Finite Group Databasebeta

← #759505

Subgroups — #759505

Order 512.

4440 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2487C211yesmaximal, characteristic, complemented
2C2×C4×#120C211yesmaximal, characteristic
3C2×#2280C211yesmaximal, characteristic, complemented
4C22×#380C211yesmaximal, characteristic, complemented
5#16394C212yesmaximal, complemented
6#16392C212yesmaximal, complemented
7#15132C212yesmaximal, complemented
8#15129C212yesmaximal, complemented
9#14841C212yesmaximal, complemented
10#14839C212yesmaximal, complemented
11#14727C212yesmaximal, complemented
12#14718C212yesmaximal
13#14130C211yesmaximal, characteristic, complemented
14#14044C212yesmaximal, complemented
15#14020C212yesmaximal, complemented
16#13951C212yesmaximal, complemented
17#13924C211yesmaximal, characteristic, complemented
18#13872C211yesmaximal, characteristic, complemented
19#13871C212yesmaximal, complemented
20C25×C4C2211yescharacteristic
21C22×#120C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×#117C2212yes—
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C22⋊C4C2212yes—
29#2487—28no—
30C2×#400C2212yescomplemented
31C2×#399C2212yescomplemented
32C2×#397C2214yes—
33C2×#394C2214yes—
34C4×#120—28no—
35C2×#389C2212yescomplemented
36C2×#389C2212yescomplemented
37C2×#386C2211yescharacteristic
38C2×#386C2212yes—
39C2×#386C2212yes—
40C2×#386C2211yescharacteristic
41C2×#386C2211yescharacteristic
42C2×#385C2211yescharacteristic
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#385C2211yescharacteristic
46C2×#385C2211yescharacteristic
47#2280—28no—
48C2×#381C2212yes—
49C2×#380—28no—
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2211yescharacteristic
55C2×#380C2212yes—
56C2×#380C2211yescharacteristic
57C2×#380C2212yescomplemented
58C2×#380C2212yescomplemented
59C2×#379C2212yes—
60C2×#379C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2212yes—
65C2×C4×C22⋊C4C2212yes—
66C22×#95C2212yes—
67#1445C2212yescomplemented
68#1445C2212yescomplemented
69#1444C2212yescomplemented
70#1443C2214yescomplemented
71#1442C2214yescomplemented
72#1442C2212yescomplemented
73#1441C2214yescomplemented
74#1441C2212yescomplemented
75#1440C2214yes—
76#1440C2214yes—
77#1440C2214yes—
78#1440C2214yescomplemented
79#1439C2214yes—
80#1439C2214yes—
81#1439C2212yescomplemented
82#1438C2214yes—
83#1437C2214yescomplemented
84#1436C2214yescomplemented
85C4⋊#95C2212yescomplemented
86C4⋊#95C2212yescomplemented
87C4⋊#95C2212yescomplemented
88C4⋊#95C2212yescomplemented
89C4⋊#95C2214yescomplemented
90#1434C2214yescomplemented
91C22⋊#95C2212yes—
92C22⋊#95C2212yes—
93C22⋊#95C2212yes—
94C22⋊#95C2212yes—
95C26C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C23×D4C2311yescharacteristic
99C24×C4—24no—
100C24×C4—24no—
101C24×C4—28no—
102C24×C4—44no—
103C24×C4D418yes—
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2312yes—
112C24×C4C2312yes—
113C2×#120—24no—
114C2×#120—24no—
115C2×#120—24no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4—24no—
120C2×C4×D4—24no—
121C2×C4×D4—28no—
122C2×C4×D4—44no—
123C2×#117—28no—
124C2×#117—28no—
125C2×#117—44no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—44no—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C22⋊C4—28no—
143C22×C22⋊C4—48no—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2314yes—
168#400—28no—
169#399—28no—
170#397—48no—
171#394—48no—
172#389—28no—
173#389—44no—
174#386—28no—
175#386—24no—
176#386—24no—
177#386—24no—
178#386—28no—
179#385—24no—
180#385—24no—
181#385—24no—
182#385—28no—
