Finite Group Databasebeta

← #734976

Subgroups — #734976

Order 512.

4760 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2591C211yesmaximal, characteristic, complemented
2C2×#2433C211yesmaximal, characteristic
3C22×#394C211yesmaximal, characteristic, complemented
4C2×#2345C211yesmaximal, characteristic, complemented
5#16802C212yesmaximal, complemented
6#16503C212yesmaximal, complemented
7#15617C214yesmaximal, complemented
8#15428C214yesmaximal, complemented
9#15127C212yesmaximal, complemented
10#15107C212yesmaximal, complemented
11#14725C212yesmaximal, complemented
12#14725C212yesmaximal, complemented
13#14271C211yesmaximal, characteristic, complemented
14#13995C212yesmaximal, complemented
15#13995C212yesmaximal, complemented
16#13902C211yesmaximal, characteristic, complemented
17#13782C211yesmaximal, characteristic, complemented
18C24×D4C2211yescharacteristic
19C22×#127C2212yes—
20C22×#121C2211yescharacteristic
21C22×#120C2212yes—
22C22×#120C2212yes—
23C23×C4⋊C4C2211yescharacteristic
24C23×C22⋊C4C2212yes—
25C23×C22⋊C4C2212yes—
26#2591—28no—
27#2433—28no—
28C2×#400C2211yescharacteristic, complemented
29C2×#400C2211yescharacteristic, complemented
30C2×#394—28no—
31C2×#394C2212yes—
32C2×#394C2212yes—
33C2×#394C2212yes—
34C2×#394C2212yes—
35C2×#394C2211yescharacteristic, complemented
36C2×#394C2211yescharacteristic, complemented
37C2×#394C2214yescomplemented
38C2×#394C2214yescomplemented
39C2×#392C2214yes—
40#2345—28no—
41C2×#390C2212yes—
42C2×#390C2214yes—
43C2×#390C2214yescomplemented
44C2×#390C2214yescomplemented
45C2×#389C2212yescomplemented
46C2×#388C2212yescomplemented
47C2×#388C2212yescomplemented
48C2×#387C2212yescomplemented
49C2×#387C2212yescomplemented
50C2×#386C2212yes—
51C2×#386C2212yes—
52C2×#386C2212yes—
53C2×#386C2212yes—
54C2×#385C2212yes—
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#379C2212yes—
59C2×#379C2212yes—
60C2×C4×C4⋊C4C2212yescomplemented
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C22×#95C2211yescharacteristic
66#1445C2212yescomplemented
67#1440C2214yescomplemented
68#1440C2214yescomplemented
69#1439C2214yescomplemented
70#1439C2214yescomplemented
71#1439C2214yescomplemented
72#1439C2214yescomplemented
73#1439C2214yescomplemented
74#1438C2212yes—
75#1438C2212yes—
76#1438C2214yescomplemented
77#1438C2214yescomplemented
78#1438C2212yescomplemented
79#1438C2214yescomplemented
80#1438C2214yescomplemented
81#1437C2214yescomplemented
82#1437C2214yescomplemented
83#1436C2214yescomplemented
84C4⋊#95C2212yescomplemented
85#1434C2212yescomplemented
86C22⋊#95C2212yes—
87C26C2312yes—
88C23×D4—24no—
89C23×D4—24no—
90C23×D4—24no—
91C23×D4—48no—
92C23×D4C2312yes—
93C23×D4C2312yes—
94C23×D4C2312yes—
95C23×D4C2314yes—
96C23×D4C2311yescharacteristic
97C23×D4C2314yes—
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C2×#127—28no—
103C2×#127—48no—
104C2×#121—24no—
105C2×#121—24no—
106C2×#121—24no—
107C2×#120—28no—
108C2×#120—28no—
109C2×#120—28no—
110C2×#120—28no—
111C2×#120—44no—
112C2×#120—44no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—24no—
115C22×C4⋊C4D418yescomplemented
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2312yes—
125C22×C22⋊C4—28no—
126C22×C22⋊C4—28no—
127C22×C22⋊C4—48no—
128C22×C22⋊C4—48no—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2311yescharacteristic
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2312yes—
154C22×C42C2312yes—
155#400—24no—
156#400—24no—
157#394—24no—
158#394—24no—
159#394—28no—
160#394—28no—
161#394—28no—
162#394—28no—
163#394—48no—
164#394—48no—
165#392—216no—
166#390—28no—
167#390—48no—
168#390—48no—
169#390—48no—
170#389—28no—
171#388—28no—
172#388—28no—
173#387—28no—
174#387—28no—
175#386—28no—
176#386—28no—
177#386—44no—
178#386—44no—
179#385—28no—
180#380—24no—
181#380—24no—
182#380—24no—
183#379—44no—
184#379—44no—
185C4×C4⋊C4—28no—
186C4×C22⋊C4—24no—
187C4×C22⋊C4—24no—
188C4×C22⋊C4—24no—
189C4×C22⋊C4D418yes—
190C2×#95—24no—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2311yescharacteristic
194C2×#95C2311yescharacteristic
