Finite Group Databasebeta

← #4306539

Subgroups — #4306539

Order 512.

4866 conjugacy classes of subgroups.

The subgroup lattice has 907 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#555C211yesmaximal, characteristic, complemented
2C2×#2366C211yesmaximal, characteristic, complemented
3C2×#2363C212yesmaximal, complemented
4#15144C211yesmaximal, characteristic, complemented
5#15128C211yesmaximal, characteristic, complemented
6#15126C212yesmaximal, complemented
7#15124C212yesmaximal, complemented
8#15123C211yesmaximal, characteristic, complemented
9#15113C212yesmaximal, complemented
10#14928C214yesmaximal, complemented
11#14915C214yesmaximal, complemented
12#14762C212yesmaximal, complemented
13#14722C212yesmaximal, complemented
14C4×#394C211yesmaximal, characteristic, complemented
15#13839C212yesmaximal, complemented
16#13820C211yesmaximal, characteristic, complemented
17#13801C212yesmaximal, complemented
18C2×#555—28no—
19C2×#555—216no—
20C22×C4⋊Q8C2211yescharacteristic
21C22×#127C2211yescharacteristic
22C22×#124C2214yes—
23C22×#121C2212yes—
24C22×#121C2212yes—
25C22×#121C2212yes—
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2212yes—
29C22×C4×D4C2211yescharacteristic
30C22×#117C2212yes—
31C22×#117C2212yes—
32C2×#395C2212yes—
33C2×#394C2211yescharacteristic
34C2×#394C2214yes—
35C2×#393C2214yes—
36C2×#392C2212yes—
37C2×#392C2214yes—
38C2×#392C2214yes—
39#2366—28no—
40#2363—216no—
41C2×#390C2211yescharacteristic
42C2×#390C2212yes—
43C2×#390C2212yes—
44C2×#390C2211yescharacteristic
45C2×#390C2212yes—
46C2×#390C2214yes—
47C2×#389C2212yes—
48C2×#388C2214yes—
49C2×#386C2212yes—
50C2×#386C2212yes—
51C2×#386C2214yes—
52C2×#380C2212yes—
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C4⋊C4C2212yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2214yes—
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yes—
60#1446C2212yes—
61#1444C2212yes—
62#1442C2211yescharacteristic
63#1441C2211yescharacteristic
64#1441C2212yes—
65#1440C2214yes—
66#1440C2212yes—
67#1439C2212yes—
68#1439C2214yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2212yes—
72#1438C2214yes—
73#1438C2214yes—
74#1438C2214yes—
75#1438C2214yes—
76#1438C2211yescharacteristic
77#1437C2214yes—
78#1437C2214yes—
79#1437C2214yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83#1434C2214yes—
84C22⋊#95C2212yes—
85C4×#95C2214yes—
86C4×#95C2211yescharacteristic
87C23×Q8C2312yes—
88C23×D4C2311yescharacteristic
89C23×D4C2311yescharacteristic
90C23×D4C2311yescharacteristic
91C23×D4C2312yes—
92C23×D4C2314yes—
93C23×D4C2314yes—
94C23×D4C2312yes—
95C24×C4C2312yes—
96C24×C4C2312yes—
97C24×C4C2312yes—
98#555—2128no—
99C2×C4⋊Q8—28no—
100C2×C4⋊Q8—24no—
101C2×#127—24no—
102C2×#127—24no—
103C2×#127—24no—
104C2×#124—216no—
105C2×#124—216no—
106C2×#124—216no—
107C2×#121—28no—
108C2×#121—28no—
109C2×#121—28no—
110C2×#121—28no—
111C2×#121—28no—
112C2×#121—28no—
113C2×#121—28no—
114C2×#121—216no—
115C2×C4×D4—28no—
116C2×C4×D4—28no—
117C2×C4×D4—28no—
118C2×C4×D4—28no—
119C2×C4×D4—24no—
120C2×C4×D4—28no—
121C2×C4×D4—24no—
122C2×C4×D4—44no—
123C2×C4×D4D418yescomplemented
124C2×#117—28no—
125C2×#117—28no—
126C2×#117—28no—
127C2×#117—216no—
128C2×#117D4116yescomplemented
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2314yes—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2314yes—
164#395—44no—
165#394—24no—
166#394—48no—
167#393—48no—
168#392—44no—
169#392—48no—
170#392—48no—
171#390—24no—
172#390—28no—
173#390—28no—
174#390—216no—
175#390—28no—
176#390—24no—
177#389—28no—
178#388—216no—
179#386—28no—
180#386—216no—
181#386—28no—
182#380—28no—
183C4×C4⋊C4—28no—
184C4×C4⋊C4—24no—
185C4×C4⋊C4—24no—
186C4×C22⋊C4—28no—
187C4×C22⋊C4—216no—
188C4×C22⋊C4—28no—
189C4×C22⋊C4—44no—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2311yescharacteristic
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2311yescharacteristic
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2311yescharacteristic
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2311yescharacteristic
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C25C2412yes—
210C25C2412yes—
211C25C2412yes—
