Finite Group Databasebeta

← #4929361

Subgroups — #4929361

Order 512.

2702 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15013C212yesmaximal, complemented
2#14986C212yesmaximal, complemented
3#14984C212yesmaximal, complemented
4#14949C212yesmaximal, complemented
5#14939C212yesmaximal, complemented
6#14924C212yesmaximal, complemented
7#14814C212yesmaximal, complemented
8#14745C212yesmaximal, complemented
9#14297C211yesmaximal, characteristic, complemented
10#14197C212yesmaximal, complemented
11#14184C212yesmaximal, complemented
12#14165C211yesmaximal, characteristic, complemented
13#14038C212yesmaximal, complemented
14#13990C212yesmaximal, complemented
15#13966C211yesmaximal, characteristic, complemented
16#13956C211yesmaximal, characteristic
17#13937C211yesmaximal, characteristic
18#13851C211yesmaximal, characteristic
19#13749C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C2×#397C2212yes—
22C2×#397C2212yes—
23C2×#391C2211yescharacteristic
24C2×#391C2211yescharacteristic
25C2×#390C2211yescharacteristic
26C2×#390C2211yescharacteristic
27C2×#388C2212yes—
28C2×#388C2212yes—
29C2×#388C2212yes—
30C2×#388C2212yes—
31C2×#387C2212yes—
32C2×#386C2211yescharacteristic
33C2×#386C2211yescharacteristic
34C2×#386C2211yescharacteristic
35C2×#386C2211yescharacteristic
36C2×#383C2212yes—
37C2×#381C2211yescharacteristic
38C2×#380C2211yescharacteristic
39C2×C4×C22⋊C4C2211yescharacteristic
40C2×C4×C22⋊C4C2211yescharacteristic
41C2×C4×C22⋊C4C2212yes—
42C2×C4×C22⋊C4C2211yescharacteristic
43C2×C4×C22⋊C4C2212yes—
44C2×C4×C22⋊C4C2211yescharacteristic
45C2×C4×C22⋊C4C2211yescharacteristic
46C2×C4×C22⋊C4C2211yescharacteristic
47C2×C4×C22⋊C4C2211yescharacteristic
48C22×#95C2211yescharacteristic
49#1446C2212yes—
50#1446C2212yes—
51#1445C2212yes—
52#1443C2212yes—
53#1443C2212yes—
54#1443C2212yes—
55#1443C2212yes—
56#1443C2212yes—
57#1442C2212yes—
58#1442C2212yes—
59#1442C2212yes—
60#1441C2212yes—
61#1441C2212yes—
62#1441C2212yes—
63#1440C2212yes—
64#1440C2212yes—
65#1440C2212yes—
66#1440C2212yes—
67#1439C2212yes—
68#1439C2212yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1439C2212yes—
73#1438C2212yes—
74#1438C2212yes—
75#1438C2212yes—
76#1438C2212yes—
77#1438C2212yes—
78#1438C2212yes—
79#1437C2212yes—
80#1437C2212yes—
81#1437C2212yes—
82#1437C2212yes—
83#1436C2212yes—
84#1436C2212yes—
85#1436C2212yes—
86#1436C2212yes—
87#1436C2212yes—
88#1436C2212yes—
89#1436C2212yes—
90#1436C2212yes—
91#1434C2212yes—
92#1434C2212yes—
93#1434C2212yes—
94#1434C2212yes—
95#1434C2212yes—
96#1434C2212yes—
97C22⋊#95C2212yes—
98C22⋊#95C2212yes—
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C4×#95C2212yes—
104C4×#95C2212yes—
105C4×#95C2212yes—
106C4×#95C2212yes—
107C22×#41—24no—
108C22×#41—24no—
109C22×#41—24no—
110C22×#41—42no—
111C22×#41—42no—
112C22×#41—42no—
113C22×#41—42no—
114C23×Q8C2311yescharacteristic
115C23×D4C2311yescharacteristic
116C23×D4C2311yescharacteristic
117C23×D4C2311yescharacteristic
118C24×C4C2311yescharacteristic
119C24×C4C2311yescharacteristic
120C24×C4C2311yescharacteristic
121C24×C4C2311yescharacteristic
122C24×C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2311yescharacteristic
147C22×C42C2312yes—
148C22×C42C2312yes—
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157#397—28no—
158#397—28no—
159#391—42no—
160#391—42no—
161#390—42no—
162#390—42no—
163#388—28no—
164#388—28no—
165#388—44no—
166#388—44no—
167#387—44no—
168#386—42no—
169#386—42no—
170#386—42no—
