Finite Group Databasebeta

← #457683

Subgroups — #457683

Order 512.

1232 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2093C211yesmaximal, characteristic
2C2×#1802C211yesmaximal, characteristic
3#15145C211yesmaximal, characteristic, complemented
4#13916C211yesmaximal, characteristic
5#11324C211yesmaximal, characteristic, complemented
6#11324C211yesmaximal, characteristic, complemented
7#11315C211yesmaximal, characteristic, complemented
8#11267C211yesmaximal, characteristic, complemented
9#11255C211yesmaximal, characteristic, complemented
10#11232C211yesmaximal, characteristic, complemented
11#11219C211yesmaximal, characteristic, complemented
12#11123C211yesmaximal, characteristic
13#11066C211yesmaximal, characteristic
14#11049C211yesmaximal, characteristic
15#10788C211yesmaximal, characteristic
16C22×C4×D4C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×C4⋊C8C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23C22×#102C2211yescharacteristic
24C22×#102C2211yescharacteristic
25C2×#398—21no—
26C2×#398—21no—
27C2×#390C2211yescharacteristic
28C2×#390C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#384C2211yescharacteristic
31C2×#384C2211yescharacteristic
32C2×#384C2211yescharacteristic
33C2×#381—21no—
34#2093—24no—
35#1802—24no—
36C2×#340C2211yescharacteristic
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#336C2211yescharacteristic
46C2×#336C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50#1444—21no—
51#1444—21no—
52#1440—21no—
53#1440—21no—
54C4⋊#95C2211yescharacteristic
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
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—22no—
70C2×C4×D4—41no—
71C2×C4×D4—41no—
72C2×C4×D4Q814yes—
73C22×C4⋊C4—21no—
74C22×C4⋊C4—21no—
75C22×C4⋊C4—21no—
76C22×C4⋊C4—21no—
77C22×C4⋊C4—21no—
78C22×C4⋊C4—21no—
79C22×C4⋊C4—21no—
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2311yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2311yescharacteristic
87C22×C22⋊C4—21no—
88C22×C22⋊C4—21no—
89C22×C22⋊C4—21no—
90C22×C22⋊C4—21no—
91C22×C22⋊C4—21no—
92C22×C42C2311yescharacteristic
93C22×C42C2311yescharacteristic
94C22×C42C2311yescharacteristic
95C2×#107—22no—
96C2×#107—22no—
97C2×#107—22no—
98C2×#107—41no—
99C2×#107—41no—
100C2×#107—41no—
101C2×#107—41no—
102C2×#107—41no—
103C2×#107—41no—
104C2×C4⋊C8—22no—
105C2×C4⋊C8—22no—
106C2×C4⋊C8—41no—
107C2×#102—22no—
108C2×#102—22no—
109C2×#102—22no—
110C2×#102—22no—
111C2×#102—22no—
112C2×#102—41no—
113C2×#102—41no—
114C2×#102—41no—
115C2×#102—41no—
116C2×#102—41no—
117C2×#102—41no—
118C2×#102D414yes—
119#398—44no—
120#398—44no—
121#390—22no—
122#390—22no—
123#390—41no—
124#390—41no—
125#389—41no—
126#389—41no—
127#384—22no—
128#384—22no—
129#384—41no—
130#384—41no—
131#384—41no—
132#384—41no—
133#381—44no—
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×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95D411yescharacteristic
146C2×#95D411yescharacteristic
147C2×#95D411yescharacteristic
148C2×#95D411yescharacteristic
149#340—22no—
150#340—22no—
151#340—22no—
152#340—41no—
153#340—41no—
154#340—41no—
155#340—41no—
156#340—41no—
157#340—41no—
158#336—22no—
159#336—22no—
160#336—22no—
161#336—22no—
162#336—41no—
163C25—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×D4—21no—
174C22×D4—21no—
175C22×D4C2×D412yes—
176C22×D4C2×Q812yes—
177C22×D4#4112yes—
178C23×C4—21no—
179C23×C4—21no—
180C23×C4—24no—
181C23×C4—21no—
182C23×C4—21no—
183C23×C4—21no—
184C23×C4—21no—
185C23×C4—21no—
186C23×C4—42no—
187C23×C4—42no—
188C23×C4—42no—
189C23×C4—42no—
190C23×C4—81no—
191C23×C4—81no—
192C23×C4C2×D411yescharacteristic
193C23×C4C2×D411yescharacteristic
194C23×C4C2×D411yescharacteristic
195C23×C4C2×D411yescharacteristic
196C23×C4C2×D411yescharacteristic
197C23×C4C2×D411yescharacteristic
198C23×C4C2411yescharacteristic
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×C8—21no—
223C22×C8—21no—
224C22×C8C2×D412yes—
225C22×C8#4112yes—
226C22×C8#4112yes—
227C4×D4—28no—
