Finite Group Databasebeta

← #649148

Subgroups — #649148

Order 512.

3798 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2502C211yesmaximal, characteristic, complemented
2C2×#2409C211yesmaximal, characteristic
3C2×D4×C4⋊C4C211yesmaximal, characteristic
4C22×#391C211yesmaximal, characteristic, complemented
5#15698C214yesmaximal, complemented
6#15378C214yesmaximal, complemented
7#15199C211yesmaximal, characteristic, complemented
8#15185C211yesmaximal, characteristic, complemented
9#15182C211yesmaximal, characteristic, complemented
10#15182C211yesmaximal, characteristic, complemented
11#14736C214yesmaximal, complemented
12#14686C211yesmaximal, characteristic, complemented
13#14139C211yesmaximal, characteristic, complemented
14#14000C211yesmaximal, characteristic, complemented
15#14000C211yesmaximal, characteristic, complemented
16#13975C214yesmaximal
17#13922C211yesmaximal, characteristic, complemented
18#13880C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2212yes—
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C42C2211yescharacteristic
28#2502—28no—
29#2409—28no—
30C2×#398C2214yes—
31C2×#395C2212yes—
32C2×#393C2212yes—
33D4×C4⋊C4—28no—
34C2×#391—28no—
35C2×#391C2214yes—
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#389C2212yes—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#385C2212yes—
50C2×#385C2214yes—
51C2×#385C2212yes—
52C2×#385C2212yes—
53C2×#385C2214yes—
54C2×#384C2211yescharacteristic
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#384C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2214yes—
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C22×#95C2214yes—
68#1446C2214yes—
69#1445C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1442C2214yes—
74#1442C2214yes—
75#1442C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1437C2212yes—
82#1436C2212yes—
83#1436C2214yes—
84#1436C2214yes—
85C4⋊#95C2214yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C22⋊#95C2214yes—
91C22⋊#95C2214yes—
92C22⋊#95C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8—24no—
96C23×Q8—24no—
97C23×Q8—24no—
98C23×Q8—24no—
99C23×Q8—24no—
100C23×Q8—42no—
101C23×Q8—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×Q8C2312yes—
105C23×D4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2312yes—
108C24×C4C2312yes—
109C24×C4C2312yes—
110C24×C4C2311yescharacteristic
111C24×C4C2312yes—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—42no—
117C2×C22⋊Q8—42no—
118C2×C4×D4—24no—
119C2×C4×D4—24no—
120C2×C4×D4—28no—
121C2×C4×D4—48no—
122C2×C4×D4D418yes—
123C22×C4⋊C4—24no—
124C22×C4⋊C4—24no—
125C22×C4⋊C4—24no—
126C22×C4⋊C4—24no—
127C22×C4⋊C4—42no—
128C22×C4⋊C4—42no—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C42—24no—
157C22×C42—24no—
158C22×C42—42no—
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2312yes—
166#398—216no—
167#395—28no—
168#393—28no—
169#391—24no—
170#391—24no—
171#391—24no—
172#391—24no—
173#391—24no—
174#391—24no—
175#391—24no—
176#391—216no—
177#391—42no—
178#391—42no—
179#391D418yescomplemented
180#389—28no—
181#386—28no—
182#386Q8116yescomplemented
183#385—28no—
184#385—28no—
185#385—28no—
186#385—216no—
187#385—48no—
188#384—24no—
189#384—24no—
190#384—24no—
191#384—42no—
192#384—42no—
193#380—24no—
194#380—24no—
195#380—24no—
196#380—48no—
197C4×C4⋊C4—24no—
198C4×C22⋊C4—24no—
199C4×C22⋊C4—24no—
200C4×C22⋊C4—42no—
201C2×#95—216no—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C25C2411yescharacteristic
230C25C2411yescharacteristic
231C22×Q8—232no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—24no—
235C22×Q8—22no—
236C22×Q8—24no—
237C22×Q8—24no—
238C22×Q8—24no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—24no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—42no—
250C22×Q8—42no—
251C22×Q8—416no—
252C22×Q8—416no—
253C22×Q8—416no—
254C22×Q8—416no—
255C22×Q8—416no—
256C22×Q8—416no—
