Finite Group Databasebeta

← #641995

Subgroups — #641995

Order 512.

2964 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#389C211yesmaximal, characteristic, complemented
2C2×#2290C211yesmaximal, characteristic
3#16985C212yesmaximal, complemented
4#16984C212yesmaximal, complemented
5#16981C212yesmaximal, complemented
6#16980C212yesmaximal, complemented
7#15133C212yesmaximal, complemented
8#15131C212yesmaximal, complemented
9#14921C212yesmaximal
10#14920C212yesmaximal, complemented
11#14729C212yesmaximal
12#14728C212yesmaximal, complemented
13#14686C211yesmaximal, characteristic, complemented
14#14266C212yesmaximal, complemented
15#14264C212yesmaximal, complemented
16#14130C211yesmaximal, characteristic, complemented
17#14130C211yesmaximal, characteristic, complemented
18#13872C211yesmaximal, characteristic
19#13872C211yesmaximal, characteristic
20C22×C4×D4C2211yescharacteristic
21C22×#117C2211yescharacteristic
22C23×C4⋊C4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2212yes—
25C23×C42C2211yescharacteristic
26C2×#398C2214yes—
27C2×#396C2214yes—
28C2×#389—28no—
29C2×#389C2212yes—
30C2×#389C2212yes—
31C2×#389C2212yes—
32C2×#389C2212yes—
33C2×#389C2212yes—
34C2×#389C2212yes—
35#2290—28no—
36C2×#388C2211yescharacteristic
37C2×#388C2211yescharacteristic
38C2×#387C2211yescharacteristic
39C2×#387C2211yescharacteristic
40C2×#386C2211yescharacteristic
41C2×#386C2211yescharacteristic
42C2×#386C2212yes—
43C2×#386C2212yes—
44C2×#385C2211yescharacteristic
45C2×#385C2211yescharacteristic
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#384C2212yes—
49C2×#380C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×#376C2211yescharacteristic
59C22×#95C2212yes—
60#1445C2214yes—
61#1444C2212yes—
62#1444C2212yes—
63#1444C2214yes—
64#1443C2214yes—
65#1442C2212yes—
66#1442C2212yes—
67#1442C2214yes—
68#1442C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2212yes—
75#1441C2212yes—
76#1441C2214yes—
77#1439C2214yes—
78#1439C2212yes—
79#1439C2212yes—
80#1439C2214yes—
81#1439C2214yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C4⋊#95C2212yes—
87C4⋊#95C2212yes—
88C4⋊#95C2212yes—
89C22⋊#95C2212yes—
90C22⋊#95C2212yes—
91C22⋊#95C2212yes—
92C22⋊#95C2212yes—
93C23×D4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2312yes—
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C2×C4×D4—24no—
101C2×C4×D4—24no—
102C2×C4×D4Q818yes—
103C2×#117—24no—
104C2×#117—44no—
105C22×C4⋊C4—24no—
106C22×C4⋊C4—28no—
107C22×C4⋊C4—28no—
108C22×C4⋊C4—24no—
109C22×C4⋊C4—44no—
110C22×C4⋊C4—48no—
111C22×C4⋊C4C2314yes—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2314yes—
128C22×C22⋊C4C2311yescharacteristic
129C22×C22⋊C4C2311yescharacteristic
130C22×C22⋊C4C2311yescharacteristic
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2311yescharacteristic
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2311yescharacteristic
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2311yescharacteristic
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2314yes—
140C22×C42—44no—
141C22×C42D418yes—
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149#398—48no—
150#396—48no—
151#389—28no—
152#389—28no—
153#389—28no—
154#389—28no—
155#389—28no—
156#389—44no—
157#388—24no—
158#388—24no—
159#387—24no—
160#387—24no—
161#386—24no—
162#386—24no—
163#386—44no—
164#386—44no—
165#385—24no—
166#385—24no—
167#385—44no—
168#385—44no—
169#384—44no—
170#380—24no—
171#380—24no—
172#380—28no—
173#380—44no—
174#380—44no—
175#380—44no—
176C4×C4⋊C4—24no—
177C4×C22⋊C4—24no—
178C4×C22⋊C4—24no—
179#376—24no—
180C2×#95—28no—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2311yescharacteristic
188C2×#95C2311yescharacteristic
189C2×#95C2311yescharacteristic
190C2×#95C2311yescharacteristic
191C2×#95C2311yescharacteristic
192C2×#95C2311yescharacteristic
193C2×#95C2311yescharacteristic
194C2×#95C2311yescharacteristic
