Finite Group Databasebeta

← #920683

Subgroups — #920683

Order 512.

4026 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2408C211yesmaximal, characteristic
2C2×#2398C211yesmaximal, characteristic, complemented
3#17175C214yesmaximal, complemented
4#16808C212yesmaximal, complemented
5#16391C212yesmaximal, complemented
6#16357C212yesmaximal, complemented
7#16297C212yesmaximal, complemented
8#15266C214yesmaximal, complemented
9#15183C212yesmaximal, complemented
10#15157C212yesmaximal, complemented
11#15126C212yesmaximal, complemented
12#14260C212yesmaximal, complemented
13#14137C212yesmaximal, complemented
14#13902C212yesmaximal, complemented
15#13872C211yesmaximal, characteristic, complemented
16C24×D4C2211yescharacteristic
17C22×#121C2212yes—
18C22×#120C2212yes—
19C22×C4×Q8C2211yescharacteristic, complemented
20C22×C4×D4C2211yescharacteristic
21C23×C4⋊C4C2211yescharacteristic, complemented
22#2408—28no—
23#2398—28no—
24C2×#400C2212yescomplemented
25C2×#397C2211yescharacteristic
26C2×#397C2211yescharacteristic, complemented
27C2×#394C2212yes—
28C2×#394C2212yes—
29C2×#394C2214yescomplemented
30C2×#393C2211yescharacteristic
31C2×#393C2211yescharacteristic, complemented
32C2×#393C2214yescomplemented
33C2×#392C2212yes—
34C2×#390C2212yes—
35C2×#390C2212yes—
36C2×#390C2212yes—
37C2×#390C2212yes—
38C2×#390C2212yes—
39C2×#389C2212yescomplemented
40C2×#386C2212yes—
41C2×#386C2214yescomplemented
42C2×#386C2214yescomplemented
43C2×#380C2211yescharacteristic
44C2×#380C2212yes—
45C2×#380C2211yescharacteristic, complemented
46C2×#379C2212yes—
47C2×#379C2214yes—
48C2×#379C2214yes—
49C2×C4×C22⋊C4C2212yes—
50C2×C4×C22⋊C4C2212yescomplemented
51C2×#376C2211yescharacteristic, complemented
52#1445C2214yescomplemented
53#1443C2214yescomplemented
54#1441C2212yescomplemented
55#1440C2214yes—
56#1440C2214yescomplemented
57#1440C2214yescomplemented
58#1440C2214yescomplemented
59#1439C2212yes—
60#1439C2214yes—
61#1439C2214yescomplemented
62#1439C2214yescomplemented
63#1439C2214yescomplemented
64#1439C2214yescomplemented
65#1439C2214yescomplemented
66#1439C2214yescomplemented
67#1439C2214yescomplemented
68#1439C2214yescomplemented
69#1438C2214yes—
70#1438C2214yes—
71#1438C2214yescomplemented
72C4⋊#95C2212yescomplemented
73C4⋊#95C2212yescomplemented
74C4⋊#95C2212yescomplemented
75C4⋊#95C2212yescomplemented
76C22⋊#95C2212yescomplemented
77C26C2312yes—
78C23×Q8C2311yescharacteristic
79C23×D4—28no—
80C23×D4—24no—
81C23×D4—42no—
82C23×D4—42no—
83C23×D4—44no—
84C23×D4C2312yes—
85C23×D4C2314yes—
86C23×D4C2311yescharacteristic
87C23×D4C2312yes—
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2312yes—
91C2×#121—28no—
92C2×#121—28no—
93C2×#121—44no—
94C2×#120—28no—
95C2×#120—44no—
96C2×#120—44no—
97C2×C4×Q8—24no—
98C2×C4×Q8—42no—
99C2×C4×Q8—42no—
100C2×C4×D4—42no—
101C2×C4×D4—42no—
102C2×C4×D4D418yes—
103C22×C4⋊C4—44no—
104C22×C4⋊C4—42no—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2311yescharacteristic
113C22×C22⋊C4C2312yes—
114C22×C22⋊C4C2312yes—
115C22×C22⋊C4C2312yes—
116C22×C22⋊C4C2312yes—
117C22×C22⋊C4C2314yes—
118C22×C22⋊C4C2314yes—
119C22×C22⋊C4C2314yes—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2314yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2311yescharacteristic
