Finite Group Databasebeta

← #636215

Subgroups — #636215

Order 512.

4172 conjugacy classes of subgroups.

The subgroup lattice has 1047 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2847C211yesmaximal, characteristic
2C2×#2500C211yesmaximal, characteristic, complemented
3C2×#2280C211yesmaximal, characteristic, complemented
4C2×#2280C211yesmaximal, characteristic, complemented
5#16397C214yesmaximal, complemented
6#16255C214yesmaximal, complemented
7#15233C211yesmaximal, characteristic, complemented
8#15219C211yesmaximal, characteristic, complemented
9#15150C211yesmaximal, characteristic, complemented
10#15130C211yesmaximal, characteristic, complemented
11#15002C214yesmaximal, complemented
12#14974C214yesmaximal, complemented
13#14340C211yesmaximal, characteristic, complemented
14#14340C211yesmaximal, characteristic, complemented
15#14257C211yesmaximal, characteristic, complemented
16#14257C211yesmaximal, characteristic, complemented
17#14136C211yesmaximal, characteristic, complemented
18#13939C211yesmaximal, characteristic, complemented
19#13879C211yesmaximal, characteristic, complemented
20C25×C4C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#121C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×#120C2212yes—
25C22×#117C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C22×#117C2211yescharacteristic
29#2847—28no—
30#2500—28no—
31C2×#397C2214yes—
32C2×#394C2214yes—
33C2×#394C2214yes—
34C2×#390C2211yescharacteristic, complemented
35C2×#390C2211yescharacteristic, complemented
36C2×#390C2211yescharacteristic, complemented
37C2×#390C2211yescharacteristic, complemented
38C2×#388C2214yescomplemented
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#384C2211yescharacteristic, complemented
43C2×#384C2211yescharacteristic, complemented
44C2×#382C2211yescharacteristic, complemented
45C2×#382C2211yescharacteristic, complemented
46#2280—28no—
47#2280—28no—
48C2×#381C2212yes—
49C2×#381C2212yes—
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2212yes—
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2212yes—
59C2×#379C2212yes—
60C2×#379C2212yes—
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2212yes—
65C2×C4×C22⋊C4C2212yes—
66C2×C4×C22⋊C4C2211yescharacteristic
67#1445C2214yescomplemented
68#1443C2214yescomplemented
69#1441C2214yescomplemented
70#1441C2214yescomplemented
71#1440C2214yes—
72#1440C2214yes—
73#1440C2214yescomplemented
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yescomplemented
78#1439C2214yescomplemented
79#1439C2214yescomplemented
80#1438C2214yes—
81#1438C2214yes—
82#1438C2214yes—
83#1438C2214yes—
84#1437C2214yescomplemented
85#1436C2214yescomplemented
86C4⋊#95C2211yescharacteristic, complemented
87C4⋊#95C2211yescharacteristic, complemented
88C4⋊#95C2211yescharacteristic, complemented
89C4⋊#95C2211yescharacteristic, complemented
90C4⋊#95C2211yescharacteristic, complemented
91C4⋊#95C2211yescharacteristic, complemented
92C4⋊#95C2211yescharacteristic, complemented
93C4⋊#95C2211yescharacteristic, complemented
94#1434C2214yescomplemented
95C26C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C23×D4C2312yes—
98C23×D4C2312yes—
99C23×D4C2312yes—
100C24×C4—24no—
101C24×C4—24no—
102C24×C4—24no—
103C24×C4—24no—
104C24×C4—42no—
105C24×C4—42no—
106C24×C4D418yes—
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C2×#121—24no—
114C2×#121—24no—
115C2×#121—24no—
116C2×#121—24no—
117C2×#121—24no—
118C2×#121—24no—
119C2×#121—24no—
120C2×#121—42no—
121C2×#121—42no—
122C2×#120—28no—
123C2×#120—48no—
124C2×#117—24no—
125C2×#117—24no—
126C2×#117—24no—
127C2×#117—24no—
128C2×#117—24no—
129C2×#117—24no—
130C2×#117—24no—
131C2×#117—24no—
132C2×#117—42no—
133C2×#117—42no—
134C2×#117—42no—
