Finite Group Databasebeta

← #803612

Subgroups — #803612

Order 512.

2766 conjugacy classes of subgroups.

The subgroup lattice has 925 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2517C211yesmaximal, characteristic, complemented
2C2×#2483C211yesmaximal, characteristic
3#16462C211yesmaximal, characteristic, complemented
4#16298C211yesmaximal, characteristic
5#16006C212yesmaximal, complemented
6#15997C212yesmaximal, complemented
7#15989C212yesmaximal, complemented
8#15385C212yesmaximal, complemented
9#15016C211yesmaximal, characteristic, complemented
10#14830C212yesmaximal, complemented
11#14828C212yesmaximal, complemented
12#14727C212yesmaximal
13#14222C212yesmaximal, complemented
14#14008C212yesmaximal, complemented
15#13991C211yesmaximal, characteristic
16#13986C212yesmaximal, complemented
17#13917C212yesmaximal, complemented
18C4×#397C211yesmaximal, characteristic, complemented
19C22⋊C42C212yesmaximal
20C23×C22⋊C4C2212yes—
21C23×C22⋊C4C2211yescharacteristic
22#2517—28no—
23#2483—28no—
24C2×#399C2211yescharacteristic
25C2×#397C2211yescharacteristic
26C2×#397C2212yes—
27C2×#397C2212yes—
28C2×#397C2212yes—
29C2×#397C2211yescharacteristic
30C2×#396C2212yes—
31C2×#388C2212yes—
32C2×#387C2212yescomplemented
33C2×#387C2212yescomplemented
34C2×#387C2212yescomplemented
35C2×#385C2212yes—
36C2×#385C2211yescharacteristic
37C2×#385C2212yes—
38C2×#385C2212yes—
39C2×#382C2212yescomplemented
40C2×#382C2211yescharacteristic, complemented
41C2×#381C2212yes—
42C2×#381C2212yes—
43C2×#379C2211yescharacteristic
44C2×#379C2212yes—
45C2×#379C2211yescharacteristic
46C2×C4×C4⋊C4C2211yescharacteristic, complemented
47C2×C4×C22⋊C4C2212yes—
48C2×C4×C22⋊C4C2212yes—
49C2×C4×C22⋊C4C2211yescharacteristic
50C2×C4×C22⋊C4C2212yes—
51C2×C4×C22⋊C4C2212yes—
52#1445C2212yescomplemented
53#1445C2211yescharacteristic, complemented
54#1445C2211yescharacteristic, complemented
55#1445C2211yescharacteristic, complemented
56#1443C2212yescomplemented
57#1443C2212yescomplemented
58#1443C2212yescomplemented
59#1443C2212yescomplemented
60#1443C2212yescomplemented
61#1443C2212yescomplemented
62#1442C2211yescharacteristic, complemented
63#1442C2212yescomplemented
64#1442C2212yescomplemented
65#1441C2212yescomplemented
66#1441C2212yescomplemented
67#1441C2212yescomplemented
68#1441C2212yescomplemented
69#1441C2212yescomplemented
70#1440C2212yes—
71#1440C2212yes—
72#1440C2212yes—
73#1440C2212yes—
74#1440C2212yes—
75#1439C2211yescharacteristic
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1437C2212yes—
84#1437C2212yes—
85#1437C2212yes—
86#1437C2212yes—
87#1437C2212yes—
88#1436C2212yescomplemented
89#1436C2212yescomplemented
90#1436C2212yescomplemented
91#1436C2212yescomplemented
92#1436C2212yescomplemented
93C4⋊#95C2212yescomplemented
94#1434C2212yescomplemented
95#1434C2212yescomplemented
96#1434C2212yescomplemented
97#1434C2211yescharacteristic, complemented
98C22⋊#95C2212yes—
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2211yescharacteristic
105C22⋊#95C2211yescharacteristic
106C22⋊#95C2212yes—
107C4×#95C2211yescharacteristic, complemented
108C4×#95C2212yescomplemented
109C26C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2312yes—
112C24×C4C2311yescharacteristic
113C24×C4C2312yes—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C22⋊C4—28no—
125C22×C22⋊C4—28no—
126C22×C22⋊C4—28no—
127C22×C22⋊C4—42no—
128C22×C22⋊C4—44no—
129C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2312yes—
149C22×C42C2311yescharacteristic
150C22×C42C2312yes—
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155#399—24no—
156#397—24no—
157#397—28no—
158#397—28no—
159#397—44no—
160#397D418yes—
161#396—28no—
162#388—28no—
163#387—28no—
164#387—28no—
165#387—28no—
166#385—28no—
167#385—24no—
168#385—28no—
169#385—28no—
170#382—28no—
171#382—42no—
172#381—28no—
173#381—28no—
174#379—24no—
175#379—24no—
176#379—28no—
