Finite Group Databasebeta

← #640574

Subgroups — #640574

Order 512.

4076 conjugacy classes of subgroups.

The subgroup lattice has 993 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#120C211yesmaximal, characteristic
2C22×#380C211yesmaximal, characteristic, complemented
3#17005C212yesmaximal, complemented
4#16986C212yesmaximal, complemented
5#16884C212yesmaximal, complemented
6#16807C212yesmaximal, complemented
7#15183C212yesmaximal, complemented
8#15181C212yesmaximal, complemented
9#15132C212yesmaximal, complemented
10#15129C212yesmaximal, complemented
11#14727C212yesmaximal, complemented
12#14718C212yesmaximal
13#14680C211yesmaximal, characteristic, complemented
14#14265C212yesmaximal, complemented
15#14259C212yesmaximal, complemented
16#14130C211yesmaximal, characteristic, complemented
17#14130C211yesmaximal, characteristic, complemented
18#13872C211yesmaximal, characteristic, complemented
19#13872C211yesmaximal, characteristic, complemented
20C25×C4C2211yescharacteristic
21C22×#120C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C22⋊C4C2212yes—
28C2×#397C2214yes—
29C2×#394C2214yes—
30C4×#120—28no—
31C2×#389C2212yescomplemented
32C2×#389C2212yescomplemented
33C2×#386C2212yes—
34C2×#386C2211yescharacteristic
35C2×#386C2211yescharacteristic
36C2×#386C2211yescharacteristic
37C2×#386C2212yes—
38C2×#385C2212yes—
39C2×#385C2211yescharacteristic
40C2×#385C2211yescharacteristic
41C2×#385C2211yescharacteristic
42C2×#385C2212yes—
43C2×#380—28no—
44C2×#380C2212yes—
45C2×#380C2211yescharacteristic
46C2×#380C2211yescharacteristic
47C2×#380C2212yes—
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#380C2212yescomplemented
53C2×#380C2212yescomplemented
54C2×#379C2211yescharacteristic
55C2×#379C2212yes—
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C22×#95C2212yes—
60#1445C2214yescomplemented
61#1444C2212yescomplemented
62#1444C2212yescomplemented
63#1443C2214yescomplemented
64#1443C2214yescomplemented
65#1442C2214yescomplemented
66#1442C2212yescomplemented
67#1442C2212yescomplemented
68#1442C2214yescomplemented
69#1441C2214yescomplemented
70#1441C2212yescomplemented
71#1441C2212yescomplemented
72#1440C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1440C2214yescomplemented
76#1439C2214yes—
77#1439C2214yes—
78#1439C2212yescomplemented
79#1439C2212yescomplemented
80#1439C2214yescomplemented
81#1438C2214yes—
82C4⋊#95C2212yescomplemented
83C4⋊#95C2212yescomplemented
84C4⋊#95C2212yescomplemented
85C4⋊#95C2212yescomplemented
86C22⋊#95C2212yes—
87C22⋊#95C2212yes—
88C22⋊#95C2212yes—
89C22⋊#95C2212yes—
90C22⋊#95C2212yes—
91C22⋊#95C2212yes—
92C22⋊#95C2212yes—
93C26C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C23×D4C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C24×C4—24no—
98C24×C4—24no—
99C24×C4—44no—
100C24×C4—44no—
101C24×C4D418yes—
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2312yes—
107C24×C4C2312yes—
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C2×#120—24no—
112C2×#120—24no—
113C2×#120—24no—
114C2×C4×D4—24no—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4—44no—
120C2×C4×D4—44no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—44no—
124C22×C4⋊C4—44no—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2314yes—
136C22×C22⋊C4—28no—
137C22×C22⋊C4—48no—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161#397—48no—
162#394—48no—
163#389—44no—
164#389—44no—
165#386—28no—
166#386—24no—
167#386—24no—
168#386—24no—
169#386—44no—
170#385—24no—
171#385—24no—
172#385—24no—
173#385—28no—
174#385—44no—
175#380—28no—
176#380—28no—
177#380—28no—
178#380—28no—
179#380—24no—
180#380—24no—
181#380—44no—
182#380—44no—
183#380—44no—
184#380—44no—
185#379—24no—
186#379—44no—
187C4×C22⋊C4—24no—
188C4×C22⋊C4—24no—
189C4×C22⋊C4—24no—
190C2×#95—28no—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2311yescharacteristic
198C2×#95C2311yescharacteristic
199C2×#95C2311yescharacteristic
200C2×#95C2311yescharacteristic
201C2×#95C2311yescharacteristic
202C2×#95C2311yescharacteristic
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C25—22no—
216C25—22no—
217C25—24no—
218C25—24no—
219C25—22no—
220C25—22no—
221C25—22no—
222C25—22no—
223C25—42no—
