Finite Group Databasebeta

← #759503

Subgroups — #759503

Order 512.

4932 conjugacy classes of subgroups.

The subgroup lattice has 1035 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2486C211yesmaximal, characteristic, complemented
2C2×#2412C212yesmaximal
3C2×C4×#120C211yesmaximal, characteristic
4C22×#380C211yesmaximal, characteristic, complemented
5C22×#380C211yesmaximal, characteristic, complemented
6#16401C212yesmaximal, complemented
7#16399C212yesmaximal, complemented
8#15132C212yesmaximal, complemented
9#15129C212yesmaximal, complemented
10#14935C212yesmaximal, complemented
11#14927C212yesmaximal, complemented
12#14766C212yesmaximal, complemented
13#14735C212yesmaximal, complemented
14#14130C211yesmaximal, characteristic, complemented
15#13907C212yesmaximal, complemented
16#13904C211yesmaximal, characteristic, complemented
17#13872C212yesmaximal, complemented
18#13872C211yesmaximal, characteristic, complemented
19#13869C212yesmaximal, complemented
20C25×C4C2211yescharacteristic
21C22×#123C2212yes—
22C22×#120C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C4⋊C4C2212yes—
28C23×C4⋊C4C2211yescharacteristic
29C23×C22⋊C4C2212yes—
30C23×C22⋊C4C2212yes—
31#2486—28no—
32#2412—216no—
33C2×#398C2212yescomplemented
34C2×#397C2214yes—
35C2×#397C2212yescomplemented
36C2×#394C2214yes—
37C4×#120—28no—
38C2×#389C2212yescomplemented
39C2×#389C2212yescomplemented
40C2×#386C2211yescharacteristic
41C2×#386C2212yes—
42C2×#386C2214yes—
43C2×#386C2211yescharacteristic
44C2×#386C2211yescharacteristic
45C2×#385C2211yescharacteristic
46C2×#385C2212yes—
47C2×#385C2211yescharacteristic
48C2×#385C2211yescharacteristic
49C2×#381C2212yes—
50C2×#381C2212yes—
51C2×#381C2212yes—
52C2×#380—28no—
53C2×#380—28no—
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#380C2212yes—
57C2×#380C2212yes—
58C2×#380C2211yescharacteristic
59C2×#380C2212yes—
60C2×#380C2212yes—
61C2×#380C2214yes—
62C2×#380C2212yes—
63C2×#380C2211yescharacteristic
64C2×#380C2212yescomplemented
65C2×#380C2212yescomplemented
66C2×#379C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2211yescharacteristic
69C2×C4×C22⋊C4C2211yescharacteristic
70C22×#95C2212yes—
71C22×#95C2212yes—
72#1445C2212yescomplemented
73#1445C2212yescomplemented
74#1444C2212yescomplemented
75#1443C2214yescomplemented
76#1442C2212yescomplemented
77#1442C2214yescomplemented
78#1441C2214yescomplemented
79#1441C2212yescomplemented
80#1441C2214yescomplemented
81#1441C2214yescomplemented
82#1441C2214yescomplemented
83#1440C2214yes—
84#1440C2214yes—
85#1440C2214yescomplemented
86#1439C2214yescomplemented
87#1439C2212yescomplemented
88C4⋊#95C2212yescomplemented
89C4⋊#95C2212yescomplemented
90C4⋊#95C2212yescomplemented
91C4⋊#95C2212yescomplemented
92C22⋊#95C2212yes—
93C22⋊#95C2214yes—
94C22⋊#95C2212yes—
95C22⋊#95C2214yes—
96C26C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C23×D4C2311yescharacteristic
99C23×D4C2311yescharacteristic
100C24×C4—24no—
101C24×C4—24no—
102C24×C4—28no—
103C24×C4—44no—
104C24×C4D418yes—
105C24×C4C2312yes—
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2314yes—
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2312yes—
115C2×#123—28no—
116C2×#123—28no—
117C2×#123—44no—
118C2×#120—24no—
119C2×#120—24no—
120C2×#120D418yes—
121C2×C4×D4—24no—
122C2×C4×D4—24no—
123C2×C4×D4—24no—
124C2×C4×D4—24no—
125C2×C4×D4—24no—
126C2×C4×D4—28no—
127C2×C4×D4—44no—
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—24no—
131C22×C4⋊C4—28no—
132C22×C4⋊C4—24no—
