Finite Group Databasebeta

← #4308751

Subgroups — #4308751

Order 512.

5302 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#525C211yesmaximal, characteristic
2C2×#2848C211yesmaximal, characteristic, complemented
3C2×#2638C212yesmaximal, complemented
4#16365C211yesmaximal, characteristic, complemented
5#16362C211yesmaximal, characteristic, complemented
6#16359C212yesmaximal, complemented
7#16262C212yesmaximal, complemented
8#16259C212yesmaximal, complemented
9#16255C214yesmaximal, complemented
10#16254C211yesmaximal, characteristic, complemented
11#16253C211yesmaximal, characteristic, complemented
12#16251C212yesmaximal, complemented
13#15203C214yesmaximal, complemented
14#15114C212yesmaximal, complemented
15#14889C212yesmaximal, complemented
16#14681C211yesmaximal, characteristic, complemented
17#14344C212yesmaximal, complemented
18C23×#41C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C2×#525—28no—
21C2×#525—216no—
22C22×#123C2212yes—
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C22×#120C2212yes—
31C22×C4×D4C2212yes—
32C22×C4×D4C2212yes—
33C22×#117C2211yescharacteristic
34#2848—28no—
35#2638—216no—
36C2×#398C2212yescomplemented
37C2×#397C2214yes—
38C2×#397C2212yescomplemented
39C2×#395C2212yescomplemented
40C2×#395C2212yescomplemented
41C2×#394C2214yes—
42C2×#394C2214yes—
43C2×#394C2212yescomplemented
44C2×#393C2212yescomplemented
45C2×#387C2214yescomplemented
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#385C2214yescomplemented
50C2×#381C2212yes—
51C2×#381C2212yes—
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#379C2212yes—
56C2×#379C2212yes—
57#1446C2212yescomplemented
58#1444C2212yescomplemented
59#1444C2214yescomplemented
60#1442C2212yescomplemented
61#1442C2214yescomplemented
62#1441C2212yescomplemented
63#1441C2212yescomplemented
64#1441C2212yescomplemented
65#1441C2212yescomplemented
66#1440C2214yes—
67#1440C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2212yescomplemented
72#1439C2212yescomplemented
73#1439C2214yescomplemented
74#1439C2214yescomplemented
75#1438C2214yes—
76#1438C2214yes—
77#1438C2214yes—
78#1438C2214yes—
79#1438C2212yescomplemented
80#1434C2214yescomplemented
81C22⋊#95C2212yes—
82C22⋊#95C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2211yescharacteristic
85C22⋊#95C2211yescharacteristic
86C22⋊#95C2214yescomplemented
87C26C2311yescharacteristic
88C22×#41—28no—
89C22×#41—24no—
90C22×#41—44no—
91C22×#41—44no—
92C23×Q8C2311yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×D4C2312yes—
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C23×D4C2312yes—
98C24×C4—28no—
99C24×C4—44no—
100C24×C4—44no—
101C24×C4D418yes—
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2312yes—
108C24×C4C2311yescharacteristic
109#525—2128no—
110C2×#123—28no—
111C2×#123—28no—
112C2×#123—28no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—28no—
119C2×C22⋊Q8—28no—
120C2×C22⋊Q8—28no—
121C2×C22⋊Q8—44no—
122C2×C22⋊Q8—44no—
123C2×#121—28no—
124C2×#121—24no—
125C2×#121—24no—
126C2×#121—28no—
127C2×#120—28no—
128C2×#120—28no—
129C2×#120—28no—
130C2×C4×D4—28no—
131C2×C4×D4—28no—
132C2×C4×D4—28no—
133C2×C4×D4—28no—
134C2×C4×D4—28no—
135C2×C4×D4D4116yes—
136C2×#117—24no—
137C2×#117—28no—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2314yes—
146C22×C4⋊C4C2314yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2314yes—
168C22×C22⋊C4C2314yes—
169C22×C42C2312yes—
170#398—28no—
171#397—216no—
172#397—28no—
173#395—28no—
174#395—44no—
175#394—216no—
176#394—44no—
177#394—48no—
178#393—28no—
179#387—216no—
180#385—28no—
181#385—28no—
182#385—28no—
183#385—216no—
184#381—28no—
185#381—44no—
186#380—24no—
187#380—24no—
188#380—24no—
189#379—28no—
190#379—44no—
191C2×#95C2314yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C25—24no—
211C25—24no—
212C25—24no—
213C25—42no—
214C25—42no—
215C25—41no—
216C25—41no—
217C25—42no—
218C25C2×D414yes—
219C25C2412yes—
220C25C2411yescharacteristic
