Finite Group Databasebeta

← #3034183

Subgroups — #3034183

Order 512.

2648 conjugacy classes of subgroups.

The subgroup lattice has 995 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838C212yesmaximal, complemented
2#16808C211yesmaximal, characteristic, complemented
3#16513C212yesmaximal, complemented
4#16358C211yesmaximal, characteristic, complemented
5#16231C212yesmaximal, complemented
6#15488C212yesmaximal, complemented
7#15419C212yesmaximal, complemented
8#15330C212yesmaximal, complemented
9#15305C212yesmaximal, complemented
10#15295C212yesmaximal, complemented
11#14868C211yesmaximal, characteristic, complemented
12#14732C212yesmaximal, complemented
13#14722C211yesmaximal, characteristic
14#14581C211yesmaximal, characteristic, complemented
15#14497C212yesmaximal, complemented
16#14361C212yesmaximal, complemented
17#14171C211yesmaximal, characteristic, complemented
18#14015C212yesmaximal, complemented
19#13872C211yesmaximal, characteristic, complemented
20C22×#121C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2212yes—
23C23×C4⋊C4C2211yescharacteristic
24C2×#398C2212yes—
25C2×#397C2211yescharacteristic
26C2×#397C2211yescharacteristic
27C2×#397C2212yes—
28C2×#396C2212yes—
29C2×#396C2212yes—
30C2×#394C2212yes—
31C2×#394C2211yescharacteristic
32C2×#394C2212yes—
33C2×#392C2211yescharacteristic
34C2×#392C2212yes—
35C2×#390C2212yes—
36C2×#389C2211yescharacteristic
37C2×#388C2212yes—
38C2×#388C2212yes—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#386C2211yescharacteristic
43C2×#386C2211yescharacteristic
44C2×#386C2212yes—
45C2×#385C2212yes—
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#380C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2212yes—
52#1445C2212yes—
53#1444C2212yes—
54#1444C2212yes—
55#1444C2212yes—
56#1443C2212yes—
57#1443C2212yes—
58#1442C2212yes—
59#1441C2212yes—
60#1441C2212yes—
61#1441C2212yes—
62#1441C2212yes—
63#1441C2211yescharacteristic
64#1441C2212yes—
65#1441C2212yes—
66#1441C2212yes—
67#1441C2212yes—
68#1440C2212yes—
69#1440C2212yes—
70#1439C2211yescharacteristic
71#1439C2211yescharacteristic
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2211yescharacteristic
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1438C2212yes—
84#1438C2212yes—
85#1438C2212yes—
86#1438C2212yes—
87#1438C2212yes—
88#1437C2212yes—
89#1437C2212yes—
90#1437C2212yes—
91#1436C2212yes—
92#1436C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97C4⋊#95C2212yes—
98#1434C2211yescharacteristic
99#1434C2212yes—
100#1434C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2211yescharacteristic
104C22⋊#95C2211yescharacteristic
105C22⋊#95C2211yescharacteristic
106C22⋊#95C2212yes—
107C23×D4C2311yescharacteristic
108C23×D4C2312yes—
109C23×D4C2311yescharacteristic
110C23×D4C2312yes—
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2312yes—
115C24×C4C2311yescharacteristic
116C2×#121—28no—
117C2×#121—42no—
118C2×C4×D4—24no—
119C2×C4×D4—42no—
120C2×C4×D4—44no—
121C2×C4×D4—44no—
122C2×C4×D4—42no—
123C2×C4×D4—44no—
124C22×C4⋊C4—44no—
125C22×C4⋊C4—42no—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2312yes—
166#398—44no—
167#397—24no—
168#397—44no—
169#397—42no—
170#396—44no—
171#396—44no—
172#394—42no—
173#394—44no—
174#394—44no—
175#392—24no—
176#392—44no—
177#390—44no—
178#389—42no—
179#388—28no—
180#388—44no—
181#386—28no—
182#386—42no—
183#386—42no—
184#386—44no—
185#386—44no—
186#386—44no—
187#385—44no—
188#385—44no—
189#385—44no—
190#385—44no—
191#380—42no—
192#380—44no—
193#380—44no—
194C2×#95C2311yescharacteristic
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2311yescharacteristic
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2311yescharacteristic
