Finite Group Databasebeta

← #649081

Subgroups — #649081

Order 512.

3344 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×#2504C211yesmaximal, characteristic, complemented
2C2×#2414C211yesmaximal, characteristic
3C2×#2352C211yesmaximal, characteristic, complemented
4C2×#2285C211yesmaximal, characteristic, complemented
5#15376C214yesmaximal, complemented
6#15295C214yesmaximal, complemented
7#15244C211yesmaximal, characteristic, complemented
8#15233C211yesmaximal, characteristic, complemented
9#15231C211yesmaximal, characteristic, complemented
10#15130C211yesmaximal, characteristic, complemented
11#14783C214yesmaximal, complemented
12#14698C211yesmaximal, characteristic, complemented
13#14195C214yesmaximal, complemented
14#14136C211yesmaximal, characteristic, complemented
15#14050C211yesmaximal, characteristic, complemented
16#14001C211yesmaximal, characteristic, complemented
17#13880C211yesmaximal, characteristic, complemented
18#13879C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic, complemented
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×#117C2211yescharacteristic
24C22×#117C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C42C2211yescharacteristic
27#2504—28no—
28#2414—28no—
29C2×#397C2214yes—
30C2×#394C2214yes—
31C2×#394C2212yes—
32C2×#392C2212yes—
33#2352—28no—
34C2×#390C2211yescharacteristic
35C2×#390C2211yescharacteristic
36C2×#390C2211yescharacteristic
37C2×#390C2212yes—
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#389C2211yescharacteristic
41C2×#388C2212yes—
42C2×#388C2212yes—
43C2×#388C2214yes—
44C2×#387C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#386C2214yes—
48C2×#386C2214yes—
49C2×#385C2214yes—
50#2285—28no—
51C2×#384C2211yescharacteristic
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#382C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#380C2214yes—
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2214yes—
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2212yes—
67C2×C4×C22⋊C4C2211yescharacteristic
68#1444C2214yes—
69#1443C2214yes—
70#1443C2214yes—
71#1442C2214yes—
72#1441C2214yes—
73#1440C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1438C2214yes—
80#1437C2214yes—
81#1437C2214yes—
82#1437C2212yes—
83#1436C2214yes—
84#1436C2214yes—
85#1436C2212yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C22⋊#95C2212yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C2×#121—24no—
104C2×#121—24no—
105C2×#121—24no—
106C2×#121—24no—
107C2×#121—24no—
108C2×#121—42no—
109C2×C4×D4—24no—
110C2×C4×D4—24no—
111C2×C4×D4D418yes—
112C2×#117—24no—
113C2×#117—24no—
114C2×#117—24no—
115C2×#117—24no—
116C2×#117—42no—
117C2×#117—42no—
118C22×C4⋊C4—24no—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—42no—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2314yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2314yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2312yes—
152C22×C42—24no—
153C22×C42—24no—
154C22×C42—24no—
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2312yes—
164#397—216no—
165#394—28no—
166#394—216no—
167#392—28no—
168#390—24no—
169#390—28no—
170#390—24no—
171#390—24no—
172#390—24no—
173#390—42no—
174#389—24no—
175#388—28no—
176#388—28no—
177#388—48no—
178#387—28no—
179#386—28no—
180#386—28no—
181#386—216no—
182#386—48no—
183#385—48no—
184#384—24no—
185#384—24no—
186#384—42no—
187#382—24no—
188#382—24no—
189#382—24no—
190#382D418yescomplemented
191#380—24no—
192#380—24no—
193#380—24no—
194#380—216no—
195C4×C4⋊C4—24no—
196C4×C4⋊C4—216no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—28no—
199C4×C22⋊C4—24no—
200C4×C22⋊C4—24no—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C25C2412yes—
225C25C2411yescharacteristic
226C25C2411yescharacteristic
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—24no—
230C22×D4—24no—
231C22×D4—24no—
232C22×D4—28no—
233C22×D4—24no—
234C22×D4—24no—
235C22×D4—22no—
236C22×D4—24no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4C2×D414yes—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—24no—
254C23×C4—22no—
255C23×C4—24no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4C2×D414yes—
272C23×C4C2×D414yes—
273C23×C4#4114yes—
274C23×C4#4114yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291#121—416no—
292#121—416no—
293C4×D4—232no—
294#117—416no—
295#117—416no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
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—28no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—416no—
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⋊C4—44no—
332C2×C4⋊C4C2×D414yes—
333C2×C4⋊C4C2×D414yes—
334C2×C4⋊C4C2×D414yes—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
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—28no—
347C2×C22⋊C4—24no—
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—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
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⋊C4C2×D414yes—
382C2×C22⋊C4C2×D414yes—
383C2×C22⋊C4#4118yes—
384C2×C42—232no—
385C2×C42—24no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
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×C42#4114yes—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—28no—
415#95—24no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—28no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—28no—
426#95—28no—
427#95—24no—
428#95—42no—
429#95—44no—
430#95—44no—
431#95—44no—
432#95—44no—
433#95C2×D4116yes—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
438C24—21no—
439C24—22no—
440C24—21no—
441C24—22no—
442C24—21no—
443C24—22no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—24no—
455C24—22no—
456C24—22no—
457C24—24no—
458C24—22no—
459C24—22no—
