Finite Group Databasebeta

← #639836

Subgroups — #639836

Order 512.

4488 conjugacy classes of subgroups.

The subgroup lattice has 951 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2847C211yesmaximal, characteristic
2C2×#2624C211yesmaximal, characteristic, complemented
3C2×#2280C211yesmaximal, characteristic, complemented
4C22×#380C211yesmaximal, characteristic, complemented
5#16401C212yesmaximal, complemented
6#16398C212yesmaximal, complemented
7#16397C214yesmaximal, complemented
8#15183C212yesmaximal, complemented
9#15126C212yesmaximal, complemented
10#14836C212yesmaximal, complemented
11#14735C212yesmaximal, complemented
12#14725C214yesmaximal, complemented
13#14343C211yesmaximal, characteristic, complemented
14#14264C211yesmaximal, characteristic, complemented
15#14257C211yesmaximal, characteristic, complemented
16#14137C212yesmaximal, complemented
17#13907C212yesmaximal, complemented
18C25×C4C2211yescharacteristic
19C22×#121C2211yescharacteristic
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#120C2212yes—
23C22×#117C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C23×C4⋊C4C2212yes—
26C23×C22⋊C4C2212yes—
27#2847—28no—
28#2624—28no—
29C2×#399C2212yescomplemented
30C2×#397C2212yescomplemented
31C2×#394C2214yes—
32C2×#394C2214yes—
33C2×#390C2212yescomplemented
34C2×#390C2212yescomplemented
35C2×#389C2212yescomplemented
36C2×#389C2212yescomplemented
37C2×#386C2212yes—
38C2×#386C2212yes—
39C2×#386C2212yes—
40C2×#386C2214yes—
41C2×#386C2214yes—
42#2280—28no—
43C2×#381C2212yes—
44C2×#380—28no—
45C2×#380C2211yescharacteristic
46C2×#380C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2212yes—
52C2×#380C2211yescharacteristic
53C2×#380C2212yes—
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2214yes—
57C2×#380C2211yescharacteristic
58C2×#379C2212yes—
59C2×C4×C22⋊C4C2212yes—
60C2×C4×C22⋊C4C2212yes—
61C22×#95C2212yes—
62#1445C2212yescomplemented
63#1445C2212yescomplemented
64#1445C2214yescomplemented
65#1444C2212yescomplemented
66#1443C2214yescomplemented
67#1442C2212yescomplemented
68#1441C2214yescomplemented
69#1441C2214yescomplemented
70#1440C2214yes—
71#1440C2214yes—
72#1440C2214yescomplemented
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yescomplemented
76#1439C2214yescomplemented
77#1439C2214yescomplemented
78#1439C2212yescomplemented
79#1439C2212yescomplemented
80#1438C2214yes—
81#1438C2214yes—
82C4⋊#95C2212yescomplemented
83C4⋊#95C2212yescomplemented
84C4⋊#95C2212yescomplemented
85C4⋊#95C2212yescomplemented
86C22⋊#95C2214yes—
87C26C2311yescharacteristic
88C23×D4C2312yes—
89C23×D4C2311yescharacteristic
90C23×D4C2312yes—
91C23×D4C2312yes—
92C24×C4—24no—
93C24×C4—24no—
94C24×C4—28no—
95C24×C4—44no—
96C24×C4D418yes—
97C24×C4C2311yescharacteristic
98C24×C4C2314yes—
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C2×#121—24no—
105C2×#121—24no—
106C2×#121—24no—
107C2×#121—24no—
108C2×#121—24no—
109C2×#121—28no—
110C2×#121—44no—
111C2×#120—28no—
112C2×#120—48no—
113C2×#117—24no—
114C2×#117—24no—
115C2×#117—24no—
116C2×#117—24no—
117C2×#117—44no—
118C22×C4⋊C4—28no—
119C22×C4⋊C4—28no—
120C22×C4⋊C4—44no—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2314yes—
133C22×C22⋊C4—28no—
134C22×C22⋊C4—44no—
135C22×C22⋊C4—44no—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C42C2312yes—
156C22×C42C2312yes—
157#399—28no—
158#397—28no—
159#394—216no—
160#394—48no—
161#390—28no—
162#390—44no—
163#389—28no—
164#389—44no—
165#386—28no—
166#386—28no—
167#386—28no—
168#386—48no—
169#386—48no—
170#381—28no—
171#380—24no—
172#380—24no—
173#380—24no—
174#380—24no—
175#380—24no—
176#380—24no—
177#380—24no—
178#380—24no—
179#380—28no—
180#380—28no—
181#380—28no—
182#380—48no—
183#380D418yescomplemented
184#379—28no—
185C4×C22⋊C4—28no—
186C4×C22⋊C4—28no—
187C2×#95—28no—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C25—22no—
209C25—22no—
210C25—22no—
211C25—22no—
212C25—22no—
213C25—22no—
214C25—24no—
215C25—24no—
216C25—42no—
217C25—42no—
218C25C2×D414yes—
219C25C2412yes—
220C25C2411yescharacteristic
221C25C2411yescharacteristic
222C25C2411yescharacteristic
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—28no—
227C22×D4—28no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—44no—
240C22×D4—44no—
241C22×D4—44no—
