Finite Group Databasebeta

← #5035127

Subgroups — #5035127

Order 512.

2442 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2665C211yesmaximal, characteristic, complemented
2C2×#2377C211yesmaximal, characteristic
3#15975C212yesmaximal, complemented
4#15851C212yesmaximal, complemented
5#15787C212yesmaximal, complemented
6#15743C212yesmaximal, complemented
7#15638C212yesmaximal, complemented
8#15508C212yesmaximal, complemented
9#15506C212yesmaximal, complemented
10#15476C212yesmaximal, complemented
11#15362C212yesmaximal, complemented
12#15331C212yesmaximal, complemented
13#15329C212yesmaximal, complemented
14#15324C212yesmaximal, complemented
15#14347C211yesmaximal, characteristic, complemented
16#14257C211yesmaximal, characteristic
17#14152C211yesmaximal, characteristic
18#14128C211yesmaximal, characteristic, complemented
19#13951C211yesmaximal, characteristic, complemented
20C22×#121C2211yescharacteristic
21C22×#117C2211yescharacteristic
22#2665—28no—
23C2×#400C2212yes—
24C2×#400C2212yes—
25C2×#396C2212yes—
26C2×#395C2212yes—
27C2×#393C2212yes—
28C2×#393C2212yes—
29C2×#393C2212yes—
30#2377—28no—
31C2×#391C2212yes—
32C2×#391C2212yes—
33C2×#390C2212yes—
34C2×#390C2212yes—
35C2×#389C2212yes—
36C2×#388C2212yes—
37C2×#387C2212yes—
38C2×#387C2212yes—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#386C2212yes—
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#385C2212yes—
46C2×#381C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2211yescharacteristic
49C2×#380C2212yes—
50C2×C4×C22⋊C4C2211yescharacteristic
51C22×#95C2211yescharacteristic
52#1446C2212yes—
53#1445C2212yes—
54#1445C2211yescharacteristic
55#1445C2211yescharacteristic
56#1445C2212yes—
57#1444C2211yescharacteristic
58#1444C2211yescharacteristic
59#1444C2212yes—
60#1443C2212yes—
61#1443C2212yes—
62#1442C2211yescharacteristic
63#1442C2212yes—
64#1442C2212yes—
65#1442C2212yes—
66#1442C2212yes—
67#1442C2212yes—
68#1442C2212yes—
69#1442C2211yescharacteristic
70#1441C2212yes—
71#1441C2212yes—
72#1441C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yes—
87#1438C2211yescharacteristic
88#1438C2211yescharacteristic
89#1438C2212yes—
90#1438C2212yes—
91#1437C2212yes—
92#1437C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2212yes—
96#1436C2212yes—
97C4⋊#95C2212yes—
98C4⋊#95C2212yes—
99C4⋊#95C2212yes—
100#1434C2212yes—
101#1434C2212yes—
102C22⋊#95C2211yescharacteristic
103C22⋊#95C2211yescharacteristic
104C22⋊#95C2211yescharacteristic
105C22⋊#95C2211yescharacteristic
106C22⋊#95C2212yes—
107C22⋊#95C2212yes—
108C22⋊#95C2212yes—
109C23×Q8C2312yes—
110C23×D4C2312yes—
111C23×D4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2312yes—
115C24×C4C2311yescharacteristic
116C2×#121—24no—
117C2×#121—24no—
118C2×#121Q818yescomplemented
119C2×#117—24no—
120C2×#117—44no—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2311yescharacteristic
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C42C2312yes—
154C22×C42C2312yes—
155C22×C42C2312yes—
156#400—28no—
157#400—44no—
158#396—28no—
159#395—28no—
160#393—28no—
161#393—44no—
162#393—44no—
163#391—28no—
164#391—44no—
165#390—28no—
166#390—44no—
167#389—44no—
168#388—28no—
169#387—28no—
170#387—28no—
171#386—28no—
172#386—28no—
173#386—44no—
174#386—44no—
175#385—28no—
176#385—44no—
177#385—44no—
178#381D418yes—
179#380—24no—
180#380—24no—
181#380—44no—
182C4×C22⋊C4—24no—
183C2×#95—24no—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2311yescharacteristic
191C2×#95C2312yes—
192C2×#95C2311yescharacteristic
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2311yescharacteristic
197C2×#95C2311yescharacteristic
198C2×#95C2312yes—
199C2×#95C2311yescharacteristic
200C2×#95C2311yescharacteristic
201C2×#95C2312yes—
202C2×#95C2312yes—
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×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2311yescharacteristic
228C2×#95C2311yescharacteristic
229C25C2412yes—
230C25C2411yescharacteristic
231C22×Q8—24no—
232C22×Q8—24no—
233C22×Q8—42no—
234C22×Q8—42no—
235C22×Q8—42no—
236C22×Q8—42no—
237C22×Q8—42no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—42no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4—42no—
247C22×D4—42no—
248C22×D4C2×Q818yes—
249C22×D4C2×Q814yes—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—24no—
253C23×C4—42no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—41no—
258C23×C4—41no—
259C23×C4—41no—
260C23×C4—41no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4C2×D414yes—
270C23×C4C2×Q814yes—
271C23×C4#4114yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289#121—232no—
290#117—416no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
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—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
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—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4C2×Q814yes—
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—24no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
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—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4—41no—
363C2×C22⋊C4—41no—
364C2×C22⋊C4—41no—
365C2×C22⋊C4—41no—
366C2×C22⋊C4—41no—
367C2×C22⋊C4—41no—
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—42no—
383C2×C22⋊C4C2×D418yes—
384C2×C22⋊C4C2×Q818yes—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394#95—22no—
