Finite Group Databasebeta

← #760869

Subgroups — #760869

Order 512.

3878 conjugacy classes of subgroups.

The subgroup lattice has 981 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2483C211yesmaximal, characteristic
2C2×#2437C211yesmaximal, characteristic
3#16832C212yesmaximal, complemented
4#16831C211yesmaximal, characteristic, complemented
5#16830C211yesmaximal, characteristic, complemented
6#15050C211yesmaximal, characteristic, complemented
7#15016C211yesmaximal, characteristic, complemented
8#14934C212yesmaximal, complemented
9#14919C212yesmaximal, complemented
10#14833C212yesmaximal, complemented
11#14767C212yesmaximal, complemented
12#14738C212yesmaximal, complemented
13#14052C212yesmaximal, complemented
14#13992C212yesmaximal, complemented
15#13896C212yesmaximal, complemented
16#13874C212yesmaximal, complemented
17#13869C212yesmaximal
18C4×#379C211yesmaximal, characteristic
19C2×C22⋊#95C212yesmaximal
20C25×C4C2211yescharacteristic
21C22×C22⋊Q8C2212yes—
22C23×C22⋊C4C2212yes—
23C23×C22⋊C4C2212yes—
24#2483—28no—
25#2437—28no—
26C2×#400C2212yescomplemented
27C2×#399C2211yescharacteristic
28C2×#397C2211yescharacteristic
29C2×#397C2211yescharacteristic
30C2×#397C2212yes—
31C2×#396C2212yes—
32C2×#393C2211yescharacteristic
33C2×#391C2211yescharacteristic, complemented
34C2×#385C2212yes—
35C2×#385C2212yes—
36C2×#385C2212yes—
37C2×#385C2212yes—
38C2×#382C2211yescharacteristic, complemented
39C2×#381C2212yes—
40C2×#381C2212yes—
41C2×#381C2212yes—
42C2×#381C2212yes—
43C2×#380C2212yes—
44C2×#379C2211yescharacteristic
45C2×#379C2211yescharacteristic
46C2×C4×C22⋊C4C2212yes—
47C2×C4×C22⋊C4C2212yes—
48C2×C4×C22⋊C4C2211yescharacteristic
49C2×C4×C22⋊C4C2211yescharacteristic
50C22×#95C2212yes—
51C22×#95C2212yes—
52C22×#95C2212yes—
53C22×#95C2212yes—
54#1446C2211yescharacteristic, complemented
55#1446C2212yescomplemented
56#1445C2211yescharacteristic, complemented
57#1445C2212yescomplemented
58#1445C2211yescharacteristic, complemented
59#1445C2211yescharacteristic, complemented
60#1443C2212yescomplemented
61#1443C2212yescomplemented
62#1443C2212yescomplemented
63#1443C2212yescomplemented
64#1443C2212yescomplemented
65#1443C2212yescomplemented
66#1442C2212yescomplemented
67#1442C2212yescomplemented
68#1442C2212yescomplemented
69#1442C2212yescomplemented
70#1442C2212yescomplemented
71#1442C2212yescomplemented
72#1442C2212yescomplemented
73#1442C2212yescomplemented
74#1442C2212yescomplemented
75#1442C2212yescomplemented
76#1442C2212yescomplemented
77#1441C2212yescomplemented
78#1441C2212yescomplemented
79#1440C2212yes—
80#1440C2212yes—
81#1440C2212yes—
82#1440C2212yes—
83#1436C2212yescomplemented
84#1436C2212yescomplemented
85#1436C2212yescomplemented
86C4⋊#95C2212yescomplemented
87#1434C2211yescharacteristic, complemented
88#1434C2212yescomplemented
89#1434C2212yescomplemented
90#1434C2211yescharacteristic, complemented
91C22⋊#95C2212yes—
92C22⋊#95C2212yes—
93C22⋊#95C2212yes—
94C22⋊#95C2212yes—
95C22⋊#95C2212yes—
96C22⋊#95C2212yes—
97C22⋊#95C2212yes—
98C22⋊#95C2212yes—
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2211yescharacteristic
108C22⋊#95C2211yescharacteristic
109C26C2311yescharacteristic
110C23×Q8C2311yescharacteristic
111C24×C4—24no—
112C24×C4—28no—
113C24×C4—42no—
114C24×C4—42no—
115C24×C4—44no—
116C24×C4C2312yes—
117C24×C4C2312yes—
118C24×C4C2311yescharacteristic
119C24×C4C2312yes—
120C24×C4C2312yes—
121C24×C4C2312yes—
122C24×C4C2311yescharacteristic
