Finite Group Databasebeta

← #687621

Subgroups — #687621

Order 512.

3110 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2500C211yesmaximal, characteristic, complemented
2C2×#2414C211yesmaximal, characteristic
3C2×#2352C211yesmaximal, characteristic, complemented
4C2×#2317C211yesmaximal, characteristic, complemented
5#16266C214yesmaximal, complemented
6#15971C214yesmaximal, complemented
7#15346C214yesmaximal, complemented
8#15244C211yesmaximal, characteristic, complemented
9#15233C211yesmaximal, characteristic, complemented
10#15231C211yesmaximal, characteristic, complemented
11#15130C211yesmaximal, characteristic, complemented
12#14749C214yesmaximal, complemented
13#14257C211yesmaximal, characteristic, complemented
14#14137C211yesmaximal, characteristic, complemented
15#14049C211yesmaximal, characteristic, complemented
16#14002C211yesmaximal, characteristic, complemented
17#13879C211yesmaximal, characteristic, complemented
18#13879C211yesmaximal, characteristic, complemented
19#13839C211yesmaximal, characteristic, complemented
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27#2500—28no—
28#2414—28no—
29C2×#394C2214yes—
30C2×#394C2212yes—
31C2×#394C2214yes—
32C2×#392C2212yes—
33#2352—28no—
34#2317—28no—
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2212yes—
40C2×#390C2211yescharacteristic
41C2×#389C2214yes—
42C2×#389C2211yescharacteristic
43C2×#388C2212yes—
44C2×#388C2212yes—
45C2×#388C2214yes—
46C2×#387C2212yes—
47C2×#387C2214yes—
48C2×#386C2212yes—
49C2×#386C2214yes—
50C2×#385C2214yes—
51C2×#384C2211yescharacteristic
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2212yes—
66#1445C2214yes—
67#1443C2214yes—
68#1442C2214yes—
69#1441C2212yes—
70#1441C2214yes—
71#1440C2212yes—
72#1440C2214yes—
73#1440C2214yes—
74#1439C2212yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1438C2212yes—
83#1438C2214yes—
84#1437C2214yes—
85#1436C2214yes—
86#1436C2214yes—
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C23×D4C2312yes—
98C23×D4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102C2×#121—24no—
103C2×#121—24no—
104C2×#121—24no—
105C2×#121—24no—
106C2×#121—24no—
107C2×#121—42no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C2×C4×D4D418yes—
111C2×#117—24no—
112C2×#117—24no—
113C2×#117—24no—
114C2×#117—24no—
115C2×#117—24no—
116C2×#117—24no—
117C2×#117—24no—
118C2×#117—42no—
119C2×#117—42no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—42no—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2314yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2312yes—
164#394—216no—
165#394—28no—
166#394—48no—
167#392—28no—
168#390—24no—
169#390—28no—
170#390—24no—
171#390—24no—
172#390—24no—
173#390—42no—
174#389—216no—
175#389—24no—
176#388—28no—
177#388—216no—
178#388—28no—
179#387—28no—
180#387—48no—
181#386—28no—
182#386—48no—
183#385—216no—
184#384—24no—
185#384—42no—
186#384D418yescomplemented
187#382—24no—
188#382—24no—
189#382—24no—
190#382—24no—
191#380—24no—
192#380—24no—
193#380—24no—
194C4×C4⋊C4—24no—
195C4×C22⋊C4—24no—
196C4×C22⋊C4—28no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—24no—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C25C2412yes—
223C25C2411yescharacteristic
224C25C2411yescharacteristic
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—24no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—42no—
240C22×D4—42no—
241C22×D4—42no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4—44no—
246C22×D4C2×D414yes—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—42no—
260C23×C4—44no—
261C23×C4—44no—
262C23×C4C2×D414yes—
263C23×C4C2×D414yes—
264C23×C4#4114yes—
265C23×C4#4114yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2412yes—
275C23×C4C2411yescharacteristic
276C23×C4C2412yes—
277C23×C4C2411yescharacteristic
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282#121—416no—
283#121—416no—
284C4×D4—232no—
285#117—232no—
286#117—416no—
287#117—416no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—28no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—416no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4—44no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—44no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4C2×D414yes—
327C2×C4⋊C4C2×D414yes—
328C2×C4⋊C4C2×D414yes—
329C2×C4⋊C4C2×D4116yes—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
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—28no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
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⋊C4C2×D414yes—
381C2×C22⋊C4C2×D414yes—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—44no—
402C2×C42C2×D414yes—
403C2×C42C2×D414yes—
404C2×C42#4114yes—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—28no—
412#95—28no—
413#95—24no—
414#95—28no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—28no—
419#95—24no—
420#95—28no—
421#95—42no—
422#95—44no—
423#95—42no—
424#95—42no—
425#95—44no—
426#95—44no—
427#95—44no—
428C24—21no—