212C22×Q8—28no—
213C22×Q8—24no—
214C22×Q8—42no—
215C22×Q8—44no—
216C22×Q8—42no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—28no—
221C22×D4—28no—
222C22×D4—28no—
223C22×D4—24no—
224C22×D4—28no—
225C22×D4—24no—
226C22×D4—22no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—22no—
230C22×D4—28no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—24no—
237C22×D4—28no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—24no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4C2×D414yes—
257C22×D4#4114yes—
258C23×C4—28no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—28no—
270C23×C4—44no—
271C23×C4—42no—
272C23×C4—44no—
273C23×C4C2×D418yes—
274C23×C4C2×D418yes—
275C23×C4C2411yescharacteristic
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2412yes—
280C23×C4C2414yes—
281C23×C4C2414yes—
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C4⋊Q8—232no—
290#127—232no—
291#124—2128no—
292#121—264no—
293#121—264no—
294#121—264no—
295C4×D4—232no—
296C4×D4—232no—
297C4×D4—432no—
298C4×D4—416no—
299#117—264no—
300#117—264no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—41no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4C2×D418yes—
320C2×C4⋊C4C2×D414yes—
321C2×C4⋊C4C2×D418yes—
322C2×C4⋊C4#4114yes—
323C2×C4⋊C4#4118yes—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4C2×D4116yes—
376C2×C22⋊C4C2×D418yes—
377C2×C42—28no—
378C2×C42—28no—
379C2×C42—24no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—28no—
390C2×C42—42no—
391C2×C42—44no—
392C2×C42—44no—
393C2×C42C2×D4116yes—
394C2×C42C2×D414yes—
395C2×C42#4114yes—
396#95—24no—
397#95—28no—
398#95—24no—
399#95—22no—
400#95—24no—
401#95—22no—
402#95—28no—
403#95—24no—
404#95—24no—
405#95—28no—
406#95—22no—
407#95—22no—
408#95—24no—
409#95—28no—
410#95—24no—
411#95—28no—
412#95—44no—
413#95—44no—
414#95—42no—
415C24—24no—
416C24—22no—
417C24—22no—
418C24—24no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—24no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—24no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—24no—
434C24—24no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—24no—
445C24—22no—
446C24—24no—
447C24—22no—
448C24—22no—
449C24C22×D414yes—
450C24C22×D414yes—
451C24C2×#4114yes—
452C24C2511yescharacteristic
453C2×Q8—216no—
454C2×Q8—88no—
455C2×Q8—84no—
456C2×Q8—84no—
457C2×Q8—88no—
458C2×D4—28no—
459C2×D4—216no—
460C2×D4—232no—
461C2×D4—232no—
462C2×D4—216no—
463C2×D4—28no—
464C2×D4—216no—
465C2×D4—28no—
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—44no—
475C2×D4—48no—
476C2×D4—44no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—48no—
483C2×D4—88no—
484C2×D4—88no—
485C2×D4—88no—
486C2×D4—88no—
487C2×D4—88no—
488C2×D4—84no—
489C2×D4—88no—
490C2×D4—88no—
491C2×D4—88no—
492C2×D4—88no—
493C2×D4—84no—
494C2×D4—88no—
495C2×D4—88no—
496C2×D4—88no—
497C2×D4—88no—
498C2×D4—88no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—21no—
544C22×C4—216no—
545C22×C4—216no—
546C22×C4—216no—
547C22×C4—216no—
548C22×C4—216no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—48no—
567C22×C4—416no—
568C22×C4—416no—
569C22×C4—48no—
570C22×C4—416no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—84no—
577C22×C4—88no—
578C22×C4C22×D414yes—
579C22×C4C22×D412yes—
580C22×C4C22×D418yes—
581C22×C4C22×D414yes—
582C22×C4C22×D418yes—
583C22×C4C22×D412yes—
584C22×C4C22×D414yes—
585C22×C4C22×D412yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4118yes—
588C22×C4C2×#4112yes—
589C22×C4C2×#4112yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4114yes—
595C22×C4H(5,𝔽2)14yes—
596C22×C4H(5,𝔽2)12yes—
597C22×C4H(5,𝔽2)12yes—
598C4⋊C4—28no—
599C4⋊C4—216no—
600C4⋊C4—216no—
601C4⋊C4—216no—
602C4⋊C4—28no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—88no—
606C4⋊C4#120116yes—
607C22⋊C4—232no—
608C22⋊C4—216no—
609C22⋊C4—232no—
610C22⋊C4—232no—
611C22⋊C4—216no—
612C22⋊C4—416no—
613C22⋊C4—48no—
614C22⋊C4—416no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—84no—
622C22⋊C4—88no—
623C22⋊C4—88no—
624C22⋊C4—88no—
625C22⋊C4—84no—
626C42—232no—
627C42—28no—
628C42—28no—
629C42—48no—
630C42—44no—
631C42—48no—
632C42—88no—
633C23—24no—