133C22×C4⋊C4—28no—
134C22×C4⋊C4—44no—
135C22×C4⋊C4—44no—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2314yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C22⋊C4—28no—
149C22×C22⋊C4—28no—
150C22×C22⋊C4—28no—
151C22×C22⋊C4—28no—
152C22×C22⋊C4—28no—
153C22×C22⋊C4—44no—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2311yescharacteristic
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2311yescharacteristic
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C22⋊C4C2311yescharacteristic
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2311yescharacteristic
168C22×C22⋊C4C2311yescharacteristic
169C22×C22⋊C4C2314yes—
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2311yescharacteristic
172C22×C22⋊C4C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176#398—28no—
177#397—216no—
178#397—28no—
179#394—216no—
180#389—28no—
181#389—44no—
182#386—28no—
183#386—216no—
184#386—24no—
185#386—24no—
186#386—24no—
187#385—24no—
188#385—24no—
189#385—24no—
190#385—28no—
191#381—28no—
192#381—28no—
193#381—44no—
194#380—28no—
195#380—28no—
196#380—28no—
197#380—24no—
198#380—28no—
199#380—28no—
200#380—28no—
201#380—216no—
202#380—28no—
203#380—28no—
204#380—44no—
205#380D418yescomplemented
206#379—24no—
207C4×C22⋊C4—24no—
208C4×C22⋊C4—24no—
209C4×C22⋊C4—24no—
210C2×#95—28no—
211C2×#95—28no—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2311yescharacteristic
223C2×#95C2311yescharacteristic
224C2×#95C2311yescharacteristic
225C2×#95C2311yescharacteristic
226C2×#95C2311yescharacteristic
227C2×#95C2311yescharacteristic
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2312yes—
235C25—22no—
236C25—22no—
237C25—24no—
238C25—22no—
239C25—24no—
240C25—22no—
241C25—42no—
242C25—42no—
243C25C2×D414yes—
244C25C2×D414yes—
245C25#4114yes—
246C25C2411yescharacteristic
247C25C2411yescharacteristic
248C25C2411yescharacteristic
249C25C2411yescharacteristic
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—24no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—24no—
261C22×D4—22no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4C2×D414yes—
265C22×D4C2×D414yes—
266C22×D4C2×D414yes—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—24no—
275C23×C4—232no—
276C23×C4—232no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—24no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—24no—
295C23×C4—28no—
296C23×C4—28no—
297C23×C4—28no—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—28no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—22no—
304C23×C4—24no—
305C23×C4—24no—
306C23×C4—416no—
307C23×C4—42no—
308C23×C4—42no—
309C23×C4—42no—
310C23×C4—432no—
311C23×C4—432no—
312C23×C4—44no—
313C23×C4—44no—
314C23×C4—44no—
315C23×C4—44no—
316C23×C4—44no—
317C23×C4C2×D414yes—
318C23×C4C2×D414yes—
319C23×C4C2×D414yes—
320C23×C4C2×D414yes—
321C23×C4C2×D414yes—
322C23×C4C2×D414yes—
323C23×C4C2×D414yes—
324C23×C4#4114yes—
325C23×C4#4118yes—
326C23×C4C2411yescharacteristic
327C23×C4C2411yescharacteristic
328C23×C4C2411yescharacteristic
329C23×C4C2411yescharacteristic
330C23×C4C2414yes—
331C23×C4C2414yes—
332C23×C4C2414yes—
333C23×C4C2414yes—
334C23×C4C2411yescharacteristic
335C23×C4C2411yescharacteristic
336C23×C4C2411yescharacteristic
337C23×C4C2411yescharacteristic
338C23×C4C2411yescharacteristic
339C23×C4C2411yescharacteristic
340C23×C4C2411yescharacteristic
341#123—432no—
342#120—232no—
343C4×D4—416no—
344C4×D4—416no—