132C22×C22⋊C4C2311yescharacteristic
133C22×C42C2312yes—
134C22×C42C2312yes—
135C22×C42C2311yescharacteristic
136#400—28no—
137#397—24no—
138#397—24no—
139#394—28no—
140#394—28no—
141#394—48no—
142#393—24no—
143#393—24no—
144#393—48no—
145#392—28no—
146#390—28no—
147#390—28no—
148#390—44no—
149#390—44no—
150#390—44no—
151#389—44no—
152#386—48no—
153#386—44no—
154#386—48no—
155#380—24no—
156#380—44no—
157#380—42no—
158#379—28no—
159#379—48no—
160#379—48no—
161C4×C22⋊C4—28no—
162C4×C22⋊C4—28no—
163#376—24no—
164C2×#95C2312yes—
165C2×#95C2311yescharacteristic
166C2×#95C2312yes—
167C2×#95C2311yescharacteristic
168C2×#95C2312yes—
169C2×#95C2314yes—
170C2×#95C2312yes—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C25—24no—
184C25—28no—
185C25—24no—
186C25—24no—
187C25—44no—
188C25—42no—
189C25—42no—
190C25—42no—
191C25—42no—
192C25—44no—
193C25—44no—
194C25C2414yes—
195C25C2411yescharacteristic
196C25C2411yescharacteristic
197C22×Q8—22no—
198C22×Q8—24no—
199C22×Q8—41no—
200C22×Q8—41no—
201C22×Q8—42no—
202C22×D4—22no—
203C22×D4—22no—
204C22×D4—22no—
205C22×D4—22no—
206C22×D4—28no—
207C22×D4—28no—
208C22×D4—28no—
209C22×D4—28no—
210C22×D4—28no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—24no—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—432no—
219C22×D4—41no—
220C22×D4—41no—
221C22×D4—44no—
222C22×D4—42no—
223C22×D4—42no—
224C22×D4—416no—
225C22×D4—44no—
226C22×D4—44no—
227C22×D4—44no—
228C22×D4—416no—
229C22×D4—432no—
230C22×D4—416no—
231C22×D4C2×D414yes—
232C22×D4#4118yes—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—44no—
243C23×C4—42no—
244C23×C4—44no—
245C23×C4—42no—
246C23×C4C2×D414yes—
247C23×C4C2×D414yes—
248C23×C4C2414yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2414yes—
253C23×C4C2414yes—
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258C23×C4C2412yes—
259C23×C4C2411yescharacteristic
260#121—432no—
261#120—432no—
262C4×Q8—416no—
263C4×D4—416no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—44no—
276C2×C4⋊C4—42no—
277C2×C4⋊C4—41no—
278C2×C4⋊C4—41no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—41no—
282C2×C4⋊C4—41no—
283C2×C4⋊C4—416no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—44no—
286C2×C4⋊C4—44no—
287C2×C4⋊C4C2×D414yes—
288C2×C22⋊C4—24no—
289C2×C22⋊C4—24no—
290C2×C22⋊C4—24no—
291C2×C22⋊C4—24no—
292C2×C22⋊C4—24no—
293C2×C22⋊C4—28no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—24no—
297C2×C22⋊C4—24no—
298C2×C22⋊C4—28no—
299C2×C22⋊C4—28no—
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—28no—
303C2×C22⋊C4—28no—
304C2×C22⋊C4—28no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—28no—
307C2×C22⋊C4—28no—
308C2×C22⋊C4—28no—
309C2×C22⋊C4—42no—
310C2×C22⋊C4—42no—
311C2×C22⋊C4—41no—
312C2×C22⋊C4—41no—
313C2×C22⋊C4—41no—
314C2×C22⋊C4—41no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—44no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—44no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4C2×D414yes—
347C2×C22⋊C4C2×D414yes—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42C2×D414yes—
357#95—22no—
358#95—22no—
359#95—24no—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—28no—
366#95—42no—
367#95—44no—
368#95—44no—
369#95—44no—
370#95—44no—
