Finite Group Databasebeta

← #687742

Subgroups — #687742

Order 512.

3118 conjugacy classes of subgroups.

The subgroup lattice has 825 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2421C211yesmaximal, characteristic
2C2×#2434C211yesmaximal, characteristic
3C2×Q8×C22⋊C4C211yesmaximal, characteristic
4C2×#2327C211yesmaximal, characteristic, complemented
5#16281C214yesmaximal, complemented
6#15957C214yesmaximal
7#15374C214yesmaximal, complemented
8#15240C211yesmaximal, characteristic, complemented
9#15233C211yesmaximal, characteristic
10#15182C211yesmaximal, characteristic
11#15180C211yesmaximal, characteristic, complemented
12#14740C214yesmaximal
13#14261C211yesmaximal, characteristic, complemented
14#14024C211yesmaximal, characteristic, complemented
15#14024C211yesmaximal, characteristic, complemented
16#13976C211yesmaximal, characteristic, complemented
17#13942C211yesmaximal, characteristic, complemented
18#13922C211yesmaximal, characteristic
19#13842C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27#2434—28no—
28#2421—28no—
29C2×#400C2212yes—
30C2×#397C2212yes—
31C2×#395C2214yes—
32Q8×C22⋊C4—28no—
33#2327—28no—
34C2×#391C2212yes—
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2212yes—
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#388C2212yes—
49C2×#387C2212yes—
50C2×#387C2214yes—
51C2×#387C2214yes—
52C2×#385C2214yes—
53C2×#384C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2212yes—
58C2×#380C2211yescharacteristic
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2212yes—
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×#376C2211yescharacteristic
65#1446C2214yes—
66#1445C2214yes—
67#1445C2214yes—
68#1444C2214yes—
69#1443C2212yes—
70#1443C2214yes—
71#1443C2214yes—
72#1442C2214yes—
73#1442C2214yes—
74#1442C2212yes—
75#1441C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1440C2212yes—
81#1440C2214yes—
82#1439C2212yes—
83#1439C2214yes—
84#1436C2214yes—
85#1436C2214yes—
86#1436C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91#1434C2214yes—
92C22⋊#95C2214yes—
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×Q8C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2312yes—
108C2×C4⋊Q8—24no—
109C2×C4⋊Q8—24no—
110C2×C4⋊Q8—24no—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—42no—
113C2×C4⋊Q8D418yes—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—42no—
117C2×C4×Q8—24no—
118C2×C4×Q8—24no—
119C2×C4×Q8—24no—
120C2×C4×Q8—24no—
121C2×C4×Q8—24no—
122C2×C4×Q8—24no—
123C2×C4×Q8—42no—
124C2×C4×Q8—42no—
125C2×C4×Q8—42no—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2312yes—
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#400—28no—
157#397—28no—
158#395—216no—
159#391—24no—
160#391—24no—
161#391—24no—
162#391—24no—
163#391—24no—
164#391—24no—
165#391—24no—
166#391—24no—
167#391—24no—
168#391—28no—
169#391—28no—
170#391—42no—
171#391—42no—
172#389—24no—
173#388—28no—
174#387—216no—
175#387—216no—
176#387—28no—
177#385—216no—
178#384—42no—
179#382—24no—
180#382—24no—
181#380—24no—
182#380—24no—
183#380—28no—
184C4×C4⋊C4—42no—
185C4×C22⋊C4—28no—
186C4×C22⋊C4—24no—
187C4×C22⋊C4—42no—
188C4×C22⋊C4D418yes—
189#376—24no—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2312yes—
223C2×#95C2311yescharacteristic
224C2×#95C2311yescharacteristic
225C25C2411yescharacteristic
226C22×Q8—232no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—24no—
231C22×Q8—22no—
232C22×Q8—24no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—24no—
238C22×Q8—24no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—24no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—42no—
249C22×Q8—42no—
250C22×Q8—416no—
251C22×Q8—416no—
252C22×Q8—416no—
253C22×Q8—416no—
254C22×Q8—416no—
255C22×Q8—416no—
256C22×Q8C2×D414yes—
257C22×Q8C2×D414yes—
258C22×Q8#4114yes—
259C22×Q8#4114yes—
260C22×Q8#4114yes—
261C23×C4—24no—
262C23×C4—22no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—42no—
273C23×C4—42no—
274C23×C4C2×D414yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C4⋊Q8—232no—
294C4⋊Q8—416no—
295C22⋊Q8—416no—
296C4×Q8—416no—
297C4×Q8—416no—
298C4×Q8—416no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4C2×D4116yes—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4C2×D414yes—
356C2×C22⋊C4C2×D414yes—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—24no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42C2×D414yes—
382C2×C42C2×D414yes—
383C2×C42C2×D414yes—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—28no—
394#95—24no—
395#95—24no—
396#95—28no—
397#95—28no—
398#95—28no—
