Finite Group Databasebeta

← #946653

Subgroups — #946653

Order 512.

2604 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2485C211yesmaximal, characteristic, complemented
2C2×#2414C211yesmaximal, characteristic
3#17087C214yesmaximal, complemented
4#16541C214yesmaximal, complemented
5#16371C214yesmaximal, complemented
6#16054C214yesmaximal, complemented
7#15233C211yesmaximal, characteristic, complemented
8#15222C211yesmaximal, characteristic, complemented
9#15219C211yesmaximal, characteristic, complemented
10#15151C211yesmaximal, characteristic, complemented
11#15130C211yesmaximal, characteristic, complemented
12#15130C211yesmaximal, characteristic, complemented
13#14276C211yesmaximal, characteristic, complemented
14#14260C211yesmaximal, characteristic, complemented
15#14136C211yesmaximal, characteristic, complemented
16#13939C211yesmaximal, characteristic, complemented
17#13879C211yesmaximal, characteristic, complemented
18#13879C211yesmaximal, characteristic, complemented
19#13847C211yesmaximal, characteristic, complemented
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C22×#117C2211yescharacteristic
25#2485—28no—
26#2414—28no—
27C2×#398C2214yes—
28C2×#397C2212yes—
29C2×#394C2212yes—
30C2×#394C2212yes—
31C2×#394C2214yes—
32C2×#394C2214yes—
33C2×#392C2212yes—
34C2×#390C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#390C2212yes—
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#388C2212yes—
44C2×#388C2212yes—
45C2×#387C2212yes—
46C2×#384C2211yescharacteristic
47C2×#384C2211yescharacteristic
48C2×#382C2211yescharacteristic
49C2×#382C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×#376C2211yescharacteristic
60#1445C2212yes—
61#1445C2214yes—
62#1443C2214yes—
63#1441C2214yes—
64#1441C2214yes—
65#1440C2214yes—
66#1440C2214yes—
67#1440C2214yes—
68#1440C2214yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1438C2212yes—
79#1438C2214yes—
80#1438C2214yes—
81#1437C2214yes—
82#1436C2214yes—
83#1436C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92#1434C2214yes—
93C23×D4C2311yescharacteristic
94C23×D4C2312yes—
95C23×D4C2312yes—
96C23×D4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C2×#121—24no—
100C2×#121—24no—
101C2×#121—24no—
102C2×#121—42no—
103C2×#121—42no—
104C2×#121—42no—
105C2×C4×D4—42no—
106C2×C4×D4—42no—
107C2×C4×D4D418yes—
108C2×#117—24no—
109C2×#117—24no—
110C2×#117—24no—
111C2×#117—42no—
112C2×#117—42no—
113C2×#117—42no—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155#398—48no—
156#397—28no—
157#394—28no—
158#394—28no—
159#394—48no—
160#394—48no—
161#392—28no—
162#390—28no—
163#390—24no—
164#390—24no—
165#390—42no—
166#390—42no—
167#390—42no—
168#389—24no—
169#389—24no—
170#389—24no—
171#388—28no—
172#388—28no—
173#387—28no—
174#384—24no—
175#384—42no—
176#382—42no—
177#382—42no—
178#380—24no—
179#380—24no—
180#380—24no—
181#380—24no—
182C4×C4⋊C4—42no—
183C4×C22⋊C4—24no—
184C4×C22⋊C4—24no—
185C4×C22⋊C4—42no—
186C4×C22⋊C4—42no—
187#376—42no—
188C2×#95C2312yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C25C2412yes—
213C25C2411yescharacteristic
214C25C2411yescharacteristic
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—24no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—41no—
226C22×D4—41no—
227C22×D4—42no—
228C22×D4—42no—
229C22×D4—42no—
230C22×D4—42no—
231C22×D4—42no—
232C22×D4—44no—
233C22×D4—44no—
234C22×D4—44no—
235C22×D4—44no—
236C22×D4C2×D414yes—
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×C4C2×D414yes—
250C23×C4C2×D414yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2411yescharacteristic
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262C23×C4C2411yescharacteristic
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267#121—416no—
268#121—416no—
269C4×D4—416no—
270#117—416no—
271#117—416no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4C2×D414yes—
310C2×C4⋊C4#4114yes—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—42no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C22⋊C4—41no—
343C2×C22⋊C4—41no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
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⋊C4C2×D414yes—
364C2×C22⋊C4C2×D414yes—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—24no—
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—42no—
382C2×C42—42no—
383C2×C42—42no—
384C2×C42C2×D414yes—
385C2×C42#4114yes—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—28no—
396#95—44no—
397#95—44no—
398#95—44no—
399#95—44no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—22no—
415C24—22no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—24no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—24no—
