Finite Group Databasebeta

← #669490

Subgroups — #669490

Order 512.

3536 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2486C211yesmaximal, characteristic
2C2×#2413C212yesmaximal
3C2×#2344C211yesmaximal, characteristic, complemented
4C2×C4×#123C211yesmaximal, characteristic
5C22×#389C211yesmaximal, characteristic, complemented
6#15778C214yesmaximal, complemented
7#15774C214yesmaximal, complemented
8#15149C212yesmaximal, complemented
9#15131C212yesmaximal, complemented
10#15073C212yesmaximal, complemented
11#14912C212yesmaximal
12#14685C211yesmaximal, characteristic, complemented
13#14151C212yesmaximal, complemented
14#13994C212yesmaximal, complemented
15#13962C212yesmaximal, complemented
16#13880C211yesmaximal, characteristic, complemented
17#13872C211yesmaximal, characteristic
18C22×#123C2212yes—
19C22×#123C2211yescharacteristic
20C22×C4×D4C2211yescharacteristic
21C22×#117C2212yes—
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2212yes—
24C23×C4⋊C4C2211yescharacteristic
25C23×C42C2211yescharacteristic
26#2486—28no—
27#2413—216no—
28C2×#398C2214yes—
29C2×#398C2212yes—
30C2×#397C2212yes—
31C2×#396C2214yes—
32#2344—28no—
33C4×#123—28no—
34C2×#389—28no—
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#389C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#389C2214yes—
40C2×#389C2212yes—
41C2×#389C2214yes—
42C2×#388C2212yes—
43C2×#388C2214yes—
44C2×#387C2214yes—
45C2×#387C2212yes—
46C2×#386C2212yes—
47C2×#386C2211yescharacteristic
48C2×#385C2212yes—
49C2×#385C2211yescharacteristic
50C2×#385C2212yes—
51C2×#384C2212yes—
52C2×#381C2212yes—
53C2×#381C2212yes—
54C2×#381C2212yes—
55C2×#381C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2212yes—
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2212yes—
62C2×C4×C4⋊C4C2212yes—
63C2×C4×C22⋊C4C2212yes—
64C2×C4×C22⋊C4C2211yescharacteristic
65C22×#95C2212yes—
66#1444C2214yes—
67#1442C2214yes—
68#1442C2214yes—
69#1442C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2212yes—
74#1441C2214yes—
75#1441C2214yes—
76#1440C2214yes—
77#1439C2214yes—
78#1439C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2214yes—
84#1434C2214yes—
85#1434C2214yes—
86C22⋊#95C2212yes—
87C22⋊#95C2212yes—
88C23×D4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2312yes—
92C24×C4C2311yescharacteristic
93C24×C4C2312yes—
94C24×C4C2311yescharacteristic
95C2×#123—28no—
96C2×#123—28no—
97C2×#123—24no—
98C2×#123—24no—
99C2×#123—44no—
100C2×#123D418yes—
101C2×C4×D4—24no—
102C2×C4×D4—24no—
103C2×C4×D4—24no—
104C2×#117—28no—
105C2×#117—28no—
106C2×#117—28no—
107C22×C4⋊C4—24no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—28no—
111C22×C4⋊C4—28no—
112C22×C4⋊C4—28no—
113C22×C4⋊C4—44no—
114C22×C4⋊C4D418yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2314yes—
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2311yescharacteristic
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C42—24no—
145C22×C42—24no—
146C22×C42—24no—
147C22×C42C2312yes—
148C22×C42C2312yes—
149C22×C42C2314yes—
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152#398—216no—
153#398—28no—
154#397—28no—
155#396—216no—
156#389—216no—
157#389—24no—
158#389—24no—
159#389—28no—
160#389—28no—
161#389—216no—
162#389—28no—
163#388—216no—
164#388—28no—
165#387—216no—
166#387—28no—
167#386—28no—
168#386—24no—
169#385—28no—
170#385—24no—
171#385—44no—
172#384—28no—
173#381—28no—
174#381—28no—
175#381—28no—
176#381—24no—
177#380—24no—
178#380—24no—
179#380—24no—
180#380—24no—
181#380—28no—
182C4×C4⋊C4—28no—
183C4×C4⋊C4—28no—
184C4×C22⋊C4—28no—
185C4×C22⋊C4D418yes—
186C2×#95—28no—
187C2×#95C2314yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C25C2411yescharacteristic
212C25C2411yescharacteristic