371#95—44no—
372#95—44no—
373#95—44no—
374#95—44no—
375#95—44no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24—21no—
381C24—22no—
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—21no—
388C24—22no—
389C24—21no—
390C24—22no—
391C24—22no—
392C24—24no—
393C24—24no—
394C24—24no—
395C24—24no—
396C24—24no—
397C24—24no—
398C24—24no—
399C24—24no—
400C24—24no—
401C24—24no—
402C24—24no—
403C24—24no—
404C24—24no—
405C24—24no—
406C24—416no—
407C24—48no—
408C24—416no—
409C24—416no—
410C24—48no—
411C24—416no—
412C24—48no—
413C24—48no—
414C24—48no—
415C24—88no—
416C24—84no—
417C24—84no—
418C24—84no—
419C24—84no—
420C24—88no—
421C24—88no—
422C24—88no—
423C24—88no—
424C24—84no—
425C24—84no—
426C24—88no—
427C24—88no—
428C24—88no—
429C24C22×D412yes—
430C24C22×D412yes—
431C24C2×#4118yes—
432C24H(5,𝔽2)12yes—
433C24H(5,𝔽2)12yes—
434C24H(5,𝔽2)12yes—
435C242−1+412yes—
436C24C2511yescharacteristic
437C2×Q8—48no—
438C2×Q8—44no—
439C2×Q8—44no—
440C2×Q8—48no—
441C2×Q8—44no—
442C2×D4—28no—
443C2×D4—28no—
444C2×D4—216no—
445C2×D4—216no—
446C2×D4—216no—
447C2×D4—44no—
448C2×D4—416no—
449C2×D4—48no—
450C2×D4—44no—
451C2×D4—44no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—48no—
455C2×D4—416no—
456C2×D4—48no—
457C2×D4—4128no—
458C2×D4—416no—
459C2×D4—416no—
460C2×D4—416no—
461C2×D4—416no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—88no—
467C2×D4—88no—
468C2×D4—88no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—216no—
496C22×C4—216no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—48no—
540C22×C4—48no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—48no—
546C22×C4—84no—
547C22×C4—88no—
548C22×C4—84no—
549C22×C4—88no—
550C22×C4C22×D412yes—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C2×#4114yes—
556C22×C4H(5,𝔽2)14yes—
557C22×C4H(5,𝔽2)12yes—
558C22×C4H(5,𝔽2)12yes—
559C22×C4H(5,𝔽2)14yes—
560C4⋊C4—44no—
561C4⋊C4—44no—
562C4⋊C4—48no—
563C4⋊C4—48no—
564C4⋊C4—48no—
565C4⋊C4—48no—
566C4⋊C4—48no—
567C4⋊C4—88no—
568C22⋊C4—44no—
569C22⋊C4—44no—
570C22⋊C4—48no—
571C22⋊C4—48no—
572C22⋊C4—416no—
573C22⋊C4—416no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—88no—
578C22⋊C4—88no—
579C22⋊C4—88no—
580C22⋊C4—88no—
581C22⋊C4—88no—
582C22⋊C4—84no—
583C22⋊C4—88no—
584C22⋊C4—88no—
585C22⋊C4—88no—
586C22⋊C4—88no—
587C22⋊C4—88no—
588C42—28no—
589C42—48no—
590C42—48no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—24no—
612C23—24no—
613C23—24no—
614C23—24no—
615C23—28no—
616C23—28no—
617C23—28no—
618C23—28no—
619C23—28no—
620C23—28no—
621C23—28no—
622C23—42no—
623C23—42no—
624C23—41no—
625C23—41no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—432no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
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—832no—
672C23—816no—
673C23—816no—
674C23—816no—
675C23—832no—
676C23—832no—
677C23—832no—
678C23—816no—
679C23—816no—
680C23—816no—
681C23#53514yes—
682C23#53714yes—
683C23C23×D411yescharacteristic
684C23C22×#4112yes—
685C23C2×H(5,𝔽2)11yescharacteristic
686C23C2×H(5,𝔽2)11yescharacteristic
687C23C2×H(5,𝔽2)11yescharacteristic
688C23C2×H(5,𝔽2)11yescharacteristic
689C23C2×H(5,𝔽2)11yescharacteristic
690C23C2×H(5,𝔽2)12yes—
691C23C2×H(5,𝔽2)12yes—
692C23C2×2−1+411yescharacteristic
693C23#58512yes—
