Finite Group Databasebeta

← #874592

Subgroups — #874592

Order 512.

3788 conjugacy classes of subgroups.

The subgroup lattice has 983 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2501C211yesmaximal, characteristic, complemented
2C2×#2432C211yesmaximal, characteristic, complemented
3C2×#2407C211yesmaximal, characteristic
4C2×#2417C211yesmaximal, characteristic, complemented
5#16467C214yesmaximal, complemented
6#15611C214yesmaximal, complemented
7#15545C214yesmaximal, complemented
8#15217C211yesmaximal, characteristic, complemented
9#15215C211yesmaximal, characteristic, complemented
10#15184C211yesmaximal, characteristic, complemented
11#15182C211yesmaximal, characteristic, complemented
12#15178C211yesmaximal, characteristic, complemented
13#15150C211yesmaximal, characteristic, complemented
14#14714C211yesmaximal, characteristic, complemented
15#14700C211yesmaximal, characteristic, complemented
16#14359C214yesmaximal, complemented
17#14139C211yesmaximal, characteristic, complemented
18#13937C211yesmaximal, characteristic, complemented
19C4×#390C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×#124C2211yescharacteristic
23C22×#123C2214yes—
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30#2501—28no—
31#2432—28no—
32#2417—28no—
33#2407—28no—
34C2×#399C2214yes—
35C2×#398C2212yes—
36C2×#397C2214yes—
37C2×#396C2212yes—
38C2×#394C2212yes—
39C2×#394C2214yes—
40C2×#392C2212yes—
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#390C2212yes—
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#388C2214yes—
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#385C2214yes—
58C2×#385C2212yes—
59C2×#384C2211yescharacteristic
60C2×#384C2211yescharacteristic
61C2×#380C2212yes—
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2211yescharacteristic
69C2×C43C2211yescharacteristic
70#1445C2214yes—
71#1444C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1440C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1438C2214yes—
82#1438C2214yes—
83#1437C2212yes—
84#1437C2212yes—
85#1437C2214yes—
86C4⋊#95C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2214yes—
92C4⋊#95C2212yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C22×#41—24no—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—42no—
99C22×#41—42no—
100C22×#41—42no—
101C22×#41—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×D4C2311yescharacteristic
105C23×D4C2312yes—
106C23×D4C2311yescharacteristic
107C23×D4C2312yes—
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C24×C4C2312yes—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—42no—
115C2×#124—24no—
116C2×#124—42no—
117C2×#124—42no—
118C2×#123—216no—
119C2×#123—216no—
120C2×#123—48no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8—42no—
127C2×C22⋊Q8—42no—
128C2×C22⋊Q8—42no—
129C2×C22⋊Q8—42no—
130C2×#121—24no—
131C2×#121—24no—
132C2×#121—42no—
133C2×C4×D4—42no—
134C2×C4×D4—42no—
135C2×C4×D4D418yes—
136C22×C4⋊C4—24no—
137C22×C4⋊C4—24no—
138C22×C4⋊C4—42no—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2314yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2311yescharacteristic
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2314yes—
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2312yes—
176C22×C42C2312yes—
177C22×C42C2311yescharacteristic
178C22×C42C2311yescharacteristic
179#399—216no—
180#398—28no—
181#397—48no—
182#396—28no—
183#394—28no—
184#394—216no—
185#392—28no—
186#391—24no—
187#391—24no—
188#391—24no—
189#391—42no—
190#391—42no—
191#391—42no—
192#391—42no—
193#390—24no—
194#390—28no—
195#390—24no—
196#390—42no—
197#390D418yescomplemented
198#389—24no—
199#388—48no—
200#386—28no—
201#386—28no—
202#385—28no—
203#385—216no—
204#384—24no—
205#384—24no—
206#380—24no—
207#380—24no—
208#380—28no—
209C4×C4⋊C4—42no—
210C4×C22⋊C4—24no—
211C4×C22⋊C4—24no—
212C4×C22⋊C4—42no—
213C4×C22⋊C4—42no—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2312yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2312yes—
233C2×#95C2312yes—
234C2×#95C2314yes—
235C43—42no—
236C25C2411yescharacteristic
237C25C2412yes—
238C25C2411yescharacteristic
239C2×#41—416no—
240C2×#41—416no—
241C2×#41—416no—
242C2×#41—416no—
243C2×#41—416no—
244C2×#41—416no—
245C2×#41—416no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
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#4114yes—
260C22×D4—24no—
261C22×D4—24no—
262C22×D4—24no—
263C22×D4—24no—
264C22×D4—24no—
