Finite Group Databasebeta

← #5083336

Subgroups — #5083336

Order 512.

2319 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2752C211yesmaximal, characteristic, complemented
2C2×#2631C211yesmaximal, characteristic
3#17201C212yesmaximal, complemented
4#17160C211yesmaximal, characteristic, complemented
5#17087C212yesmaximal, complemented
6#16530C212yesmaximal, complemented
7#16492C212yesmaximal, complemented
8#16272C212yesmaximal, complemented
9#16045C212yesmaximal, complemented
10#16032C211yesmaximal, characteristic, complemented
11#15966C212yesmaximal, complemented
12#15785C211yesmaximal, characteristic, complemented
13#15697C212yesmaximal, complemented
14#15549C212yesmaximal, complemented
15#15539C211yesmaximal, characteristic, complemented
16#15343C212yesmaximal, complemented
17#15285C212yesmaximal, complemented
18#14731C212yesmaximal, complemented
19#14651C211yesmaximal, characteristic, complemented
20C22×#124C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22#2752—28no—
23#2631—28no—
24C2×#399C2211yescharacteristic
25C2×#397C2211yescharacteristic
26C2×#397C2211yescharacteristic
27C2×#397C2212yes—
28C2×#397C2212yes—
29C2×#397C2212yes—
30C2×#397C2211yescharacteristic
31C2×#394C2212yes—
32C2×#394C2212yes—
33C2×#394C2212yes—
34C2×#393C2212yes—
35C2×#392C2212yes—
36C2×#392C2211yescharacteristic
37C2×#392C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#390C2212yes—
40C2×#388C2212yes—
41C2×#387C2212yes—
42C2×#386C2212yes—
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#386C2211yescharacteristic
46C2×#385C2211yescharacteristic
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#385C2212yes—
50C2×#383C2211yescharacteristic
51C2×#381C2211yescharacteristic
52C2×#381C2212yes—
53#1446C2211yescharacteristic
54#1446C2212yes—
55#1445C2212yes—
56#1445C2212yes—
57#1445C2212yes—
58#1445C2212yes—
59#1445C2212yes—
60#1444C2212yes—
61#1444C2212yes—
62#1443C2212yes—
63#1443C2212yes—
64#1442C2212yes—
65#1442C2212yes—
66#1442C2212yes—
67#1442C2212yes—
68#1442C2212yes—
69#1442C2212yes—
70#1441C2212yes—
71#1441C2212yes—
72#1440C2211yescharacteristic
73#1440C2212yes—
74#1440C2212yes—
75#1440C2212yes—
76#1440C2212yes—
77#1440C2212yes—
78#1440C2212yes—
79#1440C2212yes—
80#1440C2212yes—
81#1440C2211yescharacteristic
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1439C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90#1439C2212yes—
91#1438C2212yes—
92#1438C2212yes—
93#1438C2212yes—
94#1438C2212yes—
95#1438C2212yes—
96#1438C2211yescharacteristic
97#1438C2212yes—
98#1437C2212yes—
99#1437C2211yescharacteristic
100#1437C2212yes—
101#1437C2211yescharacteristic
102#1436C2212yes—
103#1436C2212yes—
104#1436C2212yes—
105C4⋊#95C2212yes—
106#1434C2212yes—
107#1434C2212yes—
108C22⋊#95C2212yes—
109C23×Q8C2311yescharacteristic
110C23×D4C2311yescharacteristic
111C23×D4C2312yes—
112C23×D4C2311yescharacteristic
113C23×D4C2312yes—
114C24×C4C2312yes—
115C24×C4C2311yescharacteristic
116C2×#124—24no—
117C2×#124—42no—
118C2×#124—42no—
119C2×C4×D4—24no—
120C2×C4×D4—42no—
121C2×C4×D4—42no—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2311yescharacteristic
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⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2311yescharacteristic
160#399—24no—
161#397—24no—
162#397—28no—
163#397—24no—
164#397—42no—
165#397—44no—
166#397—44no—
167#394—28no—
168#394—44no—
169#394—44no—
170#393—28no—
171#392—28no—
172#392—24no—
173#392D418yes—
174#391—42no—
175#390—28no—
176#388—28no—
177#387—28no—
178#386—28no—
179#386—28no—
180#386—28no—
181#386—42no—
182#385—44no—
183#385—44no—
184#385—44no—
185#385—42no—
186#383—24no—
187#381—24no—
188#381—44no—
189C2×#95C2312yes—
190C2×#95C2311yescharacteristic
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2311yescharacteristic
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2311yescharacteristic
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2311yescharacteristic
231C25C2411yescharacteristic
232C25C2411yescharacteristic
233C25C2412yes—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—41no—
237C22×Q8—42no—
238C22×Q8—42no—
239C22×D4—22no—
240C22×D4—24no—
241C22×D4—22no—
242C22×D4—41no—
243C22×D4—41no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4—41no—
247C22×D4—42no—
248C22×D4—42no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4—42no—
252C22×D4—42no—
253C22×D4—42no—
254C22×D4—42no—
255C22×D4—42no—
256C22×D4—42no—
257C22×D4—42no—
258C22×D4—42no—
259C22×D4—42no—
260C22×D4—42no—
261C22×D4C2×D414yes—
262C22×D4C2×D418yes—
263C23×C4—24no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—41no—
274C23×C4—41no—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291#124—416no—
292C4×D4—416no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—41no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—41no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—22no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—22no—
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—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
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—41no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
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—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—41no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4C2×D414yes—
