Finite Group Databasebeta

← #1409224

Subgroups — #1409224

Order 512.

2440 conjugacy classes of subgroups.

The subgroup lattice has 963 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2487C211yesmaximal, characteristic
2C2×#2419C211yesmaximal, characteristic
3#17043C211yesmaximal, characteristic, complemented
4#16983C211yesmaximal, characteristic, complemented
5#16911C212yesmaximal, complemented
6#16875C212yesmaximal, complemented
7#16844C212yesmaximal, complemented
8#16815C211yesmaximal, characteristic, complemented
9#16699C211yesmaximal, characteristic, complemented
10#16528C212yesmaximal, complemented
11#15092C211yesmaximal, characteristic, complemented
12#15012C211yesmaximal, characteristic, complemented
13#14936C211yesmaximal, characteristic, complemented
14#14912C212yesmaximal
15#14841C211yesmaximal, characteristic, complemented
16#14826C211yesmaximal, characteristic, complemented
17#14737C212yesmaximal
18#14355C211yesmaximal, characteristic, complemented
19#14326C211yesmaximal, characteristic, complemented
20#14004C212yesmaximal, complemented
21#13992C212yesmaximal, complemented
22C2×#1442C211yesmaximal, characteristic, complemented
23#13813C211yesmaximal, characteristic
24C22×#123C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27#2487—28no—
28#2419—28no—
29C2×#400C2211yescharacteristic
30C2×#400C2212yes—
31C2×#400C2211yescharacteristic
32C2×#399C2212yes—
33C2×#398C2211yescharacteristic
34C2×#397C2211yescharacteristic
35C2×#397C2211yescharacteristic
36C2×#397C2212yes—
37C2×#389C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#389C2212yes—
40C2×#387C2211yescharacteristic
41C2×#387C2211yescharacteristic
42C2×#386C2212yes—
43C2×#386C2212yes—
44C2×#386C2211yescharacteristic
45C2×#385C2212yes—
46C2×#385C2211yescharacteristic
47C2×#385C2211yescharacteristic
48C2×#385C2212yes—
49C2×#385C2212yes—
50C2×#381C2211yescharacteristic
51C2×#381C2212yes—
52C2×#381C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2212yes—
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61C22×#95C2212yes—
62C22×#95C2212yes—
63#1445C2212yes—
64#1445C2212yes—
65#1445C2211yescharacteristic
66#1445C2211yescharacteristic
67#1445C2212yes—
68#1445C2211yescharacteristic
69#1444C2212yes—
70#1444C2211yescharacteristic
71#1444C2211yescharacteristic
72#1444C2211yescharacteristic
73#1444C2211yescharacteristic
74#1444C2212yes—
75#1443C2212yes—
76#1443C2212yes—
77#1443C2212yes—
78#1443C2212yes—
79#1443C2212yes—
80#1442C2212yes—
81#1442C2212yes—
82#1442C2211yescharacteristic
83#1442C2211yescharacteristic
84#1442C2212yes—
85#1442C2211yescharacteristic
86#1442C2211yescharacteristic
87#1442C2211yescharacteristic
88#1442C2212yes—
89#1442C2212yes—
90#1442C2212yes—
91#1442C2212yes—
92#1442C2212yes—
93#1442C2212yes—
94#1441C2212yes—
95#1441C2212yes—
96#1441C2211yescharacteristic
97#1441C2212yes—
98#1441C2211yescharacteristic
99#1441C2212yes—
100#1441C2211yescharacteristic
101#1441C2212yes—
102#1440C2212yes—
103#1440C2212yes—
104#1440C2212yes—
105#1440C2212yes—
106#1439C2212yes—
107#1439C2212yes—
108#1439C2212yes—
109#1437C2212yes—
110#1436C2212yes—
111#1436C2212yes—
112#1436C2212yes—
113#1436C2212yes—
114#1436C2212yes—
115C4⋊#95C2212yes—
116#1434C2212yes—
117#1434C2212yes—
118#1434C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2212yes—
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C4×#95C2211yescharacteristic
125C23×D4C2311yescharacteristic
126C24×C4C2311yescharacteristic
127C24×C4C2312yes—
128C24×C4C2311yescharacteristic
129C24×C4C2311yescharacteristic
130C24×C4C2312yes—
131C24×C4C2311yescharacteristic
132C2×#123—24no—
133C2×#123—44no—
134C2×C4×D4—44no—
135C2×C4×D4D418yes—
136C22×C4⋊C4—24no—
137C22×C4⋊C4—44no—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2311yescharacteristic
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2311yescharacteristic
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2311yescharacteristic
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2311yescharacteristic
170C22×C42C2312yes—
171C22×C42C2312yes—
172C22×C42C2311yescharacteristic
173#400—24no—
174#400—28no—
175#400—24no—
176#399—28no—
177#398—24no—
178#397—24no—
179#397—24no—
180#397—44no—
181#389—24no—
