330#102—44no—
331#102—44no—
332#95—22no—
333#95—22no—
334#95—22no—
335#95—41no—
336#95—42no—
337#95—42no—
338#95—42no—
339#95—42no—
340#95—42no—
341#95—42no—
342#95—81no—
343#95—81no—
344#95—81no—
345#95—81no—
346#95—81no—
347#95—81no—
348#95—81no—
349#95—81no—
350#95—81no—
351#95—81no—
352C24—22no—
353C24—22no—
354C24—22no—
355C24—22no—
356C24—22no—
357C24—22no—
358C24—22no—
359C24—41no—
360C24—41no—
361C24—41no—
362C24—41no—
363C24—41no—
364C24—41no—
365C24—41no—
366C24—41no—
367C24C22×D411yescharacteristic
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—22no—
381C2×D4—22no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4C22⋊Q814yes—
390C2×D4#12314yes—
391C2×D4#12414yes—
392C2×D4#12514yes—
393C2×D4#12514yes—
394C2×D4#12614yes—
395C2×D4#12614yes—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—22no—
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—48no—
441C22×C4—48no—
442C22×C4—48no—
443C22×C4—48no—
444C22×C4—48no—
445C22×C4—48no—
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—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—84no—
491C22×C4—84no—
492C22×C4—84no—
493C22×C4—84no—
494C22×C4—84no—
495C22×C4—84no—
496C22×C4—84no—
497C22×C4—84no—
498C22×C4—84no—
499C22×C4—84no—
500C22×C4—84no—
501C22×C4—84no—
502C22×C4—84no—
503C22×C4—84no—
504C22×C4—84no—
505C22×C4#13512yes—
506C22×C4AGL(1,ℤ/8)12yes—
507C22×C4#13712yes—
508C22×C4C22×D411yescharacteristic
509C22×C4C22×Q811yescharacteristic
510C22×C4C2×#4111yescharacteristic
511C22×C4C2×#4111yescharacteristic
512C22×C4C2×#4111yescharacteristic
513C22×C4C2×#4111yescharacteristic
514C22×C4C2×#4111yescharacteristic
515C22×C4C2×#4111yescharacteristic
516C22×C4C2×#4111yescharacteristic
517C22×C4C2×#4111yescharacteristic
518C22×C4H(5,𝔽2)11yescharacteristic
519C22×C4H(5,𝔽2)11yescharacteristic
520C22×C4H(5,𝔽2)11yescharacteristic
521C22×C42−1+411yescharacteristic
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
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—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—41no—
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—41no—
578C4⋊C4—84no—
579C4⋊C4—84no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C42—41no—
584C42—41no—
585C42—41no—
586C42—41no—
587C42—41no—
588C42—41no—
589C42—41no—
590C42—41no—
591C42—41no—
592C42—41no—
593C42—41no—
594C42—41no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23#52511yescharacteristic
631C23#52511yescharacteristic
632C23#52511yescharacteristic
633C23D4211yescharacteristic
634C23#54611yescharacteristic
635C23#54611yescharacteristic
636C23D4×Q811yescharacteristic
637C23C2×#13511yescharacteristic
638C23C2×AGL(1,ℤ/8)11yescharacteristic
639C23C2×#13711yescharacteristic
640C23#57511yescharacteristic
641C23#57611yescharacteristic
642C23#57611yescharacteristic
643C23#57611yescharacteristic
644C23#57811yescharacteristic
645D4—24no—
646D4—24no—
647D4—24no—
648D4—24no—
649D4—24no—
650D4—24no—
651D4—24no—
652D4#40018yes—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—816no—
711C2×C4—816no—
712C2×C4—816no—
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×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4—81no—
737C2×C4—81no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4C2×C22⋊Q811yescharacteristic
748C2×C4C2×#12311yescharacteristic
749C2×C4C2×#12411yescharacteristic
