Finite Group Databasebeta

← #688039

Subgroups — #688039

Order 512.

5212 conjugacy classes of subgroups.

The subgroup lattice has 899 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#536C211yesmaximal, characteristic, complemented
2C2×#2407C211yesmaximal, characteristic
3C2×#2429C212yesmaximal, complemented
4C2×#2409C211yesmaximal, characteristic, complemented
5C2×#2341C211yesmaximal, characteristic, complemented
6#16265C212yesmaximal, complemented
7#16264C212yesmaximal, complemented
8#15272C214yesmaximal, complemented
9#15271C214yesmaximal, complemented
10#15226C212yesmaximal, complemented
11#15215C212yesmaximal, complemented
12#14765C212yesmaximal, complemented
13#14763C212yesmaximal, complemented
14#14264C211yesmaximal, characteristic, complemented
15#14024C212yesmaximal, complemented
16#13922C211yesmaximal, characteristic, complemented
17#13839C211yesmaximal, characteristic, complemented
18C23×#41C2211yescharacteristic
19C24×Q8C2211yescharacteristic
20C2×#536—28no—
21C2×#536—216no—
22C22×C4⋊Q8C2212yes—
23C22×#124C2212yes—
24C22×#123C2214yes—
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2212yes—
27C22×C22⋊Q8C2212yes—
28C22×C22⋊Q8C2212yes—
29C22×#121C2211yescharacteristic
30C22×C4×Q8C2212yes—
31C22×C4×D4C2211yescharacteristic
32C22×#117C2211yescharacteristic
33#2429—216no—
34#2409—28no—
35#2407—28no—
36C2×#398C2214yes—
37C2×#396C2214yes—
38C2×#395C2212yes—
39C2×#394C2212yes—
40C2×#393C2212yes—
41C2×#392C2212yes—
42#2341—28no—
43C2×#391C2212yes—
44C2×#391C2212yes—
45C2×#391C2211yescharacteristic
46C2×#391C2212yes—
47C2×#390C2212yes—
48C2×#390C2214yes—
49C2×#390C2211yescharacteristic
50C2×#389C2212yes—
51C2×#389C2214yes—
52C2×#388C2214yes—
53C2×#386C2212yes—
54C2×#386C2212yes—
55C2×#385C2212yes—
56C2×#385C2212yes—
57C2×#380C2212yes—
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2212yes—
62C2×C4×C22⋊C4C2212yes—
63#1446C2212yes—
64#1446C2212yes—
65#1444C2212yes—
66#1442C2212yes—
67#1441C2211yescharacteristic
68#1441C2211yescharacteristic
69#1441C2214yes—
70#1441C2214yes—
71#1440C2212yes—
72#1440C2214yes—
73#1440C2214yes—
74#1439C2211yescharacteristic
75#1439C2211yescharacteristic
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1438C2212yes—
82#1438C2214yes—
83#1438C2214yes—
84#1436C2214yes—
85#1436C2214yes—
86C4⋊#95C2212yes—
87C22⋊#95C2214yes—
88C4×#95C2212yes—
89C22×#41—28no—
90C22×#41—24no—
91C22×#41—24no—
92C22×#41—44no—
93C22×#41D418yes—
94C23×Q8—28no—
95C23×Q8—24no—
96C23×Q8—24no—
97C23×Q8—24no—
98C23×Q8—44no—
99C23×Q8C2312yes—
100C23×Q8C2312yes—
101C23×Q8C2311yescharacteristic
102C23×D4C2311yescharacteristic
103C23×D4C2311yescharacteristic
104C23×D4C2312yes—
105C23×D4C2312yes—
106C24×C4C2311yescharacteristic
107C24×C4C2312yes—
108C24×C4C2312yes—
109C24×C4C2311yescharacteristic
110#536—2128no—
111C2×C4⋊Q8—28no—
112C2×C4⋊Q8—28no—
113C2×C4⋊Q8D4116yescomplemented
114C2×#124—28no—
115C2×#124—28no—
116C2×#124—28no—
117C2×#123—216no—
118C2×#123—216no—
119C2×#123—216no—
120C2×C22⋊Q8—28no—
121C2×C22⋊Q8—28no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—28no—
124C2×C22⋊Q8—28no—
125C2×C22⋊Q8—216no—
126C2×C22⋊Q8—216no—
127C2×C22⋊Q8—28no—
128C2×C22⋊Q8—44no—
