Finite Group Databasebeta

← #874578

Subgroups — #874578

Order 512.

2702 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2568C211yesmaximal, characteristic, complemented
2C2×#2503C211yesmaximal, characteristic
3C2×#2429C211yesmaximal, characteristic
4C2×#2440C211yesmaximal, characteristic
5#16835C214yesmaximal, complemented
6#15624C214yesmaximal, complemented
7#15470C214yesmaximal
8#15242C211yesmaximal, characteristic, complemented
9#15237C211yesmaximal, characteristic, complemented
10#15236C211yesmaximal, characteristic
11#15236C211yesmaximal, characteristic
12#15191C211yesmaximal, characteristic, complemented
13#15188C211yesmaximal, characteristic, complemented
14#14714C211yesmaximal, characteristic, complemented
15#14707C211yesmaximal, characteristic, complemented
16#14364C214yesmaximal
17#14139C211yesmaximal, characteristic
18#13978C211yesmaximal, characteristic, complemented
19C4×#388C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2212yes—
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27#2568—28no—
28#2503—28no—
29#2440—28no—
30#2429—28no—
31C2×#400C2214yes—
32C2×#400C2214yes—
33C2×#398C2212yes—
34C2×#398C2212yes—
35C2×#396C2212yes—
36C2×#395C2212yes—
37C2×#391C2214yes—
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#389C2212yes—
48C2×#389C2211yescharacteristic
49C2×#389C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#388C2212yes—
52C2×#388C2212yes—
53C2×#385C2212yes—
54C2×#384C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#381C2214yes—
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C43C2211yescharacteristic
66#1446C2214yes—
67#1445C2214yes—
68#1443C2214yes—
69#1442C2214yes—
70#1442C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1442C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1440C2214yes—
79#1440C2214yes—
80#1437C2212yes—
81#1436C2212yes—
82#1436C2214yes—
83#1436C2214yes—
84#1436C2214yes—
85C4⋊#95C2214yes—
86C4⋊#95C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91#1434C2212yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×Q8C2312yes—
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—24no—
103C2×C4⋊Q8—24no—
104C2×C4⋊Q8—42no—
105C2×C4⋊Q8—42no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—28no—
111C2×C22⋊Q8—216no—
112C2×C22⋊Q8—42no—
113C2×C22⋊Q8—42no—
114C2×C4×Q8—24no—
115C2×C4×Q8—24no—
116C2×C4×Q8—42no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—42no—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2312yes—
150C22×C42C2312yes—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155#400—216no—
156#400—216no—
157#398—28no—
158#398—28no—
159#396—28no—
160#395—28no—
161#391—24no—
162#391—24no—
163#391—24no—
164#391—24no—
165#391—24no—
166#391—24no—
167#391—216no—
168#391—42no—
169#391—42no—
170#391—42no—
171#389—24no—
172#389—24no—
173#389—24no—
174#389—28no—
175#388—28no—
176#388—28no—
177#385—28no—
178#384—24no—
179#382—24no—
180#382—24no—
181#382—42no—
182#382D418yes—
183#381—216no—
184#380—24no—
185C4×C4⋊C4—24no—
186C4×C22⋊C4—24no—
187C4×C22⋊C4—42no—
188C4×C22⋊C4D418yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C2×#95C2314yes—
220C43—42no—
221C25C2411yescharacteristic
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—24no—
227C22×Q8—24no—
228C22×Q8—22no—
229C22×Q8—28no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—42no—
239C22×Q8—44no—
240C22×Q8#4114yes—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—24no—
248C23×C4—28no—
249C23×C4—24no—
250C23×C4—42no—
251C23×C4—44no—
252C23×C4C2×D414yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2411yescharacteristic
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C4⋊Q8—416no—
272C4⋊Q8—416no—
273C22⋊Q8—416no—
274C22⋊Q8—416no—
275C22⋊Q8—432no—
276C4×Q8—416no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
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—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—416no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4C2×D414yes—
329C2×C4⋊C4C2×D414yes—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—42no—
345C2×C22⋊C4C2×D414yes—
346C2×C22⋊C4C2×D414yes—
347C2×C22⋊C4#4118yes—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—24no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—42no—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42C2×D414yes—
373C2×C42C2×D414yes—
374C2×C42C2×D414yes—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—28no—
379#95—28no—
380#95—28no—
381#95—28no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—28no—
387#95—28no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—28no—
392#95—24no—
393#95—28no—
394#95—24no—
395#95—44no—
396#95—44no—
397#95—44no—
398#95—42no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95C2×D414yes—
