Finite Group Databasebeta

← #875228

Subgroups — #875228

Order 512.

2782 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2497C211yesmaximal, characteristic
2C2×#2434C211yesmaximal, characteristic
3#16826C214yesmaximal, complemented
4#15592C214yesmaximal, complemented
5#15555C214yesmaximal
6#15199C211yesmaximal, characteristic, complemented
7#15188C211yesmaximal, characteristic, complemented
8#15188C211yesmaximal, characteristic, complemented
9#15184C211yesmaximal, characteristic, complemented
10#15182C211yesmaximal, characteristic
11#15182C211yesmaximal, characteristic
12#14714C211yesmaximal, characteristic, complemented
13#14703C211yesmaximal, characteristic, complemented
14#14488C214yesmaximal
15#14155C211yesmaximal, characteristic, complemented
16#14000C211yesmaximal, characteristic, complemented
17#13922C211yesmaximal, characteristic
18#13922C211yesmaximal, characteristic
19C4×#388C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24#2497—28no—
25#2434—28no—
26C2×#400C2212yes—
27C2×#396C2212yes—
28C2×#395C2212yes—
29C2×#395C2212yes—
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#389C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#388C2212yes—
47C2×#388C2212yes—
48C2×#387C2212yes—
49C2×#385C2212yes—
50C2×#385C2212yes—
51C2×#384C2211yescharacteristic
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×C43C2211yescharacteristic
62#1446C2214yes—
63#1446C2214yes—
64#1445C2214yes—
65#1444C2214yes—
66#1444C2214yes—
67#1442C2214yes—
68#1442C2214yes—
69#1442C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1437C2212yes—
79#1436C2214yes—
80#1436C2214yes—
81#1436C2212yes—
82C4⋊#95C2214yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2214yes—
86C4⋊#95C2214yes—
87#1434C2214yes—
88#1434C2212yes—
89C22⋊#95C2214yes—
90C22⋊#95C2214yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8—24no—
94C23×Q8—24no—
95C23×Q8—24no—
96C23×Q8—42no—
97C23×Q8—42no—
98C23×Q8—42no—
99C23×Q8—42no—
100C23×Q8C2311yescharacteristic
101C23×Q8C2311yescharacteristic
102C23×Q8C2311yescharacteristic
103C23×Q8C2312yes—
104C24×C4C2311yescharacteristic
105C24×C4C2312yes—
106C2×C4⋊Q8—24no—
107C2×C4⋊Q8—24no—
108C2×C4⋊Q8—24no—
109C2×C4⋊Q8—24no—
110C2×C4⋊Q8—42no—
111C2×C4⋊Q8—42no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—42no—
114C2×C22⋊Q8—42no—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2312yes—
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2311yescharacteristic
144C22×C42C2311yescharacteristic
145C22×C42C2312yes—
146C22×C42C2312yes—
147C22×C42C2312yes—
148#400—28no—
149#396—28no—
150#395—28no—
151#395—28no—
152#391—24no—
153#391—24no—
154#391—24no—
155#391—24no—
156#391—42no—
157#391—42no—
158#391—42no—
159#391—42no—
160#391—42no—
161#391—42no—
162#391—42no—
163#391—42no—
164#391—42no—
165#391—42no—
166#389—24no—
167#389—24no—
168#388—28no—
169#388Q8116yescomplemented
170#387—28no—
171#385—28no—
172#385—28no—
173#384—24no—
174#384—42no—
175#384—42no—
176#380—24no—
177#380—24no—
178C4×C4⋊C4—24no—
179C4×C4⋊C4—42no—
180C4×C22⋊C4—42no—
181C4×C22⋊C4—42no—
182C4×C22⋊C4D418yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2311yescharacteristic
212C2×#95C2311yescharacteristic
213C2×#95C2312yes—
214C2×#95C2312yes—
215C43—42no—
216C25C2411yescharacteristic
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—24no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—24no—
226C22×Q8—24no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—42no—
240C22×Q8—42no—
241C22×Q8—42no—
242C22×Q8—42no—
243C22×Q8—416no—
244C22×Q8—416no—
245C22×Q8—416no—
246C22×Q8—416no—
247C22×Q8—416no—
248C22×Q8—416no—
249C22×Q8—416no—
250C22×Q8#4114yes—
251C22×Q8#4114yes—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4C2×D414yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2411yescharacteristic
283C23×C4C2411yescharacteristic
284C4⋊Q8—416no—
285C4⋊Q8—416no—
286C22⋊Q8—416no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4C2×Q818yescomplemented
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4C2×D414yes—
347C2×C22⋊C4C2×D414yes—
348C2×C22⋊C4C2×Q818yes—
349C2×C22⋊C4C2×Q818yes—
350C2×C22⋊C4C2×Q818yes—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—22no—
354C2×C42—22no—
355C2×C42—22no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—42no—
370C2×C42—42no—
371C2×C42—42no—
372C2×C42—42no—
373C2×C42—44no—
374C2×C42C2×D414yes—
375C2×C42C2×D414yes—
376C2×C42C2×Q818yescomplemented
377#95—24no—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—28no—
387#95—28no—
388#95—24no—
389#95—44no—
390#95—44no—
391#95—42no—
392#95—42no—
393#95—42no—
394#95—42no—
395#95—44no—
396#95—44no—
397#95—44no—
398#95—44no—
399#95—44no—
400#95—44no—
401#95—44no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95C2×D414yes—
406#95C2×D414yes—
407#95C2×Q818yescomplemented
408#95C2×Q818yescomplemented
