Finite Group Databasebeta

← #636431

Subgroups — #636431

Order 512.

3826 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2501C211yesmaximal, characteristic, complemented
2C2×#2486C211yesmaximal, characteristic, complemented
3C2×#2416C211yesmaximal, characteristic
4C2×#2618C212yesmaximal, complemented
5C22×#389C211yesmaximal, characteristic, complemented
6#16550C214yesmaximal, complemented
7#16549C214yesmaximal, complemented
8#15141C212yesmaximal, complemented
9#15137C212yesmaximal, complemented
10#15131C212yesmaximal, complemented
11#15126C212yesmaximal, complemented
12#14927C212yesmaximal, complemented
13#14926C212yesmaximal, complemented
14#14698C211yesmaximal, characteristic, complemented
15#14256C212yesmaximal, complemented
16#13907C211yesmaximal, characteristic, complemented
17C4×#386C211yesmaximal, characteristic, complemented
18C22×#123C2212yes—
19C22×#123C2212yes—
20C22×#123C2212yes—
21C22×#121C2211yescharacteristic
22C22×#121C2212yes—
23C22×#121C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C23×C4⋊C4C2212yes—
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28C23×C42C2211yescharacteristic
29#2618—216no—
30#2501—28no—
31#2486—28no—
32#2416—28no—
33C2×#399C2214yes—
34C2×#398C2214yes—
35C2×#398C2212yes—
36C2×#397C2212yes—
37C2×#396C2214yes—
38C2×#396C2214yes—
39C2×#396C2212yes—
40C2×#394C2214yes—
41C2×#394C2212yes—
42C2×#390C2212yes—
43C2×#390C2211yescharacteristic
44C2×#390C2212yes—
45C2×#389—28no—
46C2×#389C2212yes—
47C2×#389C2212yes—
48C2×#389C2211yescharacteristic
49C2×#389C2212yes—
50C2×#389C2214yes—
51C2×#389C2212yes—
52C2×#386C2211yescharacteristic
53C2×#386C2212yes—
54C2×#386C2212yes—
55C2×#386C2212yes—
56C2×#386C2211yescharacteristic
57C2×#384C2212yes—
58C2×#381C2212yes—
59C2×#380C2212yes—
60C2×#380C2211yescharacteristic
61C2×#380C2212yes—
62C2×#380C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2212yes—
65C22×#95C2212yes—
66#1444C2214yes—
67#1442C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1440C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1438C2214yes—
79#1437C2214yes—
80#1437C2212yes—
81#1436C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2211yescharacteristic
86C22⋊#95C2211yescharacteristic
87C4×#95C2212yes—
88C23×D4C2312yes—
89C23×D4C2311yescharacteristic
90C23×D4C2311yescharacteristic
91C23×D4C2312yes—
92C24×C4C2311yescharacteristic
93C24×C4C2312yes—
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C2×#123—28no—
99C2×#123—28no—
100C2×#123—28no—
101C2×#123—28no—
102C2×#123—28no—
103C2×#123—28no—
104C2×#123—44no—
105C2×#123—44no—
106C2×#123—44no—
107C2×#121—28no—
108C2×#121—28no—
109C2×#121—24no—
110C2×#121—24no—
111C2×#121—24no—
112C2×#121—24no—
113C2×#121—44no—
114C2×#121—44no—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—28no—
121C22×C4⋊C4—28no—
122C22×C4⋊C4—44no—
123C22×C4⋊C4—44no—
124C22×C4⋊C4D418yes—
125C22×C4⋊C4D418yescomplemented
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2312yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2312yes—
158C22×C42—24no—
159C22×C42—44no—
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2312yes—
163C22×C42C2312yes—
164#399—216no—
165#398—28no—
166#398—216no—
167#397—28no—
168#396—28no—
169#396—216no—
170#396—216no—
171#394—28no—
172#394—216no—
173#390—24no—
174#390—28no—
175#390—44no—
176#389—24no—
177#389—28no—
178#389—28no—
179#389—28no—
180#389—216no—
181#389—44no—
182#386—28no—
183#386—28no—
184#386—24no—
185#386—44no—
186#386D418yescomplemented
187#384—28no—
188#381—28no—
189#380—24no—
190#380—24no—
191#380—28no—
192#380—28no—
193C4×C22⋊C4—24no—
194C4×C22⋊C4—44no—
195C2×#95—28no—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C25C2412yes—
216C25C2411yescharacteristic
217C25C2411yescharacteristic
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—24no—
