Finite Group Databasebeta

← #432770

Subgroups — #432770

Order 512.

1188 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2451C211yesmaximal, characteristic
2C2×#2074C211yesmaximal, characteristic
3C2×#1993C211yesmaximal, characteristic
4#15235C211yesmaximal, characteristic
5#11384C211yesmaximal, characteristic
6#11293C211yesmaximal, characteristic
7#11293C211yesmaximal, characteristic
8#11292C211yesmaximal, characteristic
9#11292C211yesmaximal, characteristic
10#11190C211yesmaximal, characteristic
11#11190C211yesmaximal, characteristic
12#10928C211yesmaximal, characteristic
13#10875C211yesmaximal, characteristic
14#10789C211yesmaximal, characteristic
15#10789C211yesmaximal, characteristic
16C22×C4⋊Q8C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×#103C2211yescharacteristic
19C22×#103C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#97C2211yescharacteristic
23#2451—24no—
24#2451—24no—
25C2×#398—21no—
26C2×#395—21no—
27C2×#391—21no—
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#387—21no—
33C2×#382C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35#2074—24no—
36#1993—24no—
37C2×#340C2211yescharacteristic
38C2×#340C2211yescharacteristic
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54#1443—21no—
55#1443—21no—
56#1442—21no—
57#1442—21no—
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C4⋊#95C2211yescharacteristic
63C23×Q8—21no—
64C23×Q8C2311yescharacteristic
65C23×C8C2311yescharacteristic
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C2×C4⋊Q8—22no—
70C2×C4⋊Q8—22no—
71C2×C4⋊Q8—22no—
72C2×C4⋊Q8—41no—
73C2×C4⋊Q8—41no—
74C2×C4⋊Q8D414yes—
75C2×C4×Q8—22no—
76C2×C4×Q8—22no—
77C2×C4×Q8—22no—
78C2×C4×Q8—22no—
79C2×C4×Q8—41no—
80C2×C4×Q8—41no—
81C22×C4⋊C4—21no—
82C22×C4⋊C4—21no—
83C22×C4⋊C4—21no—
84C22×C4⋊C4—21no—
85C22×C4⋊C4D411yescharacteristic
86C22×C4⋊C4D411yescharacteristic
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2311yescharacteristic
89C22×C4⋊C4C2311yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C42—21no—
95C22×C42C2311yescharacteristic
96C22×C42C2311yescharacteristic
97C22×C42C2311yescharacteristic
98C2×#103—22no—
99C2×#103—22no—
100C2×#103—22no—
101C2×#103—22no—
102C2×#103—22no—
103C2×#103—22no—
104C2×#103—22no—
105C2×#103—22no—
106C2×#103—22no—
107C2×#103—22no—
108C2×#103—41no—
109C2×#103—41no—
110C2×#97—22no—
111C2×#97—41no—
112C2×#97—41no—
113#398—28no—
114#395—28no—
115#391—28no—
116#391—22no—
117#391—22no—
118#391—22no—
119#391D414yes—
120#389—22no—
121#389—22no—
122#389—22no—
123#389—22no—
124#387—28no—
125#382—22no—
126#382—22no—
127C4×C4⋊C4—22no—
128C4×C4⋊C4—22no—
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×#95—21no—
143C2×#95—21no—
144C2×#95—21no—
145C2×#95—21no—
146C2×#95—21no—
147C2×#95D411yescharacteristic
148C2×#95D411yescharacteristic
149#340—22no—
150#340—22no—
151#340—22no—
152#340—22no—
153#340—22no—
154#340—22no—
155#340—22no—
156#340—22no—
157#340—22no—
158#340—22no—
159#340—41no—
160#340—41no—
161#336—22no—
162#336—22no—
163#336—22no—
164#336—41no—
165#336—41no—
166C22×Q8—24no—
167C22×Q8—21no—
168C22×Q8—21no—
169C22×Q8—21no—
170C22×Q8—21no—
171C22×Q8—21no—
172C22×Q8—21no—
173C22×Q8—21no—
174C22×Q8—21no—
175C22×Q8—21no—
176C22×Q8—21no—
177C22×Q8—21no—
178C22×Q8—42no—
179C22×Q8—42no—
180C22×Q8—42no—
181C22×Q8—42no—
182C22×Q8—81no—
183C22×Q8—81no—
184C22×Q8C2×D412yes—
185C22×Q8#4112yes—
186C22×Q8#4112yes—
187C23×C4—21no—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4C2×D411yescharacteristic
196C23×C4C2×D411yescharacteristic
197C23×C4C2×D411yescharacteristic
198C23×C4C2×D411yescharacteristic
199C23×C4C2×D411yescharacteristic
200C23×C4C2×D411yescharacteristic
201C23×C4C2411yescharacteristic
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×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8#4112yes—
229C22×C8#4112yes—
230C4⋊Q8—28no—
231C4⋊Q8—44no—
