Finite Group Databasebeta

← #759299

Subgroups — #759299

Order 512.

6358 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#123C211yesmaximal, characteristic
2C2×#2413C212yesmaximal, complemented
3C2×#2405C211yesmaximal, characteristic
4C22×#385C211yesmaximal, characteristic, complemented
5C2×#2280C211yesmaximal, characteristic, complemented
6#16257C214yesmaximal, complemented
7#15069C212yesmaximal, complemented
8#14912C212yesmaximal, complemented
9#14761C214yesmaximal, complemented
10#14728C212yesmaximal, complemented
11#14726C212yesmaximal, complemented
12#14135C212yesmaximal, complemented
13#14127C211yesmaximal, characteristic, complemented
14#14043C212yesmaximal, complemented
15#13971C212yesmaximal, complemented
16#13869C211yesmaximal, characteristic, complemented
17#13867C211yesmaximal, characteristic
18C24×D4C2211yescharacteristic
19C25×C4C2211yescharacteristic
20C22×#123—28no—
21C22×#123—216no—
22C22×#123C2212yes—
23C22×#123C2212yes—
24C22×#123C2212yes—
25C22×#123C2212yes—
26C22×#123C2212yes—
27C22×#117C2212yescomplemented
28C23×C4⋊C4C2211yescharacteristic
29C23×C4⋊C4C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic, complemented
31C23×C4⋊C4C2211yescharacteristic, complemented
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37#2413—216no—
38#2405—28no—
39C2×#398C2214yescomplemented
40C2×#396C2214yescomplemented
41C2×#394C2214yes—
42C2×#389C2214yescomplemented
43C2×#388C2214yescomplemented
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#385—28no—
48C2×#385C2212yes—
49C2×#385C2212yes—
50C2×#385C2212yes—
51C2×#385C2212yes—
52C2×#385C2212yescomplemented
53C2×#385C2212yescomplemented
54C2×#385C2212yescomplemented
55#2280—28no—
56C2×#381C2212yescomplemented
57C2×#381C2212yescomplemented
58C2×#380C2212yes—
59C2×#380C2212yescomplemented
60C2×#379C2211yescharacteristic
61C2×#379C2212yes—
62C2×#379C2212yes—
63C2×#379C2211yescharacteristic
64C2×C4×C22⋊C4C2212yes—
65C2×C4×C22⋊C4C2212yescomplemented
66C22×#95C2211yescharacteristic, complemented
67C22×#95C2211yescharacteristic, complemented
68#1444C2214yescomplemented
69#1444C2214yescomplemented
70#1442C2214yescomplemented
71#1441C2214yescomplemented
72#1441C2214yescomplemented
73#1440C2214yescomplemented
74#1440C2214yescomplemented
75#1439C2214yescomplemented
76#1439C2214yescomplemented
77#1439C2214yescomplemented
78#1439C2214yescomplemented
79#1439C2214yescomplemented
80#1438C2214yes—
81#1437C2214yescomplemented
82#1436C2214yescomplemented
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C22⋊#95C2212yescomplemented
88C22⋊#95C2212yescomplemented
89C26C2311yescharacteristic
90C26C2311yescharacteristic
91C23×D4—24no—
92C23×D4—28no—
93C23×D4—24no—
94C23×D4—24no—
95C23×D4—44no—
96C23×D4C2312yes—
97C23×D4C2312yes—
98C24×C4—24no—
99C24×C4—24no—
100C24×C4—28no—
101C24×C4—44no—
102C24×C4D418yes—
103C24×C4C2311yescharacteristic
104C24×C4C2311yescharacteristic
105C24×C4C2311yescharacteristic
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C24×C4C2311yescharacteristic
116C2×#123—2128no—
117C2×#123—28no—
118C2×#123—28no—
119C2×#123—28no—
120C2×#123—28no—
121C2×#123—28no—
122C2×#123—28no—
123C2×#123—28no—
124C2×#123—28no—
125C2×#123—28no—
126C2×#123—28no—
127C2×#123—28no—
