Finite Group Databasebeta

← #779429

Subgroups — #779429

Order 512.

3392 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2443C212yesmaximal
2C2×#2359C212yesmaximal, complemented
3#16335C212yesmaximal, complemented
4#15981C211yesmaximal, characteristic, complemented
5#15949C211yesmaximal, characteristic, complemented
6#15780C211yesmaximal, characteristic, complemented
7#15406C212yesmaximal, complemented
8#15400C212yesmaximal, complemented
9#15363C211yesmaximal, characteristic, complemented
10#14927C212yesmaximal, complemented
11#14926C211yesmaximal, characteristic
12#14809C212yesmaximal, complemented
13#14761C212yesmaximal, complemented
14#14130C212yesmaximal, complemented
15#14128C211yesmaximal, characteristic, complemented
16#14112C212yesmaximal, complemented
17#14015C212yesmaximal, complemented
18#13999C212yesmaximal, complemented
19C2×#1444C211yesmaximal, characteristic, complemented
20C22×#123C2212yes—
21C22×#123C2212yes—
22C22×#121C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×#117C2211yescharacteristic
25C23×C4⋊C4C2212yes—
26C23×C4⋊C4C2211yescharacteristic
27#2443—216no—
28C2×#399C2212yes—
29C2×#398C2212yes—
30C2×#397C2212yes—
31C2×#394C2212yes—
32#2359—216no—
33C2×#389C2212yes—
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#388C2212yes—
37C2×#388C2212yes—
38C2×#388C2212yes—
39C2×#388C2212yes—
40C2×#387C2212yes—
41C2×#387C2212yes—
42C2×#387C2212yes—
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#385C2212yes—
50C2×#385C2212yes—
51C2×#385C2212yes—
52C2×#385C2212yes—
53C2×#381C2211yescharacteristic
54C2×#380C2212yes—
55C2×C4×C4⋊C4C2212yes—
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2212yes—
58C22×#95C2212yes—
59C22×#95C2211yescharacteristic
60C22×#95C2211yescharacteristic
61#1444C2211yescharacteristic
62#1444C2211yescharacteristic
63#1444C2211yescharacteristic
64#1444C2212yes—
65#1444C2211yescharacteristic
66#1444C2212yes—
67#1444C2211yescharacteristic
68#1444C2212yes—
69#1444C2211yescharacteristic
70#1444C2211yescharacteristic
71#1444C2212yes—
72#1444C2212yes—
73#1444C2212yes—
74#1444C2211yescharacteristic
75#1443C2212yes—
76#1442C2211yescharacteristic
77#1442C2212yes—
78#1442C2212yes—
79#1442C2212yes—
80#1442C2211yescharacteristic
81#1442C2212yes—
82#1442C2212yes—
83#1441C2212yes—
84#1441C2212yes—
85#1440C2212yes—
86#1440C2212yes—
87#1440C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1438C2211yescharacteristic
96#1438C2211yescharacteristic
97#1437C2212yes—
98#1436C2212yes—
99#1436C2212yes—
100#1436C2212yes—
101#1436C2212yes—
102#1436C2212yes—
103C4⋊#95C2212yes—
104C4⋊#95C2212yes—
105#1434C2212yes—
106C22⋊#95C2212yes—
107C22⋊#95C2211yescharacteristic
108C22⋊#95C2212yes—
109C23×D4C2312yes—
110C23×D4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2312yes—
114C24×C4C2311yescharacteristic
115C24×C4C2312yes—
116C24×C4C2312yes—
117C2×#123—28no—
118C2×#123—28no—
119C2×#123—28no—
120C2×#123—28no—
121C2×#123—44no—
122C2×#123—44no—
123C2×#121—28no—
124C2×#121—42no—
125C2×C4×D4—28no—
126C2×C4×D4—28no—
127C2×C4×D4—44no—
128C2×#117—28no—
129C2×#117—42no—
130C22×C4⋊C4—28no—
131C22×C4⋊C4—44no—
132C22×C4⋊C4—44no—
133C22×C4⋊C4—44no—
134C22×C4⋊C4—42no—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2311yescharacteristic
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C42C2312yes—
170C22×C42C2312yes—
171C22×C42C2312yes—
172C22×C42C2312yes—
173#399—28no—
174#398—28no—
175#397—28no—
176#394—28no—
177#389—28no—
178#389—44no—
179#389—44no—
180#388—28no—
181#388—28no—
182#388—28no—
183#388—28no—
184#387—28no—
185#387—28no—
186#387—28no—
187#386—28no—
188#386—28no—
189#386—28no—
190#386D4116yes—
191#385—28no—
192#385—28no—
193#385—28no—
194#385—28no—
195#385—44no—
196#385—44no—
197#381—24no—
198#380—28no—
199C4×C4⋊C4—28no—
200C4×C22⋊C4—28no—
201C4×C22⋊C4—28no—
202C2×#95—28no—
203C2×#95—24no—
204C2×#95—42no—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2311yescharacteristic
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2311yescharacteristic
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2311yescharacteristic