265C22×D4—28no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—24no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—24no—
274C22×D4—41no—
275C22×D4—41no—
276C22×D4—42no—
277C22×D4—42no—
278C22×D4—42no—
279C22×D4—42no—
280C22×D4—42no—
281C22×D4—44no—
282C22×D4C2×D414yes—
283C22×D4C2×D414yes—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—28no—
299C23×C4—24no—
300C23×C4—24no—
301C23×C4—24no—
302C23×C4—42no—
303C23×C4—42no—
304C23×C4—42no—
305C23×C4—42no—
306C23×C4—42no—
307C23×C4—44no—
308C23×C4C2×D414yes—
309C23×C4C2×D414yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C23×C4C2412yes—
319C23×C4C2411yescharacteristic
320C23×C4C2412yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2411yescharacteristic
325C23×C4C2411yescharacteristic
326C4⋊Q8—416no—
327#124—416no—
328#123—464no—
329C22⋊Q8—416no—
330C22⋊Q8—416no—
331C22⋊Q8—416no—
332#121—416no—
333C4×D4—416no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—416no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—41no—
368C2×C4⋊C4—41no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4C2×D414yes—
378C2×C4⋊C4C2×D414yes—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—28no—
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—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—41no—
407C2×C22⋊C4—41no—
408C2×C22⋊C4—41no—
409C2×C22⋊C4—41no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—44no—
416C2×C22⋊C4—44no—
417C2×C22⋊C4—44no—
418C2×C22⋊C4—42no—
419C2×C22⋊C4—42no—
420C2×C22⋊C4—44no—
421C2×C22⋊C4—44no—
422C2×C22⋊C4—44no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—44no—
425C2×C22⋊C4C2×D4116yes—
426C2×C22⋊C4C2×D414yes—
427C2×C22⋊C4C2×D414yes—
428C2×C22⋊C4#4118yescomplemented
429C2×C42—22no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—24no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—24no—
443C2×C42—22no—
444C2×C42—24no—
445C2×C42—24no—
446C2×C42—42no—
447C2×C42—42no—
448C2×C42C2×D414yes—
449C2×C42C2×D414yes—
450#95—24no—
451#95—24no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—28no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95—28no—
461#95—42no—
462#95—42no—
463#95—42no—
464#95—44no—
465#95—44no—
466#95—44no—
467#95—44no—
468#95—44no—
469#95—44no—
470#95—44no—
471C24—21no—
472C24—21no—
473C24—22no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—22no—
479C24—22no—
480C24—21no—
481C24—22no—
482C24—22no—
483C24—24no—
484C24—21no—
485C24—22no—
486C24—22no—
487C24—24no—
488C24—21no—
489C24—21no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—22no—
496C24—24no—
497C24—22no—
498C24—24no—
499C24—22no—
500C24C22×D412yes—
501C24C22×D414yes—
502C24C22×D412yes—
503C24C2×#4114yes—
504C24C2511yescharacteristic
505#41—4128no—
506C2×Q8—28no—
507C2×Q8—28no—
508C2×Q8—28no—
509C2×Q8—44no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×D4—28no—
521C2×D4—28no—
522C2×D4—28no—
523C2×D4—28no—
524C2×D4—28no—
525C2×D4—44no—
526C2×D4—48no—
527C2×D4—48no—
528C2×D4—48no—
529C2×D4—48no—
530C2×D4—48no—
531C2×D4—48no—
532C2×D4—48no—
533C2×D4—48no—
534C2×D4—48no—
535C2×D4—48no—
536C2×D4—416no—
537C2×D4—48no—
538C2×D4—44no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—84no—
543C2×D4—88no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—24no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—28no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—22no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—24no—
626C22×C4—22no—
627C22×C4—24no—
628C22×C4—22no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—416no—
636C22×C4—48no—
637C22×C4—48no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—44no—
644C22×C4—44no—
645C22×C4—44no—
646C22×C4—48no—
647C22×C4—84no—
648C22×C4—88no—
649C22×C4C22×D412yes—
650C22×C4C22×D412yes—
651C22×C4C22×D414yes—
652C22×C4C22×D412yes—
653C22×C4C22×D412yes—
654C22×C4C22×D414yes—
655C22×C4C22×D412yes—
656C22×C4C22×D412yes—
657C22×C4C2×#4114yes—
658C22×C4C2×#4114yes—
659C22×C4C2×#4114yes—
660C22×C4C2×#4112yes—
661C22×C4H(5,𝔽2)14yes—
662C22×C4H(5,𝔽2)12yes—
663C22×C4H(5,𝔽2)12yes—
664C22×C4H(5,𝔽2)12yes—
665C22×C4H(5,𝔽2)12yes—
666C22×C42−1+414yes—
667C22×C42−1+414yes—
668C4⋊C4—28no—
669C4⋊C4—44no—
670C4⋊C4—48no—
671C4⋊C4—48no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—416no—
675C4⋊C4—416no—
676C4⋊C4—48no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—416no—
682C4⋊C4—84no—
683C22⋊C4—232no—
684C22⋊C4—216no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—48no—
688C22⋊C4—48no—
689C22⋊C4—48no—
690C22⋊C4—48no—
691C22⋊C4—48no—
