Finite Group Databasebeta

← #649069

Subgroups — #649069

Order 512.

3630 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2502C211yesmaximal, characteristic, complemented
2C2×#2417C211yesmaximal, characteristic
3C2×D4×C4⋊C4C211yesmaximal, characteristic
4C22×#384C211yesmaximal, characteristic, complemented
5#15766C214yesmaximal, complemented
6#15392C214yesmaximal, complemented
7#15199C211yesmaximal, characteristic, complemented
8#15195C211yesmaximal, characteristic, complemented
9#15182C211yesmaximal, characteristic, complemented
10#15145C211yesmaximal, characteristic, complemented
11#14728C214yesmaximal, complemented
12#14702C211yesmaximal, characteristic, complemented
13#14139C211yesmaximal, characteristic, complemented
14#14048C211yesmaximal, characteristic, complemented
15#14015C214yesmaximal
16#14000C211yesmaximal, characteristic, complemented
17#13880C211yesmaximal, characteristic, complemented
18#13880C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2214yes—
28C23×C42C2211yescharacteristic
29#2502—28no—
30#2417—28no—
31C2×#398C2212yes—
32C2×#398C2214yes—
33C2×#398C2214yes—
34C2×#396C2212yes—
35D4×C4⋊C4—28no—
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#389C2212yes—
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#385C2212yes—
46C2×#385C2214yes—
47C2×#385C2212yes—
48C2×#385C2214yes—
49C2×#385C2214yes—
50C2×#384—28no—
51C2×#384C2214yes—
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#384C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2212yes—
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67#1444C2214yes—
68#1444C2214yes—
69#1444C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1442C2214yes—
73#1442C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1437C2212yes—
80#1436C2214yes—
81#1436C2212yes—
82#1436C2214yes—
83#1436C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C22⋊#95C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2312yes—
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—42no—
109C2×C4×D4—24no—
110C2×C4×D4—24no—
111C2×C4×D4—28no—
112C2×C4×D4—48no—
113C2×C4×D4D418yes—
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—24no—
117C22×C4⋊C4—24no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—216no—
121C22×C4⋊C4—42no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4—42no—
124C22×C4⋊C4—48no—
125C22×C4⋊C4—48no—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2314yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2314yes—
147C22×C4⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C42—24no—
159C22×C42—24no—
160C22×C42—24no—
161C22×C42C2312yes—
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2312yes—
168#398—28no—
169#398—216no—
170#398—48no—
171#396—28no—
172#391—24no—
173#391—24no—
174#391—24no—
175#391—24no—
176#391—42no—
177#389—28no—
178#389—24no—
179#386—28no—
180#386Q8116yescomplemented
181#385—216no—
182#385—28no—
183#385—28no—
184#385—48no—
185#385—48no—
186#384—24no—
187#384—24no—
188#384—24no—
189#384—216no—
190#384—24no—
191#384—24no—
192#384—42no—
193#384D418yescomplemented
194#380—24no—
195#380—24no—
196#380—24no—
197#380—28no—
198C4×C4⋊C4—24no—
199C4×C22⋊C4—24no—
200C4×C22⋊C4—24no—
201C4×C22⋊C4—24no—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C25C2411yescharacteristic
227C25C2411yescharacteristic
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—24no—
238C22×D4C2×D414yes—
239C22×D4C2×Q818yes—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—24no—
245C23×C4—22no—
246C23×C4—24no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—28no—
260C23×C4—28no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—44no—
265C23×C4—42no—
266C23×C4—44no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4C2×D414yes—
272C23×C4C2×D414yes—
273C23×C4C2×Q818yes—
274C23×C4#4114yes—
275C23×C4#4114yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C22⋊Q8—416no—
294C22⋊Q8—416no—
295C4×D4—232no—
296C4×D4—432no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—416no—
339C2×C4⋊C4—416no—
340C2×C4⋊C4—416no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—44no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—464no—
353C2×C4⋊C4—44no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—44no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4C2×D414yes—
361C2×C4⋊C4C2×D414yes—
362C2×C4⋊C4C2×D414yes—
363C2×C4⋊C4C2×D4116yes—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4C2×D414yes—
387C2×C22⋊C4C2×D414yes—
388C2×C22⋊C4C2×Q818yes—
389C2×C22⋊C4C2×Q818yes—
390C2×C22⋊C4C2×Q818yes—
391C2×C42—232no—
392C2×C42—24no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—24no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—44no—
409C2×C42C2×D414yes—
410C2×C42C2×D414yes—
411C2×C42#4114yes—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—28no—
419#95—28no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—28no—
425#95—28no—
426#95—24no—
427#95—24no—
428#95—28no—
429#95—44no—
430#95—44no—
431#95—44no—
432#95—44no—
433#95—44no—
434#95C2×Q818yes—
435#95C2×Q818yes—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—22no—
440C24—21no—
441C24—22no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—21no—
451C24C22×D412yes—
452C24C22×D412yes—
453C24C22×Q814yes—
454C24C22×Q814yes—
455C24C2×#4112yes—