177C4×C4⋊C4—42no—
178C4×C22⋊C4—28no—
179C4×C22⋊C4—28no—
180C4×C22⋊C4—44no—
181C4×C22⋊C4—42no—
182C4×C22⋊C4—44no—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2311yescharacteristic
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2311yescharacteristic
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×#95C2311yescharacteristic
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×#95C2311yescharacteristic
226C2×#95C2311yescharacteristic
227C2×#95C2311yescharacteristic
228C2×#95C2312yes—
229C25—22no—
230C25—24no—
231C25—24no—
232C25—22no—
233C25—41no—
234C25—41no—
235C25—42no—
236C25—42no—
237C25—41no—
238C25—41no—
239C25#4114yes—
240C25C2411yescharacteristic
241C25C2412yes—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—41no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—41no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—41no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2412yes—
271C23×C4C2411yescharacteristic
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4C2×D414yes—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—22no—
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—22no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—416no—
348C2×C22⋊C4—432no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4C2×D418yes—
371C2×C22⋊C4C2×D414yes—
372C2×C22⋊C4#4118yes—
373C2×C22⋊C4#4118yes—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—24no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—42no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—42no—
390#95—24no—
391#95—24no—
392#95—22no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—22no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—41no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—41no—
427#95—41no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95C2×D414yes—
435#95C2×D418yes—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—21no—
443C24—22no—
444C24—21no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—21no—
455C24—21no—
456C24—216no—
457C24—28no—
458C24—44no—
459C24—48no—
460C24—44no—
461C24—44no—
462C24—48no—
463C24—48no—
464C24—48no—
465C24—44no—
466C24—48no—
467C24—48no—
468C24—84no—
469C24—82no—
470C24—82no—
471C24—84no—
472C24—84no—
473C24—84no—
474C24—82no—
475C24—82no—
476C24—82no—
477C24—82no—
478C24—84no—
479C24C22×D412yes—
480C24C2×#4114yes—
481C24C2×#4114yes—
482C24C2×#4114yes—
483C24C2×#4112yes—
484C24H(5,𝔽2)12yes—
485C24C2511yescharacteristic
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
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—21no—
504C22×C4—21no—
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—21no—
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—21no—
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—21no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
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—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—44no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—44no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—44no—
595C22×C4—84no—
596C22×C4—82no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4—84no—
600C22×C4—84no—
601C22×C4—84no—
602C22×C4—82no—
603C22×C4—84no—
604C22×C4—84no—
605C22×C4—84no—
606C22×C4—82no—
607C22×C4—84no—
608C22×C4C22×D414yes—
609C22×C4C22×D414yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C2×#4114yes—
613C22×C4C2×#4114yes—
614C22×C4C2×#4114yes—
615C22×C4C2×#4114yes—
616C22×C4H(5,𝔽2)12yes—
617C4⋊C4—44no—
618C4⋊C4—48no—
619C4⋊C4—48no—
620C4⋊C4—48no—
621C4⋊C4—44no—
622C4⋊C4—84no—
623C4⋊C4—82no—
624C4⋊C4—82no—
625C4⋊C4—84no—
626C4⋊C4—84no—
627C22⋊C4—216no—
628C22⋊C4—216no—
629C22⋊C4—44no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—44no—
641C22⋊C4—48no—
642C22⋊C4—44no—
643C22⋊C4—48no—
644C22⋊C4—84no—
645C22⋊C4—82no—
646C22⋊C4—84no—
647C42—48no—
648C42—44no—
649C42—44no—
650C42—84no—