195C2×#95C2311yescharacteristic
196C2×#95C2311yescharacteristic
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C25C2411yescharacteristic
210C25C2411yescharacteristic
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4C2×Q814yes—
218C23×C4—24no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—28no—
227C23×C4—22no—
228C23×C4—24no—
229C23×C4—24no—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—44no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—44no—
241C23×C4—44no—
242C23×C4C2×D414yes—
243C23×C4C2×D414yes—
244C23×C4C2×D414yes—
245C23×C4C2×Q814yes—
246C23×C4C2×Q814yes—
247C23×C4#4114yes—
248C23×C4C2411yescharacteristic
249C23×C4C2414yes—
250C23×C4C2414yes—
251C23×C4C2411yescharacteristic
252C23×C4C2411yescharacteristic
253C23×C4C2411yescharacteristic
254C23×C4C2414yes—
255C23×C4C2411yescharacteristic
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258C23×C4C2411yescharacteristic
259C23×C4C2411yescharacteristic
260C23×C4C2414yes—
261C23×C4C2411yescharacteristic
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C4×D4—232no—
266#117—416no—
267C2×C4⋊C4—232no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—28no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—28no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—28no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—44no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—416no—
303C2×C4⋊C4—432no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4C2×Q814yes—
314C2×C4⋊C4#4118yes—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4C2×Q814yes—
346C2×C22⋊C4C2×Q814yes—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—24no—
350C2×C42—24no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—416no—
356C2×C42—42no—
357C2×C42—42no—
358C2×C42C2×D414yes—
359C2×C42C2×D414yes—
360C2×C42C2×D414yes—
361C2×C42C2×D414yes—
362C2×C42C2×Q814yes—
363#95—28no—
364#95—28no—
365#95—22no—
366#95—22no—
367#95—22no—
368#95—22no—
369#95—22no—
370#95—22no—
371#95—22no—
372#95—22no—
373#95—22no—
374#95—22no—
375#95—28no—
376#95—24no—
377#95—24no—
378#95—28no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386#95—44no—
387#95—44no—
388#95—44no—
389#95—44no—
390#95—44no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—22no—
395C24—21no—
396C24—22no—
397C24—21no—
398C24—22no—
399C24—22no—
400C24—21no—
401C24—21no—
402C24—22no—
403C24—21no—
404C24—21no—
405C24C22×D412yes—
406C24C22×Q812yes—
407C24C22×Q812yes—
408C24C2×#4112yes—
409C24H(5,𝔽2)12yes—
410C24H(5,𝔽2)12yes—
411C242−1+412yes—
412C242−1+412yes—
413C24C2511yescharacteristic
414C2×D4—28no—
415C2×D4—28no—
416C2×D4—28no—
417C2×D4—44no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—44no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—28no—
430C22×C4—28no—
431C22×C4—216no—
432C22×C4—216no—
433C22×C4—216no—
434C22×C4—28no—
435C22×C4—28no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—24no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—216no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—24no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—24no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—24no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—48no—
512C22×C4—48no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—416no—
516C22×C4—416no—
517C22×C4—48no—
518C22×C4—48no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—48no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—88no—
526C22×C4—88no—
527C22×C4C22⋊Q8116yes—
528C22×C4C22×D412yes—
529C22×C4C22×D412yes—
530C22×C4C22×D412yes—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×Q812yes—
535C22×C4C22×Q812yes—
536C22×C4C22×Q812yes—
537C22×C4C22×Q812yes—
538C22×C4C22×Q812yes—
539C22×C4C2×#4118yes—
540C22×C4C2×#4112yes—
541C22×C4C2×#4112yes—
542C22×C4C2×#4114yes—
543C22×C4H(5,𝔽2)14yes—
544C22×C4H(5,𝔽2)14yes—
545C22×C42−1+414yes—
546C4⋊C4—216no—
547C4⋊C4—28no—
548C4⋊C4—216no—
