Finite Group Databasebeta

← #686586

Subgroups — #686586

Order 512.

5062 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#537C211yesmaximal, characteristic
2C2×#2423C212yesmaximal, complemented
3C2×#2341C211yesmaximal, characteristic, complemented
4#16365C212yesmaximal, complemented
5#16363C212yesmaximal, complemented
6#15340C214yesmaximal, complemented
7#15338C214yesmaximal, complemented
8#15130C212yesmaximal, complemented
9#15126C212yesmaximal, complemented
10#15001C212yesmaximal, complemented
11#14996C212yesmaximal, complemented
12#14337C211yesmaximal, characteristic, complemented
13#14130C211yesmaximal, characteristic, complemented
14#13969C212yesmaximal, complemented
15#13937C211yesmaximal, characteristic, complemented
16#13880C211yesmaximal, characteristic, complemented
17#13851C211yesmaximal, characteristic, complemented
18C23×#41C2211yescharacteristic
19C23×#41C2211yescharacteristic
20C2×#537—28no—
21C2×#537—216no—
22C22×C22⋊Q8C2212yes—
23C22×C22⋊Q8C2212yes—
24C22×#121C2212yes—
25C22×#121C2212yes—
26C22×#121C2214yes—
27C22×C4×Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30#2423—216no—
31C2×#399C2214yes—
32C2×#398C2214yes—
33C2×#394C2214yes—
34C2×#394C2214yes—
35C2×#394C2214yes—
36#2341—28no—
37C2×#391C2212yes—
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2212yes—
41C2×#390C2212yes—
42C2×#390C2212yes—
43C2×#389C2212yes—
44C2×#388C2214yes—
45C2×#387C2214yes—
46C2×#385C2212yes—
47C2×#385C2214yes—
48C2×#384C2212yes—
49C2×#380C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×C4×C22⋊C4C2212yes—
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2212yes—
58C2×C4×C22⋊C4C2212yes—
59#1446C2212yes—
60#1446C2211yescharacteristic
61#1446C2211yescharacteristic
62#1444C2212yes—
63#1444C2212yes—
64#1444C2212yes—
65#1442C2212yes—
66#1441C2214yes—
67#1440C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1438C2212yes—
73#1438C2214yes—
74#1438C2214yes—
75#1438C2211yescharacteristic
76#1438C2212yes—
77#1438C2211yescharacteristic
78#1438C2212yes—
79#1438C2214yes—
80#1437C2214yes—
81#1436C2214yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C22×#41—28no—
88C22×#41—28no—
89C22×#41—24no—
90C22×#41—24no—
91C22×#41—24no—
92C22×#41—24no—
93C22×#41—24no—
94C22×#41—44no—
95C22×#41—44no—
96C22×#41D418yes—
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×D4C2311yescharacteristic
100C23×D4C2312yes—
101C23×D4C2311yescharacteristic
102C23×D4C2312yes—
103C23×D4C2314yes—
104C24×C4C2312yes—
105C24×C4C2312yes—
106C24×C4C2311yescharacteristic
107C24×C4C2312yes—
108#537—2128no—
109C2×C22⋊Q8—28no—
110C2×C22⋊Q8—28no—
111C2×C22⋊Q8—28no—
112C2×C22⋊Q8—216no—
113C2×C22⋊Q8D4116yes—
114C2×#121—28no—
115C2×#121—216no—
116C2×#121—28no—
117C2×#121—28no—
118C2×#121—28no—
119C2×#121—216no—
120C2×#121—216no—
121C2×#121—216no—
122C2×C4×Q8—24no—
123C2×C4×Q8—24no—
124C2×C4×Q8—28no—
125C2×C4×Q8—44no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—28no—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2312yes—
161C22×C42C2312yes—
162C22×C42C2312yes—
163#399—216no—
164#398—216no—
165#394—48no—
166#394—48no—
167#394—48no—
168#391—28no—
169#390—24no—
170#390—24no—
171#390—28no—
172#390—28no—
173#390—44no—
174#389—28no—
175#388—216no—
176#387—216no—
177#385—44no—
178#385—48no—
179#384—28no—
180#380—28no—
181#380—24no—
182#380—28no—
183#380—24no—
184#380—44no—
185C4×C22⋊C4—28no—
186C4×C22⋊C4—24no—
187C4×C22⋊C4—28no—
188C4×C22⋊C4—24no—
189C4×C22⋊C4—44no—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2311yescharacteristic
198C2×#95C2311yescharacteristic
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2311yescharacteristic
202C2×#95C2312yes—
203C2×#95C2311yescharacteristic
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C25C2412yes—
210C25C2412yes—
211C25C2411yescharacteristic
212C2×#41—232no—
213C2×#41—232no—
214C2×#41—232no—
215C2×#41—432no—
216C2×#41—432no—
217C2×#41—416no—
218C2×#41—432no—
219C2×#41—432no—
220C2×#41—416no—