129C2×#121—24no—
130C2×#121—44no—
131C2×C4×Q8—28no—
132C2×C4×Q8—28no—
133C2×C4×Q8—44no—
134C2×C4×D4—24no—
135C2×C4×D4—24no—
136C2×C4×D4—24no—
137C2×#117—24no—
138C2×#117—28no—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2314yes—
146C22×C4⋊C4C2314yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2314yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2312yes—
168C22×C42C2311yescharacteristic
169C22×C42C2312yes—
170C22×C42C2314yes—
171C22×C42C2312yes—
172#398—216no—
173#396—216no—
174#395—28no—
175#394—28no—
176#393—28no—
177#392—28no—
178#391—24no—
179#391—28no—
180#391—28no—
181#391—44no—
182#390—24no—
183#390—28no—
184#390—216no—
185#389—216no—
186#389—28no—
187#388—216no—
188#386—28no—
189#386—28no—
190#385—28no—
191#385—28no—
192#380—24no—
193#380—28no—
194#380D418yescomplemented
195C4×C22⋊C4—24no—
196C4×C22⋊C4—28no—
197C4×C22⋊C4—28no—
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2311yescharacteristic
210C2×#95C2311yescharacteristic
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2312yes—
219C25C2412yes—
220C25C2411yescharacteristic
221C25C2411yescharacteristic
222C2×#41—232no—
223C2×#41—232no—
224C2×#41—416no—
225C2×#41—432no—
226C2×#41—432no—
227C22×Q8—232no—
228C22×Q8—22no—
229C22×Q8—28no—
230C22×Q8—24no—
231C22×Q8—24no—
232C22×Q8—24no—
233C22×Q8—24no—
234C22×Q8—24no—
235C22×Q8—22no—
236C22×Q8—24no—
237C22×Q8—24no—
238C22×Q8—24no—
239C22×Q8—24no—
240C22×Q8—24no—
241C22×Q8—44no—
242C22×Q8—432no—
243C22×Q8—432no—
244C22×Q8—416no—
245C22×Q8—416no—
246C22×Q8C2×D418yes—
247C22×Q8C2×D418yes—
248C22×Q8C2×D414yes—
249C22×D4—22no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—24no—
256C22×D4—24no—
257C22×D4—28no—
258C22×D4—24no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—24no—
262C22×D4—22no—
263C22×D4—41no—
264C22×D4—41no—
265C22×D4—44no—
266C22×D4—44no—
267C22×D4—42no—
268C22×D4—44no—
269C22×D4C2×D414yes—
270C22×D4C2×D418yes—
271C23×C4—24no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—28no—
275C23×C4—28no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—24no—
283C23×C4—22no—
284C23×C4—24no—
285C23×C4—44no—
286C23×C4—44no—
287C23×C4C2×D418yes—
288C23×C4C2×D414yes—
289C23×C4C2×D414yes—
290C23×C4#4114yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2414yes—
298C23×C4C2412yes—
299C23×C4C2414yes—
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C4⋊Q8—264no—
306#124—264no—
307#123—2128no—
308C22⋊Q8—264no—
309C22⋊Q8—264no—
310C22⋊Q8—432no—
311C22⋊Q8—416no—
312#121—416no—
313C4×Q8—432no—
314C4×D4—416no—
315#117—232no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—28no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—28no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4C2×D418yes—
345C2×C4⋊C4C2×D4116yes—
346C2×C4⋊C4C2×D4116yes—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4C2×D418yes—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—28no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—28no—
402C2×C42—22no—
403C2×C42—24no—
404C2×C42—44no—
405C2×C42C2×D418yes—
406#95—22no—
407#95—22no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—28no—
413#95—24no—
414#95—28no—
415#95—28no—
416#95—28no—
417#95—28no—
418#95—24no—
