Finite Group Databasebeta

← #4123561

Subgroups — #4123561

Order 512.

2971 conjugacy classes of subgroups.

The subgroup lattice has 933 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2523C211yesmaximal, characteristic, complemented
2C2×#2436C211yesmaximal, characteristic
3#17201C211yesmaximal, characteristic, complemented
4#15931C212yesmaximal, complemented
5#15785C212yesmaximal, complemented
6#15687C212yesmaximal, complemented
7#15674C211yesmaximal, characteristic
8#15568C211yesmaximal, characteristic, complemented
9#15499C212yesmaximal, complemented
10#15380C212yesmaximal, complemented
11#15336C212yesmaximal, complemented
12#15260C211yesmaximal, characteristic
13#14232C211yesmaximal, characteristic, complemented
14#14196C212yesmaximal, complemented
15#14098C212yesmaximal, complemented
16#14096C212yesmaximal, complemented
17#14091C212yesmaximal, complemented
18#13990C212yesmaximal, complemented
19#13922C212yesmaximal, complemented
20C24×Q8C2211yescharacteristic
21C22×#124C2212yes—
22C22×#123C2211yescharacteristic
23C22×#121C2211yescharacteristic
24#2523—28no—
25#2436—28no—
26C2×#400C2211yescharacteristic
27C2×#399C2212yes—
28C2×#397C2211yescharacteristic
29C2×#397C2212yes—
30C2×#394C2212yes—
31C2×#393C2211yescharacteristic
32C2×#393C2211yescharacteristic
33C2×#393C2211yescharacteristic
34C2×#393C2211yescharacteristic
35C2×#391C2212yes—
36C2×#391C2212yes—
37C2×#391C2212yes—
38C2×#391C2212yes—
39C2×#391C2212yes—
40C2×#390C2211yescharacteristic
41C2×#388C2212yes—
42C2×#388C2212yes—
43C2×#387C2212yes—
44C2×#387C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2211yescharacteristic
48C2×#385C2211yescharacteristic
49C2×#383C2212yes—
50C2×#380C2212yes—
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2212yes—
54#1446C2212yes—
55#1446C2212yes—
56#1446C2212yes—
57#1446C2212yes—
58#1445C2212yes—
59#1445C2212yes—
60#1445C2212yes—
61#1444C2212yes—
62#1443C2212yes—
63#1442C2212yes—
64#1442C2212yes—
65#1442C2212yes—
66#1442C2212yes—
67#1441C2212yes—
68#1441C2212yes—
69#1440C2212yes—
70#1440C2212yes—
71#1440C2212yes—
72#1440C2211yescharacteristic
73#1440C2212yes—
74#1440C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1438C2212yes—
81#1438C2212yes—
82#1438C2211yescharacteristic
83#1438C2211yescharacteristic
84#1438C2211yescharacteristic
85#1437C2212yes—
86#1437C2212yes—
87#1437C2212yes—
88#1437C2212yes—
89#1437C2211yescharacteristic
90#1437C2212yes—
91#1437C2212yes—
92#1436C2211yescharacteristic
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97#1436C2212yes—
98C4⋊#95C2212yes—
99#1434C2212yes—
100#1434C2212yes—
101#1434C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C4×#95C2212yes—
108C4×#95C2212yes—
109C23×Q8—24no—
110C23×Q8—28no—
111C23×Q8—42no—
112C23×Q8—42no—
113C23×Q8—44no—
114C23×Q8C2311yescharacteristic
115C23×Q8C2312yes—
116C23×Q8C2311yescharacteristic
117C23×D4C2311yescharacteristic
118C23×D4C2311yescharacteristic
119C23×D4C2311yescharacteristic
120C24×C4C2311yescharacteristic
121C24×C4C2312yes—
122C24×C4C2311yescharacteristic
123C2×#124—28no—
124C2×#124—28no—
125C2×#124—44no—
126C2×#123—28no—
127C2×#123—42no—
128C2×#121—24no—
129C2×#121—42no—
130C2×#121—42no—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2312yes—
162C22×C42C2312yes—
163C22×C42C2312yes—
164C22×C42C2311yescharacteristic
165#400—42no—
166#399—44no—
167#397—28no—
168#397—24no—
169#394—28no—
170#393—24no—
171#393—24no—
172#393—24no—
173#393D418yes—
174#391—28no—
175#391—28no—
176#391—28no—
177#391—44no—
178#391—44no—
179#390—42no—
180#388—28no—
181#388—44no—
182#387—28no—
183#387—28no—
184#386—28no—
185#386—28no—
186#386—42no—
187#385—24no—
188#383—28no—
189#380—44no—
190C4×C22⋊C4—28no—
191C4×C22⋊C4—24no—
192C4×C22⋊C4—44no—
193C2×#95C2311yescharacteristic
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2311yescharacteristic
