Finite Group Databasebeta

← #719839

Subgroups — #719839

Order 512.

3642 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2535C211yesmaximal, characteristic
2C2×#2420C212yesmaximal, complemented
3C2×#2422C212yesmaximal, complemented
4C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5#16807C212yesmaximal, complemented
6#16807C212yesmaximal, complemented
7#15539C214yesmaximal, complemented
8#15370C214yesmaximal, complemented
9#15223C212yesmaximal, complemented
10#15135C212yesmaximal, complemented
11#15069C212yesmaximal, complemented
12#14777C212yesmaximal, complemented
13#14354C211yesmaximal, characteristic, complemented
14#13954C211yesmaximal, characteristic, complemented
15#13906C211yesmaximal, characteristic, complemented
16#13847C211yesmaximal, characteristic, complemented
17#13785C211yesmaximal, characteristic, complemented
18C22×#123C2214yes—
19C22×#121C2211yescharacteristic
20C22×#121C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2212yes—
23C22×C4×D4C2211yescharacteristic
24C23×C4⋊C4C2212yes—
25#2535—28no—
26#2422—216no—
27#2420—216no—
28C2×#399C2214yes—
29C2×#397C2212yes—
30C2×#397C2214yes—
31C2×#397C2214yes—
32C2×#394C2214yes—
33C2×#394C2214yes—
34C2×#392C2212yes—
35D4×C4⋊C4—28no—
36C2×#390C2212yes—
37C2×#390C2212yes—
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#389C2212yes—
41C2×#386C2214yes—
42C2×#386C2212yes—
43C2×#386C2212yes—
44C2×#385C2214yes—
45C2×#385C2214yes—
46C2×#384C2212yes—
47C2×#384C2211yescharacteristic
48C2×#382C2211yescharacteristic
49C2×#382C2212yes—
50C2×#381C2214yes—
51C2×#380C2211yescharacteristic
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2211yescharacteristic
55C2×#380C2212yes—
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yes—
60C2×#376C2211yescharacteristic
61#1445C2212yes—
62#1445C2214yes—
63#1445C2214yes—
64#1445C2214yes—
65#1444C2214yes—
66#1444C2212yes—
67#1444C2212yes—
68#1444C2214yes—
69#1444C2212yes—
70#1444C2212yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2211yescharacteristic
75#1439C2211yescharacteristic
76#1439C2211yescharacteristic
77#1439C2211yescharacteristic
78#1439C2212yes—
79#1439C2212yes—
80#1438C2212yes—
81#1437C2214yes—
82C4⋊#95C2214yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C23×D4C2311yescharacteristic
88C23×D4C2312yes—
89C23×D4C2312yes—
90C23×D4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2314yes—
94C24×C4C2312yes—
95C2×#123—216no—
96C2×#123—48no—
97C2×#123—48no—
98C2×#121—28no—
99C2×#121—28no—
100C2×#121—24no—
101C2×#121—24no—
102C2×C4×D4—28no—
103C2×C4×D4—28no—
104C2×C4×D4—28no—
105C2×C4×D4—24no—
106C2×C4×D4—24no—
107C2×C4×D4—24no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C2×C4×D4D418yes—
111C22×C4⋊C4—28no—
112C22×C4⋊C4—48no—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2314yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2311yescharacteristic
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C42C2312yes—
145C22×C42C2312yes—
146C22×C42C2312yes—
147C22×C42C2311yescharacteristic
148#399—48no—
149#397—216no—
150#397—216no—
151#397—28no—
152#394—216no—
153#394—216no—
154#392—28no—
155#390—44no—
156#390D4116yescomplemented
157#389—28no—
158#389—28no—
159#389—28no—
160#386—28no—
161#386—28no—
162#386—216no—
163#385—216no—
164#385—216no—
165#384—24no—
166#384—28no—
167#382—28no—
168#382—24no—
169#381—216no—
170#380—28no—
171#380—28no—
172#380—28no—
173#380—24no—
174#380—24no—
175C4×C4⋊C4—24no—
176C4×C4⋊C4—24no—
177C4×C22⋊C4—28no—
178C4×C22⋊C4—28no—
179#376—24no—
180C2×#95C2312yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2311yescharacteristic
191C2×#95C2311yescharacteristic
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C25C2411yescharacteristic
203C25C2411yescharacteristic
204C25C2412yes—
205C22×D4—22no—
206C22×D4—22no—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—28no—
210C22×D4—24no—
211C22×D4—24no—