228C4×D4—44no—
229C4×D4—44no—
230C4×D4—44no—
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—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—42no—
272C2×C4⋊C4—42no—
273C2×C4⋊C4—42no—
274C2×C4⋊C4—42no—
275C2×C4⋊C4—42no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C4⋊C4—42no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—81no—
287C2×C4⋊C4—81no—
288C2×C4⋊C4—81no—
289C2×C4⋊C4—81no—
290C2×C4⋊C4—81no—
291C2×C4⋊C4—81no—
292C2×C4⋊C4C2×D412yes—
293C2×C4⋊C4C2×Q812yes—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—42no—
297C2×C22⋊C4—42no—
298C2×C22⋊C4—42no—
299C2×C22⋊C4—42no—
300C2×C22⋊C4—42no—
301C2×C22⋊C4—42no—
302C2×C22⋊C4—42no—
303C2×C22⋊C4—42no—
304C2×C22⋊C4—42no—
305C2×C22⋊C4—81no—
306C2×C22⋊C4—81no—
307C2×C22⋊C4—81no—
308C2×C22⋊C4—81no—
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×C42C2×Q812yes—
326C2×C42#4112yes—
327#107—44no—
328#107—44no—
329#107—44no—
330C4⋊C8—44no—
331#102—44no—
332#102—44no—
333#102—44no—
334#102—44no—
335#95—22no—
336#95—22no—
337#95—22no—
338#95—42no—
339#95—42no—
340#95—42no—
341#95—42no—
342#95—42no—
343#95—42no—
344#95—42no—
345#95—42no—
346#95—81no—
347#95—81no—
348#95—81no—
349#95D814yes—
350C24—22no—
351C24—22no—
352C24—22no—
353C24—41no—
354C24—41no—
355C24—41no—
356C24—41no—
357C24—41no—
358C24—41no—
359C24—41no—
360C24—41no—
361C24—41no—
362C24—41no—
363C24—41no—
364C24—41no—
365C24C22×D411yescharacteristic
366C2×D4—22no—
367C2×D4—22no—
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—41no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4C22⋊Q814yes—
394C22×C4—21no—
395C22×C4—21no—
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—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—22no—
429C22×C4—22no—
430C22×C4—48no—
431C22×C4—41no—
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—48no—
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—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—84no—
480C22×C4—84no—
481C22×C4—84no—
482C22×C4—84no—
483C22×C4—84no—
484C22×C4C22⋊Q812yes—
485C22×C4C22⋊Q812yes—
486C22×C4C2×D812yes—
487C22×C4C2×D812yes—
488C22×C4C2×D812yes—
489C22×C4AGL(1,ℤ/8)12yes—
490C22×C4#13712yes—
491C22×C4#13712yes—
492C22×C4C22×D411yescharacteristic
493C22×C4C22×Q811yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4C2×#4111yescharacteristic
497C22×C4C2×#4111yescharacteristic
498C22×C4H(5,𝔽2)11yescharacteristic
499C22×C4H(5,𝔽2)11yescharacteristic
500C22×C4H(5,𝔽2)11yescharacteristic
501C22×C4H(5,𝔽2)11yescharacteristic
502C22×C4H(5,𝔽2)11yescharacteristic
503C22×C42−1+411yescharacteristic
504C22×C42−1+411yescharacteristic
505C22×C42−1+411yescharacteristic
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
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—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8—41no—
533C2×C8—41no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
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—41no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—84no—
563C4⋊C4—84no—
564C4⋊C4—84no—
565C4⋊C4—84no—
566C4⋊C4—84no—
567C4⋊C4—84no—
568C4⋊C4—84no—
569C22⋊C4—48no—
570C22⋊C4—84no—
571C22⋊C4—84no—
572C22⋊C4—84no—
573C22⋊C4—84no—
574C42—22no—
575C42—22no—
576C42—22no—
577C42—22no—
578C42—41no—
579C42—41no—
580C42—41no—
581C42—41no—
582C42—41no—
583C42—41no—
584C42—41no—
585C42—41no—
586C23—24no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—81no—
606C23—81no—
607C23—81no—
608C23—81no—
609C23—81no—
610C23—81no—
611C23—81no—
612C23—81no—
613C23—81no—
614C23—81no—
615C23—81no—
616C23—81no—
617C23—81no—
618C23—81no—
619C23—81no—
620C23—81no—
621C23C2×C22⋊Q811yescharacteristic
622C23#53511yescharacteristic
623C23#53611yescharacteristic
624C23D4211yescharacteristic
625C23#54611yescharacteristic
626C23#54711yescharacteristic
627C23#55011yescharacteristic
628C23C22×D811yescharacteristic
629C23C2×AGL(1,ℤ/8)11yescharacteristic
630C23C2×#13711yescharacteristic
631C23C2×#13711yescharacteristic
632C23#57611yescharacteristic
