Finite Group Databasebeta

← #719721

Subgroups — #719721

Order 512.

3148 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2537C211yesmaximal, characteristic
2C2×#2500C211yesmaximal, characteristic, complemented
3C2×#2504C211yesmaximal, characteristic, complemented
4C2×#2352C211yesmaximal, characteristic, complemented
5#16438C214yesmaximal, complemented
6#15386C214yesmaximal, complemented
7#15312C214yesmaximal, complemented
8#15233C211yesmaximal, characteristic, complemented
9#15219C211yesmaximal, characteristic, complemented
10#15150C211yesmaximal, characteristic, complemented
11#15130C211yesmaximal, characteristic, complemented
12#14741C214yesmaximal, complemented
13#14354C211yesmaximal, characteristic, complemented
14#13941C211yesmaximal, characteristic, complemented
15#13911C211yesmaximal, characteristic, complemented
16#13881C211yesmaximal, characteristic, complemented
17#13879C211yesmaximal, characteristic, complemented
18#13847C211yesmaximal, characteristic, complemented
19#13785C211yesmaximal, characteristic, complemented
20C22×#121C2211yescharacteristic
21C22×#121C2211yescharacteristic
22C22×#121C2212yes—
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27#2537—28no—
28#2504—28no—
29#2500—28no—
30C2×#397C2214yes—
31C2×#397C2214yes—
32C2×#394C2212yes—
33C2×#394C2214yes—
34C2×#394C2212yes—
35C2×#394C2214yes—
36#2352—28no—
37C2×#390C2211yescharacteristic
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2211yescharacteristic
41C2×#388C2214yes—
42C2×#388C2212yes—
43C2×#387C2212yes—
44C2×#386C2212yes—
45C2×#386C2214yes—
46C2×#384C2211yescharacteristic
47C2×#384C2211yescharacteristic
48C2×#384C2211yescharacteristic
49C2×#382C2211yescharacteristic
50C2×#382C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#382C2211yescharacteristic
53C2×#382C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2212yes—
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2212yes—
66C2×#376C2211yescharacteristic
67#1445C2212yes—
68#1445C2214yes—
69#1444C2214yes—
70#1444C2214yes—
71#1443C2214yes—
72#1442C2214yes—
73#1442C2214yes—
74#1440C2214yes—
75#1440C2214yes—
76#1439C2212yes—
77#1439C2212yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1438C2212yes—
82#1438C2214yes—
83#1437C2214yes—
84#1436C2214yes—
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2214yes—
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C22⋊#95C2214yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102C24×C4C2312yes—
103C2×#121—24no—
104C2×#121—24no—
105C2×#121—28no—
106C2×#121—24no—
107C2×#121—24no—
108C2×#121—48no—
109C2×#121—42no—
110C2×#121—42no—
111C2×C4×D4—24no—
112C2×C4×D4—24no—
113C2×C4×D4—24no—
114C2×C4×D4—24no—
115C2×C4×D4—24no—
116C2×C4×D4D418yes—
117C2×#117—24no—
118C2×#117—24no—
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⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
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⋊C4C2312yes—
145C22×C22⋊C4C2311yescharacteristic
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2314yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2312yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162#397—216no—
163#397—48no—
164#394—216no—
165#394—28no—
166#394—28no—
167#394—48no—
168#390—24no—
169#390—24no—
170#390—24no—
171#390D418yescomplemented
172#388—28no—
173#388—216no—
174#387—28no—
175#386—28no—
176#386—216no—
177#384—24no—
178#384—24no—
179#384—42no—
180#382—24no—
181#382—24no—
182#382—24no—
183#382—24no—
184#382—42no—
185#380—24no—
186#380—24no—
187#380—24no—
188#380—24no—
189#380—28no—
190C4×C4⋊C4—24no—
191C4×C4⋊C4—24no—
192C4×C22⋊C4—28no—
193C4×C22⋊C4—24no—
194C4×C22⋊C4—24no—
195C4×C22⋊C4—24no—
196C4×C22⋊C4—24no—
197#376—24no—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C25C2411yescharacteristic
223C25C2412yes—
224C25C2411yescharacteristic
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—28no—
230C22×D4—24no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—42no—
240C22×D4—42no—
241C22×D4—44no—
242C22×D4—42no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4C2×D414yes—
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—22no—
258C23×C4—22no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—42no—
265C23×C4—44no—
266C23×C4—44no—
267C23×C4—44no—
268C23×C4—44no—
269C23×C4C2×D414yes—
270C23×C4C2×D414yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2412yes—
274C23×C4C2412yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2411yescharacteristic
281C23×C4C2412yes—
282C23×C4C2411yescharacteristic
283C23×C4C2412yes—
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287#121—416no—
288#121—416no—
289#121—432no—
290C4×D4—232no—
291C4×D4—416no—
292#117—416no—
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—24no—
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—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—416no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—44no—
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×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
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—28no—
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—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
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⋊C4C2×D4116yes—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—24no—
397C2×C42—42no—
398C2×C42—44no—
399C2×C42C2×D414yes—
400C2×C42C2×D414yes—
401C2×C42#4114yes—
402C2×C42#4114yes—
403C2×C42#4114yes—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—24no—
413#95—28no—
414#95—28no—
415#95—28no—