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2311yescharacteristic
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C25C2412yes—
233C25C2411yescharacteristic
234C25C2411yescharacteristic
235C22×D4—22no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—22no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—24no—
242C22×D4—22no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—24no—
250C22×D4—42no—
251C22×D4—41no—
252C22×D4—41no—
253C22×D4—42no—
254C22×D4—42no—
255C22×D4—41no—
256C22×D4—42no—
257C22×D4—42no—
258C22×D4—42no—
259C22×D4—42no—
260C22×D4—41no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—22no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—42no—
274C23×C4—41no—
275C23×C4—42no—
276C23×C4—41no—
277C23×C4—41no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—41no—
287C23×C4—41no—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304#121—416no—
305C4×D4—416no—
306C4×D4—432no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—41no—
327C2×C4⋊C4—41no—
328C2×C4⋊C4—41no—
329C2×C4⋊C4—416no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—41no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—41no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—41no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4#4118yes—
416C2×C22⋊C4#4114yes—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—24no—
420C2×C42—41no—
421C2×C42—42no—
422C2×C42—42no—
423C2×C42—42no—
424C2×C42—42no—
425C2×C42—42no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—22no—
431#95—22no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—42no—
452#95—42no—
453#95—42no—
454#95—42no—
455#95—42no—
456#95—42no—
457#95—42no—
458#95—42no—
459#95—41no—
460#95—41no—
461#95—42no—
462#95—42no—
463#95—42no—
464C24—22no—
465C24—22no—
466C24—21no—
467C24—21no—
468C24—22no—
469C24—21no—
470C24—21no—
471C24—22no—
472C24—21no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—21no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—21no—
485C24—21no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—21no—
491C24—21no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24C2×#4114yes—
497C24C2×#4112yes—
498C24H(5,𝔽2)12yes—
499C24H(5,𝔽2)12yes—
500C242−1+412yes—
501C24C2511yescharacteristic
502C2×D4—28no—
503C2×D4—216no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—48no—
517C2×D4—44no—
518C2×D4—48no—
519C2×D4—44no—
520C2×D4—48no—
521C2×D4—82no—
522C2×D4—84no—
523C2×D4—84no—
524C2×D4—84no—
525C2×D4—84no—
526C2×D4—82no—
527C2×D4—84no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—28no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
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—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—48no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—44no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—84no—
636C22×C4—82no—
637C22×C4—84no—
638C22×C4—84no—
639C22×C4—84no—
640C22×C4—84no—
641C22×C4—82no—
642C22×C4—84no—
643C22×C4—82no—
644C22×C4—84no—
645C22×C4—84no—
646C22×C4—82no—
647C22×C4—84no—
648C22×C4—82no—
649C22×C4C2×#4112yes—
650C22×C4C2×#4114yes—
651C22×C4C2×#4112yes—
652C22×C4C2×#4114yes—
653C22×C4H(5,𝔽2)12yes—
654C22×C4H(5,𝔽2)12yes—
655C22×C4H(5,𝔽2)14yes—
656C22×C4H(5,𝔽2)14yes—
657C22×C4H(5,𝔽2)12yes—
658C22×C42−1+414yes—
659C4⋊C4—44no—
660C4⋊C4—48no—
661C4⋊C4—44no—
662C4⋊C4—48no—
663C4⋊C4—44no—
664C4⋊C4—48no—
665C4⋊C4—84no—
666C4⋊C4—82no—
667C4⋊C4—84no—
668C4⋊C4—84no—
669C4⋊C4—84no—
670C4⋊C4—84no—
671C4⋊C4—84no—
672C4⋊C4—84no—
673C22⋊C4—216no—
674C22⋊C4—44no—
675C22⋊C4—48no—
676C22⋊C4—44no—
677C22⋊C4—48no—
678C22⋊C4—48no—
679C22⋊C4—48no—
680C22⋊C4—48no—
681C22⋊C4—48no—
682C22⋊C4—84no—
683C22⋊C4—84no—
684C22⋊C4—84no—
685C22⋊C4—84no—
686C22⋊C4—84no—
687C22⋊C4—84no—
688C22⋊C4—84no—
689C22⋊C4—84no—