395#95—22no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—22no—
405#95—22no—
406#95—22no—
407#95—22no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—42no—
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#95C2×D414yes—
437#95C2×D418yes—
438#95C2×D414yes—
439C24—22no—
440C24—22no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24C22×D412yes—
462C24C22×Q814yes—
463C24C22×Q812yes—
464C24C2×#4112yes—
465C24C2511yescharacteristic
466C2×Q8—48no—
467C2×Q8—48no—
468C2×Q8—84no—
469C2×Q8—84no—
470C2×Q8—84no—
471C2×Q8—84no—
472C2×Q8—84no—
473C2×D4—216no—
474C2×D4—28no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—82no—
479C2×D4—82no—
480C2×D4—84no—
481C2×D4—84no—
482C2×D4—84no—
483C2×D4—84no—
484C2×D4—84no—
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—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
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—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
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—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
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—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
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—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—44no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—48no—
588C22×C4—84no—
589C22×C4—84no—
590C22×C4—84no—
591C22×C4—82no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4—82no—
595C22×C4—84no—
596C22×C4—84no—
597C22×C4—84no—
598C22×C4—84no—
599C22×C4—84no—
600C22×C4—84no—
601C22×C4—84no—
602C22×C4C22⋊Q8116yes—
603C22×C4C22×D414yes—
604C22×C4C22×D414yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×Q814yes—
608C22×C4C22×Q812yes—
609C22×C4C22×Q812yes—
610C22×C4C2×#4112yes—
611C22×C4C2×#4112yes—
612C22×C4H(5,𝔽2)14yes—
613C22×C4H(5,𝔽2)14yes—
614C4⋊C4—28no—
615C4⋊C4—28no—
616C4⋊C4—48no—
617C4⋊C4—44no—
618C4⋊C4—84no—
619C4⋊C4—84no—
620C4⋊C4—84no—
621C4⋊C4—84no—
622C4⋊C4—84no—
623C4⋊C4—84no—
624C4⋊C4—84no—
625C4⋊C4—84no—
626C4⋊C4—84no—
627C22⋊C4—216no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—84no—
633C22⋊C4—84no—
634C22⋊C4—84no—
635C22⋊C4—84no—
636C22⋊C4—84no—
637C22⋊C4—84no—
638C22⋊C4—82no—
639C22⋊C4—82no—
640C22⋊C4—82no—
641C22⋊C4—82no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C22⋊C4—84no—
645C22⋊C4—84no—
646C42—48no—
647C42—84no—
648C42—84no—
649C23—24no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
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—42no—
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—
706C23C2×C22⋊Q814yes—
707C23C23×D411yescharacteristic
708C23C23×Q811yescharacteristic
709C23C22×#4111yescharacteristic
710C23C2×H(5,𝔽2)12yes—
711C23C2×H(5,𝔽2)12yes—
712C23#58512yes—
713C23#58512yes—
714C23#58511yescharacteristic
715C23#58511yescharacteristic
716C23#58511yescharacteristic
717C23#58511yescharacteristic
718Q8—816no—
719D4—88no—
720D4—816no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—416no—
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—42no—
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—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
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—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
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—42no—
817C2×C4—42no—
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—816no—
828C2×C4—88no—
829C2×C4—88no—
830C2×C4C2×C22⋊Q814yes—
831C2×C4C2×C22⋊Q814yes—
832C22—24no—
833C22—24no—
834C22—24no—
835C22—44no—
836C22—42no—
837C22—42no—
838C22—44no—
839C22—44no—
840C22—42no—
841C22—44no—
842C22—42no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22C22×C22⋊Q811yescharacteristic
859C22#348812yes—
860C22#349011yescharacteristic
861C22#349111yescharacteristic
862C22#349311yescharacteristic
863C22#349311yescharacteristic
864C22#349612yes—
865C22#350011yescharacteristic
866C22#350011yescharacteristic
867C22#350112yes—
868C22#350112yes—
869C22#350411yescharacteristic
870C22#350411yescharacteristic
871C22#350811yescharacteristic
872C22#351011yescharacteristic
873C22#353312yes—
874C22#353312yes—
875C22#354012yes—
876C22#354612yes—
877C22#355812yes—
878C22#356012yes—
879C22#356612yes—
880C22#356612yes—
881C4—24no—
882C4—24no—
883C4—44no—
884C4—44no—
885C4—44no—
886C4—44no—
887C4—44no—
888C4—82no—
889C4—82no—
890C4—81no—
891C4—81no—
892C4—82no—
893C4—82no—
894C4—82no—
895C4—82no—
896C4—81no—
897C4—81no—
898C2—44no—
899C2—84no—
900C2#3535911yescharacteristic
901C2#3551511yescharacteristic
902C2#3562011yescharacteristic
903C2#4787312yes—
904C2#4788711yescharacteristic
905C2#4879811yescharacteristic
906C2#4958512yes—
907C2#4959811yescharacteristic
908C2#5018711yescharacteristic
909C2#5178612yes—
910C2#5179012yes—
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×#2665C2semidirect
3. #15975C2semidirect
4. #15851C2semidirect
5. #15787C2semidirect
6. #15743C2semidirect
7. #15638C2semidirect
8. #15508C2semidirect
9. #15506C2semidirect
10. #15476C2semidirect
11. #15362C2semidirect
12. #15331C2semidirect
13. #15329C2semidirect
14. #15324C2semidirect
15. #14347C2semidirect
18. #14128C2semidirect
19. #13951C2semidirect
118. C2×#121Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#26652
C2×#23772
#159752
#158512
#157872
#157432
#156382
#155082
#155062
#154762
#153622
#153312
#153292
#153242
#143472
#142572
#141522
#141282
#139512