221C25C2411yescharacteristic
222C25C2411yescharacteristic
223C2×#41—232no—
224C2×#41—464no—
225C2×#41—416no—
226C2×#41—416no—
227C22×Q8—24no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—24no—
231C22×Q8—24no—
232C22×Q8—42no—
233C22×Q8—42no—
234C22×Q8—42no—
235C22×D4—24no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—28no—
243C22×D4—28no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—22no—
247C22×D4—24no—
248C22×D4—42no—
249C22×D4—42no—
250C22×D4—44no—
251C22×D4—42no—
252C22×D4—42no—
253C22×D4—42no—
254C22×D4—44no—
255C22×D4C2×D418yes—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—232no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—416no—
270C23×C4—416no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—44no—
279C23×C4—44no—
280C23×C4—464no—
281C23×C4C2×D414yes—
282C23×C4C2×D414yes—
283C23×C4C2×D414yes—
284C23×C4C2×D414yes—
285C23×C4C2×D414yes—
286C23×C4C2×D418yes—
287C23×C4C2×D414yes—
288C23×C4C2×D418yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2414yes—
294C23×C4C2414yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302#123—264no—
303C22⋊Q8—232no—
304C22⋊Q8—232no—
305C22⋊Q8—416no—
306C22⋊Q8—416no—
307C22⋊Q8—416no—
308#121—232no—
309#121—232no—
310#120—264no—
311C4×D4—264no—
312C4×D4—264no—
313#117—232no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4C2×D418yes—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
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—28no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4C2×D418yes—
396C2×C22⋊C4C2×D418yes—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42C2×D418yes—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—28no—
404#95—24no—
405#95—24no—
406#95—28no—
407#95—28no—
408#95—28no—
409#95—28no—
410#95—24no—
411#95—24no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95—44no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—21no—
430C24—21no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—21no—
438C24—21no—
439C24—22no—
440C24—28no—
441C24—28no—
442C24—28no—
443C24—22no—
444C24—22no—
445C24—24no—
446C24—24no—
447C24—24no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—24no—
453C24—44no—
454C24—44no—
455C24—44no—
456C24—44no—
457C24—416no—
458C24—416no—
459C24—48no—
460C24—48no—
461C24—48no—
462C24—48no—
463C24—416no—
464C24—416no—
465C24—48no—
466C24—48no—
467C24C22×D414yes—
468C24C22×D412yes—
469C24C22×D414yes—
470C24C22×D412yes—
471C24C22×D412yes—
472C24H(5,𝔽2)14yes—
473C242−1+414yes—
474C24C2511yescharacteristic
475#41—4128no—
476C2×Q8—28no—
477C2×Q8—416no—
478C2×Q8—44no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—88no—
484C2×D4—216no—
485C2×D4—216no—
486C2×D4—28no—
487C2×D4—216no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—416no—
491C2×D4—416no—
492C2×D4—416no—
493C2×D4—44no—
494C2×D4—416no—
495C2×D4—416no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—44no—
505C22×C4—232no—
506C22×C4—28no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—28no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—28no—
535C22×C4—216no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—24no—
575C22×C4—22no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—416no—
584C22×C4—416no—
585C22×C4—416no—
586C22×C4—416no—
587C22×C4—416no—
588C22×C4—4128no—
589C22×C4—416no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—416no—
593C22×C4#120116yes—
594C22×C4C22×D414yes—
595C22×C4C22×D414yes—
596C22×C4C22×D412yes—
597C22×C4C22×D414yes—
598C22×C4C22×D412yes—
599C22×C4C22×D414yes—
600C22×C4C22×D414yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4H(5,𝔽2)14yes—
604C4⋊C4—28no—
605C4⋊C4—28no—
606C4⋊C4—216no—
607C4⋊C4—216no—
608C4⋊C4—416no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—48no—
612C4⋊C4—44no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—88no—
616C22⋊C4—216no—
617C22⋊C4—216no—
618C22⋊C4—216no—
619C22⋊C4—216no—