123C24×C4C2312yes—
124C2×C22⋊Q8—28no—
125C2×C22⋊Q8—28no—
126C2×C22⋊Q8—44no—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C22⋊C4—28no—
136C22×C22⋊C4—28no—
137C22×C22⋊C4—28no—
138C22×C22⋊C4—28no—
139C22×C22⋊C4—28no—
140C22×C22⋊C4—44no—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2311yescharacteristic
160#400—44no—
161#399—24no—
162#397—24no—
163#397—24no—
164#397—28no—
165#396—28no—
166#393—24no—
167#391—42no—
168#385—28no—
169#385—28no—
170#385—28no—
171#385—28no—
172#382—42no—
173#381—28no—
174#381—28no—
175#381—28no—
176#381—44no—
177#380—28no—
178#379—24no—
179#379D418yes—
180C4×C22⋊C4—28no—
181C4×C22⋊C4—42no—
182C4×C22⋊C4—42no—
183C4×C22⋊C4—44no—
184C2×#95—28no—
185C2×#95—44no—
186C2×#95—44no—
187C2×#95—44no—
188C2×#95C2312yes—
189C2×#95C2311yescharacteristic
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2311yescharacteristic
193C2×#95C2312yes—
194C2×#95C2311yescharacteristic
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2311yescharacteristic
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
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×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2311yescharacteristic
232C2×#95C2312yes—
233C2×#95C2311yescharacteristic
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C25—24no—
239C25—24no—
240C25—24no—
241C25—24no—
242C25—41no—
243C25—41no—
244C25—41no—
245C25—41no—
246C25C2×D414yes—
247C25#4114yes—
248C25#4114yes—
249C25C2411yescharacteristic
250C25C2412yes—
251C22×Q8—22no—
252C22×Q8—24no—
253C22×Q8—42no—
254C22×Q8—41no—
255C22×Q8—41no—
256C23×C4—22no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—22no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
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—24no—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—41no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—41no—
297C23×C4—416no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—42no—
307C23×C4—42no—
308C23×C4—432no—
309C23×C4—432no—
310C23×C4—416no—
311C23×C4—416no—
312C23×C4#4118yes—
313C23×C4C2411yescharacteristic
314C23×C4C2412yes—
315C23×C4C2411yescharacteristic
316C23×C4C2412yes—
317C23×C4C2412yes—
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2412yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2411yescharacteristic
324C23×C4C2411yescharacteristic
325C23×C4C2412yes—
326C23×C4C2412yes—
327C23×C4C2412yes—
328C23×C4C2411yescharacteristic
329C23×C4C2411yescharacteristic
330C22⋊Q8—432no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—41no—
348C2×C4⋊C4—41no—
349C2×C4⋊C4—41no—
350C2×C4⋊C4—41no—
351C2×C4⋊C4—41no—
352C2×C4⋊C4—41no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—432no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—41no—
392C2×C22⋊C4—41no—
393C2×C22⋊C4—41no—
394C2×C22⋊C4—41no—
395C2×C22⋊C4—41no—
396C2×C22⋊C4—41no—
397C2×C22⋊C4—41no—
398C2×C22⋊C4—41no—
399C2×C22⋊C4—432no—
400C2×C22⋊C4C2×D418yes—
401C2×C22⋊C4C2×D418yes—
402C2×C22⋊C4C2×D414yes—
403C2×C22⋊C4C2×D414yes—
404C2×C22⋊C4#4118yes—
405C2×C42—24no—
406C2×C42—22no—
407C2×C42—24no—
408C2×C42—22no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—42no—
412#95—22no—
413#95—24no—
414#95—22no—
415#95—24no—
416#95—22no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—22no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—42no—
449#95—42no—
450#95—41no—
451#95—41no—
452#95—42no—
453#95—42no—
454#95—42no—
455#95—42no—
456#95—42no—
457#95—42no—
458#95—42no—
459#95—42no—
