Finite Group Databasebeta

← #947344

Subgroups — #947344

Order 512.

3476 conjugacy classes of subgroups.

The subgroup lattice has 993 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2500C211yesmaximal, characteristic, complemented
2C2×#2428C211yesmaximal, characteristic, complemented
3#17086C214yesmaximal, complemented
4#16535C214yesmaximal, complemented
5#16260C214yesmaximal, complemented
6#15304C214yesmaximal, complemented
7#15239C211yesmaximal, characteristic, complemented
8#15142C211yesmaximal, characteristic, complemented
9#15136C211yesmaximal, characteristic, complemented
10#15127C211yesmaximal, characteristic, complemented
11#15124C211yesmaximal, characteristic, complemented
12#15124C211yesmaximal, characteristic, complemented
13#14272C211yesmaximal, characteristic, complemented
14#14260C211yesmaximal, characteristic, complemented
15#14136C211yesmaximal, characteristic, complemented
16#14136C211yesmaximal, characteristic, complemented
17#14025C211yesmaximal, characteristic, complemented
18#13906C211yesmaximal, characteristic, complemented
19#13842C211yesmaximal, characteristic, complemented
20C22×#127C2211yescharacteristic
21C22×#127C2211yescharacteristic
22C22×#127C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#121C2212yes—
27C22×C4×D4C2211yescharacteristic
28C22×#117C2211yescharacteristic
29#2500—28no—
30#2428—28no—
31C2×#397C2214yes—
32C2×#394C2212yes—
33C2×#394C2212yes—
34C2×#394C2212yes—
35C2×#394C2214yes—
36C2×#392C2212yes—
37C2×#392C2214yes—
38C2×#392C2214yes—
39C2×#392C2214yes—
40C2×#392C2214yes—
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#388C2212yes—
54C2×#388C2212yes—
55C2×#386C2212yes—
56C2×#386C2214yes—
57C2×#384C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#380C2214yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×#376C2211yescharacteristic
65#1443C2212yes—
66#1443C2214yes—
67#1442C2212yes—
68#1442C2214yes—
69#1440C2212yes—
70#1440C2214yes—
71#1439C2212yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1438C2214yes—
76#1438C2214yes—
77#1438C2214yes—
78#1438C2214yes—
79#1438C2214yes—
80#1438C2214yes—
81#1438C2214yes—
82#1438C2214yes—
83#1437C2214yes—
84#1437C2214yes—
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×D4C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C23×D4C2312yes—
98C23×D4C2312yes—
99C23×D4C2314yes—
100C23×D4C2312yes—
101C23×D4C2312yes—
102C23×D4C2314yes—
103C24×C4C2311yescharacteristic
104C24×C4C2312yes—
105C2×#127—24no—
106C2×#127—24no—
107C2×#127—24no—
108C2×#127—42no—
109C2×#127—42no—
110C2×#127—42no—
111C2×#127—42no—
112C2×#127—42no—
113C2×#127—42no—
114C2×#121—24no—
115C2×#121—24no—
116C2×#121—24no—
117C2×#121—24no—
118C2×#121—24no—
119C2×#121—28no—
120C2×#121—48no—
121C2×#121—42no—
122C2×#121—42no—
123C2×#121—42no—
124C2×#121—42no—
125C2×C4×D4—24no—
126C2×C4×D4—24no—
127C2×C4×D4—42no—
128C2×#117—24no—
129C2×#117—42no—
130C2×#117—42no—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2314yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2312yes—
170#397—48no—
171#394—28no—
172#394—28no—
173#394—28no—
174#394—48no—
175#392—28no—
176#392—48no—
177#392—48no—
178#392—48no—
179#392—48no—
180#390—24no—
181#390—24no—
182#390—24no—
183#390—24no—
184#390—42no—
185#390—42no—
186#390—42no—
187#390—42no—
188#390—42no—
189#390—42no—
190#390—42no—
191#389—24no—
192#388—28no—
193#388—28no—
194#386—28no—
195#386—48no—
196#384—24no—
197#382—24no—
198#380—48no—
199C4×C4⋊C4—42no—
200C4×C22⋊C4—42no—
201C4×C22⋊C4—42no—
202C4×C22⋊C4D418yescomplemented
203#376—42no—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2311yescharacteristic
223C2×#95C2311yescharacteristic
224C25C2412yes—
225C25C2412yes—
226C25C2411yescharacteristic
227C25C2412yes—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—28no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—24no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—28no—
259C22×D4—28no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4—42no—
263C22×D4—44no—
264C22×D4—42no—
265C22×D4—42no—
266C22×D4—42no—
267C22×D4—42no—
268C22×D4—42no—
269C22×D4—44no—
270C22×D4—44no—
271C22×D4—44no—
272C22×D4—44no—
273C22×D4—44no—
274C22×D4—44no—
275C22×D4—44no—
276C22×D4—44no—
277C22×D4—44no—
278C22×D4—44no—
279C22×D4—44no—
280C22×D4—44no—
