Finite Group Databasebeta

← #687624

Subgroups — #687624

Order 512.

3038 conjugacy classes of subgroups.

The subgroup lattice has 857 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2503C211yesmaximal, characteristic, complemented
2C2×#2415C211yesmaximal, characteristic
3C2×D4×C4⋊C4C211yesmaximal, characteristic
4C2×#2317C211yesmaximal, characteristic, complemented
5#16307C214yesmaximal, complemented
6#15398C214yesmaximal, complemented
7#15349C214yesmaximal, complemented
8#15242C211yesmaximal, characteristic, complemented
9#15236C211yesmaximal, characteristic, complemented
10#15199C211yesmaximal, characteristic, complemented
11#15150C211yesmaximal, characteristic, complemented
12#14731C214yesmaximal
13#14258C211yesmaximal, characteristic, complemented
14#14139C211yesmaximal, characteristic, complemented
15#14050C211yesmaximal, characteristic, complemented
16#14000C211yesmaximal, characteristic, complemented
17#13880C211yesmaximal, characteristic, complemented
18#13879C211yesmaximal, characteristic, complemented
19#13839C211yesmaximal, characteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28#2503—28no—
29#2415—28no—
30C2×#400C2214yes—
31C2×#397C2212yes—
32C2×#397C2214yes—
33C2×#394C2212yes—
34D4×C4⋊C4—28no—
35#2317—28no—
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#389C2214yes—
42C2×#389C2212yes—
43C2×#389C2211yescharacteristic
44C2×#389C2212yes—
45C2×#388C2212yes—
46C2×#385C2214yes—
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#385C2214yes—
50C2×#384C2211yescharacteristic
51C2×#384C2211yescharacteristic
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#381C2214yes—
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65#1445C2214yes—
66#1445C2214yes—
67#1444C2214yes—
68#1444C2214yes—
69#1444C2214yes—
70#1443C2214yes—
71#1442C2214yes—
72#1442C2214yes—
73#1441C2212yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1440C2212yes—
78#1440C2214yes—
79#1440C2214yes—
80#1439C2212yes—
81#1439C2214yes—
82#1438C2212yes—
83#1436C2214yes—
84#1436C2214yes—
85#1436C2214yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—42no—
107C2×C4×D4—24no—
108C2×C4×D4—24no—
109C2×C4×D4—28no—
110C2×C4×D4—48no—
111C2×C4×D4D418yes—
112C2×#117—24no—
113C2×#117—24no—
114C2×#117—24no—
115C2×#117—24no—
116C2×#117—24no—
117C2×#117—42no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4—42no—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2314yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2312yes—
162#400—216no—
163#397—28no—
164#397—48no—
165#394—28no—
166#391—24no—
167#391—24no—
168#391—24no—
169#391—24no—
170#391—42no—
171#389—28no—
172#389—28no—
173#389—24no—
174#389—216no—
175#388—28no—
176#385—28no—
177#385—28no—
178#385—216no—
179#385—48no—
180#384—24no—
181#384—24no—
182#384—24no—
183#384—42no—
184#382—24no—
185#382—24no—
186#382D418yescomplemented
187#381—216no—
188#380—24no—
189#380—24no—
190#380—24no—
191C4×C4⋊C4—24no—
192C4×C22⋊C4—24no—
193C4×C22⋊C4—24no—
194C4×C22⋊C4—24no—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C25C2411yescharacteristic
223C25C2411yescharacteristic
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4C2×D414yes—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—28no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—44no—
254C23×C4—44no—
255C23×C4—44no—
256C23×C4C2×D414yes—
257C23×C4C2×D414yes—
258C23×C4#4114yes—
259C23×C4#4114yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C22⋊Q8—416no—
278C22⋊Q8—416no—
279C4×D4—232no—
280C4×D4—432no—
281#117—232no—
282#117—416no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
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—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—416no—
323C2×C4⋊C4—416no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4C2×D414yes—
337C2×C4⋊C4C2×D414yes—
338C2×C4⋊C4C2×D414yes—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4C2×D414yes—
371C2×C22⋊C4C2×D414yes—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—42no—
388C2×C42—44no—
389C2×C42C2×D414yes—
390C2×C42C2×D414yes—
391C2×C42#4114yes—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—28no—
401#95—24no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—28no—
407#95—24no—
408#95—24no—
409#95—28no—
410#95—24no—
411#95—42no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95C2×D4116yes—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—21no—
426C24—21no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—21no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24C22×D412yes—