690C22⋊C4—82no—
691C22⋊C4—82no—
692C22⋊C4—84no—
693C22⋊C4—84no—
694C22⋊C4—84no—
695C22⋊C4—84no—
696C42—44no—
697C42—48no—
698C42—84no—
699C23—24no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—22no—
707C23—22no—
708C23—24no—
709C23—22no—
710C23—22no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—22no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—22no—
721C23—22no—
722C23—24no—
723C23—41no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—41no—
728C23—41no—
729C23—42no—
730C23—42no—
731C23—41no—
732C23—42no—
733C23—41no—
734C23—42no—
735C23—41no—
736C23—42no—
737C23—42no—
738C23—41no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—41no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—41no—
777C23—42no—
778C23—42no—
779C23#54014yes—
780C23C22×#4111yescharacteristic
781C23C22×#4112yes—
782C23C2×H(5,𝔽2)11yescharacteristic
783C23C2×H(5,𝔽2)11yescharacteristic
784C23C2×H(5,𝔽2)11yescharacteristic
785C23C2×H(5,𝔽2)12yes—
786C23C2×H(5,𝔽2)11yescharacteristic
787C23C2×H(5,𝔽2)11yescharacteristic
788C23C2×H(5,𝔽2)12yes—
789C23C2×2−1+412yes—
790C23C2×2−1+411yescharacteristic
791D4—416no—
792D4—432no—
793D4—816no—
794D4—88no—
795C2×C4—24no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—22no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—22no—
820C2×C4—416no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—41no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—88no—
900C2×C4—88no—
901C2×C4—816no—
902C2×C4—88no—
903C2×C4#55114yes—
904C22—24no—
905C22—28no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—44no—
911C22—44no—
912C22—42no—
913C22—44no—
914C22—42no—
915C22—44no—
916C22—42no—
917C22—44no—
918C22—44no—
919C22—44no—
920C22—42no—
921C22—44no—
922C22—44no—
923C22—42no—
924C22—44no—
925C22—44no—
926C22—44no—
927C22—81no—
928C22—82no—
929C22—81no—
930C22—81no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22—81no—
941C22C2×#54011yescharacteristic
942C22C2×#55111yescharacteristic
943C22#348112yes—
944C22#349011yescharacteristic
945C22#349212yes—
946C22#349211yescharacteristic
947C22#351112yes—
948C22#351912yes—
949C22#351912yes—
950C22#352012yes—
951C22#352012yes—
952C22#353212yes—
953C22#353211yescharacteristic
954C22#353611yescharacteristic
955C22#353611yescharacteristic
956C22#353612yes—
957C22#353711yescharacteristic
958C22#353711yescharacteristic
959C22#353712yes—
960C22#353711yescharacteristic
961C22#354812yes—
962C22#355011yescharacteristic
963C22#355212yes—
964C4—24no—
965C4—44no—
966C4—44no—
967C4—42no—
968C4—44no—
969C4—42no—
970C4—44no—
971C4—42no—
972C4—42no—
973C4—82no—
974C4—82no—
975C4—82no—
976C4—82no—
977C4—82no—
978C4—82no—
979C4—82no—
980C2—44no—
981C2—84no—
982C2—82no—
983C2#3672711yescharacteristic
984C2#3854312yes—
985C2#4345812yes—
986C2#4533011yescharacteristic
987C2#4537711yescharacteristic
988C2#4845512yes—
989C2#4970311yescharacteristic
990C2#4979712yes—
991C2#5366911yescharacteristic
992C2#5634611yescharacteristic
993C2#5937011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14722C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #16838C2semidirect
2. #16808C2semidirect
3. #16513C2semidirect
4. #16358C2semidirect
5. #16231C2semidirect
6. #15488C2semidirect
7. #15419C2semidirect
8. #15330C2semidirect
9. #15305C2semidirect
10. #15295C2semidirect
11. #14868C2semidirect
12. #14732C2semidirect
14. #14581C2semidirect
15. #14497C2semidirect
16. #14361C2semidirect
17. #14171C2semidirect
18. #14015C2semidirect
19. #13872C2semidirect

Maximal subgroups

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

subgroupindex
#168382
#168082
#165132
#163582
#162312
#154882
#154192
#153302
#153052
#152952
#148682
#147322
#147222
#145812
#144972
#143612
#141712
#140152
#138722