Finite Group Databasebeta

← #4452751

Subgroups — #4452751

Order 512.

4325 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2413C211yesmaximal, characteristic, complemented
2C2×#2613C211yesmaximal, characteristic
3C22×#394C211yesmaximal, characteristic, complemented
4C2×#2309C211yesmaximal, characteristic, complemented
5#17069C212yesmaximal, complemented
6#17022C212yesmaximal, complemented
7#17011C212yesmaximal, complemented
8#16819C212yesmaximal, complemented
9#16596C214yesmaximal, complemented
10#16552C214yesmaximal, complemented
11#14918C212yesmaximal, complemented
12#14911C212yesmaximal, complemented
13#14727C212yesmaximal, complemented
14#14718C212yesmaximal, complemented
15#14135C211yesmaximal, characteristic, complemented
16#13962C211yesmaximal, characteristic, complemented
17#13870C211yesmaximal, characteristic, complemented
18C24×D4C2211yescharacteristic
19C22×#123C2211yescharacteristic
20C22×#123C2211yescharacteristic
21C22×#120C2212yes—
22C22×#117C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C22⋊C4C2212yes—
26C23×C22⋊C4C2212yes—
27#2613—28no—
28#2413—28no—
29C2×#398C2212yescomplemented
30C2×#397C2214yescomplemented
31C2×#396C2212yescomplemented
32C2×#394—28no—
33C2×#394C2211yescharacteristic
34C2×#394C2212yes—
35C2×#394C2212yes—
36C2×#394C2214yes—
37C2×#394C2211yescharacteristic
38C2×#394C2212yes—
39C2×#394C2214yescomplemented
40C2×#392C2211yescharacteristic
41C2×#392C2212yes—
42C2×#392C2211yescharacteristic
43#2309—28no—
44C2×#390C2212yes—
45C2×#390C2212yes—
46C2×#390C2214yes—
47C2×#389C2212yescomplemented
48C2×#388C2212yescomplemented
49C2×#386C2211yescharacteristic
50C2×#386C2212yes—
51C2×#385C2211yescharacteristic
52C2×#385C2212yes—
53C2×#381C2211yescharacteristic
54C2×#381C2211yescharacteristic
55C2×#381C2212yes—
56C2×#379C2212yes—
57C2×#379C2212yes—
58C2×#379C2212yes—
59C22×#95C2211yescharacteristic
60#1441C2212yescomplemented
61#1441C2212yescomplemented
62#1441C2212yescomplemented
63#1441C2214yescomplemented
64#1440C2214yescomplemented
65#1440C2214yescomplemented
66#1440C2214yescomplemented
67#1440C2214yescomplemented
68#1440C2214yescomplemented
69#1439C2212yescomplemented
70#1439C2214yescomplemented
71#1439C2214yescomplemented
72#1439C2214yescomplemented
73#1439C2214yescomplemented
74#1439C2214yescomplemented
75#1439C2214yescomplemented
76#1438C2214yescomplemented
77#1438C2214yescomplemented
78#1438C2214yescomplemented
79#1437C2212yescomplemented
80#1436C2214yescomplemented
81#1436C2212yescomplemented
82C4⋊#95C2212yescomplemented
83#1434C2212yescomplemented
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C26C2312yes—
88C23×D4—24no—
89C23×D4—24no—
90C23×D4—44no—
91C23×D4—44no—
92C23×D4D418yes—
93C23×D4C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C23×D4C2312yes—
96C23×D4C2311yescharacteristic
97C23×D4C2312yes—
98C23×D4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C2×#123—24no—
104C2×#123—24no—
105C2×#123—24no—
106C2×#123—24no—
107C2×#123—44no—
108C2×#120—28no—
109C2×#120—44no—
110C2×#120—44no—
111C2×#117—24no—
112C2×#117—44no—
113C2×#117—44no—
114C2×#117D418yescomplemented
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2312yes—
127C22×C22⋊C4—28no—
128C22×C22⋊C4—28no—
129C22×C22⋊C4—48no—
130C22×C22⋊C4—44no—
131C22×C22⋊C4—44no—
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2311yescharacteristic
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2314yes—
156C22×C42C2312yes—
157C22×C42C2312yes—
158#398—28no—
159#397—48no—
160#396—28no—
161#394—24no—
162#394—24no—
163#394—28no—
164#394—28no—
165#394—28no—
166#394—216no—
167#394—48no—
168#392—24no—
169#392—28no—
170#392—24no—
171#390—216no—
172#390—28no—
173#390—28no—
174#389—28no—
175#388—28no—
176#386—24no—
177#386—44no—
178#385—24no—
179#385—44no—
180#381—24no—
181#381—24no—
182#381—44no—
183#379—28no—
184#379—28no—
185#379—28no—
186C2×#95—24no—
187C2×#95C2311yescharacteristic
188C2×#95C2311yescharacteristic