281C22×D4—44no—
282C22×D4—44no—
283C22×D4—44no—
284C22×D4—44no—
285C22×D4—44no—
286C22×D4—44no—
287C22×D4#4114yes—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—28no—
297C23×C4—42no—
298C23×C4—44no—
299C23×C4C2×D414yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2411yescharacteristic
314C23×C4C2411yescharacteristic
315#127—416no—
316#127—416no—
317#127—416no—
318#121—432no—
319#121—416no—
320#121—416no—
321#121—416no—
322C4×D4—416no—
323#117—416no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4#4114yes—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
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⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4C2×D414yes—
408C2×C22⋊C4C2×D414yes—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—24no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—42no—
427C2×C42—42no—
428C2×C42C2×D414yes—
429C2×C42C2×D414yes—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—28no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—28no—
438#95—24no—
439#95—42no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95—42no—
444#95—44no—
445#95—44no—
446#95—44no—
447#95—44no—
448#95C2×D414yes—
449#95C2×D414yes—
450C24—22no—
451C24—22no—
452C24—21no—
453C24—21no—
454C24—24no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—22no—
464C24—24no—
465C24—24no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—24no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—24no—
477C24—24no—
478C24—24no—
479C24—22no—
480C24—22no—
481C24—22no—
482C24—24no—
483C24—24no—
484C24—24no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—24no—
491C24—24no—
492C24C22×D412yes—
493C24C2×#4114yes—
494C24C2511yescharacteristic
495C2×D4—28no—
496C2×D4—28no—
497C2×D4—28no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—416no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—48no—
508C2×D4—416no—
509C2×D4—416no—
510C2×D4—44no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—44no—
519C2×D4—44no—
520C2×D4—44no—
521C2×D4—44no—
522C2×D4—44no—
523C2×D4—44no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—44no—
528C2×D4—84no—
529C2×D4—84no—
530C2×D4—88no—
531C2×D4—88no—
532C2×D4—88no—
533C2×D4—88no—
534C2×D4—88no—
535C2×D4—88no—
536C2×D4—84no—
537C2×D4—88no—
538C2×D4—88no—
539C2×D4—88no—
540C2×D4—84no—
541C2×D4—84no—
542C2×D4—84no—
543C2×D4—88no—
544C2×D4—88no—
545C2×D4—88no—
546C2×D4—88no—
547C2×D4—88no—
548C2×D4—88no—
549C2×D4—88no—
550C2×D4—88no—
551C2×D4—88no—
552C2×D4—88no—
553C2×D4—88no—
554C2×D4—88no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—28no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—24no—
603C22×C4—22no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—24no—
610C22×C4—22no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—24no—
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—24no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—48no—
630C22×C4—416no—
631C22×C4—44no—
632C22×C4—44no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—48no—
636C22×C4—84no—
637C22×C4—88no—
638C22×C4C22×D412yes—
639C22×C4C22×D412yes—
640C22×C4C22×D412yes—
641C22×C4C22×D412yes—
642C22×C4C22×D412yes—
643C22×C4C22×D412yes—
644C22×C4C2×#4114yes—
645C22×C4C2×#4112yes—
646C22×C4C2×#4112yes—
647C22×C4H(5,𝔽2)14yes—
648C22×C4H(5,𝔽2)14yes—
649C22×C4H(5,𝔽2)14yes—
650C22×C4H(5,𝔽2)12yes—
651C22×C4H(5,𝔽2)12yes—
652C22×C4H(5,𝔽2)12yes—
653C22×C4H(5,𝔽2)12yes—
654C4⋊C4—28no—
655C4⋊C4—48no—
656C4⋊C4—48no—
657C4⋊C4—44no—
658C4⋊C4—44no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—84no—
662C4⋊C4—84no—
663C22⋊C4—28no—
664C22⋊C4—44no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—48no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—84no—
676C22⋊C4—84no—
677C22⋊C4—84no—
678C22⋊C4—88no—
679C22⋊C4—88no—
680C22⋊C4—88no—
681C22⋊C4—88no—
682C22⋊C4—88no—
683C22⋊C4—88no—
684C22⋊C4—88no—
685C22⋊C4—88no—
686C42—28no—
687C42—28no—
688C42—48no—
689C42—44no—
690C42—44no—
691C42—44no—
692C42—44no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—24no—
697C23—24no—
698C23—22no—
699C23—22no—
700C23—24no—
701C23—22no—
702C23—22no—
703C23—28no—
704C23—28no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—42no—
712C23—41no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—44no—