212C22×D4—28no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—24no—
219C22×D4—41no—
220C22×D4—41no—
221C22×D4—44no—
222C22×D4—44no—
223C22×D4—42no—
224C22×D4—42no—
225C22×D4C2×D414yes—
226C22×D4C2×D418yes—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—28no—
230C23×C4—28no—
231C23×C4—28no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—28no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—44no—
244C23×C4—44no—
245C23×C4—44no—
246C23×C4—44no—
247C23×C4—44no—
248C23×C4C2×D418yes—
249C23×C4C2412yes—
250C23×C4C2414yes—
251C23×C4C2411yescharacteristic
252C23×C4C2411yescharacteristic
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2414yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262C23×C4C2411yescharacteristic
263#123—464no—
264#121—416no—
265#121—416no—
266C4×D4—232no—
267C4×D4—432no—
268C4×D4—416no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—28no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—432no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4C2×D414yes—
309C2×C4⋊C4C2×D418yes—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—28no—
316C2×C22⋊C4—28no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—28no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—22no—
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—28no—
338C2×C22⋊C4—44no—
339C2×C22⋊C4—44no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
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⋊C4C2×D418yes—
352C2×C22⋊C4C2×D4116yes—
353C2×C22⋊C4C2×D4116yes—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42—24no—
357C2×C42—24no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—42no—
361C2×C42—42no—
362C2×C42C2×D418yes—
363C2×C42C2×D414yes—
364C2×C42#4114yes—
365C2×C42#4114yes—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—28no—
372#95—28no—
373#95—28no—
374#95—24no—
375#95—24no—
376#95—28no—
377#95—28no—
378#95—24no—
379#95—28no—
380#95—24no—
381#95—28no—
382#95—24no—
383#95—22no—
384#95—22no—
385#95—24no—
386#95—44no—
387#95—44no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—24no—
392C24—24no—
393C24—22no—
394C24—22no—
395C24—24no—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—22no—
406C24—22no—
407C24—21no—
408C24—22no—
409C24—22no—
410C24—21no—
411C24—22no—
412C24—21no—
413C24—21no—
414C24—22no—
415C24—21no—
416C24—21no—
417C24C22×D418yes—
418C24C22×D414yes—
419C24H(5,𝔽2)12yes—
420C242−1+412yes—
421C24C2511yescharacteristic
422C2×D4—28no—
423C2×D4—28no—
424C2×D4—28no—
425C2×D4—216no—
426C2×D4—216no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—44no—
431C2×D4—44no—
432C2×D4—416no—
433C2×D4—48no—
434C2×D4—416no—
435C2×D4—48no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—44no—
439C2×D4—84no—
440C2×D4—84no—
441C2×D4—88no—
442C2×D4—88no—
443C2×D4#127116yes—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—216no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—416no—
516C22×C4—416no—
517C22×C4—416no—
518C22×C4—416no—
519C22×C4—416no—
520C22×C4—416no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—88no—
532C22×C4—88no—
533C22×C4—88no—
534C22×C4C22×D414yes—
535C22×C4C22×D414yes—
536C22×C4C22×D418yes—
537C22×C4C22×D414yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×D414yes—
542C22×C4C2×#4112yes—
543C22×C4C2×#4112yes—
544C22×C4C2×#4112yes—
545C22×C4C2×#4112yes—
546C22×C4C2×#4112yes—
547C22×C4C2×#4112yes—
548C22×C4H(5,𝔽2)14yes—
549C22×C42−1+414yes—
550C4⋊C4—28no—
551C4⋊C4—28no—
552C4⋊C4—216no—
553C4⋊C4—416no—
554C4⋊C4—416no—
555C4⋊C4—44no—
556C4⋊C4—48no—
557C4⋊C4—416no—
558C4⋊C4—44no—
559C4⋊C4—48no—
560C4⋊C4—44no—
561C4⋊C4—44no—
562C4⋊C4—84no—
563C4⋊C4—88no—
564C4⋊C4—88no—
565C22⋊C4—216no—
566C22⋊C4—216no—
567C22⋊C4—416no—
568C22⋊C4—416no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—416no—
572C22⋊C4—48no—
573C22⋊C4—416no—
574C22⋊C4—48no—
575C22⋊C4—48no—
576C22⋊C4—44no—
577C22⋊C4—44no—
578C22⋊C4—88no—
