Finite Group Databasebeta

← #696711

Subgroups — #696711

Order 512.

3886 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic
2C2×#2499C211yesmaximal, characteristic, complemented
3C2×#2485C211yesmaximal, characteristic
4C2×#2317C211yesmaximal, characteristic, complemented
5#16262C214yesmaximal, complemented
6#16104C214yesmaximal, complemented
7#15354C214yesmaximal, complemented
8#15236C211yesmaximal, characteristic, complemented
9#15230C211yesmaximal, characteristic, complemented
10#15182C211yesmaximal, characteristic, complemented
11#15143C211yesmaximal, characteristic, complemented
12#14731C214yesmaximal
13#14258C211yesmaximal, characteristic, complemented
14#13978C211yesmaximal, characteristic, complemented
15#13976C211yesmaximal, characteristic, complemented
16#13904C211yesmaximal, characteristic, complemented
17#13881C211yesmaximal, characteristic, complemented
18#13880C211yesmaximal, characteristic, complemented
19#13839C211yesmaximal, characteristic
20C2×#554—28no—
21C2×#554—28no—
22C2×#554—28no—
23C22×C4⋊Q8C2211yescharacteristic
24C22×#125C2212yes—
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2212yes—
27C22×C22⋊Q8C2212yes—
28C22×C22⋊Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×D4C2212yes—
31C22×C4×D4C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C23×C4⋊C4C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36#2499—28no—
37#2485—28no—
38C2×#397C2212yes—
39C2×#397C2214yes—
40C2×#395C2214yes—
41C2×#394C2212yes—
42#2317—28no—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#389C2214yes—
48C2×#389C2211yescharacteristic
49C2×#389C2211yescharacteristic
50C2×#388C2212yes—
51C2×#387C2212yes—
52C2×#387C2214yes—
53C2×#385C2214yes—
54C2×#385C2214yes—
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#382C2211yescharacteristic
60C2×#382C2211yescharacteristic
61C2×#381C2214yes—
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×#380C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68#1446C2214yes—
69#1445C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1442C2214yes—
74#1442C2214yes—
75#1442C2214yes—
76#1441C2212yes—
77#1441C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1440C2212yes—
81#1440C2214yes—
82#1440C2214yes—
83#1439C2212yes—
84#1439C2214yes—
85#1438C2212yes—
86#1436C2214yes—
87#1436C2214yes—
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C22⋊#95C2214yes—
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×Q8C2312yes—
99C23×D4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C24×C4C2312yes—
104#554—2128no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—24no—
107C2×C4⋊Q8—24no—
108C2×#125—28no—
109C2×#125—28no—
110C2×#125—28no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—28no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—28no—
117C2×C22⋊Q8—28no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—28no—
120C2×C22⋊Q8—28no—
121C2×C22⋊Q8—28no—
122C2×C22⋊Q8D418yes—
123C2×C4×Q8—24no—
124C2×C4×Q8—24no—
125C2×C4×Q8—24no—
126C2×C4×D4—28no—
127C2×C4×D4—28no—
128C2×C4×D4—24no—
129C2×C4×D4—24no—
130C2×C4×D4—28no—
131C2×C4×D4D418yes—
132C2×#117—24no—
133C2×#117—24no—
134C2×#117—24no—
135C2×#117—24no—
136C2×#117—24no—
137C2×#117—24no—
138C22×C4⋊C4—24no—
139C22×C4⋊C4—24no—
140C22×C4⋊C4—24no—
141C22×C4⋊C4—24no—
142C22×C4⋊C4—24no—
143C22×C4⋊C4D418yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2311yescharacteristic
154C22×C4⋊C4C2314yes—
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2314yes—
163C22×C4⋊C4C2314yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2311yescharacteristic
173C22×C22⋊C4C2311yescharacteristic
