Finite Group Databasebeta

← #440895

Subgroups — #440895

Order 512.

1432 conjugacy classes of subgroups.

The subgroup lattice has 873 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2452C211yesmaximal, characteristic
2C2×#2101C211yesmaximal, characteristic, complemented
3C2×#2073C211yesmaximal, characteristic
4#13955C211yesmaximal, characteristic, complemented
5#11384C211yesmaximal, characteristic, complemented
6#11384C211yesmaximal, characteristic, complemented
7#11346C211yesmaximal, characteristic, complemented
8#11293C211yesmaximal, characteristic, complemented
9#11292C211yesmaximal, characteristic, complemented
10#11189C211yesmaximal, characteristic
11#11189C211yesmaximal, characteristic
12#10931C211yesmaximal, characteristic
13#10885C211yesmaximal, characteristic, complemented
14#10788C211yesmaximal, characteristic
15#10788C211yesmaximal, characteristic
16C22×C4⋊Q8C2211yescharacteristic
17C22×C22⋊Q8—21no—
18C22×C4×D4C2211yescharacteristic
19C22×#102C2211yescharacteristic
20C22×#102C2211yescharacteristic
21C22×#102C2211yescharacteristic
22C22×#102C2211yescharacteristic
23#2452—24no—
24#2452—24no—
25C2×#396—21no—
26C2×#393—21no—
27C2×#390C2211yescharacteristic
28C2×#390C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#385—21no—
32C2×#382C2211yescharacteristic
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35#2101—24no—
36#2073—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
54C2×#336C2211yescharacteristic
55#1442—21no—
56#1442—21no—
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C4⋊#95C2211yescharacteristic
60C4⋊#95C2211yescharacteristic
61#1434—21no—
62#1434—21no—
63C23×Q8—21no—
64C23×D4C2311yescharacteristic
65C24×C4—21no—
66C23×C8C2311yescharacteristic
67C23×C8C2311yescharacteristic
68C23×C8C2311yescharacteristic
69C23×C8C2311yescharacteristic
70C2×C4⋊Q8—22no—
71C2×C4⋊Q8—22no—
72C2×C4⋊Q8—22no—
73C2×C4⋊Q8—22no—
74C2×C4⋊Q8—41no—
75C2×C4⋊Q8—41no—
76C2×C22⋊Q8—28no—
77C2×C22⋊Q8—44no—
78C2×C22⋊Q8—44no—
79C2×C4×D4—22no—
80C2×C4×D4—22no—
81C2×C4×D4—22no—
82C2×C4×D4—22no—
83C2×C4×D4—41no—
84C2×C4×D4—41no—
85C22×C4⋊C4—21no—
86C22×C4⋊C4—21no—
87C22×C4⋊C4—21no—
88C22×C4⋊C4D411yescharacteristic
89C22×C4⋊C4D411yescharacteristic
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2311yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C4⋊C4C2311yescharacteristic
97C22×C22⋊C4—21no—
98C22×C22⋊C4—21no—
99C22×C22⋊C4—21no—
100C22×C22⋊C4—21no—
101C22×C22⋊C4—21no—
102C22×C42—21no—
103C22×C42C2311yescharacteristic
104C22×C42C2311yescharacteristic
105C22×C42C2311yescharacteristic
106C2×#102—22no—
107C2×#102—22no—
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—41no—
117C2×#102—41no—
118#396—28no—
119#393—28no—
120#390—22no—
121#390—22no—
122#390—22no—
123#390D414yes—
124#389—22no—
125#389—22no—
126#389—22no—
127#389D414yes—
128#385—28no—
129#382—22no—
130#382—22no—
131C4×C4⋊C4—22no—
132C4×C4⋊C4—22no—
133C4×C4⋊C4—22no—
134C4×C4⋊C4—22no—
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×#95—21no—
148C2×#95D411yescharacteristic
149C2×#95D411yescharacteristic
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—22no—
160#340—41no—
161#340—41no—
162#336—22no—
163#336—22no—
164#336—41no—
165#336—41no—
166#336—41no—
167#336—41no—
168C25—21no—
169C22×Q8—24no—
170C22×Q8—42no—
171C22×Q8—42no—
172C22×Q8—42no—
173C22×Q8—42no—
174C22×Q8—81no—
175C22×Q8—81no—
176C22×D4—21no—
177C22×D4—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4—21no—
181C22×D4—21no—
182C22×D4—21no—
183C22×D4—21no—
184C22×D4—21no—
185C22×D4—21no—
186C22×D4—21no—
187C22×D4C2×D412yes—
188C22×D4#4112yes—
189C22×D4#4112yes—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—24no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—42no—
199C23×C4—42no—
200C23×C4—42no—
201C23×C4—42no—
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×C8—21no—
238C22×C8—21no—
239C4⋊Q8—44no—
240C4⋊Q8—44no—
241C4⋊Q8—44no—
242C4⋊Q8—44no—
243C22⋊Q8—432no—
244C4×D4—44no—
245C4×D4—44no—
246C4×D4—44no—
247C4×D4—44no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4—22no—