549C4⋊C4—48no—
550C4⋊C4—416no—
551C4⋊C4—44no—
552C4⋊C4—44no—
553C4⋊C4—48no—
554C4⋊C4—44no—
555C4⋊C4—416no—
556C4⋊C4—44no—
557C4⋊C4—48no—
558C4⋊C4—48no—
559C4⋊C4—88no—
560C4⋊C4—88no—
561C4⋊C4—88no—
562C4⋊C4—88no—
563C22⋊C4—28no—
564C22⋊C4—28no—
565C22⋊C4—44no—
566C22⋊C4—44no—
567C22⋊C4—44no—
568C22⋊C4—44no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—44no—
572C22⋊C4—44no—
573C22⋊C4—88no—
574C22⋊C4—88no—
575C42—28no—
576C42—28no—
577C42—28no—
578C42—44no—
579C42—44no—
580C42—44no—
581C42—44no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—42no—
612C23—42no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23C2×C22⋊Q814yes—
622C23#53714yes—
623C23#53714yes—
624C23#54014yes—
625C23#54114yes—
626C23#54414yes—
627C23#54414yes—
628C23C23×D411yescharacteristic
629C23C23×Q811yescharacteristic
630C23C22×#4111yescharacteristic
631C23C22×#4112yes—
632C23C2×H(5,𝔽2)12yes—
633C23C2×H(5,𝔽2)12yes—
634C23C2×H(5,𝔽2)11yescharacteristic
635C23C2×H(5,𝔽2)11yescharacteristic
636C23C2×2−1+412yes—
637C23C2×2−1+411yescharacteristic
638C23C2×2−1+411yescharacteristic
639D4—416no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—232no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—28no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—28no—
668C2×C4—28no—
669C2×C4—416no—
670C2×C4—416no—
671C2×C4—432no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—44no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—44no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—416no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—44no—
696C2×C4—41no—
697C2×C4—44no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4—42no—
732C2×C4—816no—
733C2×C4C2×C22⋊Q814yes—
734C2×C4C2×C22⋊Q814yes—
735C2×C4#52514yes—
736C2×C4#53414yes—
737C2×C4#53514yes—
738C2×C4#53614yes—
739C2×C4#55318yes—
740C2×C4#55418yes—
741C22—24no—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—24no—
746C22—24no—
747C22—28no—
748C22—28no—
749C22—28no—
750C22—28no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—44no—
755C22—44no—
756C22—81no—
757C22—81no—
758C22—81no—
759C22—81no—
760C22—82no—
761C22—82no—
762C22#262918yes—
763C22C22×C22⋊Q811yescharacteristic
764C22C2×#52511yescharacteristic
765C22C2×#53411yescharacteristic
766C22C2×#53511yescharacteristic
767C22C2×#53611yescharacteristic
768C22C2×#53711yescharacteristic
769C22C2×#53711yescharacteristic
770C22C2×#54011yescharacteristic
771C22C2×#54111yescharacteristic
772C22C2×#54411yescharacteristic
773C22C2×#54411yescharacteristic
774C22C2×#55312yes—
775C22C2×#55412yes—
776C22#350312yes—
777C22#351112yes—
778C22#351912yes—
779C22#352012yes—
780C22#352212yes—
781C22#352312yes—
782C22#353612yes—
783C22#353612yes—
784C22#353712yes—
785C22#353812yes—
786C4—24no—
787C4—24no—
788C4—24no—
789C4—42no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—48no—
794C4—42no—
795C4—81no—
796C4—84no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4—84no—
801C4—84no—
802C4#257918yes—
803C2—28no—
804C2—82no—
805C2C2×#262911yescharacteristic
806C2C2×#257911yescharacteristic
807C2#3523611yescharacteristic
808C2#3524711yescharacteristic
809C2#3527911yescharacteristic
810C2#3743911yescharacteristic
811C2#3744211yescharacteristic
812C2#3809812yes—
813C2#3809912yes—
814C2#3812212yes—
815C2#3812312yes—
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
1. C22×#389C2semidirect
3. #16985C2semidirect
4. #16984C2semidirect
5. #16981C2semidirect
6. #16980C2semidirect
7. #15133C2semidirect
8. #15131C2semidirect
10. #14920C2semidirect
12. #14728C2semidirect
13. #14686C2semidirect
14. #14266C2semidirect
15. #14264C2semidirect
16. #14130C2semidirect
17. #14130C2semidirect

Maximal subgroups

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

subgroupindex
C22×#3892
C2×#22902
#169852
#169842
#169812
#169802
#151332
#151312
#149212
#149202
#147292
#147282
#146862
#142662
#142642
#141302
#138722