224C25—42no—
225C25C2×D414yes—
226C25C2411yescharacteristic
227C25C2411yescharacteristic
228C25C2411yescharacteristic
229C25C2411yescharacteristic
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4#4114yes—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—232no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—416no—
276C23×C4—416no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—44no—
284C23×C4—44no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4—432no—
288C23×C4—432no—
289C23×C4C2×D414yes—
290C23×C4C2×D414yes—
291C23×C4C2×D414yes—
292C23×C4C2×D414yes—
293C23×C4C2×D414yes—
294C23×C4C2×D414yes—
295C23×C4#4114yes—
296C23×C4#4114yes—
297C23×C4C2411yescharacteristic
298C23×C4C2414yes—
299C23×C4C2414yes—
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2414yes—
303C23×C4C2414yes—
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312#120—232no—
313C4×D4—416no—
314C4×D4—416no—
315C4×D4—416no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—416no—
341C2×C4⋊C4—416no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—432no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4#4114yes—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—24no—
408C2×C42—24no—
409#95—28no—
410#95—28no—
411#95—22no—
412#95—22no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—22no—
417#95—24no—
418#95—24no—
419#95—28no—
420#95—28no—
421#95—44no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95—44no—
426#95—44no—
427#95—44no—
428#95—44no—
429#95—44no—
430#95—44no—
431#95—44no—
432#95—44no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—216no—
438C24—216no—
439C24—28no—
440C24—28no—
441C24—28no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—22no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—21no—
459C24—21no—
460C24—28no—
461C24—28no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—21no—
471C24—22no—
472C24—44no—
473C24—44no—
474C24—48no—
475C24—48no—
476C24—48no—
477C24—48no—
478C24—48no—
479C24—48no—
480C24—48no—
481C24—48no—
482C24—48no—
483C24—48no—
484C24—44no—
485C24—44no—
486C24—44no—
487C24—44no—
488C24C22×D412yes—
489C24C22×D412yes—
490C24C22×D412yes—
491C24C2×#4112yes—
492C24C2×#4112yes—
493C24C2×#4112yes—
494C24C2×#4112yes—
495C24C2×#4112yes—
496C24H(5,𝔽2)14yes—
497C24H(5,𝔽2)12yes—
498C242−1+414yes—
499C242−1+412yes—
500C24C2511yescharacteristic
501C2×D4—28no—
502C2×D4—28no—
503C2×D4—28no—
504C2×D4—28no—
505C2×D4—28no—
506C2×D4—48no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—216no—
523C22×C4—216no—
524C22×C4—28no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
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—22no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—28no—
552C22×C4—28no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—24no—
575C22×C4—24no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—4128no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4—48no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—88no—
632C22×C4—88no—
633C22×C4—88no—
634C22×C4—88no—
635C22×C4#123116yes—
636C22×C4C22×D412yes—
637C22×C4C22×D412yes—
638C22×C4C22×D412yes—
639C22×C4C22×D412yes—
640C22×C4C2×#4112yes—
641C22×C4C2×#4112yes—
642C22×C4C2×#4112yes—
643C22×C4C2×#4112yes—
644C22×C4C2×#4112yes—
645C22×C4C2×#4112yes—
646C22×C4C2×#4112yes—
647C22×C4H(5,𝔽2)14yes—
648C22×C4H(5,𝔽2)14yes—
649C4⋊C4—48no—
650C4⋊C4—48no—
651C4⋊C4—44no—
652C4⋊C4—44no—
653C4⋊C4—44no—
654C4⋊C4—48no—
655C4⋊C4—48no—
656C4⋊C4—48no—
657C4⋊C4—48no—
658C4⋊C4—88no—
659C4⋊C4—88no—
660C22⋊C4—28no—
661C22⋊C4—28no—
662C22⋊C4—28no—
663C22⋊C4—44no—
664C22⋊C4—44no—
665C22⋊C4—416no—
666C22⋊C4—44no—
667C22⋊C4—44no—
668C22⋊C4—44no—
669C22⋊C4—44no—
670C22⋊C4—416no—
671C22⋊C4—44no—
672C22⋊C4—44no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—44no—
676C22⋊C4—88no—
677C22⋊C4—88no—
678C22⋊C4—88no—
679C22⋊C4—88no—
680C42—44no—
681C42—44no—
682C42—44no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—232no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—24no—
728C23—24no—
729C23—416no—
730C23—416no—
731C23—416no—
732C23—416no—
733C23—416no—
734C23—432no—
735C23—432no—
736C23—432no—