404#95C2×D414yes—
405#95C2×D4116yes—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—21no—
410C24—22no—
411C24—22no—
412C24—21no—
413C24—21no—
414C24—22no—
415C24C22×D412yes—
416C24C2×#4114yes—
417C24C2511yescharacteristic
418C2×Q8—28no—
419C2×Q8—28no—
420C2×Q8—28no—
421C2×Q8—48no—
422C2×Q8—416no—
423C2×Q8—48no—
424C2×Q8—44no—
425C2×Q8—44no—
426C2×Q8—44no—
427C2×Q8—44no—
428C2×Q8—44no—
429C2×Q8—44no—
430C2×Q8—44no—
431C2×Q8—44no—
432C2×Q8—44no—
433C2×Q8—44no—
434C2×Q8—44no—
435C2×Q8—84no—
436C2×Q8—88no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—28no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—48no—
527C22×C4—416no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—48no—
533C22×C4—84no—
534C22×C4—88no—
535C22×C4C22×D414yes—
536C22×C4C22×D414yes—
537C22×C4C22×D414yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D412yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C2×#4114yes—
546C22×C4C2×#4114yes—
547C22×C4C2×#4114yes—
548C22×C4C2×#4112yes—
549C22×C4H(5,𝔽2)12yes—
550C22×C4H(5,𝔽2)12yes—
551C22×C42−1+414yes—
552C22×C42−1+414yes—
553C22×C42−1+412yes—
554C22×C42−1+412yes—
555C4⋊C4—28no—
556C4⋊C4—28no—
557C4⋊C4—48no—
558C4⋊C4—48no—
559C4⋊C4—48no—
560C4⋊C4—48no—
561C4⋊C4—48no—
562C4⋊C4—48no—
563C4⋊C4—48no—
564C4⋊C4—48no—
565C4⋊C4—48no—
566C4⋊C4—48no—
567C4⋊C4—48no—
568C4⋊C4—48no—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—84no—
574C22⋊C4—28no—
575C22⋊C4—48no—
576C22⋊C4—48no—
577C22⋊C4—48no—
578C22⋊C4—48no—
579C22⋊C4—48no—
580C22⋊C4#124116yes—
581C42—28no—
582C42—28no—
583C42—28no—
584C42—48no—
585C42—48no—
586C42—48no—
587C42—44no—
588C42—44no—
589C42—44no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—24no—
595C23—24no—
596C23—22no—
597C23—22no—
598C23—24no—
599C23—24no—
600C23—24no—
601C23—24no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—42no—
606C23—42no—
607C23—41no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23—42no—
612C23C2×#12414yes—
613C23C23×D411yescharacteristic
614C23C23×D411yescharacteristic
615C23C22×#4112yes—
616C23C22×#4111yescharacteristic
617C23C2×H(5,𝔽2)11yescharacteristic
618C23C2×H(5,𝔽2)11yescharacteristic
619C23C2×2−1+411yescharacteristic
620C23C2×2−1+411yescharacteristic
621C23C2×2−1+412yes—
622C23C2×2−1+412yes—
623C23#58512yes—
624Q8—416no—
625Q8—816no—
626Q8—88no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—28no—
652C2×C4—24no—
653C2×C4—28no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—41no—
662C2×C4—42no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—44no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—44no—
681C2×C4—42no—
682C2×C4—416no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
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—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—816no—
725C2×C4C2×#12414yes—
726C2×C4C2×#12414yes—
727C2×C4#53614yes—
728C2×C4#53614yes—
729C2×C4#53714yes—
730C2×C4#53914yes—
731C2×C4D4214yes—
732C2×C4#54614yes—
733C2×C4#54814yes—
734C2×C4#56214yes—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—44no—
739C22—42no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22C22×#12411yescharacteristic
747C22C2×#53611yescharacteristic
748C22C2×#53611yescharacteristic
749C22C2×#53711yescharacteristic
750C22C2×#53911yescharacteristic
751C22C2×D4211yescharacteristic
752C22C2×#54611yescharacteristic
753C22C2×#54811yescharacteristic
754C22D4×#4112yes—
755C22#348212yes—
756C22#349912yes—
757C22#349911yescharacteristic
758C22#350011yescharacteristic
759C22#350912yes—
760C22#350912yes—
761C22#351412yes—
762C22#351612yes—
763C22#352012yes—
764C22C2×#56211yescharacteristic
765C22#354112yes—
766C22#355212yes—
767C22#355512yes—
768C22#356312yes—
769C4—24no—
770C4—24no—
771C4—24no—
772C4—44no—
773C4—44no—
774C4—44no—
775C4—42no—
776C4—44no—
777C4—42no—
778C4—44no—
779C4—82no—
780C4—82no—
781C4—82no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4#268118yes—
787C2—44no—
788C2#3532011yescharacteristic
789C2D4×#12411yescharacteristic
790C2#3630311yescharacteristic
791C2#3739211yescharacteristic
792C2#3808311yescharacteristic
793C2#3936011yescharacteristic
794C2#3995912yes—
795C2#4022412yes—
796C2#4562612yes—
797C2C2×#268111yescharacteristic
798C2#5965612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
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×#2568C2semidirect
5. #16835C2semidirect
6. #15624C2semidirect
8. #15242C2semidirect
9. #15237C2semidirect
12. #15191C2semidirect
13. #15188C2semidirect
14. #14714C2semidirect
15. #14707C2semidirect
18. #13978C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25682
C2×#25032
C2×#24292
C2×#24402
#168352
#156242
#154702
#152422
#152372
#152362
#151912
#151882
#147142
#147072
#143642
#141392
#139782
C4×#3882