Finite Group Databasebeta

← #1039329

Subgroups — #1039329

Order 512.

2770 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17282C212yesmaximal, complemented
2#16753C212yesmaximal, complemented
3#16741C212yesmaximal, complemented
4#16706C211yesmaximal, characteristic, complemented
5#16666C211yesmaximal, characteristic, complemented
6#16200C212yesmaximal, complemented
7#16133C212yesmaximal, complemented
8#15484C212yesmaximal, complemented
9#14934C212yesmaximal, complemented
10C22⋊#401C212yesmaximal, complemented
11#14717C211yesmaximal, characteristic
12#14596C211yesmaximal, characteristic, complemented
13#14508C211yesmaximal, characteristic, complemented
14#13958C212yesmaximal, complemented
15#13870C212yesmaximal, complemented
16#13869C212yesmaximal
17#13869C211yesmaximal, characteristic
18#13868C212yesmaximal
19C2×#1439C211yesmaximal, characteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#117C2212yes—
22C23×C4⋊C4C2211yescharacteristic
23C23×C22⋊C4C2212yes—
24C23×C22⋊C4C2211yescharacteristic
25C23×C22⋊C4C2211yescharacteristic
26C2×#401C2212yescomplemented
27C2×#393C2211yescharacteristic
28C2×#393C2211yescharacteristic
29C2×#381C2211yescharacteristic
30C2×#381C2212yes—
31C2×#381C2212yes—
32C2×#381C2212yes—
33C2×#381C2211yescharacteristic
34C2×#379C2211yescharacteristic
35C2×#379C2212yes—
36C22×#95C2212yes—
37C22×#95C2211yescharacteristic
38#1446C2212yescomplemented
39#1446C2212yescomplemented
40#1445C2212yescomplemented
41#1445C2212yescomplemented
42#1445C2212yescomplemented
43#1445C2212yescomplemented
44#1443C2212yescomplemented
45#1443C2212yescomplemented
46#1443C2212yescomplemented
47#1443C2212yescomplemented
48#1443C2212yescomplemented
49#1443C2212yescomplemented
50#1443C2212yescomplemented
51#1442C2212yescomplemented
52#1442C2212yescomplemented
53#1442C2212yescomplemented
54#1442C2212yescomplemented
55#1442C2212yescomplemented
56#1442C2212yescomplemented
57#1441C2212yescomplemented
58#1441C2212yescomplemented
59#1441C2212yescomplemented
60#1441C2212yescomplemented
61#1440C2212yes—
62#1440C2212yes—
63#1440C2212yes—
64#1440C2212yes—
65#1440C2212yes—
66#1440C2212yes—
67#1439C2211yescharacteristic
68#1439C2212yes—
69#1439C2212yes—
70#1439C2212yes—
71#1439C2211yescharacteristic
72#1439C2211yescharacteristic
73#1439C2212yes—
74#1439C2211yescharacteristic
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2211yescharacteristic
79#1439C2212yes—
80#1439C2211yescharacteristic
81#1437C2212yes—
82#1437C2212yes—
83#1437C2212yes—
84#1437C2212yes—
85#1436C2212yescomplemented
86#1436C2212yescomplemented
87#1436C2212yescomplemented
88#1436C2212yescomplemented
89#1434C2212yescomplemented
90#1434C2212yescomplemented
91#1434C2212yescomplemented
92#1434C2212yescomplemented
93C22⋊#95C2212yes—
94C22⋊#95C2211yescharacteristic
95C22⋊#95C2211yescharacteristic
96C22⋊#95C2212yes—
97C22⋊#95C2212yes—
98C22⋊#95C2212yes—
99C22⋊#95C2212yes—
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2211yescharacteristic
107C26C2311yescharacteristic
108C23×Q8C2311yescharacteristic
109C24×C4C2312yes—
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2312yes—
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C2×C22⋊Q8—44no—
116C2×C22⋊Q8—42no—
117C2×#117—28no—
118C2×#117—44no—
119C2×#117—44no—
120C22×C4⋊C4—28no—
121C22×C4⋊C4—42no—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C22⋊C4—28no—
130C22×C22⋊C4—24no—
131C22×C22⋊C4—28no—
132C22×C22⋊C4—24no—
133C22×C22⋊C4—42no—
134C22×C22⋊C4—42no—
135C22×C22⋊C4—42no—
136C22×C22⋊C4—44no—
137C22×C22⋊C4—42no—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2311yescharacteristic
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160#401—44no—
161#393—24no—
162#393—42no—
163#381—24no—
164#381—42no—
165#381—44no—
166#381—44no—
167#381—44no—
168#379—42no—
169#379—44no—
170C2×#95—42no—
171C2×#95—44no—
172C2×#95C2312yes—
173C2×#95C2311yescharacteristic
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2311yescharacteristic
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
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×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222C25—22no—
223C25—22no—
224C25—24no—
225C25—22no—
226C25—24no—
227C25—22no—
228C25—41no—
229C25—42no—
230C25—42no—
231C25—41no—
232C25#4114yes—
233C25C2411yescharacteristic
234C25C2411yescharacteristic
235C25C2411yescharacteristic
236C22×Q8—22no—
237C22×Q8—42no—
238C22×Q8—41no—
239C22×Q8—42no—