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—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
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—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—41no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4C2×D412yes—
299C2×C4⋊C4C2×D412yes—
300C2×C4⋊C4C2×D412yes—
301C2×C4⋊C4#4112yes—
302C2×C4⋊C4#4112yes—
303C2×C4⋊C4#4112yes—
304C2×C4⋊C4#4112yes—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—42no—
312C2×C22⋊C4—42no—
313C2×C22⋊C4—42no—
314C2×C22⋊C4—42no—
315C2×C22⋊C4—42no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—81no—
319C2×C22⋊C4—81no—
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—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—24no—
337C2×C42—81no—
338C2×C42—81no—
339C2×C42C2×D412yes—
340C2×C42C2×D412yes—
341#102—44no—
342#102—44no—
343#102—44no—
344#102—44no—
345#95—24no—
346#95—24no—
347#95—24no—
348#95—22no—
349#95—22no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—42no—
354#95—42no—
355#95—42no—
356#95—81no—
357#95—81no—
358#95—81no—
359#95—81no—
360C24—22no—
361C24—22no—
362C24—22no—
363C24—41no—
364C24—41no—
365C24—41no—
366C24—41no—
367C24—41no—
368C24—41no—
369C24—41no—
370C24—41no—
371C24—41no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24C22×D411yescharacteristic
376C2×Q8—48no—
377C2×Q8—48no—
378C2×Q8—84no—
379C2×Q8—84no—
380C2×Q8—84no—
381C2×Q8—84no—
382C2×Q8—84no—
383C2×D4—22no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—41no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4—41no—
405C2×D4—41no—
406C2×D4—41no—
407C2×D4—41no—
408C2×D4—41no—
409C2×D4—41no—
410C2×D4#12414yes—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
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—22no—
426C22×C4—22no—
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—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—48no—
456C22×C4—48no—
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—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—84no—
500C22×C4—84no—
501C22×C4—84no—
502C22×C4—84no—
503C22×C4—84no—
504C22×C4#12012yes—
505C22×C4#12012yes—
506C22×C4#13512yes—
507C22×C4AGL(1,ℤ/8)12yes—
508C22×C4AGL(1,ℤ/8)12yes—
509C22×C4C22×D411yescharacteristic
510C22×C4C22×D411yescharacteristic
511C22×C4C2×#4111yescharacteristic
512C22×C4C2×#4111yescharacteristic
513C22×C4C2×#4111yescharacteristic
514C22×C4C2×#4111yescharacteristic
515C22×C4C2×#4111yescharacteristic
516C22×C4C2×#4111yescharacteristic
517C22×C4H(5,𝔽2)11yescharacteristic
518C22×C4H(5,𝔽2)11yescharacteristic
519C22×C42−1+411yescharacteristic
520C22×C42−1+411yescharacteristic
521C22×C42−1+411yescharacteristic
522C22×C42−1+411yescharacteristic
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—
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—
551C4⋊C4—28no—
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—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—44no—
564C4⋊C4—48no—
565C4⋊C4—48no—
566C4⋊C4—48no—
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—41no—
579C4⋊C4—41no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—41no—
583C4⋊C4#12414yes—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—84no—
589C42—22no—
590C42—22no—
591C42—22no—
592C42—22no—
593C42—41no—
594C42—41no—
595C42—41no—
596C42—41no—
597C42—41no—
598C42—41no—
599C42—41no—
600C42—41no—
601C42—84no—
602C23—24no—
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—81no—
622C23—81no—
623C23—81no—
624C23—81no—
625C23—81no—
626C23—81no—
627C23—81no—
628C23—81no—
629C23—81no—
630C23—81no—
631C23—81no—
632C23—81no—
633C23—81no—
634C23—81no—
635C23—81no—
636C23—81no—
637C23C2×#12011yescharacteristic
638C23#52511yescharacteristic
639C23#53611yescharacteristic
640C23#54611yescharacteristic
641C23#54611yescharacteristic
642C23#54811yescharacteristic
643C23#54811yescharacteristic
644C23C2×#13511yescharacteristic
645C23C2×AGL(1,ℤ/8)11yescharacteristic
646C23C2×AGL(1,ℤ/8)11yescharacteristic
647C23#57511yescharacteristic
648C23#57611yescharacteristic
649C23#57711yescharacteristic
