Finite Group Databasebeta

← #725952

Subgroups — #725952

Order 512.

3908 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#556C211yesmaximal, characteristic, complemented
2C2×#2628C211yesmaximal, characteristic, complemented
3C2×#2392C211yesmaximal, characteristic
4C2×#2323C211yesmaximal, characteristic, complemented
5#16681C212yesmaximal, complemented
6#16680C212yesmaximal
7#15940C214yesmaximal, complemented
8#15939C214yesmaximal, complemented
9#15179C212yesmaximal, complemented
10#15177C212yesmaximal, complemented
11#14882C212yesmaximal, complemented
12#14879C212yesmaximal, complemented
13#14161C211yesmaximal, characteristic, complemented
14#14129C212yesmaximal, complemented
15#13942C211yesmaximal, characteristic, complemented
16#13905C211yesmaximal, characteristic, complemented
17#13871C212yesmaximal, complemented
18C2×#556—28no—
19C2×#556—28no—
20C2×#556—28no—
21C22×C4⋊Q8C2211yescharacteristic
22C22×#126C2214yes—
23C22×#124C2212yes—
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2212yes—
26C22×C4×Q8C2212yes—
27C22×C4×Q8C2211yescharacteristic
28C22×C4×D4C2212yes—
29C22×C4×D4C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C22×#117C2212yes—
32#2628—28no—
33C2×#400C2212yes—
34C2×#399C2212yes—
35#2392—28no—
36C2×#398C2211yescharacteristic
37C2×#397C2211yescharacteristic
38C2×#396C2212yes—
39C2×#395C2212yes—
40C2×#394C2211yescharacteristic
41C2×#394C2212yes—
42C2×#393C2212yes—
43C2×#392C2211yescharacteristic
44#2323—28no—
45C2×#391C2211yescharacteristic
46C2×#391C2212yes—
47C2×#389C2211yescharacteristic
48C2×#389C2212yes—
49C2×#389C2212yes—
50C2×#388C2212yes—
51C2×#388C2212yes—
52C2×#387C2212yes—
53C2×#382C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2212yes—
56C2×#380C2212yes—
57C2×#380C2212yes—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2212yes—
61#1446C2212yes—
62#1446C2212yes—
63#1445C2212yes—
64#1444C2214yes—
65#1442C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1440C2214yes—
69#1440C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1438C2212yes—
76#1438C2214yes—
77#1438C2214yes—
78#1437C2214yes—
79#1437C2214yes—
80#1436C2214yes—
81#1436C2214yes—
82#1436C2214yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C4⋊#95C2214yes—
87#1434C2212yes—
88#1434C2212yes—
89C23×Q8C2311yescharacteristic
90C23×Q8C2312yes—
91C23×D4C2312yes—
92C23×D4C2311yescharacteristic
93C24×C4C2312yes—
94C24×C4C2311yescharacteristic
95#556—2128no—
96C2×C4⋊Q8—24no—
97C2×C4⋊Q8—24no—
98C2×C4⋊Q8D418yescomplemented
99C2×#126—216no—
100C2×#126—216no—
101C2×#126—216no—
102C2×#124—28no—
103C2×#124—28no—
104C2×#124—28no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—28no—
107C2×C22⋊Q8—28no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—28no—
110C2×C22⋊Q8—24no—
111C2×C4×Q8—28no—
112C2×C4×Q8—28no—
113C2×C4×Q8—28no—
114C2×C4×Q8—24no—
115C2×C4×Q8—24no—
116C2×C4×Q8D418yescomplemented
117C2×C4×D4—28no—
118C2×C4×D4—28no—
119C2×C4×D4—24no—
120C2×C4×D4—24no—
121C2×C4×D4—44no—
122C2×C4×D4D418yes—
123C2×#117—28no—
124C2×#117—28no—
125C2×#117—28no—
126C2×#117—24no—
127C2×#117—24no—
128C2×#117—24no—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C42C2314yes—
160C22×C42C2311yescharacteristic
161C22×C42C2312yes—
162C22×C42C2312yes—
163C22×C42C2312yes—
164C22×C42C2311yescharacteristic
165#400—28no—
166#399—28no—
167#398—24no—
168#397—24no—
169#396—28no—
170#395—28no—
171#394—24no—
172#394—28no—
173#393—28no—
174#392—24no—
175#391—24no—
176#391—44no—
177#389—28no—
178#389—24no—
179#389—28no—
180#388—28no—
181#388—28no—
182#387—28no—
183#382—24no—
184#380—24no—
185#380—28no—
186#380—28no—
187#380—44no—
188C4×C4⋊C4—24no—
189C4×C4⋊C4—24no—
190C4×C22⋊C4—28no—