579C22⋊C4—84no—
580C22⋊C4—84no—
581C42—216no—
582C42—48no—
583C42—84no—
584C42#123116yescomplemented
585C23—24no—
586C23—24no—
587C23—28no—
588C23—28no—
589C23—28no—
590C23—24no—
591C23—28no—
592C23—24no—
593C23—28no—
594C23—24no—
595C23—28no—
596C23—24no—
597C23—24no—
598C23—22no—
599C23—24no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—44no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23—44no—
616C23—44no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—41no—
631C23—41no—
632C23—42no—
633C23—41no—
634C23—41no—
635C23—42no—
636C23—42no—
637C23—41no—
638C23—42no—
639C23—41no—
640C23—42no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23C2×#12718yes—
654C23C23×D411yescharacteristic
655C23C23×D412yes—
656C23C22×#4111yescharacteristic
657C23C22×#4111yescharacteristic
658C23C2×H(5,𝔽2)12yes—
659C23C2×H(5,𝔽2)11yescharacteristic
660C23C2×2−1+412yes—
661C23C2×2−1+411yescharacteristic
662C23#58512yes—
663C23#58511yescharacteristic
664C23#58511yescharacteristic
665D4—232no—
666D4—416no—
667D4—816no—
668D4—816no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—28no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—28no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—28no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—432no—
695C2×C4—42no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—44no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—42no—
730C2×C4—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—832no—
748C2×C4—88no—
749C2×C4—88no—
750C2×C4C2×#12314yes—
751C2×C4C2×#12314yes—
752C2×C4C2×#12314yes—
753C2×C4C2×#12714yes—
754C2×C4#53614yes—
755C2×C4#54718yes—
756C2×C4#54718yes—
757C22—28no—
758C22—28no—
759C22—28no—
760C22—44no—
761C22—48no—
762C22—48no—
763C22—48no—
764C22—44no—
765C22—44no—
766C22—48no—
767C22—44no—
768C22—42no—
769C22—44no—
770C22—44no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—44no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—82no—
782C22—82no—
783C22—82no—
784C22—82no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22C22×#12311yescharacteristic
791C22C22×#12711yescharacteristic
792C22C2×#53611yescharacteristic
793C22#346012yes—
794C22C2×#54712yes—
795C22C2×#54712yes—
796C22#348411yescharacteristic
797C22#348412yes—
798C22#348511yescharacteristic
799C22#348512yes—
800C22#348812yes—
801C22#348811yescharacteristic
802C22#348912yes—
803C22#348911yescharacteristic
804C22#349211yescharacteristic
805C22#349311yescharacteristic
806C22#349411yescharacteristic
807C22#349511yescharacteristic
808C22#350612yes—
809C22#354712yes—
810C22#355212yes—
811C22#355912yes—
812C22#356512yes—
813C4—24no—
814C4—24no—
815C4—44no—
816C4—44no—
817C4—44no—
818C4—48no—
819C4—44no—
820C4—84no—
821C4—82no—
822C4—81no—
823C4—81no—
824C4—82no—
825C4—82no—
826C4#250118yes—
827C2—48no—
828C2—82no—
829C2—82no—
830C2C2×#250111yescharacteristic
831C2#3515211yescharacteristic
832C2#3551611yescharacteristic
833C2#3592111yescharacteristic
834C2#3606011yescharacteristic
835C2#3776412yes—
836C2#3776712yes—
837C2#4248511yescharacteristic
838C2#4268211yescharacteristic
839C2#4490612yes—
840C2#4525512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2535C2
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×#2420C2semidirect
3. C2×#2422C2semidirect
4. C2×D4×C4⋊C4C2semidirect
5. #16807C2semidirect
6. #16807C2semidirect
7. #15539C2semidirect
8. #15370C2semidirect
9. #15223C2semidirect
10. #15135C2semidirect
11. #15069C2semidirect
12. #14777C2semidirect
13. #14354C2semidirect
14. #13954C2semidirect
15. #13906C2semidirect
16. #13847C2semidirect
17. #13785C2semidirect
156. #390D4semidirect
584. C42#123semidirect

Maximal subgroups

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

subgroupindex
C2×#25352
C2×#24202
C2×#24222
C2×D4×C4⋊C42
#168072
#155392
#153702
#152232
#151352
#150692
#147772
#143542
#139542
#139062
#138472
#137852