Finite Group Databasebeta

← #875551

Subgroups — #875551

Order 512.

3294 conjugacy classes of subgroups.

The subgroup lattice has 919 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2541C211yesmaximal, characteristic
2C2×#2507C211yesmaximal, characteristic, complemented
3#16372C214yesmaximal, complemented
4#15617C214yesmaximal, complemented
5#15319C214yesmaximal, complemented
6#15244C211yesmaximal, characteristic, complemented
7#15222C211yesmaximal, characteristic, complemented
8#15140C211yesmaximal, characteristic, complemented
9#15140C211yesmaximal, characteristic, complemented
10#15140C211yesmaximal, characteristic, complemented
11#15140C211yesmaximal, characteristic, complemented
12#14713C211yesmaximal, characteristic, complemented
13#14700C211yesmaximal, characteristic, complemented
14#14418C214yesmaximal, complemented
15#14154C211yesmaximal, characteristic, complemented
16#14002C211yesmaximal, characteristic, complemented
17#13979C211yesmaximal, characteristic, complemented
18#13979C211yesmaximal, characteristic, complemented
19C4×#387C211yesmaximal, characteristic, complemented
20C22×#127C2211yescharacteristic
21C22×#127C2211yescharacteristic
22C22×#127C2211yescharacteristic
23C22×#121C2212yes—
24C22×#121C2212yes—
25C22×C4×D4C2211yescharacteristic
26#2541—28no—
27#2507—28no—
28C2×#398C2212yes—
29C2×#398C2212yes—
30C2×#394C2214yes—
31C2×#394C2214yes—
32C2×#394C2214yes—
33C2×#394C2214yes—
34C2×#392C2212yes—
35C2×#392C2212yes—
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2214yes—
43C2×#390C2214yes—
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#390C2214yes—
53C2×#389C2212yes—
54C2×#389C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#389C2211yescharacteristic
58C2×#388C2214yes—
59C2×#387C2212yes—
60C2×#387C2212yes—
61C2×#384C2211yescharacteristic
62C2×#382C2211yescharacteristic
63C2×#382C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C4⋊C4C2211yescharacteristic
67C2×C43C2211yescharacteristic
68#1440C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1438C2214yes—
76#1438C2214yes—
77#1438C2214yes—
78#1438C2214yes—
79#1438C2214yes—
80#1437C2214yes—
81#1437C2214yes—
82#1436C2212yes—
83#1436C2212yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86#1434C2212yes—
87C22⋊#95C2214yes—
88C22⋊#95C2214yes—
89C4×#95C2211yescharacteristic
90C4×#95C2211yescharacteristic
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×D4C2311yescharacteristic
94C23×D4C2311yescharacteristic
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C23×D4C2312yes—
98C23×D4C2312yes—
99C23×D4C2312yes—
100C23×D4C2312yes—
101C23×D4C2312yes—
102C24×C4C2312yes—
103C2×#127—24no—
104C2×#127—24no—
105C2×#127—24no—
106C2×#127—24no—
107C2×#127—24no—
108C2×#127—42no—
109C2×#127—42no—
110C2×#127—42no—
111C2×#127—42no—
112C2×#121—28no—
113C2×#121—28no—
114C2×#121—216no—
115C2×#121—48no—
116C2×C4×D4—24no—
117C2×C4×D4—42no—
118C2×C4×D4—42no—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2312yes—
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2312yes—
160#398—28no—
161#398—28no—
162#394—48no—
163#394—48no—
164#394—48no—
165#394—48no—
166#392—28no—
167#392—28no—
168#390—24no—
169#390—24no—
170#390—24no—
171#390—24no—
172#390—24no—
173#390—24no—
174#390—48no—
175#390—48no—
176#390—42no—
177#390—42no—
178#390—42no—
179#390—42no—
180#390—42no—
181#390—42no—
182#390—42no—
183#390—42no—
184#390—48no—
185#389—24no—
186#389—24no—
187#389—24no—
188#389—24no—
189#389—28no—
190#388—48no—
191#387—28no—
192#387—28no—
193#384—24no—