191C2×#95C2311yescharacteristic
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2311yescharacteristic
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C25C2412yes—
215C25C2411yescharacteristic
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—24no—
219C22×Q8—24no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—44no—
225C22×Q8—44no—
226C22×Q8C2×D414yes—
227C22×Q8C2×D418yes—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—24no—
233C22×D4—42no—
234C22×D4—42no—
235C22×D4—42no—
236C22×D4—42no—
237C22×D4—42no—
238C22×D4—42no—
239C22×D4C2×D414yes—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—24no—
246C23×C4—22no—
247C23×C4—24no—
248C23×C4—22no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—22no—
252C23×C4C2×D418yes—
253C23×C4#4114yes—
254C23×C4C2411yescharacteristic
255C23×C4C2411yescharacteristic
256C23×C4C2414yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2414yes—
261C23×C4C2412yes—
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2411yescharacteristic
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C4⋊Q8—232no—
270#126—2128no—
271#124—264no—
272C22⋊Q8—232no—
273C22⋊Q8—264no—
274C4×Q8—264no—
275C4×Q8—232no—
276C4×D4—232no—
277C4×D4—432no—
278#117—264no—
279#117—416no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—28no—
288C2×C4⋊C4—28no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
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—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4C2×D414yes—
322C2×C4⋊C4C2×D418yes—
323C2×C4⋊C4C2×D414yes—
324C2×C4⋊C4C2×D418yes—
325C2×C4⋊C4C2×D418yes—
326C2×C4⋊C4#4114yes—
327C2×C22⋊C4—28no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—42no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4C2×D418yes—
368C2×C42—28no—
369C2×C42—28no—
370C2×C42—28no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—44no—
381C2×C42C2×D418yes—
382C2×C42C2×D414yes—
383C2×C42C2×D414yes—
384C2×C42C2×D414yes—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—22no—
389#95—22no—
390#95—24no—
391#95—28no—
392#95—24no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408C24—21no—
409C24—21no—
410C24—22no—
411C24—22no—
412C24—21no—
413C24—21no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—21no—
418C24—22no—
419C24—22no—
420C24—21no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24C22×D414yes—
433C24C2×#4112yes—
434C24C2511yescharacteristic
435C2×Q8—28no—
436C2×Q8—216no—
437C2×Q8—28no—
438C2×Q8—28no—
439C2×Q8—416no—
440C2×Q8—416no—
441C2×Q8—48no—
442C2×Q8—48no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×D4—28no—
448C2×D4—48no—
449C2×D4—48no—
450C2×D4—48no—
451C2×D4—48no—
452C2×D4—44no—
453C2×D4—44no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—48no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—24no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—24no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—216no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—216no—
505C22×C4—216no—
506C22×C4—28no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—44no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—44no—
544C22×C4C22×D414yes—
545C22×C4C22×D414yes—
546C22×C4C22×D418yes—
547C22×C4C22×D414yes—
548C22×C4C22×D412yes—
549C22×C4C22×D412yes—
550C22×C4C22×D412yes—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C2×#4114yes—
558C22×C4C2×#4112yes—
559C22×C4C2×#4112yes—
560C22×C4C2×#4112yes—
561C22×C4H(5,𝔽2)12yes—
562C22×C42−1+414yes—
563C22×C42−1+412yes—
564C4⋊C4—232no—
565C4⋊C4—216no—
566C4⋊C4—28no—
567C4⋊C4—216no—
568C4⋊C4—28no—
569C4⋊C4—216no—
570C4⋊C4—216no—
571C4⋊C4—28no—
572C4⋊C4—48no—
573C4⋊C4—48no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—48no—