235C22×D4—22no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—44no—
239C22×D4—42no—
240C22×D4—44no—
241C22×D4C2×D414yes—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—22no—
246C23×C4—24no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—22no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—42no—
266C23×C4—44no—
267C23×C4—44no—
268C23×C4C2×D418yes—
269C23×C4C2×D414yes—
270C23×C4C2×D414yes—
271C23×C4C2×D414yes—
272C23×C4C2×D418yes—
273C23×C4#4114yes—
274C23×C4C2414yes—
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2414yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288#123—432no—
289#123—432no—
290#123—432no—
291#121—416no—
292#121—432no—
293#121—416no—
294C4×D4—416no—
295C2×C4⋊C4—232no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—28no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—416no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—432no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4C2×D414yes—
336C2×C4⋊C4C2×D414yes—
337C2×C4⋊C4C2×D418yes—
338C2×C4⋊C4C2×D418yes—
339C2×C4⋊C4C2×D418yes—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—22no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4C2×D414yes—
387C2×C22⋊C4C2×D418yes—
388C2×C22⋊C4#4114yes—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—416no—
402#95—28no—
403#95—28no—
404#95—24no—
405#95—28no—
406#95—24no—
407#95—28no—
408#95—24no—
409#95—28no—
410#95—24no—
411#95—28no—
412#95—24no—
413#95—24no—
414#95—42no—
415#95—44no—
416#95—42no—
417#95—42no—
418#95—44no—
419#95—44no—
420#95C2×D418yes—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—21no—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—21no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—24no—
442C24—22no—
443C24—24no—
444C24—24no—
445C24—24no—
446C24C22×D412yes—
447C24C22×D412yes—
448C24C22×D412yes—
449C24C22×D412yes—
450C24C2×#4112yes—
451C24C2×#4112yes—
452C24H(5,𝔽2)12yes—
453C24H(5,𝔽2)12yes—
454C24C2511yescharacteristic
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—28no—
458C2×D4—48no—
459C2×D4—48no—
460C2×D4—44no—
461C2×D4—44no—
462C2×D4—44no—
463C2×D4—44no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—48no—
475C2×D4—48no—
476C2×D4—84no—
477C2×D4—88no—
478C2×D4—88no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—216no—
484C22×C4—216no—
485C22×C4—28no—
486C22×C4—216no—
487C22×C4—28no—
488C22×C4—216no—
489C22×C4—216no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—21no—
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—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—216no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—24no—
538C22×C4—21no—
539C22×C4—24no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—44no—
572C22×C4—48no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—88no—
579C22×C4—88no—
580C22×C4#121116yes—
581C22×C4C22×D414yes—
582C22×C4C22×D414yes—
583C22×C4C22×D414yes—
584C22×C4C22×D414yes—
585C22×C4C22×D418yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C2×#4114yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4112yes—
594C22×C4H(5,𝔽2)14yes—
595C22×C42−1+414yes—
596C22×C42−1+414yes—
597C4⋊C4—216no—
598C4⋊C4—216no—
599C4⋊C4—28no—
600C4⋊C4—28no—
601C4⋊C4—48no—
602C4⋊C4—416no—
603C4⋊C4—416no—
604C4⋊C4—48no—
605C4⋊C4—416no—
606C4⋊C4—416no—
607C4⋊C4—416no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—48no—
611C4⋊C4—88no—
612C22⋊C4—28no—
613C22⋊C4—28no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—416no—
618C22⋊C4—416no—
619C22⋊C4—48no—
620C22⋊C4—416no—
621C22⋊C4—48no—
622C22⋊C4—44no—
623C22⋊C4—48no—
624C22⋊C4—44no—
625C22⋊C4—48no—
626C22⋊C4—84no—
627C22⋊C4—88no—
628C22⋊C4—88no—
629C42—48no—
630C42—44no—
631C42—48no—
632C42—48no—
633C23—22no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—22no—