228C2×#95C2311yescharacteristic
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2311yescharacteristic
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2312yes—
237C2×#95C2312yes—
238C2×#95C2312yes—
239C2×#95C2311yescharacteristic
240C2×#95C2311yescharacteristic
241C2×#95C2311yescharacteristic
242C2×#95C2311yescharacteristic
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2311yescharacteristic
246C25C2412yes—
247C25C2411yescharacteristic
248C22×D4—24no—
249C22×D4—24no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—24no—
253C22×D4—24no—
254C22×D4—24no—
255C22×D4—22no—
256C22×D4—41no—
257C22×D4—42no—
258C22×D4—41no—
259C22×D4C2×D418yes—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—24no—
269C23×C4—22no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—24no—
279C23×C4—22no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—41no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4C2×D418yes—
295C23×C4#4114yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2412yes—
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2412yes—
313#123—264no—
314#123—432no—
315#121—416no—
316C4×D4—432no—
317#117—416no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
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—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—432no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—41no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—41no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—41no—
361C2×C4⋊C4—41no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—41no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—416no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
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—24no—
379C2×C22⋊C4—24no—
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—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
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⋊C4—42no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4C2×D418yes—
414C2×C22⋊C4C2×D418yes—
415C2×C22⋊C4C2×D418yes—
416C2×C22⋊C4#4118yes—
417C2×C42—24no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—24no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—42no—
426C2×C42—42no—
427C2×C42—42no—
428C2×C42—42no—
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—24no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—22no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—22no—
449#95—22no—
450#95—24no—
451#95—24no—
452#95—24no—
453#95—24no—
454#95—22no—
455#95—24no—
456#95—41no—
457#95—41no—
458#95—41no—
459#95—41no—
460#95—41no—
461#95—42no—
462#95—42no—
463#95—42no—
464#95—42no—
465#95—42no—
466#95—42no—
467#95C2×D418yes—
468#95C2×D418yes—
469#95#4114yes—
470C24—21no—
471C24—22no—
472C24—21no—
473C24—22no—
474C24—21no—
475C24—21no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24C22×D414yes—
491C24C22×D414yes—
492C24C2×#4112yes—
493C24C2×#4114yes—
494C24H(5,𝔽2)12yes—
495C242−1+412yes—
496C24C2511yescharacteristic
497C2×D4—216no—
498C2×D4—216no—
499C2×D4—216no—
500C2×D4—48no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—44no—
506C2×D4—82no—
507C2×D4—84no—
508C2×D4—82no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—28no—
514C22×C4—216no—
515C22×C4—28no—
516C22×C4—216no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
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—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
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—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—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—216no—
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—21no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—48no—
624C22×C4—44no—
625C22×C4—44no—
626C22×C4—48no—
627C22×C4—44no—
628C22×C4—84no—
629C22×C4—84no—
630C22×C4—84no—
631C22×C4—84no—
632C22×C4—84no—
633C22×C4—84no—
634C22×C4—82no—
635C22×C4—84no—
636C22×C4—84no—
637C22×C4C22×D414yes—
638C22×C4C22×D414yes—
639C22×C4C22×D414yes—
640C22×C4C22×D414yes—
641C22×C4C22×D414yes—
642C22×C4C2×#4112yes—
