Finite Group Databasebeta

← #4930593

Subgroups — #4930593

Order 512.

5442 conjugacy classes of subgroups.

The subgroup lattice has 869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#518C211yesmaximal, characteristic
2C2×#2562C211yesmaximal, characteristic, complemented
3C2×#2611C211yesmaximal, characteristic, complemented
4C2×#2633C211yesmaximal, characteristic, complemented
5#14906C212yesmaximal, complemented
6#14860C212yesmaximal, complemented
7#14825C212yesmaximal, complemented
8#14824C212yesmaximal, complemented
9#14820C212yesmaximal, complemented
10#14801C212yesmaximal, complemented
11#14734C212yesmaximal, complemented
12#14724C212yesmaximal
13#14185C214yesmaximal, complemented
14#13971C214yesmaximal, complemented
15#13959C211yesmaximal, characteristic, complemented
16#13938C211yesmaximal, characteristic, complemented
17#13847C211yesmaximal, characteristic, complemented
18C24×D4C2211yescharacteristic
19C22×#125C2211yescharacteristic, complemented
20C2×#518—28no—
21C2×#518—28no—
22C2×#518—28no—
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2212yes—
25C22×C4×D4C2211yescharacteristic
26C22×C4×D4C2212yes—
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C23×C22⋊C4C2212yes—
32C23×C22⋊C4C2212yes—
33#2633—28no—
34#2611—28no—
35#2562—28no—
36C2×#400C2212yescomplemented
37C2×#400C2211yescharacteristic, complemented
38C2×#399C2211yescharacteristic
39C2×#399C2212yescomplemented
40C2×#398C2212yescomplemented
41C2×#398C2211yescharacteristic, complemented
42C2×#397C2211yescharacteristic
43C2×#397C2212yescomplemented
44C2×#394C2212yes—
45C2×#394C2212yes—
46C2×#394C2214yes—
47C2×#389C2212yescomplemented
48C2×#388C2212yes—
49C2×#388C2214yescomplemented
50C2×#387C2212yescomplemented
51C2×#385C2212yes—
52C2×#385C2214yescomplemented
53C2×#385C2214yescomplemented
54C2×#383C2211yescharacteristic, complemented
55C2×#380C2212yescomplemented
56C2×#380C2212yescomplemented
57C2×#379C2214yes—
58C2×#379C2214yes—
59C2×C4×C4⋊C4C2211yescharacteristic, complemented
60C2×C4×C22⋊C4C2214yescomplemented
61C2×#376C2211yescharacteristic, complemented
62#1445C2212yescomplemented
63#1445C2212yescomplemented
64#1441C2212yescomplemented
65#1440C2214yes—
66#1440C2214yescomplemented
67#1440C2214yescomplemented
68#1439C2214yes—
69#1439C2212yes—
70#1439C2214yescomplemented
71#1439C2212yescomplemented
72#1439C2212yescomplemented
73#1439C2214yescomplemented
74#1438C2212yes—
75#1438C2214yes—
76#1438C2212yes—
77#1437C2212yes—
78#1437C2214yescomplemented
79#1436C2214yescomplemented
80#1436C2214yescomplemented
81#1436C2212yescomplemented
82#1434C2212yescomplemented
83C22⋊#95C2212yes—
84C22⋊#95C2214yescomplemented
85C22⋊#95C2214yescomplemented
86C22⋊#95C2214yescomplemented
87C22⋊#95C2212yescomplemented
88C22⋊#95C2212yescomplemented
89C26C2312yes—
90C23×D4—28no—
91C23×D4—24no—
92C23×D4—24no—
93C23×D4—28no—
94C23×D4—24no—
95C23×D4C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C23×D4C2312yes—
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C24×C4C2312yes—
101C24×C4C2312yes—
102C24×C4C2312yes—
103C2×#125—24no—
104C2×#125—24no—
105C2×#125—24no—
106#518—2128no—
107C2×C4×D4—24no—
108C2×C4×D4—24no—
109C2×C4×D4—28no—
110C2×C4×D4—28no—
111C2×C4×D4—24no—
112C2×C4×D4—24no—
113C2×C4×D4—28no—
114C2×C4×D4—28no—
115C2×C4×D4—28no—
116C2×C4×D4—28no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4—24no—
120C2×C4×D4—24no—
121C2×C4×D4—24no—
122C2×C4×D4—24no—
123C2×C4×D4D418yes—
124C2×C4×D4D418yes—
125C2×#117—24no—
126C2×#117—24no—
127C2×#117—24no—
128C2×#117—24no—
129C2×#117—24no—
130C2×#117D418yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2312yes—
143C22×C22⋊C4—28no—
144C22×C22⋊C4—28no—
145C22×C22⋊C4—28no—
146C22×C22⋊C4—28no—
147C22×C22⋊C4—28no—
148C22×C22⋊C4—28no—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2314yes—
167C22×C42C2312yes—
168C22×C42C2312yes—
169C22×C42C2311yescharacteristic
170C22×C42C2312yes—
171C22×C42C2311yescharacteristic
172#400—28no—
173#400—24no—
174#399—24no—
175#399—28no—
176#398—24no—
177#398—28no—
178#397—24no—
179#397—28no—
180#394—28no—
181#394—28no—
182#394—216no—
