Finite Group Databasebeta

← #1395633

Subgroups — #1395633

Order 512.

5208 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#547C211yesmaximal, characteristic, complemented
2C2×#2407C212yesmaximal, complemented
3C2×#2422C211yesmaximal, characteristic, complemented
4#16657C214yesmaximal, complemented
5#16654C214yesmaximal, complemented
6#16259C212yesmaximal, complemented
7#16250C212yesmaximal, complemented
8#15188C211yesmaximal, characteristic, complemented
9#15182C212yesmaximal, complemented
10#15178C211yesmaximal, characteristic, complemented
11#15177C212yesmaximal, complemented
12#15129C211yesmaximal, characteristic, complemented
13#15092C212yesmaximal, complemented
14#14256C212yesmaximal, complemented
15#13937C212yesmaximal, complemented
16#13916C211yesmaximal, characteristic, complemented
17C4×#392C211yesmaximal, characteristic, complemented
18C23×#41C2212yes—
19C2×#547—216no—
20C2×#547—28no—
21C22×C4⋊Q8C2211yescharacteristic
22C22×#123C2214yes—
23C22×#123C2212yes—
24C22×C22⋊Q8C2212yes—
25C22×C22⋊Q8C2212yes—
26C22×#121C2211yescharacteristic
27C22×#121C2212yes—
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2212yes—
31C23×C4⋊C4C2212yes—
32#2422—28no—
33#2407—216no—
34C2×#397C2212yes—
35C2×#394C2212yes—
36C2×#394C2214yes—
37C2×#394C2212yes—
38C2×#392C2214yes—
39C2×#392C2211yescharacteristic
40C2×#391C2212yes—
41C2×#391C2212yes—
42C2×#391C2212yes—
43C2×#390C2212yes—
44C2×#390C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#386C2214yes—
47C2×#385C2214yes—
48C2×#385C2212yes—
49C2×#384C2211yescharacteristic
50C2×#381C2212yes—
51C2×#380C2212yes—
52C2×#380C2211yescharacteristic
53C2×#380C2212yes—
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2212yes—
56#1444C2212yes—
57#1444C2214yes—
58#1444C2211yescharacteristic
59#1444C2212yes—
60#1442C2214yes—
61#1441C2214yes—
62#1441C2214yes—
63#1441C2212yes—
64#1441C2212yes—
65#1441C2212yes—
66#1440C2214yes—
67#1440C2214yes—
68#1439C2212yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2212yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2211yescharacteristic
75#1439C2212yes—
76#1438C2212yes—
77#1438C2214yes—
78#1438C2214yes—
79#1438C2214yes—
80#1438C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2212yes—
83C22⋊#95C2214yes—
84C22⋊#95C2214yes—
85C22⋊#95C2212yes—
86C4×#95C2211yescharacteristic
87C22×#41—28no—
88C22×#41—28no—
89C22×#41—44no—
90C22×#41—44no—
91C22×#41—44no—
92C22×#41—44no—
93C22×#41D4116yescomplemented
94C23×Q8C2312yes—
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C23×D4C2314yes—
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102C24×C4C2312yes—
103C24×C4C2314yes—
104#547—2128no—
105C2×C4⋊Q8—28no—
106C2×C4⋊Q8—24no—
107C2×#123—216no—
108C2×#123—216no—
109C2×#123—28no—
110C2×#123—216no—
111C2×#123—28no—
112C2×#123—44no—
113C2×C22⋊Q8—28no—
114C2×C22⋊Q8—28no—
115C2×C22⋊Q8—28no—
116C2×C22⋊Q8—28no—
117C2×C22⋊Q8—44no—
118C2×C22⋊Q8—44no—
119C2×#121—216no—
120C2×#121—28no—
121C2×#121—28no—
122C2×#121—24no—
123C2×C4×D4—28no—
124C2×C4×D4—28no—
125C2×C4×D4—28no—
126C2×C4×D4—24no—
127C2×C4×D4—44no—
128C2×C4×D4—44no—
129C2×C4×D4D418yescomplemented
130C22×C4⋊C4—216no—
131C22×C4⋊C4—28no—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C42C2312yes—
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166#397—28no—
167#394—216no—
168#394—28no—
169#394—44no—
170#392—216no—
171#392—24no—
172#391—28no—
173#391—44no—
174#391—44no—
175#390—28no—
176#390—24no—
177#389—24no—
178#386—216no—
179#385—216no—
180#385—28no—
181#384—24no—
182#381—44no—
183#380—28no—
184#380—24no—
185#380—44no—
186C4×C22⋊C4—24no—
187C4×C22⋊C4—44no—
188C2×#95C2311yescharacteristic
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2311yescharacteristic
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2311yescharacteristic
197C2×#95C2311yescharacteristic
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C25C2412yes—
210C25C2411yescharacteristic
211C25C2412yes—
212C2×#41—264no—
213C2×#41—432no—
214C2×#41—432no—
215C2×#41—432no—
216C2×#41—432no—
217C2×#41—432no—