650C23#57711yescharacteristic
651C23#57811yescharacteristic
652Q8—816no—
653D4—24no—
654D4—24no—
655D4—42no—
656D4—42no—
657D4—42no—
658D4—42no—
659D4—42no—
660D4—42no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
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—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—816no—
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×C4—81no—
748C2×C4—81no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—81no—
753C2×C4C2×#12411yescharacteristic
754C2×C4C2×#12411yescharacteristic
755C2×C4#52911yescharacteristic
756C2×C4#52911yescharacteristic
757C2×C4#53511yescharacteristic
758C2×C4#53611yescharacteristic
759C2×C4#53911yescharacteristic
760C2×C4#53911yescharacteristic
761C2×C4#54111yescharacteristic
762C2×C4#54111yescharacteristic
763C2×C4#54211yescharacteristic
764C2×C4#54211yescharacteristic
765C2×C4#54611yescharacteristic
766C2×C4#54611yescharacteristic
767C2×C4#54711yescharacteristic
768C2×C4#54711yescharacteristic
769C2×C4#54711yescharacteristic
770C2×C4#54711yescharacteristic
771C2×C4#54811yescharacteristic
772C2×C4#54811yescharacteristic
773C2×C4#55111yescharacteristic
774C2×C4#55111yescharacteristic
775C2×C4#55211yescharacteristic
776C2×C4#55211yescharacteristic
777C2×C4#55211yescharacteristic
778C2×C4#55211yescharacteristic
779C2×C4#56311yescharacteristic
780C2×C4#56311yescharacteristic
781C8—81no—
782C8—81no—
783C8—81no—
784C8—81no—
785C22—44no—
786C22—44no—
787C22—44no—
788C22—82no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22—82no—
793C22—82no—
794C22—82no—
795C22—82no—
796C22—82no—
797C22—82no—
798C22—82no—
799C22—82no—
800C22#240611yescharacteristic
801C22#243511yescharacteristic
802C22#243611yescharacteristic
803C22#247711yescharacteristic
804C22#247711yescharacteristic
805C22#269011yescharacteristic
806C22#269011yescharacteristic
807C22#300211yescharacteristic
808C22#300311yescharacteristic
809C22#301211yescharacteristic
810C22#301311yescharacteristic
811C22#310611yescharacteristic
812C22#311511yescharacteristic
813C22#311811yescharacteristic
814C22#312111yescharacteristic
815C22#322811yescharacteristic
816C22#323511yescharacteristic
817C22#324311yescharacteristic
818C22#324411yescharacteristic
819C22#330011yescharacteristic
820C22#330111yescharacteristic
821C22#331011yescharacteristic
822C22#331011yescharacteristic
823C22#331811yescharacteristic
824C22#331811yescharacteristic
825C22#332611yescharacteristic
826C22#332711yescharacteristic
827C22#336011yescharacteristic
828C22#336111yescharacteristic
829C22#336711yescharacteristic
830C22#336711yescharacteristic
831C22#337011yescharacteristic
832C22#337311yescharacteristic
833C22#337311yescharacteristic
834C22#337611yescharacteristic
835C4—42no—
836C4—42no—
837C4—42no—
838C4—42no—
839C4—44no—
840C4—42no—
841C4—81no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—161no—
847C4—161no—
848C4#248811yescharacteristic
849C4#248811yescharacteristic
850C4#248911yescharacteristic
851C4#248911yescharacteristic
852C4#269811yescharacteristic
853C4#269811yescharacteristic
854C4#272311yescharacteristic
855C4#272311yescharacteristic
856C2—84no—
857C2#1567011yescharacteristic
858C2#2406211yescharacteristic
859C2#2407511yescharacteristic
860C2#2588911yescharacteristic
861C2#2589111yescharacteristic
862C2#2593811yescharacteristic
863C2#2593911yescharacteristic
864C2#2743111yescharacteristic
865C2#2743511yescharacteristic
866C2#2744611yescharacteristic
867C2#2745011yescharacteristic
868C2#3145511yescharacteristic
869C2#3145911yescharacteristic
870C2#3147811yescharacteristic
871C2#3148211yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC23×C4C24
prime radicalC23×D4C23
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2101C2semidirect
4. #13955C2semidirect
5. #11384C2semidirect
6. #11384C2semidirect
7. #11346C2semidirect
8. #11293C2semidirect
9. #11292C2semidirect
13. #10885C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24522
C2×#21012
C2×#20732
#139552
#113842
#113462
#112932
#112922
#111892
#109312
#108852
#107882