Finite Group Databasebeta

← #946562

Subgroups — #946562

Order 512.

2920 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2482C211yesmaximal, characteristic
2C2×#2483C211yesmaximal, characteristic
3#17163C212yesmaximal, complemented
4#17108C212yesmaximal, complemented
5#16675C211yesmaximal, characteristic, complemented
6#16668C211yesmaximal, characteristic, complemented
7#16579C212yesmaximal, complemented
8#16542C212yesmaximal, complemented
9#16470C211yesmaximal, characteristic, complemented
10#16321C211yesmaximal, characteristic, complemented
11#15560C212yesmaximal, complemented
12#15359C212yesmaximal, complemented
13#15019C212yesmaximal, complemented
14#14821C212yesmaximal, complemented
15#14820C212yesmaximal
16#14275C212yesmaximal, complemented
17#13878C212yesmaximal, complemented
18#13877C212yesmaximal
19C2×#1439C211yesmaximal, characteristic
20C22×#117C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic
22C23×C22⋊C4C2212yes—
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25#2483—28no—
26#2482—28no—
27C2×#399C2211yescharacteristic
28C2×#399C2211yescharacteristic
29C2×#398C2212yescomplemented
30C2×#398C2212yescomplemented
31C2×#397C2211yescharacteristic
32C2×#397C2212yes—
33C2×#397C2211yescharacteristic
34C2×#397C2212yes—
35C2×#397C2212yes—
36C2×#397C2212yes—
37C2×#388C2212yes—
38C2×#388C2212yes—
39C2×#385C2211yescharacteristic
40C2×#385C2212yes—
41C2×#385C2211yescharacteristic
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#381C2211yescharacteristic
46C2×#381C2212yes—
47C2×#381C2211yescharacteristic
48C2×#381C2211yescharacteristic
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#379C2212yes—
53C2×#379C2211yescharacteristic
54C22×#95C2212yes—
55C22×#95C2211yescharacteristic
56#1445C2212yescomplemented
57#1445C2212yescomplemented
58#1444C2212yescomplemented
59#1444C2212yescomplemented
60#1444C2212yescomplemented
61#1444C2212yescomplemented
62#1443C2212yescomplemented
63#1443C2212yescomplemented
64#1443C2212yescomplemented
65#1443C2212yescomplemented
66#1442C2212yescomplemented
67#1442C2212yescomplemented
68#1442C2212yescomplemented
69#1442C2212yescomplemented
70#1442C2212yescomplemented
71#1442C2212yescomplemented
72#1441C2212yescomplemented
73#1441C2212yescomplemented
74#1441C2212yescomplemented
75#1441C2212yescomplemented
76#1441C2212yescomplemented
77#1441C2212yescomplemented
78#1441C2212yescomplemented
79#1441C2212yescomplemented
80#1441C2212yescomplemented
81#1441C2212yescomplemented
82#1440C2212yes—
83#1440C2212yes—
84#1440C2212yes—
85#1440C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90#1439C2211yescharacteristic
91#1439C2211yescharacteristic
92#1439C2211yescharacteristic
93#1439C2211yescharacteristic
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1436C2212yescomplemented
99#1436C2212yescomplemented
100#1436C2212yescomplemented
101#1436C2212yescomplemented
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C22⋊#95C2212yes—
109C26C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2312yes—
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2312yes—
115C24×C4C2311yescharacteristic
116C2×#117—24no—
117C2×#117—42no—
118C2×#117—42no—
119C22×C4⋊C4—44no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C22⋊C4—24no—
137C22×C22⋊C4—28no—
138C22×C22⋊C4—44no—
139C22×C22⋊C4—44no—
140C22×C22⋊C4—42no—
141C22×C22⋊C4—42no—
142C22×C22⋊C4—42no—
143C22×C22⋊C4—42no—
144C22×C22⋊C4D418yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2311yescharacteristic
164C22×C22⋊C4C2311yescharacteristic
165C22×C42C2312yes—
166#399—24no—
167#399—24no—
168#398—44no—
169#398—44no—
170#397—24no—
171#397—24no—
172#397—28no—
173#397—28no—
174#397—44no—
175#397—44no—
176#388—28no—
177#388—28no—
178#385—28no—
179#385—28no—
180#385—24no—
181#385—24no—
182#385—44no—
183#385—44no—
184#381—24no—
185#381—28no—
186#381—24no—
187#381—24no—
188#380—28no—
189#380—44no—
190#380—44no—
191#379—28no—
192#379—24no—
193C2×#95—28no—
194C2×#95—42no—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2311yescharacteristic
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×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2311yescharacteristic
237C2×#95C2312yes—
238C2×#95C2311yescharacteristic
239C25—22no—
240C25—22no—
241C25—24no—
242C25—22no—
243C25—22no—
244C25—24no—
245C25—42no—
246C25—41no—
247C25—41no—