578C4⋊C4—88no—
579C4⋊C4—84no—
580C22⋊C4—232no—
581C22⋊C4—216no—
582C22⋊C4—232no—
583C22⋊C4—216no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—44no—
589C22⋊C4—44no—
590C22⋊C4—88no—
591C22⋊C4—84no—
592C22⋊C4—88no—
593C22⋊C4—88no—
594C42—232no—
595C42—216no—
596C42—44no—
597C42—48no—
598C42—84no—
599C42#120116yes—
600C23—24no—
601C23—22no—
602C23—24no—
603C23—24no—
604C23—22no—
605C23—24no—
606C23—24no—
607C23—22no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—24no—
612C23—41no—
613C23—42no—
614C23—41no—
615C23—42no—
616C23—42no—
617C23—41no—
618C23—42no—
619C23—41no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—41no—
627C23—41no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—41no—
638C23—41no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23C23×D411yescharacteristic
659C23C23×D411yescharacteristic
660C23C23×D411yescharacteristic
661C23C22×#4111yescharacteristic
662C23C22×#4111yescharacteristic
663C23C2×H(5,𝔽2)11yescharacteristic
664C23C2×2−1+411yescharacteristic
665C23C2×2−1+412yes—
666C23#58512yes—
667C23#58512yes—
668C23#58512yes—
669Q8—432no—
670Q8—416no—
671D4—416no—
672D4—432no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—28no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—432no—
727C2×C4—416no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—44no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4C2×#12014yes—
758C2×C4C2×#12014yes—
759C2×C4C2×#12014yes—
760C2×C4#52514yes—
761C2×C4#53714yes—
762C2×C4#54614yes—
763C2×C4#54714yes—
764C2×C4#54814yes—
765C2×C4#55014yes—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—42no—
771C22—44no—
772C22—44no—
773C22—42no—
774C22—42no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—82no—
779C22—82no—
780C22—82no—
781C22—82no—
782C22—82no—
783C22—81no—
784C22—81no—
785C22—82no—
786C22—81no—
787C22—82no—
788C22—81no—
789C22—82no—
790C22—82no—
791C22—82no—
792C22C22×#12011yescharacteristic
793C22C2×#52511yescharacteristic
794C22C2×#53711yescharacteristic
795C22#344912yes—
796C22C2×#54611yescharacteristic
797C22C2×#54711yescharacteristic
798C22C2×#54811yescharacteristic
799C22C2×#55011yescharacteristic
800C22#348512yes—
801C22#348711yescharacteristic
802C22#348711yescharacteristic
803C22#348912yes—
804C22#349312yes—
805C22#349512yes—
806C22#349712yes—
807C22#349911yescharacteristic
808C22#350011yescharacteristic
809C22#351812yes—
810C22#352112yes—
811C22#354012yes—
812C22#354112yes—
813C22#355512yes—
814C22#356512yes—
815C4—24no—
816C4—24no—
817C4—44no—
818C4—48no—
819C4—44no—
820C4—42no—
821C4—44no—
822C4—44no—
823C4—44no—
824C4—84no—
825C4—81no—
826C4—81no—
827C4—82no—
828C4—82no—
829C4#240718yes—
830C2—82no—
831C2—84no—
832C2C2×#240711yescharacteristic
833C2#3514911yescharacteristic
834C2#3566011yescharacteristic
835C2#3601911yescharacteristic
836C2#3603011yescharacteristic
837C2#3784412yes—
838C2#3805112yes—
839C2#4287811yescharacteristic
840C2#4288211yescharacteristic
841C2#4509812yes—
842C2#4510112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#392C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#556C2semidirect
2. C2×#2628C2semidirect
4. C2×#2323C2semidirect
5. #16681C2semidirect
7. #15940C2semidirect
8. #15939C2semidirect
9. #15179C2semidirect
10. #15177C2semidirect
11. #14882C2semidirect
12. #14879C2semidirect
13. #14161C2semidirect
14. #14129C2semidirect
15. #13942C2semidirect
16. #13905C2semidirect
17. #13871C2semidirect
98. C2×C4⋊Q8D4semidirect
116. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5562
C2×#26282
C2×#23922
C2×#23232
#166812
#166802
#159402
#159392
#151792
#151772
#148822
#148792
#141612
#141292
#139422
#139052
#138712