171#386—42no—
172#383—44no—
173#381—24no—
174#380—24no—
175C4×C22⋊C4—24no—
176C4×C22⋊C4—24no—
177C4×C22⋊C4—24no—
178C4×C22⋊C4—28no—
179C4×C22⋊C4—28no—
180C4×C22⋊C4—42no—
181C4×C22⋊C4—42no—
182C4×C22⋊C4—42no—
183C4×C22⋊C4—42no—
184C2×#95—24no—
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×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
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—
229C25C2411yescharacteristic
230C25C2411yescharacteristic
231C25C2411yescharacteristic
232C2×#41—416no—
233C2×#41—416no—
234C2×#41—416no—
235C2×#41—416no—
236C2×#41—416no—
237C2×#41—416no—
238C2×#41—416no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—41no—
245C22×Q8—41no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—41no—
262C22×D4—41no—
263C22×D4—41no—
264C22×D4—41no—
265C22×D4—41no—
266C22×D4—41no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—41no—
282C23×C4—41no—
283C23×C4—41no—
284C23×C4—41no—
285C23×C4—41no—
286C23×C4—41no—
287C23×C4—41no—
288C23×C4—41no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—41no—
292C23×C4—41no—
293C23×C4—41no—
294C23×C4—41no—
295C23×C4#4114yes—
296C23×C4#4114yes—
297C23×C4#4114yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C2×C4⋊C4—24no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—41no—
329C2×C4⋊C4—41no—
330C2×C4⋊C4—41no—
331C2×C4⋊C4—41no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
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—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—41no—
381C2×C22⋊C4—41no—
382C2×C22⋊C4—41no—
383C2×C22⋊C4—41no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—41no—
398C2×C42—41no—
399C2×C42—41no—
400C2×C42—41no—
401C2×C42—41no—
402C2×C42—41no—
403C2×C42—41no—
404C2×C42—41no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—42no—
408C2×C42—41no—
409C2×C42—41no—
410C2×C42—41no—
411C2×C42—41no—
412C2×C42—42no—
413C2×C42—42no—
414C2×C42—42no—
415C2×C42#4118yescomplemented
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
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—42no—
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#4118yescomplemented
460C24—22no—
461C24—22no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24C2×#4112yes—
489C24C2×#4112yes—
490C24C2×#4112yes—
491C24H(5,𝔽2)12yes—
492C24H(5,𝔽2)12yes—
493C24C2511yescharacteristic
494#41—4128no—
495C2×Q8—28no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×D4—28no—
503C2×D4—28no—
504C2×D4—28no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—28no—
532C22×C4—28no—
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—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
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—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
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—28no—
582C22×C4—28no—
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—22no—
624C22×C4—22no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—84no—
644C22×C4—84no—
645C22×C4—84no—
646C22×C4—84no—
647C22×C4—82no—
648C22×C4—82no—
649C22×C4—82no—
650C22×C4—82no—
651C22×C4#126116yes—
652C22×C4C2×#4114yes—
653C22×C4C2×#4114yes—
654C22×C4C2×#4114yes—
655C22×C4C2×#4114yes—
656C22×C4C2×#4114yes—
657C22×C4C2×#4114yes—
658C22×C4C2×#4112yes—
659C22×C4C2×#4112yes—
660C22×C4C2×#4112yes—
661C22×C4C2×#4112yes—
662C22×C4C2×#4112yes—
663C22×C4C2×#4112yes—
664C22×C4H(5,𝔽2)12yes—
665C22×C4H(5,𝔽2)12yes—
666C4⋊C4—48no—
667C4⋊C4—82no—
668C4⋊C4—82no—