242C22×D4—44no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—24no—
251C23×C4—232no—
252C23×C4—232no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—28no—
264C23×C4—28no—
265C23×C4—28no—
266C23×C4—28no—
267C23×C4—416no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—432no—
272C23×C4—432no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4C2×D414yes—
277C23×C4C2×D414yes—
278C23×C4C2×D414yes—
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4C2×D414yes—
283C23×C4#4114yes—
284C23×C4#4118yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2414yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2414yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298#121—416no—
299#121—416no—
300#121—416no—
301#120—432no—
302#117—416no—
303#117—416no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—432no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4C2×D418yes—
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—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—24no—
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—28no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—44no—
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—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—432no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4C2×D418yes—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396#95—28no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—28no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95C2×D418yes—
416C24—21no—
417C24—21no—
418C24—22no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24—28no—
423C24—28no—
424C24—28no—
425C24—28no—
426C24—28no—
427C24—28no—
428C24—28no—
429C24—21no—
430C24—21no—
431C24—22no—
432C24—22no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—21no—
441C24—21no—
442C24—21no—
443C24—22no—
444C24—22no—
445C24—28no—
446C24—28no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—24no—
451C24—22no—
452C24—22no—
453C24—24no—
454C24—24no—
455C24—22no—
456C24—22no—
457C24—24no—
458C24—44no—
459C24—44no—
460C24—48no—
461C24—48no—
462C24—48no—
463C24—48no—
464C24—48no—
465C24—48no—
466C24—48no—
467C24—48no—
468C24—48no—
469C24—48no—
470C24—48no—
471C24—48no—
472C24C22×D412yes—
473C24C22×D412yes—
474C24C22×D412yes—
475C24C22×D412yes—
476C24C2×#4112yes—
477C24C2×#4114yes—
478C24H(5,𝔽2)12yes—
479C24H(5,𝔽2)14yes—
480C24H(5,𝔽2)12yes—
481C242−1+412yes—
482C242−1+412yes—
483C24C2511yescharacteristic
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—416no—
494C2×D4—416no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—88no—
501C2×D4—88no—
502C2×D4—88no—
503C2×D4—88no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—216no—
514C22×C4—216no—
515C22×C4—216no—
516C22×C4—216no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—21no—
520C22×C4—24no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
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—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
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—24no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—4128no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—416no—
597C22×C4—416no—
598C22×C4—416no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—416no—
602C22×C4—88no—
603C22×C4—88no—
604C22×C4—88no—
605C22×C4#121116yes—
606C22×C4#123116yes—
607C22×C4C22×D412yes—
608C22×C4C22×D418yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4114yes—
616C22×C4C2×#4112yes—
617C22×C4C2×#4114yes—
618C22×C4H(5,𝔽2)14yes—
619C4⋊C4—216no—
620C4⋊C4—416no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—48no—
629C4⋊C4—88no—
630C4⋊C4—88no—
631C22⋊C4—48no—
632C22⋊C4—416no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—88no—
647C22⋊C4—88no—
648C22⋊C4—88no—
649C22⋊C4—88no—
650C42—48no—
651C42—48no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—22no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—232no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—24no—
684C23—24no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—24no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—416no—
700C23—416no—
701C23—416no—
702C23—416no—
703C23—432no—
704C23—432no—
705C23—416no—
706C23—432no—
707C23—432no—