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C25—24no—
211C25—28no—
212C25—24no—
213C25—24no—
214C25—24no—
215C25—24no—
216C25—24no—
217C25—24no—
218C25—44no—
219C25—44no—
220C25—44no—
221C25C2412yes—
222C25C2414yes—
223C25C2411yescharacteristic
224C22×D4—28no—
225C22×D4—28no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—28no—
234C22×D4—28no—
235C22×D4—24no—
236C22×D4—22no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—28no—
241C22×D4—28no—
242C22×D4—22no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—28no—
246C22×D4—28no—
247C22×D4—22no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4—432no—
260C22×D4—432no—
261C22×D4—432no—
262C22×D4—416no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—42no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4C2×D414yes—
277C23×C4C2×D414yes—
278C23×C4C2×D414yes—
279C23×C4C2×D414yes—
280C23×C4#4114yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2414yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295#127—432no—
296#121—416no—
297#120—432no—
298#120—432no—
299C2×C4⋊C4—232no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
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—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4C2×D414yes—
322C2×C4⋊C4C2×D414yes—
323C2×C4⋊C4C2×D414yes—
324C2×C4⋊C4C2×D414yes—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—432no—
363C2×C22⋊C4—432no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
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⋊C4C2×D414yes—
383C2×C22⋊C4C2×D414yes—
384C2×C22⋊C4#4118yes—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—44no—
390C2×C42—42no—
391C2×C42—44no—
392C2×C42—44no—
393C2×C42C2×D418yes—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—22no—
399#95—22no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—28no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95—44no—
412#95C2×D418yes—
413C24—22no—
414C24—24no—
415C24—22no—
416C24—216no—
417C24—24no—
418C24—24no—
419C24—24no—
420C24—24no—
421C24—24no—
422C24—24no—
423C24—24no—
424C24—24no—
425C24—24no—
426C24—24no—
427C24—24no—
428C24—24no—
429C24—24no—
430C24—24no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—24no—
437C24—22no—
438C24—22no—
439C24—24no—
440C24—24no—
441C24—24no—
442C24—416no—
443C24—416no—
444C24—416no—
445C24—416no—
446C24—416no—
447C24—416no—
448C24—48no—
449C24—48no—
450C24—48no—
451C24—48no—
452C24—48no—
453C24—48no—
454C24—48no—
455C24—48no—
456C24—48no—
457C24—48no—
458C24—88no—
459C24—88no—
460C24—88no—
461C24—88no—
462C24—88no—
463C24—88no—
464C24C22×D412yes—
465C24C22×D412yes—
466C24C2×#4112yes—
467C24C2×#4114yes—
468C24H(5,𝔽2)18yes—
469C24H(5,𝔽2)14yes—
470C24C2511yescharacteristic
471C2×D4—216no—
472C2×D4—216no—
473C2×D4—416no—
474C2×D4—416no—
475C2×D4—416no—
476C2×D4—416no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—416no—
480C2×D4—416no—
481C2×D4—416no—
482C2×D4—416no—
483C2×D4—416no—
484C2×D4—48no—
485C2×D4—4128no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—44no—
496C2×D4—416no—
497C2×D4—84no—
498C2×D4—88no—
499C2×D4—84no—
500C2×D4—88no—
501C2×D4—88no—
502C2×D4—88no—
503C2×D4—88no—
504C2×D4—88no—
505C2×D4—88no—
506C2×D4—88no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—28no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—44no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—84no—
577C22×C4—84no—
578C22×C4—88no—
579C22×C4—88no—
580C22×C4#121116yes—
581C22×C4C22×D414yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D414yes—
590C22×C4C22×D412yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4118yes—
594C22×C4H(5,𝔽2)14yes—
595C4⋊C4—28no—
596C4⋊C4—28no—
597C4⋊C4—28no—
598C4⋊C4—28no—
599C4⋊C4—48no—
600C4⋊C4—44no—
601C4⋊C4—84no—
602C4⋊C4—88no—
603C4⋊C4—84no—
604C22⋊C4—28no—
605C22⋊C4—416no—
606C22⋊C4—416no—
607C22⋊C4—48no—
608C22⋊C4—416no—
609C22⋊C4—416no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—416no—
615C22⋊C4—48no—
616C22⋊C4—416no—
617C22⋊C4—84no—
618C22⋊C4—84no—
619C22⋊C4—88no—
620C22⋊C4—88no—
621C22⋊C4—88no—
622C22⋊C4—88no—
623C22⋊C4—88no—
624C22⋊C4—88no—
