Finite Group Databasebeta

← #875311

Subgroups — #875311

Order 512.

3022 conjugacy classes of subgroups.

The subgroup lattice has 877 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2562C211yesmaximal, characteristic
2C2×#2409C211yesmaximal, characteristic
3#16874C214yesmaximal, complemented
4#15586C214yesmaximal, complemented
5#15494C214yesmaximal
6#15238C211yesmaximal, characteristic, complemented
7#15238C211yesmaximal, characteristic, complemented
8#15236C211yesmaximal, characteristic, complemented
9#15233C211yesmaximal, characteristic, complemented
10#15182C211yesmaximal, characteristic, complemented
11#15150C211yesmaximal, characteristic, complemented
12#14702C211yesmaximal, characteristic, complemented
13#14702C211yesmaximal, characteristic, complemented
14#14525C214yesmaximal, complemented
15#14003C211yesmaximal, characteristic, complemented
16#14000C211yesmaximal, characteristic, complemented
17#13922C211yesmaximal, characteristic, complemented
18#13922C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2562—28no—
27#2409—28no—
28C2×#400C2212yes—
29C2×#397C2214yes—
30C2×#395C2212yes—
31C2×#394C2212yes—
32C2×#393C2212yes—
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#388C2212yes—
44C2×#388C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#385C2212yes—
48C2×#384C2211yescharacteristic
49C2×#382C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59#1446C2214yes—
60#1446C2214yes—
61#1445C2214yes—
62#1443C2214yes—
63#1443C2214yes—
64#1442C2214yes—
65#1442C2214yes—
66#1442C2214yes—
67#1442C2214yes—
68#1442C2214yes—
69#1442C2214yes—
70#1441C2214yes—
71#1440C2214yes—
72#1440C2214yes—
73#1439C2214yes—
74#1437C2212yes—
75#1436C2214yes—
76#1436C2214yes—
77#1436C2214yes—
78#1436C2212yes—
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85#1434C2214yes—
86C22⋊#95C2214yes—
87C22⋊#95C2214yes—
88C22⋊#95C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2212yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8—24no—
94C23×Q8—24no—
95C23×Q8—24no—
96C23×Q8—42no—
97C23×Q8—42no—
98C23×Q8—42no—
99C23×Q8—42no—
100C23×Q8C2311yescharacteristic
101C23×Q8C2311yescharacteristic
102C23×Q8C2312yes—
103C23×D4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2312yes—
107C24×C4C2312yes—
108C2×#125—24no—
109C2×#125—42no—
110C2×#125—42no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—42no—
116C2×C22⋊Q8—42no—
117C2×C4×D4—42no—
118C2×C4×D4—42no—
119C2×C4×D4D418yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2312yes—
144C22×C42—42no—
145C22×C42—42no—
146C22×C42—42no—
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2312yes—
153C22×C42C2312yes—
154#400—28no—
155#397—216no—
156#395—28no—
157#394—28no—
158#393—28no—
159#391—24no—
160#391—24no—
161#391—24no—
162#391—24no—
163#391—42no—
164#391—42no—
165#391—42no—
166#391—42no—
167#391—42no—
168#391—42no—
169#388—28no—
170#388—28no—
171#386—28no—
172#386—28no—
173#385—28no—
174#384—42no—
175#382—42no—
176#380—24no—
177#380—24no—
178#380—24no—
179#380—24no—
180#380—24no—
181C4×C4⋊C4—24no—
182C4×C22⋊C4—42no—
183C4×C22⋊C4—42no—
184C4×C22⋊C4—42no—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C25C2411yescharacteristic
218C25C2411yescharacteristic
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—24no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—24no—
225C22×Q8—24no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—42no—
235C22×Q8—42no—
236C22×Q8—42no—
237C22×Q8—42no—
238C22×Q8—416no—
239C22×Q8—416no—
240C22×Q8—416no—
241C22×Q8—416no—
242C22×Q8—416no—
243C22×Q8—416no—
244C22×Q8—416no—
245C22×Q8#4114yes—
246C22×Q8#4114yes—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—41no—
250C22×D4—41no—
251C22×D4C2×D414yes—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4C2×D414yes—
279C23×C4C2×D414yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2411yescharacteristic
297#125—416no—
298C22⋊Q8—416no—
299C22⋊Q8—416no—
300C4×D4—416no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—41no—
327C2×C4⋊C4—41no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4C2×D414yes—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4C2×D414yes—
366C2×C22⋊C4C2×D414yes—
367C2×C22⋊C4#4118yes—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—42no—