240C22×Q8—41no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—22no—
254C23×C4—24no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—42no—
262C23×C4—41no—
263C23×C4—41no—
264C23×C4—41no—
265C23×C4—41no—
266C23×C4—41no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—41no—
272C23×C4—42no—
273C23×C4—41no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4#4118yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C22⋊Q8—416no—
294#117—432no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—41no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—41no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—416no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—41no—
345C2×C22⋊C4—41no—
346C2×C22⋊C4—41no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—41no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—432no—
357C2×C22⋊C4—416no—
358C2×C22⋊C4—416no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—42no—
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—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—41no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4#4114yes—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—42no—
383#95—24no—
384#95—24no—
385#95—22no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—42no—
391#95—42no—
392#95—41no—
393#95—41no—
394#95—42no—
395#95—42no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—42no—
401#95—42no—
402#95—42no—
403#95—42no—
404#95—42no—
405#95—42no—
406#95—42no—
407#95—42no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
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—41no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—42no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—22no—
438C24—21no—
439C24—22no—
440C24—21no—
441C24—22no—
442C24—21no—
443C24—21no—
444C24—22no—
445C24—22no—
446C24—21no—
447C24—28no—
448C24—22no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—21no—
455C24—22no—
456C24—22no—
457C24—21no—
458C24—28no—
459C24—216no—
460C24—48no—
461C24—44no—
462C24—44no—
463C24—48no—
464C24—44no—
465C24—48no—
466C24—48no—
467C24—48no—
468C24—44no—
469C24—44no—
470C24—48no—
471C24—44no—
472C24—44no—
473C24—84no—
474C24—84no—
475C24—82no—
476C24—84no—
477C24—84no—
478C24—82no—
479C24—84no—
480C24C2×#4112yes—
481C24C2×#4112yes—
482C24C2×#4112yes—
483C24C2×#4112yes—
484C24C2×#4114yes—
485C24H(5,𝔽2)12yes—
486C24H(5,𝔽2)12yes—
487C24H(5,𝔽2)14yes—
488C242−1+412yes—
489C24C2511yescharacteristic
490C2×Q8—44no—
491C2×Q8—82no—
492C2×Q8—84no—
493C2×Q8—84no—
494C2×Q8—82no—
495C22×C4—28no—
496C22×C4—216no—
497C22×C4—216no—
498C22×C4—216no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
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—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
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—21no—
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—22no—
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—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—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
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—48no—
599C22×C4—48no—
600C22×C4—44no—
601C22×C4—48no—
602C22×C4—44no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—44no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—84no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4—84no—
620C22×C4—84no—
621C22×C4—84no—
622C22×C4—82no—
623C22×C4—84no—
624C22×C4—84no—
625C22×C4—82no—
626C22×C4—82no—
627C22×C4—82no—
628C22×C4—82no—
629C22×C4—84no—
630C22×C4C2×#4112yes—
631C22×C4C2×#4112yes—
632C22×C4C2×#4114yes—
633C22×C4C2×#4114yes—
634C22×C4H(5,𝔽2)12yes—
635C4⋊C4—44no—
636C4⋊C4—48no—
637C4⋊C4—44no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—44no—
641C4⋊C4—48no—
642C22⋊C4—44no—
643C22⋊C4—44no—
644C22⋊C4—48no—
645C22⋊C4—48no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—44no—
649C22⋊C4—44no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—82no—
656C22⋊C4—84no—
657C22⋊C4—84no—
658C22⋊C4—82no—
659C22⋊C4—84no—
660C22⋊C4—84no—
661C22⋊C4—84no—
662C42—48no—
663C42—48no—
664C23—22no—
665C23—24no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—22no—
670C23—24no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—22no—
678C23—22no—
679C23—24no—
680C23—22no—
681C23—24no—
682C23—22no—
683C23—24no—
684C23—24no—
685C23—22no—
686C23—24no—
687C23—22no—
688C23—24no—
689C23—22no—
690C23—24no—