345C4×D4—416no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—28no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—28no—
372C2×C4⋊C4—432no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—416no—
378C2×C4⋊C4—416no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4C2×D418yes—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—28no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—28no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—22no—
413C2×C22⋊C4—28no—
414C2×C22⋊C4—22no—
415C2×C22⋊C4—22no—
416C2×C22⋊C4—22no—
417C2×C22⋊C4—22no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—432no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—42no—
425C2×C22⋊C4—42no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—44no—
428C2×C22⋊C4—432no—
429C2×C22⋊C4—44no—
430C2×C22⋊C4—44no—
431C2×C22⋊C4C2×D418yes—
432C2×C22⋊C4C2×D414yes—
433C2×C22⋊C4C2×D414yes—
434C2×C22⋊C4C2×D414yes—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—24no—
441C2×C42—24no—
442#95—28no—
443#95—28no—
444#95—24no—
445#95—28no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—28no—
453#95—28no—
454#95—28no—
455#95—28no—
456#95—28no—
457#95—28no—
458#95—44no—
459#95—44no—
460#95—44no—
461#95—44no—
462#95—44no—
463#95—44no—
464#95C2×D418yes—
465C24—21no—
466C24—21no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—21no—
471C24—22no—
472C24—21no—
473C24—22no—
474C24—22no—
475C24—28no—
476C24—28no—
477C24—28no—
478C24—28no—
479C24—28no—
480C24—28no—
481C24—216no—
482C24—28no—
483C24—216no—
484C24—28no—
485C24—21no—
486C24—21no—
487C24—22no—
488C24—21no—
489C24—22no—
490C24—22no—
491C24—21no—
492C24—22no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—22no—
497C24—21no—
498C24—21no—
499C24—22no—
500C24—22no—
501C24—21no—
502C24—22no—
503C24—44no—
504C24—44no—
505C24—48no—
506C24—48no—
507C24—48no—
508C24—48no—
509C24—48no—
510C24—48no—
511C24—48no—
512C24—48no—
513C24—48no—
514C24—48no—
515C24#121116yes—
516C24C22×D412yes—
517C24C22×D412yes—
518C24C22×D412yes—
519C24C22×D412yes—
520C24C22×D412yes—
521C24C22×D412yes—
522C24C22×D412yes—
523C24C22×D412yes—
524C24C2×#4112yes—
525C24C2×#4112yes—
526C24C2×#4112yes—
527C24C2×#4112yes—
528C24C2×#4114yes—
529C24H(5,𝔽2)12yes—
530C242−1+414yes—
531C242−1+412yes—
532C24C2511yescharacteristic
533C2×D4—28no—
534C2×D4—28no—
535C2×D4—28no—
536C2×D4—28no—
537C2×D4—28no—
538C2×D4—216no—
539C2×D4—48no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—48no—
543C2×D4—44no—
544C2×D4—44no—
545C2×D4—44no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—48no—
549C2×D4—44no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—216no—
560C22×C4—216no—
561C22×C4—216no—
562C22×C4—216no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—24no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—24no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—24no—
588C22×C4—22no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—28no—
595C22×C4—28no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—21no—
614C22×C4—22no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—22no—
620C22×C4—24no—
621C22×C4—22no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—24no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—24no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—48no—
641C22×C4—48no—
642C22×C4—4128no—
643C22×C4—48no—
644C22×C4—48no—
645C22×C4—48no—
646C22×C4—48no—
647C22×C4—416no—
648C22×C4—416no—
649C22×C4—416no—
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—48no—
659C22×C4—416no—
660C22×C4—48no—
661C22×C4—48no—
