Finite Group Databasebeta

← #646732

Subgroups — #646732

Order 512.

4068 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#120C211yesmaximal, characteristic
2C22×#380C211yesmaximal, characteristic, complemented
3#16986C212yesmaximal, complemented
4#16884C212yesmaximal, complemented
5#16394C212yesmaximal, complemented
6#16392C212yesmaximal, complemented
7#15073C211yesmaximal, characteristic, complemented
8#15069C211yesmaximal, characteristic, complemented
9#15063C212yesmaximal, complemented
10#14918C212yesmaximal, complemented
11#14911C212yesmaximal
12#14843C211yesmaximal, characteristic, complemented
13#14825C212yesmaximal, complemented
14#14777C211yesmaximal, characteristic, complemented
15#14681C211yesmaximal, characteristic, complemented
16#14344C212yesmaximal, complemented
17#14295C212yesmaximal, complemented
18#13992C212yesmaximal, complemented
19#13968C212yesmaximal, complemented
20C25×C4C2211yescharacteristic
21C22×#123C2212yes—
22C22×#120C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C22⋊C4C2212yes—
29C2×#400C2212yescomplemented
30C2×#399C2212yescomplemented
31C4×#120—28no—
32C2×#386C2211yescharacteristic
33C2×#386C2211yescharacteristic
34C2×#386C2211yescharacteristic
35C2×#386C2212yes—
36C2×#385C2211yescharacteristic
37C2×#385C2211yescharacteristic
38C2×#385C2211yescharacteristic
39C2×#385C2212yes—
40C2×#381C2212yes—
41C2×#381C2212yes—
42C2×#381C2212yes—
43C2×#381C2212yes—
44C2×#381C2212yes—
45C2×#380—28no—
46C2×#380C2212yes—
47C2×#380C2212yes—
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#379C2211yescharacteristic
51C2×#379C2212yes—
52C2×C4×C22⋊C4C2211yescharacteristic
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C22×#95C2212yes—
56#1445C2212yescomplemented
57#1445C2212yescomplemented
58#1444C2212yescomplemented
59#1444C2212yescomplemented
60#1444C2212yescomplemented
61#1443C2214yescomplemented
62#1442C2214yescomplemented
63#1442C2212yescomplemented
64#1442C2212yescomplemented
65#1442C2212yescomplemented
66#1441C2212yescomplemented
67#1441C2212yescomplemented
68#1441C2214yescomplemented
69#1441C2212yescomplemented
70#1440C2214yes—
71#1440C2214yes—
72#1440C2214yescomplemented
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2212yescomplemented
78#1439C2212yescomplemented
79#1439C2212yescomplemented
80#1438C2214yes—
81#1438C2214yes—
82#1436C2214yescomplemented
83#1436C2214yescomplemented
84#1434C2214yescomplemented
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C22⋊#95C2212yes—
88C22⋊#95C2212yes—
89C22⋊#95C2211yescharacteristic
90C22⋊#95C2212yes—
91C22⋊#95C2211yescharacteristic
92C22⋊#95C2214yescomplemented
93C26C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C23×D4C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C24×C4—28no—
98C24×C4—44no—
99C24×C4—44no—
100C24×C4D418yes—
101C24×C4C2312yes—
102C24×C4C2311yescharacteristic
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2312yes—
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C2×#123—28no—
111C2×#123—44no—
112C2×#123—44no—
113C2×#120—24no—
114C2×#120—24no—
115C2×#120—24no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4—28no—
120C2×C4×D4—44no—
121C2×C4×D4—44no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—44no—
125C22×C4⋊C4—44no—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2314yes—
135C22×C22⋊C4—28no—
136C22×C22⋊C4—44no—
137C22×C22⋊C4—44no—
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2314yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161#400—44no—
162#399—44no—
163#386—24no—
164#386—24no—
165#386—24no—
166#386—44no—
167#385—24no—
168#385—24no—
169#385—24no—
170#385—44no—
171#381—28no—
172#381—28no—
173#381—44no—
174#381—44no—
175#381—44no—
176#380—28no—
177#380—28no—
178#380—28no—
179#380—28no—
180#379—24no—
181#379—44no—
182C4×C22⋊C4—24no—
183C4×C22⋊C4—24no—
184C4×C22⋊C4—24no—
185C2×#95—28no—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2311yescharacteristic
196C2×#95C2311yescharacteristic