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2311yescharacteristic
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2311yescharacteristic
236C2×#95C2312yes—
237C25C2411yescharacteristic
238C25C2411yescharacteristic
239C25C2411yescharacteristic
240C22×Q8—24no—
241C22×Q8—22no—
242C22×Q8—24no—
243C22×Q8—24no—
244C22×Q8—24no—
245C22×Q8—24no—
246C22×Q8—24no—
247C22×Q8—24no—
248C22×Q8—41no—
249C22×Q8—42no—
250C22×Q8—41no—
251C22×Q8—42no—
252C22×Q8—41no—
253C22×Q8—42no—
254C22×Q8—41no—
255C22×Q8—416no—
256C22×Q8—432no—
257C22×Q8—432no—
258C22×Q8—416no—
259C22×Q8—416no—
260C22×Q8C2×D414yes—
261C22×Q8#4118yes—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—24no—
265C22×D4—24no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—24no—
270C22×D4—22no—
271C22×D4—41no—
272C22×D4—41no—
273C22×D4—41no—
274C22×D4—42no—
275C22×D4—42no—
276C22×D4—42no—
277C23×C4—22no—
278C23×C4—24no—
279C23×C4—22no—
280C23×C4—24no—
281C23×C4—22no—
282C23×C4—24no—
283C23×C4—22no—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—41no—
292C23×C4—42no—
293C23×C4—41no—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2411yescharacteristic
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2411yescharacteristic
310#124—432no—
311#123—416no—
312#121—416no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—41no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—41no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—41no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—41no—
371C2×C22⋊C4—41no—
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—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—41no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4C2×D418yes—
392C2×C22⋊C4C2×D414yes—
393C2×C22⋊C4#4118yes—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—42no—
406C2×C42—41no—
407C2×C42—42no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411#95—24no—
412#95—24no—
413#95—22no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—22no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—42no—
448#95—42no—
449#95—42no—
450#95—42no—
451#95—41no—
452#95—42no—
453#95C2×D414yes—
454#95C2×D418yes—
455C24—21no—
456C24—22no—
457C24—22no—
458C24—21no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—21no—
466C24—21no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—21no—
475C24—21no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24C22×D412yes—
480C24C2×#4114yes—
481C24H(5,𝔽2)12yes—
482C24C2511yescharacteristic
483C2×Q8—216no—
484C2×Q8—216no—
485C2×Q8—216no—
486C2×Q8—44no—
487C2×Q8—48no—
488C2×Q8—48no—
489C2×Q8—44no—
490C2×Q8—48no—
491C2×Q8—48no—
492C2×Q8—48no—
493C2×Q8—44no—
494C2×Q8—48no—
495C2×Q8—48no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—48no—
499C2×Q8—4128no—
500C2×Q8—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—44no—
506C2×D4—48no—
507C2×D4—44no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—84no—
511C2×D4—82no—
512C2×D4—84no—
513C2×D4—82no—
514C2×D4—84no—
515C2×D4—82no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—28no—
524C22×C4—216no—
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—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
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—21no—
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—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—21no—
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—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—44no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—44no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—44no—
622C22×C4—84no—
623C22×C4—82no—
624C22×C4—82no—
625C22×C4C22×D412yes—
626C22×C4C22×D414yes—
627C22×C4C22×D412yes—
628C22×C4C22×D414yes—
629C22×C4C2×#4114yes—
630C22×C4C2×#4114yes—
631C22×C4C2×#4114yes—
632C22×C4C2×#4114yes—
633C22×C4C2×#4114yes—
634C22×C4H(5,𝔽2)14yes—
635C22×C4H(5,𝔽2)12yes—