634C23—24no—
635C23—28no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—28no—
651C23—24no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—44no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—44no—
660C23—44no—
661C23—42no—
662C23—42no—
663C23—44no—
664C23—44no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—44no—
672C23—42no—
673C23—44no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—44no—
685C23—42no—
686C23—44no—
687C23—44no—
688C23—42no—
689C23—44no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—44no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—44no—
698C23—42no—
699C23—42no—
700C23—44no—
701C23—44no—
702C23—42no—
703C23—42no—
704C23—44no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—44no—
710C23—44no—
711C23—42no—
712C23—44no—
713C23—42no—
714C23C23×D411yescharacteristic
715C23C23×D412yes—
716C23C22×#4111yescharacteristic
717C23C22×#4111yescharacteristic
718C23C22×#4112yes—
719C23C22×#4111yescharacteristic
720C23C2×H(5,𝔽2)11yescharacteristic
721C23C2×H(5,𝔽2)11yescharacteristic
722C23C2×H(5,𝔽2)12yes—
723C23#58512yes—
724C23#58511yescharacteristic
725Q8—816no—
726D4—432no—
727D4—416no—
728D4—416no—
729D4—416no—
730D4—832no—
731D4—816no—
732D4—832no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—28no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—28no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—28no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—28no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—28no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—28no—
763C2×C4—28no—
764C2×C4—24no—
765C2×C4—28no—
766C2×C4—432no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—44no—
782C2×C4—41no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—432no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—816no—
810C2×C4C2×#12018yes—
811C2×C4C2×#12014yes—
812C2×C4#52514yes—
813C2×C4#52518yes—
814C2×C4#53218yes—
815C2×C4#53214yes—
816C2×C4#54614yes—
817C2×C4#55514yescomplemented
818C22—44no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—48no—
824C22—44no—
825C22—44no—
826C22—48no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—84no—
843C22—82no—
844C22—84no—
845C22—82no—
846C22—84no—
847C22—84no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—84no—
853C22—84no—
854C22—82no—
855C22C22×#12011yescharacteristic
856C22C2×#52511yescharacteristic
857C22C2×#52512yes—
858C22C2×#53211yescharacteristic
859C22C2×#53212yes—
860C22C2×#54611yescharacteristic
861C22D4×#4112yes—
862C22C2×#55511yescharacteristic
863C22#347511yescharacteristic
864C22#348312yes—
865C22#348511yescharacteristic
866C22#348811yescharacteristic
867C22#348812yes—
868C22#348812yes—
869C22#349412yes—
870C22#349811yescharacteristic
871C22#349812yes—
872C22#350611yescharacteristic
873C22#351412yes—
874C22#351412yes—
875C22#351912yes—
876C22#351911yescharacteristic
877C22#352412yes—
878C4—24no—
879C4—24no—
880C4—28no—
881C4—42no—
882C4—48no—
883C4—42no—
884C4—44no—
885C4—44no—
886C4—48no—
887C4—42no—
888C4—82no—
889C4—82no—
890C4—81no—
891C4#238818yes—
892C2—84no—
893C2—84no—
894C2—84no—
895C2C2×#238811yescharacteristic
896C2#3583012yes—
897C2#3600412yes—
898C2#3602211yescharacteristic
899C2#3605111yescharacteristic
900C2#3609111yescharacteristic
901C2#3616011yescharacteristic
902C2#3621211yescharacteristic
903C2#3623112yes—
904C2#3627312yes—
905C2#3641211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#555C2semidirect
2. C2×#2366C2semidirect
3. C2×#2363C2semidirect
4. #15144C2semidirect
5. #15128C2semidirect
6. #15126C2semidirect
7. #15124C2semidirect
8. #15123C2semidirect
9. #15113C2semidirect
10. #14928C2semidirect
11. #14915C2semidirect
12. #14762C2semidirect
13. #14722C2semidirect
14. C4×#394C2semidirect
15. #13839C2semidirect
16. #13820C2semidirect
17. #13801C2semidirect
123. C2×C4×D4D4semidirect
128. C2×#117D4semidirect
817. C2×C4#555semidirect

Maximal subgroups

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

subgroupindex
C22×#5552
C2×#23662
C2×#23632
#151442
#151282
#151262
#151242
#151232
#151132
#149282
#149152
#147622
#147222
C4×#3942
#138392
#138202
#138012