Finite Group Databasebeta

← #630316

Subgroups — #630316

Order 512.

2644 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×#2620C211yesmaximal, characteristic
2C2×#2317C211yesmaximal, characteristic, complemented
3#15943C214yesmaximal, complemented
4#15771C214yesmaximal, complemented
5#15602C214yesmaximal, complemented
6#15405C214yesmaximal, complemented
7#15226C211yesmaximal, characteristic, complemented
8#15226C211yesmaximal, characteristic, complemented
9#15197C211yesmaximal, characteristic, complemented
10#15153C211yesmaximal, characteristic, complemented
11#14703C211yesmaximal, characteristic, complemented
12#14700C211yesmaximal, characteristic, complemented
13#14261C211yesmaximal, characteristic, complemented
14#14260C211yesmaximal, characteristic, complemented
15#14139C211yesmaximal, characteristic, complemented
16#14138C211yesmaximal, characteristic, complemented
17#14137C211yesmaximal, characteristic
18#14136C211yesmaximal, characteristic
19#13761C211yesmaximal, characteristic, complemented
20C22×#124C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26#2620—28no—
27C2×#400C2214yes—
28C2×#396C2212yes—
29C2×#396C2212yes—
30C2×#394C2212yes—
31C2×#394C2212yes—
32#2317—28no—
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#389C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#389C2211yescharacteristic
47C2×#388C2214yes—
48C2×#386C2214yes—
49C2×#385C2212yes—
50C2×#385C2212yes—
51C2×#384C2212yes—
52C2×#384C2211yescharacteristic
53C2×#382C2212yes—
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×#376C2211yescharacteristic
57C2×C43C2211yescharacteristic
58#1445C2214yes—
59#1443C2214yes—
60#1442C2214yes—
61#1442C2214yes—
62#1441C2214yes—
63#1441C2214yes—
64#1440C2214yes—
65#1440C2214yes—
66#1440C2214yes—
67#1440C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1438C2214yes—
73#1437C2212yes—
74#1437C2214yes—
75#1437C2214yes—
76#1437C2212yes—
77#1436C2214yes—
78#1436C2214yes—
79#1436C2212yes—
80#1436C2212yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89#1434C2214yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C23×D4C2312yes—
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C2×#124—24no—
99C2×#124—42no—
100C2×#124—42no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×#121—24no—
105C2×#121—24no—
106C2×#121—24no—
107C2×#117—24no—
108C2×#117—24no—
109C2×#117—24no—
110C2×#117—42no—
111C2×#117—42no—
112C2×#117D418yes—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—42no—
115C22×C4⋊C4—42no—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2311yescharacteristic
147C22×C42C2312yes—
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2312yes—
156#400—48no—
157#396—28no—
158#396—28no—
159#394—28no—
160#394—28no—
161#391—24no—
162#391—24no—
163#391—24no—
164#391—42no—
165#391—42no—
166#390—24no—
167#390—24no—
168#390—24no—
169#390—42no—
170#390—42no—
171#389—24no—
172#389—24no—
173#389—24no—
174#389—24no—
175#388—48no—
176#386—48no—
177#385—28no—
178#385—28no—
179#384—28no—
180#384—24no—
181#382—28no—
182C4×C22⋊C4—24no—
183C4×C22⋊C4—24no—
184#376—42no—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C43—42no—
212C25C2412yes—
213C25C2411yescharacteristic
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×D4—24no—
222C22×D4—24no—
223C22×D4—24no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—44no—
232C22×D4—44no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—42no—
239C23×C4—42no—
240C23×C4—44no—
241C23×C4—44no—
242C23×C4C2×D414yes—
243C23×C4#4114yes—
244C23×C4#4114yes—
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2412yes—
252C23×C4C2411yescharacteristic
253C23×C4C2411yescharacteristic
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262#124—416no—
263C22⋊Q8—416no—
264#121—416no—
265#117—232no—
266#117—416no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—41no—
297C2×C4⋊C4—41no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—416no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4C2×D414yes—
307C2×C4⋊C4C2×D414yes—
308C2×C4⋊C4#4114yes—
309C2×C4⋊C4#4114yes—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
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—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—42no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—41no—
334C2×C22⋊C4—41no—
335C2×C22⋊C4—41no—
336C2×C22⋊C4—41no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
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×D414yes—
352C2×C22⋊C4C2×D414yes—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—42no—
375C2×C42—42no—
376C2×C42—42no—
377C2×C42—42no—
378C2×C42C2×D414yes—
379C2×C42C2×D414yes—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—28no—
389#95—28no—
390#95—28no—
391#95—28no—
392#95—24no—
393#95—24no—
394#95—44no—
395#95—44no—
396#95—42no—
397#95—42no—
398#95—42no—
399#95—42no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—44no—
406C24—21no—
407C24—21no—
408C24—22no—
409C24—21no—
410C24—21no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—24no—
420C24—22no—
421C24—22no—
422C24—24no—
423C24—24no—