750C2×C4C2×#12511yescharacteristic
751C2×C4C2×#12511yescharacteristic
752C2×C4C2×#12611yescharacteristic
753C2×C4C2×#12611yescharacteristic
754C2×C4#52911yescharacteristic
755C2×C4#52911yescharacteristic
756C2×C4#52911yescharacteristic
757C2×C4#53811yescharacteristic
758C2×C4#53811yescharacteristic
759C2×C4#53811yescharacteristic
760C2×C4#53911yescharacteristic
761C2×C4#53911yescharacteristic
762C2×C4#53911yescharacteristic
763C2×C4#54611yescharacteristic
764C2×C4#54611yescharacteristic
765C2×C4#54711yescharacteristic
766C2×C4#55111yescharacteristic
767C2×C4#55111yescharacteristic
768C2×C4#55111yescharacteristic
769C2×C4#55111yescharacteristic
770C2×C4#55211yescharacteristic
771C2×C4#55211yescharacteristic
772C2×C4#55411yescharacteristic
773C2×C4#55411yescharacteristic
774C2×C4#55411yescharacteristic
775C8—42no—
776C8—42no—
777C8—81no—
778C8—81no—
779C22—28no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—44no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22#241811yescharacteristic
795C22#244911yescharacteristic
796C22#247211yescharacteristic
797C22#247311yescharacteristic
798C22#247311yescharacteristic
799C22#248011yescharacteristic
800C22#285211yescharacteristic
801C22#310211yescharacteristic
802C22#310511yescharacteristic
803C22#310711yescharacteristic
804C22#311011yescharacteristic
805C22#311411yescharacteristic
806C22#311611yescharacteristic
807C22#312211yescharacteristic
808C22#312211yescharacteristic
809C22#312211yescharacteristic
810C22#312411yescharacteristic
811C22#312411yescharacteristic
812C22#312411yescharacteristic
813C22#326411yescharacteristic
814C22#326811yescharacteristic
815C22#327611yescharacteristic
816C22#328011yescharacteristic
817C22#329711yescharacteristic
818C22#330211yescharacteristic
819C22#331411yescharacteristic
820C22#331411yescharacteristic
821C22#331511yescharacteristic
822C22#331811yescharacteristic
823C22#332211yescharacteristic
824C22#332511yescharacteristic
825C22#338011yescharacteristic
826C22#338511yescharacteristic
827C22#338611yescharacteristic
828C22#338911yescharacteristic
829C4—42no—
830C4—42no—
831C4—42no—
832C4—82no—
833C4—82no—
834C4—82no—
835C4—81no—
836C4—81no—
837C4—82no—
838C4—81no—
839C4—82no—
840C4—161no—
841C4—161no—
842C4C2×#40011yescharacteristic
843C4#241911yescharacteristic
844C4#245011yescharacteristic
845C4#248811yescharacteristic
846C4#249311yescharacteristic
847C4#250511yescharacteristic
848C4#250511yescharacteristic
849C4#264311yescharacteristic
850C2—48no—
851C2#1473811yescharacteristic
852C2#2489711yescharacteristic
853C2#2491911yescharacteristic
854C2#2637011yescharacteristic
855C2#2638411yescharacteristic
856C2#2723711yescharacteristic
857C2#2724011yescharacteristic
858C2#2730111yescharacteristic
859C2#2730911yescharacteristic
860C2#2731011yescharacteristic
861C2#2732011yescharacteristic
862C2#2752811yescharacteristic
863C2#2754111yescharacteristic
864C2#3308411yescharacteristic
865C2#3308811yescharacteristic
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. #15187C2semidirect
5. #11377C2semidirect
6. #11315C2semidirect
7. #11298C2semidirect
8. #11293C2semidirect
9. #11256C2semidirect
10. #11256C2semidirect
11. #11219C2semidirect

Maximal subgroups

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

subgroupindex
C2×#18622
#151872
D4×#952
#113772
#113152
#112982
#112932
#112562
#112192
#107882