669C4⋊C4—84no—
670C4⋊C4—84no—
671C4⋊C4—84no—
672C22⋊C4—216no—
673C22⋊C4—216no—
674C22⋊C4—48no—
675C22⋊C4—48no—
676C22⋊C4—48no—
677C22⋊C4—48no—
678C22⋊C4—48no—
679C22⋊C4—48no—
680C22⋊C4—48no—
681C22⋊C4—48no—
682C22⋊C4—48no—
683C22⋊C4—84no—
684C22⋊C4—84no—
685C22⋊C4—84no—
686C22⋊C4—84no—
687C22⋊C4—82no—
688C22⋊C4—82no—
689C22⋊C4—84no—
690C42—48no—
691C42—82no—
692C42—82no—
693C42—82no—
694C42—82no—
695C42—82no—
696C42—82no—
697C42—84no—
698C42—84no—
699C42—84no—
700C23—24no—
701C23—24no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—24no—
711C23—22no—
712C23—22no—
713C23—24no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—42no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23C2×#12614yes—
769C23C22×#4111yescharacteristic
770C23C22×#4111yescharacteristic
771C23C22×#4111yescharacteristic
772C23C22×#4112yes—
773C23C22×#4112yes—
774C23C2×H(5,𝔽2)11yescharacteristic
775C23C2×H(5,𝔽2)11yescharacteristic
776C23C2×H(5,𝔽2)11yescharacteristic
777C23C2×H(5,𝔽2)11yescharacteristic
778C23#58512yes—
779C23#58512yes—
780Q8—416no—
781D4—416no—
782D4—416no—
783D4—416no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—416no—
821C2×C4—416no—
822C2×C4—416no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
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—88no—
898C2×C4—88no—
899C2×C4C2×#12614yes—
900C2×C4C2×#12614yes—
901C22—24no—
902C22—24no—
903C22—24no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—44no—
909C22—44no—
910C22—44no—
911C22—44no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—44no—
919C22—44no—
920C22—44no—
921C22—44no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22C22×#12611yescharacteristic
935C22#344411yescharacteristic
936C22#344411yescharacteristic
937C22#344412yes—
938C22#344412yes—
939C22#349011yescharacteristic
940C22#349011yescharacteristic
941C22#349011yescharacteristic
942C22#349011yescharacteristic
943C22#349011yescharacteristic
944C22#349011yescharacteristic
945C22#349312yes—
946C22#349412yes—
947C22#349412yes—
948C22#350512yes—
949C22#350612yes—
950C22#351011yescharacteristic
951C22#351011yescharacteristic
952C22#351212yes—
953C22#351312yes—
954C22#351312yes—
955C22#351412yes—
956C22#351712yes—
957C4—24no—
958C4—24no—
959C4—42no—
960C4—42no—
961C4—44no—
962C4—44no—
963C4—44no—
964C4—44no—
965C4—44no—
966C4—44no—
967C4—82no—
968C4—82no—
969C4—82no—
970C4—82no—
971C4—82no—
972C4—82no—
973C2—44no—
974C2—82no—
975C2—82no—
976C2#3536911yescharacteristic
977C2#3540811yescharacteristic
978C2#3543011yescharacteristic
979C2#3543911yescharacteristic
980C2#3544111yescharacteristic
981C2#3562911yescharacteristic
982C2#3570712yes—
983C2#3573312yes—
984C2#3576612yes—
985C2#3576912yes—
986C2#3664111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×#41C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #15013C2semidirect
2. #14986C2semidirect
3. #14984C2semidirect
4. #14949C2semidirect
5. #14939C2semidirect
6. #14924C2semidirect
7. #14814C2semidirect
8. #14745C2semidirect
9. #14297C2semidirect
10. #14197C2semidirect
11. #14184C2semidirect
12. #14165C2semidirect
13. #14038C2semidirect
14. #13990C2semidirect
15. #13966C2semidirect
19. #13749C2semidirect
415. C2×C42#41semidirect
459. #95#41semidirect

Maximal subgroups

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

subgroupindex
#150132
#149862
#149842
#149492
#149392
#149242
#148142
#147452
#142972
#141972
#141842
#141652
#140382
#139902
#139662
#139562
#139372
#138512
#137492