Finite Group Databasebeta

← #676558

Subgroups — #676558

Order 512.

2970 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic
2C2×#2568C211yesmaximal, characteristic, complemented
3C2×#2365C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Q8C211yesmaximal, characteristic
5#15819C214yesmaximal, complemented
6#15787C214yesmaximal
7#15220C212yesmaximal
8#15192C212yesmaximal, complemented
9#15189C212yesmaximal, complemented
10#15182C212yesmaximal
11#14006C212yesmaximal, complemented
12#13997C212yesmaximal
13#13969C212yesmaximal
14#13926C211yesmaximal, characteristic, complemented
15#13926C212yesmaximal, complemented
16#13910C211yesmaximal, characteristic, complemented
17C4×#380C211yesmaximal, characteristic
18C22×C4⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C22×C22⋊Q8C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C22×C4×Q8C2212yes—
23C23×C42C2211yescharacteristic
24#2857—28no—
25#2568—28no—
26C2×#400C2214yes—
27#2365—28no—
28C4×C22⋊Q8—28no—
29C2×#391C2212yes—
30C2×#391C2212yes—
31C2×#391C2212yes—
32C2×#391C2211yescharacteristic
33C2×#391C2212yes—
34C2×#391C2212yes—
35C2×#391C2212yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#389C2212yes—
40C2×#389C2211yescharacteristic
41C2×#389C2212yes—
42C2×#387C2214yes—
43C2×#387C2212yes—
44C2×#385C2212yes—
45C2×#384C2211yescharacteristic
46C2×#384C2212yes—
47C2×#382C2212yes—
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C4⋊C4C2212yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2212yes—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yes—
60#1445C2214yes—
61#1444C2214yes—
62#1443C2214yes—
63#1443C2214yes—
64#1442C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1437C2214yes—
75#1436C2214yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2211yescharacteristic
79C4⋊#95C2212yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2212yes—
82C4⋊#95C2214yes—
83C4⋊#95C2214yes—
84#1434C2212yes—
85C22⋊#95C2212yes—
86C4×#95C2212yes—
87C23×Q8C2312yes—
88C23×Q8C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C2×C4⋊Q8—24no—
93C2×C4⋊Q8—24no—
94C2×C4⋊Q8D418yes—
95C2×C22⋊Q8—28no—
96C2×C22⋊Q8—28no—
97C2×C22⋊Q8—24no—
98C2×C22⋊Q8—24no—
99C2×C22⋊Q8—44no—
100C2×C22⋊Q8Q818yescomplemented
101C2×C4×Q8—28no—
102C2×C4×Q8—24no—
103C2×C4×Q8—28no—
104C2×C4×Q8—24no—
105C2×C4×Q8—24no—
106C2×C4×Q8—44no—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2314yes—
115C22×C4⋊C4C2314yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C22⋊C4C2314yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C42—24no—
132C22×C42—24no—
133C22×C42—24no—
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2311yescharacteristic
137C22×C42C2312yes—
138C22×C42C2312yes—
139C22×C42C2312yes—
140C22×C42C2314yes—
141C22×C42C2312yes—
142C22×C42C2311yescharacteristic
143#400—216no—
144#391—28no—
145#391—28no—
146#391—28no—
147#391—28no—
148#391—24no—
149#391—28no—
150#391—44no—
151#389—28no—
152#389—28no—
153#389—28no—
154#389—24no—
155#389—28no—
156#389—44no—
157#387—216no—
158#387—28no—
159#385—28no—
160#384—24no—
161#384—44no—
162#382—28no—
163#380—24no—
164#380—28no—
165#380—28no—
166#380—24no—
167#380—24no—
168C4×C4⋊C4—28no—
169C4×C4⋊C4—24no—
170C4×C4⋊C4—24no—
171C4×C4⋊C4—28no—
172C4×C4⋊C4D418yes—
173C4×C22⋊C4—28no—
174C4×C22⋊C4—44no—
175C2×#95C2312yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C25C2411yescharacteristic
203C22×Q8—22no—
204C22×Q8—24no—
205C22×Q8—22no—
206C22×Q8—22no—
207C22×Q8—24no—
208C22×Q8—22no—
209C22×Q8—24no—
210C22×Q8—24no—
211C22×Q8—24no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—24no—
215C22×Q8C2×D418yes—
216C22×Q8C2×Q814yes—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—41no—
235C23×C4—41no—
236C23×C4C2×Q814yes—
237C23×C4#4114yes—
238C23×C4C2414yes—
239C23×C4C2412yes—
240C23×C4C2412yes—
241C23×C4C2412yes—
242C23×C4C2412yes—
243C23×C4C2412yes—