651C42—84no—
652C42—84no—
653C23—24no—
654C23—24no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—22no—
682C23—22no—
683C23—432no—
684C23—416no—
685C23—42no—
686C23—42no—
687C23—41no—
688C23—42no—
689C23—41no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—41no—
703C23—42no—
704C23—42no—
705C23—41no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—816no—
712C23—88no—
713C23—816no—
714C23—88no—
715C23—88no—
716C23—88no—
717C23—88no—
718C23—88no—
719C23—816no—
720C23#52918yes—
721C23#54614yes—
722C23C23×D411yescharacteristic
723C23C22×#4111yescharacteristic
724C23C22×#4112yes—
725C23C22×#4112yes—
726C23C2×H(5,𝔽2)11yescharacteristic
727C23C2×H(5,𝔽2)11yescharacteristic
728C23#58511yescharacteristic
729C23#58512yes—
730C23#58512yes—
731C23#58511yescharacteristic
732C23#58511yescharacteristic
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—41no—
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—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—41no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—88no—
840C2×C4—88no—
841C2×C4—816no—
842C2×C4—816no—
843C2×C4#55114yes—
844C22—28no—
845C22—28no—
846C22—28no—
847C22—28no—
848C22—24no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—42no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—42no—
858C22—42no—
859C22—44no—
860C22—44no—
861C22—42no—
862C22—44no—
863C22—42no—
864C22—42no—
865C22—44no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—832no—
871C22C2×#52912yes—
872C22#345911yescharacteristic
873C22C2×#54611yescharacteristic
874C22D4×#4112yes—
875C22D4×#4112yes—
876C22C2×#55111yescharacteristic
877C22#347512yes—
878C22#348111yescharacteristic
879C22#349112yes—
880C22#349111yescharacteristic
881C22#349112yes—
882C22#349611yescharacteristic
883C22#350011yescharacteristic
884C22#351012yes—
885C22#351312yes—
886C22#351312yes—
887C22#352112yes—
888C22#352112yes—
889C22#353311yescharacteristic
890C22#353411yescharacteristic
891C22#355111yescharacteristic
892C22#356011yescharacteristic
893C22#356612yes—
894C4—24no—
895C4—44no—
896C4—42no—
897C4—44no—
898C4—42no—
899C4—44no—
900C4—44no—
901C4—44no—
902C4—82no—
903C4—82no—
904C4—82no—
905C4—81no—
906C4—81no—
907C4—82no—
908C4—81no—
909C4—82no—
910C4—82no—
911C2—48no—
912C2—44no—
913C2#3475411yescharacteristic
914C2#3601312yes—
915C2#3610912yes—
916C2#3941411yescharacteristic
917C2#4160411yescharacteristic
918C2#4322011yescharacteristic
919C2#4330912yes—
920C2#4346711yescharacteristic
921C2#5961112yes—
922C2#5984311yescharacteristic
923C2#5984611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2517C2semidirect
3. #16462C2semidirect
5. #16006C2semidirect
6. #15997C2semidirect
7. #15989C2semidirect
8. #15385C2semidirect
9. #15016C2semidirect
10. #14830C2semidirect
11. #14828C2semidirect
13. #14222C2semidirect
14. #14008C2semidirect
16. #13986C2semidirect
17. #13917C2semidirect
18. C4×#397C2semidirect
32. C2×#387C22semidirect
33. C2×#387C22semidirect
34. C2×#387C22semidirect
39. C2×#382C22semidirect
40. C2×#382C22semidirect
46. C2×C4×C4⋊C4C22semidirect
52. #1445C22semidirect
53. #1445C22semidirect
54. #1445C22semidirect
55. #1445C22semidirect
56. #1443C22semidirect
57. #1443C22semidirect
58. #1443C22semidirect
59. #1443C22semidirect
60. #1443C22semidirect
61. #1443C22semidirect
62. #1442C22semidirect
63. #1442C22semidirect
64. #1442C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
88. #1436C22semidirect
89. #1436C22semidirect
90. #1436C22semidirect
91. #1436C22semidirect
92. #1436C22semidirect
93. C4⋊#95C22semidirect
94. #1434C22semidirect
95. #1434C22semidirect
96. #1434C22semidirect
97. #1434C22semidirect
107. C4×#95C22semidirect
108. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#25172
C2×#24832
#164622
#162982
#160062
#159972
#159892
#153852
#150162
#148302
#148282
#147272
#142222
#140082
#139912
#139862
#139172
C4×#3972
C22⋊C422