183#385—28no—
184#381—28no—
185#380—28no—
186#380—28no—
187#380—28no—
188#380—28no—
189#380—24no—
190#380—28no—
191#380—28no—
192#380—44no—
193#380D418yescomplemented
194#379—24no—
195#379—28no—
196C4×C22⋊C4—24no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—24no—
199C4×C22⋊C4—28no—
200C4×C22⋊C4—28no—
201C2×#95—28no—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2311yescharacteristic
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2311yescharacteristic
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2311yescharacteristic
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2312yes—
225C25—24no—
226C25—24no—
227C25—22no—
228C25—22no—
229C25—22no—
230C25—22no—
231C25—22no—
232C25—22no—
233C25—42no—
234C25—42no—
235C25C2×D414yes—
236C25C2411yescharacteristic
237C25C2411yescharacteristic
238C25C2411yescharacteristic
239C25C2411yescharacteristic
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—42no—
255C22×D4—42no—
256C22×D4#4114yes—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—24no—
265C23×C4—232no—
266C23×C4—232no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—24no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—416no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—432no—
293C23×C4—432no—
294C23×C4—44no—
295C23×C4—44no—
296C23×C4—44no—
297C23×C4—44no—
298C23×C4C2×D414yes—
299C23×C4C2×D414yes—
300C23×C4C2×D414yes—
301C23×C4C2×D414yes—
302C23×C4C2×D414yes—
303C23×C4C2×D414yes—
304C23×C4C2×D414yes—
305C23×C4#4114yes—
306C23×C4#4118yes—
307C23×C4C2411yescharacteristic
308C23×C4C2414yes—
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2414yes—
313C23×C4C2414yes—
314C23×C4C2414yes—
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2411yescharacteristic
322#120—232no—
323C4×D4—416no—
324C4×D4—416no—
325C4×D4—416no—
326#117—432no—
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—24no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—416no—
353C2×C4⋊C4—416no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4C2×D418yes—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—432no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4C2×D418yes—
413C2×C22⋊C4#4114yes—
414C2×C42—28no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—28no—
420C2×C42—22no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—44no—
424#95—28no—
425#95—28no—
426#95—28no—
427#95—24no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—28no—
435#95—28no—
436#95—28no—
437#95—28no—
438#95—44no—
439#95—44no—
440#95—44no—
441#95—44no—
442#95—44no—
443#95—44no—
444#95—44no—
445#95—44no—
446#95C2×D418yes—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—216no—
452C24—216no—
453C24—28no—
454C24—28no—
455C24—28no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—22no—
473C24—22no—
474C24—28no—
475C24—28no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—22no—
480C24—21no—
481C24—22no—
482C24—22no—
483C24—21no—
484C24—21no—
485C24—22no—
486C24—44no—
487C24—44no—
488C24—48no—
489C24—48no—
490C24—48no—
491C24—48no—
492C24—48no—
493C24—48no—
494C24—48no—
495C24—48no—
496C24—48no—
497C24—48no—
498C24—44no—
499C24—44no—
500C24—44no—
501C24—44no—
502C24C22×D412yes—
503C24C22×D412yes—
504C24C22×D412yes—
505C24C22×D412yes—
506C24C2×#4112yes—
507C24C2×#4114yes—
508C24C2×#4112yes—
509C24C2×#4112yes—
510C24C2×#4112yes—
511C24H(5,𝔽2)14yes—
512C242−1+412yes—
513C242−1+412yes—
514C24C2511yescharacteristic
515C2×D4—28no—
516C2×D4—28no—
517C2×D4—28no—
518C2×D4—28no—
519C2×D4—28no—
520C2×D4—48no—
521C2×D4—48no—