135C2×#117—42no—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2314yes—
146C22×C4⋊C4C2314yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2314yes—
168C22×C22⋊C4C2312yes—
169C22×C42C2312yes—
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2311yescharacteristic
174C22×C42C2312yes—
175#397—48no—
176#394—216no—
177#394—48no—
178#390—24no—
179#390—24no—
180#390—42no—
181#390—42no—
182#388—216no—
183#386—28no—
184#386—28no—
185#386—28no—
186#384—24no—
187#384—42no—
188#382—24no—
189#382—42no—
190#381—28no—
191#381—28no—
192#380—24no—
193#380—24no—
194#380—24no—
195#380—24no—
196#380—24no—
197#380—24no—
198#380—24no—
199#380—28no—
200#380—28no—
201#379—28no—
202#379—28no—
203C4×C22⋊C4—28no—
204C4×C22⋊C4—28no—
205C4×C22⋊C4—24no—
206C4×C22⋊C4—24no—
207C4×C22⋊C4—24no—
208C4×C22⋊C4D418yescomplemented
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2312yes—
230C25—22no—
231C25—22no—
232C25—22no—
233C25—22no—
234C25—24no—
235C25—41no—
236C25—41no—
237C25—42no—
238C25—42no—
239C25—42no—
240C25C2×D414yes—
241C25C2412yes—
242C25C2411yescharacteristic
243C25C2411yescharacteristic
244C25C2411yescharacteristic
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—24no—
249C22×D4—24no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—28no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4—44no—
265C22×D4—44no—
266C22×D4—44no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—232no—
280C23×C4—232no—
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—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—416no—
296C23×C4—41no—
297C23×C4—41no—
298C23×C4—41no—
299C23×C4—41no—
300C23×C4—41no—
301C23×C4—41no—
302C23×C4—416no—
303C23×C4—416no—
304C23×C4—416no—
305C23×C4—416no—
306C23×C4C2×D414yes—
307C23×C4C2×D414yes—
308C23×C4C2×D414yes—
309C23×C4C2×D414yes—
310C23×C4C2×D414yes—
311C23×C4C2×D414yes—
312C23×C4C2×D414yes—
313C23×C4#4114yes—
314C23×C4#4114yes—
315C23×C4#4114yes—
316C23×C4C2412yes—
317C23×C4C2412yes—
318C23×C4C2412yes—
319C23×C4C2412yes—
320C23×C4C2412yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2412yes—
325C23×C4C2412yes—
326C23×C4C2412yes—
327C23×C4C2411yescharacteristic
328C23×C4C2411yescharacteristic
329C23×C4C2411yescharacteristic
330C23×C4C2411yescharacteristic
331#121—416no—
332#121—416no—
333#121—416no—
334#120—432no—
335#117—416no—
336#117—416no—
337#117—416no—
338#117—416no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
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—28no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—28no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—42no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4—44no—
413C2×C22⋊C4—44no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—42no—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4—42no—
421C2×C22⋊C4—42no—
422C2×C22⋊C4—44no—
423C2×C22⋊C4—44no—
424C2×C22⋊C4—44no—
425C2×C22⋊C4—44no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4—44no—
428C2×C22⋊C4—44no—
429C2×C22⋊C4—44no—
430C2×C22⋊C4C2×D418yes—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—24no—
436C2×C42—24no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—24no—
440C2×C42—24no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—42no—
446C2×C42—42no—
447C2×C42C2×D414yes—
448C2×C42C2×D414yes—
449#95—24no—
450#95—24no—
451#95—24no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—24no—
457#95—24no—
458#95—24no—
459#95—28no—
460#95—44no—
461#95—44no—
462#95—44no—
463#95—44no—
464#95—44no—
465#95—44no—
466#95—44no—
467#95—44no—
468#95—44no—
469#95C2×D418yes—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—21no—
481C24—21no—
482C24—22no—
483C24—22no—
484C24—21no—
485C24—21no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—28no—