244C23×C4C2414yes—
245C23×C4C2412yes—
246C23×C4C2411yescharacteristic
247C23×C4C2412yes—
248C23×C4C2411yescharacteristic
249C23×C4C2411yescharacteristic
250C23×C4C2411yescharacteristic
251C23×C4C2412yes—
252C23×C4C2411yescharacteristic
253C23×C4C2411yescharacteristic
254C4⋊Q8—232no—
255C22⋊Q8—232no—
256C22⋊Q8—432no—
257C4×Q8—432no—
258C4×Q8—416no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—24no—
261C2×C4⋊C4—24no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—28no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—28no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4C2×D418yes—
309C2×C4⋊C4C2×D418yes—
310C2×C4⋊C4C2×D414yes—
311C2×C4⋊C4C2×D414yes—
312C2×C4⋊C4C2×Q818yes—
313C2×C4⋊C4C2×Q814yes—
314C2×C4⋊C4#4114yes—
315C2×C4⋊C4#4114yes—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—28no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4C2×Q818yes—
331C2×C42—24no—
332C2×C42—24no—
333C2×C42—24no—
334C2×C42—28no—
335C2×C42—24no—
336C2×C42—24no—
337C2×C42—22no—
338C2×C42—24no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—28no—
345C2×C42—24no—
346C2×C42—24no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—24no—
351C2×C42—24no—
352C2×C42—24no—
353C2×C42—44no—
354C2×C42—416no—
355C2×C42C2×D418yes—
356C2×C42C2×D414yes—
357C2×C42C2×D414yes—
358C2×C42#4114yes—
359#95—24no—
360#95—24no—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—28no—
365#95—24no—
366#95—28no—
367#95—28no—
368#95—28no—
369#95—28no—
370#95—28no—
371#95—28no—
372#95—28no—
373#95—24no—
374#95—24no—
375#95—28no—
376#95—24no—
377#95—42no—
378#95—44no—
379#95—44no—
380#95—42no—
381#95—42no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95C2×D418yes—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24C22×Q812yes—
399C24C2×#4112yes—
400C242−1+412yes—
401C24C2511yescharacteristic
402C2×Q8—216no—
403C2×Q8—28no—
404C2×Q8—216no—
405C2×Q8—216no—
406C2×Q8—28no—
407C2×Q8—28no—
408C2×Q8—44no—
409C2×Q8—48no—
410C2×Q8—44no—
411C2×Q8—48no—
412C2×Q8—48no—
413C2×Q8—48no—
414C2×Q8—44no—
415C2×Q8—44no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—28no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—22no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—21no—
445C22×C4—24no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—24no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—28no—
472C22×C4—28no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—24no—
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—24no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—22no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4C22×D418yes—
523C22×C4C22×D414yes—
524C22×C4C22×D412yes—
525C22×C4C22×D412yes—
526C22×C4C22×D414yes—
527C22×C4C22×D412yes—
528C22×C4C22×D412yes—
529C22×C4C22×D412yes—
530C22×C4C22×D412yes—
531C22×C4C22×Q814yes—
532C22×C4C22×Q812yes—
533C22×C4C22×Q814yes—
534C22×C4C22×Q812yes—
535C22×C4C2×#4112yes—
536C22×C4C2×#4114yes—
537C22×C4C2×#4112yes—
538C22×C4C2×#4114yes—
539C22×C4C2×#4112yes—
540C22×C4C2×#4112yes—
541C22×C4C2×#4112yes—
542C22×C4C2×#4112yes—
543C22×C4C2×#4112yes—
544C22×C4H(5,𝔽2)12yes—
545C22×C4H(5,𝔽2)12yes—
546C22×C42−1+412yes—
547C22×C42−1+412yes—
548C22×C42−1+412yes—
549C4⋊C4—216no—
550C4⋊C4—216no—
551C4⋊C4—216no—
552C4⋊C4—28no—
553C4⋊C4—28no—
554C4⋊C4—48no—
555C4⋊C4—416no—
556C4⋊C4—416no—
557C4⋊C4—48no—
558C4⋊C4—48no—
559C4⋊C4—44no—
560C4⋊C4—44no—
561C4⋊C4—48no—
562C4⋊C4—44no—
563C4⋊C4—44no—
564C4⋊C4—48no—
565C4⋊C4—88no—
566C4⋊C4—88no—
567C4⋊C4C22⋊Q8116yescomplemented
568C22⋊C4—216no—
569C22⋊C4—48no—
570C22⋊C4—48no—
571C22⋊C4—416no—
572C22⋊C4—48no—
573C42—216no—
574C42—416no—
575C42—44no—
576C42—44no—
577C42—44no—
578C42—48no—
579C42—48no—
580C42—48no—
581C42#121116yes—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23#55714yes—
617C23C23×D411yescharacteristic
618C23C23×D411yescharacteristic
