Finite Group Databasebeta

← #4453121

Subgroups — #4453121

Order 512.

3010 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2414C211yesmaximal, characteristic
2C2×#2624C211yesmaximal, characteristic, complemented
3C2×#2395C211yesmaximal, characteristic, complemented
4C2×#2317C211yesmaximal, characteristic, complemented
5#17071C212yesmaximal, complemented
6#17039C212yesmaximal, complemented
7#16888C212yesmaximal, complemented
8#16821C212yesmaximal, complemented
9#16288C214yesmaximal, complemented
10#16285C214yesmaximal, complemented
11#15221C212yesmaximal, complemented
12#15219C212yesmaximal, complemented
13#15134C212yesmaximal, complemented
14#15131C212yesmaximal, complemented
15#14137C211yesmaximal, characteristic, complemented
16#13951C211yesmaximal, characteristic, complemented
17#13872C211yesmaximal, characteristic, complemented
18C22×#121C2211yescharacteristic
19C22×#121C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C22×#117C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24#2624—28no—
25#2414—28no—
26#2395—28no—
27C2×#400C2211yescharacteristic
28C2×#399C2212yes—
29C2×#399C2211yescharacteristic
30C2×#398C2211yescharacteristic
31C2×#397C2212yes—
32C2×#397C2212yes—
33C2×#397C2211yescharacteristic
34C2×#396C2214yes—
35C2×#396C2214yes—
36C2×#396C2214yes—
37C2×#394C2214yes—
38C2×#394C2212yes—
39C2×#394C2212yes—
40C2×#392C2212yes—
41#2317—28no—
42C2×#390C2211yescharacteristic
43C2×#390C2212yes—
44C2×#390C2212yes—
45C2×#390C2212yes—
46C2×#389C2212yes—
47C2×#389C2212yes—
48C2×#389C2212yes—
49C2×#389C2211yescharacteristic
50C2×#389C2212yes—
51C2×#388C2212yes—
52C2×#386C2212yes—
53C2×#386C2214yes—
54C2×#385C2214yes—
55C2×#384C2212yes—
56C2×#382C2212yes—
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2212yes—
60C2×C4×C4⋊C4C2212yes—
61C2×C4×C22⋊C4C2212yes—
62C2×C4×C22⋊C4C2211yescharacteristic
63#1445C2214yes—
64#1444C2214yes—
65#1442C2214yes—
66#1442C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1441C2212yes—
70#1440C2214yes—
71#1440C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2212yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2214yes—
79#1438C2214yes—
80#1438C2214yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85#1434C2212yes—
86C22⋊#95C2212yes—
87C23×D4C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C23×D4C2312yes—
90C23×D4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2312yes—
94C2×#121—24no—
95C2×#121—24no—
96C2×#121—24no—
97C2×#121—24no—
98C2×#121—44no—
99C2×C4×D4—24no—
100C2×C4×D4—24no—
101C2×C4×D4—24no—
102C2×#117—24no—
103C2×#117—24no—
104C2×#117—44no—
105C2×#117D418yes—
106C2×#117D418yescomplemented
107C22×C4⋊C4—24no—
108C22×C4⋊C4—44no—
109C22×C4⋊C4C2311yescharacteristic
110C22×C4⋊C4C2312yes—
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2312yes—
125C22×C22⋊C4C2311yescharacteristic
126C22×C22⋊C4C2311yescharacteristic
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C42C2311yescharacteristic
144C22×C42C2312yes—
145C22×C42C2312yes—
146C22×C42C2312yes—
147#400—24no—
148#399—28no—
149#399—24no—
150#398—24no—
151#397—28no—
152#397—24no—
153#397—28no—
154#396—48no—
155#396—48no—
156#396—48no—
157#394—216no—
158#394—28no—
159#394—28no—
160#392—28no—
161#390—24no—
162#390—28no—
163#390—28no—
164#390—44no—
165#389—24no—
166#389—28no—
167#389—28no—
168#389—28no—
169#389—44no—
170#388—28no—
171#386—44no—
172#386—48no—
173#385—216no—
174#384—28no—
175#382—28no—
176#380—24no—
177#380—24no—
178#380—44no—
179C4×C4⋊C4—28no—
180C4×C22⋊C4—24no—
181C4×C22⋊C4—28no—
182C2×#95C2312yes—
183C2×#95C2314yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2311yescharacteristic
192C2×#95C2312yes—