737C23—432no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—416no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—42no—
766C23—42no—
767C23—41no—
768C23—41no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—42no—
776C23—42no—
777C23C2×#12314yes—
778C23#52514yes—
779C23#53514yes—
780C23#53614yes—
781C23#53714yes—
782C23#55214yes—
783C23#55314yes—
784C23#55514yes—
785C23#55614yes—
786C23C23×D411yescharacteristic
787C23C22×#4111yescharacteristic
788C23C22×#4111yescharacteristic
789C23C22×#4111yescharacteristic
790C23C22×#4111yescharacteristic
791C23C2×H(5,𝔽2)12yes—
792C23C2×H(5,𝔽2)12yes—
793C23C2×H(5,𝔽2)12yes—
794C23C2×H(5,𝔽2)11yescharacteristic
795C23C2×2−1+412yes—
796C23C2×2−1+411yescharacteristic
797D4—416no—
798D4—416no—
799D4—416no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—232no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—416no—
819C2×C4—416no—
820C2×C4—416no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—416no—
836C2×C4—416no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—44no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—44no—
872C2×C4—44no—
873C2×C4—44no—
874C2×C4—44no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—44no—
878C2×C4—44no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—42no—
883C2×C4—44no—
884C2×C4—42no—
885C2×C4—816no—
886C2×C4—816no—
887C2×C4—88no—
888C2×C4C2×#12314yes—
889C2×C4C2×#12314yes—
890C2×C4#53414yes—
891C2×C4#53414yes—
892C2×C4#53818yes—
893C2×C4#53818yes—
894C22—24no—
895C22—24no—
896C22—28no—
897C22—28no—
898C22—24no—
899C22—24no—
900C22—24no—
901C22—28no—
902C22—28no—
903C22—24no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—24no—
908C22—24no—
909C22—24no—
910C22—464no—
911C22—42no—
912C22—42no—
913C22—44no—
914C22—44no—
915C22—44no—
916C22—44no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—44no—
930C22—42no—
931C22—44no—
932C22—82no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—82no—
937C22—81no—
938C22#248518yes—
939C22C22×#12311yescharacteristic
940C22C2×#52511yescharacteristic
941C22C2×#53411yescharacteristic
942C22C2×#53411yescharacteristic
943C22C2×#53511yescharacteristic
944C22C2×#53611yescharacteristic
945C22C2×#53711yescharacteristic
946C22C2×#53812yes—
947C22C2×#53812yes—
948C22C2×#55211yescharacteristic
949C22C2×#55311yescharacteristic
950C22C2×#55511yescharacteristic
951C22C2×#55611yescharacteristic
952C22#349212yes—
953C22#349212yes—
954C22#351912yes—
955C22#351912yes—
956C22#352012yes—
957C22#352012yes—
958C22#353612yes—
959C22#353612yes—
960C22#353712yes—
961C22#353812yes—
962C4—24no—
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—84no—
969C4—84no—
970C4—81no—
971C4—84no—
972C4—81no—
973C4—81no—
974C4—84no—
975C4—81no—
976C4#262218yes—
977C2—28no—
978C2—44no—
979C2—44no—
980C2—82no—
981C2C2×#262211yescharacteristic
982C2C2×#248511yescharacteristic
983C2#3507611yescharacteristic
984C2#3508411yescharacteristic
985C2#3522711yescharacteristic
986C2#3743911yescharacteristic
987C2#3744211yescharacteristic
988C2#3892812yes—
989C2#3893812yes—
990C2#3914412yes—
991C2#3915412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#380C2semidirect
3. #17005C2semidirect
4. #16986C2semidirect
5. #16884C2semidirect
6. #16807C2semidirect
7. #15183C2semidirect
8. #15181C2semidirect
9. #15132C2semidirect
10. #15129C2semidirect
11. #14727C2semidirect
13. #14680C2semidirect
14. #14265C2semidirect
15. #14259C2semidirect
16. #14130C2semidirect
17. #14130C2semidirect
18. #13872C2semidirect
19. #13872C2semidirect
31. C2×#389C22semidirect
32. C2×#389C22semidirect
52. C2×#380C22semidirect
53. C2×#380C22semidirect
60. #1445C22semidirect
61. #1444C22semidirect
62. #1444C22semidirect
63. #1443C22semidirect
64. #1443C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1442C22semidirect
68. #1442C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
71. #1441C22semidirect
75. #1440C22semidirect
78. #1439C22semidirect
79. #1439C22semidirect
80. #1439C22semidirect
82. C4⋊#95C22semidirect
83. C4⋊#95C22semidirect
84. C4⋊#95C22semidirect
85. C4⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1202
C22×#3802
#170052
#169862
#168842
#168072
#151832
#151812
#151322
#151292
#147272
#147182
#146802
#142652
#142592
#141302
#138722