394C2×C22⋊C4C2×D418yes—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—41no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42—42no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—22no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—22no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—41no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95C2×D414yes—
445C24—22no—
446C24—21no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—21no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—21no—
468C24—21no—
469C24—22no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24C22×D412yes—
477C24C22×D414yes—
478C24C2511yescharacteristic
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—84no—
482C2×Q8—82no—
483C2×Q8—84no—
484C2×D4—44no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—48no—
493C2×D4—44no—
494C2×D4—48no—
495C2×D4—82no—
496C2×D4—84no—
497C2×D4—84no—
498C2×D4—84no—
499C2×D4—84no—
500C2×D4—84no—
501C2×D4—84no—
502C2×D4—84no—
503C2×D4—84no—
504C2×D4—84no—
505C2×D4—84no—
506C2×D4—84no—
507C2×D4—84no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
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—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
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—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—21no—
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—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—44no—
607C22×C4—84no—
608C22×C4—84no—
609C22×C4—84no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—84no—
613C22×C4—84no—
614C22×C4—84no—
615C22×C4—84no—
616C22×C4C22×D414yes—
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4H(5,𝔽2)12yes—
620C22×C4H(5,𝔽2)14yes—
621C22×C4H(5,𝔽2)12yes—
622C4⋊C4—48no—
623C4⋊C4—44no—
624C4⋊C4—82no—
625C4⋊C4—84no—
626C4⋊C4—84no—
627C4⋊C4—84no—
628C4⋊C4—84no—
629C4⋊C4—84no—
630C4⋊C4—84no—
631C22⋊C4—48no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—48no—
635C22⋊C4—44no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4—48no—
641C22⋊C4—84no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C22⋊C4—84no—
645C22⋊C4—84no—
646C22⋊C4—84no—
647C22⋊C4—84no—
648C22⋊C4—82no—
649C22⋊C4—84no—
650C22⋊C4—84no—
651C22⋊C4—84no—
652C22⋊C4—82no—
653C22⋊C4—84no—
654C22⋊C4—84no—
655C22⋊C4—84no—
656C22⋊C4—84no—
657C42—28no—
658C42—84no—
659C42—82no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—22no—
671C23—24no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—41no—
677C23—41no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—42no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—41no—
724C23—41no—
725C23—42no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23C23×D411yescharacteristic
738C23C2×H(5,𝔽2)11yescharacteristic
739C23C2×H(5,𝔽2)11yescharacteristic
740C23C2×H(5,𝔽2)12yes—
741C23#58512yes—
742C23#58512yes—
743C23#58512yes—
744C23#58512yes—
745C23#58512yes—
746Q8—88no—
747D4—416no—
748D4—816no—
749D4—88no—
750D4—816no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—41no—
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—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—816no—
854C2×C4—88no—
855C22—42no—
856C22—44no—
857C22—44no—
858C22—42no—
859C22—44no—
860C22—44no—
861C22—44no—
862C22—44no—
863C22—42no—
864C22—44no—
865C22—44no—
866C22—44no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22—82no—
875C22—82no—
876C22—82no—
877C22—82no—
878C22—82no—
879C22—81no—
880C22—82no—
881C22—81no—
882C22—82no—
883C22—81no—
884C22—82no—
885C22—82no—
886C22—82no—
887C22—82no—
888C22#348411yescharacteristic
889C22#348512yes—
890C22#348511yescharacteristic
891C22#348512yes—
892C22#349811yescharacteristic
893C22#352911yescharacteristic
894C22#353311yescharacteristic
895C22#353311yescharacteristic
896C22#353312yes—
897C22#353312yes—
898C22#353912yes—
899C22#354012yes—
900C22#354011yescharacteristic
901C22#354212yes—
902C22#355812yes—
903C22#356212yes—
904C22#356212yes—
905C22#356612yes—
906C22#356612yes—
907C22#356612yes—
908C22#356812yes—
909C4—42no—
910C4—42no—
911C4—42no—
912C4—42no—
913C4—44no—
914C4—44no—
915C4—81no—
916C4—82no—
917C4—82no—
918C4—82no—
919C4—82no—
920C4—82no—
921C4—82no—
922C4—82no—
923C4—82no—
924C4—82no—
925C2—82no—
926C2—84no—
927C2—161no—
928C2#4544111yescharacteristic
929C2#4642411yescharacteristic
930C2#4721312yes—
931C2#4877512yes—
932C2#5205411yescharacteristic
933C2#5236512yes—
934C2#5384712yes—
935C2#5626312yes—
936C2#5650112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2631C2
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×#2752C2semidirect
3. #17201C2semidirect
4. #17160C2semidirect
5. #17087C2semidirect
6. #16530C2semidirect
7. #16492C2semidirect
8. #16272C2semidirect
9. #16045C2semidirect
10. #16032C2semidirect
11. #15966C2semidirect
12. #15785C2semidirect
13. #15697C2semidirect
14. #15549C2semidirect
15. #15539C2semidirect
16. #15343C2semidirect
17. #15285C2semidirect
18. #14731C2semidirect
19. #14651C2semidirect

Maximal subgroups

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

subgroupindex
C2×#27522
C2×#26312
#172012
#171602
#170872
#165302
#164922
#162722
#160452
#160322
#159662
#157852
#156972
#155492
#155392
#153432
#152852
#147312
#146512