424C24—24no—
425C24C22×D412yes—
426C24C2×#4112yes—
427C24C2×#4112yes—
428C24C2511yescharacteristic
429C2×Q8—44no—
430C2×Q8—44no—
431C2×Q8—44no—
432C2×Q8—44no—
433C2×Q8—44no—
434C2×Q8—44no—
435C2×Q8—44no—
436C2×D4—416no—
437C2×D4—48no—
438C2×D4—44no—
439C2×D4—44no—
440C2×D4—44no—
441C2×D4—44no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—44no—
445C2×D4—88no—
446C2×D4—84no—
447C2×D4—84no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—28no—
453C22×C4—28no—
454C22×C4—28no—
455C22×C4—28no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—24no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
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—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—48no—
536C22×C4—84no—
537C22×C4—84no—
538C22×C4—88no—
539C22×C4—88no—
540C22×C4#124116yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C2×#4114yes—
548C22×C4C2×#4114yes—
549C22×C4C2×#4112yes—
550C22×C4C2×#4112yes—
551C22×C4C2×#4112yes—
552C22×C4C2×#4112yes—
553C22×C4C2×#4112yes—
554C22×C4C2×#4112yes—
555C22×C4H(5,𝔽2)14yes—
556C22×C4H(5,𝔽2)12yes—
557C22×C4H(5,𝔽2)12yes—
558C22×C42−1+414yes—
559C4⋊C4—28no—
560C4⋊C4—28no—
561C4⋊C4—44no—
562C4⋊C4—44no—
563C4⋊C4—48no—
564C4⋊C4—44no—
565C4⋊C4—44no—
566C4⋊C4—48no—
567C4⋊C4—44no—
568C4⋊C4—44no—
569C4⋊C4—84no—
570C4⋊C4—84no—
571C4⋊C4—84no—
572C4⋊C4—84no—
573C4⋊C4—84no—
574C4⋊C4—84no—
575C22⋊C4—216no—
576C22⋊C4—44no—
577C22⋊C4—44no—
578C22⋊C4—416no—
579C22⋊C4—48no—
580C22⋊C4—48no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C22⋊C4—48no—
585C22⋊C4—84no—
586C22⋊C4—84no—
587C22⋊C4—88no—
588C22⋊C4—88no—
589C22⋊C4—88no—
590C42—216no—
591C42—28no—
592C42—28no—
593C42—48no—
594C42—48no—
595C42—44no—
596C42—44no—
597C42—44no—
598C42—44no—
599C23—22no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—24no—
608C23—24no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—44no—
625C23—44no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—44no—
631C23—44no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23C2×#12414yes—
645C23C23×D411yescharacteristic
646C23C22×#4111yescharacteristic
647C23C22×#4111yescharacteristic
648C23C22×#4111yescharacteristic
649C23C22×#4111yescharacteristic
650C23C2×H(5,𝔽2)11yescharacteristic
651C23C2×H(5,𝔽2)11yescharacteristic
652C23C2×H(5,𝔽2)12yes—
653C23C2×2−1+412yes—
654C23#58512yes—
655C23#58512yes—
656Q8—88no—
657D4—816no—
658D4—88no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—232no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—24no—
683C2×C4—28no—
684C2×C4—28no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
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—44no—
698C2×C4—44no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
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—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—816no—
752C2×C4#52514yes—
753C2×C4C2×#12414yes—
754C2×C4C2×#12414yes—
755C2×C4#53414yes—
756C2×C4#55314yes—
757C2×C4#55314yes—
758C2×C4#55314yes—
759C2×C4#55314yes—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—42no—
764C22—42no—
765C22—44no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—42no—
770C22—42no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22—84no—
775C22—84no—
776C22—84no—
777C22—84no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22C2×#52511yescharacteristic
783C22C22×#12411yescharacteristic
784C22C2×#53411yescharacteristic
785C22#346012yes—
786C22#346112yes—
787C22C2×#55311yescharacteristic
788C22C2×#55311yescharacteristic
789C22C2×#55311yescharacteristic
790C22C2×#55311yescharacteristic
791C22#349412yes—
792C22#349512yes—
793C22#349811yescharacteristic
794C22#349911yescharacteristic
795C22#350011yescharacteristic
796C22#350011yescharacteristic
797C22#352012yes—
798C22#352112yes—
799C22#352212yes—
800C22#352412yes—
801C22#354112yes—
802C22#354212yes—
803C22#354612yes—
804C22#354712yes—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—44no—
809C4—44no—
810C4—44no—
811C4—42no—
812C4—42no—
813C4—44no—
814C4—82no—
815C4—82no—
816C4—82no—
817C4—82no—
818C4—82no—
819C4—82no—
820C4—82no—
821C4#259118yes—
822C2—44no—
823C2—162no—
824C2C2×#259111yescharacteristic
825C2#3526411yescharacteristic
826C2#3531211yescharacteristic
827C2#3553511yescharacteristic
828C2#3562311yescharacteristic
829C2#3730011yescharacteristic
830C2#3738811yescharacteristic
831C2#3821212yes—
832C2#3821312yes—
833C2#3905612yes—
834C2#3905712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2317C2semidirect
3. #15943C2semidirect
4. #15771C2semidirect
5. #15602C2semidirect
6. #15405C2semidirect
7. #15226C2semidirect
8. #15226C2semidirect
9. #15197C2semidirect
10. #15153C2semidirect
11. #14703C2semidirect
12. #14700C2semidirect
13. #14261C2semidirect
14. #14260C2semidirect
15. #14139C2semidirect
16. #14138C2semidirect
19. #13761C2semidirect

Maximal subgroups

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

subgroupindex
C2×#26202
C2×#23172
#159432
#157712
#156022
#154052
#152262
#151972
#151532
#147032
#147002
#142612
#142602
#141392
#141382
#141372
#141362
#137612