643C22×C4C2×#4114yes—
644C22×C4C2×#4114yes—
645C22×C4C2×#4112yes—
646C22×C4C2×#4112yes—
647C22×C4C2×#4114yes—
648C22×C4H(5,𝔽2)14yes—
649C22×C4H(5,𝔽2)12yes—
650C22×C42−1+412yes—
651C22×C42−1+414yes—
652C4⋊C4—216no—
653C4⋊C4—216no—
654C4⋊C4—216no—
655C4⋊C4—48no—
656C4⋊C4—48no—
657C4⋊C4—48no—
658C4⋊C4—48no—
659C4⋊C4—48no—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—44no—
663C4⋊C4—48no—
664C4⋊C4—44no—
665C4⋊C4—48no—
666C4⋊C4—48no—
667C4⋊C4—48no—
668C4⋊C4—44no—
669C4⋊C4—84no—
670C4⋊C4—84no—
671C22⋊C4—216no—
672C22⋊C4—216no—
673C22⋊C4—216no—
674C22⋊C4—216no—
675C22⋊C4—216no—
676C22⋊C4—48no—
677C22⋊C4—48no—
678C22⋊C4—48no—
679C22⋊C4—48no—
680C22⋊C4—48no—
681C22⋊C4—48no—
682C22⋊C4—48no—
683C22⋊C4—48no—
684C22⋊C4—48no—
685C22⋊C4—84no—
686C42—48no—
687C42—48no—
688C42—48no—
689C42—84no—
690C23—24no—
691C23—22no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—22no—
696C23—24no—
697C23—24no—
698C23—22no—
699C23—24no—
700C23—22no—
701C23—24no—
702C23—24no—
703C23—22no—
704C23—22no—
705C23—24no—
706C23—22no—
707C23—22no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
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—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23#52518yes—
744C23#53914yes—
745C23D4214yes—
746C23#54718yes—
747C23#55914yes—
748C23C23×D412yes—
749C23C22×#4111yescharacteristic
750C23C22×#4112yes—
751C23C22×#4111yescharacteristic
752C23C2×H(5,𝔽2)11yescharacteristic
753C23C2×H(5,𝔽2)12yes—
754C23C2×H(5,𝔽2)11yescharacteristic
755C23C2×2−1+411yescharacteristic
756C23C2×2−1+412yes—
757C23C2×2−1+411yescharacteristic
758C23#58511yescharacteristic
759D4—432no—
760D4—88no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—432no—
799C2×C4—416no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—416no—
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—41no—
837C2×C4—41no—
838C2×C4—42no—
839C2×C4—41no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—41no—
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—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—816no—
871C2×C4—816no—
872C2×C4—88no—
873C2×C4#54718yes—
874C22—28no—
875C22—28no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—24no—
880C22—28no—
881C22—24no—
882C22—28no—
883C22—24no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—82no—
895C22—82no—
896C22—82no—
897C22—82no—
898C22—82no—
899C22#245518yes—
900C22C2×#52512yes—
901C22C2×#53911yescharacteristic
902C22C2×D4211yescharacteristic
903C22C2×#54712yes—
904C22C2×#54712yes—
905C22C2×#55911yescharacteristic
906C22#348011yescharacteristic
907C22#348112yes—
908C22#348412yes—
909C22#348812yes—
910C22#349211yescharacteristic
911C22#349912yes—
912C22#351112yes—
913C22#351111yescharacteristic
914C22#351512yes—
915C22#352012yes—
916C22#352012yes—
917C22#352011yescharacteristic
918C22#353211yescharacteristic
919C22#353411yescharacteristic
920C22#353812yes—
921C22#354411yescharacteristic
922C22#356311yescharacteristic
923C4—28no—
924C4—44no—
925C4—44no—
926C4—44no—
927C4—42no—
928C4—42no—
929C4—42no—
930C4—44no—
931C4—44no—
932C4—44no—
933C4—44no—
934C4—42no—
935C4—42no—
936C4—82no—
937C4—81no—
938C4—82no—
939C4—82no—
940C2—28no—
941C2—84no—
942C2C2×#245511yescharacteristic
943C2#3574012yes—
944C2#3636112yes—
945C2#3848511yescharacteristic
946C2#4202111yescharacteristic
947C2#4309811yescharacteristic
948C2#4328911yescharacteristic
949C2#4404212yes—
950C2#5910712yes—
951C2#5931311yescharacteristic
952C2#5962411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2359C2semidirect
3. #16335C2semidirect
4. #15981C2semidirect
5. #15949C2semidirect
6. #15780C2semidirect
7. #15406C2semidirect
8. #15400C2semidirect
9. #15363C2semidirect
10. #14927C2semidirect
12. #14809C2semidirect
13. #14761C2semidirect
14. #14130C2semidirect
15. #14128C2semidirect
16. #14112C2semidirect
17. #14015C2semidirect
18. #13999C2semidirect
19. C2×#1444C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24432
C2×#23592
#163352
#159812
#159492
#157802
#154062
#154002
#153632
#149272
#149262
#148092
#147612
#141302
#141282
#141122
#140152
#139992
C2×#14442