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4C2×D414yes—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—22no—
224C23×C4—24no—
225C23×C4—24no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—24no—
234C23×C4—22no—
235C23×C4—24no—
236C23×C4—28no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—42no—
248C23×C4—44no—
249C23×C4C2×D414yes—
250C23×C4C2×D418yes—
251C23×C4C2×D414yes—
252C23×C4C2×D414yes—
253C23×C4#4114yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2411yescharacteristic
257C23×C4C2414yes—
258C23×C4C2411yescharacteristic
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2411yescharacteristic
264C23×C4C2414yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269#123—232no—
270#123—432no—
271C4×D4—416no—
272#117—432no—
273C2×C4⋊C4—232no—
274C2×C4⋊C4—232no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—28no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
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—22no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—42no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—432no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4C2×D414yes—
323C2×C4⋊C4C2×D414yes—
324C2×C4⋊C4C2×D418yes—
325C2×C4⋊C4C2×D418yes—
326C2×C4⋊C4#4118yes—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4C2×D418yes—
356C2×C22⋊C4C2×D414yes—
357C2×C22⋊C4C2×D414yes—
358C2×C22⋊C4C2×D414yes—
359C2×C22⋊C4#4114yes—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—28no—
363C2×C42—28no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—28no—
371C2×C42—22no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—416no—
375C2×C42C2×D418yes—
376#95—28no—
377#95—28no—
378#95—24no—
379#95—24no—
380#95—28no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—28no—
388#95—28no—
389#95—28no—
390#95—24no—
391#95—24no—
392#95—28no—
393#95—28no—
394#95—28no—
395#95—28no—
396#95—44no—
397#95—44no—
398#95—44no—
399#95C2×D418yes—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—21no—
405C24—21no—
406C24—22no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—22no—
411C24—22no—
412C24—21no—
413C24—22no—
414C24C22×D412yes—
415C24C22×D412yes—
416C24C22×D412yes—
417C24C22×D412yes—
418C24C2×#4112yes—
419C24C2×#4112yes—
420C24H(5,𝔽2)12yes—
421C242−1+412yes—
422C24C2511yescharacteristic
423C2×D4—28no—
424C2×D4—28no—
425C2×D4—28no—
426C2×D4—44no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—44no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—28no—
437C22×C4—28no—
438C22×C4—216no—
439C22×C4—216no—
440C22×C4—216no—
441C22×C4—28no—
442C22×C4—216no—
443C22×C4—28no—
444C22×C4—28no—
445C22×C4—216no—
446C22×C4—216no—
447C22×C4—28no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—21no—
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—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—21no—
503C22×C4—24no—
504C22×C4—21no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—416no—
518C22×C4—48no—
519C22×C4—48no—
520C22×C4—416no—
521C22×C4—48no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—48no—
526C22×C4—48no—
527C22×C4—44no—
528C22×C4—48no—
529C22×C4—44no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4#121116yes—
539C22×C4C22×D414yes—
540C22×C4C22×D414yes—
541C22×C4C22×D414yes—
542C22×C4C22×D414yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×D414yes—
547C22×C4C22×D414yes—
548C22×C4C22×D412yes—
549C22×C4C22×D412yes—
550C22×C4C2×#4118yes—
551C22×C4C2×#4114yes—
552C22×C4C2×#4112yes—
553C22×C4C2×#4112yes—
554C22×C4C2×#4114yes—
555C22×C42−1+414yes—
556C22×C42−1+414yes—
557C4⋊C4—216no—
558C4⋊C4—216no—
559C4⋊C4—28no—
560C4⋊C4—28no—
561C4⋊C4—216no—
562C4⋊C4—216no—
563C4⋊C4—416no—
564C4⋊C4—48no—
565C4⋊C4—416no—
566C4⋊C4—416no—
567C4⋊C4—48no—
568C4⋊C4—48no—
569C4⋊C4—416no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—48no—
574C4⋊C4—88no—
575C22⋊C4—28no—
