Finite Group Databasebeta

← #687681

Subgroups — #687681

Order 512.

3102 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2565C211yesmaximal, characteristic, complemented
2C2×#2441C211yesmaximal, characteristic
3C2×Q8×C22⋊C4C211yesmaximal, characteristic
4C2×#2310C211yesmaximal, characteristic
5#16300C214yesmaximal
6#15965C214yesmaximal, complemented
7#15333C214yesmaximal, complemented
8#15238C211yesmaximal, characteristic, complemented
9#15237C211yesmaximal, characteristic, complemented
10#15237C211yesmaximal, characteristic, complemented
11#15199C211yesmaximal, characteristic, complemented
12#14773C214yesmaximal
13#14340C211yesmaximal, characteristic
14#13978C211yesmaximal, characteristic, complemented
15#13976C211yesmaximal, characteristic, complemented
16#13926C211yesmaximal, characteristic, complemented
17#13922C211yesmaximal, characteristic
18#13879C211yesmaximal, characteristic
19#13844C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×#125C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26#2565—28no—
27#2441—28no—
28C2×#399C2212yes—
29C2×#398C2214yes—
30C2×#396C2212yes—
31Q8×C22⋊C4—28no—
32#2310—28no—
33C2×#391C2212yes—
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2212yes—
37C2×#391C2211yescharacteristic
38C2×#391C2214yes—
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#389C2211yescharacteristic
47C2×#389C2211yescharacteristic
48C2×#389C2212yes—
49C2×#387C2214yes—
50C2×#387C2212yes—
51C2×#384C2211yescharacteristic
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#381C2214yes—
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2212yes—
64C2×C4×C22⋊C4C2211yescharacteristic
65#1446C2214yes—
66#1444C2212yes—
67#1444C2214yes—
68#1444C2214yes—
69#1444C2214yes—
70#1443C2214yes—
71#1443C2214yes—
72#1442C2212yes—
73#1442C2214yes—
74#1442C2214yes—
75#1442C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1439C2214yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2214yes—
84#1436C2214yes—
85#1436C2214yes—
86#1436C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2214yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8—24no—
96C23×Q8—24no—
97C23×Q8—24no—
98C23×Q8—24no—
99C23×Q8—42no—
100C23×Q8—42no—
101C23×Q8Q818yes—
102C23×Q8C2311yescharacteristic
103C23×Q8C2312yes—
104C23×Q8C2311yescharacteristic
105C24×C4C2312yes—
106C24×C4C2311yescharacteristic
107C2×#125—24no—
108C2×#125—24no—
109C2×#125—42no—
110C2×C4×Q8—24no—
111C2×C4×Q8—24no—
112C2×C4×Q8—24no—
113C2×C4×Q8—24no—
114C2×C4×Q8—42no—
115C2×C4×Q8—42no—
116C2×#117—24no—
117C2×#117—24no—
118C2×#117—24no—
119C2×#117—24no—
120C2×#117—42no—
121C2×#117—42no—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2314yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2312yes—
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#399—28no—
158#398—216no—
159#396—28no—
160#391—24no—
161#391—24no—
162#391—24no—
163#391—24no—
164#391—24no—
165#391—24no—
166#391—24no—
167#391—216no—
168#391—28no—
169#391—28no—
170#391—42no—
171#391—42no—
172#391D418yes—
173#389—24no—
174#389—24no—
175#389—28no—
176#387—216no—
177#387—28no—
178#384—24no—
179#384—24no—
180#384—42no—
181#382—24no—
182#382—42no—
183#381—216no—
184#380—24no—
185#380—24no—
186#380—28no—
187C4×C4⋊C4—24no—
188C4×C4⋊C4—42no—
189C4×C22⋊C4—24no—
190C4×C22⋊C4—28no—
191C4×C22⋊C4D418yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2311yescharacteristic
222C2×#95C2311yescharacteristic
223C25C2411yescharacteristic
224C22×Q8—232no—
225C22×Q8—232no—
226C22×Q8—22no—
227C22×Q8—24no—
228C22×Q8—24no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—24no—
233C22×Q8—24no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—42no—
241C22×Q8—42no—
242C22×Q8—416no—
243C22×Q8—416no—
244C22×Q8—416no—
245C22×Q8—416no—
246C22×Q8—416no—
247C22×Q8C2×D414yes—
248C22×Q8C2×Q814yes—
249C22×Q8C2×Q818yes—
250C22×Q8C2×Q814yes—
251C22×Q8#4114yes—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4C2×D414yes—
263C23×C4C2×Q818yes—
264C23×C4C2×Q814yes—
265C23×C4#4114yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284#125—416no—
285C4×Q8—416no—
286C4×Q8—416no—
287#117—416no—
288#117—416no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4C2×D414yes—
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—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—42no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4C2×D414yes—
358C2×C22⋊C4C2×D414yes—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—22no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—24no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—24no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—42no—
383C2×C42C2×D414yes—
384C2×C42C2×D414yes—
385C2×C42C2×D414yes—
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—28no—
395#95—28no—
396#95—28no—
397#95—24no—
398#95—24no—
399#95—28no—
400#95—24no—