257C22×Q8C2×D414yes—
258C22×Q8#4114yes—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—24no—
262C22×D4C2×D414yes—
263C22×D4C2×Q818yes—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—24no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—22no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—24no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—28no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—44no—
295C23×C4—44no—
296C23×C4—44no—
297C23×C4C2×D414yes—
298C23×C4C2×D414yes—
299C23×C4C2×Q818yes—
300C23×C4#4114yes—
301C23×C4#4114yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2411yescharacteristic
316C23×C4C2412yes—
317C23×C4C2411yescharacteristic
318C23×C4C2411yescharacteristic
319C22⋊Q8—416no—
320C22⋊Q8—416no—
321C4×D4—232no—
322C4×D4—432no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—416no—
356C2×C4⋊C4—416no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4C2×D414yes—
373C2×C4⋊C4C2×D414yes—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
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—28no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4C2×D414yes—
397C2×C22⋊C4C2×D414yes—
398C2×C22⋊C4C2×Q818yes—
399C2×C22⋊C4C2×Q818yescomplemented
400C2×C22⋊C4C2×Q818yescomplemented
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—24no—
406C2×C42—22no—
407C2×C42—24no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—24no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—416no—
418C2×C42—44no—
419C2×C42—42no—
420C2×C42C2×D414yes—
421C2×C42C2×D414yes—
422#95—28no—
423#95—28no—
424#95—28no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—28no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—28no—
437#95—24no—
438#95—42no—
439#95—42no—
440#95—44no—
441#95—44no—
442#95—44no—
443#95—44no—
444#95—44no—
445#95—44no—
446#95C2×D4116yes—
447#95C2×Q818yescomplemented
448#95C2×Q818yescomplemented
449C24—21no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—22no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24C22×D412yes—
465C24C22×D412yes—
466C24C22×Q814yes—
467C24C22×Q814yes—
468C24C2×#4112yes—
469C24C2×#4112yes—
470C24H(5,𝔽2)14yes—
471C24C2511yescharacteristic
472C2×Q8—216no—
473C2×Q8—28no—
474C2×Q8—28no—
475C2×Q8—28no—
476C2×Q8—28no—
477C2×Q8—28no—
478C2×Q8—28no—
479C2×Q8—48no—
480C2×Q8—48no—
481C2×Q8—48no—
482C2×Q8—48no—
483C2×Q8—48no—
484C2×Q8—4128no—
485C2×Q8—48no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×D4—28no—
495C2×D4—28no—
496C2×D4—216no—
497C2×D4—216no—
498C2×D4C4⋊Q8116yes—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—28no—
513C22×C4—28no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—216no—
517C22×C4—216no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
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—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—21no—
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—24no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—216no—
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—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—416no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—44no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—88no—
612C22×C4—84no—
613C22×C4—84no—
614C22×C4—88no—
615C22×C4—88no—
616C22×C4#123116yes—
617C22×C4C22×D412yes—
618C22×C4C22×D414yes—
619C22×C4C22×D414yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D414yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×Q814yes—
627C22×C4C22×Q814yes—
628C22×C4C22×Q814yes—
629C22×C4C22×Q814yes—
630C22×C4C22×Q814yes—
631C22×C4C2×#4114yes—
632C22×C4C2×#4112yes—
633C22×C4C2×#4112yes—
634C22×C4C2×#4112yes—
635C22×C4C2×#4112yes—
636C22×C4C2×#4112yes—
637C22×C4H(5,𝔽2)12yes—
638C22×C4H(5,𝔽2)12yes—
639C22×C42−1+414yes—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—48no—
643C4⋊C4—48no—
644C4⋊C4—48no—
645C4⋊C4—48no—