633C23#57611yescharacteristic
634C23#57711yescharacteristic
635C23#57811yescharacteristic
636D4—24no—
637D4—24no—
638D4—42no—
639D4—42no—
640D4—42no—
641D4—42no—
642D4—42no—
643D4—42no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
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—22no—
663C2×C4—22no—
664C2×C4—22no—
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—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—816no—
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×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#47414yes—
736C2×C4C2×C22⋊Q811yescharacteristic
737C2×C4#53311yescharacteristic
738C2×C4#53411yescharacteristic
739C2×C4#53611yescharacteristic
740C2×C4#53911yescharacteristic
741C2×C4#53911yescharacteristic
742C2×C4#53911yescharacteristic
743C2×C4#53911yescharacteristic
744C2×C4#54011yescharacteristic
745C2×C4#54011yescharacteristic
746C2×C4#54211yescharacteristic
747C2×C4#54211yescharacteristic
748C2×C4#54311yescharacteristic
749C2×C4#54411yescharacteristic
750C2×C4#54411yescharacteristic
751C2×C4#54411yescharacteristic
752C2×C4#54611yescharacteristic
753C2×C4#54611yescharacteristic
754C2×C4#54711yescharacteristic
755C2×C4#55111yescharacteristic
756C2×C4#55111yescharacteristic
757C2×C4#55211yescharacteristic
758C2×C4#55211yescharacteristic
759C2×C4#55311yescharacteristic
760C2×C4#56011yescharacteristic
761C2×C4#56211yescharacteristic
762C2×C4#56211yescharacteristic
763C2×C4#56311yescharacteristic
764C8—42no—
765C8—42no—
766C8—42no—
767C8—81no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22#243711yescharacteristic
784C22#244111yescharacteristic
785C22#262811yescharacteristic
786C22#267311yescharacteristic
787C22#268011yescharacteristic
788C22#269411yescharacteristic
789C22#270611yescharacteristic
790C22C2×#47411yescharacteristic
791C22#307911yescharacteristic
792C22#308111yescharacteristic
793C22#308311yescharacteristic
794C22#320511yescharacteristic
795C22#321811yescharacteristic
796C22#322011yescharacteristic
797C22#322511yescharacteristic
798C22#322611yescharacteristic
799C22#323811yescharacteristic
800C22#324111yescharacteristic
801C22#324311yescharacteristic
802C22#326411yescharacteristic
803C22#326611yescharacteristic
804C22#327611yescharacteristic
805C22D4×D811yescharacteristic
806C22#329411yescharacteristic
807C22#331411yescharacteristic
808C22#331411yescharacteristic
809C22#333011yescharacteristic
810C22#333411yescharacteristic
811C22#334511yescharacteristic
812C22#334611yescharacteristic
813C22#335711yescharacteristic
814C22#339111yescharacteristic
815C22#339811yescharacteristic
816C22#339911yescharacteristic
817C22#340011yescharacteristic
818C4—24no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—82no—
825C4—82no—
826C4—161no—
827C4—161no—
828C4—161no—
829C4—161no—
830C4—161no—
831C4#243811yescharacteristic
832C4#262711yescharacteristic
833C4#266711yescharacteristic
834C4#268711yescharacteristic
835C4#270111yescharacteristic
836C4#273811yescharacteristic
837C4#274611yescharacteristic
838C4#284111yescharacteristic
839C2—84no—
840C2#1630011yescharacteristic
841C2#2595011yescharacteristic
842C2#2597011yescharacteristic
843C2#2608611yescharacteristic
844C2#2610211yescharacteristic
845C2#2998011yescharacteristic
846C2#2999111yescharacteristic
847C2#3073311yescharacteristic
848C2#3075711yescharacteristic
849C2#3107811yescharacteristic
850C2#3110411yescharacteristic
851C2#3157011yescharacteristic
852C2#3158611yescharacteristic
853C2#3193011yescharacteristic
854C2#3195411yescharacteristic
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. #15145C2semidirect
5. #11324C2semidirect
6. #11324C2semidirect
7. #11315C2semidirect
8. #11267C2semidirect
9. #11255C2semidirect
10. #11232C2semidirect
11. #11219C2semidirect

Maximal subgroups

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

subgroupindex
C2×#20932
C2×#18022
#151452
#139162
#113242
#113152
#112672
#112552
#112322
#112192
#111232
#110662
#110492
#107882