692C22⋊C4—416no—
693C22⋊C4—48no—
694C22⋊C4—416no—
695C22⋊C4—48no—
696C22⋊C4—48no—
697C22⋊C4—84no—
698C22⋊C4—88no—
699C22⋊C4—84no—
700C22⋊C4—84no—
701C42—28no—
702C42—28no—
703C42—48no—
704C42—48no—
705C42—44no—
706C42—44no—
707C42—44no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—24no—
712C23—22no—
713C23—24no—
714C23—22no—
715C23—22no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—22no—
721C23—22no—
722C23—24no—
723C23—22no—
724C23—22no—
725C23—24no—
726C23—28no—
727C23—22no—
728C23—24no—
729C23—22no—
730C23—28no—
731C23—22no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—41no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—41no—
745C23—42no—
746C23—42no—
747C23—41no—
748C23—42no—
749C23—41no—
750C23—42no—
751C23—44no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—44no—
757C23—42no—
758C23—42no—
759C23—42no—
760C23—42no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—42no—
766C23—42no—
767C23—41no—
768C23—44no—
769C23—42no—
770C23—44no—
771C23—44no—
772C23—42no—
773C23—42no—
774C23—42no—
775C23—44no—
776C23#53214yes—
777C23C23×D411yescharacteristic
778C23C23×D411yescharacteristic
779C23C22×#4112yes—
780C23C22×#4111yescharacteristic
781C23C2×H(5,𝔽2)11yescharacteristic
782C23C2×H(5,𝔽2)11yescharacteristic
783C23C2×H(5,𝔽2)11yescharacteristic
784C23C2×H(5,𝔽2)11yescharacteristic
785C23C2×H(5,𝔽2)12yes—
786C23C2×2−1+412yes—
787C23C2×2−1+412yes—
788Q8—416no—
789Q8—88no—
790D4—416no—
791D4—432no—
792D4—416no—
793D4—816no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—28no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—432no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—44no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—416no—
851C2×C4—416no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—44no—
865C2×C4—42no—
866C2×C4—44no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—44no—
880C2×C4—42no—
881C2×C4—44no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—816no—
887C2×C4#53414yes—
888C2×C4#53514yes—
889C2×C4#53614yes—
890C2×C4#53814yes—
891C2×C4D4214yes—
892C2×C4#54618yes—
893C2×C4#54614yes—
894C2×C4#54614yes—
895C2×C4#56014yes—
896C22—24no—
897C22—24no—
898C22—24no—
899C22—44no—
900C22—44no—
901C22—44no—
902C22—42no—
903C22—44no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—48no—
909C22—42no—
910C22—44no—
911C22—42no—
912C22—48no—
913C22—42no—
914C22—44no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—44no—
919C22—82no—
920C22—82no—
921C22—84no—
922C22—82no—
923C22—82no—
924C22—82no—
925C22—82no—
926C22—84no—
927C22—82no—
928C22—82no—
929C22C2×#53211yescharacteristic
930C22C2×#53411yescharacteristic
931C22C2×#53511yescharacteristic
932C22C2×#53611yescharacteristic
933C22C2×#53811yescharacteristic
934C22C2×D4211yescharacteristic
935C22C2×#54611yescharacteristic
936C22C2×#54612yes—
937C22C2×#54611yescharacteristic
938C22#348212yes—
939C22#349811yescharacteristic
940C22#349912yes—
941C22#349911yescharacteristic
942C22#350812yes—
943C22#352012yes—
944C22#352012yes—
945C22#352012yes—
946C22#352212yes—
947C22C2×#56011yescharacteristic
948C22#353612yes—
949C22#354812yes—
950C22#354812yes—
951C22#355212yes—
952C4—24no—
953C4—28no—
954C4—44no—
955C4—44no—
956C4—44no—
957C4—42no—
958C4—42no—
959C4—44no—
960C4—42no—
961C4—82no—
962C4—82no—
963C4—82no—
964C4—82no—
965C4—82no—
966C4—82no—
967C4#267818yes—
968C2—44no—
969C2—82no—
970C2—84no—
971C2#3508511yescharacteristic
972C2#3612111yescharacteristic
973C2#3637611yescharacteristic
974C2#3729611yescharacteristic
975C2#3895112yes—
976C2#3895211yescharacteristic
977C2#3936011yescharacteristic
978C2#4021412yes—
979C2#4563212yes—
980C2C2×#267811yescharacteristic
981C2#5940912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2407C2
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×#2501C2semidirect
2. C2×#2432C2semidirect
4. C2×#2417C2semidirect
5. #16467C2semidirect
6. #15611C2semidirect
7. #15545C2semidirect
8. #15217C2semidirect
9. #15215C2semidirect
10. #15184C2semidirect
11. #15182C2semidirect
12. #15178C2semidirect
13. #15150C2semidirect
14. #14714C2semidirect
15. #14700C2semidirect
16. #14359C2semidirect
17. #14139C2semidirect
18. #13937C2semidirect
19. C4×#390C2semidirect
197. #390D4semidirect
428. C2×C22⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
C2×#25012
C2×#24322
C2×#24072
C2×#24172
#164672
#156112
#155452
#152172
#152152
#151842
#151822
#151782
#151502
#147142
#147002
#143592
#141392
#139372
C4×#3902