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C42C2312yes—
177C22×C42C2312yes—
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180C22×C42C2311yescharacteristic
181C22×C42C2311yescharacteristic
182C22×C42C2311yescharacteristic
183#397—28no—
184#397—216no—
185#395—48no—
186#394—28no—
187#391—24no—
188#391—24no—
189#391—24no—
190#391—24no—
191#389—216no—
192#389—24no—
193#389—24no—
194#388—28no—
195#387—28no—
196#387—216no—
197#385—216no—
198#385—48no—
199#384—24no—
200#384—24no—
201#384—24no—
202#382—24no—
203#382—24no—
204#382—24no—
205#381—48no—
206#380—24no—
207#380—24no—
208#380—24no—
209C4×C22⋊C4—24no—
210C4×C22⋊C4—24no—
211C4×C22⋊C4—24no—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2314yes—
231C2×#95C2312yes—
232C2×#95C2314yes—
233C2×#95C2312yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C25C2411yescharacteristic
238C25C2411yescharacteristic
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—24no—
242C22×Q8—24no—
243C22×Q8—24no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—44no—
249C22×Q8—44no—
250C22×Q8C2×D414yes—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—24no—
254C22×D4—24no—
255C22×D4C2×D414yes—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—44no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4C2×D414yes—
276C23×C4C2×D414yes—
277C23×C4C2×D414yes—
278C23×C4C2×D414yes—
279C23×C4C2×D418yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C4⋊Q8—232no—
298#125—264no—
299C22⋊Q8—232no—
300C22⋊Q8—264no—
301C22⋊Q8—264no—
302C22⋊Q8—232no—
303C4×Q8—232no—
304C4×D4—264no—
305C4×D4—232no—
306#117—232no—
307#117—416no—
308C2×C4⋊C4—232no—
309C2×C4⋊C4—232no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4C2×D414yes—
363C2×C4⋊C4C2×D414yes—
364C2×C4⋊C4C2×D418yes—
365C2×C4⋊C4C2×D414yes—
366C2×C4⋊C4C2×D414yes—
367C2×C4⋊C4C2×D418yes—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
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—24no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4C2×D418yes—
399C2×C22⋊C4C2×D414yes—
400C2×C22⋊C4C2×D414yes—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—24no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42C2×D414yes—
420C2×C42#4114yes—
421C2×C42#4114yes—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—28no—
427#95—28no—
428#95—28no—
429#95—24no—
430#95—28no—
431#95—28no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—28no—
436#95—28no—
437#95—28no—
438#95—28no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—42no—
443#95—44no—
444#95—44no—
445#95—44no—
446#95—44no—
447C24—21no—
448C24—21no—
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—22no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24C22×D412yes—
465C24C22×D412yes—
466C24C22×D412yes—
467C24C22×D412yes—
468C242−1+414yes—
469C24C2511yescharacteristic
470C2×Q8—216no—
471C2×Q8—28no—
472C2×Q8—28no—
473C2×Q8—28no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—88no—
479C2×Q8—88no—
480C2×Q8—84no—
481C2×Q8—84no—
482C2×D4—216no—
483C2×D4—216no—
484C2×D4—28no—
485C2×D4—28no—
486C2×D4—28no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—216no—
547C22×C4—216no—
548C22×C4—28no—
549C22×C4—28no—
550C22×C4—28no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—416no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—88no—
584C22×C4—88no—
585C22×C4—88no—
586C22×C4—84no—
587C22×C4—84no—
588C22×C4—84no—
589C22×C4—84no—
590C22×C4#120116yes—
591C22×C4C22×D414yes—
592C22×C4C22×D412yes—
593C22×C4C22×D414yes—
594C22×C4C22×D412yes—
595C22×C4C22×D414yes—
596C22×C4C22×D414yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C2×#4114yes—
