Finite Group Databasebeta

← #947162

Subgroups — #947162

Order 512.

2912 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2535C211yesmaximal, characteristic
2C2×#2417C211yesmaximal, characteristic, complemented
3#17173C214yesmaximal, complemented
4#16348C214yesmaximal, complemented
5#16270C214yesmaximal, complemented
6#15958C214yesmaximal, complemented
7#15241C211yesmaximal, characteristic, complemented
8#15239C211yesmaximal, characteristic, complemented
9#15215C211yesmaximal, characteristic, complemented
10#15215C211yesmaximal, characteristic, complemented
11#15182C211yesmaximal, characteristic, complemented
12#15150C211yesmaximal, characteristic, complemented
13#14258C211yesmaximal, characteristic, complemented
14#14257C211yesmaximal, characteristic, complemented
15#14137C211yesmaximal, characteristic, complemented
16#14027C211yesmaximal, characteristic, complemented
17#13977C211yesmaximal, characteristic, complemented
18#13924C211yesmaximal, characteristic, complemented
19#13839C211yesmaximal, characteristic, complemented
20C22×#124C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29#2535—28no—
30#2417—28no—
31C2×#398C2212yes—
32C2×#397C2212yes—
33C2×#397C2214yes—
34C2×#396C2212yes—
35C2×#392C2212yes—
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2214yes—
48C2×#385C2214yes—
49C2×#384C2211yescharacteristic
50C2×#382C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2212yes—
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58#1445C2214yes—
59#1445C2214yes—
60#1443C2214yes—
61#1443C2214yes—
62#1443C2214yes—
63#1442C2214yes—
64#1441C2212yes—
65#1441C2214yes—
66#1441C2214yes—
67#1440C2212yes—
68#1440C2214yes—
69#1440C2214yes—
70#1439C2212yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1438C2212yes—
78#1438C2214yes—
79#1438C2214yes—
80#1438C2214yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C23×D4C2312yes—
96C23×D4C2312yes—
97C23×D4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2312yes—
102C2×#124—24no—
103C2×#124—42no—
104C2×#124—42no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—42no—
109C2×C22⋊Q8—42no—
110C2×C22⋊Q8—42no—
111C2×#121—24no—
112C2×#121—24no—
113C2×#121—24no—
114C2×#121—24no—
115C2×#121—42no—
116C2×#121—42no—
117C2×C4×D4—24no—
118C2×C4×D4—42no—
119C2×C4×D4—42no—
120C2×C4×D4—42no—
121C2×C4×D4—42no—
122C2×C4×D4D418yes—
123C2×#117—42no—
124C2×#117—42no—
125C2×#117—42no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—24no—
128C22×C4⋊C4—42no—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165#398—28no—
166#397—28no—
167#397—48no—
168#396—28no—
169#392—28no—
170#391—24no—
171#391—42no—
172#391—42no—
173#391—42no—
174#390—24no—
175#390—42no—
176#390—42no—
177#389—24no—
178#386—28no—
179#386—28no—
180#386—28no—
181#386—48no—
182#385—48no—
183#384—42no—
184#382—24no—
185#380—24no—
186#380—24no—
187#380—24no—
188#380—28no—
189C4×C22⋊C4—42no—
190C4×C22⋊C4—42no—
191C4×C22⋊C4—42no—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C25C2411yescharacteristic
219C25C2412yes—
220C25C2411yescharacteristic
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—28no—
233C22×D4—24no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—41no—
241C22×D4—41no—
242C22×D4—42no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4C2×D414yes—
249C22×D4#4114yes—
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—44no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4—44no—
272C23×C4C2×D414yes—
273C23×C4C2×D414yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290#124—416no—
291C22⋊Q8—416no—
292C22⋊Q8—416no—
293#121—416no—
294#121—416no—
295C4×D4—416no—
296C4×D4—416no—
297#117—416no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
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—24no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—416no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—41no—
328C2×C4⋊C4—41no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4C2×D414yes—
336C2×C4⋊C4#4114yes—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—41no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4C2×D414yes—
387C2×C22⋊C4C2×D414yes—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42C2×D414yes—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—28no—
413#95—42no—
414#95—42no—
415#95—44no—
416#95—42no—
417#95—44no—
418#95—44no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95—44no—
426#95—44no—
427#95—44no—
428#95—44no—
429C24—21no—
430C24—21no—
431C24—22no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—21no—
440C24—22no—
441C24—21no—
442C24—22no—
443C24—24no—
444C24—21no—
445C24—22no—
446C24—21no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—21no—
451C24—22no—
452C24—22no—
453C24—24no—
454C24—24no—
455C24—24no—
456C24—22no—
457C24—22no—
458C24C22×D412yes—
459C24C22×D412yes—
460C24C2×#4114yes—
461C242−1+414yes—
462C24C2511yescharacteristic
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×D4—28no—
471C2×D4—28no—
472C2×D4—28no—
