Finite Group Databasebeta

← #4894730

Subgroups — #4894730

Order 512.

2022 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17304C212yesmaximal, complemented
2#17185C212yesmaximal, complemented
3#16987C212yesmaximal, complemented
4#16824C211yesmaximal, characteristic, complemented
5#16707C211yesmaximal, characteristic, complemented
6#16706C211yesmaximal, characteristic, complemented
7#16670C212yesmaximal, complemented
8#16572C212yesmaximal, complemented
9#16521C212yesmaximal, complemented
10#16403C212yesmaximal, complemented
11#16305C211yesmaximal, characteristic, complemented
12#16304C212yesmaximal, complemented
13#15328C212yesmaximal
14#15327C212yesmaximal
15#14822C212yesmaximal, complemented
16#14736C212yesmaximal, complemented
17#14345C211yesmaximal, characteristic
18#13960C211yesmaximal, characteristic
19#13872C211yesmaximal, characteristic
20C22×C4×D4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C2×#400C2212yes—
23C2×#400C2212yes—
24C2×#399C2212yes—
25C2×#398C2212yes—
26C2×#398C2212yes—
27C2×#396C2212yes—
28C2×#386C2211yescharacteristic
29C2×#386C2211yescharacteristic
30C2×#386C2212yes—
31C2×#385C2212yes—
32C2×#385C2212yes—
33C2×#385C2212yes—
34C2×#383C2211yescharacteristic
35C2×#382C2211yescharacteristic
36C2×#380C2211yescharacteristic
37C2×#380C2212yes—
38C2×#380C2211yescharacteristic
39C2×#380C2212yes—
40C22×#95C2211yescharacteristic
41#1445C2212yes—
42#1445C2212yes—
43#1445C2212yes—
44#1445C2212yes—
45#1444C2212yes—
46#1444C2212yes—
47#1444C2212yes—
48#1444C2212yes—
49#1444C2212yes—
50#1444C2212yes—
51#1443C2212yes—
52#1443C2212yes—
53#1443C2212yes—
54#1442C2212yes—
55#1442C2212yes—
56#1442C2212yes—
57#1442C2212yes—
58#1442C2212yes—
59#1442C2212yes—
60#1442C2212yes—
61#1442C2212yes—
62#1442C2212yes—
63#1442C2212yes—
64#1442C2212yes—
65#1441C2212yes—
66#1441C2212yes—
67#1441C2212yes—
68#1441C2212yes—
69#1441C2211yescharacteristic
70#1441C2212yes—
71#1441C2212yes—
72#1441C2212yes—
73#1441C2212yes—
74#1441C2212yes—
75#1441C2212yes—
76#1441C2212yes—
77#1441C2211yescharacteristic
78#1441C2212yes—
79#1441C2212yes—
80#1441C2212yes—
81#1439C2211yescharacteristic
82#1439C2211yescharacteristic
83#1439C2211yescharacteristic
84#1439C2211yescharacteristic
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1439C2211yescharacteristic
89#1439C2212yes—
90#1439C2211yescharacteristic
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1438C2212yes—
95C4⋊#95C2212yes—
96#1434C2212yes—
97C22⋊#95C2212yes—
98C22⋊#95C2212yes—
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2211yescharacteristic
102C22⋊#95C2211yescharacteristic
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C23×D4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2312yes—
113C2×C4×D4—42no—
114C2×C4×D4—42no—
115C2×C4×D4Q818yes—
116C22×C4⋊C4—44no—
117C22×C4⋊C4—42no—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2311yescharacteristic
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C42C2311yescharacteristic
150#400—44no—
151#400—44no—
152#399—44no—
153#398—44no—
154#398—44no—
155#396—44no—
156#386—42no—
157#386—42no—
158#386—44no—
159#385—44no—
160#385—44no—
161#385—44no—
162#383—42no—
163#382—42no—
164#380—44no—
165#380—42no—
166#380—44no—
167#380—42no—
168C2×#95—42no—
169C2×#95C2312yes—
170C2×#95C2312yes—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2311yescharacteristic
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C2×#95C2312yes—
216C2×#95C2311yescharacteristic
217C2×#95C2312yes—
218C25C2411yescharacteristic
219C25C2411yescharacteristic
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—41no—
225C22×D4—41no—
226C22×D4C2×Q814yes—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—24no—
233C23×C4—22no—
234C23×C4—24no—
235C23×C4—42no—
236C23×C4—42no—
237C23×C4—41no—
238C23×C4—41no—
239C23×C4—42no—
240C23×C4—42no—
241C23×C4—42no—
242C23×C4—42no—
243C23×C4—42no—
244C23×C4—42no—
245C23×C4—42no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—42no—
249C23×C4—41no—
250C23×C4—41no—
251C23×C4—42no—
252C23×C4C2×Q814yes—
253C23×C4C2×Q814yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2412yes—
270C23×C4C2411yescharacteristic
271C4×D4—416no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—42no—
278C2×C4⋊C4—42no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—41no—
281C2×C4⋊C4—41no—
282C2×C4⋊C4—416no—
283C2×C4⋊C4—42no—
284C2×C4⋊C4—42no—
285C2×C4⋊C4—42no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