194#382—42no—
195#382—42no—
196C4×C4⋊C4—24no—
197C4×C4⋊C4—42no—
198C4×C4⋊C4D418yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2311yescharacteristic
218C2×#95C2311yescharacteristic
219C43—42no—
220C25C2412yes—
221C25C2412yes—
222C25C2412yes—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—22no—
228C22×D4—24no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—24no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—28no—
242C22×D4—28no—
243C22×D4—28no—
244C22×D4—22no—
245C22×D4—22no—
246C22×D4—22no—
247C22×D4—22no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—28no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4—42no—
260C22×D4—42no—
261C22×D4—42no—
262C22×D4—42no—
263C22×D4—42no—
264C22×D4—42no—
265C22×D4—42no—
266C22×D4—42no—
267C22×D4—44no—
268C22×D4—44no—
269C22×D4—44no—
270C22×D4—44no—
271C22×D4—44no—
272C22×D4—44no—
273C22×D4#4114yes—
274C23×C4—24no—
275C23×C4—28no—
276C23×C4—42no—
277C23×C4—42no—
278C23×C4—44no—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295#127—416no—
296#127—416no—
297#127—416no—
298#121—432no—
299#121—432no—
300C4×D4—416no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—44no—
331C2×C4⋊C4C2×D414yes—
332C2×C4⋊C4C2×D414yes—
333C2×C4⋊C4#4114yes—
334C2×C4⋊C4#4118yes—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—28no—
346C2×C22⋊C4—28no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—24no—
405C2×C42—42no—
406C2×C42—42no—
407C2×C42—44no—
408C2×C42C2×D414yes—
409C2×C42C2×D414yes—
410C2×C42C2×D414yes—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—42no—
425#95—44no—
426#95—44no—
427#95—44no—
428#95—44no—
429#95C2×D414yes—
430#95C2×D414yes—
431C24—22no—
432C24—22no—
433C24—24no—
434C24—24no—
435C24—24no—
436C24—22no—
437C24—22no—
438C24—24no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—24no—
446C24—24no—
447C24—22no—
448C24—22no—
449C24—24no—
450C24—24no—
451C24—24no—
452C24—24no—
453C24—24no—
454C24—24no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24C2×#4114yes—
464C24C2511yescharacteristic
465C2×D4—28no—
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—416no—
473C2×D4—416no—
474C2×D4—416no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—48no—
479C2×D4—48no—
480C2×D4—48no—
481C2×D4—48no—
482C2×D4—44no—
483C2×D4—48no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—44no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—84no—
502C2×D4—84no—
503C2×D4—84no—
504C2×D4—88no—
505C2×D4—88no—
506C2×D4—88no—
507C2×D4—88no—
508C2×D4—88no—
509C2×D4—84no—
510C2×D4—84no—
511C2×D4—84no—
512C2×D4—88no—
513C2×D4—88no—
514C2×D4—88no—
515C2×D4—88no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—88no—
590C22×C4—88no—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C2×#4114yes—
599C22×C4C2×#4114yes—
600C22×C4C2×#4114yes—
601C22×C4C2×#4114yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4H(5,𝔽2)14yes—
605C22×C4H(5,𝔽2)14yes—
606C22×C4H(5,𝔽2)14yes—
607C22×C4H(5,𝔽2)12yes—
608C22×C4H(5,𝔽2)12yes—
609C22×C4H(5,𝔽2)12yes—
610C22×C42−1+412yes—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—48no—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—84no—
620C4⋊C4—84no—
621C4⋊C4—84no—
622C4⋊C4—84no—
623C4⋊C4—84no—
624C4⋊C4#124116yes—
625C22⋊C4—416no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—88no—
632C22⋊C4—88no—
633C22⋊C4—88no—
634C22⋊C4—88no—
635C22⋊C4—88no—
636C22⋊C4—88no—
637C22⋊C4—88no—
638C22⋊C4—88no—
639C22⋊C4—88no—
640C22⋊C4—88no—
641C22⋊C4—88no—
642C42—28no—
643C42—28no—
644C42—28no—
645C42—48no—
646C42—48no—
647C42—44no—