193C2×#95C2311yescharacteristic
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C25C2412yes—
203C25C2411yescharacteristic
204C25C2411yescharacteristic
205C22×D4—22no—
206C22×D4—22no—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—24no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—24no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—24no—
219C22×D4—24no—
220C22×D4—41no—
221C22×D4—41no—
222C22×D4—44no—
223C22×D4—42no—
224C22×D4—44no—
225C22×D4—44no—
226C22×D4—44no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—44no—
236C23×C4—42no—
237C23×C4—42no—
238C23×C4—44no—
239C23×C4C2×D414yes—
240C23×C4C2×D414yes—
241C23×C4#4114yes—
242C23×C4C2411yescharacteristic
243C23×C4C2414yes—
244C23×C4C2412yes—
245C23×C4C2414yes—
246C23×C4C2411yescharacteristic
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2411yescharacteristic
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256#121—416no—
257#121—416no—
258C4×D4—416no—
259#117—232no—
260#117—416no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—44no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—416no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4C2×D414yes—
303C2×C4⋊C4C2×D414yes—
304C2×C4⋊C4C2×D414yes—
305C2×C4⋊C4C2×D414yes—
306C2×C22⋊C4—24no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—22no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—22no—
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—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—44no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4C2×D418yes—
355C2×C22⋊C4C2×D418yes—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—24no—
361C2×C42—22no—
362C2×C42—24no—
363C2×C42—24no—
364C2×C42—44no—
365C2×C42C2×D418yes—
366C2×C42C2×D418yes—
367#95—24no—
368#95—22no—
369#95—24no—
370#95—22no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—28no—
376#95—28no—
377#95—24no—
378#95—28no—
379#95—28no—
380#95—28no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387C24—22no—
388C24—22no—
389C24—21no—
390C24—22no—
391C24—21no—
392C24—21no—
393C24—22no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—22no—
399C24—21no—
400C24—22no—
401C24—22no—
402C24—21no—
403C24—22no—
404C24—21no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—24no—
410C24—24no—
411C24—24no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24C22×D412yes—
417C24C22×D412yes—
418C24C2×#4112yes—
419C242−1+412yes—
420C24C2511yescharacteristic
421C2×D4—28no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—48no—
425C2×D4—48no—
426C2×D4—44no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—416no—
431C2×D4—48no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—48no—
436C2×D4—48no—
437C2×D4—84no—
438C2×D4—88no—
439C2×D4—88no—
440C2×D4—84no—
441C2×D4—84no—
442C2×D4—88no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—28no—
446C22×C4—28no—
447C22×C4—216no—
448C22×C4—216no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—48no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—84no—
524C22×C4—84no—
525C22×C4—88no—
526C22×C4—88no—
527C22×C4#121116yes—
528C22×C4C22×D414yes—
529C22×C4C22×D414yes—
530C22×C4C22×D414yes—
531C22×C4C22×D414yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C2×#4112yes—
537C22×C4C2×#4112yes—
538C22×C4H(5,𝔽2)12yes—
539C22×C4H(5,𝔽2)14yes—
540C22×C4H(5,𝔽2)14yes—
541C22×C42−1+414yes—
542C4⋊C4—28no—
543C4⋊C4—28no—
544C4⋊C4—28no—
545C4⋊C4—28no—
546C4⋊C4—48no—
547C4⋊C4—48no—
548C4⋊C4—48no—
549C4⋊C4—44no—
550C4⋊C4—44no—
551C4⋊C4—48no—
552C4⋊C4—48no—
553C4⋊C4—88no—
554C4⋊C4—88no—
555C4⋊C4—88no—
556C4⋊C4—84no—
557C4⋊C4—88no—
558C22⋊C4—216no—
559C22⋊C4—48no—
560C22⋊C4—48no—