419#95—24no—
420#95—42no—
421#95—44no—
422#95—44no—
423#95—42no—
424#95—44no—
425#95—44no—
426#95C2×D418yes—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—21no—
431C24—21no—
432C24—22no—
433C24—21no—
434C24—21no—
435C24—22no—
436C24—21no—
437C24—24no—
438C24—22no—
439C24—21no—
440C24—21no—
441C24—22no—
442C24—22no—
443C24—24no—
444C24—22no—
445C24—22no—
446C24—24no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—21no—
452C24—24no—
453C24—22no—
454C24—21no—
455C24C22×D414yes—
456C24C22×D412yes—
457C24C22×D412yes—
458C24C2×#4112yes—
459C242−1+412yes—
460C24C2511yescharacteristic
461#41—4128no—
462C2×Q8—216no—
463C2×Q8—216no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—216no—
467C2×Q8—216no—
468C2×Q8—216no—
469C2×Q8—216no—
470C2×Q8—416no—
471C2×Q8—416no—
472C2×Q8—48no—
473C2×Q8—4128no—
474C2×Q8—48no—
475C2×Q8—48no—
476C2×Q8—48no—
477C2×Q8—48no—
478C2×Q8—48no—
479C2×Q8#120116yes—
480C2×D4—28no—
481C2×D4—216no—
482C2×D4—216no—
483C2×D4—28no—
484C2×D4—28no—
485C2×D4—28no—
486C2×D4—48no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—416no—
490C2×D4—416no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—84no—
500C2×D4—88no—
501C2×D4—88no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—216no—
510C22×C4—216no—
511C22×C4—216no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—21no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—24no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—216no—
549C22×C4—216no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—48no—
578C22×C4—416no—
579C22×C4—416no—
580C22×C4—416no—
581C22×C4—416no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4#121116yes—
590C22×C4C22×D414yes—
591C22×C4C22×D418yes—
592C22×C4C22×D418yes—
593C22×C4C22×D414yes—
594C22×C4C22×D414yes—
595C22×C4C22×D418yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C22×D414yes—
600C22×C4C22×D412yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4112yes—
603C22×C4H(5,𝔽2)14yes—
604C22×C42−1+412yes—
605C22×C42−1+414yes—
606C4⋊C4—28no—
607C4⋊C4—28no—
608C4⋊C4—232no—
609C4⋊C4—232no—
610C4⋊C4—216no—
611C4⋊C4—416no—
612C4⋊C4—416no—
613C4⋊C4—416no—
614C4⋊C4—44no—
615C4⋊C4—48no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C22⋊C4—216no—
619C22⋊C4—216no—
620C22⋊C4—232no—
621C22⋊C4—232no—
622C22⋊C4—48no—
623C22⋊C4—416no—
624C22⋊C4—416no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—44no—
630C22⋊C4—48no—
631C22⋊C4—44no—
632C22⋊C4—88no—
633C22⋊C4—84no—
634C22⋊C4—84no—
635C42—216no—
636C42—416no—
637C42—44no—
638C42—48no—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—22no—
658C23—24no—
659C23—22no—
660C23—24no—
661C23—22no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—44no—
678C23—42no—
679C23—44no—
680C23—44no—
681C23—42no—
682C23—42no—
683C23—41no—
684C23—42no—
685C23—44no—
686C23—42no—
687C23—44no—
688C23—44no—
689C23—41no—
690C23—42no—
691C23—41no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—44no—
696C23—44no—
697C23—42no—
698C23—41no—
699C23—41no—
700C23—44no—
701C23—42no—
702C23—42no—
703C23—44no—
704C23—44no—
705C23—42no—
706C23—44no—
707C23C2×#12114yes—
708C23C23×D411yescharacteristic
709C23C23×D412yes—
710C23C23×D411yescharacteristic
