Finite Group Databasebeta

← #874517

Subgroups — #874517

Order 512.

2872 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2499C211yesmaximal, characteristic, complemented
2C2×#2503C211yesmaximal, characteristic, complemented
3C2×#2415C211yesmaximal, characteristic
4C2×#2417C211yesmaximal, characteristic
5#16879C214yesmaximal, complemented
6#15626C214yesmaximal, complemented
7#15300C214yesmaximal
8#15237C211yesmaximal, characteristic, complemented
9#15236C211yesmaximal, characteristic, complemented
10#15236C211yesmaximal, characteristic, complemented
11#15184C211yesmaximal, characteristic, complemented
12#15178C211yesmaximal, characteristic, complemented
13#15178C211yesmaximal, characteristic, complemented
14#14714C211yesmaximal, characteristic, complemented
15#14707C211yesmaximal, characteristic, complemented
16#14381C214yesmaximal, complemented
17#13880C211yesmaximal, characteristic, complemented
18#13879C211yesmaximal, characteristic, complemented
19C4×#390C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28#2503—28no—
29#2499—28no—
30#2417—28no—
31#2415—28no—
32C2×#400C2214yes—
33C2×#398C2212yes—
34C2×#397C2212yes—
35C2×#397C2214yes—
36C2×#396C2212yes—
37C2×#394C2212yes—
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#390C2212yes—
47C2×#389C2212yes—
48C2×#389C2211yescharacteristic
49C2×#389C2211yescharacteristic
50C2×#388C2212yes—
51C2×#387C2214yes—
52C2×#386C2212yes—
53C2×#385C2214yes—
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#381C2214yes—
60C2×#380C2212yes—
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C43C2211yescharacteristic
69#1444C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1443C2214yes—
73#1442C2214yes—
74#1442C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1440C2214yes—
79#1440C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1437C2212yes—
84#1437C2212yes—
85#1436C2214yes—
86#1436C2214yes—
87#1436C2214yes—
88C4⋊#95C2212yes—
89C4⋊#95C2214yes—
90C4⋊#95C2214yes—
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C2×C4⋊Q8—24no—
102C2×C4⋊Q8—42no—
103C2×C4⋊Q8—42no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—42no—
111C2×C22⋊Q8—42no—
112C2×C22⋊Q8—42no—
113C2×C22⋊Q8—42no—
114C2×C22⋊Q8—42no—
115C2×C22⋊Q8—42no—
116C2×C4×D4—42no—
117C2×C4×D4—42no—
118C2×C4×D4D418yes—
119C2×#117—24no—
120C2×#117—24no—
121C2×#117—42no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—42no—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2311yescharacteristic
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⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2312yes—
164#400—216no—
165#398—28no—
166#397—28no—
167#397—216no—
168#396—28no—
169#394—28no—
170#391—24no—
171#391—24no—
172#391—24no—
173#391—24no—
174#391—24no—
175#391—24no—
176#391—42no—
177#391—42no—
178#390—28no—
179#389—28no—
180#389—24no—
181#389—24no—
182#388—28no—
183#387—216no—
184#386—28no—
185#385—216no—
186#384—24no—
187#384—42no—
188#382—24no—
189#382—42no—
190#382D418yescomplemented
191#381—216no—
192#380—24no—
193#380—24no—
194#380—28no—
195C4×C4⋊C4—42no—
196C4×C22⋊C4—24no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—24no—
199C4×C22⋊C4—24no—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C43—42no—
227C25C2411yescharacteristic
228C25C2411yescharacteristic
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—41no—
246C22×D4—41no—
247C22×D4C2×D414yes—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—28no—
262C23×C4—24no—
263C23×C4—42no—
264C23×C4—44no—
265C23×C4C2×D414yes—
266C23×C4C2×D414yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C4⋊Q8—416no—
285C22⋊Q8—416no—
286C22⋊Q8—416no—
287C22⋊Q8—416no—
288C22⋊Q8—416no—
289C4×D4—416no—
290#117—416no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—416no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—41no—
328C2×C4⋊C4—41no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4C2×D414yes—
342C2×C4⋊C4C2×D414yes—
343C2×C4⋊C4C2×D414yes—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—41no—
368C2×C22⋊C4—41no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—41no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4C2×D414yes—
379C2×C22⋊C4C2×D414yes—
380C2×C22⋊C4#4118yes—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—42no—
402C2×C42C2×D414yes—
403C2×C42C2×D414yes—
404C2×C42#4114yes—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—28no—
411#95—28no—
412#95—28no—
413#95—24no—
414#95—24no—
415#95—28no—
416#95—28no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—28no—
423#95—28no—
424#95—28no—
425#95—44no—
426#95—42no—
427#95—44no—
428#95—44no—
429#95—44no—