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C25—24no—
207C25—24no—
208C25—24no—
209C25—24no—
210C25—24no—
211C25—24no—
212C25—44no—
213C25—44no—
214C25—44no—
215C25—44no—
216C25C2×D418yes—
217C25C2411yescharacteristic
218C25C2412yes—
219C25C2412yes—
220C25C2411yescharacteristic
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—232no—
229C22×D4—24no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—24no—
234C22×D4—22no—
235C22×D4—432no—
236C22×D4—42no—
237C22×D4—42no—
238C22×D4—42no—
239C22×D4—42no—
240C22×D4—42no—
241C22×D4—42no—
242C22×D4—42no—
243C22×D4—42no—
244C22×D4—416no—
245C22×D4—416no—
246C22×D4—432no—
247C22×D4—42no—
248C22×D4—42no—
249C22×D4—42no—
250C22×D4—42no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4C2×D414yes—
256C22×D4C2×D418yes—
257C22×D4C2×D414yes—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—22no—
261C23×C4—24no—
262C23×C4—22no—
263C23×C4—24no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—42no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4C2×D414yes—
276C23×C4C2×D414yes—
277C23×C4#4114yes—
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2414yes—
281C23×C4C2412yes—
282C23×C4C2414yes—
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291#123—416no—
292#123—416no—
293#120—432no—
294#117—416no—
295#117—416no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—416no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4C2×D418yes—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—28no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—432no—
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—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⋊C4C2×D414yes—
387C2×C22⋊C4C2×D414yes—
388C2×C42—24no—
389C2×C42—44no—
390C2×C42—44no—
391C2×C42C2×D418yes—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—22no—
397#95—22no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—28no—
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—24no—
414C24—216no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—24no—
420C24—24no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—24no—
430C24—24no—
431C24—24no—
432C24—24no—
433C24—24no—
434C24—24no—
435C24—216no—
436C24—216no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—24no—
445C24—48no—
446C24—48no—
447C24—48no—
448C24—48no—
449C24—416no—
450C24—416no—
451C24—416no—
452C24—416no—
453C24—48no—
454C24—48no—
455C24—48no—
456C24—48no—
457C24—88no—
458C24—88no—
459C24—88no—
460C24—88no—
461C24—88no—
462C24—88no—
463C24—88no—
464C24—88no—
465C24C22×D414yes—
466C24C22×D414yes—
467C24C22×D412yes—
468C24C22×D412yes—
469C24C2×#4112yes—
470C24H(5,𝔽2)14yes—
471C24H(5,𝔽2)14yes—
472C24C2511yescharacteristic
473C2×D4—216no—
474C2×D4—28no—
475C2×D4—28no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—4128no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—48no—
484C2×D4—48no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—44no—
494C2×D4—48no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—48no—
498C2×D4—84no—
499C2×D4—84no—
500C2×D4—84no—
501C2×D4—84no—
502C2×D4—88no—
503C2×D4—88no—
504C2×D4—88no—
505C2×D4—88no—
506C22×C4—28no—
507C22×C4—216no—
508C22×C4—28no—
509C22×C4—216no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—28no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—44no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—48no—
584C22×C4—88no—
585C22×C4—88no—
586C22×C4#121116yes—
587C22×C4C22×D414yes—
588C22×C4C22×D414yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4H(5,𝔽2)14yes—
596C4⋊C4—48no—
597C4⋊C4—48no—
598C4⋊C4—48no—
599C4⋊C4—48no—
600C4⋊C4—48no—
601C4⋊C4—48no—
602C4⋊C4—44no—
603C4⋊C4—44no—
604C4⋊C4—88no—
605C22⋊C4—28no—
606C22⋊C4—28no—
607C22⋊C4—48no—
608C22⋊C4—416no—
609C22⋊C4—416no—
610C22⋊C4—48no—
611C22⋊C4—416no—
612C22⋊C4—416no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—44no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—88no—
621C22⋊C4—88no—
622C22⋊C4—88no—
