Finite Group Databasebeta

← #687722

Subgroups — #687722

Order 512.

3722 conjugacy classes of subgroups.

The subgroup lattice has 927 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2546C211yesmaximal, characteristic, complemented
2C2×#2432C211yesmaximal, characteristic
3C2×#2432C211yesmaximal, characteristic
4C2×#2621C211yesmaximal, characteristic, complemented
5C2×#2360C211yesmaximal, characteristic, complemented
6C2×#2311C211yesmaximal, characteristic
7#16286C214yesmaximal, complemented
8#15441C214yesmaximal, complemented
9#15306C214yesmaximal, complemented
10#15243C211yesmaximal, characteristic, complemented
11#15222C211yesmaximal, characteristic, complemented
12#15188C211yesmaximal, characteristic, complemented
13#15180C211yesmaximal, characteristic, complemented
14#14802C214yesmaximal, complemented
15#14153C211yesmaximal, characteristic, complemented
16#14139C211yesmaximal, characteristic, complemented
17#14026C211yesmaximal, characteristic, complemented
18#14003C211yesmaximal, characteristic, complemented
19#13844C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×#124C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31#2621—28no—
32#2546—28no—
33#2432—28no—
34#2432—28no—
35C2×#398C2214yes—
36C2×#398C2214yes—
37C2×#397C2214yes—
38C2×#394C2212yes—
39C2×#394C2214yes—
40C2×#394C2212yes—
41#2360—28no—
42#2311—28no—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#389C2214yes—
57C2×#389C2211yescharacteristic
58C2×#389C2212yes—
59C2×#387C2212yes—
60C2×#386C2214yes—
61C2×#385C2212yes—
62C2×#385C2214yes—
63C2×#385C2212yes—
64C2×#385C2212yes—
65C2×#382C2211yescharacteristic
66C2×#380C2214yes—
67C2×C4×C4⋊C4C2211yescharacteristic
68C2×C4×C4⋊C4C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2212yes—
72C2×C4×C22⋊C4C2211yescharacteristic
73#1444C2212yes—
74#1443C2214yes—
75#1442C2212yes—
76#1442C2214yes—
77#1442C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1441C2214yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2214yes—
84#1439C2214yes—
85#1439C2214yes—
86#1439C2214yes—
87#1439C2214yes—
88#1439C2214yes—
89#1437C2214yes—
90#1437C2214yes—
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93#1434C2214yes—
94C22⋊#95C2214yes—
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C22×#41—24no—
98C22×#41—24no—
99C22×#41—24no—
100C22×#41—24no—
101C22×#41—24no—
102C22×#41—42no—
103C22×#41—42no—
104C23×Q8C2311yescharacteristic
105C23×Q8C2311yescharacteristic
106C23×Q8C2311yescharacteristic
107C23×D4C2311yescharacteristic
108C23×D4C2312yes—
109C24×C4C2312yes—
110C24×C4C2311yescharacteristic
111C24×C4C2312yes—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—24no—
118C2×C4⋊Q8—42no—
119C2×C4⋊Q8—42no—
120C2×C4⋊Q8—42no—
121C2×#124—24no—
122C2×#124—24no—
123C2×#124—24no—
124C2×#124—24no—
125C2×#124—42no—
126C2×#124—42no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—24no—
131C2×C22⋊Q8—24no—
132C2×C22⋊Q8D418yes—
133C2×C4×Q8—24no—
134C2×C4×Q8—24no—
135C2×C4×Q8—42no—
136C2×#117—24no—
137C2×#117—24no—
138C2×#117—42no—
139C22×C4⋊C4—24no—
140C22×C4⋊C4—24no—
141C22×C4⋊C4—42no—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2311yescharacteristic
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2314yes—
170C22×C22⋊C4C2314yes—
171C22×C22⋊C4C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2312yes—
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178C22×C42C2311yescharacteristic
179C22×C42C2312yes—
180#398—216no—
181#398—216no—
182#397—216no—
183#394—28no—
184#394—28no—
185#394—216no—
186#391—24no—
187#391—24no—
188#391—24no—
189#391—24no—
190#391—24no—
191#391—24no—
192#391—24no—
193#391—42no—
194#391D418yes—
195#390—24no—
196#390—24no—
197#390—24no—
198#390—24no—
199#389—24no—
200#389—28no—
201#389—216no—
202#387—28no—
203#386—216no—