197C2×#95C2311yescharacteristic
198C2×#95C2311yescharacteristic
199C2×#95C2311yescharacteristic
200C2×#95C2311yescharacteristic
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C25—24no—
213C25—24no—
214C25—24no—
215C25—22no—
216C25—22no—
217C25—24no—
218C25—42no—
219C25—42no—
220C25C2×D414yes—
221C25C2411yescharacteristic
222C25C2411yescharacteristic
223C25C2411yescharacteristic
224C25C2411yescharacteristic
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—42no—
238C22×D4—42no—
239C22×D4#4114yes—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—232no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—416no—
264C23×C4—416no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—44no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—44no—
276C23×C4—464no—
277C23×C4C2×D414yes—
278C23×C4C2×D414yes—
279C23×C4C2×D414yes—
280C23×C4C2×D414yes—
281C23×C4C2×D414yes—
282C23×C4C2×D414yes—
283C23×C4#4118yes—
284C23×C4C2411yescharacteristic
285C23×C4C2414yes—
286C23×C4C2414yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2414yes—
290C23×C4C2414yes—
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299#123—432no—
300#120—232no—
301C4×D4—416no—
302C4×D4—416no—
303C4×D4—416no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—416no—
323C2×C4⋊C4—416no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
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—22no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—432no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4#4114yes—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—24no—
383C2×C42—42no—
384C2×C42—42no—
385#95—28no—
386#95—28no—
387#95—22no—
388#95—22no—
389#95—22no—
390#95—22no—
391#95—22no—
392#95—22no—
393#95—28no—
394#95—24no—
395#95—24no—
396#95—28no—
397#95—28no—
398#95—24no—
399#95—24no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95—44no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—232no—
416C24—28no—
417C24—28no—
418C24—28no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—28no—
434C24—28no—
435C24—21no—
436C24—22no—
437C24—21no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—44no—
444C24—44no—
445C24—416no—
446C24—48no—
447C24—48no—
448C24—48no—
449C24—48no—
450C24—416no—
451C24—416no—
452C24—48no—
453C24—48no—
454C24C22×D412yes—
455C24C22×D412yes—
456C24C22×D412yes—
457C24C2×#4112yes—
458C24C2×#4114yes—
459C24C2×#4112yes—
460C24C2×#4112yes—
461C24H(5,𝔽2)14yes—
462C24H(5,𝔽2)14yes—
463C242−1+414yes—
464C24C2511yescharacteristic
465C2×D4—28no—
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—216no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—48no—
480C22×C4—232no—
481C22×C4—28no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
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—28no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
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—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—416no—
564C22×C4—416no—
565C22×C4—416no—
566C22×C4—416no—
567C22×C4—4128no—
568C22×C4—416no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—44no—
582C22×C4—88no—
583C22×C4—88no—
584C22×C4—88no—
585C22×C4#123116yescomplemented
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4114yes—
594C22×C4C2×#4114yes—
595C22×C4H(5,𝔽2)14yes—
596C4⋊C4—48no—
597C4⋊C4—48no—
598C4⋊C4—48no—
599C4⋊C4—44no—
600C4⋊C4—416no—
601C4⋊C4—44no—
602C4⋊C4—48no—
603C4⋊C4—44no—
604C4⋊C4—88no—
605C22⋊C4—28no—
606C22⋊C4—28no—
607C22⋊C4—28no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—416no—
611C22⋊C4—416no—
612C22⋊C4—44no—
613C22⋊C4—416no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—44no—
621C22⋊C4—44no—
622C22⋊C4—88no—
623C22⋊C4—88no—
624C22⋊C4—88no—
625C42—44no—
626C42—44no—
627C42—44no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—24no—
634C23—28no—
635C23—28no—
636C23—24no—
637C23—24no—
638C23—28no—
639C23—28no—
640C23—232no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—28no—