639C23—22no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—24no—
653C23—24no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—41no—
660C23—42no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—44no—
677C23—44no—
678C23—42no—
679C23—44no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—44no—
687C23—44no—
688C23—44no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23C2×#12114yes—
696C23#53214yes—
697C23#54014yes—
698C23D4214yes—
699C23D4214yes—
700C23#54614yes—
701C23#55014yes—
702C23C23×D411yescharacteristic
703C23C23×D411yescharacteristic
704C23C23×D411yescharacteristic
705C23C22×#4111yescharacteristic
706C23C22×#4111yescharacteristic
707C23C2×H(5,𝔽2)12yes—
708C23C2×H(5,𝔽2)11yescharacteristic
709C23C2×H(5,𝔽2)11yescharacteristic
710C23C2×2−1+412yes—
711C23C2×2−1+412yes—
712C23#58512yes—
713D4—416no—
714D4—816no—
715D4—816no—
716D4—88no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—232no—
722C2×C4—28no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—28no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—28no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—416no—
747C2×C4—416no—
748C2×C4—41no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—432no—
755C2×C4—44no—
756C2×C4—41no—
757C2×C4—44no—
758C2×C4—41no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—816no—
802C2×C4—88no—
803C2×C4C2×#12114yes—
804C2×C4C2×#12114yes—
805C2×C4#53414yes—
806C2×C4#53614yes—
807C2×C4#53718yes—
808C2×C4#53918yes—
809C22—28no—
810C22—24no—
811C22—28no—
812C22—24no—
813C22—24no—
814C22—28no—
815C22—28no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—44no—
823C22—44no—
824C22—82no—
825C22—81no—
826C22—82no—
827C22—81no—
828C22—81no—
829C22—81no—
830C22—84no—
831C22—82no—
832C22—82no—
833C22—84no—
834C22—82no—
835C22—82no—
836C22—84no—
837C22—84no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22#242818yes—
842C22C22×#12111yescharacteristic
843C22C2×#53211yescharacteristic
844C22C2×#53411yescharacteristic
845C22C2×#53611yescharacteristic
846C22C2×#53712yes—
847C22C2×#53912yes—
848C22C2×#54011yescharacteristic
849C22#346112yes—
850C22C2×D4211yescharacteristic
851C22C2×D4211yescharacteristic
852C22C2×#54611yescharacteristic
853C22C2×#55011yescharacteristic
854C22#348511yescharacteristic
855C22#348611yescharacteristic
856C22#349612yes—
857C22#349712yes—
858C22#349912yes—
859C22#351512yes—
860C22#352012yes—
861C22#353612yes—
862C22#354212yes—
863C22#354412yes—
864C22#355912yes—
865C4—24no—
866C4—44no—
867C4—48no—
868C4—42no—
869C4—44no—
870C4—44no—
871C4—44no—
872C4—44no—
873C4—44no—
874C4—81no—
875C4—82no—
876C4—84no—
877C4—81no—
878C4#261818yescomplemented
879C2—28no—
880C2—82no—
881C2—162no—
882C2C2×#261811yescharacteristic
883C2C2×#242811yescharacteristic
884C2#3500812yes—
885C2#3515311yescharacteristic
886C2#3750212yes—
887C2#3895012yes—
888C2#3913311yescharacteristic
889C2#3913411yescharacteristic
890C2#3933711yescharacteristic
891C2#3933811yescharacteristic
892C2#3935912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2416C2
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×#2501C2semidirect
2. C2×#2486C2semidirect
4. C2×#2618C2semidirect
5. C22×#389C2semidirect
6. #16550C2semidirect
7. #16549C2semidirect
8. #15141C2semidirect
9. #15137C2semidirect
10. #15131C2semidirect
11. #15126C2semidirect
12. #14927C2semidirect
13. #14926C2semidirect
14. #14698C2semidirect
15. #14256C2semidirect
16. #13907C2semidirect
17. C4×#386C2semidirect
125. C22×C4⋊C4D4semidirect
186. #386D4semidirect
878. C4#2618semidirect

Maximal subgroups

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

subgroupindex
C2×#25012
C2×#24862
C2×#24162
C2×#26182
C22×#3892
#165502
#165492
#151412
#151372
#151312
#151262
#149272
#149262
#146982
#142562
#139072
C4×#3862