460#95—42no—
461#95—42no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—216no—
471C24—216no—
472C24—216no—
473C24—216no—
474C24—216no—
475C24—216no—
476C24—22no—
477C24—22no—
478C24—21no—
479C24—21no—
480C24—22no—
481C24—22no—
482C24—21no—
483C24—21no—
484C24—44no—
485C24—44no—
486C24—44no—
487C24—44no—
488C24—44no—
489C24—44no—
490C24—44no—
491C24—48no—
492C24—44no—
493C24—48no—
494C24—44no—
495C24—48no—
496C24—48no—
497C24—48no—
498C24—48no—
499C24—44no—
500C24#124116yes—
501C24C22×D412yes—
502C24C22×D414yes—
503C24C2×#4112yes—
504C24C2×#4112yes—
505C24C2×#4114yes—
506C24C2×#4114yes—
507C24C2×#4114yes—
508C24C2×#4114yes—
509C24H(5,𝔽2)14yes—
510C242−1+414yes—
511C24C2511yescharacteristic
512C2×Q8—48no—
513C2×Q8—44no—
514C2×Q8—82no—
515C2×Q8—84no—
516C2×Q8—82no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—28no—
521C22×C4—216no—
522C22×C4—216no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
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—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—216no—
560C22×C4—22no—
561C22×C4—22no—
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—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—44no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4—48no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—44no—
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—44no—
642C22×C4—4128no—
643C22×C4—44no—
644C22×C4—48no—
645C22×C4—44no—
646C22×C4—48no—
647C22×C4—48no—
648C22×C4—48no—
649C22×C4—48no—
650C22×C4—48no—
651C22×C4—48no—
652C22×C4—48no—
653C22×C4—48no—
654C22×C4—48no—
655C22×C4—48no—
656C22×C4—48no—
657C22×C4—48no—
658C22×C4—84no—
659C22×C4—84no—
660C22×C4—84no—
661C22×C4—84no—
662C22×C4—84no—
663C22×C4—84no—
664C22×C4—84no—
665C22×C4—84no—
666C22×C4—84no—
667C22×C4—84no—
668C22×C4C22×D412yes—
669C22×C4C22×D414yes—
670C22×C4C22×D412yes—
671C22×C4C2×#4114yes—
672C22×C4C2×#4114yes—
673C22×C4C2×#4114yes—
674C22×C4C2×#4114yes—
675C22×C4H(5,𝔽2)12yes—
676C22×C4H(5,𝔽2)12yes—
677C4⋊C4—48no—
678C4⋊C4—48no—
679C4⋊C4—48no—
680C4⋊C4—84no—
681C4⋊C4—82no—
682C4⋊C4—84no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C22⋊C4—216no—
686C22⋊C4—216no—
687C22⋊C4—216no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—48no—
691C22⋊C4—48no—
692C22⋊C4—44no—
693C22⋊C4—44no—
694C22⋊C4—48no—
695C22⋊C4—48no—
696C22⋊C4—48no—
697C22⋊C4—48no—
698C22⋊C4—48no—
699C22⋊C4—48no—
700C22⋊C4—48no—
701C42—44no—
702C42—84no—
703C42—82no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
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—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—24no—
734C23—22no—
735C23—22no—
736C23—24no—
737C23—24no—
738C23—24no—
739C23—24no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—264no—
745C23—416no—
746C23—416no—
747C23—432no—
748C23—416no—
749C23—416no—
750C23—416no—
751C23—416no—
752C23—432no—
753C23—432no—
754C23—416no—
755C23—41no—
756C23—42no—
757C23—41no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—42no—
762C23—41no—
763C23—42no—
764C23—41no—
765C23C2×#12414yes—
766C23C2×#12418yes—
767C23#52918yes—
768C23#53918yes—
769C23#54618yes—
770C23#54718yes—
771C23#55118yes—
772C23#55218yes—
773C23C23×D411yescharacteristic
774C23C22×#4111yescharacteristic
775C23C22×#4111yescharacteristic
776C23C22×#4112yes—
777C23C22×#4112yes—
778C23C2×H(5,𝔽2)12yes—
779C23C2×H(5,𝔽2)11yescharacteristic
780C23C2×H(5,𝔽2)11yescharacteristic
781C23C2×2−1+412yes—
782C23#58511yescharacteristic
