Finite Group Databasebeta

← #440833

Subgroups — #440833

Order 512.

1232 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2446C211yesmaximal, characteristic
2C2×#2097C211yesmaximal, characteristic
3C2×#2074C211yesmaximal, characteristic
4#13955C211yesmaximal, characteristic
5#11346C211yesmaximal, characteristic
6#11220C211yesmaximal, characteristic
7#11219C211yesmaximal, characteristic
8#11124C211yesmaximal, characteristic
9#11122C211yesmaximal, characteristic
10#11010C211yesmaximal, characteristic
11#11010C211yesmaximal, characteristic
12#10932C211yesmaximal, characteristic
13#10932C211yesmaximal, characteristic
14#10789C211yesmaximal, characteristic
15#10789C211yesmaximal, characteristic
16C22×C4⋊Q8C2211yescharacteristic
17C22×C4×Q8C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×#106C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×#103C2211yescharacteristic
25C22×#103C2211yescharacteristic
26C22×#103C2211yescharacteristic
27C22×#103C2211yescharacteristic
28#2446—24no—
29#2446—24no—
30C2×#400—21no—
31C2×#398—21no—
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#387—21no—
37C2×#387—21no—
38C2×#382C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41#2097—24no—
42#2074—24no—
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51C2×#336C2211yescharacteristic
52C2×#336C2211yescharacteristic
53C2×#336C2211yescharacteristic
54C2×#336C2211yescharacteristic
55#1442—21no—
56#1442—21no—
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61#1434—21no—
62#1434—21no—
63C23×Q8C2311yescharacteristic
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—22no—
73C2×C4⋊Q8—41no—
74C2×C4⋊Q8—41no—
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×C42—21no—
94C22×C42—21no—
95C22×C42C2311yescharacteristic
96C22×C42C2311yescharacteristic
97C22×C42C2311yescharacteristic
98C2×#107—22no—
99C2×#107—22no—
100C2×#107—41no—
101C2×#106—22no—
102C2×#106—22no—
103C2×#106—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—22no—
118C2×#103—41no—
119C2×#103—41no—
120C2×#103—41no—
121C2×#103—41no—
122C2×#103—41no—
123C2×#103—41no—
124C2×#103—41no—
125C2×#103—41no—
126C2×#103—41no—
127C2×#103—41no—
128#400—28no—
129#398—28no—
130#391—22no—
131#391—22no—
132#391—22no—
133#391—22no—
134#391D414yes—
135#391D414yes—
136#389—22no—
137#389—22no—
138#387—28no—
139#387—28no—
140#382—22no—
141#382—22no—
142C4×C4⋊C4—22no—
143C4×C4⋊C4—22no—
144C4×C4⋊C4—22no—
145C4×C4⋊C4—22no—
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×#95—21no—
159C2×#95—21no—
160C2×#95—21no—
161C2×#95—21no—
162C2×#95—21no—
163C2×#95—21no—
164C2×#95D411yescharacteristic
165C2×#95D411yescharacteristic
166#340—22no—
167#340—22no—
168#340—41no—
169#340—41no—
170#340—41no—
171#340—41no—
172#336—22no—
173#336—22no—
174#336—41no—
175#336—41no—
176#336—41no—
177#336—41no—
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×Q8—21no—
199C22×Q8—21no—
200C22×Q8—21no—
201C22×Q8—21no—
202C22×Q8C2×D412yes—
203C22×Q8C2×D412yes—
204C22×Q8#4112yes—
205C22×Q8#4112yes—
206C23×C4—21no—
207C23×C4—21no—
208C23×C4—21no—
209C23×C4—21no—
210C23×C4—21no—
211C23×C4—21no—
212C23×C4—21no—
213C23×C4—21no—
214C23×C4C2×D411yescharacteristic
215C23×C4C2×D411yescharacteristic
216C23×C4C2×D411yescharacteristic
217C23×C4C2×D411yescharacteristic
218C23×C4C2×D411yescharacteristic
219C23×C4C2×D411yescharacteristic
220C23×C4C2411yescharacteristic
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×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#4112yes—
248C22×C8#4112yes—
249C4⋊Q8—44no—
250C4⋊Q8—44no—
251C4⋊Q8—44no—
252C4⋊Q8—44no—
253C4×Q8—44no—
254C4×Q8—44no—
255C4×Q8—44no—