248C25—42no—
249C25C2×D414yes—
250C25C2411yescharacteristic
251C25C2411yescharacteristic
252C25C2411yescharacteristic
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—24no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—41no—
275C23×C4—41no—
276C23×C4—41no—
277C23×C4—41no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—41no—
283C23×C4—41no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4C2×D414yes—
287C23×C4C2×D414yes—
288C23×C4#4118yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305#117—416no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
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—41no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—41no—
323C2×C4⋊C4—41no—
324C2×C4⋊C4—41no—
325C2×C4⋊C4—41no—
326C2×C4⋊C4—416no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
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—22no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—432no—
383C2×C22⋊C4—416no—
384C2×C22⋊C4—41no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—41no—
387C2×C22⋊C4—41no—
388C2×C22⋊C4—41no—
389C2×C22⋊C4—41no—
390C2×C22⋊C4—41no—
391C2×C22⋊C4—41no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—41no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—41no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—416no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4C2×D414yes—
410C2×C22⋊C4C2×D414yes—
411C2×C22⋊C4C2×D414yes—
412C2×C22⋊C4C2×D414yes—
413C2×C42—24no—
414C2×C42—42no—
415C2×C42—42no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—22no—
424#95—22no—
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—41no—
437#95—42no—
438#95—41no—
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—42no—
451#95—42no—
452#95—42no—
453#95—42no—
454#95—42no—
455#95—42no—
456#95—42no—
457#95—42no—
458#95—42no—
459#95—42no—
460C24—22no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—21no—
469C24—21no—
470C24—22no—
471C24—21no—
472C24—21no—
473C24—22no—
474C24—28no—
475C24—22no—
476C24—22no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—21no—
481C24—22no—
482C24—21no—
483C24—21no—
484C24—22no—
485C24—28no—
486C24—216no—
487C24—44no—
488C24—48no—
489C24—48no—
490C24—48no—
491C24—44no—
492C24—44no—
493C24—48no—
494C24—44no—
495C24—44no—
496C24—48no—
497C24—48no—
498C24—44no—
499C24—44no—
500C24—84no—
501C24—84no—
502C24—82no—
503C24—82no—
504C24—84no—
505C24—84no—
506C24—84no—
507C24C22×D412yes—
508C24C22×D412yes—
509C24C22×D412yes—
510C24C2×#4114yes—
511C24H(5,𝔽2)12yes—
512C24H(5,𝔽2)12yes—
513C24H(5,𝔽2)12yes—
514C242−1+412yes—
515C242−1+414yes—
516C24C2511yescharacteristic
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—216no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—216no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
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—22no—
576C22×C4—22no—
577C22×C4—22no—
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—22no—
599C22×C4—22no—
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—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—44no—
629C22×C4—44no—
630C22×C4—44no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—48no—
635C22×C4—84no—
636C22×C4—84no—
637C22×C4—84no—
638C22×C4—84no—
639C22×C4—84no—
640C22×C4—84no—
641C22×C4—84no—
642C22×C4—84no—
643C22×C4—82no—
644C22×C4—82no—
645C22×C4—82no—
646C22×C4—82no—
647C22×C4—82no—
648C22×C4—82no—
649C22×C4—84no—
650C22×C4C22×D412yes—
651C22×C4C22×D412yes—
652C22×C4C22×D412yes—
653C22×C4C22×D412yes—
654C22×C4C2×#4114yes—
655C22×C4C2×#4114yes—
656C22×C4H(5,𝔽2)14yes—
657C4⋊C4—44no—
658C4⋊C4—48no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—84no—
663C4⋊C4—84no—
664C4⋊C4—84no—
665C4⋊C4—84no—
666C4⋊C4—84no—
667C4⋊C4—84no—
668C4⋊C4—84no—
669C4⋊C4—84no—
670C4⋊C4—84no—
671C4⋊C4—84no—
672C22⋊C4—216no—
673C22⋊C4—44no—
674C22⋊C4—44no—
675C22⋊C4—44no—
676C22⋊C4—44no—
677C22⋊C4—48no—
678C22⋊C4—48no—
679C22⋊C4—48no—
680C22⋊C4—44no—
681C22⋊C4—48no—
682C22⋊C4—48no—
683C22⋊C4—48no—
684C22⋊C4—48no—
685C22⋊C4—44no—
686C22⋊C4—48no—
687C22⋊C4—48no—
688C22⋊C4—48no—
689C22⋊C4—84no—
690C22⋊C4—84no—
691C22⋊C4—84no—
692C42—48no—
693C23—22no—
694C23—22no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—24no—
705C23—22no—
706C23—22no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—22no—
712C23—22no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—24no—
