Finite Group Databasebeta

← #657000

Subgroups — #657000

Order 512.

4400 conjugacy classes of subgroups.

The subgroup lattice has 927 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2487C211yesmaximal, characteristic, complemented
2C2×#2352C211yesmaximal, characteristic, complemented
3C2×C4×#120C211yesmaximal, characteristic
4C22×#380C211yesmaximal, characteristic, complemented
5#15525C214yesmaximal, complemented
6#15394C214yesmaximal, complemented
7#15220C212yesmaximal, complemented
8#15129C212yesmaximal, complemented
9#14945C212yesmaximal, complemented
10#14725C212yesmaximal
11#14680C211yesmaximal, characteristic, complemented
12#14149C212yesmaximal, complemented
13#13991C212yesmaximal, complemented
14#13974C212yesmaximal, complemented
15#13924C211yesmaximal, characteristic, complemented
16#13907C211yesmaximal, characteristic, complemented
17#13871C212yesmaximal, complemented
18C25×C4C2211yescharacteristic
19C22×#120C2211yescharacteristic
20C22×C4×D4C2212yes—
21C22×C4×D4C2211yescharacteristic
22C22×#117C2211yescharacteristic, complemented
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C22⋊C4C2212yes—
26#2487—28no—
27C2×#400C2212yescomplemented
28C2×#399C2212yescomplemented
29C2×#394C2214yes—
30#2352—28no—
31C4×#120—28no—
32C2×#389C2212yescomplemented
33C2×#389C2212yescomplemented
34C2×#388C2214yes—
35C2×#388C2212yescomplemented
36C2×#387C2212yescomplemented
37C2×#386C2212yes—
38C2×#386C2212yes—
39C2×#386C2211yescharacteristic
40C2×#386C2212yes—
41C2×#385C2211yescharacteristic
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#382C2211yescharacteristic, complemented
45C2×#380—28no—
46C2×#380C2212yes—
47C2×#380C2212yes—
48C2×#380C2214yes—
49C2×#380C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2211yescharacteristic
53C2×#380C2212yes—
54C2×#380C2211yescharacteristic, complemented
55C2×#380C2212yescomplemented
56C2×#379C2212yes—
57C2×#379C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic, complemented
59C2×C4×C22⋊C4C2212yes—
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2212yes—
62C22×#95C2212yes—
63#1445C2214yescomplemented
64#1443C2214yescomplemented
65#1443C2214yescomplemented
66#1441C2214yescomplemented
67#1441C2214yescomplemented
68#1441C2214yescomplemented
69#1440C2214yes—
70#1440C2214yes—
71#1440C2214yescomplemented
72#1440C2214yescomplemented
73#1439C2214yes—
74#1439C2214yes—
75#1438C2214yes—
76#1437C2214yes—
77#1436C2214yescomplemented
78#1436C2214yescomplemented
79C4⋊#95C2212yescomplemented
80C4⋊#95C2212yescomplemented
81C4⋊#95C2212yescomplemented
82C22⋊#95C2214yes—
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C26C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C23×D4C2312yes—
90C24×C4—24no—
91C24×C4—28no—
92C24×C4—24no—
93C24×C4—24no—
94C24×C4—44no—
95C24×C4C2311yescharacteristic
96C24×C4C2312yes—
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2312yes—
102C2×#120—24no—
103C2×#120—24no—
104C2×#120—24no—
105C2×C4×D4—24no—
106C2×C4×D4—24no—
107C2×C4×D4—28no—
108C2×C4×D4—28no—
109C2×C4×D4—44no—
110C2×C4×D4D418yes—
111C2×#117—24no—
112C2×#117—44no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—44no—
117C22×C4⋊C4D418yescomplemented
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2312yes—
130C22×C22⋊C4—28no—
131C22×C22⋊C4—48no—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C42C2312yes—
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2312yes—
153#400—28no—
154#399—28no—
155#394—48no—
156#389—28no—
157#389—44no—
158#388—28no—
159#388—48no—
160#387—28no—
161#386—28no—
162#386—24no—
163#386—28no—
164#386—28no—
165#385—28no—
166#385—28no—
167#385—24no—
168#382—24no—
169#380—24no—
170#380—24no—
171#380—28no—
172#380—28no—
173#380—24no—
174#380—28no—
175#380—28no—
176#380—216no—
177#380—28no—
178#380—44no—
179#379—28no—
180#379—24no—
181C4×C4⋊C4—24no—
182C4×C22⋊C4—28no—
183C4×C22⋊C4—24no—
184C4×C22⋊C4—28no—
185C2×#95—28no—
186C2×#95C2312yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C25—22no—
