Finite Group Databasebeta

← #687686

Subgroups — #687686

Order 512.

3134 conjugacy classes of subgroups.

The subgroup lattice has 819 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2568C211yesmaximal, characteristic, complemented
2C2×#2439C211yesmaximal, characteristic
3C2×Q8×C22⋊C4C211yesmaximal, characteristic
4C2×#2310C211yesmaximal, characteristic
5#16301C214yesmaximal
6#15964C214yesmaximal, complemented
7#15336C214yesmaximal, complemented
8#15240C211yesmaximal, characteristic, complemented
9#15237C211yesmaximal, characteristic, complemented
10#15191C211yesmaximal, characteristic, complemented
11#15184C211yesmaximal, characteristic, complemented
12#14768C214yesmaximal
13#14340C211yesmaximal, characteristic
14#13976C211yesmaximal, characteristic, complemented
15#13976C211yesmaximal, characteristic, complemented
16#13942C211yesmaximal, characteristic, complemented
17#13922C211yesmaximal, characteristic
18#13879C211yesmaximal, characteristic
19#13844C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26#2568—28no—
27#2439—28no—
28C2×#400C2214yes—
29C2×#396C2212yes—
30C2×#393C2212yes—
31Q8×C22⋊C4—28no—
32#2310—28no—
33C2×#391C2211yescharacteristic
34C2×#391C2212yes—
35C2×#391C2211yescharacteristic
36C2×#391C2212yes—
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2212yes—
40C2×#391C2214yes—
41C2×#391C2214yes—
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#389C2211yescharacteristic
50C2×#387C2212yes—
51C2×#384C2211yescharacteristic
52C2×#384C2211yescharacteristic
53C2×#382C2211yescharacteristic
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#1446C2214yes—
67#1445C2214yes—
68#1445C2214yes—
69#1444C2212yes—
70#1444C2214yes—
71#1444C2214yes—
72#1443C2214yes—
73#1442C2212yes—
74#1442C2214yes—
75#1441C2214yes—
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
91#1434C2214yes—
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×Q8Q818yescomplemented
102C23×Q8C2311yescharacteristic
103C23×Q8C2312yes—
104C23×Q8C2312yes—
105C23×Q8C2311yescharacteristic
106C24×C4C2312yes—
107C24×C4C2311yescharacteristic
108C2×C4⋊Q8—24no—
109C2×C4⋊Q8—24no—
110C2×C4⋊Q8—42no—
111C2×C4×Q8—24no—
112C2×C4×Q8—24no—
113C2×C4×Q8—24no—
114C2×C4×Q8—24no—
115C2×C4×Q8—42no—
116C2×C4×Q8—42no—
117C2×#117—24no—
118C2×#117—24no—
119C2×#117—24no—
120C2×#117—24no—
121C2×#117—42no—
122C2×#117—42no—
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⋊C4C2314yes—
138C22×C4⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2312yes—
150C22×C42C2312yes—
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155#400—216no—
156#396—28no—
157#393—28no—
158#391—24no—
159#391—24no—
160#391—24no—
161#391—24no—
162#391—24no—
163#391—24no—
164#391—24no—
165#391—216no—
166#391—216no—
167#391—28no—
168#391—28no—
169#391—28no—
170#391—42no—
171#391—42no—
172#391D418yes—
173#389—24no—
174#389—24no—
175#387—28no—
176#384—42no—
177#384—42no—
178#382—24no—
179#382—24no—
180#382—24no—
181#381—216no—
182#380—24no—
183#380—24no—
184#380—28no—
185C4×C4⋊C4—24no—
186C4×C4⋊C4—42no—
187C4×C22⋊C4—24no—
188C4×C22⋊C4—28no—
189C4×C22⋊C4D418yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
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—24no—
232C22×Q8—24no—
233C22×Q8—22no—
234C22×Q8—24no—
235C22×Q8—24no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—28no—
243C22×Q8—42no—
244C22×Q8—42no—
245C22×Q8—42no—
246C22×Q8—44no—
247C22×Q8—416no—
248C22×Q8—416no—
249C22×Q8—416no—
250C22×Q8—416no—
251C22×Q8—416no—
252C22×Q8C2×D414yes—
253C22×Q8C2×Q814yes—
254C22×Q8C2×Q818yes—
255C22×Q8C2×Q814yes—
256C22×Q8#4114yes—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—42no—
266C23×C4—42no—
267C23×C4C2×D414yes—
268C23×C4C2×Q818yes—
269C23×C4C2×Q814yes—
270C23×C4#4114yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C4⋊Q8—416no—
290C4×Q8—416no—
291C4×Q8—416no—
292#117—416no—
293#117—416no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
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—24no—
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—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—44no—
339C2×C4⋊C4C2×D414yes—
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—24no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—42no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—44no—
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—22no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—24no—
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—28no—
392#95—28no—
393#95—28no—
394#95—24no—
395#95—24no—
396#95—28no—
397#95—28no—
398#95—24no—
