Finite Group Databasebeta

← #732502

Subgroups — #732502

Order 512.

2924 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2537C211yesmaximal, characteristic
2C2×#2352C211yesmaximal, characteristic, complemented
3#16442C214yesmaximal, complemented
4#16076C214yesmaximal, complemented
5#15984C214yesmaximal, complemented
6#15233C211yesmaximal, characteristic, complemented
7#15233C211yesmaximal, characteristic, complemented
8#15219C211yesmaximal, characteristic, complemented
9#15219C211yesmaximal, characteristic, complemented
10#14838C214yesmaximal, complemented
11#14348C211yesmaximal, characteristic, complemented
12#14137C211yesmaximal, characteristic, complemented
13#14136C211yesmaximal, characteristic, complemented
14#13941C211yesmaximal, characteristic, complemented
15#13939C211yesmaximal, characteristic, complemented
16#13911C211yesmaximal, characteristic, complemented
17#13904C211yesmaximal, characteristic, complemented
18#13847C211yesmaximal, characteristic, complemented
19#13785C211yesmaximal, characteristic, complemented
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#121C2212yes—
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27#2537—28no—
28C2×#394C2212yes—
29C2×#394C2212yes—
30#2352—28no—
31C2×#390C2211yescharacteristic
32C2×#390C2211yescharacteristic
33C2×#390C2211yescharacteristic
34C2×#390C2211yescharacteristic
35C2×#388C2212yes—
36C2×#387C2212yes—
37C2×#386C2212yes—
38C2×#386C2214yes—
39C2×#384C2211yescharacteristic
40C2×#382C2211yescharacteristic
41C2×#382C2211yescharacteristic
42C2×#382C2211yescharacteristic
43C2×#381C2214yes—
44C2×#380C2211yescharacteristic
45C2×#380C2211yescharacteristic
46C2×#380C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2212yes—
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×#376C2211yescharacteristic
57#1445C2212yes—
58#1445C2214yes—
59#1443C2214yes—
60#1443C2214yes—
61#1442C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1440C2214yes—
65#1440C2214yes—
66#1440C2214yes—
67#1440C2214yes—
68#1440C2214yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2214yes—
72#1439C2214yes—
73#1438C2212yes—
74#1438C2214yes—
75#1438C2214yes—
76#1438C2214yes—
77#1437C2214yes—
78#1437C2214yes—
79C4⋊#95C2211yescharacteristic
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2214yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90#1434C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2214yes—
93C23×D4C2311yescharacteristic
94C23×D4C2312yes—
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C24×C4C2312yes—
101C2×#121—28no—
102C2×#121—24no—
103C2×#121—24no—
104C2×#121—24no—
105C2×#121—24no—
106C2×#121—48no—
107C2×#121—42no—
108C2×#121—42no—
109C2×C4×D4—24no—
110C2×C4×D4—24no—
111C2×C4×D4—24no—
112C2×C4×D4—24no—
113C2×C4×D4—24no—
114C2×C4×D4D418yes—
115C2×#117—24no—
116C2×#117—24no—
117C2×#117—42no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2312yes—
156C22×C42C2312yes—
157C22×C42C2311yescharacteristic
158#394—28no—
159#394—28no—
160#390—24no—
161#390—24no—
162#390—42no—
163#390—42no—
164#388—28no—
165#387—28no—
166#386—28no—
167#386—48no—
168#384—24no—
169#382—24no—
170#382—42no—
171#382—42no—
172#381—48no—
173#380—24no—
174#380—24no—
175#380—24no—
176#380—24no—
177#380—28no—
178C4×C4⋊C4—24no—
179C4×C4⋊C4—24no—
180C4×C22⋊C4—28no—
181C4×C22⋊C4—42no—
182C4×C22⋊C4—42no—
183C4×C22⋊C4—42no—
184C4×C22⋊C4—42no—
185#376—24no—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C25C2411yescharacteristic
213C25C2412yes—
214C25C2411yescharacteristic
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—28no—
220C22×D4—24no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—42no—
230C22×D4—44no—
231C22×D4—42no—
232C22×D4—42no—
233C22×D4—44no—
234C22×D4—44no—
235C22×D4C2×D414yes—
236C22×D4#4114yes—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—28no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—42no—
256C23×C4—44no—
257C23×C4—44no—
258C23×C4—44no—
259C23×C4C2×D414yes—
260C23×C4C2×D414yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277#121—416no—
278#121—416no—
279#121—432no—
280C4×D4—232no—
281C4×D4—416no—
282#117—416no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—416no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4C2×D414yes—
317C2×C4⋊C4#4114yes—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
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—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4C2×D414yes—
367C2×C22⋊C4C2×D414yes—
368C2×C42—24no—
369C2×C42—24no—
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—44no—
385C2×C42C2×D414yes—
386C2×C42#4114yes—
387C2×C42#4114yes—
388#95—24no—
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—44no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95—44no—
412#95—44no—
413#95—44no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—21no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—21no—
432C24—22no—
433C24—21no—
434C24—24no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—24no—
439C24—24no—
440C24—22no—
441C24—22no—
442C24—24no—
443C24C22×D412yes—
444C24C22×D412yes—
445C24C2×#4114yes—
446C24H(5,𝔽2)14yes—
447C24C2511yescharacteristic
448C2×D4—28no—
449C2×D4—28no—
450C2×D4—28no—
451C2×D4—28no—
452C2×D4—28no—