662C22×C4—48no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—48no—
667C22×C4—48no—
668C22×C4—88no—
669C22×C4—88no—
670C22×C4—88no—
671C22×C4—88no—
672C22×C4—88no—
673C22×C4#121116yes—
674C22×C4#123116yescomplemented
675C22×C4C22×D412yes—
676C22×C4C22×D412yes—
677C22×C4C22×D412yes—
678C22×C4C22×D412yes—
679C22×C4C22×D418yes—
680C22×C4C22×D412yes—
681C22×C4C22×D412yes—
682C22×C4C22×D412yes—
683C22×C4C22×D412yes—
684C22×C4C22×D412yes—
685C22×C4C2×#4112yes—
686C22×C4C2×#4114yes—
687C22×C4C2×#4112yes—
688C22×C4C2×#4114yes—
689C22×C4H(5,𝔽2)14yes—
690C4⋊C4—216no—
691C4⋊C4—416no—
692C4⋊C4—416no—
693C4⋊C4—48no—
694C4⋊C4—44no—
695C4⋊C4—48no—
696C4⋊C4—48no—
697C4⋊C4—44no—
698C4⋊C4—44no—
699C4⋊C4—48no—
700C4⋊C4—48no—
701C4⋊C4—88no—
702C22⋊C4—28no—
703C22⋊C4—28no—
704C22⋊C4—28no—
705C22⋊C4—216no—
706C22⋊C4—416no—
707C22⋊C4—416no—
708C22⋊C4—44no—
709C22⋊C4—44no—
710C22⋊C4—44no—
711C22⋊C4—416no—
712C22⋊C4—416no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4—44no—
716C22⋊C4—44no—
717C22⋊C4—48no—
718C22⋊C4—44no—
719C22⋊C4—44no—
720C22⋊C4—88no—
721C42—44no—
722C42—44no—
723C42—44no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—24no—
734C23—24no—
735C23—22no—
736C23—24no—
737C23—22no—
738C23—24no—
739C23—24no—
740C23—24no—
741C23—22no—
742C23—24no—
743C23—24no—
744C23—24no—
745C23—24no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—22no—
759C23—22no—
760C23—232no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—24no—
768C23—22no—
769C23—24no—
770C23—22no—
771C23—24no—
772C23—24no—
773C23—232no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—24no—
778C23—24no—
779C23—416no—
780C23—416no—
781C23—432no—
782C23—432no—
783C23—416no—
784C23—432no—
785C23—432no—
786C23—416no—
787C23—416no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—42no—
803C23—41no—
804C23—42no—
805C23—42no—
806C23—41no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23C2×#12114yes—
815C23C2×#12114yes—
816C23C2×#12114yes—
817C23C2×#12114yes—
818C23C2×#12314yes—
819C23#53614yes—
820C23#53714yes—
821C23D4214yes—
822C23#54714yes—
823C23#54718yes—
824C23#54814yes—
825C23#55218yes—
826C23#55314yes—
827C23C23×D411yescharacteristic
828C23C23×D411yescharacteristic
829C23C23×D411yescharacteristic
830C23C22×#4111yescharacteristic
831C23C22×#4111yescharacteristic
832C23C22×#4112yes—
833C23C2×H(5,𝔽2)12yes—
834C23C2×H(5,𝔽2)11yescharacteristic
835C23C2×2−1+412yes—
836C23C2×2−1+411yescharacteristic
837C23#58512yes—
838D4—416no—
839D4—416no—
840D4—416no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—232no—
850C2×C4—232no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—28no—
858C2×C4—22no—
859C2×C4—28no—
860C2×C4—22no—
861C2×C4—24no—
862C2×C4—28no—
863C2×C4—24no—
864C2×C4—416no—
865C2×C4—416no—
866C2×C4—416no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—42no—
874C2×C4—44no—
875C2×C4—41no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—41no—
879C2×C4—44no—
880C2×C4—44no—
881C2×C4—42no—
882C2×C4—44no—
883C2×C4—416no—
884C2×C4—41no—
885C2×C4—44no—
886C2×C4—44no—
887C2×C4—41no—
888C2×C4—44no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—44no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—44no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—44no—
902C2×C4—44no—
903C2×C4—44no—
904C2×C4—44no—
905C2×C4—42no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—44no—
909C2×C4—42no—
910C2×C4—44no—
911C2×C4—42no—
912C2×C4—44no—
913C2×C4—42no—
914C2×C4—44no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—44no—