416#95—24no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—44no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95—44no—
426#95—44no—
427#95—44no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—21no—
438C24—22no—
439C24—21no—
440C24—22no—
441C24—21no—
442C24—21no—
443C24—22no—
444C24—22no—
445C24—21no—
446C24—24no—
447C24—22no—
448C24—22no—
449C24—21no—
450C24—22no—
451C24—24no—
452C24—22no—
453C24—24no—
454C24—22no—
455C24—24no—
456C24—22no—
457C24C22×D414yes—
458C24C22×D412yes—
459C24C22×D412yes—
460C24H(5,𝔽2)14yes—
461C24C2511yescharacteristic
462C2×D4—28no—
463C2×D4—28no—
464C2×D4—28no—
465C2×D4—28no—
466C2×D4—28no—
467C2×D4—44no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—416no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—88no—
480C2×D4—84no—
481C2×D4—84no—
482C2×D4—88no—
483C2×D4—88no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—28no—
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—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—44no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—88no—
580C22×C4—88no—
581C22×C4—88no—
582C22×C4—84no—
583C22×C4—88no—
584C22×C4C22×D412yes—
585C22×C4C22×D414yes—
586C22×C4C22×D414yes—
587C22×C4C22×D412yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C2×#4114yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4C2×#4112yes—
596C22×C4C2×#4112yes—
597C22×C4C2×#4112yes—
598C22×C4C2×#4112yes—
599C22×C4C2×#4112yes—
600C22×C4H(5,𝔽2)12yes—
601C22×C42−1+412yes—
602C4⋊C4—28no—
603C4⋊C4—28no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—44no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—84no—
614C4⋊C4—88no—
615C4⋊C4—88no—
616C22⋊C4—28no—
617C22⋊C4—28no—
618C22⋊C4—416no—
619C22⋊C4—48no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—88no—
631C22⋊C4—88no—
632C22⋊C4—88no—
633C22⋊C4—84no—
634C42—28no—
635C42—28no—
636C42—48no—
637C42—44no—
638C42—44no—
639C42—84no—
640C42#123116yes—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—22no—
660C23—24no—
661C23—28no—
662C23—28no—
663C23—22no—
664C23—22no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—41no—
677C23—42no—
678C23—42no—
679C23—41no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—41no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—44no—
701C23—44no—
702C23—42no—
703C23—44no—
704C23—42no—
705C23—42no—
706C23—44no—
707C23—44no—
708C23—42no—
709C23#53514yes—
710C23C23×D411yescharacteristic
711C23C23×D411yescharacteristic
712C23C22×#4111yescharacteristic
713C23C22×#4111yescharacteristic
714C23C22×#4111yescharacteristic
715C23C2×H(5,𝔽2)12yes—
716C23C2×H(5,𝔽2)11yescharacteristic
717C23C2×2−1+411yescharacteristic
718C23#58512yes—
719C23#58512yes—
720C23#58512yes—
721D4—416no—
722D4—416no—
723D4—816no—
724D4—816no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—28no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—416no—
767C2×C4—416no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
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—42no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—816no—
813C2×C4—816no—
814C2×C4C2×#12314yes—
815C2×C4C2×#12314yes—
816C2×C4C2×#12314yes—
817C2×C4#53214yes—
818C2×C4#54214yes—
819C2×C4D4214yes—
820C2×C4#54714yes—
821C2×C4#54714yes—
822C2×C4#55314yes—
823C22—24no—
824C22—24no—
825C22—24no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—44no—
830C22—42no—
831C22—44no—
832C22—44no—
833C22—42no—
834C22—42no—
835C22—44no—
836C22—42no—
837C22—42no—
838C22—44no—
839C22—48no—
840C22—42no—
841C22—44no—
842C22—42no—
843C22—48no—
844C22—42no—
845C22—42no—
846C22—82no—
847C22—82no—
848C22—82no—
849C22—84no—
850C22—82no—
851C22—82no—
852C22—84no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22C22×#12311yescharacteristic
857C22C2×#53211yescharacteristic
858C22C2×#53511yescharacteristic
859C22#344911yescharacteristic
860C22C2×#54211yescharacteristic
861C22C2×D4211yescharacteristic
862C22C2×#54711yescharacteristic
863C22C2×#54711yescharacteristic
864C22C2×#55311yescharacteristic
865C22#348512yes—
866C22#348812yes—
867C22#349312yes—
868C22#349312yes—
869C22#349412yes—
870C22#349412yes—
871C22#349412yes—
872C22#350011yescharacteristic
873C22#350011yescharacteristic
874C22#351212yes—
875C22#355812yes—
876C22#355912yes—
877C22#356212yes—
878C22#356512yes—
879C4—24no—
880C4—24no—
881C4—44no—
882C4—44no—
883C4—44no—
884C4—42no—
885C4—42no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—82no—
890C4—82no—
891C4—82no—
892C4—82no—
893C4—82no—
894C4#242218yes—
895C2—44no—
896C2—82no—
897C2—84no—
898C2C2×#242211yescharacteristic
899C2#3526211yescharacteristic
900C2#3561811yescharacteristic
901C2#3606212yes—
902C2#3767711yescharacteristic
903C2#3768211yescharacteristic
904C2#3786411yescharacteristic
905C2#3787111yescharacteristic
906C2#4269312yes—
907C2#4513512yes—
908C2#4516012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2537C2
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×#2504C2semidirect
4. C2×#2352C2semidirect
5. #16438C2semidirect
6. #15386C2semidirect
7. #15312C2semidirect
8. #15233C2semidirect
9. #15219C2semidirect
10. #15150C2semidirect
11. #15130C2semidirect
12. #14741C2semidirect
13. #14354C2semidirect
14. #13941C2semidirect
15. #13911C2semidirect
16. #13881C2semidirect
17. #13879C2semidirect
18. #13847C2semidirect
19. #13785C2semidirect
171. #390D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25372
C2×#25002
C2×#25042
C2×#23522
#164382
#153862
#153122
#152332
#152192
#151502
#151302
#147412
#143542
#139412
#139112
#138812
#138792
#138472
#137852