Finite Group Databasebeta

← #875309

Subgroups — #875309

Order 512.

3396 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2547C211yesmaximal, characteristic, complemented
2C2×#2407C211yesmaximal, characteristic
3#16856C214yesmaximal, complemented
4#15494C214yesmaximal, complemented
5#15314C214yesmaximal, complemented
6#15236C211yesmaximal, characteristic, complemented
7#15233C211yesmaximal, characteristic, complemented
8#15195C211yesmaximal, characteristic, complemented
9#15191C211yesmaximal, characteristic, complemented
10#15144C211yesmaximal, characteristic, complemented
11#15130C211yesmaximal, characteristic, complemented
12#14702C211yesmaximal, characteristic, complemented
13#14698C211yesmaximal, characteristic, complemented
14#14553C214yesmaximal, complemented
15#14002C211yesmaximal, characteristic, complemented
16#14000C211yesmaximal, characteristic, complemented
17#13937C211yesmaximal, characteristic, complemented
18#13937C211yesmaximal, characteristic, complemented
19C4×#386C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×#124C2212yes—
23C22×C22⋊Q8C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C23×C42C2211yescharacteristic
27#2547—28no—
28#2407—28no—
29C2×#397C2212yes—
30C2×#397C2212yes—
31C2×#394C2212yes—
32C2×#394C2214yes—
33C2×#393C2214yes—
34C2×#392C2212yes—
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2212yes—
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#386C2214yes—
49C2×#385C2212yes—
50C2×#384C2211yescharacteristic
51C2×#382C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2211yescharacteristic
61#1446C2214yes—
62#1443C2214yes—
63#1442C2214yes—
64#1442C2214yes—
65#1442C2214yes—
66#1442C2214yes—
67#1440C2214yes—
68#1440C2214yes—
69#1440C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1438C2214yes—
74#1438C2214yes—
75#1437C2214yes—
76#1437C2214yes—
77#1437C2212yes—
78#1436C2214yes—
79#1436C2214yes—
80#1436C2212yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C22⋊#95C2214yes—
88C22⋊#95C2214yes—
89C22⋊#95C2214yes—
90C22⋊#95C2212yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C22×#41—24no—
94C22×#41—24no—
95C22×#41—24no—
96C22×#41—42no—
97C22×#41—42no—
98C22×#41—42no—
99C22×#41—42no—
100C23×Q8C2311yescharacteristic
101C23×Q8C2312yes—
102C23×D4C2311yescharacteristic
103C23×D4C2312yes—
104C23×D4C2311yescharacteristic
105C23×D4C2312yes—
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2312yes—
109C24×C4C2312yes—
110C2×C4⋊Q8—24no—
111C2×C4⋊Q8—42no—
112C2×C4⋊Q8—42no—
113C2×#124—28no—
114C2×#124—48no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—42no—
118C2×#121—24no—
119C2×#121—24no—
120C2×#121—42no—
121C2×C4×D4—42no—
122C2×C4×D4—42no—
123C2×C4×D4D418yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2311yescharacteristic
152C22×C42—42no—
153C22×C42—42no—
154C22×C42—42no—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2312yes—
161C22×C42C2312yes—
162#397—28no—
163#397—28no—
164#394—28no—
165#394—48no—
166#393—216no—
167#392—28no—
168#391—24no—
169#391—28no—
170#391—24no—
171#391—42no—
172#391—42no—
173#391—42no—
174#390—24no—
175#390—24no—
176#390—42no—
177#390—42no—
178#390—42no—
179#386—28no—
180#386—28no—
181#386—48no—
182#385—28no—
183#384—42no—
184#382—42no—
185#380—24no—
186#380—24no—
187#380—24no—
188#380—24no—
189#380—24no—
190C4×C4⋊C4—24no—
191C4×C22⋊C4—42no—
192C4×C22⋊C4—42no—
193C4×C22⋊C4—42no—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C25C2411yescharacteristic
221C25C2412yes—
222C25C2411yescharacteristic
223C2×#41—416no—
224C2×#41—416no—
225C2×#41—416no—
226C2×#41—416no—
227C2×#41—416no—
228C2×#41—416no—
229C2×#41—416no—
230C22×Q8—22no—
231C22×Q8—24no—
232C22×Q8—22no—
233C22×Q8—28no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—44no—
239C22×Q8—42no—
240C22×Q8—42no—