182#389—24no—
183#389—44no—
184#387—24no—
185#387—24no—
186#386—24no—
187#386—28no—
188#386—28no—
189#385—24no—
190#385—24no—
191#385—28no—
192#385—28no—
193#385—44no—
194#381—24no—
195#381—24no—
196#381—28no—
197#380—24no—
198#380—24no—
199#380—24no—
200#380—24no—
201C4×C22⋊C4—24no—
202C4×C22⋊C4—44no—
203C2×#95—24no—
204C2×#95—24no—
205C2×#95—44no—
206C2×#95—44no—
207C2×#95C2311yescharacteristic
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211C2×#95C2311yescharacteristic
212C2×#95C2311yescharacteristic
213C2×#95C2312yes—
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2311yescharacteristic
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2311yescharacteristic
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2311yescharacteristic
226C2×#95C2311yescharacteristic
227C2×#95C2312yes—
228C2×#95C2311yescharacteristic
229C2×#95C2311yescharacteristic
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2311yescharacteristic
240C2×#95C2311yescharacteristic
241C2×#95C2311yescharacteristic
242C2×#95C2312yes—
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2311yescharacteristic
264C25C2411yescharacteristic
265C25C2411yescharacteristic
266C22×D4—24no—
267C22×D4—24no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4C2×D414yes—
271C23×C4—24no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—22no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—42no—
296C23×C4—41no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4C2×D414yes—
304C23×C4C2×D414yes—
305C23×C4C2411yescharacteristic
306C23×C4C2412yes—
307C23×C4C2411yescharacteristic
308C23×C4C2412yes—
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2412yes—
317C23×C4C2411yescharacteristic
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326#123—416no—
327C4×D4—416no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—41no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—416no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4C2×D414yes—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—41no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—42no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4C2×D414yes—
409C2×C22⋊C4C2×D414yes—
410C2×C22⋊C4#4118yes—
411C2×C42—24no—
412C2×C42—42no—
413C2×C42—42no—
414C2×C42—42no—
415C2×C42—42no—
416C2×C42—42no—
417C2×C42—42no—
418C2×C42C2×D414yes—
419#95—22no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—22no—
424#95—24no—
425#95—24no—
426#95—22no—
427#95—24no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—22no—
440#95—22no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—24no—
452#95—24no—
453#95—22no—
454#95—42no—
455#95—42no—
456#95—42no—
457#95—42no—
458#95—42no—
459#95—42no—
460#95—42no—
461#95—42no—
462#95—42no—
463#95—42no—
464#95—42no—
465#95—42no—
466#95—42no—
467#95—42no—
468#95—42no—
469#95—42no—
470#95—42no—
471#95—42no—
472#95—42no—
473#95—42no—
474#95—42no—
475#95#4114yes—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—22no—
480C24—22no—
481C24—21no—
482C24—21no—
483C24—22no—
484C24—21no—
485C24—22no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24C22×D412yes—
493C24C22×D412yes—
494C24C2×#4114yes—
495C24H(5,𝔽2)14yes—
496C242−1+412yes—
497C242−1+412yes—
498C24C2511yescharacteristic
499C2×D4—28no—
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—48no—
503C2×D4—48no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—28no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
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—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
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—21no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
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—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4—44no—
626C22×C4—48no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—48no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—48no—
639C22×C4—84no—
640C22×C4—84no—
641C22×C4—82no—
642C22×C4—84no—
643C22×C4—84no—
644C22×C4—84no—
645C22×C4—84no—
646C22×C4—84no—
647C22×C4—84no—
648C22×C4—84no—
649C22×C4—84no—
650C22×C4C22×D412yes—
651C22×C4C22×D412yes—
652C22×C4C22×D412yes—
653C22×C4C22×D412yes—
654C22×C4C22×D412yes—