232C4⋊Q8—44no—
233C4⋊Q8—44no—
234C4×Q8—44no—
235C4×Q8—44no—
236C4×Q8—44no—
237C4×Q8—44no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4—22no—
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—24no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—22no—
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—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—41no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—81no—
290C2×C4⋊C4—81no—
291C2×C4⋊C4—81no—
292C2×C4⋊C4—81no—
293C2×C4⋊C4C2×D412yes—
294C2×C4⋊C4C2×D412yes—
295C2×C4⋊C4C2×D412yes—
296C2×C4⋊C4#4112yes—
297C2×C4⋊C4#4112yes—
298C2×C42—21no—
299C2×C42—21no—
300C2×C42—21no—
301C2×C42—21no—
302C2×C42—24no—
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—21no—
314C2×C42—21no—
315C2×C42—42no—
316C2×C42—42no—
317C2×C42C2×D412yes—
318C2×C42C2×D412yes—
319#103—44no—
320#103—44no—
321#103—44no—
322#103—44no—
323#97—44no—
324#95—24no—
325#95—24no—
326#95—24no—
327#95—24no—
328#95—24no—
329#95—24no—
330#95—22no—
331#95—22no—
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—
341#95—81no—
342#95—81no—
343#95—81no—
344C24C22×D411yescharacteristic
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—22no—
351C2×Q8—22no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—22no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—48no—
361C2×Q8—48no—
362C2×Q8—41no—
363C2×Q8—41no—
364C2×Q8—41no—
365C2×Q8—41no—
366C2×Q8—41no—
367C2×Q8—41no—
368C2×Q8—41no—
369C2×Q8—41no—
370C2×Q8—41no—
371C2×Q8—41no—
372C2×Q8—41no—
373C2×Q8—41no—
374C2×Q8—84no—
375C2×Q8—84no—
376C2×Q8—84no—
377C2×Q8—84no—
378C2×Q8—84no—
379C2×Q8#12414yes—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
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—22no—
412C22×C4—22no—
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—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
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—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#12012yes—
475C22×C4#12012yes—
476C22×C4#13712yes—
477C22×C4#13712yes—
478C22×C4C22×D411yescharacteristic
479C22×C4C22×D411yescharacteristic
480C22×C4C2×#4111yescharacteristic
481C22×C4C2×#4111yescharacteristic
482C22×C4C2×#4111yescharacteristic
483C22×C4C2×#4111yescharacteristic
484C22×C4C2×#4111yescharacteristic
485C22×C4C2×#4111yescharacteristic
486C22×C4H(5,𝔽2)11yescharacteristic
487C22×C4H(5,𝔽2)11yescharacteristic
488C22×C42−1+411yescharacteristic
489C22×C42−1+411yescharacteristic
490C22×C42−1+411yescharacteristic
491C22×C42−1+411yescharacteristic
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
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—
520C4⋊C4—28no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—48no—
529C4⋊C4—44no—
530C4⋊C4—48no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
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—84no—
552C4⋊C4—84no—
553C4⋊C4#12314yes—
554C42—22no—
555C42—22no—
556C42—22no—
557C42—22no—
558C42—48no—
559C42—41no—
560C42—41no—
561C42—41no—
562C42—41no—
563C42—41no—
564C42—41no—
565C42—41no—
566C42—41no—
567C23C2×#12011yescharacteristic
568C23#53211yescharacteristic
569C23#53611yescharacteristic
570C23#54611yescharacteristic
571C23#54611yescharacteristic
572C23#54811yescharacteristic
573C23#54811yescharacteristic
574C23C2×#13711yescharacteristic
575C23C2×#13711yescharacteristic
576C23#57511yescharacteristic
577C23#57511yescharacteristic
578C23#57611yescharacteristic
579C23#57711yescharacteristic
580C23#57711yescharacteristic
581C23#57811yescharacteristic
582Q8—24no—
583Q8—24no—
584Q8—42no—
585Q8—42no—
586Q8—42no—
587Q8—42no—
588Q8—42no—
589Q8—42no—
590Q8—816no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—42no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—42no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—42no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—42no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—42no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—41no—