183#389—28no—
184#388—216no—
185#388—28no—
186#387—28no—
187#385—28no—
188#385—216no—
189#385—48no—
190#383—24no—
191#380—28no—
192#380—28no—
193#379—216no—
194#379—48no—
195C4×C4⋊C4—24no—
196C4×C22⋊C4—48no—
197#376—24no—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2311yescharacteristic
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2311yescharacteristic
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C25—24no—
220C25—24no—
221C25—24no—
222C25—24no—
223C25—24no—
224C25—24no—
225C25—44no—
226C25—44no—
227C25—44no—
228C25—44no—
229C25#4118yes—
230C25C2411yescharacteristic
231C25C2412yes—
232C25C2412yes—
233C22×D4—232no—
234C22×D4—264no—
235C22×D4—264no—
236C22×D4—232no—
237C22×D4—232no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4C2×D414yes—
253C22×D4C2×D414yes—
254C22×D4#4118yes—
255C23×C4—24no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4—44no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4C2×D414yes—
278C23×C4C2×D418yes—
279C23×C4C2×D418yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2414yes—
283C23×C4C2414yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294#125—416no—
295C4×D4—264no—
296C4×D4—264no—
297C4×D4—232no—
298C4×D4—232no—
299C4×D4—232no—
300C4×D4—232no—
301#117—232no—
302#117—232no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4C2×D414yes—
334C2×C4⋊C4C2×D414yes—
335C2×C4⋊C4C2×D414yes—
336C2×C4⋊C4C2×D414yes—
337C2×C22⋊C4—264no—
338C2×C22⋊C4—264no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
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—28no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—42no—
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⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4C2×D414yes—
389C2×C22⋊C4C2×D414yes—
390C2×C22⋊C4C2×D418yes—
391C2×C22⋊C4C2×D418yes—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—42no—
401C2×C42—44no—
402C2×C42C2×D414yes—
403C2×C42C2×D414yes—
404C2×C42C2×D414yes—
405C2×C42C2×D414yes—
406#95—24no—
407#95—22no—
408#95—22no—
409#95—24no—
410#95—28no—
411#95—28no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—28no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—28no—
421#95—28no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95—44no—
426#95—44no—
427C24—216no—
428C24—216no—
429C24—216no—
430C24—216no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—24no—
443C24—24no—
444C24—22no—
445C24—24no—
446C24—24no—
447C24—24no—
448C24—24no—
449C24—24no—
450C24—24no—
451C24—22no—
452C24—24no—
453C24—216no—
454C24—216no—
455C24—216no—
456C24—416no—
457C24—416no—
458C24—84no—
459C24—84no—
460C24—88no—
461C24—88no—
462C24—88no—
463C24—84no—
464C24—88no—
465C24—84no—
466C24—88no—
467C24—88no—
468C24—88no—
469C24—88no—
470C24—88no—
471C24—88no—
472C24C22×D412yes—
473C24C22×D414yes—
474C24C22×D414yes—
475C24C2×#4114yes—
476C24C2×#4114yes—
477C24C2×#4114yes—
478C24C2×#4114yes—
479C24C2×#4114yes—
480C24C2511yescharacteristic
481C2×D4—216no—
482C2×D4—2256no—
483C2×D4—216no—
484C2×D4—216no—
485C2×D4—28no—
486C2×D4—28no—
487C2×D4—28no—
488C2×D4—28no—
489C2×D4—216no—
490C2×D4—216no—
491C2×D4—216no—
492C2×D4—216no—
493C2×D4—216no—
494C2×D4—216no—
495C2×D4—216no—
496C2×D4—28no—
497C2×D4—28no—
498C2×D4—216no—
499C22×C4—216no—
500C22×C4—216no—
501C22×C4—28no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—216no—
532C22×C4—216no—
533C22×C4—216no—
534C22×C4—216no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—416no—
569C22×C4—88no—
570C22×C4—84no—
571C22×C4—88no—
572C22×C4—88no—
573C22×C4—84no—
574C22×C4—84no—
575C22×C4—84no—
576C22×C4—88no—
577C22×C4—88no—
578C22×C4—88no—
579C22×C4—84no—
580C22×C4—88no—
581C22×C4—84no—
582C22×C4C22×D414yes—
583C22×C4C22×D412yes—
584C22×C4C22×D414yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C2×#4114yes—
597C22×C4H(5,𝔽2)14yes—
598C4⋊C4—28no—
599C4⋊C4—28no—
600C4⋊C4—28no—
601C4⋊C4—28no—
602C4⋊C4—48no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—88no—
610C22⋊C4—216no—
611C22⋊C4—216no—
612C22⋊C4—216no—
613C22⋊C4—28no—
614C22⋊C4—28no—
615C22⋊C4—216no—
616C22⋊C4—216no—
617C22⋊C4—48no—