783C23#58511yescharacteristic
784Q8—88no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—432no—
808C2×C4—416no—
809C2×C4—432no—
810C2×C4—416no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—41no—
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—42no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—41no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—41no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—41no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—41no—
895C2×C4—816no—
896C2×C4—816no—
897C2×C4—816no—
898C2×C4—816no—
899C2×C4#55114yes—
900C22—28no—
901C22—28no—
902C22—28no—
903C22—28no—
904C22—28no—
905C22—28no—
906C22—28no—
907C22—28no—
908C22—28no—
909C22—28no—
910C22—28no—
911C22—28no—
912C22—28no—
913C22—28no—
914C22—24no—
915C22—28no—
916C22—464no—
917C22—42no—
918C22—44no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—44no—
924C22—44no—
925C22—42no—
926C22#2488116yes—
927C22C22×#12411yescharacteristic
928C22C2×#52912yes—
929C22C2×#53912yes—
930C22#345911yescharacteristic
931C22#345911yescharacteristic
932C22C2×#54612yes—
933C22C2×#54712yes—
934C22C2×#55112yes—
935C22C2×#55111yescharacteristic
936C22C2×#55212yes—
937C22#347512yes—
938C22#348111yescharacteristic
939C22#349011yescharacteristic
940C22#349012yes—
941C22#349111yescharacteristic
942C22#349512yes—
943C22#349611yescharacteristic
944C22#349611yescharacteristic
945C22#351312yes—
946C22#352012yes—
947C22#353211yescharacteristic
948C22#353512yes—
949C22#353811yescharacteristic
950C4—24no—
951C4—44no—
952C4—42no—
953C4—42no—
954C4—44no—
955C4—42no—
956C4—44no—
957C4—44no—
958C4—81no—
959C4—82no—
960C4—82no—
961C4—82no—
962C4—82no—
963C4—82no—
964C4—82no—
965C4—82no—
966C4—81no—
967C2—216no—
968C2—44no—
969C2C2×#248812yes—
970C2#3475411yescharacteristic
971C2#3499311yescharacteristic
972C2#3499912yes—
973C2#3748611yescharacteristic
974C2#5919211yescharacteristic
975C2#5919612yes—
976C2#5919811yescharacteristic
977C2#5928511yescharacteristic
978C2#5931112yes—
979C2#5980211yescharacteristic
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
3. #16832C2semidirect
4. #16831C2semidirect
5. #16830C2semidirect
6. #15050C2semidirect
7. #15016C2semidirect
8. #14934C2semidirect
9. #14919C2semidirect
10. #14833C2semidirect
11. #14767C2semidirect
12. #14738C2semidirect
13. #14052C2semidirect
14. #13992C2semidirect
15. #13896C2semidirect
16. #13874C2semidirect
26. C2×#400C22semidirect
33. C2×#391C22semidirect
38. C2×#382C22semidirect
54. #1446C22semidirect
55. #1446C22semidirect
56. #1445C22semidirect
57. #1445C22semidirect
58. #1445C22semidirect
59. #1445C22semidirect
60. #1443C22semidirect
61. #1443C22semidirect
62. #1443C22semidirect
63. #1443C22semidirect
64. #1443C22semidirect
65. #1443C22semidirect
66. #1442C22semidirect
67. #1442C22semidirect
68. #1442C22semidirect
69. #1442C22semidirect
70. #1442C22semidirect
71. #1442C22semidirect
72. #1442C22semidirect
73. #1442C22semidirect
74. #1442C22semidirect
75. #1442C22semidirect
76. #1442C22semidirect
77. #1441C22semidirect
78. #1441C22semidirect
83. #1436C22semidirect
84. #1436C22semidirect
85. #1436C22semidirect
86. C4⋊#95C22semidirect
87. #1434C22semidirect
88. #1434C22semidirect
89. #1434C22semidirect
90. #1434C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24832
C2×#24372
#168322
#168312
#168302
#150502
#150162
#149342
#149192
#148332
#147672
#147382
#140522
#139922
#138962
#138742
#138692
C4×#3792
C2×C22⋊#952