648C42—44no—
649C42—44no—
650C42—44no—
651C42—84no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—28no—
656C23—28no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—44no—
663C23—42no—
664C23—42no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—42no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—44no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—44no—
711C23—42no—
712C23—42no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23C23×D411yescharacteristic
722C23C22×#4112yes—
723C23C22×#4111yescharacteristic
724C23C22×#4111yescharacteristic
725C23C2×H(5,𝔽2)11yescharacteristic
726C23C2×H(5,𝔽2)11yescharacteristic
727C23C2×H(5,𝔽2)12yes—
728C23C2×H(5,𝔽2)11yescharacteristic
729C23C2×H(5,𝔽2)12yes—
730C23C2×H(5,𝔽2)12yes—
731C23C2×2−1+411yescharacteristic
732D4—416no—
733D4—816no—
734D4—816no—
735D4—816no—
736D4—816no—
737D4—816no—
738D4—816no—
739D4—88no—
740D4—88no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—28no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—42no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—816no—
821C2×C4C2×#12414yes—
822C2×C4C2×#12414yes—
823C2×C4C2×#12414yes—
824C2×C4#53514yes—
825C2×C4#53514yes—
826C2×C4#53914yes—
827C2×C4#54014yes—
828C2×C4#54614yes—
829C2×C4#54814yes—
830C2×C4#55314yes—
831C2×C4#56214yes—
832C22—48no—
833C22—44no—
834C22—44no—
835C22—44no—
836C22—48no—
837C22—82no—
838C22—84no—
839C22—82no—
840C22—82no—
841C22—84no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—84no—
846C22—84no—
847C22—84no—
848C22—84no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—84no—
856C22—84no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—84no—
862C22—84no—
863C22—82no—
864C22—82no—
865C22C22×#12411yescharacteristic
866C22C2×#53511yescharacteristic
867C22C2×#53511yescharacteristic
868C22C2×#53911yescharacteristic
869C22C2×#54011yescharacteristic
870C22C2×#54611yescharacteristic
871C22C2×#54811yescharacteristic
872C22C2×#55311yescharacteristic
873C22#348112yes—
874C22#348312yes—
875C22#349811yescharacteristic
876C22#349811yescharacteristic
877C22#350812yes—
878C22#350812yes—
879C22#351912yes—
880C22#351912yes—
881C22#351912yes—
882C22#352212yes—
883C22C2×#56211yescharacteristic
884C22#353712yes—
885C22#354312yes—
886C22#354312yes—
887C22#354812yes—
888C4—24no—
889C4—24no—
890C4—24no—
891C4—24no—
892C4—44no—
893C4—44no—
894C4—42no—
895C4—44no—
896C4—42no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4#271118yes—
904C2—84no—
905C2—162no—
906C2—162no—
907C2#3528511yescharacteristic
908C2#3628911yescharacteristic
909C2#3645711yescharacteristic
910C2#3730211yescharacteristic
911C2#3808011yescharacteristic
912C2#3916911yescharacteristic
913C2#4012612yes—
914C2#4014112yes—
915C2#4561012yes—
916C2C2×#271111yescharacteristic
917C2#5969612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2541C2
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×#2507C2semidirect
3. #16372C2semidirect
4. #15617C2semidirect
5. #15319C2semidirect
6. #15244C2semidirect
7. #15222C2semidirect
8. #15140C2semidirect
9. #15140C2semidirect
10. #15140C2semidirect
11. #15140C2semidirect
12. #14713C2semidirect
13. #14700C2semidirect
14. #14418C2semidirect
15. #14154C2semidirect
16. #14002C2semidirect
17. #13979C2semidirect
18. #13979C2semidirect
19. C4×#387C2semidirect

Maximal subgroups

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

subgroupindex
C2×#25412
C2×#25072
#163722
#156172
#153192
#152442
#152222
#151402
#147132
#147002
#144182
#141542
#140022
#139792
C4×#3872