496C24—28no—
497C24—28no—
498C24—22no—
499C24—22no—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—24no—
506C24—24no—
507C24—24no—
508C24—24no—
509C24—44no—
510C24—44no—
511C24—44no—
512C24—44no—
513C24—44no—
514C24—44no—
515C24—44no—
516C24—44no—
517C24—48no—
518C24—48no—
519C24—48no—
520C24—48no—
521C24—48no—
522C24—48no—
523C24—48no—
524C24—48no—
525C24—48no—
526C24—48no—
527C24—48no—
528C24—48no—
529C24C22×D412yes—
530C24C22×D412yes—
531C24C22×D412yes—
532C24C22×D412yes—
533C24C2×#4112yes—
534C24C2×#4112yes—
535C24C2×#4112yes—
536C24H(5,𝔽2)14yes—
537C24C2511yescharacteristic
538C2×D4—48no—
539C2×D4—48no—
540C2×D4—48no—
541C2×D4—48no—
542C2×D4—48no—
543C2×D4—48no—
544C2×D4—48no—
545C2×D4—48no—
546C2×D4—48no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4—88no—
555C2×D4—88no—
556C2×D4—88no—
557C2×D4—88no—
558C2×D4—88no—
559C2×D4—88no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—28no—
569C22×C4—28no—
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—22no—
584C22×C4—22no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—28no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—28no—
604C22×C4—28no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—24no—
632C22×C4—22no—
633C22×C4—24no—
634C22×C4—24no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—24no—
647C22×C4—24no—
648C22×C4—24no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—24no—
655C22×C4—24no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—4128no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4#121116yes—
677C22×C4#123116yes—
678C22×C4C22×D412yes—
679C22×C4C22×D414yes—
680C22×C4C22×D414yes—
681C22×C4C22×D412yes—
682C22×C4C22×D412yes—
683C22×C4C22×D412yes—
684C22×C4C22×D412yes—
685C22×C4C22×D412yes—
686C22×C4C2×#4112yes—
687C22×C4C2×#4112yes—
688C22×C4C2×#4112yes—
689C22×C4C2×#4112yes—
690C22×C4C2×#4112yes—
691C22×C4C2×#4112yes—
692C22×C4H(5,𝔽2)12yes—
693C22×C4H(5,𝔽2)12yes—
694C4⋊C4—48no—
695C4⋊C4—48no—
696C4⋊C4—44no—
697C4⋊C4—44no—
698C4⋊C4—44no—
699C4⋊C4—44no—
700C4⋊C4—44no—
701C4⋊C4—44no—
702C4⋊C4—44no—
703C4⋊C4—88no—
704C4⋊C4—88no—
705C22⋊C4—48no—
706C22⋊C4—48no—
707C22⋊C4—48no—
708C22⋊C4—48no—
709C22⋊C4—48no—
710C22⋊C4—416no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—48no—
714C22⋊C4—48no—
715C22⋊C4—48no—
716C22⋊C4—48no—
717C22⋊C4—48no—
718C22⋊C4—48no—
719C22⋊C4—48no—
720C22⋊C4—48no—
721C22⋊C4—48no—
722C22⋊C4—48no—
723C22⋊C4—48no—
724C22⋊C4—88no—
725C22⋊C4—88no—
726C22⋊C4—88no—
727C42—28no—
728C42—28no—
729C42—48no—
730C42—48no—
731C42—44no—
732C42—44no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—24no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—24no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—24no—
762C23—24no—
763C23—24no—
764C23—24no—
765C23—24no—
766C23—24no—
767C23—24no—
768C23—24no—
769C23—24no—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—416no—
774C23—416no—
775C23—416no—
776C23—416no—
777C23—416no—
778C23—416no—
779C23—416no—
780C23—432no—
781C23—432no—
782C23—432no—
783C23—432no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—44no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—44no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—44no—
824C23—44no—
825C23—44no—
826C23—44no—
827C23—44no—
828C23—44no—
829C23—44no—
830C23—44no—
831C23—44no—
832C23—44no—
833C23C2×#12114yes—
834C23C2×#12314yes—
835C23#53514yes—
836C23C23×D411yescharacteristic
837C23C23×D411yescharacteristic
838C23C22×#4111yescharacteristic
839C23C22×#4111yescharacteristic
840C23C22×#4111yescharacteristic
841C23C2×H(5,𝔽2)11yescharacteristic
842C23C2×H(5,𝔽2)11yescharacteristic
843C23C2×H(5,𝔽2)12yes—
844C23#58512yes—
845C23#58512yes—
846C23#58512yes—
847D4—816no—
848D4—816no—
