Finite Group Databasebeta

← #722882

Subgroups — #722882

Order 512.

3188 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2563C211yesmaximal, characteristic, complemented
2C2×#2546C211yesmaximal, characteristic, complemented
3C2×#2580C211yesmaximal, characteristic, complemented
4C2×#2628C211yesmaximal, characteristic, complemented
5C2×#2396C211yesmaximal, characteristic, complemented
6C2×#2324C211yesmaximal, characteristic
7#16814C212yesmaximal, complemented
8#16511C212yesmaximal, complemented
9#15513C214yesmaximal, complemented
10#15505C214yesmaximal, complemented
11#15223C212yesmaximal, complemented
12#15148C212yesmaximal, complemented
13#15144C212yesmaximal, complemented
14#15065C212yesmaximal, complemented
15#13998C212yesmaximal
16#13954C212yesmaximal, complemented
17#13804C211yesmaximal, characteristic, complemented
18C22×C4⋊Q8C2211yescharacteristic
19C22×C4⋊Q8C2212yes—
20C22×#121C2211yescharacteristic
21C22×C4×Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×#117C2211yescharacteristic
24#2628—28no—
25#2580—28no—
26#2563—28no—
27#2546—28no—
28#2396—28no—
29C2×#400C2212yes—
30C2×#400C2211yescharacteristic
31C2×#399C2212yes—
32C2×#399C2212yes—
33C2×#399C2211yescharacteristic
34C2×#399C2214yes—
35C2×#398C2214yes—
36C2×#398C2212yes—
37C2×#396C2212yes—
38C2×#395C2212yes—
39C2×#395C2211yescharacteristic
40C2×#393C2211yescharacteristic
41C2×#393C2212yes—
42C2×#393C2212yes—
43C2×#393C2212yes—
44C2×#393C2212yes—
45#2324—28no—
46C2×#391C2212yes—
47C2×#390C2212yes—
48C2×#390C2211yescharacteristic
49C2×#390C2212yes—
50C2×#390C2212yes—
51C2×#390C2214yes—
52C2×#389C2211yescharacteristic
53C2×#389C2212yes—
54C2×#389C2212yes—
55C2×#389C2212yes—
56C2×#389C2212yes—
57C2×#388C2212yes—
58C2×#386C2212yes—
59C2×#385C2212yes—
60C2×#385C2214yes—
61C2×#382C2212yes—
62C2×#382C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×#380C2212yes—
65C2×#380C2214yes—
66C2×C4×C4⋊C4C2212yes—
67C2×C4×C4⋊C4C2212yes—
68C2×C4×C4⋊C4C2211yescharacteristic
69C2×C4×C4⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2212yes—
71#1445C2214yes—
72#1445C2214yes—
73#1444C2214yes—
74#1444C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1438C2214yes—
82#1437C2214yes—
83#1436C2214yes—
84C4⋊#95C2214yes—
85C4⋊#95C2212yes—
86C4⋊#95C2214yes—
87#1434C2212yes—
88C4×#95C2212yes—
89C23×Q8C2311yescharacteristic
90C23×Q8C2312yes—
91C23×D4C2311yescharacteristic
92C23×D4C2312yes—
93C24×C4C2311yescharacteristic
94C24×C4C2312yes—
95C2×C4⋊Q8—24no—
96C2×C4⋊Q8—24no—
97C2×C4⋊Q8—28no—
98C2×C4⋊Q8—24no—
99C2×C4⋊Q8—48no—
100C2×#121—24no—
101C2×#121—24no—
102C2×#121Q818yescomplemented
103C2×C4×Q8—24no—
104C2×C4×Q8—24no—
105C2×C4×Q8—24no—
106C2×C4×D4—24no—
107C2×C4×D4—24no—
108C2×C4×D4—24no—
109C2×#117—24no—
110C2×#117—24no—
111C2×#117—24no—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C22⋊C4C2311yescharacteristic
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C42C2311yescharacteristic
145C22×C42C2312yes—
146C22×C42C2312yes—
147C22×C42C2314yes—
148C22×C42C2312yes—
149C22×C42C2311yescharacteristic
150#400—28no—
151#400—24no—
152#399—28no—
153#399—28no—
154#399—24no—
155#399—48no—
156#398—28no—
157#398—216no—
158#396—28no—
159#395—28no—
160#395—24no—
161#393—28no—
162#393—28no—
163#393—28no—
164#393—28no—
165#393—24no—
166#391—28no—
167#390—24no—
168#390—28no—
169#390—28no—
170#390—28no—
171#390—48no—
172#389—24no—
173#389—28no—
174#389—28no—
175#389—28no—
176#389—28no—
177#388—28no—
178#386—28no—
179#385—28no—
180#385—216no—
181#382—28no—
182#382D418yescomplemented
183#380—216no—
184#380—24no—
185#380—28no—
186C4×C4⋊C4—28no—
187C4×C4⋊C4—28no—
188C4×C4⋊C4D418yes—
189C4×C4⋊C4D418yescomplemented
190C4×C22⋊C4—28no—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2311yescharacteristic
208C2×#95C2312yes—
209C2×#95C2311yescharacteristic
210C2×#95C2312yes—
211C2×#95C2312yes—
212C25C2411yescharacteristic