708C23—416no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—42no—
737C23—42no—
738C23—44no—
739C23—42no—
740C23—42no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23C2×#12114yes—
749C23C2×#12314yes—
750C23#53514yes—
751C23#53714yes—
752C23#53714yes—
753C23#54018yes—
754C23#54218yes—
755C23C23×D411yescharacteristic
756C23C23×D411yescharacteristic
757C23C22×#4111yescharacteristic
758C23C22×#4112yes—
759C23C2×H(5,𝔽2)12yes—
760C23C2×H(5,𝔽2)12yes—
761C23C2×H(5,𝔽2)11yescharacteristic
762C23C2×H(5,𝔽2)11yescharacteristic
763C23C2×2−1+411yescharacteristic
764C23C2×2−1+411yescharacteristic
765C23#58512yes—
766D4—816no—
767D4—816no—
768D4—816no—
769D4—88no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—232no—
779C2×C4—232no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—28no—
784C2×C4—28no—
785C2×C4—28no—
786C2×C4—416no—
787C2×C4—416no—
788C2×C4—416no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—416no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
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—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—44no—
837C2×C4—42no—
838C2×C4—44no—
839C2×C4—42no—
840C2×C4—44no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—44no—
845C2×C4—42no—
846C2×C4—832no—
847C2×C4C2×#12114yes—
848C2×C4C2×#12114yes—
849C2×C4C2×#12314yes—
850C2×C4C2×#12314yes—
851C2×C4#53414yes—
852C2×C4#54618yes—
853C2×C4#55118yes—
854C22—28no—
855C22—28no—
856C22—24no—
857C22—24no—
858C22—24no—
859C22—24no—
860C22—24no—
861C22—24no—
862C22—28no—
863C22—28no—
864C22—24no—
865C22—24no—
866C22—24no—
867C22—24no—
868C22—24no—
869C22—24no—
870C22—464no—
871C22—44no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—84no—
888C22—84no—
889C22—82no—
890C22—82no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—82no—
895C22—82no—
896C22—84no—
897C22—84no—
898C22#262418yescomplemented
899C22C22×#12111yescharacteristic
900C22C22×#12311yescharacteristic
901C22C2×#53411yescharacteristic
902C22C2×#53511yescharacteristic
903C22C2×#53711yescharacteristic
904C22C2×#53711yescharacteristic
905C22#344911yescharacteristic
906C22C2×#54012yes—
907C22C2×#54212yes—
908C22C2×#54612yes—
909C22C2×#55112yes—
910C22#348411yescharacteristic
911C22#348611yescharacteristic
912C22#348812yes—
913C22#349211yescharacteristic
914C22#349211yescharacteristic
915C22#349412yes—
916C22#349412yes—
917C22#349512yes—
918C22#353612yes—
919C22#353712yes—
920C22#354112yes—
921C22#354212yes—
922C4—24no—
923C4—24no—
924C4—48no—
925C4—42no—
926C4—84no—
927C4—82no—
928C4—82no—
929C4—82no—
930C4—82no—
931C4—82no—
932C4—82no—
933C4—82no—
934C4#241218yes—
935C2—28no—
936C2—44no—
937C2—44no—
938C2—162no—
939C2C2×#262411yescharacteristic
940C2C2×#241211yescharacteristic
941C2#3522311yescharacteristic
942C2#3525211yescharacteristic
943C2#3526311yescharacteristic
944C2#3743911yescharacteristic
945C2#3744411yescharacteristic
946C2#3766212yes—
947C2#3766512yes—
948C2#3785112yes—
949C2#3785212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2847C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2624C2semidirect
3. C2×#2280C2semidirect
4. C22×#380C2semidirect
5. #16401C2semidirect
6. #16398C2semidirect
7. #16397C2semidirect
8. #15183C2semidirect
9. #15126C2semidirect
10. #14836C2semidirect
11. #14735C2semidirect
12. #14725C2semidirect
13. #14343C2semidirect
14. #14264C2semidirect
15. #14257C2semidirect
16. #14137C2semidirect
17. #13907C2semidirect
29. C2×#399C22semidirect
30. C2×#397C22semidirect
33. C2×#390C22semidirect
34. C2×#390C22semidirect
35. C2×#389C22semidirect
36. C2×#389C22semidirect
62. #1445C22semidirect
63. #1445C22semidirect
64. #1445C22semidirect
65. #1444C22semidirect
66. #1443C22semidirect
67. #1442C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
72. #1440C22semidirect
75. #1439C22semidirect
76. #1439C22semidirect
77. #1439C22semidirect
78. #1439C22semidirect
79. #1439C22semidirect
82. C4⋊#95C22semidirect
83. C4⋊#95C22semidirect
84. C4⋊#95C22semidirect
85. C4⋊#95C22semidirect
183. #380D4semidirect
898. C22#2624semidirect

Maximal subgroups

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

subgroupindex
C2×#28472
C2×#26242
C2×#22802
C22×#3802
#164012
#163982
#163972
#151832
#151262
#148362
#147352
#147252
#143432
#142642
#142572
#141372
#139072