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24C22×D412yes—
419C24C22×Q814yes—
420C24C2511yescharacteristic
421C2×Q8—28no—
422C2×Q8—28no—
423C2×Q8—28no—
424C2×Q8—28no—
425C2×Q8—28no—
426C2×Q8—28no—
427C2×Q8—48no—
428C2×Q8—48no—
429C2×Q8—48no—
430C2×Q8—48no—
431C2×Q8—48no—
432C2×Q8—48no—
433C2×Q8—4128no—
434C2×Q8—48no—
435C2×Q8—44no—
436C2×Q8—44no—
437C2×Q8—44no—
438C2×Q8—44no—
439C2×Q8—44no—
440C2×Q8—44no—
441C2×Q8—44no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×Q8—44no—
449C2×Q8—44no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—28no—
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—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—48no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—44no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4C22×D412yes—
552C22×C4C22×D412yes—
553C22×C4C22×D412yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C22×Q814yes—
558C22×C4C22×Q814yes—
559C22×C4C22×Q814yes—
560C22×C4C22×Q814yes—
561C22×C4C22×Q814yes—
562C22×C4C22×Q814yes—
563C22×C4C2×#4114yes—
564C22×C4C2×#4114yes—
565C22×C4C2×#4112yes—
566C22×C4C2×#4112yes—
567C22×C4H(5,𝔽2)12yes—
568C22×C4H(5,𝔽2)12yes—
569C22×C4H(5,𝔽2)12yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C42−1+414yes—
572C4⋊C4—48no—
573C4⋊C4—48no—
574C4⋊C4—48no—
575C4⋊C4—48no—
576C4⋊C4—48no—
577C4⋊C4—48no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—48no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—84no—
585C4⋊C4—84no—
586C4⋊C4—84no—
587C4⋊C4—88no—
588C4⋊C4—88no—
589C22⋊C4—28no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—84no—
594C22⋊C4—84no—
595C22⋊C4C4⋊Q8116yes—
596C42—28no—
597C42—28no—
598C42—48no—
599C42—48no—
600C42—44no—
601C42—44no—
602C42—44no—
603C42—44no—
604C42—84no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—24no—
616C23—24no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—42no—
621C23—42no—
622C23—41no—
623C23—42no—
624C23—42no—
625C23—42no—
626C23—42no—
627C23C2×C4⋊Q814yes—
628C23C23×D411yescharacteristic
629C23C23×Q812yes—
630C23C22×#4111yescharacteristic
631C23C22×#4111yescharacteristic
632C23C2×H(5,𝔽2)11yescharacteristic
633C23C2×H(5,𝔽2)11yescharacteristic
634C23C2×H(5,𝔽2)11yescharacteristic
635C23C2×H(5,𝔽2)11yescharacteristic
636C23C2×2−1+412yes—
637C23#58512yes—
638C23#58512yes—
639Q8—432no—
640Q8—416no—
641Q8—416no—
642Q8—88no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—432no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—41no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
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—416no—
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—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—42no—
731C2×C4—42no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—42no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4C2×C4⋊Q814yes—
744C2×C4C2×C4⋊Q814yes—
745C2×C4#53514yes—
746C2×C4#53614yes—
747C2×C4#53814yes—
748C2×C4#53814yes—
749C2×C4#54614yes—
750C2×C4#54614yes—
751C2×C4#55114yes—
752C2×C4#56014yes—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—44no—
759C22—42no—
760C22—44no—
761C22—42no—
762C22—44no—
763C22—44no—
764C22C22×C4⋊Q811yescharacteristic
765C22C2×#53511yescharacteristic
766C22C2×#53611yescharacteristic
767C22C2×#53811yescharacteristic
768C22C2×#53811yescharacteristic
769C22C2×#54611yescharacteristic
770C22C2×#54611yescharacteristic
771C22C2×#55111yescharacteristic
772C22Q8×#4112yes—
773C22Q8×#4112yes—
774C22#350011yescharacteristic
775C22#350011yescharacteristic
776C22#350112yes—
777C22#350112yes—
778C22#350312yes—
779C22#350312yes—
780C22#351612yes—
781C22#351812yes—
782C22C2×#56011yescharacteristic
783C22#354112yes—
784C22#354712yes—
785C22#356212yes—
786C22#356212yes—
787C4—24no—
788C4—24no—
789C4—24no—
790C4—42no—
791C4—42no—
792C4—44no—
793C4—44no—
794C4—44no—
795C4—44no—
796C4—44no—
797C4—44no—
798C4—82no—
799C4—82no—
800C4—82no—
801C4—82no—
802C4—82no—
803C4—82no—
804C4#268518yes—
805C2—44no—
806C2#3528111yescharacteristic
807C2#3627611yescharacteristic
808C2#3627611yescharacteristic
809C2#3742211yescharacteristic
810C2#3808511yescharacteristic
811C2#3895811yescharacteristic
812C2#3965412yes—
813C2#3965912yes—
814C2#4549712yes—
815C2C2×#268511yescharacteristic
816C2#5947712yes—
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
3. #16826C2semidirect
4. #15592C2semidirect
6. #15199C2semidirect
7. #15188C2semidirect
8. #15188C2semidirect
9. #15184C2semidirect
12. #14714C2semidirect
13. #14703C2semidirect
15. #14155C2semidirect
16. #14000C2semidirect
169. #388Q8semidirect
333. C2×C4⋊C4C2×Q8semidirect
376. C2×C42C2×Q8semidirect
407. #95C2×Q8semidirect
408. #95C2×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#24972
C2×#24342
#168262
#155922
#155552
#151992
#151882
#151842
#151822
#147142
#147032
#144882
#141552
#140002
#139222
C4×#3882