439C24—24no—
440C24—24no—
441C24C22×D412yes—
442C24C22×D412yes—
443C24C2511yescharacteristic
444C2×D4—44no—
445C2×D4—44no—
446C2×D4—44no—
447C2×D4—48no—
448C2×D4—48no—
449C2×D4—48no—
450C2×D4—48no—
451C2×D4—48no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—44no—
455C2×D4—44no—
456C2×D4—44no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—88no—
460C2×D4—84no—
461C2×D4—84no—
462C2×D4—84no—
463C2×D4—88no—
464C2×D4—88no—
465C2×D4—88no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—24no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
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—24no—
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—24no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C2×#4114yes—
566C22×C4C2×#4114yes—
567C22×C4C2×#4112yes—
568C22×C4C2×#4112yes—
569C22×C4H(5,𝔽2)14yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C4H(5,𝔽2)12yes—
573C22×C42−1+412yes—
574C4⋊C4—28no—
575C4⋊C4—44no—
576C4⋊C4—48no—
577C4⋊C4—48no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—84no—
585C4⋊C4—84no—
586C4⋊C4—88no—
587C4⋊C4—88no—
588C22⋊C4—44no—
589C22⋊C4—44no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—88no—
601C22⋊C4—84no—
602C22⋊C4—88no—
603C22⋊C4—84no—
604C22⋊C4—84no—
605C22⋊C4—84no—
606C22⋊C4—88no—
607C22⋊C4—88no—
608C42—28no—
609C42—28no—
610C42—48no—
611C42—48no—
612C42—44no—
613C42—44no—
614C42—44no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—41no—
644C23—41no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—44no—
670C23—44no—
671C23—42no—
672C23—42no—
673C23—44no—
674C23—44no—
675C23—42no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23C23×D411yescharacteristic
685C23C22×#4111yescharacteristic
686C23C22×#4111yescharacteristic
687C23C2×H(5,𝔽2)11yescharacteristic
688C23C2×H(5,𝔽2)11yescharacteristic
689C23C2×H(5,𝔽2)11yescharacteristic
690C23C2×H(5,𝔽2)12yes—
691C23C2×2−1+411yescharacteristic
692C23#58512yes—
693C23#58512yes—
694C23#58512yes—
695D4—416no—
696D4—816no—
697D4—816no—
698D4—88no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—28no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—416no—
743C2×C4—416no—
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—44no—
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—44no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4#53414yes—
789C2×C4#54014yes—
790C2×C4#54214yes—
791C2×C4#54614yes—
792C2×C4#54714yes—
793C2×C4#55314yes—
794C2×C4#56214yes—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—82no—
810C22—82no—
811C22—82no—
812C22—82no—
813C22—82no—
814C22—82no—
815C22—82no—
816C22—82no—
817C22—84no—
818C22—82no—
819C22—84no—
820C22—82no—
821C22—82no—
822C22—84no—
823C22—82no—
824C22—82no—
825C22—82no—
826C22—82no—
827C22—84no—
828C22C2×#53411yescharacteristic
829C22#344911yescharacteristic
830C22#344911yescharacteristic
831C22C2×#54011yescharacteristic
832C22C2×#54211yescharacteristic
833C22C2×#54611yescharacteristic
834C22C2×#54711yescharacteristic
835C22C2×#55311yescharacteristic
836C22#349312yes—
837C22#349412yes—
838C22#349811yescharacteristic
839C22#350011yescharacteristic
840C22#351412yes—
841C22#352412yes—
842C22C2×#56211yescharacteristic
843C22#353912yes—
844C22#353912yes—
845C22#354012yes—
846C22#354212yes—
847C22#354212yes—
848C22#354612yes—
849C22#354712yes—
850C22#356512yes—
851C4—42no—
852C4—44no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—44no—
857C4—44no—
858C4—82no—
859C4—82no—
860C4—82no—
861C4—82no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4—82no—
866C4#270118yes—
867C2—82no—
868C2—82no—
869C2—162no—
870C2#3730011yescharacteristic
871C2#3745511yescharacteristic
872C2#3786911yescharacteristic
873C2#3787011yescharacteristic
874C2#3809011yescharacteristic
875C2#3809311yescharacteristic
876C2#4268812yes—
877C2#4273412yes—
878C2#4539812yes—
879C2C2×#270111yescharacteristic
880C2#5306212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2414C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2485C2semidirect
3. #17087C2semidirect
4. #16541C2semidirect
5. #16371C2semidirect
6. #16054C2semidirect
7. #15233C2semidirect
8. #15222C2semidirect
9. #15219C2semidirect
10. #15151C2semidirect
11. #15130C2semidirect
12. #15130C2semidirect
13. #14276C2semidirect
14. #14260C2semidirect
15. #14136C2semidirect
16. #13939C2semidirect
17. #13879C2semidirect
18. #13879C2semidirect
19. #13847C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24852
C2×#24142
#170872
#165412
#163712
#160542
#152332
#152222
#152192
#151512
#151302
#142762
#142602
#141362
#139392
#138792
#138472