256C4×Q8—44no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
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—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
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—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4C2×D412yes—
308C2×C4⋊C4C2×D412yes—
309C2×C4⋊C4#4112yes—
310C2×C4⋊C4#4112yes—
311C2×C42—21no—
312C2×C42—21no—
313C2×C42—21no—
314C2×C42—21no—
315C2×C42—24no—
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—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—24no—
329C2×C42—42no—
330C2×C42—42no—
331C2×C42—81no—
332C2×C42—81no—
333C2×C42C2×D412yes—
334C2×C42C2×D412yes—
335#107—44no—
336#106—44no—
337#103—44no—
338#103—44no—
339#103—44no—
340#103—44no—
341#103—44no—
342#103—44no—
343#103—44no—
344#103—44no—
345#95—24no—
346#95—24no—
347#95—24no—
348#95—24no—
349#95—24no—
350#95—24no—
351#95—24no—
352#95—24no—
353#95—22no—
354#95—22no—
355#95—42no—
356#95—42no—
357#95—42no—
358#95—42no—
359#95—42no—
360#95—42no—
361#95—81no—
362#95—81no—
363#95—81no—
364#95—81no—
365C24C22×D411yescharacteristic
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—22no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—22no—
381C2×Q8—22no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8—22no—
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—41no—
412C2×Q8—41no—
413C2×Q8—41no—
414C2×Q8—41no—
415C2×Q8—41no—
416C2×Q8—41no—
417C2×Q8—41no—
418C2×Q8—41no—
419C2×Q8—41no—
420C2×Q8—41no—
421C2×Q8#12414yes—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
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—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
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—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4#12012yes—
516C22×C4#12012yes—
517C22×C4#13512yes—
518C22×C4#13712yes—
519C22×C4#13712yes—
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C2×#4111yescharacteristic
523C22×C4C2×#4111yescharacteristic
524C22×C4C2×#4111yescharacteristic
525C22×C4C2×#4111yescharacteristic
526C22×C4C2×#4111yescharacteristic
527C22×C4C2×#4111yescharacteristic
528C22×C4H(5,𝔽2)11yescharacteristic
529C22×C4H(5,𝔽2)11yescharacteristic
530C22×C4H(5,𝔽2)11yescharacteristic
531C22×C4H(5,𝔽2)11yescharacteristic
532C22×C42−1+411yescharacteristic
533C22×C42−1+411yescharacteristic
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8—22no—
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—
553C2×C8—41no—
554C2×C8—41no—
555C2×C8—41no—
556C2×C8—41no—
557C2×C8—41no—
558C2×C8—41no—
559C2×C8—41no—
560C2×C8—41no—
561C2×C8—41no—
562C4⋊C4—28no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—44no—
572C4⋊C4—48no—
573C4⋊C4—48no—
574C4⋊C4—48no—
575C4⋊C4—48no—
576C4⋊C4—41no—
577C4⋊C4—41no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4—41no—
584C4⋊C4—41no—
585C4⋊C4—41no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C4⋊C4—41no—
589C4⋊C4—41no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C42—22no—
593C42—22no—
594C42—22no—
595C42—22no—
596C42—48no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—41no—
602C42—41no—
603C42—41no—
604C42—41no—
605C42—84no—
606C23C2×#12011yescharacteristic
607C23#52511yescharacteristic
608C23#53611yescharacteristic
609C23#54611yescharacteristic
610C23#54611yescharacteristic
611C23#55011yescharacteristic
612C23#55011yescharacteristic
613C23C2×#13511yescharacteristic
614C23C2×#13711yescharacteristic
615C23C2×#13711yescharacteristic
616C23#57511yescharacteristic
617C23#57711yescharacteristic
618C23#57711yescharacteristic
619C23#57811yescharacteristic
620C23#57811yescharacteristic