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⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4C2×Q814yes—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—41no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—41no—
360C2×C22⋊C4C2×Q814yes—
361C2×C22⋊C4C2×Q814yes—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42C2×Q814yes—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—41no—
374#95—41no—
375#95—42no—
376#95—42no—
377#95—42no—
378#95—42no—
379#95—42no—
380#95—42no—
381#95—42no—
382#95—42no—
383#95—42no—
384#95—42no—
385#95—42no—
386#95—42no—
387#95—42no—
388#95—42no—
389#95—42no—
390#95—42no—
391#95—42no—
392#95—41no—
393#95—41no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414C24—22no—
415C24—21no—
416C24—21no—
417C24—22no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24C22×Q812yes—
431C24C22×Q812yes—
432C24H(5,𝔽2)12yes—
433C24H(5,𝔽2)12yes—
434C242−1+412yes—
435C242−1+412yes—
436C24C2511yescharacteristic
437C2×D4—28no—
438C2×D4—28no—
439C2×D4—44no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—44no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—44no—
557C22×C4—48no—
558C22×C4—82no—
559C22×C4—82no—
560C22×C4—84no—
561C22×C4—84no—
562C22×C4—82no—
563C22×C4—84no—
564C22×C4—84no—
565C22×C4—84no—
566C22×C4—82no—
567C22×C4—84no—
568C22×C4—82no—
569C22×C4—84no—
570C22×C4—84no—
571C22×C4—82no—
572C22×C4—84no—
573C22×C4—84no—
574C22×C4C22×Q812yes—
575C22×C4C22×Q812yes—
576C22×C4C22×Q812yes—
577C22×C4C22×Q812yes—
578C22×C4C22×Q812yes—
579C22×C4H(5,𝔽2)14yes—
580C22×C4H(5,𝔽2)12yes—
581C22×C4H(5,𝔽2)12yes—
582C4⋊C4—44no—
583C4⋊C4—48no—
584C4⋊C4—48no—
585C4⋊C4—84no—
586C4⋊C4—84no—
587C4⋊C4—82no—
588C4⋊C4—82no—
589C4⋊C4—84no—
590C4⋊C4—82no—
591C4⋊C4—82no—
592C4⋊C4—84no—
593C4⋊C4—84no—
594C4⋊C4—84no—
595C4⋊C4—84no—
596C4⋊C4—84no—
597C4⋊C4—84no—
598C4⋊C4—84no—
599C4⋊C4—84no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—84no—
606C22⋊C4—84no—
607C22⋊C4—82no—
608C22⋊C4—82no—
609C22⋊C4—84no—
610C22⋊C4—84no—
611C22⋊C4—84no—
612C22⋊C4—84no—
613C42—28no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23#54414yes—
659C23#54414yes—
660C23C23×Q811yescharacteristic
661C23C2×H(5,𝔽2)11yescharacteristic
662C23C2×H(5,𝔽2)11yescharacteristic
663C23C2×H(5,𝔽2)11yescharacteristic
664C23C2×H(5,𝔽2)11yescharacteristic
665C23C2×H(5,𝔽2)12yes—
666C23C2×2−1+411yescharacteristic
667C23C2×2−1+411yescharacteristic
668C23#58512yes—
669C23#58512yes—
670C23#58512yes—
671D4—416no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—416no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—88no—
784C2×C4—88no—
785C2×C4—88no—
786C2×C4—816no—
787C2×C4#54314yes—
788C22—24no—
789C22—24no—
790C22—28no—
791C22—28no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—44no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22—44no—
809C22—44no—
810C22C2×#54311yescharacteristic
811C22C2×#54411yescharacteristic
812C22C2×#54411yescharacteristic
813C22#350112yes—
814C22#350412yes—
815C22#353211yescharacteristic
816C22#353311yescharacteristic
817C22#353312yes—
818C22#353412yes—
819C22#353512yes—
820C22#353611yescharacteristic
821C22#353611yescharacteristic
822C22#353711yescharacteristic
823C22#353811yescharacteristic
824C22#353912yes—
825C22#354112yes—
826C22#354212yes—
827C22#355111yescharacteristic
828C22#355111yescharacteristic
829C22#355312yes—
830C22#355812yes—
831C22#356012yes—
832C22#356412yes—
833C4—24no—
834C4—42no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—44no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4—82no—
848C4—82no—
849C4—82no—
850C2—44no—
851C2—44no—
852C2#3674711yescharacteristic
853C2#3742511yescharacteristic
854C2#3747711yescharacteristic
855C2#4061712yes—
856C2#4061812yes—
857C2#5381111yescharacteristic
858C2#5387611yescharacteristic
859C2#5419012yes—
860C2#5445812yes—
861C2#5616411yescharacteristic
862C2#5825911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #17304C2semidirect
2. #17185C2semidirect
3. #16987C2semidirect
4. #16824C2semidirect
5. #16707C2semidirect
6. #16706C2semidirect
7. #16670C2semidirect
8. #16572C2semidirect
9. #16521C2semidirect
10. #16403C2semidirect
11. #16305C2semidirect
12. #16304C2semidirect
15. #14822C2semidirect
16. #14736C2semidirect

Maximal subgroups

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

subgroupindex
#173042
#171852
#169872
#168242
#167072
#167062
#166702
#165722
#165212
#164032
#163052
#163042
#153282
#153272
#148222
#147362
#143452
#139602
#138722