221C2×#41—416no—
222C22×Q8—24no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—24no—
229C22×Q8—42no—
230C22×Q8C2×D414yes—
231C22×Q8C2×D418yes—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—28no—
238C22×D4—28no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—28no—
243C22×D4—22no—
244C22×D4—24no—
245C22×D4—28no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—24no—
251C22×D4—44no—
252C22×D4—42no—
253C22×D4—42no—
254C22×D4—42no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4C2×D414yes—
260C22×D4C2×D418yes—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—28no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—28no—
274C23×C4—44no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—44no—
278C23×C4C2×D418yes—
279C23×C4C2×D418yes—
280C23×C4C2×D414yes—
281C23×C4#4114yes—
282C23×C4#4114yes—
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2414yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2414yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C22⋊Q8—264no—
298C22⋊Q8—264no—
299#121—264no—
300#121—2128no—
301#121—264no—
302C4×Q8—416no—
303C4×Q8—416no—
304C2×C4⋊C4—232no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4C2×D418yes—
332C2×C4⋊C4C2×D4116yes—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—22no—
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—24no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4C2×D4116yes—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—28no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—44no—
398#95—22no—
399#95—24no—
400#95—22no—
401#95—24no—
402#95—24no—
403#95—28no—
404#95—28no—
405#95—28no—
406#95—28no—
407#95—22no—
408#95—22no—
409#95—24no—
410#95—28no—
411#95—28no—
412#95—42no—
413#95—42no—
414#95—44no—
415#95—44no—
416#95—44no—
417C24—22no—
418C24—21no—
419C24—22no—
420C24—22no—
421C24—21no—
422C24—22no—
423C24—21no—
424C24—21no—
425C24—22no—
426C24—22no—
427C24—24no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—24no—
437C24—22no—
438C24—22no—
439C24—24no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—24no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24C22×D414yes—
450C24C22×D414yes—
451C24C22×D412yes—
452C24C2×#4112yes—
453C24C2×#4112yes—
454C24C2511yescharacteristic
455#41—4128no—
456#41—4128no—
457C2×Q8—28no—
458C2×Q8—28no—
459C2×Q8—28no—
460C2×Q8—216no—
461C2×Q8—216no—
462C2×Q8—48no—
463C2×Q8—48no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×Q8#120116yes—
467C2×D4—28no—
468C2×D4—216no—
469C2×D4—216no—
470C2×D4—232no—
471C2×D4—216no—
472C2×D4—28no—
473C2×D4—28no—
474C2×D4—28no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—416no—
479C2×D4—416no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—44no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—44no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—88no—
491C2×D4—88no—
492C2×D4—88no—
493C2×D4—88no—
494C2×D4—88no—
495C2×D4—88no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—216no—
504C22×C4—216no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—216no—
538C22×C4—216no—
539C22×C4—216no—
540C22×C4—216no—
541C22×C4—216no—
542C22×C4—216no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—48no—
571C22×C4—416no—
572C22×C4—416no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—88no—
578C22×C4—88no—
579C22×C4—84no—
580C22×C4—84no—
581C22×C4#123116yes—
582C22×C4C22×D414yes—
583C22×C4C22×D418yes—
584C22×C4C22×D418yes—
585C22×C4C22×D414yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D414yes—
589C22×C4C2×#4112yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4112yes—
593C22×C4H(5,𝔽2)12yes—
594C22×C4H(5,𝔽2)14yes—
595C22×C4H(5,𝔽2)14yes—
596C22×C42−1+412yes—
597C22×C42−1+414yes—
598C4⋊C4—216no—
599C4⋊C4—216no—
600C4⋊C4—232no—
601C4⋊C4—416no—
602C4⋊C4—48no—
603C4⋊C4—48no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—48no—
607C4⋊C4—88no—
608C4⋊C4—88no—
609C22⋊C4—216no—
610C22⋊C4—216no—
611C22⋊C4—232no—