453C2×D4—44no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—416no—
459C2×D4—48no—
460C2×D4—48no—
461C2×D4—44no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—84no—
466C2×D4—84no—
467C2×D4—88no—
468C2×D4—88no—
469C2×D4—88no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—24no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
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—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
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—48no—
555C22×C4—416no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—88no—
569C22×C4—88no—
570C22×C4—84no—
571C22×C4—88no—
572C22×C4C22×D412yes—
573C22×C4C22×D412yes—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C22×D412yes—
577C22×C4C2×#4114yes—
578C22×C4C2×#4112yes—
579C22×C4C2×#4112yes—
580C22×C4C2×#4112yes—
581C22×C4C2×#4112yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4112yes—
584C22×C4C2×#4112yes—
585C22×C4C2×#4112yes—
586C22×C4H(5,𝔽2)12yes—
587C22×C4H(5,𝔽2)12yes—
588C4⋊C4—28no—
589C4⋊C4—28no—
590C4⋊C4—48no—
591C4⋊C4—48no—
592C4⋊C4—48no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—84no—
600C22⋊C4—28no—
601C22⋊C4—28no—
602C22⋊C4—48no—
603C22⋊C4—48no—
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—88no—
614C22⋊C4—84no—
615C22⋊C4—88no—
616C22⋊C4—88no—
617C22⋊C4—88no—
618C42—48no—
619C42—44no—
620C42—44no—
621C42—44no—
622C42—44no—
623C42—84no—
624C42#123116yes—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—24no—
630C23—24no—
631C23—22no—
632C23—22no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—22no—
638C23—24no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—24no—
643C23—22no—
644C23—24no—
645C23—22no—
646C23—22no—
647C23—28no—
648C23—28no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—41no—
661C23—42no—
662C23—42no—
663C23—41no—
664C23—42no—
665C23—42no—
666C23—41no—
667C23—41no—
668C23—42no—
669C23—44no—
670C23—42no—
671C23—44no—
672C23—44no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—44no—
678C23—42no—
679C23—44no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—44no—
684C23—42no—
685C23—42no—
686C23—44no—
687C23—42no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—42no—
692C23—42no—
693C23#53514yes—
694C23C23×D411yescharacteristic
695C23C22×#4111yescharacteristic
696C23C22×#4111yescharacteristic
697C23C22×#4111yescharacteristic
698C23C22×#4111yescharacteristic
699C23C2×H(5,𝔽2)12yes—
700C23C2×H(5,𝔽2)11yescharacteristic
701C23C2×H(5,𝔽2)11yescharacteristic
702C23#58512yes—
703C23#58512yes—
704C23#58512yes—
705D4—416no—
706D4—416no—
707D4—816no—
708D4—816no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—28no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—416no—
737C2×C4—416no—
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—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—816no—
797C2×C4—816no—
798C2×C4C2×#12314yes—
799C2×C4C2×#12314yes—
800C2×C4C2×#12314yes—
801C2×C4#52914yes—
802C2×C4#54014yes—
803C2×C4#54614yes—
804C2×C4#54614yes—
805C2×C4#55314yes—
806C2×C4#55514yes—
807C22—24no—
808C22—24no—
809C22—24no—
810C22—44no—
811C22—44no—
812C22—42no—
813C22—42no—
814C22—44no—
815C22—42no—
816C22—42no—
817C22—44no—
818C22—48no—
819C22—48no—
820C22—42no—
821C22—42no—
822C22—44no—
823C22—42no—
824C22—42no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—84no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—84no—
840C22C22×#12311yescharacteristic
841C22C2×#52911yescharacteristic
842C22C2×#53511yescharacteristic
843C22#344911yescharacteristic
844C22C2×#54011yescharacteristic
845C22C2×#54611yescharacteristic
846C22C2×#54611yescharacteristic
847C22C2×#55311yescharacteristic
848C22C2×#55511yescharacteristic
849C22#349312yes—
850C22#349412yes—
851C22#349412yes—
852C22#350011yescharacteristic
853C22#350011yescharacteristic
854C22#351212yes—
855C22#351312yes—
856C22#351312yes—
857C22#352112yes—
858C22#352412yes—
859C22#353912yes—
860C22#354012yes—
861C22#354212yes—
862C22#354212yes—
863C4—24no—
864C4—24no—
865C4—42no—
866C4—42no—
867C4—44no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4—82no—
873C4—82no—
874C4—82no—
875C4—82no—
876C4—82no—
877C4—82no—
878C4#242018yes—
879C2—44no—
880C2—84no—
881C2—82no—
882C2C2×#242011yescharacteristic
883C2#3526211yescharacteristic
884C2#3561811yescharacteristic
885C2#3584912yes—
886C2#3808211yescharacteristic
887C2#3808411yescharacteristic
888C2#3809211yescharacteristic
889C2#3809511yescharacteristic
890C2#4268812yes—
891C2#4505212yes—
892C2#4506612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2537C2
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×#2352C2semidirect
3. #16442C2semidirect
4. #16076C2semidirect
5. #15984C2semidirect
6. #15233C2semidirect
7. #15233C2semidirect
8. #15219C2semidirect
9. #15219C2semidirect
10. #14838C2semidirect
11. #14348C2semidirect
12. #14137C2semidirect
13. #14136C2semidirect
14. #13941C2semidirect
15. #13939C2semidirect
16. #13911C2semidirect
17. #13904C2semidirect
18. #13847C2semidirect
19. #13785C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25372
C2×#23522
#164422
#160762
#159842
#152332
#152192
#148382
#143482
#141372
#141362
#139412
#139392
#139112
#139042
#138472
#137852