429C24—21no—
430C24—22no—
431C24—21no—
432C24—21no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—21no—
440C24—22no—
441C24—21no—
442C24—21no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—24no—
452C24—22no—
453C24—22no—
454C24—24no—
455C24—24no—
456C24—24no—
457C24C22×D412yes—
458C24C22×D412yes—
459C24C2×#4112yes—
460C24C2×#4112yes—
461C24C2511yescharacteristic
462C2×D4—28no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—416no—
470C2×D4—48no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—88no—
479C2×D4—84no—
480C2×D4—88no—
481C2×D4—84no—
482C2×D4—84no—
483C2×D4—88no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—28no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—24no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—48no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—48no—
575C22×C4—88no—
576C22×C4—84no—
577C22×C4—88no—
578C22×C4#123116yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D414yes—
582C22×C4C22×D412yes—
583C22×C4C22×D414yes—
584C22×C4C22×D414yes—
585C22×C4C22×D412yes—
586C22×C4C22×D412yes—
587C22×C4C22×D412yes—
588C22×C4C2×#4114yes—
589C22×C4C2×#4112yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4112yes—
594C22×C4H(5,𝔽2)14yes—
595C22×C4H(5,𝔽2)12yes—
596C22×C42−1+412yes—
597C4⋊C4—216no—
598C4⋊C4—28no—
599C4⋊C4—28no—
600C4⋊C4—28no—
601C4⋊C4—416no—
602C4⋊C4—48no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—44no—
608C4⋊C4—88no—
609C4⋊C4—84no—
610C4⋊C4—88no—
611C22⋊C4—216no—
612C22⋊C4—28no—
613C22⋊C4—28no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—416no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—88no—
625C22⋊C4—88no—
626C22⋊C4—84no—
627C22⋊C4—88no—
628C22⋊C4—84no—
629C22⋊C4—84no—
630C42—28no—
631C42—28no—
632C42—28no—
633C42—48no—
634C42—48no—
635C42—44no—
636C42—44no—
637C42—84no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
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—42no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—42no—
699C23—42no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23—44no—
705C23—44no—
706C23C2×#12314yes—
707C23C23×D411yescharacteristic
708C23C23×D411yescharacteristic
709C23C22×#4111yescharacteristic
710C23C22×#4111yescharacteristic
711C23C22×#4111yescharacteristic
712C23C2×H(5,𝔽2)11yescharacteristic
713C23C2×H(5,𝔽2)12yes—
714C23C2×2−1+411yescharacteristic
715C23#58512yes—
716C23#58512yes—
717C23#58512yes—
718D4—416no—
719D4—816no—
720D4—816no—
721D4—88no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—232no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—28no—
745C2×C4—24no—
746C2×C4—28no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—44no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—416no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—44no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—816no—
811C2×C4C2×#12314yes—
812C2×C4C2×#12314yes—
813C2×C4#52514yes—
814C2×C4#53914yes—
815C2×C4D4214yes—
816C2×C4#54714yes—
817C2×C4#54814yes—
818C2×C4#55314yes—
819C22—24no—
820C22—24no—
821C22—24no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—84no—
846C22—84no—
847C22—84no—
848C22—82no—
849C22—82no—
850C22—84no—
851C22—82no—
852C22C22×#12311yescharacteristic
853C22C2×#52511yescharacteristic
854C22#344911yescharacteristic
855C22#344911yescharacteristic
856C22C2×#53911yescharacteristic
857C22C2×D4211yescharacteristic
858C22C2×#54711yescharacteristic
859C22C2×#54811yescharacteristic
860C22C2×#55311yescharacteristic
861C22#348712yes—
862C22#349312yes—
863C22#349312yes—
864C22#349412yes—
865C22#349412yes—
866C22#349612yes—
867C22#349811yescharacteristic
868C22#350011yescharacteristic
869C22#350612yes—
870C22#351212yes—
871C22#354712yes—
872C22#355812yes—
873C22#356212yes—
874C22#356512yes—
875C4—24no—
876C4—42no—
877C4—42no—
878C4—44no—
879C4—44no—
880C4—44no—
881C4—44no—
882C4—44no—
883C4—42no—
884C4—82no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4#244318yes—
891C2—44no—
892C2—82no—
893C2—162no—
894C2C2×#244311yescharacteristic
895C2#3515711yescharacteristic
896C2#3553111yescharacteristic
897C2#3575212yes—
898C2#3768311yescharacteristic
899C2#3786911yescharacteristic
900C2#3935511yescharacteristic
901C2#3948511yescharacteristic
902C2#4246512yes—
903C2#4489312yes—
904C2#4516012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2414C2
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
3. C2×#2352C2semidirect
4. C2×#2317C2semidirect
5. #16266C2semidirect
6. #15971C2semidirect
7. #15346C2semidirect
8. #15244C2semidirect
9. #15233C2semidirect
10. #15231C2semidirect
11. #15130C2semidirect
12. #14749C2semidirect
13. #14257C2semidirect
14. #14137C2semidirect
15. #14049C2semidirect
16. #14002C2semidirect
17. #13879C2semidirect
18. #13879C2semidirect
19. #13839C2semidirect
186. #384D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25002
C2×#24142
C2×#23522
C2×#23172
#162662
#159712
#153462
#152442
#152332
#152312
#151302
#147492
#142572
#141372
#140492
#140022
#138792
#138392