241C22×Q8#4114yes—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—28no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—41no—
257C22×D4—41no—
258C22×D4—42no—
259C22×D4—42no—
260C22×D4—42no—
261C22×D4—42no—
262C22×D4—42no—
263C22×D4—44no—
264C22×D4C2×D414yes—
265C22×D4#4114yes—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—42no—
285C23×C4—42no—
286C23×C4—42no—
287C23×C4—42no—
288C23×C4—42no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4C2×D414yes—
293C23×C4C2×D414yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C4⋊Q8—416no—
311#124—432no—
312C22⋊Q8—416no—
313#121—416no—
314C4×D4—416no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—41no—
337C2×C4⋊C4—41no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—44no—
344C2×C4⋊C4C2×D414yes—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—28no—
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—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—28no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—41no—
370C2×C22⋊C4—41no—
371C2×C22⋊C4—41no—
372C2×C22⋊C4—41no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
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⋊C4C2×D414yes—
391C2×C22⋊C4C2×D414yes—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—24no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—44no—
408C2×C42—42no—
409C2×C42—42no—
410C2×C42—42no—
411C2×C42—416no—
412C2×C42C2×D414yes—
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—28no—
423#95—28no—
424#95—28no—
425#95—24no—
426#95—44no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—44no—
432#95—44no—
433#95—44no—
434#95—44no—
435#95—44no—
436#95—44no—
437#95—44no—
438#95#4118yescomplemented
439C24—21no—
440C24—22no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—21no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—24no—
450C24—22no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—22no—
455C24—24no—
456C24—21no—
457C24—21no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—21no—
462C24—21no—
463C24—22no—
464C24—24no—
465C24—22no—
466C24—22no—
467C24—24no—
468C24C22×D412yes—
469C24C22×D412yes—
470C24C2×#4114yes—
471C24H(5,𝔽2)14yes—
472C24C2511yescharacteristic
473#41—4128no—
474C2×Q8—28no—
475C2×Q8—28no—
476C2×Q8—28no—
477C2×Q8—48no—
478C2×Q8—48no—
479C2×Q8—48no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—88no—
485C2×Q8—88no—
486C2×D4—28no—
487C2×D4—28no—
488C2×D4—28no—
489C2×D4—28no—
490C2×D4—28no—
491C2×D4—44no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—48no—
502C2×D4—416no—
503C2×D4—48no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—84no—
509C2×D4—88no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
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—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—28no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C2×#4114yes—
624C22×C4C2×#4114yes—
625C22×C4C2×#4114yes—
626C22×C4C2×#4114yes—
627C22×C4C2×#4112yes—
628C22×C4C2×#4112yes—
629C22×C4H(5,𝔽2)12yes—
630C22×C4H(5,𝔽2)12yes—
631C22×C4H(5,𝔽2)12yes—
632C22×C4H(5,𝔽2)12yes—
633C22×C42−1+414yes—
634C4⋊C4—44no—
635C4⋊C4—48no—
636C4⋊C4—48no—
637C4⋊C4—44no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—44no—
642C4⋊C4—44no—
643C4⋊C4—88no—
644C22⋊C4—44no—
645C22⋊C4—44no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—84no—
657C22⋊C4—88no—
658C22⋊C4—88no—
659C22⋊C4—88no—
660C22⋊C4—84no—
661C22⋊C4—88no—
662C42—28no—
663C42—48no—
664C42—48no—
665C42—44no—
666C42—44no—
667C42—44no—
668C42—44no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—24no—
686C23—22no—
687C23—22no—
688C23—24no—
689C23—28no—
690C23—22no—
691C23—22no—
692C23—28no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—41no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—41no—