204#385—216no—
205#385—28no—
206#385—28no—
207#385—28no—
208#382—24no—
209#380—216no—
210C4×C4⋊C4—24no—
211C4×C4⋊C4—24no—
212C4×C4⋊C4—42no—
213C4×C22⋊C4—24no—
214C4×C22⋊C4—28no—
215C4×C22⋊C4D418yes—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2314yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2312yes—
238C2×#95C2314yes—
239C2×#95C2311yescharacteristic
240C2×#95C2311yescharacteristic
241C25C2412yes—
242C25C2411yescharacteristic
243C2×#41—232no—
244C2×#41—416no—
245C2×#41—416no—
246C2×#41—416no—
247C2×#41—416no—
248C2×#41—416no—
249C2×#41—416no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8C2×D414yes—
270C22×Q8C2×D414yes—
271C22×D4—24no—
272C22×D4—24no—
273C22×D4—24no—
274C22×D4—24no—
275C22×D4—22no—
276C22×D4—22no—
277C22×D4—24no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—42no—
283C22×D4—42no—
284C22×D4#4114yes—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—44no—
300C23×C4—44no—
301C23×C4C2×D414yes—
302C23×C4C2×D414yes—
303C23×C4#4114yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2411yescharacteristic
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315C23×C4C2412yes—
316C23×C4C2412yes—
317C23×C4C2412yes—
318C23×C4C2411yescharacteristic
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C4⋊Q8—416no—
322C4⋊Q8—416no—
323C4⋊Q8—416no—
324#124—416no—
325#124—416no—
326C22⋊Q8—232no—
327C22⋊Q8—416no—
328C4×Q8—416no—
329#117—416no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—28no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—416no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4C2×D414yes—
376C2×C4⋊C4C2×D414yes—
377C2×C4⋊C4C2×D418yes—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—28no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4C2×D418yes—
414C2×C22⋊C4C2×D414yes—
415C2×C22⋊C4C2×D414yes—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—24no—
434C2×C42—42no—
435C2×C42—44no—
436C2×C42C2×D414yes—
437C2×C42C2×D414yes—
438C2×C42C2×D414yes—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—28no—
445#95—28no—
446#95—24no—
447#95—28no—
448#95—24no—
449#95—24no—
450#95—28no—
451#95—28no—
452#95—28no—
453#95—24no—
454#95—44no—
455#95—42no—
456#95—42no—
457#95—44no—
458#95—42no—
459#95—42no—
460#95—44no—
461#95C2×D414yes—
462#95C2×D414yes—
463#95C2×D4116yes—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—24no—
479C24—24no—
480C24—24no—
481C24—24no—
482C24C22×D412yes—
483C24C22×D412yes—
484C24C2×#4114yes—
485C24C2×#4112yes—
486C24C2511yescharacteristic
487#41—4128no—
488C2×Q8—28no—
489C2×Q8—28no—
490C2×Q8—28no—
491C2×Q8—28no—
492C2×Q8—28no—
493C2×Q8—28no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8—44no—
509C2×D4—216no—
510C2×D4—28no—
511C2×D4—28no—
512C2×D4—28no—
513C2×D4—48no—
514C2×D4—48no—
515C2×D4—48no—
516C2×D4—48no—
517C2×D4—48no—
518C2×D4—48no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—216no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—24no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—24no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—24no—
610C22×C4—22no—
611C22×C4—24no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—88no—
621C22×C4—84no—
622C22×C4—88no—
623C22×C4#121116yes—
624C22×C4C22×D412yes—
625C22×C4C22×D414yes—
626C22×C4C22×D412yes—
627C22×C4C22×D414yes—
628C22×C4C22×D414yes—
629C22×C4C22×D414yes—
630C22×C4C22×D414yes—
631C22×C4C22×D412yes—
632C22×C4C22×D412yes—
633C22×C4C22×D412yes—
634C22×C4C22×D412yes—
635C22×C4C22×D412yes—
636C22×C4C22×D412yes—
637C22×C4C22×D412yes—
638C22×C4C2×#4112yes—
639C22×C4C2×#4112yes—
640C22×C4C2×#4112yes—
641C22×C4H(5,𝔽2)12yes—
642C22×C4H(5,𝔽2)12yes—
643C22×C42−1+414yes—
644C22×C42−1+414yes—
645C4⋊C4—216no—
646C4⋊C4—28no—
647C4⋊C4—216no—
648C4⋊C4—28no—
649C4⋊C4—48no—
650C4⋊C4—48no—
651C4⋊C4—48no—
652C4⋊C4—48no—