430#95C2×D4116yes—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24—21no—
438C24—22no—
439C24—22no—
440C24—21no—
441C24—21no—
442C24—22no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24C22×D412yes—
451C24C22×D412yes—
452C24C2×#4114yes—
453C24C2511yescharacteristic
454C2×Q8—44no—
455C2×Q8—44no—
456C2×Q8—44no—
457C2×Q8—44no—
458C2×Q8—44no—
459C2×Q8—44no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—44no—
471C2×D4—48no—
472C2×D4—48no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—28no—
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—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—48no—
564C22×C4—416no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—48no—
574C22×C4—84no—
575C22×C4—88no—
576C22×C4C22×D414yes—
577C22×C4C22×D412yes—
578C22×C4C22×D414yes—
579C22×C4C22×D414yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C2×#4114yes—
586C22×C4C2×#4114yes—
587C22×C4C2×#4114yes—
588C22×C4C2×#4112yes—
589C22×C4H(5,𝔽2)12yes—
590C22×C4H(5,𝔽2)12yes—
591C22×C4H(5,𝔽2)12yes—
592C22×C42−1+414yes—
593C22×C42−1+414yes—
594C22×C42−1+412yes—
595C4⋊C4—28no—
596C4⋊C4—28no—
597C4⋊C4—44no—
598C4⋊C4—48no—
599C4⋊C4—416no—
600C4⋊C4—48no—
601C4⋊C4—48no—
602C4⋊C4—48no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—416no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—48no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—88no—
612C4⋊C4—84no—
613C22⋊C4—216no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—84no—
626C42—28no—
627C42—28no—
628C42—28no—
629C42—48no—
630C42—48no—
631C42—48no—
632C42—44no—
633C42—44no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—24no—
639C23—24no—
640C23—22no—
641C23—22no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—42no—
657C23—42no—
658C23—41no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—41no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23#53214yes—
680C23C23×D411yescharacteristic
681C23C23×D411yescharacteristic
682C23C22×#4112yes—
683C23C22×#4111yescharacteristic
684C23C2×H(5,𝔽2)11yescharacteristic
685C23C2×H(5,𝔽2)11yescharacteristic
686C23C2×H(5,𝔽2)11yescharacteristic
687C23C2×2−1+412yes—
688C23C2×2−1+411yescharacteristic
689C23C2×2−1+412yes—
690C23#58512yes—
691Q8—88no—
692Q8—88no—
693D4—416no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—28no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—416no—
748C2×C4—416no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—44no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—44no—
781C2×C4—44no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—816no—
791C2×C4#53414yes—
792C2×C4#53614yes—
793C2×C4#53714yes—
794C2×C4#53814yes—
795C2×C4D4214yes—
796C2×C4#54714yes—
797C2×C4#55014yes—
798C2×C4#55218yes—
799C2×C4#56214yes—
800C22—24no—
801C22—24no—
802C22—24no—
803C22—42no—
804C22—44no—
805C22—44no—
806C22—44no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—44no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22C2×#53211yescharacteristic
823C22C2×#53411yescharacteristic
824C22C2×#53611yescharacteristic
825C22C2×#53711yescharacteristic
826C22C2×#53811yescharacteristic
827C22C2×D4211yescharacteristic
828C22C2×#54711yescharacteristic
829C22C2×#55011yescharacteristic
830C22D4×#4112yes—
831C22C2×#55212yes—
832C22#349911yescharacteristic
833C22#349912yes—
834C22#350011yescharacteristic
835C22#350712yes—
836C22#350912yes—
837C22#351412yes—
838C22#352012yes—
839C22#352012yes—
840C22C2×#56211yescharacteristic
841C22#354112yes—
842C22#354712yes—
843C22#355212yes—
844C22#355512yes—
845C4—24no—
846C4—28no—
847C4—42no—
848C4—44no—
849C4—44no—
850C4—44no—
851C4—42no—
852C4—42no—
853C4—44no—
854C4—82no—
855C4—82no—
856C4—82no—
857C4—82no—
858C4—82no—
859C4—82no—
860C4—82no—
861C4#268218yes—
862C2—44no—
863C2—82no—
864C2#3508511yescharacteristic
865C2#3612411yescharacteristic
866C2#3618111yescharacteristic
867C2#3738811yescharacteristic
868C2#3897412yes—
869C2#3936011yescharacteristic
870C2#3949011yescharacteristic
871C2#3995912yes—
872C2#4605512yes—
873C2C2×#268211yescharacteristic
874C2#5944412yes—
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×#2499C2semidirect
2. C2×#2503C2semidirect
5. #16879C2semidirect
6. #15626C2semidirect
8. #15237C2semidirect
9. #15236C2semidirect
10. #15236C2semidirect
11. #15184C2semidirect
12. #15178C2semidirect
13. #15178C2semidirect
14. #14714C2semidirect
15. #14707C2semidirect
16. #14381C2semidirect
17. #13880C2semidirect
18. #13879C2semidirect
190. #382D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24992
C2×#25032
C2×#24152
C2×#24172
#168792
#156262
#153002
#152372
#152362
#151842
#151782
#147142
#147072
#143812
#138802
#138792
C4×#3902