708C23—41no—
709C23—42no—
710C23—41no—
711C23—42no—
712C23—44no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—44no—
718C23—42no—
719C23—44no—
720C23—44no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—44no—
725C23—42no—
726C23—44no—
727C23—42no—
728C23—41no—
729C23—44no—
730C23—42no—
731C23—42no—
732C23—44no—
733C23—44no—
734C23—42no—
735C23—42no—
736C23—44no—
737C23#53514yes—
738C23C23×D411yescharacteristic
739C23C22×#4112yes—
740C23C22×#4111yescharacteristic
741C23C22×#4111yescharacteristic
742C23C2×H(5,𝔽2)11yescharacteristic
743C23C2×H(5,𝔽2)11yescharacteristic
744C23C2×H(5,𝔽2)12yes—
745C23C2×H(5,𝔽2)11yescharacteristic
746C23C2×H(5,𝔽2)11yescharacteristic
747C23C2×2−1+412yes—
748C23#58512yes—
749Q8—416no—
750Q8—816no—
751D4—416no—
752D4—432no—
753D4—416no—
754D4—816no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—432no—
781C2×C4—432no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—416no—
809C2×C4—416no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—44no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—44no—
833C2×C4—42no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—42no—
837C2×C4—44no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—42no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—42no—
847C2×C4#53214yes—
848C2×C4#53414yes—
849C2×C4#53814yes—
850C2×C4#53814yes—
851C2×C4#54614yes—
852C2×C4#54614yes—
853C2×C4#55114yes—
854C2×C4H(3,𝔽4)14yes—
855C22—24no—
856C22—24no—
857C22—24no—
858C22—42no—
859C22—44no—
860C22—42no—
861C22—44no—
862C22—42no—
863C22—44no—
864C22—42no—
865C22—44no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—44no—
870C22—42no—
871C22—48no—
872C22—44no—
873C22—42no—
874C22—42no—
875C22—44no—
876C22—42no—
877C22—48no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—84no—
882C22—84no—
883C22—82no—
884C22—82no—
885C22—82no—
886C22—82no—
887C22—82no—
888C22C2×#53211yescharacteristic
889C22C2×#53411yescharacteristic
890C22C2×#53511yescharacteristic
891C22C2×#53811yescharacteristic
892C22C2×#53811yescharacteristic
893C22C2×#54611yescharacteristic
894C22C2×#54611yescharacteristic
895C22C2×#55111yescharacteristic
896C22#348012yes—
897C22#348212yes—
898C22#349911yescharacteristic
899C22#350011yescharacteristic
900C22#350612yes—
901C22#351312yes—
902C22#351912yes—
903C22#351912yes—
904C22#352012yes—
905C22#352212yes—
906C22C2×H(3,𝔽4)11yescharacteristic
907C22#353612yes—
908C22#354112yes—
909C22#354212yes—
910C22#354712yes—
911C4—24no—
912C4—42no—
913C4—44no—
914C4—44no—
915C4—44no—
916C4—42no—
917C4—42no—
918C4—44no—
919C4—82no—
920C4—82no—
921C4—82no—
922C4—82no—
923C4—82no—
924C4—82no—
925C4—82no—
926C4#268418yes—
927C2—44no—
928C2—82no—
929C2—84no—
930C2#3507811yescharacteristic
931C2#3640611yescharacteristic
932C2#3641911yescharacteristic
933C2#3738811yescharacteristic
934C2#3807911yescharacteristic
935C2#3808211yescharacteristic
936C2#3922212yes—
937C2#4006812yes—
938C2#4560112yes—
939C2C2×#268411yescharacteristic
940C2#5938112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2407C2
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×#2547C2semidirect
3. #16856C2semidirect
4. #15494C2semidirect
5. #15314C2semidirect
6. #15236C2semidirect
7. #15233C2semidirect
8. #15195C2semidirect
9. #15191C2semidirect
10. #15144C2semidirect
11. #15130C2semidirect
12. #14702C2semidirect
13. #14698C2semidirect
14. #14553C2semidirect
15. #14002C2semidirect
16. #14000C2semidirect
17. #13937C2semidirect
18. #13937C2semidirect
19. C4×#386C2semidirect
438. #95#41semidirect

Maximal subgroups

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

subgroupindex
C2×#25472
C2×#24072
#168562
#154942
#153142
#152362
#152332
#151952
#151912
#151442
#151302
#147022
#146982
#145532
#140022
#140002
#139372
C4×#3862