653C4⋊C4—416no—
654C4⋊C4—48no—
655C4⋊C4—416no—
656C4⋊C4—48no—
657C4⋊C4—44no—
658C4⋊C4—48no—
659C4⋊C4—44no—
660C4⋊C4—84no—
661C22⋊C4—216no—
662C22⋊C4—28no—
663C22⋊C4—44no—
664C22⋊C4—416no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—416no—
670C22⋊C4—48no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—88no—
674C22⋊C4—88no—
675C42—28no—
676C42—28no—
677C42—28no—
678C42—48no—
679C42—44no—
680C42—44no—
681C42—44no—
682C42—84no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—24no—
692C23—24no—
693C23—22no—
694C23—22no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—28no—
701C23—28no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—42no—
720C23—44no—
721C23—42no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23C2×#12114yes—
729C23C23×D411yescharacteristic
730C23C23×D411yescharacteristic
731C23C23×D411yescharacteristic
732C23C22×#4111yescharacteristic
733C23C22×#4111yescharacteristic
734C23C2×H(5,𝔽2)11yescharacteristic
735C23C2×H(5,𝔽2)11yescharacteristic
736C23C2×2−1+412yes—
737C23C2×2−1+412yes—
738C23#58512yes—
739C23#58512yes—
740Q8—416no—
741Q8—416no—
742Q8—88no—
743D4—432no—
744D4—416no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—232no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—28no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—28no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—432no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—44no—
832C2×C4—42no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—44no—
841C2×C4—816no—
842C2×C4C2×#12114yes—
843C2×C4C2×#12114yes—
844C2×C4#52514yes—
845C2×C4#53614yes—
846C2×C4#53814yes—
847C2×C4D4214yes—
848C2×C4D4214yes—
849C2×C4#54614yes—
850C2×C4#54614yes—
851C22—24no—
852C22—24no—
853C22—24no—
854C22—42no—
855C22—42no—
856C22—44no—
857C22—44no—
858C22—42no—
859C22—44no—
860C22—42no—
861C22—44no—
862C22—44no—
863C22—44no—
864C22—48no—
865C22—48no—
866C22—44no—
867C22—82no—
868C22—82no—
869C22—82no—
870C22—82no—
871C22—84no—
872C22—84no—
873C22C22×#12111yescharacteristic
874C22C2×#52511yescharacteristic
875C22C2×#53611yescharacteristic
876C22#344911yescharacteristic
877C22C2×#53811yescharacteristic
878C22C2×D4211yescharacteristic
879C22C2×D4211yescharacteristic
880C22C2×#54611yescharacteristic
881C22C2×#54611yescharacteristic
882C22#348612yes—
883C22#348912yes—
884C22#349712yes—
885C22#349911yescharacteristic
886C22#350011yescharacteristic
887C22#350012yes—
888C22#350712yes—
889C22#350712yes—
890C22#351512yes—
891C22#351512yes—
892C22#354112yes—
893C22#354712yes—
894C22#355212yes—
895C22#356212yes—
896C4—24no—
897C4—24no—
898C4—44no—
899C4—42no—
900C4—44no—
901C4—44no—
902C4—42no—
903C4—44no—
904C4—44no—
905C4—44no—
906C4—42no—
907C4—82no—
908C4—82no—
909C4—82no—
910C4—82no—
911C4—82no—
912C4#242418yes—
913C2—44no—
914C2—84no—
915C2C2×#242411yescharacteristic
916C2#3517811yescharacteristic
917C2#3562111yescharacteristic
918C2#3571212yes—
919C2#3767511yescharacteristic
920C2#3808811yescharacteristic
921C2#3895511yescharacteristic
922C2#3935711yescharacteristic
923C2#4269612yes—
924C2#4517512yes—
925C2#4524512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×#41C22
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×#2546C2semidirect
4. C2×#2621C2semidirect
5. C2×#2360C2semidirect
7. #16286C2semidirect
8. #15441C2semidirect
9. #15306C2semidirect
10. #15243C2semidirect
11. #15222C2semidirect
12. #15188C2semidirect
13. #15180C2semidirect
14. #14802C2semidirect
15. #14153C2semidirect
16. #14139C2semidirect
17. #14026C2semidirect
18. #14003C2semidirect
19. #13844C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25462
C2×#24322
C2×#26212
C2×#23602
C2×#23112
#162862
#154412
#153062
#152432
#152222
#151882
#151802
#148022
#141532
#141392
#140262
#140032
#138442