522C2×D4—48no—
523C2×D4—48no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—44no—
528C2×D4—44no—
529C2×D4—44no—
530C2×D4—44no—
531C2×D4—44no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—216no—
542C22×C4—216no—
543C22×C4—216no—
544C22×C4—216no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—24no—
597C22×C4—22no—
598C22×C4—24no—
599C22×C4—22no—
600C22×C4—24no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—24no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—22no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—4128no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—48no—
641C22×C4—48no—
642C22×C4—88no—
643C22×C4—88no—
644C22×C4—88no—
645C22×C4—88no—
646C22×C4#121116yes—
647C22×C4#123116yes—
648C22×C4C22×D412yes—
649C22×C4C22×D418yes—
650C22×C4C22×D412yes—
651C22×C4C22×D412yes—
652C22×C4C22×D412yes—
653C22×C4C22×D412yes—
654C22×C4C22×D412yes—
655C22×C4C2×#4112yes—
656C22×C4C2×#4112yes—
657C22×C4C2×#4112yes—
658C22×C4C2×#4112yes—
659C22×C4C2×#4114yes—
660C22×C4C2×#4112yes—
661C22×C4C2×#4114yes—
662C22×C4H(5,𝔽2)14yes—
663C4⋊C4—216no—
664C4⋊C4—48no—
665C4⋊C4—44no—
666C4⋊C4—48no—
667C4⋊C4—48no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—48no—
671C4⋊C4—48no—
672C4⋊C4—88no—
673C4⋊C4—88no—
674C22⋊C4—28no—
675C22⋊C4—28no—
676C22⋊C4—28no—
677C22⋊C4—216no—
678C22⋊C4—416no—
679C22⋊C4—416no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—416no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—416no—
688C22⋊C4—44no—
689C22⋊C4—48no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—88no—
693C22⋊C4—88no—
694C42—416no—
695C42—44no—
696C42—44no—
697C42—44no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—24no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—232no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—24no—
743C23—24no—
744C23—416no—
745C23—416no—
746C23—416no—
747C23—416no—
748C23—416no—
749C23—432no—
750C23—432no—
751C23—432no—
752C23—432no—
753C23—416no—
754C23—42no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—42no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—42no—
765C23—42no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—42no—
770C23—42no—
771C23—42no—
772C23—42no—
773C23—42no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—42no—
781C23—41no—
782C23—42no—
783C23—41no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23C2×#12114yes—
793C23C2×#12314yes—
794C23#52514yes—
795C23#53514yes—
796C23#53614yes—
797C23#54714yes—
798C23#54814yes—
799C23#55214yes—
800C23#55614yes—
801C23C23×D411yescharacteristic
802C23C23×D411yescharacteristic
803C23C22×#4111yescharacteristic
804C23C22×#4112yes—
805C23C22×#4111yescharacteristic
806C23C22×#4111yescharacteristic
807C23C2×H(5,𝔽2)12yes—
808C23C2×H(5,𝔽2)12yes—
809C23C2×2−1+411yescharacteristic
810C23C2×2−1+411yescharacteristic
811C23#58512yes—
812D4—416no—
813D4—416no—
814D4—416no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—232no—
824C2×C4—232no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—28no—
832C2×C4—28no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—28no—
837C2×C4—24no—
838C2×C4—416no—
839C2×C4—416no—
840C2×C4—416no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—42no—
848C2×C4—41no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—44no—
852C2×C4—42no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—42no—
856C2×C4—44no—
857C2×C4—416no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—44no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—44no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—44no—