460C24—24no—
461C24—24no—
462C24C22×D412yes—
463C24C22×D412yes—
464C24C2×#4112yes—
465C24C2×#4112yes—
466C24C2×#4114yes—
467C24C2511yescharacteristic
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—44no—
471C2×D4—48no—
472C2×D4—416no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—416no—
476C2×D4—48no—
477C2×D4—48no—
478C2×D4—44no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—44no—
485C2×D4—84no—
486C2×D4—88no—
487C2×D4—88no—
488C2×D4—84no—
489C2×D4—84no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—28no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—216no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
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—22no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
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—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—44no—
583C22×C4—48no—
584C22×C4—44no—
585C22×C4—48no—
586C22×C4—88no—
587C22×C4—84no—
588C22×C4—88no—
589C22×C4#123116yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D414yes—
593C22×C4C22×D414yes—
594C22×C4C22×D412yes—
595C22×C4C22×D414yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C22×D412yes—
599C22×C4C2×#4114yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4112yes—
602C22×C4C2×#4114yes—
603C22×C4C2×#4114yes—
604C22×C4C2×#4112yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4H(5,𝔽2)14yes—
608C22×C4H(5,𝔽2)12yes—
609C22×C42−1+412yes—
610C4⋊C4—28no—
611C4⋊C4—28no—
612C4⋊C4—28no—
613C4⋊C4—416no—
614C4⋊C4—416no—
615C4⋊C4—48no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—44no—
621C4⋊C4—84no—
622C4⋊C4—88no—
623C22⋊C4—28no—
624C22⋊C4—28no—
625C22⋊C4—216no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—416no—
635C22⋊C4—88no—
636C22⋊C4—88no—
637C22⋊C4—84no—
638C22⋊C4—88no—
639C22⋊C4—84no—
640C22⋊C4—84no—
641C42—216no—
642C42—28no—
643C42—28no—
644C42—28no—
645C42—48no—
646C42—48no—
647C42—44no—
648C42—44no—
649C42—84no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—24no—
662C23—24no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—41no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—44no—
703C23—44no—
704C23—42no—
705C23—44no—
706C23—44no—
707C23—44no—
708C23—44no—
709C23—44no—
710C23—42no—
711C23—42no—
712C23—44no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23C2×#12314yes—
718C23#53214yes—
719C23C23×D411yescharacteristic
720C23C23×D411yescharacteristic
721C23C22×#4111yescharacteristic
722C23C22×#4111yescharacteristic
723C23C22×#4111yescharacteristic
724C23C22×#4112yes—
725C23C2×H(5,𝔽2)11yescharacteristic
726C23C2×H(5,𝔽2)12yes—
727C23C2×2−1+411yescharacteristic
728C23#58512yes—
729C23#58512yes—
730D4—416no—
731D4—816no—
732D4—816no—
733D4—88no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—232no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—28no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—28no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—432no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—41no—
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—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—416no—
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—44no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—44no—
816C2×C4—42no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—42no—
822C2×C4—816no—
823C2×C4C2×#12314yes—
824C2×C4C2×#12314yes—
825C2×C4#52514yes—
826C2×C4#53914yes—
827C2×C4D4214yes—
828C2×C4#54714yes—
829C2×C4#54814yes—
830C2×C4#55318yes—
831C2×C4#55314yes—
832C22—24no—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—24no—
838C22—44no—
839C22—44no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—44no—
844C22—44no—
845C22—42no—
846C22—44no—
847C22—44no—
848C22—42no—
849C22—42no—
850C22—44no—
851C22—44no—
852C22—42no—
853C22—42no—
854C22—84no—
855C22—82no—
856C22—82no—
857C22—84no—
858C22—82no—
859C22—84no—
860C22—82no—
861C22—82no—
862C22—84no—
863C22—82no—
864C22—82no—
865C22C22×#12311yescharacteristic
866C22C2×#52511yescharacteristic
867C22C2×#53211yescharacteristic
868C22#344911yescharacteristic
869C22C2×#53911yescharacteristic
870C22C2×D4211yescharacteristic
871C22C2×#54711yescharacteristic
872C22C2×#54811yescharacteristic
873C22D4×#4112yes—
874C22C2×#55311yescharacteristic
875C22C2×#55312yes—
876C22#347512yes—
877C22#347512yes—
878C22#348812yes—
879C22#349312yes—
880C22#349412yes—
881C22#349811yescharacteristic
882C22#350011yescharacteristic
883C22#350612yes—
884C22#351112yes—
885C22#351412yes—
886C22#354612yes—
887C22#356512yes—
888C4—28no—
889C4—24no—
890C4—44no—
891C4—44no—
892C4—44no—
893C4—44no—
894C4—42no—
895C4—42no—
896C4—42no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4#244318yes—
904C2—44no—
905C2—44no—
906C2—162no—
907C2C2×#244311yescharacteristic
908C2#3481011yescharacteristic
909C2#3553111yescharacteristic
910C2#3612411yescharacteristic
911C2#3618211yescharacteristic
912C2#3643812yes—
913C2#3768111yescharacteristic
914C2#3787111yescharacteristic
915C2#3991212yes—
916C2#5913712yes—
917C2#5921212yes—
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×#2504C2semidirect
3. C2×#2352C2semidirect
4. C2×#2285C2semidirect
5. #15376C2semidirect
6. #15295C2semidirect
7. #15244C2semidirect
8. #15233C2semidirect
9. #15231C2semidirect
10. #15130C2semidirect
11. #14783C2semidirect
12. #14698C2semidirect
13. #14195C2semidirect
14. #14136C2semidirect
15. #14050C2semidirect
16. #14001C2semidirect
17. #13880C2semidirect
18. #13879C2semidirect
19. C4×#386C2semidirect
190. #382D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25042
C2×#24142
C2×#23522
C2×#22852
#153762
#152952
#152442
#152332
#152312
#151302
#147832
#146982
#141952
#141362
#140502
#140012
#138802
#138792
C4×#3862