213C25C2412yes—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—24no—
218C22×Q8—24no—
219C22×Q8—24no—
220C22×Q8—24no—
221C22×Q8—42no—
222C22×Q8—44no—
223C22×Q8—44no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—24no—
228C22×D4—22no—
229C22×D4—24no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—44no—
233C22×D4—44no—
234C22×D4C2×Q814yes—
235C22×D4C2×Q818yes—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—44no—
246C23×C4—44no—
247C23×C4C2×Q814yes—
248C23×C4C2411yescharacteristic
249C23×C4C2414yes—
250C23×C4C2411yescharacteristic
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2414yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2411yescharacteristic
258C23×C4C2412yes—
259C23×C4C2411yescharacteristic
260C23×C4C2411yescharacteristic
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C4⋊Q8—432no—
264C4⋊Q8—416no—
265#121—232no—
266C4×Q8—416no—
267C4×D4—416no—
268#117—416no—
269C2×C4⋊C4—24no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—24no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—28no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4C2×D414yes—
317C2×C4⋊C4C2×D418yes—
318C2×C4⋊C4C2×D418yes—
319C2×C4⋊C4C2×D414yes—
320C2×C4⋊C4C2×Q814yes—
321C2×C4⋊C4#4114yes—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—22no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4C2×Q818yes—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—24no—
367C2×C42—24no—
368C2×C42—24no—
369C2×C42—28no—
370C2×C42—44no—
371C2×C42—44no—
372C2×C42—44no—
373C2×C42C2×D418yes—
374C2×C42C2×D418yes—
375C2×C42C2×D414yes—
376C2×C42C2×D414yes—
377C2×C42C2×D414yes—
378#95—24no—
379#95—24no—
380#95—24no—
381#95—24no—
382#95—28no—
383#95—28no—
384#95—24no—
385#95—28no—
386#95—28no—
387#95—24no—
388#95—28no—
389#95—28no—
390#95—28no—
391#95—28no—
392#95—44no—
393#95—44no—
394#95C2×D418yes—
395#95C2×D414yes—
396#95C2×D414yes—
397#95C2×D418yes—
398#95C2×D418yes—
399C24—21no—
400C24—21no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—21no—
405C24—22no—
406C24—21no—
407C24—24no—
408C24—22no—
409C24—21no—
410C24—21no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—24no—
416C24—24no—
417C24—24no—
418C24—22no—
419C24C22×Q814yes—
420C24C22×Q812yes—
421C24C2511yescharacteristic
422C2×Q8—28no—
423C2×Q8—48no—
424C2×Q8—48no—
425C2×Q8—44no—
426C2×Q8—48no—
427C2×Q8—48no—
428C2×Q8—44no—
429C2×Q8—48no—
430C2×Q8—88no—
431C2×Q8—88no—
432C2×D4—28no—
433C2×D4—216no—
434C2×D4—28no—
435C2×D4—28no—
436C2×D4—416no—
437C2×D4—44no—
438C2×D4—44no—
439C2×D4—44no—
440C2×D4—44no—
441C2×D4—84no—
442C2×D4—84no—
443C2×D4—88no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—24no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—28no—
485C22×C4—28no—
486C22×C4—28no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—416no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—48no—
522C22×C4—84no—
523C22×C4—88no—
524C22×C4—84no—
525C22×C4C22×D414yes—
526C22×C4C22×D418yes—
527C22×C4C22×D414yes—
528C22×C4C22×D414yes—
529C22×C4C22×D414yes—
530C22×C4C22×D412yes—
531C22×C4C22×D412yes—
532C22×C4C22×D412yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×Q812yes—
540C22×C4C22×Q814yes—
541C22×C4C22×Q812yes—
542C22×C4C2×#4114yes—
543C22×C4C2×#4112yes—
544C22×C4H(5,𝔽2)14yes—
545C22×C42−1+412yes—
546C22×C42−1+412yes—
547C4⋊C4—28no—
548C4⋊C4—216no—
549C4⋊C4—48no—
550C4⋊C4—48no—
551C4⋊C4—416no—
552C4⋊C4—416no—
553C4⋊C4—48no—
554C4⋊C4—44no—
555C4⋊C4—44no—
556C4⋊C4—44no—
557C4⋊C4—48no—
558C4⋊C4—44no—
559C4⋊C4—48no—
560C4⋊C4—48no—
561C4⋊C4—84no—
562C4⋊C4—88no—
563C4⋊C4—88no—
564C4⋊C4C22⋊Q8116yes—
565C22⋊C4—216no—
566C22⋊C4—416no—
567C22⋊C4—48no—
568C22⋊C4—48no—
569C22⋊C4—44no—
570C22⋊C4—44no—
571C22⋊C4—48no—
572C22⋊C4—84no—
573C22⋊C4—88no—
574C22⋊C4—88no—
575C22⋊C4—88no—
576C22⋊C4—84no—
577C22⋊C4—84no—
578C22⋊C4—88no—
579C42—216no—
580C42—48no—
581C42—44no—
582C42—48no—