691C23—24no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—24no—
696C23—22no—
697C23—24no—
698C23—22no—
699C23—432no—
700C23—416no—
701C23—42no—
702C23—41no—
703C23—42no—
704C23—42no—
705C23—41no—
706C23—41no—
707C23—42no—
708C23—42no—
709C23—41no—
710C23—42no—
711C23—42no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—41no—
721C23—416no—
722C23—42no—
723C23—41no—
724C23—42no—
725C23—41no—
726C23—41no—
727C23—42no—
728C23—41no—
729C23—42no—
730C23—816no—
731C23—88no—
732C23—88no—
733C23—816no—
734C23—88no—
735C23—816no—
736C23—88no—
737C23—88no—
738C23#53818yes—
739C23#53814yes—
740C23#55114yes—
741C23#55118yes—
742C23#55214yes—
743C23#56014yes—
744C23C22×#4111yescharacteristic
745C23C22×#4112yes—
746C23C22×#4111yescharacteristic
747C23C2×H(5,𝔽2)11yescharacteristic
748C23C2×H(5,𝔽2)11yescharacteristic
749C23C2×H(5,𝔽2)12yes—
750C23C2×H(5,𝔽2)11yescharacteristic
751C23C2×2−1+411yescharacteristic
752C23#58512yes—
753C23#58512yes—
754C23#58511yescharacteristic
755Q8—88no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—416no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—432no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
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—41no—
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—42no—
828C2×C4—41no—
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—42no—
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—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—88no—
863C2×C4—816no—
864C2×C4—88no—
865C2×C4—88no—
866C22—24no—
867C22—28no—
868C22—24no—
869C22—28no—
870C22—28no—
871C22—28no—
872C22—24no—
873C22—24no—
874C22—24no—
875C22—24no—
876C22—28no—
877C22—24no—
878C22—42no—
879C22—44no—
880C22—42no—
881C22—44no—
882C22—44no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—44no—
888C22—44no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—832no—
893C22—81no—
894C22—82no—
895C22—81no—
896C22—82no—
897C22—81no—
898C22—81no—
899C22#276018yes—
900C22C2×#53812yes—
901C22C2×#53811yescharacteristic
902C22C2×#55111yescharacteristic
903C22C2×#55112yes—
904C22C2×#55211yescharacteristic
905C22#347512yes—
906C22#349011yescharacteristic
907C22#349112yes—
908C22#349412yes—
909C22#349411yescharacteristic
910C22#349512yes—
911C22#350511yescharacteristic
912C22#351012yes—
913C22#351312yes—
914C22C2×#56011yescharacteristic
915C22#353311yescharacteristic
916C22#353312yes—
917C22#353512yes—
918C22#353511yescharacteristic
919C22#353611yescharacteristic
920C22#354212yes—
921C22#354511yescharacteristic
922C22#356012yes—
923C4—42no—
924C4—42no—
925C4—44no—
926C4—44no—
927C4—42no—
928C4—82no—
929C4—82no—
930C4—82no—
931C4—82no—
932C4—82no—
933C4—82no—
934C4—82no—
935C4—82no—
936C4—82no—
937C4—81no—
938C4—82no—
939C2—28no—
940C2—44no—
941C2—82no—
942C2#3788111yescharacteristic
943C2#3846812yes—
944C2#4142711yescharacteristic
945C2#4201212yes—
946C2#4393312yes—
947C2#4478611yescharacteristic
948C2#4633411yescharacteristic
949C2C2×#276011yescharacteristic
950C2#5274111yescharacteristic
951C2#5919311yescharacteristic
952C2#5919612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #17282C2semidirect
2. #16753C2semidirect
3. #16741C2semidirect
4. #16706C2semidirect
5. #16666C2semidirect
6. #16200C2semidirect
7. #16133C2semidirect
8. #15484C2semidirect
9. #14934C2semidirect
10. C22⋊#401C2semidirect
12. #14596C2semidirect
13. #14508C2semidirect
14. #13958C2semidirect
15. #13870C2semidirect
26. C2×#401C22semidirect
38. #1446C22semidirect
39. #1446C22semidirect
40. #1445C22semidirect
41. #1445C22semidirect
42. #1445C22semidirect
43. #1445C22semidirect
44. #1443C22semidirect
45. #1443C22semidirect
46. #1443C22semidirect
47. #1443C22semidirect
48. #1443C22semidirect
49. #1443C22semidirect
50. #1443C22semidirect
51. #1442C22semidirect
52. #1442C22semidirect
53. #1442C22semidirect
54. #1442C22semidirect
55. #1442C22semidirect
56. #1442C22semidirect
57. #1441C22semidirect
58. #1441C22semidirect
59. #1441C22semidirect
60. #1441C22semidirect
85. #1436C22semidirect
86. #1436C22semidirect
87. #1436C22semidirect
88. #1436C22semidirect
89. #1434C22semidirect
90. #1434C22semidirect
91. #1434C22semidirect
92. #1434C22semidirect

Maximal subgroups

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

subgroupindex
#172822
#167532
#167412
#167062
#166662
#162002
#161332
#154842
#149342
C22⋊#4012
#147172
#145962
#145082
#139582
#138702
#138692
#138682
C2×#14392