401#95—28no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—28no—
406#95—42no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95—42no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95C2×D414yes—
415#95C2×D414yes—
416#95C2×D4116yes—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24C22×D412yes—
426C24C22×Q812yes—
427C24C2×#4112yes—
428C24C2511yescharacteristic
429C2×Q8—28no—
430C2×Q8—216no—
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—48no—
441C2×Q8—48no—
442C2×Q8—48no—
443C2×Q8—48no—
444C2×Q8—48no—
445C2×Q8—4128no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—44no—
450C2×Q8C22⋊Q8116yes—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—28no—
463C22×C4—28no—
464C22×C4—28no—
465C22×C4—28no—
466C22×C4—28no—
467C22×C4—28no—
468C22×C4—216no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—216no—
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—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4C22⋊Q8116yes—
549C22×C4C22×D414yes—
550C22×C4C22×D412yes—
551C22×C4C22×D412yes—
552C22×C4C22×D414yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D414yes—
556C22×C4C22×D412yes—
557C22×C4C22×D412yes—
558C22×C4C22×D412yes—
559C22×C4C22×Q814yes—
560C22×C4C22×Q812yes—
561C22×C4C22×Q814yes—
562C22×C4C22×Q812yes—
563C22×C4C2×#4114yes—
564C22×C4C2×#4112yes—
565C22×C4C2×#4112yes—
566C22×C4C2×#4112yes—
567C22×C4H(5,𝔽2)12yes—
568C22×C4H(5,𝔽2)12yes—
569C22×C42−1+414yes—
570C22×C42−1+414yes—
571C4⋊C4—28no—
572C4⋊C4—48no—
573C4⋊C4—48no—
574C4⋊C4—48no—
575C4⋊C4—48no—
576C4⋊C4—48no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—48no—
580C4⋊C4—416no—
581C4⋊C4—48no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—84no—
588C4⋊C4—84no—
589C4⋊C4—88no—
590C22⋊C4—28no—
591C22⋊C4—44no—
592C22⋊C4—48no—
593C22⋊C4—48no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—84no—
597C42—28no—
598C42—28no—
599C42—28no—
600C42—48no—
601C42—48no—
602C42—48no—
603C42—44no—
604C42—44no—
605C42—44no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—24no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23C2×C22⋊Q814yes—
629C23C23×D411yescharacteristic
630C23C23×D411yescharacteristic
631C23C23×Q811yescharacteristic
632C23C22×#4111yescharacteristic
633C23C22×#4111yescharacteristic
634C23C2×H(5,𝔽2)11yescharacteristic
635C23C2×H(5,𝔽2)11yescharacteristic
636C23C2×2−1+412yes—
637C23C2×2−1+412yes—
638C23#58512yes—
639C23#58512yes—
640Q8—232no—
641Q8—432no—
642Q8—416no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—232no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—28no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—432no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—44no—
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—44no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—42no—
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—44no—
731C2×C4—44no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—44no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4C2×C22⋊Q818yes—
742C2×C4C2×C22⋊Q814yes—
743C2×C4C2×C22⋊Q814yes—
744C2×C4C2×C22⋊Q814yes—
745C2×C4#53614yes—
746C2×C4#54314yes—
747C2×C4D4214yes—
748C2×C4#54614yes—
749C2×C4#54614yes—
750C2×C4#55114yes—
751C22—24no—
752C22—24no—
753C22—24no—
754C22—44no—
755C22—42no—
756C22—42no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—42no—
761C22—42no—
762C22C22×C22⋊Q811yescharacteristic
763C22C22×C22⋊Q811yescharacteristic
764C22C2×#53611yescharacteristic
765C22#344911yescharacteristic
766C22C2×#54311yescharacteristic
767C22C2×D4211yescharacteristic
768C22C2×#54611yescharacteristic
769C22C2×#54611yescharacteristic
770C22C2×#55111yescharacteristic
771C22#348712yes—
772C22#349512yes—
773C22#349912yes—
774C22#349911yescharacteristic
775C22#350011yescharacteristic
776C22#350212yes—
777C22#350212yes—
778C22#350712yes—
779C22#351612yes—
780C22#351612yes—
781C22#354112yes—
782C22#354712yes—
783C22#355212yes—
784C22#356212yes—
785C4—24no—
786C4—28no—
787C4—24no—
788C4—42no—
789C4—42no—
790C4—44no—
791C4—44no—
792C4—44no—
793C4—42no—
794C4—44no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4#243718yes—
803C2—44no—
804C2C2×#243711yescharacteristic
805C2#3517911yescharacteristic
806C2#3566811yescharacteristic
807C2#3584512yes—
808C2#3768311yescharacteristic
809C2#3808511yescharacteristic
810C2#3894611yescharacteristic
811C2#3936011yescharacteristic
812C2#4281612yes—
813C2#4511712yes—
814C2#4523712yes—
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
1. C2×#2565C2semidirect
6. #15965C2semidirect
7. #15333C2semidirect
8. #15238C2semidirect
9. #15237C2semidirect
10. #15237C2semidirect
11. #15199C2semidirect
14. #13978C2semidirect
15. #13976C2semidirect
16. #13926C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25652
C2×#24412
C2×Q8×C22⋊C42
C2×#23102
#163002
#159652
#153332
#152382
#152372
#151992
#147732
#143402
#139782
#139762
#139262
#139222
#138792
#138442