646C4⋊C4—48no—
647C4⋊C4—44no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—44no—
652C4⋊C4—88no—
653C4⋊C4—88no—
654C4⋊C4—88no—
655C4⋊C4—84no—
656C4⋊C4—88no—
657C22⋊C4—28no—
658C22⋊C4—216no—
659C22⋊C4—28no—
660C22⋊C4—216no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C42—28no—
668C42—28no—
669C42—48no—
670C42—48no—
671C42—44no—
672C42—44no—
673C42—44no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—24no—
680C23—22no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—22no—
701C23—22no—
702C23—24no—
703C23—24no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23C2×#12314yes—
715C23C2×C4⋊Q814yes—
716C23C2×C4⋊Q814yes—
717C23#53514yes—
718C23#55418yes—
719C23#55418yes—
720C23C23×D411yescharacteristic
721C23C23×D411yescharacteristic
722C23C23×Q812yes—
723C23C22×#4111yescharacteristic
724C23C22×#4111yescharacteristic
725C23C22×#4111yescharacteristic
726C23C2×H(5,𝔽2)12yes—
727C23C2×H(5,𝔽2)11yescharacteristic
728C23C2×H(5,𝔽2)11yescharacteristic
729C23C2×2−1+412yes—
730C23#58512yes—
731Q8—432no—
732Q8—416no—
733Q8—416no—
734D4—232no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—232no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—28no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—432no—
776C2×C4—432no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—41no—
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—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—416no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—816no—
833C2×C4—816no—
834C2×C4C2×#12314yes—
835C2×C4C2×#12314yes—
836C2×C4#52514yes—
837C2×C4C2×C4⋊Q814yes—
838C2×C4#53814yes—
839C2×C4D4214yes—
840C2×C4#54614yes—
841C2×C4#54614yes—
842C2×C4D4×Q818yes—
843C2×C4#55114yes—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—28no—
849C22—28no—
850C22—24no—
851C22—24no—
852C22—28no—
853C22—28no—
854C22—24no—
855C22—24no—
856C22—24no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—44no—
861C22—44no—
862C22—42no—
863C22—44no—
864C22—44no—
865C22#250218yescomplemented
866C22C22×#12311yescharacteristic
867C22C2×#52511yescharacteristic
868C22C22×C4⋊Q811yescharacteristic
869C22C2×#53511yescharacteristic
870C22C2×#53811yescharacteristic
871C22C2×D4211yescharacteristic
872C22C2×#54611yescharacteristic
873C22C2×#54611yescharacteristic
874C22C2×D4×Q812yes—
875C22C2×#55111yescharacteristic
876C22C2×#55412yes—
877C22C2×#55412yes—
878C22Q8×#4112yes—
879C22#348812yes—
880C22#349512yes—
881C22#349911yescharacteristic
882C22#350011yescharacteristic
883C22#350112yes—
884C22#350312yes—
885C22#350712yes—
886C22#352212yes—
887C22#353612yes—
888C22#355812yes—
889C4—24no—
890C4—28no—
891C4—24no—
892C4—42no—
893C4—44no—
894C4—42no—
895C4—44no—
896C4—44no—
897C4—44no—
898C4—44no—
899C4—44no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4—82no—
904C4—82no—
905C4#241818yes—
906C2—28no—
907C2—44no—
908C2C2×#241811yescharacteristic
909C2C2×#250211yescharacteristic
910C2#3561911yescharacteristic
911C2D4×C4⋊Q811yescharacteristic
912C2#3627611yescharacteristic
913C2#3654412yes—
914C2#3767711yescharacteristic
915C2#3807911yescharacteristic
916C2#3963212yes—
917C2#5901612yes—
918C2#5927412yes—
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×#391C2semidirect
5. #15698C2semidirect
6. #15378C2semidirect
7. #15199C2semidirect
8. #15185C2semidirect
9. #15182C2semidirect
10. #15182C2semidirect
11. #14736C2semidirect
12. #14686C2semidirect
13. #14139C2semidirect
14. #14000C2semidirect
15. #14000C2semidirect
17. #13922C2semidirect
18. #13880C2semidirect
179. #391D4semidirect
182. #386Q8semidirect
399. C2×C22⋊C4C2×Q8semidirect
400. C2×C22⋊C4C2×Q8semidirect
447. #95C2×Q8semidirect
448. #95C2×Q8semidirect
865. 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×#24092
C2×D4×C4⋊C42
C22×#3912
#156982
#153782
#151992
#151852
#151822
#147362
#146862
#141392
#140002
#139752
#139222
#138802
C4×#3862