849D4—816no—
850D4—88no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—232no—
864C2×C4—232no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—416no—
875C2×C4—416no—
876C2×C4—416no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—42no—
882C2×C4—42no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—42no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—416no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—44no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—44no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—44no—
920C2×C4—44no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—44no—
933C2×C4—42no—
934C2×C4—44no—
935C2×C4—44no—
936C2×C4—44no—
937C2×C4—42no—
938C2×C4—44no—
939C2×C4C2×#12114yes—
940C2×C4C2×#12114yes—
941C2×C4C2×#12314yes—
942C2×C4C2×#12314yes—
943C2×C4#53414yes—
944C2×C4#54614yes—
945C2×C4#54614yes—
946C2×C4#55114yes—
947C2×C4#55114yes—
948C22—24no—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—24no—
957C22—464no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—82no—
983C22—82no—
984C22—82no—
985C22—82no—
986C22—82no—
987C22—82no—
988C22—82no—
989C22—84no—
990C22—84no—
991C22—84no—
992C22—84no—
993C22C22×#12111yescharacteristic
994C22C22×#12311yescharacteristic
995C22C2×#53411yescharacteristic
996C22C2×#53511yescharacteristic
997C22#344911yescharacteristic
998C22#344911yescharacteristic
999C22#344912yes—
1000C22#344911yescharacteristic
1001C22#345512yes—
1002C22C2×#54611yescharacteristic
1003C22C2×#54611yescharacteristic
1004C22C2×#55111yescharacteristic
1005C22C2×#55111yescharacteristic
1006C22#348812yes—
1007C22#349312yes—
1008C22#349312yes—
1009C22#349412yes—
1010C22#349412yes—
1011C22#349412yes—
1012C22#353912yes—
1013C22#354012yes—
1014C22#354212yes—
1015C22#354212yes—
1016C4—24no—
1017C4—24no—
1018C4—42no—
1019C4—44no—
1020C4—44no—
1021C4—82no—
1022C4—82no—
1023C4—82no—
1024C4—82no—
1025C4—82no—
1026C4—82no—
1027C4—82no—
1028C4—82no—
1029C4—82no—
1030C4#241218yes—
1031C2—44no—
1032C2—44no—
1033C2—44no—
1034C2—162no—
1035C2#3463311yescharacteristic
1036C2C2×#241211yescharacteristic
1037C2#3515711yescharacteristic
1038C2#3525211yescharacteristic
1039C2#3526211yescharacteristic
1040C2#3744811yescharacteristic
1041C2#3745511yescharacteristic
1042C2#3784512yes—
1043C2#3784612yes—
1044C2#3785712yes—
1045C2#3785812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2847C2
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×#2500C2semidirect
3. C2×#2280C2semidirect
4. C2×#2280C2semidirect
5. #16397C2semidirect
6. #16255C2semidirect
7. #15233C2semidirect
8. #15219C2semidirect
9. #15150C2semidirect
10. #15130C2semidirect
11. #15002C2semidirect
12. #14974C2semidirect
13. #14340C2semidirect
14. #14340C2semidirect
15. #14257C2semidirect
16. #14257C2semidirect
17. #14136C2semidirect
18. #13939C2semidirect
19. #13879C2semidirect
34. C2×#390C22semidirect
35. C2×#390C22semidirect
36. C2×#390C22semidirect
37. C2×#390C22semidirect
38. C2×#388C22semidirect
42. C2×#384C22semidirect
43. C2×#384C22semidirect
44. C2×#382C22semidirect
45. C2×#382C22semidirect
67. #1445C22semidirect
68. #1443C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
73. #1440C22semidirect
77. #1439C22semidirect
78. #1439C22semidirect
79. #1439C22semidirect
84. #1437C22semidirect
85. #1436C22semidirect
86. C4⋊#95C22semidirect
87. C4⋊#95C22semidirect
88. C4⋊#95C22semidirect
89. C4⋊#95C22semidirect
90. C4⋊#95C22semidirect
91. C4⋊#95C22semidirect
92. C4⋊#95C22semidirect
93. C4⋊#95C22semidirect
94. #1434C22semidirect
208. C4×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28472
C2×#25002
C2×#22802
#163972
#162552
#152332
#152192
#151502
#151302
#150022
#149742
#143402
#142572
#141362
#139392
#138792