636C22×C42−1+414yes—
637C4⋊C4—48no—
638C4⋊C4—44no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—84no—
642C4⋊C4—82no—
643C4⋊C4—84no—
644C4⋊C4—84no—
645C22⋊C4—216no—
646C22⋊C4—216no—
647C22⋊C4—44no—
648C22⋊C4—44no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—44no—
654C22⋊C4—48no—
655C22⋊C4—44no—
656C22⋊C4—48no—
657C22⋊C4—84no—
658C22⋊C4—84no—
659C22⋊C4—84no—
660C22⋊C4—84no—
661C22⋊C4—84no—
662C22⋊C4—84no—
663C22⋊C4—82no—
664C22⋊C4—84no—
665C42—48no—
666C42—48no—
667C42—84no—
668C42—84no—
669C42—84no—
670C42—82no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—22no—
681C23—24no—
682C23—24no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—42no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—42no—
691C23—42no—
692C23—41no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—41no—
697C23—41no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—41no—
707C23—42no—
708C23—41no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—42no—
717C23—42no—
718C23—41no—
719C23—41no—
720C23—42no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—41no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23#55114yes—
734C23C23×D411yescharacteristic
735C23C22×#4112yes—
736C23C22×#4112yes—
737C23C2×H(5,𝔽2)12yes—
738C23C2×H(5,𝔽2)11yescharacteristic
739C23C2×H(5,𝔽2)11yescharacteristic
740C23C2×2−1+412yes—
741C23#58512yes—
742C23#58512yes—
743Q8—416no—
744Q8—432no—
745Q8—416no—
746D4—88no—
747D4—88no—
748D4—88no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—432no—
779C2×C4—416no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
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—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
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—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—41no—
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—41no—
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—88no—
854C2×C4#54618yes—
855C2×C4#55114yes—
856C22—24no—
857C22—28no—
858C22—44no—
859C22—44no—
860C22—42no—
861C22—44no—
862C22—42no—
863C22—44no—
864C22—44no—
865C22—44no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—44no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22—82no—
875C22—82no—
876C22—81no—
877C22—81no—
878C22—82no—
879C22—81no—
880C22—82no—
881C22—82no—
882C22—82no—
883C22C2×#54612yes—
884C22D4×#4112yes—
885C22C2×#55111yescharacteristic
886C22C2×#55111yescharacteristic
887C22#348012yes—
888C22#348212yes—
889C22#348411yescharacteristic
890C22#348711yescharacteristic
891C22#349012yes—
892C22#349911yescharacteristic
893C22#351112yes—
894C22#351412yes—
895C22#351412yes—
896C22#351612yes—
897C22#352412yes—
898C22#353211yescharacteristic
899C22#353512yes—
900C22#354511yescharacteristic
901C22#355412yes—
902C22#356112yes—
903C22#356212yes—
904C4—28no—
905C4—24no—
906C4—44no—
907C4—44no—
908C4—44no—
909C4—42no—
910C4—44no—
911C4—42no—
912C4—44no—
913C4—82no—
914C4—81no—
915C4—82no—
916C4—82no—
917C4—82no—
918C4—82no—
919C4—82no—
920C2—44no—
921C2—82no—
922C2—161no—
923C2#4636111yescharacteristic
924C2#4660712yes—
925C2#4749612yes—
926C2#5900611yescharacteristic
927C2#5910412yes—
928C2#5916211yescharacteristic
929C2#5941512yes—
930C2#5948912yes—
931C2#5988212yes—
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×#2523C2semidirect
3. #17201C2semidirect
4. #15931C2semidirect
5. #15785C2semidirect
6. #15687C2semidirect
8. #15568C2semidirect
9. #15499C2semidirect
10. #15380C2semidirect
11. #15336C2semidirect
13. #14232C2semidirect
14. #14196C2semidirect
15. #14098C2semidirect
16. #14096C2semidirect
17. #14091C2semidirect
18. #13990C2semidirect
19. #13922C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25232
C2×#24362
#172012
#159312
#157852
#156872
#156742
#155682
#154992
#153802
#153362
#152602
#142322
#141962
#140982
#140962
#140912
#139902
#139222