867C2×C4—44no—
868C2×C4—44no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—42no—
878C2×C4—44no—
879C2×C4—42no—
880C2×C4—44no—
881C2×C4—44no—
882C2×C4—44no—
883C2×C4—42no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—44no—
890C2×C4—44no—
891C2×C4—44no—
892C2×C4—44no—
893C2×C4—44no—
894C2×C4—44no—
895C2×C4—44no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—44no—
899C2×C4—816no—
900C2×C4—816no—
901C2×C4—88no—
902C2×C4C2×#12114yes—
903C2×C4C2×#12114yes—
904C2×C4C2×#12314yes—
905C2×C4C2×#12314yes—
906C2×C4#53414yes—
907C2×C4#54618yes—
908C2×C4#55118yes—
909C22—24no—
910C22—24no—
911C22—28no—
912C22—28no—
913C22—24no—
914C22—28no—
915C22—28no—
916C22—24no—
917C22—24no—
918C22—24no—
919C22—24no—
920C22—24no—
921C22—24no—
922C22—24no—
923C22—24no—
924C22—24no—
925C22—464no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—44no—
933C22—42no—
934C22—44no—
935C22—44no—
936C22—44no—
937C22—44no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—44no—
944C22—44no—
945C22—42no—
946C22—42no—
947C22—81no—
948C22—82no—
949C22—81no—
950C22—82no—
951C22—81no—
952C22—81no—
953C22#241518yes—
954C22C22×#12111yescharacteristic
955C22C22×#12311yescharacteristic
956C22C2×#52511yescharacteristic
957C22C2×#53411yescharacteristic
958C22C2×#53511yescharacteristic
959C22C2×#53611yescharacteristic
960C22#344911yescharacteristic
961C22C2×#54612yes—
962C22C2×#54711yescharacteristic
963C22C2×#54811yescharacteristic
964C22C2×#55112yes—
965C22C2×#55211yescharacteristic
966C22C2×#55611yescharacteristic
967C22#347512yes—
968C22#347512yes—
969C22#348812yes—
970C22#349212yes—
971C22#349212yes—
972C22#349412yes—
973C22#351912yes—
974C22#351912yes—
975C22#354112yes—
976C22#354112yes—
977C4—24no—
978C4—24no—
979C4—42no—
980C4—42no—
981C4—48no—
982C4—42no—
983C4—42no—
984C4—84no—
985C4—81no—
986C4—81no—
987C4—84no—
988C4—81no—
989C4—81no—
990C4—84no—
991C4#241218yes—
992C2—28no—
993C2—44no—
994C2—44no—
995C2—82no—
996C2C2×#241211yescharacteristic
997C2C2×#241511yescharacteristic
998C2#3480911yescharacteristic
999C2#3507611yescharacteristic
1000C2#3522711yescharacteristic
1001C2#3525211yescharacteristic
1002C2#3743811yescharacteristic
1003C2#5902112yes—
1004C2#5902412yes—
1005C2#5920412yes—
1006C2#5920512yes—
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
3. C2×#2280C2semidirect
4. C22×#380C2semidirect
5. #16394C2semidirect
6. #16392C2semidirect
7. #15132C2semidirect
8. #15129C2semidirect
9. #14841C2semidirect
10. #14839C2semidirect
11. #14727C2semidirect
13. #14130C2semidirect
14. #14044C2semidirect
15. #14020C2semidirect
16. #13951C2semidirect
17. #13924C2semidirect
18. #13872C2semidirect
19. #13871C2semidirect
30. C2×#400C22semidirect
31. C2×#399C22semidirect
35. C2×#389C22semidirect
36. C2×#389C22semidirect
57. C2×#380C22semidirect
58. C2×#380C22semidirect
67. #1445C22semidirect
68. #1445C22semidirect
69. #1444C22semidirect
70. #1443C22semidirect
71. #1442C22semidirect
72. #1442C22semidirect
73. #1441C22semidirect
74. #1441C22semidirect
78. #1440C22semidirect
81. #1439C22semidirect
83. #1437C22semidirect
84. #1436C22semidirect
85. C4⋊#95C22semidirect
86. C4⋊#95C22semidirect
87. C4⋊#95C22semidirect
88. C4⋊#95C22semidirect
89. C4⋊#95C22semidirect
90. #1434C22semidirect
193. #380D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24872
C2×C4×#1202
C2×#22802
C22×#3802
#163942
#163922
#151322
#151292
#148412
#148392
#147272
#147182
#141302
#140442
#140202
#139512
#139242
#138722
#138712