648C2×C4—42no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—81no—
654C2×C4—81no—
655C2×C4—81no—
656C2×C4—81no—
657C2×C4—81no—
658C2×C4—81no—
659C2×C4—81no—
660C2×C4—81no—
661C2×C4—81no—
662C2×C4—81no—
663C2×C4—81no—
664C2×C4—81no—
665C2×C4—81no—
666C2×C4—81no—
667C2×C4—81no—
668C2×C4—81no—
669C2×C4—81no—
670C2×C4—81no—
671C2×C4—81no—
672C2×C4—81no—
673C2×C4—81no—
674C2×C4—81no—
675C2×C4—81no—
676C2×C4—81no—
677C2×C4—81no—
678C2×C4—81no—
679C2×C4—81no—
680C2×C4—81no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—81no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—81no—
688C2×C4—81no—
689C2×C4C2×#12311yescharacteristic
690C2×C4C2×#12411yescharacteristic
691C2×C4#52911yescharacteristic
692C2×C4#52911yescharacteristic
693C2×C4#53411yescharacteristic
694C2×C4#53611yescharacteristic
695C2×C4#53911yescharacteristic
696C2×C4#53911yescharacteristic
697C2×C4#53911yescharacteristic
698C2×C4#53911yescharacteristic
699C2×C4#54111yescharacteristic
700C2×C4#54111yescharacteristic
701C2×C4#54611yescharacteristic
702C2×C4#54611yescharacteristic
703C2×C4#54711yescharacteristic
704C2×C4#54711yescharacteristic
705C2×C4#54811yescharacteristic
706C2×C4#54811yescharacteristic
707C2×C4#54811yescharacteristic
708C2×C4#54811yescharacteristic
709C2×C4#55111yescharacteristic
710C2×C4#55111yescharacteristic
711C2×C4#55211yescharacteristic
712C2×C4#55211yescharacteristic
713C2×C4#55611yescharacteristic
714C2×C4#55611yescharacteristic
715C2×C4#56311yescharacteristic
716C2×C4#56311yescharacteristic
717C8—42no—
718C8—42no—
719C8—81no—
720C8—81no—
721C22#240511yescharacteristic
722C22#243211yescharacteristic
723C22#243611yescharacteristic
724C22#256011yescharacteristic
725C22#256011yescharacteristic
726C22#269011yescharacteristic
727C22#269011yescharacteristic
728C22#300411yescharacteristic
729C22#300511yescharacteristic
730C22#301211yescharacteristic
731C22#301311yescharacteristic
732C22#317211yescharacteristic
733C22#317811yescharacteristic
734C22#317911yescharacteristic
735C22#318111yescharacteristic
736C22#323611yescharacteristic
737C22#323711yescharacteristic
738C22#324311yescharacteristic
739C22#324411yescharacteristic
740C22#331111yescharacteristic
741C22#331211yescharacteristic
742C22#331911yescharacteristic
743C22#332011yescharacteristic
744C22#332211yescharacteristic
745C22#332311yescharacteristic
746C22#332811yescharacteristic
747C22#332911yescharacteristic
748C22#336911yescharacteristic
749C22#336911yescharacteristic
750C22#337111yescharacteristic
751C22#337111yescharacteristic
752C22#337511yescharacteristic
753C22#337511yescharacteristic
754C22#337711yescharacteristic
755C22#337711yescharacteristic
756C4—42no—
757C4—44no—
758C4—42no—
759C4—44no—
760C4—42no—
761C4—42no—
762C4—81no—
763C4—82no—
764C4—81no—
765C4—82no—
766C4—161no—
767C4—161no—
768C4—161no—
769C4—161no—
770C4#242111yescharacteristic
771C4#242111yescharacteristic
772C4#248811yescharacteristic
773C4#248811yescharacteristic
774C4#268911yescharacteristic
775C4#268911yescharacteristic
776C4#272811yescharacteristic
777C4#272811yescharacteristic
778C2#1546511yescharacteristic
779C2#2405011yescharacteristic
780C2#2405311yescharacteristic
781C2#2567711yescharacteristic
782C2#2568411yescharacteristic
783C2#2594111yescharacteristic
784C2#2594211yescharacteristic
785C2#2908111yescharacteristic
786C2#2908511yescharacteristic
787C2#2908911yescharacteristic
788C2#2909311yescharacteristic
789C2#3148011yescharacteristic
790C2#3148111yescharacteristic
791C2#3148411yescharacteristic
792C2#3148511yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ 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×#24512
C2×#20742
C2×#19932
#152352
#113842
#112932
#112922
#111902
#109282
#108752
#107892