561C22⋊C4—48no—
562C22⋊C4—48no—
563C22⋊C4—48no—
564C22⋊C4—48no—
565C22⋊C4—44no—
566C22⋊C4—44no—
567C22⋊C4—48no—
568C22⋊C4—88no—
569C22⋊C4—88no—
570C22⋊C4—84no—
571C22⋊C4—84no—
572C22⋊C4—88no—
573C22⋊C4—84no—
574C22⋊C4—88no—
575C22⋊C4—88no—
576C42—216no—
577C42—48no—
578C42—44no—
579C42—48no—
580C23—22no—
581C23—22no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—24no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—24no—
598C23—24no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—42no—
611C23—42no—
612C23—42no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—44no—
629C23—44no—
630C23—42no—
631C23—42no—
632C23—44no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23C2×#12114yes—
649C23C23×D411yescharacteristic
650C23C23×D411yescharacteristic
651C23C22×#4111yescharacteristic
652C23C2×H(5,𝔽2)12yes—
653C23C2×H(5,𝔽2)11yescharacteristic
654C23C2×H(5,𝔽2)12yes—
655C23C2×2−1+412yes—
656C23C2×2−1+411yescharacteristic
657C23#58511yescharacteristic
658C23#58511yescharacteristic
659C23#58512yes—
660D4—416no—
661D4—816no—
662D4—816no—
663D4—88no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—232no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—44no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—41no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—816no—
744C2×C4—88no—
745C2×C4C2×#12114yes—
746C2×C4C2×#12114yes—
747C2×C4#53414yes—
748C2×C4#53614yes—
749C2×C4#53718yes—
750C2×C4#53918yes—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—44no—
755C22—44no—
756C22—42no—
757C22—42no—
758C22—44no—
759C22—42no—
760C22—42no—
761C22—44no—
762C22—44no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—44no—
767C22—82no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22—82no—
772C22—81no—
773C22—84no—
774C22—84no—
775C22—82no—
776C22—82no—
777C22—82no—
778C22—82no—
779C22—84no—
780C22—82no—
781C22—82no—
782C22—84no—
783C22—82no—
784C22C22×#12111yescharacteristic
785C22C2×#53411yescharacteristic
786C22C2×#53611yescharacteristic
787C22C2×#53712yes—
788C22C2×#53912yes—
789C22#348811yescharacteristic
790C22#348812yes—
791C22#348811yescharacteristic
792C22#348911yescharacteristic
793C22#348911yescharacteristic
794C22#349211yescharacteristic
795C22#349311yescharacteristic
796C22#349811yescharacteristic
797C22#350011yescharacteristic
798C22#350612yes—
799C22#354312yes—
800C22#354612yes—
801C22#354712yes—
802C22#355212yes—
803C22#355912yes—
804C22#356112yes—
805C22#356212yes—
806C22#356512yes—
807C4—24no—
808C4—44no—
809C4—44no—
810C4—42no—
811C4—44no—
812C4—44no—
813C4—44no—
814C4—84no—
815C4—82no—
816C4—81no—
817C4—82no—
818C4—84no—
819C4—81no—
820C4#261818yes—
821C2—44no—
822C2—82no—
823C2—162no—
824C2C2×#261811yescharacteristic
825C2#3551811yescharacteristic
826C2#3553311yescharacteristic
827C2#3727612yes—
828C2#3727712yes—
829C2#4245312yes—
830C2#4246412yes—
831C2#4291411yescharacteristic
832C2#4294311yescharacteristic
833C2#4296511yescharacteristic
834C2#4296911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2414C2
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×#2624C2semidirect
3. C2×#2395C2semidirect
4. C2×#2317C2semidirect
5. #17071C2semidirect
6. #17039C2semidirect
7. #16888C2semidirect
8. #16821C2semidirect
9. #16288C2semidirect
10. #16285C2semidirect
11. #15221C2semidirect
12. #15219C2semidirect
13. #15134C2semidirect
14. #15131C2semidirect
15. #14137C2semidirect
16. #13951C2semidirect
17. #13872C2semidirect
106. C2×#117D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24142
C2×#26242
C2×#23952
C2×#23172
#170712
#170392
#168882
#168212
#162882
#162852
#152212
#152192
#151342
#151312
#141372
#139512
#138722