Finite Group Databasebeta

← #946448

Subgroups — #946448

Order 512.

2714 conjugacy classes of subgroups.

The subgroup lattice has 843 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2565C211yesmaximal, characteristic, complemented
2C2×#2500C211yesmaximal, characteristic
3C2×#2441C211yesmaximal, characteristic, complemented
4C2×#2426C211yesmaximal, characteristic
5#17103C214yesmaximal, complemented
6#16330C214yesmaximal, complemented
7#16292C214yesmaximal, complemented
8#15977C214yesmaximal, complemented
9#15229C211yesmaximal, characteristic, complemented
10#15226C211yesmaximal, characteristic, complemented
11#15182C211yesmaximal, characteristic, complemented
12#15145C211yesmaximal, characteristic, complemented
13#15134C211yesmaximal, characteristic, complemented
14#15130C211yesmaximal, characteristic
15#14277C211yesmaximal, characteristic, complemented
16#14273C211yesmaximal, characteristic, complemented
17#14138C211yesmaximal, characteristic, complemented
18#13976C211yesmaximal, characteristic, complemented
19#13842C211yesmaximal, characteristic, complemented
20C22×#125C2211yescharacteristic
21C22×#124C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25C22×#117C2211yescharacteristic
26#2565—28no—
27#2500—28no—
28#2441—28no—
29#2426—28no—
30C2×#399C2212yes—
31C2×#398C2214yes—
32C2×#398C2214yes—
33C2×#396C2212yes—
34C2×#396C2212yes—
35C2×#396C2214yes—
36C2×#394C2212yes—
37C2×#394C2214yes—
38C2×#394C2214yes—
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2212yes—
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#389C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#389C2212yes—
53C2×#388C2212yes—
54C2×#388C2214yes—
55C2×#387C2214yes—
56C2×#387C2212yes—
57C2×#384C2211yescharacteristic
58C2×#384C2211yescharacteristic
59C2×#384C2211yescharacteristic
60C2×#384C2211yescharacteristic
61C2×#382C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×#376C2211yescharacteristic
68#1444C2214yes—
69#1444C2214yes—
70#1444C2214yes—
71#1443C2212yes—
72#1442C2212yes—
73#1442C2214yes—
74#1441C2214yes—
75#1440C2212yes—
76#1440C2214yes—
77#1440C2214yes—
78#1439C2212yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1439C2214yes—
85#1439C2214yes—
86#1439C2214yes—
87#1436C2214yes—
88#1436C2214yes—
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C23×D4C2312yes—
98C24×C4C2311yescharacteristic
99C2×#125—24no—
100C2×#125—24no—
101C2×#125—42no—
102C2×#124—24no—
103C2×#124—24no—
104C2×#124—42no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—42no—
108C2×#121—24no—
109C2×#121—24no—
110C2×#121—42no—
111C2×C4×Q8—24no—
112C2×C4×Q8—24no—
113C2×C4×Q8—42no—
114C2×#117—24no—
115C2×#117—24no—
116C2×#117—42no—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2312yes—
156C22×C42C2312yes—
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160#399—28no—
161#398—216no—
162#398—48no—
163#396—28no—
164#396—28no—
165#396—48no—
166#394—28no—
167#394—216no—
168#394—48no—
169#391—24no—
170#391—24no—
171#391—24no—
172#391—42no—
173#390—24no—
174#390—28no—
175#390—24no—
176#390—24no—
177#390—42no—
178#390—42no—
179#389—24no—
180#389—24no—
181#389—24no—
182#389—28no—
183#388—28no—
184#388—216no—
185#387—216no—
186#387—28no—
187#384—24no—
188#384—24no—
189#384—24no—
190#384—42no—
191#382D418yes—
192#380—24no—
193C4×C4⋊C4—24no—
194C4×C22⋊C4—24no—
195C4×C22⋊C4—42no—
196C4×C22⋊C4D418yes—
197#376—42no—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222C25C2412yes—
223C25C2411yescharacteristic
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8#4114yes—
231C22×D4—24no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—24no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—42no—
241C22×D4—44no—
242C22×D4—44no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4C2×D414yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2411yescharacteristic
256C23×C4C2411yescharacteristic
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2411yescharacteristic
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267#125—416no—
268#124—416no—
269C22⋊Q8—416no—
270#121—416no—
271C4×Q8—416no—
272#117—416no—
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—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4C2×D414yes—
324C2×C4⋊C4C2×D414yes—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—44no—
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—42no—
356C2×C22⋊C4—42no—
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—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—24no—
375C2×C42—24no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42C2×D414yes—
390C2×C42C2×D414yes—
391C2×C42C2×D414yes—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—28no—
398#95—28no—
399#95—24no—
400#95—28no—
401#95—28no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—42no—
406#95—44no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—44no—
