Finite Group Databasebeta

← #611373

Subgroups — #611373

Order 512.

5612 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#532C211yesmaximal, characteristic, complemented
2C2×#2388C212yesmaximal, complemented
3C2×C4×#123C211yesmaximal, characteristic, complemented
4#16681C212yesmaximal, complemented
5#16680C212yesmaximal, complemented
6#16603C211yesmaximal, characteristic, complemented
7#16602C211yesmaximal, characteristic, complemented
8#16503C211yesmaximal, characteristic, complemented
9#16502C211yesmaximal, characteristic, complemented
10#16361C212yesmaximal, complemented
11#16259C212yesmaximal, complemented
12#16258C212yesmaximal, complemented
13#16250C212yesmaximal, complemented
14C4×#394C212yesmaximal, complemented
15C4×#394C212yesmaximal, complemented
16C4×#392C212yesmaximal, complemented
17C4×#392C212yesmaximal, complemented
18#13851C212yesmaximal, complemented
19C4×#381C211yesmaximal, characteristic, complemented
20C23×#41C2212yes—
21C2×#532—28no—
22C2×#532—216no—
23C22×C4⋊Q8C2211yescharacteristic
24C22×#127C2211yescharacteristic
25C22×#124C2212yes—
26C22×#123C2211yescharacteristic
27C22×#121C2212yes—
28C22×#121C2212yes—
29C22×C4×D4C2212yes—
30C22×C4×D4C2212yes—
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2214yes—
33C23×C42C2211yescharacteristic
34#2388—216no—
35C2×#395C2212yes—
36C2×#394C2212yes—
37C2×#394C2212yes—
38C2×#394C2212yes—
39C2×#394C2214yes—
40C2×#393C2212yes—
41C2×#392C2212yes—
42C2×#392C2212yes—
43C2×#392C2212yes—
44C2×#392C2214yes—
45C4×#123—28no—
46C2×#388C2211yescharacteristic
47C2×#388C2211yescharacteristic
48C2×#387C2211yescharacteristic
49C2×#387C2211yescharacteristic
50C2×#386C2211yescharacteristic
51C2×#385C2211yescharacteristic
52C2×#381C2212yes—
53C2×#381C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2214yes—
61C2×C4×C22⋊C4C2214yes—
62C2×C4×C22⋊C4C2214yes—
63#1446C2212yes—
64#1446C2212yes—
65#1444C2212yes—
66#1444C2212yes—
67#1442C2212yes—
68#1442C2212yes—
69#1441C2212yes—
70#1441C2212yes—
71#1440C2214yes—
72#1440C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2214yes—
78#1439C2214yes—
79#1438C2212yes—
80#1438C2212yes—
81#1438C2214yes—
82#1438C2214yes—
83#1438C2214yes—
84#1438C2214yes—
85#1438C2212yes—
86#1438C2212yes—
87#1438C2212yes—
88#1438C2212yes—
89#1434C2212yes—
90#1434C2211yescharacteristic
91#1434C2211yescharacteristic
92C22⋊#95C2212yes—
93C4×#95C2212yes—
94C4×#95C2212yes—
95C22×#41—28no—
96C22×#41—28no—
97C22×#41—48no—
98C22×#41—48no—
99C22×#41D4116yescomplemented
100C23×Q8C2312yes—
101C23×D4C2311yescharacteristic
102C23×D4C2312yes—
103C23×D4C2312yes—
104C23×D4C2314yes—
105C23×D4C2314yes—
106C23×D4C2312yes—
107C24×C4C2311yescharacteristic
108C24×C4C2314yes—
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112#532—2128no—
113C2×C4⋊Q8—28no—
114C2×C4⋊Q8—24no—
115C2×#127—28no—
116C2×#127—24no—
117C2×#124—28no—
118C2×#124—28no—
119C2×#124—28no—
120C2×#123—24no—
121C2×#123—24no—
122C2×#123—24no—
123C2×#121—216no—
124C2×#121—216no—
125C2×#121—28no—
126C2×#121—28no—
127C2×C4×D4—216no—
128C2×C4×D4—216no—
129C2×C4×D4—216no—
130C2×C4×D4—28no—
131C2×C4×D4—24no—
132C2×C4×D4—28no—
133C2×C4×D4—28no—
134C2×C4×D4—48no—
135C2×C4×D4—48no—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2311yescharacteristic
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2314yes—
163C22×C42—28no—
164C22×C42D418yescomplemented
165C22×C42C2314yes—
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173#395—28no—
174#394—216no—
175#394—28no—
176#394—28no—
177#394—28no—
178#393—28no—
179#392—216no—
180#392—28no—
181#392—28no—
182#392—28no—
183#388—24no—
184#388—24no—
185#387—24no—
186#387—24no—
187#386—24no—
188#385—24no—
189#381—24no—
190#381—28no—
191C4×C4⋊C4—24no—
192C4×C4⋊C4—24no—
193C4×C22⋊C4—216no—
194C4×C22⋊C4—28no—
195C4×C22⋊C4—24no—
196C4×C22⋊C4—24no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—48no—
199C4×C22⋊C4—48no—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2311yescharacteristic
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211C2×#95C2311yescharacteristic
212C2×#95C2311yescharacteristic
213C2×#95C2311yescharacteristic
214C2×#95C2311yescharacteristic
215C2×#95C2311yescharacteristic
216C2×#95C2311yescharacteristic
217C2×#95C2311yescharacteristic
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C25C2414yes—
225C25C2411yescharacteristic
226C25C2411yescharacteristic
227C2×#41—264no—