612C22⋊C4—232no—
613C22⋊C4—48no—
614C22⋊C4—44no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—44no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—88no—
622C22⋊C4—88no—
623C22⋊C4—84no—
624C22⋊C4—84no—
625C22⋊C4—84no—
626C22⋊C4—88no—
627C22⋊C4—88no—
628C42—48no—
629C42—48no—
630C42—44no—
631C42—44no—
632C42—48no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—22no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—44no—
676C23—42no—
677C23—44no—
678C23—42no—
679C23—42no—
680C23—44no—
681C23—42no—
682C23—44no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—44no—
688C23—42no—
689C23—44no—
690C23—42no—
691C23—44no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—44no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—44no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—44no—
707C23—42no—
708C23—42no—
709C23—44no—
710C23—42no—
711C23—42no—
712C23—44no—
713C23C2×#12314yes—
714C23C23×D411yescharacteristic
715C23C23×D412yes—
716C23C22×#4111yescharacteristic
717C23C22×#4111yescharacteristic
718C23C2×H(5,𝔽2)12yes—
719C23C2×H(5,𝔽2)11yescharacteristic
720C23C2×H(5,𝔽2)12yes—
721C23C2×2−1+411yescharacteristic
722C23C2×2−1+412yes—
723C23#58511yescharacteristic
724C23#58511yescharacteristic
725Q8—232no—
726Q8—416no—
727D4—432no—
728D4—416no—
729D4—432no—
730D4—416no—
731D4—832no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—28no—
739C2×C4—28no—
740C2×C4—232no—
741C2×C4—28no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—28no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—28no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—432no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—432no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—44no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—816no—
809C2×C4C2×#12018yes—
810C2×C4C2×#12014yes—
811C2×C4C2×#12314yes—
812C2×C4C2×#12314yes—
813C2×C4#53414yes—
814C2×C4#54618yes—
815C2×C4#54618yes—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—44no—
820C22—42no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—84no—
842C22—82no—
843C22—82no—
844C22—84no—
845C22—82no—
846C22—84no—
847C22—82no—
848C22—84no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22C22×#12011yescharacteristic
854C22C22×#12311yescharacteristic
855C22C2×#53411yescharacteristic
856C22#346011yescharacteristic
857C22#346111yescharacteristic
858C22C2×#54612yes—
859C22C2×#54612yes—
860C22#348612yes—
861C22#348812yes—
862C22#348811yescharacteristic
863C22#348911yescharacteristic
864C22#349212yes—
865C22#349712yes—
866C22#349812yes—
867C22#349811yescharacteristic
868C22#349911yescharacteristic
869C22#351112yes—
870C22#351111yescharacteristic
871C22#351211yescharacteristic
872C22#353612yes—
873C22#354212yes—
874C22#354712yes—
875C22#354812yes—
876C4—24no—
877C4—28no—
878C4—44no—
879C4—42no—
880C4—44no—
881C4—44no—
882C4—42no—
883C4—48no—
884C4—84no—
885C4—81no—
886C4—82no—
887C4—81no—
888C4—82no—
889C4#240518yes—
890C2—44no—
891C2—84no—
892C2—84no—
893C2C2×#240511yescharacteristic
894C2#3525511yescharacteristic
895C2#3553011yescharacteristic
896C2#3568711yescharacteristic
897C2#3609111yescharacteristic
898C2#3778112yes—
899C2#3943312yes—
900C2#4290911yescharacteristic
901C2#4298411yescharacteristic
902C2#4491312yes—
903C2#4491512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#537C2
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×#2423C2semidirect
3. C2×#2341C2semidirect
4. #16365C2semidirect
5. #16363C2semidirect
6. #15340C2semidirect
7. #15338C2semidirect
8. #15130C2semidirect
9. #15126C2semidirect
10. #15001C2semidirect
11. #14996C2semidirect
12. #14337C2semidirect
13. #14130C2semidirect
14. #13969C2semidirect
15. #13937C2semidirect
16. #13880C2semidirect
17. #13851C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5372
C2×#24232
C2×#23412
#163652
#163632
#153402
#153382
#151302
#151262
#150012
#149962
#143372
#141302
#139692
#139372
#138802
#138512