411#95—44no—
412#95—44no—
413#95C2×D414yes—
414#95C2×D414yes—
415#95C2×D4116yes—
416C24—21no—
417C24—21no—
418C24—22no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24—21no—
423C24—21no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—24no—
430C24—22no—
431C24—22no—
432C24—24no—
433C24—22no—
434C24—22no—
435C24—24no—
436C24—24no—
437C24C22×D412yes—
438C24C2511yescharacteristic
439C2×Q8—28no—
440C2×Q8—28no—
441C2×Q8—28no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×D4—48no—
447C2×D4—48no—
448C2×D4—44no—
449C2×D4—44no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—44no—
455C2×D4—88no—
456C2×D4—84no—
457C2×D4—88no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
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—24no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
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—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4C22×D414yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C22×D414yes—
550C22×C4C22×D412yes—
551C22×C4C22×D414yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C2×#4114yes—
557C22×C4C2×#4112yes—
558C22×C4H(5,𝔽2)14yes—
559C22×C4H(5,𝔽2)12yes—
560C22×C4H(5,𝔽2)12yes—
561C22×C42−1+414yes—
562C22×C42−1+412yes—
563C22×C42−1+412yes—
564C4⋊C4—28no—
565C4⋊C4—28no—
566C4⋊C4—48no—
567C4⋊C4—416no—
568C4⋊C4—48no—
569C4⋊C4—48no—
570C4⋊C4—48no—
571C4⋊C4—48no—
572C4⋊C4—48no—
573C4⋊C4—48no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—88no—
579C4⋊C4—84no—
580C4⋊C4—84no—
581C4⋊C4—84no—
582C4⋊C4—88no—
583C22⋊C4—44no—
584C22⋊C4—44no—
585C22⋊C4—48no—
586C22⋊C4—416no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—88no—
595C22⋊C4—84no—
596C22⋊C4—88no—
597C22⋊C4—84no—
598C22⋊C4—88no—
599C42—28no—
600C42—28no—
601C42—28no—
602C42—48no—
603C42—48no—
604C42—44no—
605C42—44no—
606C42—44no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—41no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—44no—
639C23—44no—
640C23—42no—
641C23—42no—
642C23—44no—
643C23—44no—
644C23—42no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23C23×D411yescharacteristic
654C23C23×D411yescharacteristic
655C23C22×#4111yescharacteristic
656C23C2×H(5,𝔽2)11yescharacteristic
657C23C2×H(5,𝔽2)11yescharacteristic
658C23C2×H(5,𝔽2)12yes—
659C23C2×2−1+411yescharacteristic
660C23C2×2−1+411yescharacteristic
661C23C2×2−1+412yes—
662C23#58512yes—
663C23#58512yes—
664Q8—416no—
665D4—816no—
666D4—88no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—28no—
687C2×C4—24no—
688C2×C4—28no—
689C2×C4—24no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—41no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—416no—
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—44no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4#53614yes—
761C2×C4#53714yes—
762C2×C4#53914yes—
763C2×C4D4214yes—
764C2×C4#54614yes—
765C2×C4#54814yes—
766C2×C4#56214yes—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—82no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—84no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—84no—
783C22—84no—
784C22—82no—
785C22—82no—
786C22—82no—
787C22—82no—
788C22—84no—
789C22C2×#53611yescharacteristic
790C22C2×#53711yescharacteristic
791C22#344911yescharacteristic
792C22#344911yescharacteristic
793C22C2×#53911yescharacteristic
794C22C2×D4211yescharacteristic
795C22C2×#54611yescharacteristic
796C22C2×#54811yescharacteristic
797C22#348812yes—
798C22#348912yes—
799C22#349811yescharacteristic
800C22#349911yescharacteristic
801C22#351612yes—
802C22#351712yes—
803C22C2×#56211yescharacteristic
804C22#354212yes—
805C22#354412yes—
806C22#354612yes—
807C22#354712yes—
808C22#355212yes—
809C22#355412yes—
810C22#356512yes—
811C22#356512yes—
812C4—44no—
813C4—42no—
814C4—42no—
815C4—44no—
816C4—42no—
817C4—44no—
818C4—42no—
819C4—44no—
820C4—42no—
821C4—44no—
822C4—44no—
823C4—82no—
824C4—82no—
825C4—82no—
826C4—82no—
827C4—82no—
828C4#268118yes—
829C2—82no—
830C2—162no—
831C2#3730311yescharacteristic
832C2#3754511yescharacteristic
833C2#3768011yescharacteristic
834C2#3768111yescharacteristic
835C2#3808911yescharacteristic
836C2#3894611yescharacteristic
837C2#4286812yes—
838C2#4297012yes—
839C2#4531312yes—
840C2C2×#268111yescharacteristic
841C2#5304912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2565C2semidirect
3. C2×#2441C2semidirect
5. #17103C2semidirect
6. #16330C2semidirect
7. #16292C2semidirect
8. #15977C2semidirect
9. #15229C2semidirect
10. #15226C2semidirect
11. #15182C2semidirect
12. #15145C2semidirect
13. #15134C2semidirect
15. #14277C2semidirect
16. #14273C2semidirect
17. #14138C2semidirect
18. #13976C2semidirect
19. #13842C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25652
C2×#25002
C2×#24412
C2×#24262
#171032
#163302
#162922
#159772
#152292
#152262
#151822
#151452
#151342
#151302
#142772
#142732
#141382
#139762
#138422