384C2×C42—42no—
385C2×C42—42no—
386C2×C42—416no—
387C2×C42—44no—
388C2×C42C2×D414yes—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—28no—
402#95—28no—
403#95—28no—
404#95—28no—
405#95—28no—
406#95—24no—
407#95—28no—
408#95—44no—
409#95—42no—
410#95—44no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95—44no—
419#95—44no—
420#95—44no—
421C24—21no—
422C24—21no—
423C24—22no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24C22×D412yes—
440C24C22×D412yes—
441C24C2×#4114yes—
442C242−1+414yes—
443C24C2511yescharacteristic
444C2×Q8—28no—
445C2×Q8—28no—
446C2×Q8—28no—
447C2×Q8—28no—
448C2×Q8—28no—
449C2×Q8—28no—
450C2×Q8—48no—
451C2×Q8—48no—
452C2×Q8—48no—
453C2×Q8—48no—
454C2×Q8—48no—
455C2×Q8—48no—
456C2×Q8—4128no—
457C2×Q8—48no—
458C2×Q8—44no—
459C2×Q8—44no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—44no—
469C2×D4—48no—
470C2×D4—48no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C2×#4114yes—
592C22×C4C2×#4114yes—
593C22×C4C2×#4114yes—
594C22×C4C2×#4114yes—
595C22×C4C2×#4112yes—
596C22×C4C2×#4112yes—
597C22×C4H(5,𝔽2)12yes—
598C22×C4H(5,𝔽2)12yes—
599C22×C4H(5,𝔽2)12yes—
600C22×C4H(5,𝔽2)12yes—
601C22×C42−1+414yes—
602C4⋊C4—44no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—88no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—84no—
625C22⋊C4—84no—
626C42—28no—
627C42—48no—
628C42—44no—
629C42—44no—
630C42—44no—
631C42—44no—
632C42—84no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—24no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—41no—
670C23—41no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23#53214yes—
678C23#53614yes—
679C23C23×D411yescharacteristic
680C23C22×#4112yes—
681C23C22×#4111yescharacteristic
682C23C22×#4111yescharacteristic
683C23C2×H(5,𝔽2)11yescharacteristic
684C23C2×H(5,𝔽2)11yescharacteristic
685C23C2×H(5,𝔽2)11yescharacteristic
686C23C2×H(5,𝔽2)11yescharacteristic
687C23C2×2−1+412yes—
688C23C2×2−1+412yes—
689C23#58512yes—
690Q8—432no—
691Q8—416no—
692Q8—416no—
693D4—416no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—432no—
722C2×C4—432no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—416no—
756C2×C4—416no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4#53414yes—
795C2×C4#53814yes—
796C2×C4#53814yes—
797C2×C4#54614yes—
798C2×C4#54614yes—
799C2×C4#55114yes—
800C2×C4H(3,𝔽4)14yes—
801C22—24no—
802C22—24no—
803C22—24no—
804C22—24no—
805C22—24no—
806C22—24no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22—42no—
816C22—42no—
817C22—44no—
818C22—44no—
819C22—42no—
820C22—42no—
821C22—44no—
822C22—44no—
823C22C2×#53211yescharacteristic
824C22C2×#53411yescharacteristic
825C22C2×#53611yescharacteristic
826C22C2×#53811yescharacteristic
827C22C2×#53811yescharacteristic
828C22C2×#54611yescharacteristic
829C22C2×#54611yescharacteristic
830C22C2×#55111yescharacteristic
831C22#348012yes—
832C22#348212yes—
833C22#349911yescharacteristic
834C22#350011yescharacteristic
835C22#350512yes—
836C22#351612yes—
837C22#352012yes—
838C22#352012yes—
839C22#352012yes—
840C22#352312yes—
841C22C2×H(3,𝔽4)11yescharacteristic
842C22#353812yes—
843C22#354112yes—
844C22#354112yes—
845C22#354712yes—
846C4—42no—
847C4—42no—
848C4—44no—
849C4—44no—
850C4—42no—
851C4—42no—
852C4—44no—
853C4—44no—
854C4—44no—
855C4—82no—
856C4—82no—
857C4—82no—
858C4—82no—
859C4—82no—
860C4—82no—
861C4—82no—
862C4#268418yes—
863C2—44no—
864C2—44no—
865C2#3508511yescharacteristic
866C2#3637611yescharacteristic
867C2#3639611yescharacteristic
868C2#3738811yescharacteristic
869C2#3808111yescharacteristic
870C2#3808511yescharacteristic
871C2#3924412yes—
872C2#4009412yes—
873C2#4566712yes—
874C2C2×#268411yescharacteristic
875C2#5938312yes—
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. #16874C2semidirect
4. #15586C2semidirect
6. #15238C2semidirect
7. #15238C2semidirect
8. #15236C2semidirect
9. #15233C2semidirect
10. #15182C2semidirect
11. #15150C2semidirect
12. #14702C2semidirect
13. #14702C2semidirect
14. #14525C2semidirect
15. #14003C2semidirect
16. #14000C2semidirect
17. #13922C2semidirect
18. #13922C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25622
C2×#24092
#168742
#155862
#154942
#152382
#152362
#152332
#151822
#151502
#147022
#145252
#140032
#140002
#139222
C4×#3862