209C25—24no—
210C25—24no—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—22no—
215C25—22no—
216C25—42no—
217C25—42no—
218C25#4114yes—
219C25C2411yescharacteristic
220C25C2412yes—
221C25C2411yescharacteristic
222C22×D4—24no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—24no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—42no—
234C22×D4—42no—
235C22×D4C2×D414yes—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—232no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—432no—
267C23×C4—432no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4—44no—
272C23×C4—416no—
273C23×C4—416no—
274C23×C4C2×D414yes—
275C23×C4C2×D414yes—
276C23×C4C2×D414yes—
277C23×C4C2×D418yes—
278C23×C4#4118yes—
279C23×C4#4114yes—
280C23×C4C2414yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2414yes—
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294#120—232no—
295C4×D4—232no—
296C4×D4—432no—
297#117—416no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—416no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—416no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4C2×D414yes—
328C2×C4⋊C4C2×D414yes—
329C2×C4⋊C4C2×D414yes—
330C2×C4⋊C4C2×D418yes—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—432no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4C2×D414yes—
379C2×C22⋊C4C2×D414yes—
380C2×C22⋊C4#4114yes—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—44no—
389C2×C42—44no—
390C2×C42C2×D414yes—
391#95—28no—
392#95—28no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—28no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—28no—
404#95—28no—
405#95—28no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95—44no—
412#95—44no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—28no—
418C24—28no—
419C24—216no—
420C24—28no—
421C24—216no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—28no—
435C24—28no—
436C24—21no—
437C24—21no—
438C24—22no—
439C24—21no—
440C24—21no—
441C24—22no—
442C24—22no—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—48no—
447C24—48no—
448C24—48no—
449C24—48no—
450C24—48no—
451C24—48no—
452C24—48no—
453C24—48no—
454C24—48no—
455C24—44no—
456C24—44no—
457C24—48no—
458C24—44no—
459C24—44no—
460C24—44no—
461C24—44no—
462C24C22×D412yes—
463C24C22×D412yes—
464C24C22×D412yes—
465C24C2×#4114yes—
466C24C2×#4114yes—
467C24C2×#4112yes—
468C24C2×#4112yes—
469C24C2×#4112yes—
470C24H(5,𝔽2)14yes—
471C242−1+412yes—
472C242−1+412yes—
473C24C2511yescharacteristic
474C2×D4—216no—
475C2×D4—28no—
476C2×D4—28no—
477C2×D4—28no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—48no—
487C2×D4—44no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—216no—
493C22×C4—216no—
494C22×C4—216no—
495C22×C4—28no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—216no—
531C22×C4—28no—
532C22×C4—216no—
533C22×C4—216no—
534C22×C4—216no—
535C22×C4—216no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—4128no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—88no—
591C22×C4—88no—
592C22×C4—88no—
593C22×C4—88no—
594C22×C4#121116yes—
595C22×C4C22×D412yes—
596C22×C4C22×D414yes—
597C22×C4C22×D412yes—
598C22×C4C22×D414yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C2×#4114yes—
605C22×C4C2×#4114yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4112yes—
608C22×C4C2×#4114yes—
609C22×C4H(5,𝔽2)14yes—
610C4⋊C4—28no—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—48no—
620C4⋊C4—88no—
621C4⋊C4—88no—
622C22⋊C4—216no—
623C22⋊C4—28no—
624C22⋊C4—28no—
625C22⋊C4—28no—
626C22⋊C4—48no—
627C22⋊C4—416no—
628C22⋊C4—416no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—44no—
634C22⋊C4—48no—
635C22⋊C4—416no—
636C22⋊C4—84no—
637C22⋊C4—88no—
638C22⋊C4—88no—
639C42—28no—
640C42—48no—
641C42—48no—
642C42—84no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—232no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—24no—
682C23—24no—
683C23—432no—
684C23—432no—
685C23—416no—
686C23—416no—
687C23—416no—