128C2×#123—28no—
129C2×#123—28no—
130C2×#123—44no—
131C2×#123D4116yes—
132C2×#117—28no—
133C2×#117—28no—
134C2×#117—44no—
135C22×C4⋊C4—24no—
136C22×C4⋊C4—24no—
137C22×C4⋊C4—28no—
138C22×C4⋊C4—28no—
139C22×C4⋊C4—28no—
140C22×C4⋊C4—24no—
141C22×C4⋊C4—24no—
142C22×C4⋊C4—44no—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C22⋊C4—24no—
155C22×C22⋊C4—24no—
156C22×C22⋊C4—24no—
157C22×C22⋊C4—24no—
158C22×C22⋊C4—28no—
159C22×C22⋊C4—28no—
160C22×C22⋊C4—28no—
161C22×C22⋊C4—28no—
162C22×C22⋊C4—24no—
163C22×C22⋊C4—24no—
164C22×C22⋊C4—24no—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2314yes—
174C22×C22⋊C4C2314yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2314yes—
182C22×C22⋊C4C2314yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C42C2314yes—
186#398—216no—
187#396—216no—
188#394—216no—
189#389—216no—
190#388—216no—
191#386—28no—
192#386—28no—
193#386—44no—
194#385—28no—
195#385—28no—
196#385—28no—
197#385—28no—
198#385—28no—
199#385—28no—
200#385—28no—
201#381—28no—
202#381—28no—
203#380—28no—
204#380—28no—
205#379—24no—
206#379—28no—
207#379—28no—
208#379D418yes—
209C4×C22⋊C4—28no—
210C4×C22⋊C4—28no—
211C2×#95—24no—
212C2×#95—24no—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2312yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C25—24no—
230C25—24no—
231C25—24no—
232C25—24no—
233C25—24no—
234C25—22no—
235C25—22no—
236C25—22no—
237C25—24no—
238C25—24no—
239C25—42no—
240C25—42no—
241C25—42no—
242C25—42no—
243C25—42no—
244C25C2×D414yes—
245C25C2×D414yes—
246C25#4114yes—
247C25C2412yes—
248C25C2411yescharacteristic
249C25C2411yescharacteristic
250C25C2411yescharacteristic
251C22×D4—232no—
252C22×D4—24no—
253C22×D4—24no—
254C22×D4—24no—
255C22×D4—24no—
256C22×D4—24no—
257C22×D4—24no—
258C22×D4—24no—
259C22×D4—24no—
260C22×D4—24no—
261C22×D4—24no—
262C22×D4—24no—
263C22×D4—42no—
264C22×D4—42no—
265C22×D4—432no—
266C22×D4—432no—
267C22×D4—416no—
268C22×D4—416no—
269C22×D4C2×D418yes—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—24no—
273C23×C4—232no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—24no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—24no—
291C23×C4—232no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—24no—
297C23×C4—24no—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—24no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—24no—
305C23×C4—24no—
306C23×C4—22no—
307C23×C4—22no—
308C23×C4—22no—
309C23×C4—24no—
310C23×C4—24no—
311C23×C4—24no—
312C23×C4—24no—
313C23×C4—22no—
314C23×C4—22no—
315C23×C4—416no—
316C23×C4—42no—
317C23×C4—42no—
318C23×C4—42no—
319C23×C4—42no—
320C23×C4—42no—
321C23×C4—42no—
322C23×C4—42no—
323C23×C4—42no—
324C23×C4—42no—
325C23×C4—42no—
326C23×C4—42no—
327C23×C4—432no—
328C23×C4—432no—
329C23×C4C2×D414yes—
330C23×C4C2×D414yes—
331C23×C4C2×D414yes—
332C23×C4C2×D414yes—
333C23×C4C2×D414yes—
334C23×C4C2×D418yes—
335C23×C4C2×D414yes—
336C23×C4C2414yes—
337C23×C4C2412yes—
338C23×C4C2412yes—
339C23×C4C2414yes—
340C23×C4C2412yes—
341C23×C4C2412yes—
342C23×C4C2411yescharacteristic
343C23×C4C2411yescharacteristic
344C23×C4C2412yes—
345C23×C4C2412yes—
346C23×C4C2412yes—
347C23×C4C2411yescharacteristic
348C23×C4C2411yescharacteristic
349#123—264no—
350#123—264no—