625C22⋊C4#124116yes—
626C42—48no—
627C42—48no—
628C42—84no—
629C42—84no—
630C23—22no—
631C23—22no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—28no—
638C23—28no—
639C23—28no—
640C23—28no—
641C23—28no—
642C23—28no—
643C23—28no—
644C23—28no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—432no—
649C23—432no—
650C23—432no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
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—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—832no—
703C23—832no—
704C23—832no—
705C23—832no—
706C23—816no—
707C23—816no—
708C23—816no—
709C23—816no—
710C23C2×#12114yes—
711C23C2×#12414yes—
712C23#53514yes—
713C23#55018yes—
714C23#55918yes—
715C23C23×D411yescharacteristic
716C23C23×D411yescharacteristic
717C23C22×#4111yescharacteristic
718C23C22×#4112yes—
719C23C2×H(5,𝔽2)12yes—
720C23C2×H(5,𝔽2)12yes—
721C23C2×H(5,𝔽2)14yes—
722C23#58512yes—
723D4—432no—
724D4—432no—
725D4—832no—
726D4—88no—
727D4—832no—
728D4—816no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—28no—
742C2×C4—28no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—416no—
754C2×C4—416no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—44no—
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—42no—
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—88no—
798C2×C4—816no—
799C2×C4C2×#12114yes—
800C2×C4C2×#12114yes—
801C2×C4C2×#12418yes—
802C2×C4#53514yes—
803C22—24no—
804C22—28no—
805C22—28no—
806C22—216no—
807C22—24no—
808C22—28no—
809C22—28no—
810C22—48no—
811C22—48no—
812C22—48no—
813C22—48no—
814C22—48no—
815C22—48no—
816C22—48no—
817C22—864no—
818C22—84no—
819C22—84no—
820C22—84no—
821C22—84no—
822C22—84no—
823C22—84no—
824C22—84no—
825C22—84no—
826C22—82no—
827C22—84no—
828C22—82no—
829C22—84no—
830C22—84no—
831C22—84no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22#254818yes—
838C22C22×#12111yescharacteristic
839C22C22×#12411yescharacteristic
840C22C2×#53511yescharacteristic
841C22C2×#53511yescharacteristic
842C22#344911yescharacteristic
843C22C2×#55012yes—
844C22C2×#55912yes—
845C22#348412yes—
846C22#348412yes—
847C22#348812yes—
848C22#349012yes—
849C22#349412yes—
850C22#351314yes—
851C22#351914yes—
852C22#353414yes—
853C22#353714yes—
854C4—24no—
855C4—24no—
856C4—28no—
857C4—24no—
858C4—42no—
859C4—42no—
860C4—44no—
861C4—42no—
862C4—82no—
863C4—82no—
864C4—82no—
865C4—82no—
866C4—82no—
867C4—84no—
868C2—28no—
869C2—88no—
870C2—162no—
871C2C2×#254811yescharacteristic
872C2#3525211yescharacteristic
873C2#3534811yescharacteristic
874C2#3590312yes—
875C2#3912812yes—
876C2#3913212yes—
877C2#4059412yes—
878C2#4317814yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2433C2
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×#2591C2semidirect
3. C22×#394C2semidirect
4. C2×#2345C2semidirect
5. #16802C2semidirect
6. #16503C2semidirect
7. #15617C2semidirect
8. #15428C2semidirect
9. #15127C2semidirect
10. #15107C2semidirect
11. #14725C2semidirect
12. #14725C2semidirect
13. #14271C2semidirect
14. #13995C2semidirect
15. #13995C2semidirect
16. #13902C2semidirect
17. #13782C2semidirect
28. C2×#400C22semidirect
29. C2×#400C22semidirect
35. C2×#394C22semidirect
36. C2×#394C22semidirect
37. C2×#394C22semidirect
38. C2×#394C22semidirect
43. C2×#390C22semidirect
44. C2×#390C22semidirect
45. C2×#389C22semidirect
46. C2×#388C22semidirect
47. C2×#388C22semidirect
48. C2×#387C22semidirect
49. C2×#387C22semidirect
60. C2×C4×C4⋊C4C22semidirect
66. #1445C22semidirect
67. #1440C22semidirect
68. #1440C22semidirect
69. #1439C22semidirect
70. #1439C22semidirect
71. #1439C22semidirect
72. #1439C22semidirect
73. #1439C22semidirect
76. #1438C22semidirect
77. #1438C22semidirect
78. #1438C22semidirect
79. #1438C22semidirect
80. #1438C22semidirect
81. #1437C22semidirect
82. #1437C22semidirect
83. #1436C22semidirect
84. C4⋊#95C22semidirect
85. #1434C22semidirect
115. C22×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25912
C2×#24332
C22×#3942
C2×#23452
#168022
#165032
#156172
#154282
#151272
#151072
#147252
#142712
#139952
#139022
#137822