583C42—88no—
584C42#127116yes—
585C23—24no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—28no—
593C23—24no—
594C23—28no—
595C23—41no—
596C23—42no—
597C23—41no—
598C23—42no—
599C23—42no—
600C23—44no—
601C23—41no—
602C23—41no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—41no—
607C23—42no—
608C23—41no—
609C23—44no—
610C23—42no—
611C23—42no—
612C23—44no—
613C23—41no—
614C23—44no—
615C23—42no—
616C23—42no—
617C23—41no—
618C23—42no—
619C23—42no—
620C23—44no—
621C23—44no—
622C23—42no—
623C23—44no—
624C23—42no—
625C23—44no—
626C23—42no—
627C23—42no—
628C23—44no—
629C23—42no—
630C23—44no—
631C23C23×D411yescharacteristic
632C23C23×D411yescharacteristic
633C23C23×D411yescharacteristic
634C23C23×Q811yescharacteristic
635C23C22×#4111yescharacteristic
636C23C2×H(5,𝔽2)12yes—
637C23C2×2−1+411yescharacteristic
638C23C2×2−1+411yescharacteristic
639C23#58512yes—
640C23#58512yes—
641C23#58512yes—
642Q8—416no—
643Q8—816no—
644D4—416no—
645D4—816no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—24no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—28no—
657C2×C4—28no—
658C2×C4—22no—
659C2×C4—24no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—28no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—28no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—28no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—44no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—416no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—41no—
709C2×C4—44no—
710C2×C4—41no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—44no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—816no—
729C2×C4C2×C22⋊Q818yes—
730C2×C4C2×C22⋊Q814yes—
731C2×C4C2×#12714yes—
732C2×C4C2×#12714yes—
733C2×C4C2×#12714yes—
734C2×C4#53614yes—
735C2×C4#54714yes—
736C2×C4#54714yes—
737C2×C4D4×Q814yes—
738C2×C4D4×Q814yes—
739C22—42no—
740C22—44no—
741C22—42no—
742C22—44no—
743C22—44no—
744C22—48no—
745C22—44no—
746C22—48no—
747C22—44no—
748C22—42no—
749C22—82no—
750C22—81no—
751C22—81no—
752C22—82no—
753C22—82no—
754C22—84no—
755C22—82no—
756C22—84no—
757C22—81no—
758C22—82no—
759C22—81no—
760C22—82no—
761C22C22×C22⋊Q811yescharacteristic
762C22C22×#12711yescharacteristic
763C22C2×#53611yescharacteristic
764C22#344912yes—
765C22C2×#54711yescharacteristic
766C22C2×#54711yescharacteristic
767C22C2×D4×Q811yescharacteristic
768C22C2×D4×Q811yescharacteristic
769C22#348411yescharacteristic
770C22#348711yescharacteristic
771C22#348812yes—
772C22#348812yes—
773C22#350011yescharacteristic
774C22#350012yes—
775C22#350011yescharacteristic
776C22#350112yes—
777C22#350412yes—
778C22#351412yes—
779C22#352412yes—
780C22#354712yes—
781C22#355412yes—
782C22#355712yes—
783C22#356512yes—
784C4—24no—
785C4—28no—
786C4—24no—
787C4—42no—
788C4—48no—
789C4—44no—
790C4—44no—
791C4—44no—
792C4—44no—
793C4—81no—
794C4—82no—
795C4—82no—
796C4—81no—
797C4—84no—
798C4#254218yes—
799C2—82no—
800C2—84no—
801C2C2×#254211yescharacteristic
802C2#3532911yescharacteristic
803C2#3556511yescharacteristic
804C2#3570211yescharacteristic
805C2#3604011yescharacteristic
806C2#3805012yes—
807C2#3959012yes—
808C2#4243111yescharacteristic
809C2#4287511yescharacteristic
810C2#4493912yes—
811C2#4520712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2563C2semidirect
2. C2×#2546C2semidirect
3. C2×#2580C2semidirect
4. C2×#2628C2semidirect
5. C2×#2396C2semidirect
7. #16814C2semidirect
8. #16511C2semidirect
9. #15513C2semidirect
10. #15505C2semidirect
11. #15223C2semidirect
12. #15148C2semidirect
13. #15144C2semidirect
14. #15065C2semidirect
16. #13954C2semidirect
17. #13804C2semidirect
102. C2×#121Q8semidirect
182. #382D4semidirect
189. C4×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25632
C2×#25462
C2×#25802
C2×#26282
C2×#23962
C2×#23242
#168142
#165112
#155132
#155052
#152232
#151482
#151442
#150652
#139982
#139542
#138042