623C22⋊C4—88no—
624C22⋊C4—84no—
625C22⋊C4—84no—
626C22⋊C4—84no—
627C22⋊C4—84no—
628C22⋊C4—88no—
629C42—48no—
630C42—48no—
631C23—22no—
632C23—24no—
633C23—22no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—28no—
639C23—28no—
640C23—28no—
641C23—28no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—432no—
657C23—432no—
658C23—432no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23—44no—
678C23—44no—
679C23—44no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—44no—
685C23—44no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—41no—
692C23—41no—
693C23—42no—
694C23—41no—
695C23—42no—
696C23—41no—
697C23—42no—
698C23—41no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—816no—
708C23—816no—
709C23—816no—
710C23—816no—
711C23—832no—
712C23—832no—
713C23—832no—
714C23—832no—
715C23C2×#12114yes—
716C23#53414yes—
717C23#53418yes—
718C23#53514yes—
719C23#53818yes—
720C23C23×D411yescharacteristic
721C23C23×D411yescharacteristic
722C23C22×#4111yescharacteristic
723C23C2×H(5,𝔽2)12yes—
724C23C2×H(5,𝔽2)12yes—
725C23C2×H(5,𝔽2)12yes—
726C23#58512yes—
727C23#58514yes—
728D4—416no—
729D4—416no—
730D4—432no—
731D4—816no—
732D4—816no—
733D4—88no—
734C2×C4—232no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—416no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—816no—
805C2×C4—88no—
806C2×C4C2×#12114yes—
807C2×C4C2×#12114yes—
808C22—24no—
809C22—28no—
810C22—28no—
811C22—24no—
812C22—28no—
813C22—28no—
814C22—216no—
815C22—44no—
816C22—44no—
817C22—44no—
818C22—44no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—864no—
830C22—84no—
831C22—84no—
832C22—84no—
833C22—84no—
834C22—84no—
835C22—84no—
836C22—84no—
837C22—84no—
838C22—81no—
839C22—82no—
840C22—82no—
841C22—81no—
842C22—82no—
843C22—82no—
844C22—84no—
845C22—81no—
846C22#261718yes—
847C22C22×#12111yescharacteristic
848C22C2×#53412yes—
849C22C2×#53411yescharacteristic
850C22C2×#53511yescharacteristic
851C22C2×#53812yes—
852C22#348411yescharacteristic
853C22#348512yes—
854C22#348511yescharacteristic
855C22#348812yes—
856C22#349412yes—
857C22#350012yes—
858C22#351012yes—
859C22#353314yes—
860C22#353314yes—
861C22#354214yes—
862C22#354214yes—
863C4—24no—
864C4—24no—
865C4—44no—
866C4—44no—
867C4—44no—
868C4—81no—
869C4—82no—
870C4—84no—
871C4—82no—
872C4—81no—
873C4—84no—
874C4—82no—
875C4—81no—
876C2—28no—
877C2—84no—
878C2—84no—
879C2—161no—
880C2C2×#261711yescharacteristic
881C2#3551411yescharacteristic
882C2#3561711yescharacteristic
883C2#3671512yes—
884C2#3696512yes—
885C2#4193312yes—
886C2#4193512yes—
887C2#4196314yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2613C2
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×#2413C2semidirect
3. C22×#394C2semidirect
4. C2×#2309C2semidirect
5. #17069C2semidirect
6. #17022C2semidirect
7. #17011C2semidirect
8. #16819C2semidirect
9. #16596C2semidirect
10. #16552C2semidirect
11. #14918C2semidirect
12. #14911C2semidirect
13. #14727C2semidirect
14. #14718C2semidirect
15. #14135C2semidirect
16. #13962C2semidirect
17. #13870C2semidirect
29. C2×#398C22semidirect
30. C2×#397C22semidirect
31. C2×#396C22semidirect
39. C2×#394C22semidirect
47. C2×#389C22semidirect
48. C2×#388C22semidirect
60. #1441C22semidirect
61. #1441C22semidirect
62. #1441C22semidirect
63. #1441C22semidirect
64. #1440C22semidirect
65. #1440C22semidirect
66. #1440C22semidirect
67. #1440C22semidirect
68. #1440C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
72. #1439C22semidirect
73. #1439C22semidirect
74. #1439C22semidirect
75. #1439C22semidirect
76. #1438C22semidirect
77. #1438C22semidirect
78. #1438C22semidirect
79. #1437C22semidirect
80. #1436C22semidirect
81. #1436C22semidirect
82. C4⋊#95C22semidirect
83. #1434C22semidirect
114. C2×#117D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24132
C2×#26132
C22×#3942
C2×#23092
#170692
#170222
#170112
#168192
#165962
#165522
#149182
#149112
#147272
#147182
#141352
#139622
#138702