621Q8—24no—
622Q8—24no—
623Q8—42no—
624Q8—42no—
625Q8—42no—
626Q8—42no—
627Q8—42no—
628Q8—42no—
629Q8—42no—
630Q8—42no—
631Q8—42no—
632Q8—42no—
633Q8—81no—
634Q8—81no—
635Q8—81no—
636Q8—81no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
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—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—42no—
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—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
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×C4C2×#12411yescharacteristic
736C2×C4#52911yescharacteristic
737C2×C4#52911yescharacteristic
738C2×C4#53211yescharacteristic
739C2×C4#53511yescharacteristic
740C2×C4#53511yescharacteristic
741C2×C4#53911yescharacteristic
742C2×C4#53911yescharacteristic
743C2×C4#53911yescharacteristic
744C2×C4#53911yescharacteristic
745C2×C4#54011yescharacteristic
746C2×C4#54011yescharacteristic
747C2×C4#54611yescharacteristic
748C2×C4#54611yescharacteristic
749C2×C4#54611yescharacteristic
750C2×C4#54611yescharacteristic
751C2×C4#54711yescharacteristic
752C2×C4#54711yescharacteristic
753C2×C4#54711yescharacteristic
754C2×C4#54711yescharacteristic
755C2×C4#55111yescharacteristic
756C2×C4#55111yescharacteristic
757C2×C4#55111yescharacteristic
758C2×C4#55111yescharacteristic
759C2×C4#55211yescharacteristic
760C2×C4#55211yescharacteristic
761C2×C4#56211yescharacteristic
762C2×C4#56211yescharacteristic
763C8—42no—
764C8—42no—
765C8—81no—
766C8—81no—
767C22#240611yescharacteristic
768C22#243111yescharacteristic
769C22#243511yescharacteristic
770C22#247111yescharacteristic
771C22#247111yescharacteristic
772C22#269411yescharacteristic
773C22#269411yescharacteristic
774C22#300211yescharacteristic
775C22#300411yescharacteristic
776C22#301311yescharacteristic
777C22#301311yescharacteristic
778C22#310711yescharacteristic
779C22#311611yescharacteristic
780C22#312311yescharacteristic
781C22#312711yescharacteristic
782C22#323111yescharacteristic
783C22#323711yescharacteristic
784C22#324211yescharacteristic
785C22#324211yescharacteristic
786C22#330011yescharacteristic
787C22#330111yescharacteristic
788C22#331211yescharacteristic
789C22#331211yescharacteristic
790C22#332011yescharacteristic
791C22#332011yescharacteristic
792C22#332611yescharacteristic
793C22#332711yescharacteristic
794C22#339311yescharacteristic
795C22#339411yescharacteristic
796C22#339811yescharacteristic
797C22#339811yescharacteristic
798C22#340011yescharacteristic
799C22#340011yescharacteristic
800C22#340111yescharacteristic
801C22#340211yescharacteristic
802C4—42no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—44no—
808C4—81no—
809C4—82no—
810C4—82no—
811C4—82no—
812C4—82no—
813C4—82no—
814C4—161no—
815C4—161no—
816C4#248811yescharacteristic
817C4#248811yescharacteristic
818C4#255311yescharacteristic
819C4#255311yescharacteristic
820C4#270611yescharacteristic
821C4#270611yescharacteristic
822C4#270611yescharacteristic
823C4#270611yescharacteristic
824C2#1566911yescharacteristic
825C2#2406511yescharacteristic
826C2#2407211yescharacteristic
827C2#2563611yescharacteristic
828C2#2564011yescharacteristic
829C2#2588911yescharacteristic
830C2#2589411yescharacteristic
831C2#2720111yescharacteristic
832C2#2720511yescharacteristic
833C2#2721611yescharacteristic
834C2#2722011yescharacteristic
835C2#3157111yescharacteristic
836C2#3157511yescharacteristic
837C2#3159611yescharacteristic
838C2#3160011yescharacteristic
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×#24462
C2×#20972
C2×#20742
#139552
#113462
#112202
#112192
#111242
#111222
#110102
#109322
#107892