456C24C2×#4112yes—
457C24H(5,𝔽2)14yes—
458C24C2511yescharacteristic
459C2×Q8—44no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—216no—
469C2×D4—216no—
470C2×D4C4⋊Q8116yes—
471C22×C4—216no—
472C22×C4—216no—
473C22×C4—216no—
474C22×C4—216no—
475C22×C4—216no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—216no—
497C22×C4—28no—
498C22×C4—216no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
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—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—416no—
568C22×C4—416no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—88no—
577C22×C4—84no—
578C22×C4—84no—
579C22×C4—84no—
580C22×C4—88no—
581C22×C4—88no—
582C22×C4—88no—
583C22×C4#123116yes—
584C22×C4C22×D412yes—
585C22×C4C22×D412yes—
586C22×C4C22×D414yes—
587C22×C4C22×D414yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D414yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×Q814yes—
594C22×C4C22×Q814yes—
595C22×C4C22×Q814yes—
596C22×C4C22×Q814yes—
597C22×C4C22×Q814yes—
598C22×C4C2×#4112yes—
599C22×C4C2×#4112yes—
600C22×C4C2×#4114yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4H(5,𝔽2)14yes—
605C22×C4H(5,𝔽2)12yes—
606C22×C42−1+414yes—
607C22×C42−1+412yes—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—28no—
611C4⋊C4—416no—
612C4⋊C4—48no—
613C4⋊C4—48no—
614C4⋊C4—416no—
615C4⋊C4—416no—
616C4⋊C4—48no—
617C4⋊C4—48no—
618C4⋊C4—416no—
619C4⋊C4—48no—
620C4⋊C4—44no—
621C4⋊C4—48no—
622C4⋊C4—44no—
623C4⋊C4—44no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C4⋊C4—88no—
627C4⋊C4—84no—
628C4⋊C4—84no—
629C4⋊C4—88no—
630C22⋊C4—28no—
631C22⋊C4—216no—
632C22⋊C4—28no—
633C22⋊C4—216no—
634C22⋊C4—216no—
635C22⋊C4—48no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—84no—
640C42—216no—
641C42—28no—
642C42—28no—
643C42—28no—
644C42—48no—
645C42—44no—
646C42—44no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
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—
687C23C2×#12314yes—
688C23C2×C4⋊Q814yes—
689C23C2×C4⋊Q814yes—
690C23#53514yes—
691C23#55418yes—
692C23#55418yes—
693C23C23×D411yescharacteristic
694C23C23×D411yescharacteristic
695C23C23×Q812yes—
696C23C22×#4111yescharacteristic
697C23C22×#4111yescharacteristic
698C23C22×#4111yescharacteristic
699C23C2×H(5,𝔽2)12yes—
700C23C2×H(5,𝔽2)11yescharacteristic
701C23C2×H(5,𝔽2)12yes—
702C23C2×2−1+411yescharacteristic
703C23C2×2−1+412yes—
704Q8—88no—
705D4—232no—
706C2×C4—264no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—232no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—28no—
741C2×C4—28no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—41no—
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—44no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—416no—
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—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—816no—
800C2×C4—816no—
801C2×C4—816no—
802C2×C4C2×#12314yes—
803C2×C4C2×#12314yes—
804C2×C4#52514yes—
805C2×C4C2×C4⋊Q814yes—
806C2×C4#53914yes—
807C2×C4D4214yes—
808C2×C4#54714yes—
809C2×C4#54814yes—
810C2×C4D4×Q818yes—
811C2×C4#55314yes—
812C2×C4#55418yes—
813C22—28no—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—28no—
819C22—28no—
820C22—28no—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—24no—
825C22—24no—
826C22—44no—
827C22—42no—
828C22—42no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22—42no—
833C22—42no—
834C22#250218yescomplemented
835C22C22×#12311yescharacteristic
836C22C2×#52511yescharacteristic
837C22C22×C4⋊Q811yescharacteristic
838C22C2×#53511yescharacteristic
839C22C2×#53911yescharacteristic
840C22C2×D4211yescharacteristic
841C22C2×#54711yescharacteristic
842C22C2×#54811yescharacteristic
843C22C2×D4×Q812yes—
844C22C2×#55311yescharacteristic
845C22C2×#55412yes—
846C22C2×#55412yes—
847C22C2×#55412yes—
848C22#348412yes—
849C22#349212yes—
850C22#349212yes—
851C22#349811yescharacteristic
852C22#349911yescharacteristic
853C22#350312yes—
854C22#350312yes—
855C22#351112yes—
856C22#354312yes—
857C22#354412yes—
858C4—24no—
859C4—28no—
860C4—28no—
861C4—24no—
862C4—44no—
863C4—44no—
864C4—44no—
865C4—42no—
866C4—44no—
867C4—42no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4—82no—
873C4—82no—
874C4#244318yes—
875C2—28no—
876C2—44no—
877C2C2×#244311yescharacteristic
878C2C2×#250211yescharacteristic
879C2#3553011yescharacteristic
880C2D4×C4⋊Q811yescharacteristic
881C2#3618011yescharacteristic
882C2#3654612yes—
883C2#3767411yescharacteristic
884C2#3786311yescharacteristic
885C2#3960412yes—
886C2#5913612yes—
887C2#5930512yes—
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×#2502C2semidirect
4. C22×#384C2semidirect
5. #15766C2semidirect
6. #15392C2semidirect
7. #15199C2semidirect
8. #15195C2semidirect
9. #15182C2semidirect
10. #15145C2semidirect
11. #14728C2semidirect
12. #14702C2semidirect
13. #14139C2semidirect
14. #14048C2semidirect
16. #14000C2semidirect
17. #13880C2semidirect
18. #13880C2semidirect
180. #386Q8semidirect
193. #384D4semidirect
834. C22#2502semidirect

Maximal subgroups

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

subgroupindex
C2×#25022
C2×#24172
C2×D4×C4⋊C42
C22×#3842
#157662
#153922
#151992
#151952
#151822
#151452
#147282
#147022
#141392
#140482
#140152
#140002
#138802
C4×#3862