351#123—264no—
352#123—264no—
353#123—432no—
354#117—432no—
355C2×C4⋊C4—232no—
356C2×C4⋊C4—232no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—28no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—28no—
375C2×C4⋊C4—28no—
376C2×C4⋊C4—28no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—28no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—44no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—44no—
384C2×C4⋊C4—416no—
385C2×C4⋊C4—416no—
386C2×C4⋊C4C2×D418yes—
387C2×C4⋊C4C2×D418yes—
388C2×C22⋊C4—232no—
389C2×C22⋊C4—232no—
390C2×C22⋊C4—232no—
391C2×C22⋊C4—232no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—24no—
422C2×C22⋊C4—28no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—28no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—24no—
431C2×C22⋊C4—28no—
432C2×C22⋊C4—28no—
433C2×C22⋊C4—28no—
434C2×C22⋊C4—28no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—44no—
438C2×C22⋊C4—42no—
439C2×C22⋊C4—42no—
440C2×C22⋊C4—44no—
441C2×C22⋊C4—416no—
442C2×C22⋊C4—44no—
443C2×C22⋊C4—44no—
444C2×C22⋊C4—44no—
445C2×C22⋊C4—44no—
446C2×C22⋊C4C2×D418yes—
447C2×C22⋊C4C2×D418yes—
448C2×C22⋊C4C2×D418yes—
449C2×C22⋊C4C2×D418yes—
450C2×C22⋊C4C2×D418yes—
451C2×C22⋊C4C2×D418yes—
452C2×C22⋊C4#4118yes—
453C2×C42—28no—
454C2×C42—28no—
455C2×C42—44no—
456#95—24no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95—28no—
461#95—28no—
462#95—28no—
463#95—28no—
464#95—28no—
465#95—28no—
466#95—28no—
467#95—28no—
468#95—44no—
469#95—44no—
470#95—44no—
471#95—44no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—28no—
481C24—28no—
482C24—28no—
483C24—28no—
484C24—216no—
485C24—216no—
486C24—216no—
487C24—216no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—28no—
495C24—22no—
496C24—22no—
497C24—22no—
498C24—24no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—24no—
503C24—24no—
504C24—24no—
505C24—44no—
506C24—44no—
507C24—48no—
508C24—48no—
509C24—416no—
510C24—416no—
511C24—416no—
512C24—416no—
513C24—48no—
514C24—48no—
515C24—416no—
516C24—416no—
517C24—44no—
518C24—44no—
519C24—44no—
520C24—44no—
521C24—44no—
522C24—44no—
523C24—48no—
524C24—48no—
525C24—84no—
526C24—84no—
527C24—88no—
528C24—88no—
529C24#121116yes—
530C24C22×D414yes—
531C24C22×D412yes—
532C24C22×D412yes—
533C24C22×D412yes—
534C24C22×D414yes—
535C24C22×D412yes—
536C24C22×D412yes—
537C24C22×D412yes—
538C24C2×#4112yes—
539C24C2×#4112yes—
540C24C2×#4112yes—
541C24C2×#4114yes—
542C24H(5,𝔽2)14yes—
543C242−1+414yes—
544C24C2511yescharacteristic
545C2×D4—216no—
546C2×D4—216no—
547C2×D4—216no—
548C2×D4—216no—
549C2×D4—48no—
550C2×D4—48no—
551C2×D4—48no—
552C2×D4—48no—
553C2×D4—4128no—
554C2×D4—48no—
555C2×D4—48no—
556C2×D4—48no—
557C2×D4—48no—
558C2×D4—48no—
559C2×D4—48no—
560C22×C4—28no—
561C22×C4—28no—
562C22×C4—216no—
563C22×C4—216no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—28no—
575C22×C4—28no—
576C22×C4—28no—
577C22×C4—28no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—28no—
619C22×C4—28no—
620C22×C4—28no—
621C22×C4—28no—
622C22×C4—22no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—22no—
626C22×C4—24no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—24no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—24no—