655C22×C4C2×#4114yes—
656C22×C4C2×#4114yes—
657C22×C4C2×#4114yes—
658C22×C4C2×#4112yes—
659C22×C4H(5,𝔽2)12yes—
660C22×C42−1+412yes—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—48no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—48no—
668C4⋊C4—44no—
669C4⋊C4—44no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—82no—
673C4⋊C4—82no—
674C4⋊C4—84no—
675C4⋊C4—84no—
676C4⋊C4—84no—
677C4⋊C4—84no—
678C4⋊C4—84no—
679C22⋊C4—28no—
680C22⋊C4—216no—
681C22⋊C4—44no—
682C22⋊C4—48no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—48no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—84no—
690C22⋊C4—82no—
691C22⋊C4—84no—
692C22⋊C4—84no—
693C42—44no—
694C42—84no—
695C42—84no—
696C23—22no—
697C23—24no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—24no—
702C23—24no—
703C23—24no—
704C23—22no—
705C23—22no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—22no—
711C23—24no—
712C23—22no—
713C23—24no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—41no—
728C23—41no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—41no—
734C23—42no—
735C23—41no—
736C23—42no—
737C23#53214yes—
738C23#53414yes—
739C23#53614yes—
740C23#53918yes—
741C23#54218yes—
742C23C23×D411yescharacteristic
743C23C22×#4112yes—
744C23C22×#4111yescharacteristic
745C23C2×H(5,𝔽2)12yes—
746C23C2×H(5,𝔽2)11yescharacteristic
747C23C2×2−1+411yescharacteristic
748C23C2×2−1+411yescharacteristic
749C23C2×2−1+411yescharacteristic
750C23#58512yes—
751C23#58512yes—
752C23#58511yescharacteristic
753D4—416no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—416no—
782C2×C4—41no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
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—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—41no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—41no—
845C2×C4—41no—
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—41no—
855C2×C4—41no—
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—41no—
873C2×C4—42no—
874C2×C4—41no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—88no—
878C2×C4—88no—
879C2×C4—816no—
880C2×C4—816no—
881C2×C4—88no—
882C2×C4#54714yes—
883C22—28no—
884C22—24no—
885C22—28no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—28no—
891C22—24no—
892C22—28no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—82no—
901C22—82no—
902C22—82no—
903C22—82no—
904C22#266318yes—
905C22C2×#53211yescharacteristic
906C22C2×#53411yescharacteristic
907C22C2×#53611yescharacteristic
908C22C2×#53912yes—
909C22C2×#54212yes—
910C22C2×#54711yescharacteristic
911C22#347512yes—
912C22#348511yescharacteristic
913C22#348811yescharacteristic
914C22#350011yescharacteristic
915C22#351312yes—
916C22#351312yes—
917C22#351512yes—
918C22#351611yescharacteristic
919C22#352011yescharacteristic
920C22#352112yes—
921C22#353312yes—
922C22#353512yes—
923C22#354212yes—
924C22#355211yescharacteristic
925C22#355312yes—
926C22#356311yescharacteristic
927C22#356412yes—
928C4—24no—
929C4—44no—
930C4—42no—
931C4—42no—
932C4—42no—
933C4—42no—
934C4—44no—
935C4—42no—
936C4—44no—
937C4—82no—
938C4—81no—
939C4—81no—
940C4—81no—
941C4—82no—
942C4—81no—
943C4—81no—
944C4—81no—
945C4—81no—
946C4—82no—
947C4—82no—
948C4—82no—
949C2—28no—
950C2—82no—
951C2C2×#266311yescharacteristic
952C2#3585011yescharacteristic
953C2#3618411yescharacteristic
954C2#3803811yescharacteristic
955C2#3804011yescharacteristic
956C2#3813412yes—
957C2#3814512yes—
958C2#4086412yes—
959C2#4137411yescharacteristic
960C2#4151312yes—
961C2#4193311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #17043C2semidirect
4. #16983C2semidirect
5. #16911C2semidirect
6. #16875C2semidirect
7. #16844C2semidirect
8. #16815C2semidirect
9. #16699C2semidirect
10. #16528C2semidirect
11. #15092C2semidirect
12. #15012C2semidirect
13. #14936C2semidirect
15. #14841C2semidirect
16. #14826C2semidirect
18. #14355C2semidirect
19. #14326C2semidirect
20. #14004C2semidirect
21. #13992C2semidirect
22. C2×#1442C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24872
C2×#24192
#170432
#169832
#169112
#168752
#168442
#168152
#166992
#165282
#150922
#150122
#149362
#149122
#148412
#148262
#147372
#143552
#143262
#140042
#139922
C2×#14422
#138132