656C23—28no—
657C23—28no—
658C23—24no—
659C23—24no—
660C23—28no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—416no—
666C23—416no—
667C23—416no—
668C23—416no—
669C23—464no—
670C23—464no—
671C23—416no—
672C23—416no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—44no—
680C23—42no—
681C23—42no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—42no—
692C23—42no—
693C23—44no—
694C23—44no—
695C23—42no—
696C23—44no—
697C23—44no—
698C23C2×#12314yes—
699C23#52514yes—
700C23#53414yes—
701C23#53514yes—
702C23#53614yes—
703C23#53818yes—
704C23#54018yes—
705C23C23×D411yescharacteristic
706C23C22×#4112yes—
707C23C22×#4111yescharacteristic
708C23C22×#4111yescharacteristic
709C23C2×H(5,𝔽2)12yes—
710C23C2×H(5,𝔽2)12yes—
711C23C2×H(5,𝔽2)12yes—
712C23C2×2−1+412yes—
713C23#58512yes—
714D4—416no—
715D4—416no—
716D4—416no—
717C2×C4—232no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—28no—
725C2×C4—28no—
726C2×C4—28no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—416no—
737C2×C4—416no—
738C2×C4—416no—
739C2×C4—416no—
740C2×C4—416no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—44no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—44no—
779C2×C4—44no—
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—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—88no—
796C2×C4—816no—
797C2×C4—816no—
798C2×C4C2×#12314yes—
799C2×C4C2×#12314yes—
800C2×C4#53414yes—
801C22—24no—
802C22—216no—
803C22—216no—
804C22—24no—
805C22—24no—
806C22—24no—
807C22—24no—
808C22—24no—
809C22—24no—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—24no—
814C22—24no—
815C22—464no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—48no—
820C22—48no—
821C22—48no—
822C22—48no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—48no—
831C22—42no—
832C22—84no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22#263518yes—
838C22C22×#12311yescharacteristic
839C22C2×#52511yescharacteristic
840C22C2×#53411yescharacteristic
841C22C2×#53411yescharacteristic
842C22C2×#53511yescharacteristic
843C22C2×#53611yescharacteristic
844C22#344911yescharacteristic
845C22C2×#53812yes—
846C22C2×#54012yes—
847C22#347512yes—
848C22#347512yes—
849C22#349014yes—
850C22#349214yes—
851C22#352012yes—
852C22#352012yes—
853C22#353514yes—
854C22#354214yes—
855C4—24no—
856C4—24no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—84no—
863C4—84no—
864C4—84no—
865C4—81no—
866C4—81no—
867C4—84no—
868C4—81no—
869C4—81no—
870C2—28no—
871C2—44no—
872C2—44no—
873C2—82no—
874C2C2×#263511yescharacteristic
875C2#3480911yescharacteristic
876C2#3499211yescharacteristic
877C2#3508411yescharacteristic
878C2#3522711yescharacteristic
879C2#3744711yescharacteristic
880C2#3744811yescharacteristic
881C2#3790914yes—
882C2#3791114yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×#380C2semidirect
3. #16986C2semidirect
4. #16884C2semidirect
5. #16394C2semidirect
6. #16392C2semidirect
7. #15073C2semidirect
8. #15069C2semidirect
9. #15063C2semidirect
10. #14918C2semidirect
12. #14843C2semidirect
13. #14825C2semidirect
14. #14777C2semidirect
15. #14681C2semidirect
16. #14344C2semidirect
17. #14295C2semidirect
18. #13992C2semidirect
19. #13968C2semidirect
29. C2×#400C22semidirect
30. C2×#399C22semidirect
56. #1445C22semidirect
57. #1445C22semidirect
58. #1444C22semidirect
59. #1444C22semidirect
60. #1444C22semidirect
61. #1443C22semidirect
62. #1442C22semidirect
63. #1442C22semidirect
64. #1442C22semidirect
65. #1442C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
72. #1440C22semidirect
77. #1439C22semidirect
78. #1439C22semidirect
79. #1439C22semidirect
82. #1436C22semidirect
83. #1436C22semidirect
84. #1434C22semidirect
92. C22⋊#95C22semidirect
585. C22×C4#123semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#1202
C22×#3802
#169862
#168842
#163942
#163922
#150732
#150692
#150632
#149182
#149112
#148432
#148252
#147772
#146812
#143442
#142952
#139922
#139682