218C2×#41—432no—
219C22×Q8—24no—
220C22×Q8—24no—
221C22×Q8—24no—
222C22×Q8—24no—
223C22×Q8—24no—
224C22×Q8—24no—
225C22×Q8C2×D418yes—
226C22×D4—24no—
227C22×D4—28no—
228C22×D4—28no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—28no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—24no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—24no—
241C22×D4—42no—
242C22×D4—42no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—42no—
251C22×D4—44no—
252C22×D4C2×D418yes—
253C22×D4C2×D414yes—
254C22×D4C2×D4116yes—
255C23×C4—28no—
256C23×C4—28no—
257C23×C4—28no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—22no—
271C23×C4—44no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4C2×D418yes—
277C23×C4C2×D418yes—
278C23×C4C2×D4116yes—
279C23×C4C2412yes—
280C23×C4C2414yes—
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2414yes—
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2412yes—
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C4⋊Q8—232no—
294#123—2128no—
295#123—432no—
296C22⋊Q8—264no—
297C22⋊Q8—432no—
298#121—264no—
299#121—416no—
300C4×D4—232no—
301C4×D4—232no—
302C4×D4—432no—
303C2×C4⋊C4—264no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4C2×D414yes—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—41no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4C2×D418yes—
388C2×C22⋊C4#4114yescomplemented
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—22no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42C2×D414yes—
396#95—22no—
397#95—22no—
398#95—28no—
399#95—24no—
400#95—28no—
401#95—28no—
402#95—24no—
403#95—22no—
404#95—22no—
405#95—24no—
406#95—24no—
407#95—42no—
408#95—44no—
409#95—42no—
410#95—42no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95—44no—
416#95—44no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—24no—
422C24—22no—
423C24—24no—
424C24—22no—
425C24—24no—
426C24—21no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—21no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—21no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—22no—
450C24C22×D414yes—
451C24C22×D418yes—
452C24C22×D414yes—
453C24C2×#4112yes—
454C24C2511yescharacteristic
455#41—4256no—
456C2×Q8—216no—
457C2×Q8—216no—
458C2×Q8—216no—
459C2×Q8—48no—
460C2×Q8—48no—
461C2×Q8—48no—
462C2×Q8—48no—
463C2×D4—28no—
464C2×D4—232no—
465C2×D4—216no—
466C2×D4—216no—
467C2×D4—28no—
468C2×D4—28no—
469C2×D4—416no—
470C2×D4—416no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—44no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—416no—
481C2×D4—416no—
482C2×D4—416no—
483C2×D4—416no—
484C2×D4—48no—
485C2×D4—48no—
486C2×D4—416no—
487C2×D4—48no—
488C2×D4—44no—
489C2×D4—84no—
490C2×D4—88no—
491C2×D4#120116yes—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—216no—
495C22×C4—232no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—216no—
531C22×C4—216no—
532C22×C4—216no—
533C22×C4—216no—
534C22×C4—21no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—48no—
566C22×C4—416no—
567C22×C4—416no—
568C22×C4—416no—
569C22×C4—416no—
570C22×C4—416no—
571C22×C4—416no—
572C22×C4—416no—
573C22×C4—416no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—44no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4C22×D412yes—
584C22×C4C22×D414yes—
585C22×C4C22×D418yes—
586C22×C4C22×D414yes—
587C22×C4C22×D412yes—
588C22×C4C22×D414yes—
589C22×C4C22×D412yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4H(5,𝔽2)12yes—
593C22×C4H(5,𝔽2)12yes—
594C22×C4H(5,𝔽2)14yes—
595C22×C4H(5,𝔽2)12yes—
596C22×C42−1+414yes—
597C22×C42−1+412yes—
598C4⋊C4—28no—
599C4⋊C4—216no—
600C4⋊C4—232no—
601C4⋊C4—216no—
602C4⋊C4—28no—
603C4⋊C4—48no—
604C4⋊C4—48no—
605C4⋊C4—416no—
606C4⋊C4—44no—
607C4⋊C4—48no—
608C4⋊C4—44no—
609C4⋊C4—48no—
610C4⋊C4—84no—
611C22⋊C4—216no—
612C22⋊C4—232no—
613C22⋊C4—216no—
614C22⋊C4—28no—
615C22⋊C4—44no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—416no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—416no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—88no—