576C22⋊C4—216no—
577C22⋊C4—48no—
578C22⋊C4—416no—
579C22⋊C4—48no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C22⋊C4—44no—
583C22⋊C4—48no—
584C22⋊C4—44no—
585C22⋊C4#121116yes—
586C42—216no—
587C42—48no—
588C42—48no—
589C42—416no—
590C42—44no—
591C23—22no—
592C23—22no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—22no—
598C23—22no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—24no—
611C23—24no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—42no—
617C23—41no—
618C23—42no—
619C23—41no—
620C23—42no—
621C23—41no—
622C23—41no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23C2×#12114yes—
631C23C2×#12114yes—
632C23#53714yes—
633C23D4214yes—
634C23#54714yes—
635C23#54714yes—
636C23#55514yes—
637C23C23×D411yescharacteristic
638C23C23×D411yescharacteristic
639C23C23×D411yescharacteristic
640C23C22×#4111yescharacteristic
641C23C22×#4111yescharacteristic
642C23C22×#4112yes—
643C23C2×H(5,𝔽2)11yescharacteristic
644C23C2×2−1+412yes—
645C23C2×2−1+411yescharacteristic
646C23C2×2−1+412yes—
647C23#58512yes—
648D4—416no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—232no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—28no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—28no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—28no—
681C2×C4—432no—
682C2×C4—416no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—44no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—44no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—432no—
711C2×C4—416no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—44no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—88no—
741C2×C4C2×#12118yes—
742C2×C4C2×#12114yes—
743C2×C4C2×#12114yes—
744C2×C4#52514yes—
745C2×C4#53614yes—
746C2×C4#54718yes—
747C2×C4#55218yes—
748C22—24no—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—28no—
753C22—28no—
754C22—28no—
755C22—28no—
756C22—24no—
757C22—24no—
758C22—42no—
759C22—42no—
760C22—44no—
761C22—44no—
762C22—42no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—82no—
767C22—82no—
768C22—81no—
769C22#253718yes—
770C22C22×#12111yescharacteristic
771C22C22×#12111yescharacteristic
772C22C2×#52511yescharacteristic
773C22C2×#53611yescharacteristic
774C22C2×#53711yescharacteristic
775C22C2×D4211yescharacteristic
776C22C2×#54711yescharacteristic
777C22C2×#54711yescharacteristic
778C22C2×#54712yes—
779C22D4×#4112yes—
780C22C2×#55212yes—
781C22C2×#55511yescharacteristic
782C22#348212yes—
783C22#348611yescharacteristic
784C22#348711yescharacteristic
785C22#348912yes—
786C22#349512yes—
787C22#349912yes—
788C22#351312yes—
789C22#351512yes—
790C22#352312yes—
791C22#354412yes—
792C22#356312yes—
793C4—28no—
794C4—24no—
795C4—48no—
796C4—44no—
797C4—44no—
798C4—44no—
799C4—44no—
800C4—42no—
801C4—44no—
802C4—82no—
803C4—81no—
804C4—84no—
805C4—82no—
806C4—81no—
807C4#241318yescomplemented
808C2—28no—
809C2—82no—
810C2C2×#241311yescharacteristic
811C2C2×#253711yescharacteristic
812C2#3566111yescharacteristic
813C2#3610211yescharacteristic
814C2#3625912yes—
815C2#3642311yescharacteristic
816C2#3804312yes—
817C2#3891911yescharacteristic
818C2#3933711yescharacteristic
819C2#5922512yes—
820C2#5929012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#2344C2semidirect
5. C22×#389C2semidirect
6. #15778C2semidirect
7. #15774C2semidirect
8. #15149C2semidirect
9. #15131C2semidirect
10. #15073C2semidirect
12. #14685C2semidirect
13. #14151C2semidirect
14. #13994C2semidirect
15. #13962C2semidirect
16. #13880C2semidirect
807. C4#2413semidirect

Maximal subgroups

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

subgroupindex
C2×#24862
C2×#24132
C2×#23442
C2×C4×#1232
C22×#3892
#157782
#157742
#151492
#151312
#150732
#149122
#146852
#141512
#139942
#139622
#138802
#138722