437C24C22×D412yes—
438C24C2×#4112yes—
439C24C2×#4112yes—
440C24H(5,𝔽2)14yes—
441C24C2511yescharacteristic
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×D4—216no—
450C2×D4—216no—
451C2×D4—28no—
452C2×D4—28no—
453C2×D4—28no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—28no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—416no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—88no—
555C22×C4—84no—
556C22×C4—84no—
557C22×C4—88no—
558C22×C4—88no—
559C22×C4#123116yes—
560C22×C4C22×D412yes—
561C22×C4C22×D414yes—
562C22×C4C22×D412yes—
563C22×C4C22×D414yes—
564C22×C4C22×D414yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C22×D412yes—
568C22×C4C22×D412yes—
569C22×C4C2×#4114yes—
570C22×C4C2×#4112yes—
571C22×C4C2×#4112yes—
572C22×C4C2×#4112yes—
573C22×C4C2×#4112yes—
574C22×C4C2×#4112yes—
575C22×C4H(5,𝔽2)12yes—
576C22×C42−1+414yes—
577C22×C42−1+414yes—
578C22×C42−1+412yes—
579C4⋊C4—216no—
580C4⋊C4—28no—
581C4⋊C4—28no—
582C4⋊C4—28no—
583C4⋊C4—48no—
584C4⋊C4—48no—
585C4⋊C4—48no—
586C4⋊C4—48no—
587C4⋊C4—44no—
588C4⋊C4—48no—
589C4⋊C4—48no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—88no—
595C4⋊C4—88no—
596C4⋊C4—84no—
597C4⋊C4—88no—
598C22⋊C4—216no—
599C22⋊C4—216no—
600C22⋊C4—28no—
601C22⋊C4—28no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—48no—
606C22⋊C4—48no—
607C22⋊C4—48no—
608C22⋊C4—48no—
609C22⋊C4—48no—
610C42—28no—
611C42—28no—
612C42—28no—
613C42—48no—
614C42—48no—
615C42—44no—
616C42—44no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23C2×#12314yes—
662C23#53514yes—
663C23C23×D411yescharacteristic
664C23C23×D411yescharacteristic
665C23C22×#4111yescharacteristic
666C23C22×#4111yescharacteristic
667C23C22×#4111yescharacteristic
668C23C2×H(5,𝔽2)12yes—
669C23C2×H(5,𝔽2)11yescharacteristic
670C23C2×2−1+412yes—
671C23C2×2−1+411yescharacteristic
672C23C2×2−1+412yes—
673C23#58512yes—
674Q8—88no—
675D4—232no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—232no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—28no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—28no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—44no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—416no—
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—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—44no—
768C2×C4—44no—
769C2×C4—44no—
770C2×C4—816no—
771C2×C4—816no—
772C2×C4C2×#12314yes—
773C2×C4C2×#12314yes—
774C2×C4#52514yes—
775C2×C4#53614yes—
776C2×C4#53914yes—
777C2×C4D4214yes—
778C2×C4#54714yes—
779C2×C4#54814yes—
780C2×C4#55314yes—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—42no—
788C22—42no—
789C22—44no—
790C22—44no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—44no—
795C22—44no—
796C22—44no—
797C22—44no—
798C22—42no—
799C22—42no—
800C22—44no—
801C22—44no—
802C22—42no—
803C22C22×#12311yescharacteristic
804C22C2×#52511yescharacteristic
805C22C2×#53511yescharacteristic
806C22C2×#53611yescharacteristic
807C22C2×#53911yescharacteristic
808C22C2×D4211yescharacteristic
809C22C2×#54711yescharacteristic
810C22C2×#54811yescharacteristic
811C22C2×#55311yescharacteristic
812C22#348812yes—
813C22#349212yes—
814C22#349212yes—
815C22#349212yes—
816C22#349512yes—
817C22#349911yescharacteristic
818C22#349912yes—
819C22#350011yescharacteristic
820C22#350712yes—
821C22#350712yes—
822C22#354412yes—
823C22#355212yes—
824C22#355512yes—
825C22#355812yes—
826C4—24no—
827C4—24no—
828C4—42no—
829C4—44no—
830C4—44no—
831C4—42no—
832C4—44no—
833C4—44no—
834C4—44no—
835C4—82no—
836C4—82no—
837C4—82no—
838C4—82no—
839C4—82no—
840C4—82no—
841C4—82no—
842C4#244318yes—
843C2—44no—
844C2—44no—
845C2C2×#244311yescharacteristic
846C2#3522711yescharacteristic
847C2#3561911yescharacteristic
848C2#3568612yes—
849C2#3767711yescharacteristic
850C2#3786311yescharacteristic
851C2#3936011yescharacteristic
852C2#3949011yescharacteristic
853C2#4245212yes—
854C2#4497112yes—
855C2#4512012yes—
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. C2×#2503C2semidirect
4. C2×#2317C2semidirect
5. #16307C2semidirect
6. #15398C2semidirect
7. #15349C2semidirect
8. #15242C2semidirect
9. #15236C2semidirect
10. #15199C2semidirect
11. #15150C2semidirect
13. #14258C2semidirect
14. #14139C2semidirect
15. #14050C2semidirect
16. #14000C2semidirect
17. #13880C2semidirect
18. #13879C2semidirect
186. #382D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25032
C2×#24152
C2×D4×C4⋊C42
C2×#23172
#163072
#153982
#153492
#152422
#152362
#151992
#151502
#147312
#142582
#141392
#140502
#140002
#138802
#138792
#138392