473C2×D4—28no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—416no—
481C2×D4—48no—
482C2×D4—48no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—84no—
488C2×D4—84no—
489C2×D4—88no—
490C2×D4—88no—
491C2×D4—88no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—28no—
523C22×C4—28no—
524C22×C4—28no—
525C22×C4—28no—
526C22×C4—28no—
527C22×C4—28no—
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—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—44no—
588C22×C4—44no—
589C22×C4—44no—
590C22×C4—44no—
591C22×C4—48no—
592C22×C4—84no—
593C22×C4—84no—
594C22×C4—88no—
595C22×C4—84no—
596C22×C4—88no—
597C22×C4—88no—
598C22×C4—88no—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C2×#4114yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4H(5,𝔽2)14yes—
608C22×C4H(5,𝔽2)12yes—
609C22×C4H(5,𝔽2)12yes—
610C22×C4H(5,𝔽2)12yes—
611C22×C4H(5,𝔽2)12yes—
612C4⋊C4—28no—
613C4⋊C4—44no—
614C4⋊C4—48no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—44no—
622C4⋊C4—44no—
623C4⋊C4—84no—
624C4⋊C4—88no—
625C22⋊C4—44no—
626C22⋊C4—44no—
627C22⋊C4—416no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—48no—
636C22⋊C4—416no—
637C22⋊C4—48no—
638C22⋊C4—84no—
639C22⋊C4—84no—
640C22⋊C4—84no—
641C22⋊C4—88no—
642C22⋊C4—88no—
643C42—28no—
644C42—44no—
645C42—44no—
646C42—44no—
647C42—44no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—24no—
664C23—22no—
665C23—24no—
666C23—22no—
667C23—24no—
668C23—22no—
669C23—22no—
670C23—28no—
671C23—28no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—42no—
676C23—42no—
677C23—41no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—41no—
687C23—42no—
688C23—42no—
689C23—41no—
690C23—42no—
691C23—42no—
692C23—44no—
693C23—42no—
694C23—44no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—41no—
699C23—42no—
700C23—44no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—42no—
708C23—42no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—44no—
716C23#53614yes—
717C23C23×D411yescharacteristic
718C23C22×#4111yescharacteristic
719C23C22×#4111yescharacteristic
720C23C2×H(5,𝔽2)11yescharacteristic
721C23C2×H(5,𝔽2)11yescharacteristic
722C23C2×H(5,𝔽2)11yescharacteristic
723C23C2×H(5,𝔽2)11yescharacteristic
724C23C2×H(5,𝔽2)12yes—
725C23C2×2−1+412yes—
726C23#58512yes—
727C23#58512yes—
728Q8—88no—
729D4—416no—
730D4—416no—
731D4—816no—
732D4—816no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—28no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—416no—
770C2×C4—416no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—44no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—44no—
824C2×C4—816no—
825C2×C4—816no—
826C2×C4#53414yes—
827C2×C4#53814yes—
828C2×C4#54014yes—
829C2×C4#54614yes—
830C2×C4#54614yes—
831C2×C4#55314yes—
832C2×C4#56014yes—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—42no—
837C22—42no—
838C22—44no—
839C22—44no—
840C22—42no—
841C22—44no—
842C22—42no—
843C22—44no—
844C22—42no—
845C22—42no—
846C22—44no—
847C22—48no—
848C22—42no—
849C22—42no—
850C22—44no—
851C22—48no—
852C22—42no—
853C22—44no—
854C22—42no—
855C22—42no—
856C22—82no—
857C22—82no—
858C22—84no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—84no—
866C22C2×#53411yescharacteristic
867C22C2×#53611yescharacteristic
868C22#344911yescharacteristic
869C22C2×#53811yescharacteristic
870C22C2×#54011yescharacteristic
871C22C2×#54611yescharacteristic
872C22C2×#54611yescharacteristic
873C22C2×#55311yescharacteristic
874C22#349811yescharacteristic
875C22#350011yescharacteristic
876C22#351312yes—
877C22#351612yes—
878C22#352012yes—
879C22#352112yes—
880C22C2×#56011yescharacteristic
881C22#353612yes—
882C22#354112yes—
883C22#354112yes—
884C22#354112yes—
885C22#354212yes—
886C22#354612yes—
887C22#354612yes—
888C22#355112yes—
889C4—44no—
890C4—44no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—42no—
895C4—82no—
896C4—82no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4—82no—
904C4#268818yes—
905C2—44no—
906C2—82no—
907C2—84no—
908C2#3730011yescharacteristic
909C2#3744911yescharacteristic
910C2#3807811yescharacteristic
911C2#3808511yescharacteristic
912C2#3894511yescharacteristic
913C2#3894711yescharacteristic
914C2#4254112yes—
915C2#4255512yes—
916C2#4520312yes—
917C2C2×#268811yescharacteristic
918C2#5295612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2535C2
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×#2417C2semidirect
3. #17173C2semidirect
4. #16348C2semidirect
5. #16270C2semidirect
6. #15958C2semidirect
7. #15241C2semidirect
8. #15239C2semidirect
9. #15215C2semidirect
10. #15215C2semidirect
11. #15182C2semidirect
12. #15150C2semidirect
13. #14258C2semidirect
14. #14257C2semidirect
15. #14137C2semidirect
16. #14027C2semidirect
17. #13977C2semidirect
18. #13924C2semidirect
19. #13839C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25352
C2×#24172
#171732
#163482
#162702
#159582
#152412
#152392
#152152
#151822
#151502
#142582
#142572
#141372
#140272
#139772
#139242
#138392