605C22×C4C2×#4114yes—
606C22×C4C2×#4112yes—
607C22×C4C2×#4112yes—
608C22×C4H(5,𝔽2)14yes—
609C22×C42−1+414yes—
610C22×C42−1+412yes—
611C22×C42−1+412yes—
612C4⋊C4—216no—
613C4⋊C4—216no—
614C4⋊C4—216no—
615C4⋊C4—216no—
616C4⋊C4—216no—
617C4⋊C4—28no—
618C4⋊C4—216no—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—28no—
622C4⋊C4—216no—
623C4⋊C4—416no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—48no—
627C4⋊C4—44no—
628C4⋊C4—44no—
629C4⋊C4—88no—
630C4⋊C4—88no—
631C4⋊C4—84no—
632C22⋊C4—216no—
633C22⋊C4—216no—
634C22⋊C4—216no—
635C22⋊C4—216no—
636C22⋊C4—28no—
637C22⋊C4—28no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—48no—
642C22⋊C4—84no—
643C22⋊C4—84no—
644C42—216no—
645C42—28no—
646C42—28no—
647C42—28no—
648C42—48no—
649C42—44no—
650C42—44no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23C2×#12014yes—
696C23#53614yes—
697C23C23×D411yescharacteristic
698C23C23×D411yescharacteristic
699C23C23×D411yescharacteristic
700C23C22×#4111yescharacteristic
701C23C22×#4111yescharacteristic
702C23C2×H(5,𝔽2)12yes—
703C23C2×2−1+411yescharacteristic
704C23C2×2−1+411yescharacteristic
705C23C2×2−1+412yes—
706C23C2×2−1+412yes—
707C23#58512yes—
708Q8—416no—
709Q8—816no—
710D4—232no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—232no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—28no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—416no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—816no—
806C2×C4—816no—
807C2×C4C2×#12014yes—
808C2×C4C2×#12014yes—
809C2×C4#52514yes—
810C2×C4#53614yes—
811C2×C4#53614yes—
812C2×C4#54714yes—
813C2×C4#54714yes—
814C2×C4#54714yes—
815C2×C4#54714yes—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—44no—
823C22—44no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—42no—
833C22—42no—
834C22—44no—
835C22—44no—
836C22—42no—
837C22—42no—
838C22C22×#12011yescharacteristic
839C22C2×#52511yescharacteristic
840C22C2×#53611yescharacteristic
841C22C2×#53611yescharacteristic
842C22C2×#53611yescharacteristic
843C22C2×#54711yescharacteristic
844C22C2×#54711yescharacteristic
845C22C2×#54711yescharacteristic
846C22C2×#54711yescharacteristic
847C22#348612yes—
848C22#348612yes—
849C22#348812yes—
850C22#349212yes—
851C22#349512yes—
852C22#349612yes—
853C22#349811yescharacteristic
854C22#350011yescharacteristic
855C22#350712yes—
856C22#351112yes—
857C22#354412yes—
858C22#355212yes—
859C22#355512yes—
860C22#356312yes—
861C4—24no—
862C4—24no—
863C4—44no—
864C4—44no—
865C4—44no—
866C4—42no—
867C4—44no—
868C4—44no—
869C4—44no—
870C4—44no—
871C4—42no—
872C4—82no—
873C4—82no—
874C4—82no—
875C4—82no—
876C4—82no—
877C4#240618yes—
878C2—44no—
879C2—44no—
880C2C2×#240611yescharacteristic
881C2#3524211yescharacteristic
882C2#3551311yescharacteristic
883C2#3568812yes—
884C2#3786211yescharacteristic
885C2#3786511yescharacteristic
886C2#3948911yescharacteristic
887C2#3949011yescharacteristic
888C2#4243612yes—
889C2#4492112yes—
890C2#4533312yes—
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
2. C2×#2499C2semidirect
4. C2×#2317C2semidirect
5. #16262C2semidirect
6. #16104C2semidirect
7. #15354C2semidirect
8. #15236C2semidirect
9. #15230C2semidirect
10. #15182C2semidirect
11. #15143C2semidirect
13. #14258C2semidirect
14. #13978C2semidirect
15. #13976C2semidirect
16. #13904C2semidirect
17. #13881C2semidirect
18. #13880C2semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#24992
C2×#24852
C2×#23172
#162622
#161042
#153542
#152362
#152302
#151822
#151432
#147312
#142582
#139782
#139762
#139042
#138812
#138802
#138392