620C22⋊C4—216no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—416no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—88no—
629C22⋊C4—88no—
630C22⋊C4—88no—
631C22⋊C4—84no—
632C22⋊C4—84no—
633C22⋊C4—88no—
634C22⋊C4—88no—
635C42—216no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—24no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—28no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—28no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—28no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—28no—
670C23—28no—
671C23—416no—
672C23—416no—
673C23—416no—
674C23—416no—
675C23—416no—
676C23—416no—
677C23—416no—
678C23—464no—
679C23—464no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—44no—
697C23—44no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23C2×#12014yes—
717C23#53414yes—
718C23#53614yes—
719C23C23×D411yescharacteristic
720C23C23×D412yes—
721C23C2×H(5,𝔽2)12yes—
722C23C2×H(5,𝔽2)12yes—
723C23C2×2−1+412yes—
724C23#58512yes—
725C23#58511yescharacteristic
726C23#58511yescharacteristic
727C23#58512yes—
728Q8—416no—
729Q8—88no—
730D4—416no—
731D4—432no—
732D4—432no—
733D4—432no—
734C2×C4—232no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—28no—
753C2×C4—28no—
754C2×C4—416no—
755C2×C4—416no—
756C2×C4—416no—
757C2×C4—416no—
758C2×C4—416no—
759C2×C4—432no—
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—44no—
769C2×C4—44no—
770C2×C4—44no—
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—44no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4C2×#12014yes—
808C2×C4C2×#12014yes—
809C2×C4#53414yes—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—464no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—48no—
831C22—48no—
832C22—48no—
833C22—48no—
834C22—48no—
835C22—48no—
836C22—42no—
837C22—42no—
838C22—44no—
839C22—48no—
840C22—48no—
841C22—44no—
842C22—44no—
843C22—82no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—84no—
848C22—84no—
849C22C22×#12011yescharacteristic
850C22C2×#53411yescharacteristic
851C22C2×#53411yescharacteristic
852C22C2×#53611yescharacteristic
853C22#344911yescharacteristic
854C22#344911yescharacteristic
855C22#344911yescharacteristic
856C22#344912yes—
857C22#344912yes—
858C22#348414yes—
859C22#348914yes—
860C22#353314yes—
861C22#353512yes—
862C22#353512yes—
863C22#353912yes—
864C22#354012yes—
865C22#354114yes—
866C4—24no—
867C4—24no—
868C4—24no—
869C4—44no—
870C4—42no—
871C4—44no—
872C4—44no—
873C4—82no—
874C4—82no—
875C4—82no—
876C4—84no—
877C4—84no—
878C4—82no—
879C2—44no—
880C2—44no—
881C2—44no—
882C2—84no—
883C2#3463211yescharacteristic
884C2#3498011yescharacteristic
885C2#3530511yescharacteristic
886C2#3671214yes—
887C2#3672314yes—
888C2#3744511yescharacteristic
889C2#3744711yescharacteristic
890C2#3744911yescharacteristic
891C2#3745411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#525C2
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×#2848C2semidirect
3. C2×#2638C2semidirect
4. #16365C2semidirect
5. #16362C2semidirect
6. #16359C2semidirect
7. #16262C2semidirect
8. #16259C2semidirect
9. #16255C2semidirect
10. #16254C2semidirect
11. #16253C2semidirect
12. #16251C2semidirect
13. #15203C2semidirect
14. #15114C2semidirect
15. #14889C2semidirect
16. #14681C2semidirect
17. #14344C2semidirect
36. C2×#398C22semidirect
38. C2×#397C22semidirect
39. C2×#395C22semidirect
40. C2×#395C22semidirect
43. C2×#394C22semidirect
44. C2×#393C22semidirect
45. C2×#387C22semidirect
49. C2×#385C22semidirect
57. #1446C22semidirect
58. #1444C22semidirect
59. #1444C22semidirect
60. #1442C22semidirect
61. #1442C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
65. #1441C22semidirect
71. #1439C22semidirect
72. #1439C22semidirect
73. #1439C22semidirect
74. #1439C22semidirect
79. #1438C22semidirect
80. #1434C22semidirect
86. C22⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C22×#5252
C2×#28482
C2×#26382
#163652
#163622
#163592
#162622
#162592
#162552
#162542
#162532
#162512
#152032
#151142
#148892
#146812
#143442