637C22×C4—24no—
638C22×C4—24no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—44no—
643C22×C4—416no—
644C22×C4—416no—
645C22×C4—416no—
646C22×C4—416no—
647C22×C4—4128no—
648C22×C4—48no—
649C22×C4—48no—
650C22×C4—48no—
651C22×C4—48no—
652C22×C4—48no—
653C22×C4—48no—
654C22×C4—48no—
655C22×C4—48no—
656C22×C4—48no—
657C22×C4—48no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—48no—
669C22×C4—48no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—48no—
677C22×C4—48no—
678C22×C4—84no—
679C22×C4—84no—
680C22×C4#120116yes—
681C22×C4C22×D414yes—
682C22×C4C22×D418yes—
683C22×C4C22×D414yes—
684C22×C4C22×D412yes—
685C22×C4C22×D412yes—
686C22×C4C22×D414yes—
687C22×C4C22×D412yes—
688C22×C4C22×D412yes—
689C22×C4C22×D414yes—
690C22×C4C22×D414yes—
691C22×C4C2×#4114yes—
692C22×C4C2×#4114yes—
693C4⋊C4—216no—
694C4⋊C4—216no—
695C4⋊C4—216no—
696C4⋊C4—216no—
697C4⋊C4—416no—
698C4⋊C4—416no—
699C4⋊C4—416no—
700C4⋊C4—48no—
701C4⋊C4—48no—
702C4⋊C4—48no—
703C4⋊C4—48no—
704C22⋊C4—216no—
705C22⋊C4—216no—
706C22⋊C4—216no—
707C22⋊C4—216no—
708C22⋊C4—216no—
709C22⋊C4—216no—
710C22⋊C4—216no—
711C22⋊C4—216no—
712C22⋊C4—216no—
713C22⋊C4—216no—
714C22⋊C4—48no—
715C22⋊C4—416no—
716C22⋊C4—416no—
717C22⋊C4—48no—
718C22⋊C4—48no—
719C22⋊C4—48no—
720C22⋊C4—48no—
721C22⋊C4—48no—
722C22⋊C4—88no—
723C22⋊C4—88no—
724C42—416no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—24no—
734C23—24no—
735C23—24no—
736C23—28no—
737C23—28no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—28no—
742C23—28no—
743C23—24no—
744C23—24no—
745C23—28no—
746C23—28no—
747C23—28no—
748C23—28no—
749C23—22no—
750C23—232no—
751C23—22no—
752C23—232no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—24no—
764C23—24no—
765C23—24no—
766C23—28no—
767C23—28no—
768C23—416no—
769C23—416no—
770C23—464no—
771C23—464no—
772C23—416no—
773C23—416no—
774C23—416no—
775C23—416no—
776C23—416no—
777C23—416no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—44no—
791C23—44no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—44no—
800C23—832no—
801C23—832no—
802C23—88no—
803C23—88no—
804C23—88no—
805C23—88no—
806C23C2×#12014yes—
807C23C2×#12114yes—
808C23C2×#12114yes—
809C23C2×#12114yes—
810C23#52514yes—
811C23#53414yes—
812C23#53614yes—
813C23D4218yes—
814C23#54618yes—
815C23#54718yes—
816C23#55218yes—
817C23C23×D411yescharacteristic
818C23C23×D412yes—
819C23C23×D411yescharacteristic
820C23C22×#4111yescharacteristic
821C23C22×#4112yes—
822C23C2×H(5,𝔽2)12yes—
823C23C2×2−1+412yes—
824C23#58512yes—
825C23#58512yes—
826D4—432no—
827D4—432no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—232no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—24no—
835C2×C4—24no—
836C2×C4—24no—
837C2×C4—24no—
838C2×C4—24no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—28no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—28no—
852C2×C4—28no—
853C2×C4—28no—
854C2×C4—28no—
855C2×C4—28no—
856C2×C4—28no—
857C2×C4—416no—
858C2×C4—416no—
859C2×C4—416no—
860C2×C4—416no—
861C2×C4—416no—
862C2×C4—416no—
863C2×C4—416no—
864C2×C4—416no—
865C2×C4—416no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—416no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—44no—
884C2×C4—44no—
885C2×C4—44no—