627C22⋊C4—88no—
628C22⋊C4—88no—
629C42—28no—
630C42—48no—
631C42—44no—
632C23—28no—
633C23—28no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—28no—
638C23—24no—
639C23—28no—
640C23—24no—
641C23—28no—
642C23—28no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—22no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—42no—
657C23—42no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—42no—
663C23—44no—
664C23—42no—
665C23—44no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—41no—
674C23—41no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—41no—
679C23—42no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—41no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—41no—
704C23—42no—
705C23—41no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23C2×#12018yes—
713C23C23×D412yes—
714C23C23×D411yescharacteristic
715C23C22×#4111yescharacteristic
716C23C2×H(5,𝔽2)11yescharacteristic
717C23C2×H(5,𝔽2)11yescharacteristic
718C23C2×H(5,𝔽2)12yes—
719C23C2×H(5,𝔽2)11yescharacteristic
720C23C2×2−1+411yescharacteristic
721C23C2×2−1+412yes—
722C23#58512yes—
723C23#58511yescharacteristic
724Q8—432no—
725D4—232no—
726D4—416no—
727D4—464no—
728D4—432no—
729D4—816no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—28no—
738C2×C4—24no—
739C2×C4—28no—
740C2×C4—24no—
741C2×C4—28no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—432no—
754C2×C4—464no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—44no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—432no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—44no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—88no—
810C2×C4C2×#12014yes—
811C2×C4#53418yes—
812C2×C4#53418yes—
813C2×C4#53514yes—
814C2×C4#53514yes—
815C2×C4#54614yes—
816C22—28no—
817C22—28no—
818C22—28no—
819C22—48no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—48no—
824C22—48no—
825C22—44no—
826C22—48no—
827C22—44no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—44no—
832C22—42no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—44no—
837C22—44no—
838C22—44no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—81no—
844C22—82no—
845C22—82no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—81no—
850C22—82no—
851C22—81no—
852C22—81no—
853C22C22×#12011yescharacteristic
854C22C2×#53412yes—
855C22C2×#53412yes—
856C22C2×#53511yescharacteristic
857C22C2×#53511yescharacteristic
858C22C2×#54611yescharacteristic
859C22D4×#4112yes—
860C22#348511yescharacteristic
861C22#348812yes—
862C22#348911yescharacteristic
863C22#348912yes—
864C22#349912yes—
865C22#349911yescharacteristic
866C22#350611yescharacteristic
867C22#351111yescharacteristic
868C22#352012yes—
869C22#353912yes—
870C22#354112yes—
871C22#354112yes—
872C22#354611yescharacteristic
873C22#354812yes—
874C22#354811yescharacteristic
875C22#355412yes—
876C4—24no—
877C4—42no—
878C4—44no—
879C4—42no—
880C4—44no—
881C4—42no—
882C4—44no—
883C4—48no—
884C4—82no—
885C4—82no—
886C4—82no—
887C4—84no—
888C4—81no—
889C4#261318yes—
890C2—48no—
891C2—82no—
892C2—84no—
893C2C2×#261311yescharacteristic
894C2#3608511yescharacteristic
895C2#3621211yescharacteristic
896C2#3895111yescharacteristic
897C2#3947111yescharacteristic
898C2#3988412yes—
899C2#3995612yes—
900C2#4264811yescharacteristic
901C2#4267911yescharacteristic
902C2#4291612yes—
903C2#4292712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#547C2semidirect
2. C2×#2407C2semidirect
3. C2×#2422C2semidirect
4. #16657C2semidirect
5. #16654C2semidirect
6. #16259C2semidirect
7. #16250C2semidirect
8. #15188C2semidirect
9. #15182C2semidirect
10. #15178C2semidirect
11. #15177C2semidirect
12. #15129C2semidirect
13. #15092C2semidirect
14. #14256C2semidirect
15. #13937C2semidirect
16. #13916C2semidirect
17. C4×#392C2semidirect
93. C22×#41D4semidirect
129. C2×C4×D4D4semidirect
388. C2×C22⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
C22×#5472
C2×#24072
C2×#24222
#166572
#166542
#162592
#162502
#151882
#151822
#151782
#151772
#151292
#150922
#142562
#139372
#139162
C4×#3922