918C2×C4—44no—
919C2×C4—44no—
920C2×C4—44no—
921C2×C4—44no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—42no—
925C2×C4—832no—
926C2×C4—816no—
927C2×C4—816no—
928C2×C4—88no—
929C2×C4C2×#12114yes—
930C2×C4C2×#12114yes—
931C2×C4C2×#12314yes—
932C2×C4C2×#12314yes—
933C2×C4#53414yes—
934C2×C4#54618yes—
935C2×C4#55118yes—
936C22—28no—
937C22—28no—
938C22—28no—
939C22—28no—
940C22—24no—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—24no—
945C22—28no—
946C22—28no—
947C22—28no—
948C22—28no—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—24no—
957C22—24no—
958C22—24no—
959C22—464no—
960C22—44no—
961C22—44no—
962C22—42no—
963C22—42no—
964C22—44no—
965C22—44no—
966C22—42no—
967C22—42no—
968C22—44no—
969C22—42no—
970C22—44no—
971C22—42no—
972C22—42no—
973C22—82no—
974C22—81no—
975C22—81no—
976C22—82no—
977C22—81no—
978C22—81no—
979C22#241618yes—
980C22#248618yescomplemented
981C22C22×#12111yescharacteristic
982C22C22×#12111yescharacteristic
983C22C22×#12311yescharacteristic
984C22C2×#53411yescharacteristic
985C22C2×#53611yescharacteristic
986C22C2×#53711yescharacteristic
987C22#344911yescharacteristic
988C22C2×D4211yescharacteristic
989C22C2×#54612yes—
990C22C2×#54711yescharacteristic
991C22C2×#54712yes—
992C22C2×#54811yescharacteristic
993C22C2×#55112yes—
994C22C2×#55212yes—
995C22C2×#55311yescharacteristic
996C22#348912yes—
997C22#349412yes—
998C22#349512yes—
999C22#349512yes—
1000C22#349612yes—
1001C22#350512yes—
1002C22#353612yes—
1003C22#353812yes—
1004C4—24no—
1005C4—24no—
1006C4—42no—
1007C4—42no—
1008C4—48no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—84no—
1014C4—84no—
1015C4—84no—
1016C4—81no—
1017C4—81no—
1018C4#241218yescomplemented
1019C2—28no—
1020C2—28no—
1021C2—44no—
1022C2—82no—
1023C2C2×#241211yescharacteristic
1024C2C2×#241611yescharacteristic
1025C2C2×#248611yescharacteristic
1026C2#3500011yescharacteristic
1027C2#3526311yescharacteristic
1028C2#3530611yescharacteristic
1029C2#3744211yescharacteristic
1030C2#5901412yes—
1031C2#5901512yes—
1032C2#5919712yes—
1033C2#5919812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
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×#2486C2semidirect
4. C22×#380C2semidirect
5. C22×#380C2semidirect
6. #16401C2semidirect
7. #16399C2semidirect
8. #15132C2semidirect
9. #15129C2semidirect
10. #14935C2semidirect
11. #14927C2semidirect
12. #14766C2semidirect
13. #14735C2semidirect
14. #14130C2semidirect
15. #13907C2semidirect
16. #13904C2semidirect
17. #13872C2semidirect
18. #13872C2semidirect
19. #13869C2semidirect
33. C2×#398C22semidirect
35. C2×#397C22semidirect
38. C2×#389C22semidirect
39. C2×#389C22semidirect
64. C2×#380C22semidirect
65. C2×#380C22semidirect
72. #1445C22semidirect
73. #1445C22semidirect
74. #1444C22semidirect
75. #1443C22semidirect
76. #1442C22semidirect
77. #1442C22semidirect
78. #1441C22semidirect
79. #1441C22semidirect
80. #1441C22semidirect
81. #1441C22semidirect
82. #1441C22semidirect
85. #1440C22semidirect
86. #1439C22semidirect
87. #1439C22semidirect
88. C4⋊#95C22semidirect
89. C4⋊#95C22semidirect
90. C4⋊#95C22semidirect
91. C4⋊#95C22semidirect
205. #380D4semidirect
674. C22×C4#123semidirect
980. C22#2486semidirect
1018. C4#2412semidirect

Maximal subgroups

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

subgroupindex
C2×#24862
C2×#24122
C2×C4×#1202
C22×#3802
#164012
#163992
#151322
#151292
#149352
#149272
#147662
#147352
#141302
#139072
#139042
#138722
#138692