688C23—432no—
689C23—416no—
690C23—432no—
691C23—416no—
692C23—42no—
693C23—416no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—42no—
716C23—41no—
717C23—42no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23C2×#12114yes—
728C23#52514yes—
729C23#53614yes—
730C23#54714yes—
731C23#54814yes—
732C23#55214yes—
733C23#55318yes—
734C23#55614yes—
735C23C23×D411yescharacteristic
736C23C23×D411yescharacteristic
737C23C22×#4111yescharacteristic
738C23C22×#4112yes—
739C23C22×#4111yescharacteristic
740C23C22×#4111yescharacteristic
741C23C2×H(5,𝔽2)12yes—
742C23C2×H(5,𝔽2)12yes—
743C23C2×2−1+411yescharacteristic
744C23C2×2−1+411yescharacteristic
745C23#58512yes—
746D4—432no—
747D4—416no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—232no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—432no—
773C2×C4—416no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—416no—
797C2×C4—432no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—42no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—42no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—42no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—816no—
830C2×C4—816no—
831C2×C4C2×#12114yes—
832C2×C4C2×#12114yes—
833C2×C4#52514yes—
834C2×C4#53414yes—
835C2×C4#54618yes—
836C2×C4#55118yes—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—28no—
841C22—28no—
842C22—28no—
843C22—24no—
844C22—28no—
845C22—24no—
846C22—24no—
847C22—28no—
848C22—28no—
849C22—28no—
850C22—464no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—44no—
863C22—42no—
864C22—44no—
865C22—42no—
866C22—44no—
867C22—42no—
868C22—81no—
869C22—81no—
870C22—82no—
871C22—82no—
872C22—81no—
873C22—81no—
874C22#241518yes—
875C22C22×#12111yescharacteristic
876C22C2×#52511yescharacteristic
877C22C2×#52511yescharacteristic
878C22C2×#53411yescharacteristic
879C22C2×#53611yescharacteristic
880C22C2×#54612yes—
881C22C2×#54711yescharacteristic
882C22C2×#54811yescharacteristic
883C22C2×#55112yes—
884C22C2×#55211yescharacteristic
885C22C2×#55312yes—
886C22C2×#55611yescharacteristic
887C22#347512yes—
888C22#348411yescharacteristic
889C22#348711yescharacteristic
890C22#348812yes—
891C22#349212yes—
892C22#349412yes—
893C22#349512yes—
894C22#350512yes—
895C22#351912yes—
896C22#353612yes—
897C22#354112yes—
898C4—24no—
899C4—42no—
900C4—44no—
901C4—44no—
902C4—44no—
903C4—44no—
904C4—42no—
905C4—42no—
906C4—82no—
907C4—84no—
908C4—82no—
909C4—82no—
910C4—84no—
911C4#253418yes—
912C2—28no—
913C2—48no—
914C2—82no—
915C2C2×#241511yescharacteristic
916C2C2×#253411yescharacteristic
917C2#3556311yescharacteristic
918C2#3615712yes—
919C2#3642711yescharacteristic
920C2#3658111yescharacteristic
921C2#3783812yes—
922C2#3891611yescharacteristic
923C2#3972311yescharacteristic
924C2#5919712yes—
925C2#5920412yes—
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
1. C2×#2487C2semidirect
2. C2×#2352C2semidirect
4. C22×#380C2semidirect
5. #15525C2semidirect
6. #15394C2semidirect
7. #15220C2semidirect
8. #15129C2semidirect
9. #14945C2semidirect
11. #14680C2semidirect
12. #14149C2semidirect
13. #13991C2semidirect
14. #13974C2semidirect
15. #13924C2semidirect
16. #13907C2semidirect
17. #13871C2semidirect
22. C22×#117C22semidirect
27. C2×#400C22semidirect
28. C2×#399C22semidirect
32. C2×#389C22semidirect
33. C2×#389C22semidirect
35. C2×#388C22semidirect
36. C2×#387C22semidirect
44. C2×#382C22semidirect
54. C2×#380C22semidirect
55. C2×#380C22semidirect
58. C2×C4×C4⋊C4C22semidirect
63. #1445C22semidirect
64. #1443C22semidirect
65. #1443C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
71. #1440C22semidirect
72. #1440C22semidirect
77. #1436C22semidirect
78. #1436C22semidirect
79. C4⋊#95C22semidirect
80. C4⋊#95C22semidirect
81. C4⋊#95C22semidirect
117. C22×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24872
C2×#23522
C2×C4×#1202
C22×#3802
#155252
#153942
#152202
#151292
#149452
#147252
#146802
#141492
#139912
#139742
#139242
#139072
#138712