718C23—44no—
719C23—42no—
720C23—42no—
721C23—41no—
722C23—42no—
723C23—44no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—42no—
731C23—42no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—44no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—42no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23—44no—
764C23—44no—
765C23—44no—
766C23—44no—
767C23—42no—
768C23—42no—
769C23—44no—
770C23—44no—
771C23—44no—
772C23—44no—
773C23—44no—
774C23—44no—
775C23—44no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—44no—
781C23—44no—
782C23—44no—
783C23—44no—
784C23—44no—
785C23C23×D411yescharacteristic
786C23C22×#4111yescharacteristic
787C23C22×#4111yescharacteristic
788C23C2×H(5,𝔽2)11yescharacteristic
789C23C2×H(5,𝔽2)11yescharacteristic
790C23C2×H(5,𝔽2)12yes—
791C23C2×H(5,𝔽2)11yescharacteristic
792C23C2×H(5,𝔽2)11yescharacteristic
793C23C2×H(5,𝔽2)12yes—
794C23C2×H(5,𝔽2)12yes—
795C23#58512yes—
796D4—416no—
797D4—816no—
798D4—832no—
799D4—816no—
800D4—816no—
801D4—832no—
802D4—816no—
803D4—816no—
804D4—88no—
805D4—88no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—24no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—24no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—28no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—24no—
829C2×C4—24no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—41no—
842C2×C4—44no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—416no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—44no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—44no—
876C2×C4—44no—
877C2×C4—44no—
878C2×C4—44no—
879C2×C4—42no—
880C2×C4—42no—
881C2×C4—44no—
882C2×C4—44no—
883C2×C4—42no—
884C2×C4—44no—
885C2×C4—42no—
886C2×C4—816no—
887C2×C4#53514yes—
888C2×C4#53514yes—
889C2×C4#53814yes—
890C2×C4#54014yes—
891C2×C4#54614yes—
892C2×C4#54614yes—
893C2×C4#55314yes—
894C2×C4#56014yes—
895C22—44no—
896C22—42no—
897C22—48no—
898C22—42no—
899C22—44no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—44no—
904C22—42no—
905C22—48no—
906C22—42no—
907C22—82no—
908C22—84no—
909C22—82no—
910C22—82no—
911C22—84no—
912C22—82no—
913C22—82no—
914C22—82no—
915C22—82no—
916C22—82no—
917C22—82no—
918C22—82no—
919C22—84no—
920C22—84no—
921C22—84no—
922C22—84no—
923C22—84no—
924C22—84no—
925C22—82no—
926C22—82no—
927C22—82no—
928C22—82no—
929C22—82no—
930C22—82no—
931C22—82no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—84no—
936C22—84no—
937C22—82no—
938C22—82no—
939C22C2×#53511yescharacteristic
940C22C2×#53511yescharacteristic
941C22#344911yescharacteristic
942C22C2×#53811yescharacteristic
943C22C2×#54011yescharacteristic
944C22C2×#54611yescharacteristic
945C22C2×#54611yescharacteristic
946C22C2×#55311yescharacteristic
947C22#349811yescharacteristic
948C22#349811yescharacteristic
949C22#351412yes—
950C22#351712yes—
951C22#351912yes—
952C22#351912yes—
953C22C2×#56011yescharacteristic
954C22#353712yes—
955C22#354212yes—
956C22#354212yes—
957C22#354312yes—
958C22#354312yes—
959C22#354612yes—
960C22#354612yes—
961C22#354912yes—
962C4—24no—
963C4—42no—
964C4—44no—
965C4—44no—
966C4—42no—
967C4—44no—
968C4—42no—
969C4—42no—
970C4—82no—
971C4—82no—
972C4—82no—
973C4—82no—
974C4—82no—
975C4—82no—
976C4#270318yes—
977C2—84no—
978C2—82no—
979C2—162no—
980C2—162no—
981C2#3730211yescharacteristic
982C2#3761811yescharacteristic
983C2#3808011yescharacteristic
984C2#3808911yescharacteristic
985C2#3809011yescharacteristic
986C2#3895311yescharacteristic
987C2#4257812yes—
988C2#4258112yes—
989C2#4503312yes—
990C2C2×#270311yescharacteristic
991C2#5310212yes—
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. C2×#2500C2semidirect
2. C2×#2428C2semidirect
3. #17086C2semidirect
4. #16535C2semidirect
5. #16260C2semidirect
6. #15304C2semidirect
7. #15239C2semidirect
8. #15142C2semidirect
9. #15136C2semidirect
10. #15127C2semidirect
11. #15124C2semidirect
12. #15124C2semidirect
13. #14272C2semidirect
14. #14260C2semidirect
15. #14136C2semidirect
16. #14136C2semidirect
17. #14025C2semidirect
18. #13906C2semidirect
19. #13842C2semidirect
202. C4×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25002
C2×#24282
#170862
#165352
#162602
#153042
#152392
#151422
#151362
#151272
#151242
#142722
#142602
#141362
#140252
#139062
#138422