727C23—24no—
728C23—416no—
729C23—432no—
730C23—42no—
731C23—41no—
732C23—42no—
733C23—42no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—41no—
742C23—42no—
743C23—42no—
744C23—416no—
745C23—42no—
746C23—42no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—88no—
760C23—816no—
761C23—816no—
762C23—88no—
763C23—88no—
764C23—88no—
765C23—88no—
766C23—816no—
767C23#53414yes—
768C23#53714yes—
769C23#53918yes—
770C23#54718yes—
771C23#55914yes—
772C23#56314yes—
773C23C23×D411yescharacteristic
774C23C22×#4112yes—
775C23C2×H(5,𝔽2)11yescharacteristic
776C23C2×H(5,𝔽2)11yescharacteristic
777C23C2×H(5,𝔽2)11yescharacteristic
778C23C2×H(5,𝔽2)12yes—
779C23C2×2−1+411yescharacteristic
780C23C2×2−1+412yes—
781C23#58511yescharacteristic
782C23#58511yescharacteristic
783C23#58512yes—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
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—24no—
801C2×C4—416no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—416no—
809C2×C4—42no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
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—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
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—42no—
849C2×C4—42no—
850C2×C4—42no—
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—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
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—816no—
891C2×C4—816no—
892C2×C4—88no—
893C2×C4—88no—
894C22—28no—
895C22—24no—
896C22—24no—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—24no—
901C22—28no—
902C22—28no—
903C22—28no—
904C22—24no—
905C22—28no—
906C22—44no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—44no—
914C22—44no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—44no—
919C22—44no—
920C22—832no—
921C22—82no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—82no—
927C22#272418yes—
928C22C2×#53411yescharacteristic
929C22C2×#53711yescharacteristic
930C22#344911yescharacteristic
931C22C2×#53912yes—
932C22C2×#54712yes—
933C22C2×#55911yescharacteristic
934C22#349012yes—
935C22#349112yes—
936C22#349412yes—
937C22#349512yes—
938C22#349612yes—
939C22C2×#56311yescharacteristic
940C22#353211yescharacteristic
941C22#353311yescharacteristic
942C22#353411yescharacteristic
943C22#353411yescharacteristic
944C22#353511yescharacteristic
945C22#353512yes—
946C22#353511yescharacteristic
947C22#353812yes—
948C22#354212yes—
949C22#356112yes—
950C22#356412yes—
951C4—42no—
952C4—42no—
953C4—44no—
954C4—42no—
955C4—42no—
956C4—44no—
957C4—44no—
958C4—82no—
959C4—82no—
960C4—82no—
961C4—82no—
962C4—82no—
963C4—82no—
964C4—82no—
965C4—82no—
966C4—82no—
967C2—28no—
968C2—44no—
969C2—82no—
970C2#3673711yescharacteristic
971C2#3745211yescharacteristic
972C2#3786112yes—
973C2#3786612yes—
974C2#4063912yes—
975C2#4201012yes—
976C2#4317511yescharacteristic
977C2#4359811yescharacteristic
978C2C2×#272411yescharacteristic
979C2#5239611yescharacteristic
980C2#5251111yescharacteristic
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. #17163C2semidirect
4. #17108C2semidirect
5. #16675C2semidirect
6. #16668C2semidirect
7. #16579C2semidirect
8. #16542C2semidirect
9. #16470C2semidirect
10. #16321C2semidirect
11. #15560C2semidirect
12. #15359C2semidirect
13. #15019C2semidirect
14. #14821C2semidirect
16. #14275C2semidirect
17. #13878C2semidirect
29. C2×#398C22semidirect
30. C2×#398C22semidirect
56. #1445C22semidirect
57. #1445C22semidirect
58. #1444C22semidirect
59. #1444C22semidirect
60. #1444C22semidirect
61. #1444C22semidirect
62. #1443C22semidirect
63. #1443C22semidirect
64. #1443C22semidirect
65. #1443C22semidirect
66. #1442C22semidirect
67. #1442C22semidirect
68. #1442C22semidirect
69. #1442C22semidirect
70. #1442C22semidirect
71. #1442C22semidirect
72. #1441C22semidirect
73. #1441C22semidirect
74. #1441C22semidirect
75. #1441C22semidirect
76. #1441C22semidirect
77. #1441C22semidirect
78. #1441C22semidirect
79. #1441C22semidirect
80. #1441C22semidirect
81. #1441C22semidirect
98. #1436C22semidirect
99. #1436C22semidirect
100. #1436C22semidirect
101. #1436C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24822
C2×#24832
#171632
#171082
#166752
#166682
#165792
#165422
#164702
#163212
#155602
#153592
#150192
#148212
#148202
#142752
#138782
#138772
C2×#14392