618C22⋊C4—416no—
619C22⋊C4—416no—
620C22⋊C4—416no—
621C22⋊C4—48no—
622C22⋊C4—416no—
623C22⋊C4—416no—
624C22⋊C4—88no—
625C22⋊C4—88no—
626C22⋊C4—88no—
627C22⋊C4—88no—
628C42—216no—
629C42—28no—
630C42—48no—
631C42—84no—
632C42#120116yes—
633C23—264no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—22no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—28no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—24no—
658C23—28no—
659C23—24no—
660C23—24no—
661C23—28no—
662C23—28no—
663C23—28no—
664C23—28no—
665C23—28no—
666C23—28no—
667C23—28no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—42no—
677C23—42no—
678C23—41no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—42no—
683C23—42no—
684C23—41no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—816no—
694C23—832no—
695C23—832no—
696C23—816no—
697C23—816no—
698C23—816no—
699C23—832no—
700C23—832no—
701C23—816no—
702C23—816no—
703C23#52514yes—
704C23#52518yes—
705C23#52518yes—
706C23C23×D411yescharacteristic
707C23C23×D411yescharacteristic
708C23C23×D411yescharacteristic
709C23C22×#4112yes—
710C23C22×#4112yes—
711C23C2×H(5,𝔽2)12yes—
712C23#58514yes—
713C23#58512yes—
714D4—232no—
715D4—232no—
716D4—264no—
717C2×C4—232no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—28no—
742C2×C4—24no—
743C2×C4—28no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—816no—
789C2×C4—816no—
790C2×C4—816no—
791C2×C4—816no—
792C2×C4C2×#12014yes—
793C2×C4C2×#12014yes—
794C2×C4C2×#12014yes—
795C2×C4#52514yes—
796C22—28no—
797C22—24no—
798C22—28no—
799C22—28no—
800C22—216no—
801C22—28no—
802C22—28no—
803C22—44no—
804C22—44no—
805C22—44no—
806C22—44no—
807C22—44no—
808C22—44no—
809C22—42no—
810C22—48no—
811C22—48no—
812C22—48no—
813C22—48no—
814C22—48no—
815C22—48no—
816C22—44no—
817C22—48no—
818C22—48no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—42no—
826C22—864no—
827C22C22×#12011yescharacteristic
828C22C2×#52512yes—
829C22C2×#52512yes—
830C22C2×#52511yescharacteristic
831C22C2×#52511yescharacteristic
832C22#348512yes—
833C22#348812yes—
834C22#349114yes—
835C22#349612yes—
836C22#349811yescharacteristic
837C22#350012yes—
838C22#350012yes—
839C22#350011yescharacteristic
840C22#350514yes—
841C22#351314yes—
842C22#352114yes—
843C4—24no—
844C4—24no—
845C4—24no—
846C4—24no—
847C4—44no—
848C4—42no—
849C4—44no—
850C4—42no—
851C4—44no—
852C4—84no—
853C4—82no—
854C4—84no—
855C4—82no—
856C4—82no—
857C2—48no—
858C2—48no—
859C2—44no—
860C2#3536214yes—
861C2#3551311yescharacteristic
862C2#3561611yescharacteristic
863C2#3575312yes—
864C2#3584012yes—
865C2#3598212yes—
866C2#3601012yes—
867C2#3661411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2562C2semidirect
3. C2×#2611C2semidirect
4. C2×#2633C2semidirect
5. #14906C2semidirect
6. #14860C2semidirect
7. #14825C2semidirect
8. #14824C2semidirect
9. #14820C2semidirect
10. #14801C2semidirect
11. #14734C2semidirect
13. #14185C2semidirect
14. #13971C2semidirect
15. #13959C2semidirect
16. #13938C2semidirect
17. #13847C2semidirect
19. C22×#125C22semidirect
36. C2×#400C22semidirect
37. C2×#400C22semidirect
39. C2×#399C22semidirect
40. C2×#398C22semidirect
41. C2×#398C22semidirect
43. C2×#397C22semidirect
47. C2×#389C22semidirect
49. C2×#388C22semidirect
50. C2×#387C22semidirect
52. C2×#385C22semidirect
53. C2×#385C22semidirect
54. C2×#383C22semidirect
55. C2×#380C22semidirect
56. C2×#380C22semidirect
59. C2×C4×C4⋊C4C22semidirect
60. C2×C4×C22⋊C4C22semidirect
61. C2×#376C22semidirect
62. #1445C22semidirect
63. #1445C22semidirect
64. #1441C22semidirect
66. #1440C22semidirect
67. #1440C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
72. #1439C22semidirect
73. #1439C22semidirect
78. #1437C22semidirect
79. #1436C22semidirect
80. #1436C22semidirect
81. #1436C22semidirect
82. #1434C22semidirect
84. C22⋊#95C22semidirect
85. C22⋊#95C22semidirect
86. C22⋊#95C22semidirect
87. C22⋊#95C22semidirect
88. C22⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C22×#5182
C2×#25622
C2×#26112
C2×#26332
#149062
#148602
#148252
#148242
#148202
#148012
#147342
#147242
#141852
#139712
#139592
#139382
#138472