228C2×#41—464no—
229C2×#41—464no—
230C2×#41—432no—
231C2×#41—432no—
232C22×Q8—24no—
233C22×Q8—24no—
234C22×Q8—44no—
235C22×Q8—44no—
236C22×Q8C2×D418yes—
237C22×D4—28no—
238C22×D4—28no—
239C22×D4—22no—
240C22×D4—28no—
241C22×D4—28no—
242C22×D4—22no—
243C22×D4—28no—
244C22×D4—24no—
245C22×D4—28no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—24no—
250C22×D4—22no—
251C22×D4—28no—
252C22×D4—24no—
253C22×D4—24no—
254C22×D4—24no—
255C22×D4—24no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4—42no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4—44no—
265C22×D4—44no—
266C22×D4—44no—
267C22×D4—44no—
268C22×D4—44no—
269C22×D4C2×D4116yes—
270C22×D4C2×D418yes—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—28no—
276C23×C4—28no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—28no—
281C23×C4—28no—
282C23×C4—28no—
283C23×C4—28no—
284C23×C4—24no—
285C23×C4—22no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4C2×D4116yes—
291C23×C4C2×D414yes—
292C23×C4C2×D414yes—
293C23×C4C2×D414yes—
294C23×C4C2×D418yes—
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2414yes—
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2414yes—
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2414yes—
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311C4⋊Q8—232no—
312#127—232no—
313#124—264no—
314#123—232no—
315#121—264no—
316#121—264no—
317C4×D4—264no—
318C4×D4—264no—
319C4×D4—464no—
320C4×D4—416no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4#4114yescomplemented
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—22no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4#4114yescomplemented
392C2×C42—232no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—28no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—28no—
403C2×C42—28no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42C2×D414yes—
407C2×C42C2×D414yes—
408C2×C42C2×D414yes—
409C2×C42C2×D414yes—
410#95—22no—
411#95—22no—
412#95—22no—
413#95—22no—
414#95—22no—
415#95—22no—
416#95—28no—
417#95—24no—
418#95—28no—
419#95—24no—
420#95—22no—
421#95—22no—
422#95—22no—
423#95—22no—
424#95—28no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—44no—
429#95—44no—
430#95—44no—
431#95—44no—
432#95—44no—
433#95#4118yescomplemented
434C24—22no—
435C24—21no—
436C24—21no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—21no—
442C24—22no—
443C24—24no—
444C24—24no—
445C24—21no—
446C24—24no—
447C24—24no—
448C24—24no—
449C24—24no—
450C24—22no—
451C24—24no—
452C24—24no—
453C24—22no—
454C24—22no—
455C24—24no—
456C24—24no—
457C24—24no—
458C24—24no—
459C24—22no—
460C24—24no—
461C24—24no—
462C24—22no—
463C24C22×D418yes—
464C24C22×D414yes—
465C24C22×D412yes—
466C24C2×#4112yes—
467C24C2511yescharacteristic
468#41—4256no—
469C2×Q8—216no—
470C2×Q8—416no—
471C2×Q8—416no—
472C2×Q8—48no—
473C2×Q8—48no—
474C2×D4—216no—
475C2×D4—216no—
476C2×D4—28no—
477C2×D4—232no—
478C2×D4—216no—
479C2×D4—416no—
480C2×D4—416no—
481C2×D4—416no—
482C2×D4—416no—
483C2×D4—416no—
484C2×D4—416no—
485C2×D4—416no—
486C2×D4—48no—
487C2×D4—416no—
488C2×D4—416no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—416no—
492C2×D4—416no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—416no—
497C2×D4—416no—
498C2×D4—44no—
499C2×D4—416no—
500C2×D4—416no—
501C2×D4—416no—
502C2×D4—416no—
503C2×D4—416no—
504C2×D4—416no—
505C2×D4—44no—
506C2×D4—48no—
507C2×D4—48no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—232no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—232no—
551C22×C4—28no—
552C22×C4—28no—
553C22×C4—232no—
554C22×C4—232no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—416no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—416no—
584C22×C4—416no—
585C22×C4—416no—
586C22×C4—416no—
587C22×C4—44no—
588C22×C4—416no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4#120116yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D418yes—
595C22×C4C22×D414yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D414yes—
600C22×C4C22×D412yes—
601C22×C4C2×#4118yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4C2×#4112yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4114yes—
608C22×C4H(5,𝔽2)14yes—
609C22×C4H(5,𝔽2)14yes—
610C4⋊C4—216no—
611C4⋊C4—216no—
612C4⋊C4—28no—
613C4⋊C4—28no—
614C4⋊C4—44no—
615C4⋊C4—416no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C22⋊C4—232no—
619C22⋊C4—232no—