399#95—28no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—28no—
404#95—28no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—28no—
409#95—42no—
410#95—44no—
411#95—44no—
412#95—44no—
413#95—42no—
414#95—42no—
415#95—44no—
416#95—44no—
417#95C2×D414yes—
418#95C2×D414yes—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—21no—
424C24—21no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24C22×D412yes—
429C242−1+414yes—
430C24C2511yescharacteristic
431C2×Q8—216no—
432C2×Q8—28no—
433C2×Q8—28no—
434C2×Q8—28no—
435C2×Q8—28no—
436C2×Q8—28no—
437C2×Q8—28no—
438C2×Q8—28no—
439C2×Q8—28no—
440C2×Q8—28no—
441C2×Q8—28no—
442C2×Q8—28no—
443C2×Q8—28no—
444C2×Q8—48no—
445C2×Q8—48no—
446C2×Q8—48no—
447C2×Q8—48no—
448C2×Q8—48no—
449C2×Q8—4128no—
450C2×Q8—48no—
451C2×Q8—44no—
452C2×Q8—44no—
453C2×Q8—44no—
454C2×Q8—44no—
455C2×Q8—44no—
456C2×Q8—44no—
457C2×Q8—44no—
458C2×Q8—44no—
459C2×Q8#123116yes—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—216no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—22no—
521C22×C4—22no—
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—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—48no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4C22×D414yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C22×D412yes—
568C22×C4C22×D414yes—
569C22×C4C22×D414yes—
570C22×C4C22×D412yes—
571C22×C4C22×D412yes—
572C22×C4C2×#4114yes—
573C22×C4C2×#4114yes—
574C22×C4C2×#4114yes—
575C22×C4C2×#4112yes—
576C22×C4C2×#4112yes—
577C22×C4C2×#4112yes—
578C22×C4H(5,𝔽2)12yes—
579C22×C4H(5,𝔽2)12yes—
580C22×C42−1+414yes—
581C22×C42−1+414yes—
582C4⋊C4—232no—
583C4⋊C4—48no—
584C4⋊C4—48no—
585C4⋊C4—48no—
586C4⋊C4—48no—
587C4⋊C4—416no—
588C4⋊C4—48no—
589C4⋊C4—48no—
590C4⋊C4—44no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—44no—
594C4⋊C4—44no—
595C4⋊C4—88no—
596C22⋊C4—216no—
597C22⋊C4—28no—
598C22⋊C4—44no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C42—28no—
604C42—28no—
605C42—28no—
606C42—48no—
607C42—48no—
608C42—48no—
609C42—44no—
610C42—44no—
611C42—44no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23#53614yes—
635C23C23×D411yescharacteristic
636C23C23×D411yescharacteristic
637C23C22×#4111yescharacteristic
638C23C22×#4111yescharacteristic
639C23C22×#4111yescharacteristic
640C23C2×H(5,𝔽2)11yescharacteristic
641C23C2×H(5,𝔽2)11yescharacteristic
642C23C2×2−1+412yes—
643C23C2×2−1+412yes—
644C23C2×2−1+412yes—
645C23#58512yes—
646Q8—232no—
647Q8—432no—
648Q8—416no—
649Q8—416no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—432no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—416no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—44no—
752C2×C4C2×#12318yes—
753C2×C4C2×#12314yes—
754C2×C4#52514yes—
755C2×C4#53814yes—
756C2×C4D4214yes—
757C2×C4#54614yes—
758C2×C4#54614yes—
759C2×C4#55114yes—
760C22—24no—
761C22—24no—
762C22—24no—
763C22—42no—
764C22—42no—
765C22—44no—
766C22—44no—
767C22—42no—
768C22—44no—
769C22—42no—
770C22—44no—
771C22C22×#12311yescharacteristic
772C22C2×#52511yescharacteristic
773C22C2×#53611yescharacteristic
774C22#344911yescharacteristic
775C22C2×#53811yescharacteristic
776C22C2×D4211yescharacteristic
777C22C2×#54611yescharacteristic
778C22C2×#54611yescharacteristic
779C22C2×#55111yescharacteristic
780C22#348612yes—
781C22#349712yes—
782C22#349911yescharacteristic
783C22#349911yescharacteristic
784C22#351612yes—
785C22#351612yes—
786C22#351812yes—
787C22#352312yes—
788C22#352312yes—
789C22#352312yes—
790C22#353812yes—
791C22#354112yes—
792C22#355212yes—
793C22#356112yes—
794C4—28no—
795C4—42no—
796C4—42no—
797C4—44no—
798C4—44no—
799C4—44no—
800C4—44no—
801C4—42no—
802C4—42no—
803C4—44no—
804C4—42no—
805C4—82no—
806C4—82no—
807C4—82no—
808C4—82no—
809C4—82no—
810C4—82no—
811C4#241818yes—
812C2—44no—
813C2C2×#241811yescharacteristic
814C2#3524611yescharacteristic
815C2#3567011yescharacteristic
816C2#3572312yes—
817C2#3767511yescharacteristic
818C2#3808111yescharacteristic
819C2#3809111yescharacteristic
820C2#3935611yescharacteristic
821C2#4284412yes—
822C2#4524912yes—
823C2#4530512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
4. C2×#2327C2semidirect
5. #16281C2semidirect
7. #15374C2semidirect
8. #15240C2semidirect
11. #15180C2semidirect
13. #14261C2semidirect
14. #14024C2semidirect
15. #14024C2semidirect
16. #13976C2semidirect
17. #13942C2semidirect

Maximal subgroups

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

subgroupindex
C2×#24212
C2×#24342
C2×Q8×C22⋊C42
C2×#23272
#162812
#159572
#153742
#152402
#152332
#151822
#151802
#147402
#142612
#140242
#139762
#139422
#139222
#138422