619C23C23×Q811yescharacteristic
620C23C22×#4111yescharacteristic
621C23C22×#4111yescharacteristic
622C23C22×#4111yescharacteristic
623C23C22×#4111yescharacteristic
624C23C2×H(5,𝔽2)11yescharacteristic
625C23C2×H(5,𝔽2)11yescharacteristic
626C23C2×2−1+411yescharacteristic
627C23C2×2−1+411yescharacteristic
628C23C2×2−1+411yescharacteristic
629C23C2×2−1+411yescharacteristic
630C23#58511yescharacteristic
631C23#58511yescharacteristic
632Q8—432no—
633Q8—416no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—28no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—28no—
654C2×C4—22no—
655C2×C4—28no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—416no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—44no—
673C2×C4—42no—
674C2×C4—41no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—44no—
678C2×C4—44no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—44no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—416no—
697C2×C4—416no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—44no—
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—44no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4C2×#12114yes—
734C2×C4C2×#12114yes—
735C2×C4C2×#12114yes—
736C2×C4C2×C22⋊Q818yes—
737C2×C4C2×C22⋊Q814yes—
738C2×C4#52914yes—
739C2×C4#53714yes—
740C2×C4#54214yes—
741C2×C4#54614yes—
742C2×C4#54614yes—
743C2×C4#54714yes—
744C2×C4#54814yes—
745C2×C4D4×Q814yes—
746C2×C4#55014yes—
747C2×C4#55414yes—
748C2×C4#55614yes—
749C22—24no—
750C22—24no—
751C22—24no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22C22×#12111yescharacteristic
765C22C22×C22⋊Q811yescharacteristic
766C22C2×#52911yescharacteristic
767C22C2×#53711yescharacteristic
768C22C2×#54211yescharacteristic
769C22C2×#54611yescharacteristic
770C22C2×#54611yescharacteristic
771C22C2×#54711yescharacteristic
772C22C2×#54811yescharacteristic
773C22C2×D4×Q811yescharacteristic
774C22C2×#55011yescharacteristic
775C22C2×#55411yescharacteristic
776C22C2×#55611yescharacteristic
777C22C2×#55711yescharacteristic
778C22Q8×#4111yescharacteristic
779C22#348011yescharacteristic
780C22#348211yescharacteristic
781C22#348611yescharacteristic
782C22#348711yescharacteristic
783C22#348911yescharacteristic
784C22#348911yescharacteristic
785C22#349511yescharacteristic
786C22#349511yescharacteristic
787C22#350211yescharacteristic
788C22#350311yescharacteristic
789C22#350611yescharacteristic
790C22#350911yescharacteristic
791C22#351411yescharacteristic
792C22#351511yescharacteristic
793C22#352011yescharacteristic
794C22#352311yescharacteristic
795C22#354611yescharacteristic
796C22#355011yescharacteristic
797C22#355211yescharacteristic
798C22#355511yescharacteristic
799C4—24no—
800C4—28no—
801C4—42no—
802C4—42no—
803C4—44no—
804C4—42no—
805C4—48no—
806C4—44no—
807C4—44no—
808C4—82no—
809C4—82no—
810C4—84no—
811C4—82no—
812C4—82no—
813C4#242718yes—
814C4#253818yes—
815C2—44no—
816C2C2×#242711yescharacteristic
817C2C2×#253811yescharacteristic
818C2#3566111yescharacteristic
819C2#3627411yescharacteristic
820C2#3645011yescharacteristic
821C2#3655211yescharacteristic
822C2#3657711yescharacteristic
823C2#3890811yescharacteristic
824C2#3915911yescharacteristic
825C2#3960911yescharacteristic
826C2#3972711yescharacteristic
827C2#5904911yescharacteristic
828C2#5905511yescharacteristic
829C2#5906711yescharacteristic
830C2#5914411yescharacteristic
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
2. C2×#2568C2semidirect
3. C2×#2365C2semidirect
5. #15819C2semidirect
8. #15192C2semidirect
9. #15189C2semidirect
11. #14006C2semidirect
14. #13926C2semidirect
15. #13926C2semidirect
16. #13910C2semidirect
100. C2×C22⋊Q8Q8semidirect
567. C4⋊C4C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25682
C2×#23652
C2×C4×C22⋊Q82
#158192
#157872
#152202
#151922
#151892
#151822
#140062
#139972
#139692
#139262
#139102
C4×#3802