886C2×C4—44no—
887C2×C4—44no—
888C2×C4—44no—
889C2×C4—44no—
890C2×C4—44no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—44no—
898C2×C4—44no—
899C2×C4—44no—
900C2×C4—44no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—44no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—88no—
909C2×C4—88no—
910C2×C4C2×#12014yes—
911C2×C4C2×#12014yes—
912C22—24no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—24no—
917C22—216no—
918C22—216no—
919C22—216no—
920C22—216no—
921C22—24no—
922C22—24no—
923C22—24no—
924C22—24no—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—24no—
929C22—24no—
930C22—24no—
931C22—464no—
932C22—42no—
933C22—48no—
934C22—48no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—44no—
939C22—48no—
940C22—48no—
941C22—44no—
942C22—44no—
943C22—832no—
944C22—82no—
945C22—82no—
946C22—84no—
947C22—84no—
948C22—82no—
949C22—82no—
950C22#241018yes—
951C22#241318yescomplemented
952C22C22×#12011yescharacteristic
953C22C22×#12111yescharacteristic
954C22C2×#52511yescharacteristic
955C22C2×#53411yescharacteristic
956C22C2×#53611yescharacteristic
957C22#344911yescharacteristic
958C22#344911yescharacteristic
959C22C2×D4212yes—
960C22C2×#54612yes—
961C22C2×#54712yes—
962C22D4×#4114yes—
963C22C2×#55212yes—
964C22#348512yes—
965C22#348914yes—
966C22#349112yes—
967C22#351314yes—
968C22#353514yes—
969C4—24no—
970C4—24no—
971C4—42no—
972C4—42no—
973C4—44no—
974C4—48no—
975C4—44no—
976C4—44no—
977C4—44no—
978C4—44no—
979C4—82no—
980C4—82no—
981C4—84no—
982C2—28no—
983C2—28no—
984C2—44no—
985C2—84no—
986C2C2×#241011yescharacteristic
987C2C2×#241311yescharacteristic
988C2#3473611yescharacteristic
989C2#3506211yescharacteristic
990C2#3508911yescharacteristic
991C2#3530511yescharacteristic
992C2#3744111yescharacteristic
993C2#5899514yes—
994C2#5901214yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2413C2semidirect
4. C22×#385C2semidirect
5. C2×#2280C2semidirect
6. #16257C2semidirect
7. #15069C2semidirect
8. #14912C2semidirect
9. #14761C2semidirect
10. #14728C2semidirect
11. #14726C2semidirect
12. #14135C2semidirect
13. #14127C2semidirect
14. #14043C2semidirect
15. #13971C2semidirect
16. #13869C2semidirect
27. C22×#117C22semidirect
30. C23×C4⋊C4C22semidirect
31. C23×C4⋊C4C22semidirect
39. C2×#398C22semidirect
40. C2×#396C22semidirect
42. C2×#389C22semidirect
43. C2×#388C22semidirect
52. C2×#385C22semidirect
53. C2×#385C22semidirect
54. C2×#385C22semidirect
56. C2×#381C22semidirect
57. C2×#381C22semidirect
59. C2×#380C22semidirect
65. C2×C4×C22⋊C4C22semidirect
66. C22×#95C22semidirect
67. C22×#95C22semidirect
68. #1444C22semidirect
69. #1444C22semidirect
70. #1442C22semidirect
71. #1441C22semidirect
72. #1441C22semidirect
73. #1440C22semidirect
74. #1440C22semidirect
75. #1439C22semidirect
76. #1439C22semidirect
77. #1439C22semidirect
78. #1439C22semidirect
79. #1439C22semidirect
81. #1437C22semidirect
82. #1436C22semidirect
87. C22⋊#95C22semidirect
88. C22⋊#95C22semidirect
951. C22#2413semidirect

Maximal subgroups

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

subgroupindex
C23×#1232
C2×#24132
C2×#24052
C22×#3852
C2×#22802
#162572
#150692
#149122
#147612
#147282
#147262
#141352
#141272
#140432
#139712
#138692
#138672