694Q8—416no—
695D4—416no—
696D4—432no—
697D4—432no—
698D4—832no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—416no—
729C2×C4—416no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—44no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—816no—
773C2×C4#53414yes—
774C2×C4#53818yes—
775C2×C4#54618yes—
776C2×C4#55114yes—
777C2×C4H(3,𝔽4)14yes—
778C22—24no—
779C22—24no—
780C22—28no—
781C22—28no—
782C22—44no—
783C22—44no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—44no—
789C22—44no—
790C22—44no—
791C22—42no—
792C22—42no—
793C22—44no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—48no—
801C22—48no—
802C22—48no—
803C22—48no—
804C22—48no—
805C22—48no—
806C22—48no—
807C22—864no—
808C22—84no—
809C22—84no—
810C22—84no—
811C22—84no—
812C22—84no—
813C22—84no—
814C22—84no—
815C22—84no—
816C22C2×#53411yescharacteristic
817C22C2×#53511yescharacteristic
818C22C2×#53711yescharacteristic
819C22C2×#53812yes—
820C22C2×#54612yes—
821C22C2×#55111yescharacteristic
822C22#348812yes—
823C22#351312yes—
824C22#351312yes—
825C22#351912yes—
826C22#352012yes—
827C22C2×H(3,𝔽4)11yescharacteristic
828C22#353611yescharacteristic
829C22#353611yescharacteristic
830C22#353711yescharacteristic
831C22#353711yescharacteristic
832C22#353711yescharacteristic
833C22#354011yescharacteristic
834C22#354212yes—
835C22#354312yes—
836C22#354312yes—
837C22#355812yes—
838C22#356112yes—
839C4—42no—
840C4—42no—
841C4—42no—
842C4—42no—
843C4—44no—
844C4—82no—
845C4—84no—
846C4—82no—
847C4—82no—
848C4—84no—
849C4—84no—
850C4#268418yes—
851C2—44no—
852C2—44no—
853C2—88no—
854C2#3726911yescharacteristic
855C2#3743911yescharacteristic
856C2#3802412yes—
857C2#3802612yes—
858C2#4253512yes—
859C2#4256612yes—
860C2#4537711yescharacteristic
861C2#4538011yescharacteristic
862C2C2×#268411yescharacteristic
863C2#5298611yescharacteristic
864C2#5299011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2408C2
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×#2398C2semidirect
3. #17175C2semidirect
4. #16808C2semidirect
5. #16391C2semidirect
6. #16357C2semidirect
7. #16297C2semidirect
8. #15266C2semidirect
9. #15183C2semidirect
10. #15157C2semidirect
11. #15126C2semidirect
12. #14260C2semidirect
13. #14137C2semidirect
14. #13902C2semidirect
15. #13872C2semidirect
19. C22×C4×Q8C22semidirect
21. C23×C4⋊C4C22semidirect
24. C2×#400C22semidirect
26. C2×#397C22semidirect
29. C2×#394C22semidirect
31. C2×#393C22semidirect
32. C2×#393C22semidirect
39. C2×#389C22semidirect
41. C2×#386C22semidirect
42. C2×#386C22semidirect
45. C2×#380C22semidirect
50. C2×C4×C22⋊C4C22semidirect
51. C2×#376C22semidirect
52. #1445C22semidirect
53. #1443C22semidirect
54. #1441C22semidirect
56. #1440C22semidirect
57. #1440C22semidirect
58. #1440C22semidirect
61. #1439C22semidirect
62. #1439C22semidirect
63. #1439C22semidirect
64. #1439C22semidirect
65. #1439C22semidirect
66. #1439C22semidirect
67. #1439C22semidirect
68. #1439C22semidirect
71. #1438C22semidirect
72. C4⋊#95C22semidirect
73. C4⋊#95C22semidirect
74. C4⋊#95C22semidirect
75. C4⋊#95C22semidirect
76. C22⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24082
C2×#23982
#171752
#168082
#163912
#163572
#162972
#152662
#151832
#151572
#151262
#142602
#141372
#139022
#138722