399#95—24no—
400#95—28no—
401#95—24no—
402#95—28no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—44no—
407#95—42no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95—42no—
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—48no—
446C2×Q8—416no—
447C2×Q8—4128no—
448C2×Q8—48no—
449C2×Q8—44no—
450C2×Q8—44no—
451C2×Q8—44no—
452C2×Q8—44no—
453C2×Q8—84no—
454C2×Q8—88no—
455C2×Q8C22⋊Q8116yes—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—216no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—216no—
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—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—48no—
549C22×C4—48no—
550C22×C4—48no—
551C22×C4—48no—
552C22×C4—48no—
553C22×C4C22⋊Q8116yes—
554C22×C4C22×D412yes—
555C22×C4C22×D414yes—
556C22×C4C22×D414yes—
557C22×C4C22×D412yes—
558C22×C4C22×D412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D414yes—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×Q814yes—
565C22×C4C22×Q812yes—
566C22×C4C22×Q814yes—
567C22×C4C22×Q812yes—
568C22×C4C2×#4114yes—
569C22×C4C2×#4112yes—
570C22×C4C2×#4112yes—
571C22×C4C2×#4112yes—
572C22×C4H(5,𝔽2)12yes—
573C22×C4H(5,𝔽2)12yes—
574C22×C42−1+414yes—
575C22×C42−1+414yes—
576C4⋊C4—28no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—48no—
580C4⋊C4—48no—
581C4⋊C4—48no—
582C4⋊C4—48no—
583C4⋊C4—48no—
584C4⋊C4—44no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—44no—
588C4⋊C4—44no—
589C4⋊C4—84no—
590C4⋊C4—88no—
591C4⋊C4—88no—
592C22⋊C4—28no—
593C22⋊C4—44no—
594C22⋊C4—48no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—48no—
598C22⋊C4—84no—
599C42—28no—
600C42—28no—
601C42—28no—
602C42—48no—
603C42—48no—
604C42—48no—
605C42—44no—
606C42—44no—
607C42—44no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—24no—
617C23—22no—
618C23—22no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23C2×C22⋊Q814yes—
631C23C23×D411yescharacteristic
632C23C23×D411yescharacteristic
633C23C23×Q811yescharacteristic
634C23C22×#4111yescharacteristic
635C23C22×#4111yescharacteristic
636C23C2×H(5,𝔽2)11yescharacteristic
637C23C2×H(5,𝔽2)11yescharacteristic
638C23C2×2−1+412yes—
639C23C2×2−1+412yes—
640C23#58512yes—
641C23#58512yes—
642Q8—232no—
643Q8—432no—
644Q8—416no—
645Q8—816no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—232no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—28no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—432no—
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—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—44no—
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—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4C2×C22⋊Q818yes—
745C2×C4C2×C22⋊Q814yes—
746C2×C4C2×C22⋊Q814yes—
747C2×C4C2×C22⋊Q814yes—
748C2×C4#53614yes—
749C2×C4#54314yes—
750C2×C4D4214yes—
751C2×C4#54614yes—
752C2×C4#54614yes—
753C2×C4#55114yes—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—44no—
758C22—42no—
759C22—42no—
760C22—44no—
761C22—44no—
762C22—42no—
763C22—44no—
764C22—42no—
765C22C22×C22⋊Q811yescharacteristic
766C22C22×C22⋊Q811yescharacteristic
767C22C2×#53611yescharacteristic
768C22#344911yescharacteristic
769C22C2×#54311yescharacteristic
770C22C2×D4211yescharacteristic
771C22C2×#54611yescharacteristic
772C22C2×#54611yescharacteristic
773C22C2×#55111yescharacteristic
774C22#348912yes—
775C22#349512yes—
776C22#349712yes—
777C22#349911yescharacteristic
778C22#350011yescharacteristic
779C22#350212yes—
780C22#350212yes—
781C22#350712yes—
782C22#352312yes—
783C22#352412yes—
784C22#354012yes—
785C22#355012yes—
786C22#356112yes—
787C22#356112yes—
788C4—24no—
789C4—24no—
790C4—28no—
791C4—44no—
792C4—42no—
793C4—44no—
794C4—44no—
795C4—44no—
796C4—42no—
797C4—42no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4—82no—
805C4#243718yes—
806C2—44no—
807C2C2×#243711yescharacteristic
808C2#3517911yescharacteristic
809C2#3566811yescharacteristic
810C2#3578612yes—
811C2#3767611yescharacteristic
812C2#3809511yescharacteristic
813C2#3895411yescharacteristic
814C2#3935611yescharacteristic
815C2#4281712yes—
816C2#4511612yes—
817C2#4532512yes—
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×#2568C2semidirect
6. #15964C2semidirect
7. #15336C2semidirect
8. #15240C2semidirect
9. #15237C2semidirect
10. #15191C2semidirect
11. #15184C2semidirect
14. #13976C2semidirect
15. #13976C2semidirect
16. #13942C2semidirect
101. C23×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25682
C2×#24392
C2×Q8×C22⋊C42
C2×#23102
#163012
#159642
#153362
#152402
#152372
#151912
#151842
#147682
#143402
#139762
#139422
#139222
#138792
#138442