711C23C22×#4111yescharacteristic
712C23C2×H(5,𝔽2)12yes—
713C23C2×2−1+412yes—
714C23C2×2−1+411yescharacteristic
715C23C2×2−1+411yescharacteristic
716C23#58512yes—
717C23#58511yescharacteristic
718C23#58511yescharacteristic
719Q8—232no—
720Q8—432no—
721Q8—432no—
722D4—432no—
723D4—416no—
724D4—416no—
725D4—816no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—28no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—28no—
734C2×C4—232no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—28no—
738C2×C4—28no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—28no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—28no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—432no—
754C2×C4—432no—
755C2×C4—41no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—88no—
807C2×C4C2×#12018yes—
808C2×C4C2×#12014yes—
809C2×C4C2×#12114yes—
810C2×C4C2×#12114yes—
811C2×C4#53414yes—
812C2×C4D4218yes—
813C2×C4#54618yes—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—42no—
818C22—44no—
819C22—42no—
820C22—42no—
821C22—44no—
822C22—42no—
823C22—44no—
824C22—44no—
825C22—42no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—42no—
830C22—44no—
831C22—44no—
832C22—44no—
833C22—42no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—81no—
838C22—84no—
839C22—81no—
840C22—81no—
841C22—82no—
842C22—84no—
843C22—84no—
844C22—81no—
845C22—84no—
846C22—82no—
847C22C22×#12011yescharacteristic
848C22C22×#12111yescharacteristic
849C22C2×#53411yescharacteristic
850C22#346112yes—
851C22C2×D4212yes—
852C22C2×#54612yes—
853C22#348511yescharacteristic
854C22#348611yescharacteristic
855C22#348612yes—
856C22#348712yes—
857C22#348911yescharacteristic
858C22#348911yescharacteristic
859C22#348912yes—
860C22#349511yescharacteristic
861C22#349511yescharacteristic
862C22#349712yes—
863C22#349712yes—
864C22#349911yescharacteristic
865C22#350011yescharacteristic
866C22#355212yes—
867C22#355412yes—
868C22#356112yes—
869C22#356212yes—
870C4—24no—
871C4—28no—
872C4—42no—
873C4—48no—
874C4—44no—
875C4—44no—
876C4—48no—
877C4—44no—
878C4—81no—
879C4—82no—
880C4—82no—
881C4—82no—
882C4—81no—
883C4#241018yes—
884C2—44no—
885C2—82no—
886C2—84no—
887C2C2×#241011yescharacteristic
888C2#3530811yescharacteristic
889C2#3563311yescharacteristic
890C2#3568711yescharacteristic
891C2#3575711yescharacteristic
892C2#3774912yes—
893C2#3941712yes—
894C2#4291711yescharacteristic
895C2#4294311yescharacteristic
896C2#4524112yes—
897C2#4524812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2407C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#536C2semidirect
3. C2×#2429C2semidirect
4. C2×#2409C2semidirect
5. C2×#2341C2semidirect
6. #16265C2semidirect
7. #16264C2semidirect
8. #15272C2semidirect
9. #15271C2semidirect
10. #15226C2semidirect
11. #15215C2semidirect
12. #14765C2semidirect
13. #14763C2semidirect
14. #14264C2semidirect
15. #14024C2semidirect
16. #13922C2semidirect
17. #13839C2semidirect
113. C2×C4⋊Q8D4semidirect
194. #380D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5362
C2×#24072
C2×#24292
C2×#24092
C2×#23412
#162652
#162642
#152722
#152712
#152262
#152152
#147652
#147632
#142642
#140242
#139222
#138392