Finite Group Databasebeta

← #947148

Subgroups — #947148

Order 512.

2812 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2562C211yesmaximal, characteristic
2C2×#2409C211yesmaximal, characteristic
3#17211C214yesmaximal, complemented
4#16447C214yesmaximal, complemented
5#16432C214yesmaximal
6#16039C214yesmaximal, complemented
7#15238C211yesmaximal, characteristic, complemented
8#15238C211yesmaximal, characteristic, complemented
9#15236C211yesmaximal, characteristic, complemented
10#15233C211yesmaximal, characteristic, complemented
11#15195C211yesmaximal, characteristic, complemented
12#15182C211yesmaximal, characteristic, complemented
13#14258C211yesmaximal, characteristic, complemented
14#14258C211yesmaximal, characteristic, complemented
15#14003C211yesmaximal, characteristic, complemented
16#14000C211yesmaximal, characteristic, complemented
17#13922C211yesmaximal, characteristic, complemented
18#13922C211yesmaximal, characteristic, complemented
19#13839C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×#117C2211yescharacteristic
26#2562—28no—
27#2409—28no—
28C2×#400C2212yes—
29C2×#395C2212yes—
30C2×#394C2212yes—
31C2×#393C2212yes—
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#388C2212yes—
43C2×#388C2212yes—
44C2×#386C2212yes—
45C2×#385C2212yes—
46C2×#384C2211yescharacteristic
47C2×#382C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57#1446C2214yes—
58#1446C2214yes—
59#1443C2214yes—
60#1443C2214yes—
61#1442C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1442C2214yes—
65#1442C2214yes—
66#1442C2214yes—
67#1442C2214yes—
68#1441C2212yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1440C2212yes—
73#1440C2214yes—
74#1440C2214yes—
75#1440C2214yes—
76#1440C2214yes—
77#1439C2212yes—
78#1439C2214yes—
79#1439C2214yes—
80#1438C2212yes—
81#1436C2214yes—
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88#1434C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
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—
107C2×#125—24no—
108C2×#125—42no—
109C2×#125—42no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—42no—
115C2×C22⋊Q8—42no—
116C2×C4×D4—42no—
117C2×C4×D4—42no—
118C2×C4×D4D418yes—
119C2×#117—42no—
120C2×#117—42no—
121C2×#117—42no—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2312yes—
154#400—28no—
155#395—28no—
156#394—28no—
157#393—28no—
158#391—24no—
159#391—24no—
160#391—24no—
161#391—24no—
162#391—42no—
163#391—42no—
164#391—42no—
165#391—42no—
166#391—42no—
167#391—42no—
168#388—28no—
169#388—28no—
170#386—28no—
171#385—28no—
172#384—42no—
173#382—42no—
174#380—24no—
175#380—24no—
176#380—24no—
177#380—24no—
178#380—24no—
179C4×C4⋊C4—24no—
180C4×C22⋊C4—42no—
181C4×C22⋊C4—42no—
182C4×C22⋊C4—42no—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C25C2411yescharacteristic
216C25C2411yescharacteristic
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—24no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—24no—
223C22×Q8—24no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—42no—
233C22×Q8—42no—
234C22×Q8—42no—
235C22×Q8—42no—
236C22×Q8—416no—
237C22×Q8—416no—
238C22×Q8—416no—
239C22×Q8—416no—
240C22×Q8—416no—
241C22×Q8—416no—
242C22×Q8—416no—
243C22×Q8#4114yes—
244C22×Q8#4114yes—
245C22×D4—24no—
246C22×D4—41no—
247C22×D4—41no—
248C22×D4—42no—
249C22×D4C2×D414yes—
250C23×C4—22no—
251C23×C4—22no—
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—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4C2×D414yes—
270C23×C4C2×D414yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288#125—416no—
289C22⋊Q8—416no—
290C22⋊Q8—416no—
291C4×D4—416no—
292#117—416no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
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—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4C2×D414yes—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
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—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4C2×D414yes—
365C2×C22⋊C4C2×D414yes—
366C2×C42—22no—
367C2×C42—22no—
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—24no—
381C2×C42—44no—
382C2×C42C2×D414yes—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—28no—
394#95—28no—
395#95—24no—