620C22⋊C4—28no—
621C22⋊C4—28no—
622C22⋊C4—28no—
623C22⋊C4—416no—
624C22⋊C4—416no—
625C22⋊C4—416no—
626C22⋊C4—416no—
627C22⋊C4—44no—
628C22⋊C4—416no—
629C22⋊C4—416no—
630C22⋊C4—416no—
631C22⋊C4—44no—
632C22⋊C4—416no—
633C22⋊C4—416no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—44no—
637C42—28no—
638C42—28no—
639C42—28no—
640C42—28no—
641C42—44no—
642C42—416no—
643C42—44no—
644C42—44no—
645C23—22no—
646C23—22no—
647C23—28no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—28no—
653C23—24no—
654C23—24no—
655C23—28no—
656C23—22no—
657C23—28no—
658C23—28no—
659C23—24no—
660C23—28no—
661C23—28no—
662C23—24no—
663C23—28no—
664C23—28no—
665C23—24no—
666C23—42no—
667C23—42no—
668C23—44no—
669C23—42no—
670C23—42no—
671C23—44no—
672C23—41no—
673C23—44no—
674C23—41no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—44no—
685C23—41no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—42no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—42no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—42no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23C2×#12014yes—
714C23C23×D411yescharacteristic
715C23C23×D412yes—
716C23C22×#4111yescharacteristic
717C23C22×#4111yescharacteristic
718C23C22×#4112yes—
719C23C2×H(5,𝔽2)12yes—
720C23C2×H(5,𝔽2)12yes—
721C23#58512yes—
722C23#58512yes—
723Q8—432no—
724D4—432no—
725D4—432no—
726D4—432no—
727D4—416no—
728D4—464no—
729D4—464no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—28no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—28no—
740C2×C4—232no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—28no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—28no—
750C2×C4—28no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—28no—
755C2×C4—24no—
756C2×C4—28no—
757C2×C4—24no—
758C2×C4—28no—
759C2×C4—416no—
760C2×C4—416no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—44no—
781C2×C4—464no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—88no—
806C2×C4C2×#12014yes—
807C2×C4C2×#12014yes—
808C2×C4#52514yes—
809C2×C4#53214yes—
810C2×C4#534116yes—
811C2×C4#53514yes—
812C2×C4#53514yes—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—48no—
821C22—48no—
822C22—42no—
823C22—42no—
824C22—48no—
825C22—42no—
826C22—48no—
827C22—48no—
828C22—48no—
829C22—48no—
830C22—48no—
831C22—48no—
832C22—48no—
833C22—84no—
834C22—81no—
835C22—84no—
836C22—84no—
837C22—81no—
838C22—84no—
839C22—81no—
840C22—84no—
841C22—84no—
842C22—84no—
843C22—84no—
844C22—84no—
845C22—81no—
846C22C22×#12011yescharacteristic
847C22C2×#52511yescharacteristic
848C22C2×#53211yescharacteristic
849C22C2×#53414yes—
850C22C2×#53511yescharacteristic
851C22C2×#53511yescharacteristic
852C22#344911yescharacteristic
853C22#344911yescharacteristic
854C22#346012yes—
855C22#346012yes—
856C22#346014yes—
857C22D4×#4112yes—
858C22D4×#4112yes—
859C22D4×#4114yes—
860C22#348112yes—
861C22#348312yes—
862C22#352914yes—
863C4—24no—
864C4—24no—
865C4—24no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—48no—
872C4—48no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4—84no—
877C4—81no—
878C4#261318yes—
879C2—44no—
880C2—82no—
881C2—88no—
882C2C2×#261311yescharacteristic
883C2#3460911yescharacteristic
884C2#3462411yescharacteristic
885C2#3473611yescharacteristic
886C2#3473811yescharacteristic
887C2#3497711yescharacteristic
888C2#3668711yescharacteristic
889C2#5216514yes—
890C2#5216714yes—
subgroupG/H
centerC23×C4C24
commutator, Frattini, socle, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C23×C4 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#532C2semidirect
2. C2×#2388C2semidirect
3. C2×C4×#123C2semidirect
4. #16681C2semidirect
5. #16680C2semidirect
6. #16603C2semidirect
7. #16602C2semidirect
8. #16503C2semidirect
9. #16502C2semidirect
10. #16361C2semidirect
11. #16259C2semidirect
12. #16258C2semidirect
13. #16250C2semidirect
14. C4×#394C2semidirect
15. C4×#394C2semidirect
16. C4×#392C2semidirect
17. C4×#392C2semidirect
18. #13851C2semidirect
19. C4×#381C2semidirect
99. C22×#41D4semidirect
164. C22×C42D4semidirect
339. C2×C4⋊C4#41semidirect
391. C2×C22⋊C4#41semidirect
433. #95#41semidirect

Maximal subgroups

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

subgroupindex
C22×#5322
C2×#23882
C2×C4×#1232
#166812
#166802
#166032
#166022
#165032
#165022
#163612
#162592
#162582
#162502
C4×#3942
C4×#3922
#138512
C4×#3812