396#95—28no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95—44no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24C22×D412yes—
435C24C22×D412yes—
436C242−1+414yes—
437C24C2511yescharacteristic
438C2×Q8—28no—
439C2×Q8—28no—
440C2×Q8—28no—
441C2×Q8—28no—
442C2×Q8—28no—
443C2×Q8—28no—
444C2×Q8—48no—
445C2×Q8—48no—
446C2×Q8—48no—
447C2×Q8—48no—
448C2×Q8—48no—
449C2×Q8—48no—
450C2×Q8—4128no—
451C2×Q8—48no—
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×Q8—44no—
456C2×Q8—44no—
457C2×Q8—44no—
458C2×Q8—44no—
459C2×Q8—44no—
460C2×D4—28no—
461C2×D4—44no—
462C2×D4—44no—
463C2×D4—48no—
464C2×D4—48no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
508C22×C4—28no—
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—22no—
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—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
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—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4C22×D412yes—
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C2×#4114yes—
581C22×C4C2×#4114yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4112yes—
584C22×C4H(5,𝔽2)12yes—
585C22×C4H(5,𝔽2)12yes—
586C22×C4H(5,𝔽2)12yes—
587C22×C4H(5,𝔽2)12yes—
588C22×C42−1+414yes—
589C4⋊C4—44no—
590C4⋊C4—48no—
591C4⋊C4—48no—
592C4⋊C4—48no—
593C4⋊C4—48no—
594C4⋊C4—48no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—88no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—84no—
614C22⋊C4—84no—
615C42—28no—
616C42—44no—
617C42—44no—
618C42—44no—
619C42—44no—
620C42—84no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—42no—
644C23—42no—
645C23—41no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—41no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23#53614yes—
667C23C23×D411yescharacteristic
668C23C22×#4111yescharacteristic
669C23C22×#4111yescharacteristic
670C23C2×H(5,𝔽2)11yescharacteristic
671C23C2×H(5,𝔽2)11yescharacteristic
672C23C2×H(5,𝔽2)11yescharacteristic
673C23C2×H(5,𝔽2)11yescharacteristic
674C23C2×2−1+412yes—
675C23C2×2−1+412yes—
676C23#58512yes—
677C23#58512yes—
678Q8—432no—
679Q8—416no—
680Q8—416no—
681D4—416no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—432no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—416no—
729C2×C4—416no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4#53414yes—
782C2×C4#53814yes—
783C2×C4#53814yes—
784C2×C4#54614yes—
785C2×C4#54614yes—
786C2×C4#55114yes—
787C2×C4H(3,𝔽4)14yes—
788C22—24no—
789C22—24no—
790C22—24no—
791C22—44no—
792C22—42no—
793C22—44no—
794C22—42no—
795C22—42no—
796C22—44no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—82no—
807C22—82no—
808C22—82no—
809C22—82no—
810C22C2×#53411yescharacteristic
811C22C2×#53611yescharacteristic
812C22#344911yescharacteristic
813C22C2×#53811yescharacteristic
814C22C2×#53811yescharacteristic
815C22C2×#54611yescharacteristic
816C22C2×#54611yescharacteristic
817C22C2×#55111yescharacteristic
818C22#349911yescharacteristic
819C22#350011yescharacteristic
820C22#351612yes—
821C22#351612yes—
822C22#352312yes—
823C22#352412yes—
824C22C2×H(3,𝔽4)11yescharacteristic
825C22#353812yes—
826C22#354112yes—
827C22#354112yes—
828C22#354112yes—
829C22#354112yes—
830C22#354712yes—
831C22#354712yes—
832C22#355112yes—
833C4—42no—
834C4—42no—
835C4—44no—
836C4—42no—
837C4—42no—
838C4—44no—
839C4—44no—
840C4—82no—
841C4—82no—
842C4—82no—
843C4—82no—
844C4—82no—
845C4—82no—
846C4—82no—
847C4—82no—
848C4—82no—
849C4#268418yes—
850C2—44no—
851C2—82no—
852C2#3738811yescharacteristic
853C2#3744911yescharacteristic
854C2#3808111yescharacteristic
855C2#3808511yescharacteristic
856C2#3894611yescharacteristic
857C2#3894811yescharacteristic
858C2#4283112yes—
859C2#4285212yes—
860C2#4532012yes—
861C2C2×#268411yescharacteristic
862C2#5300512yes—
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. #17211C2semidirect
4. #16447C2semidirect
6. #16039C2semidirect
7. #15238C2semidirect
8. #15238C2semidirect
9. #15236C2semidirect
10. #15233C2semidirect
11. #15195C2semidirect
12. #15182C2semidirect
13. #14258C2semidirect
14. #14258C2semidirect
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
#172112
#164472
#164322
#160392
#152382
#152362
#152332
#151952
#151822
#142582
#140032
#140002
#139222
#138392