Finite Group Databasebeta

← #626525

Subgroups — #626525

Order 512.

3628 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2486C211yesmaximal, characteristic, complemented
2C2×#2407C211yesmaximal, characteristic
3C2×#2311C211yesmaximal, characteristic, complemented
4C2×#2293C211yesmaximal, characteristic, complemented
5#15921C214yesmaximal, complemented
6#15687C214yesmaximal, complemented
7#15436C214yesmaximal, complemented
8#15272C214yesmaximal, complemented
9#15237C211yesmaximal, characteristic, complemented
10#15219C211yesmaximal, characteristic, complemented
11#15182C211yesmaximal, characteristic, complemented
12#15134C211yesmaximal, characteristic, complemented
13#14703C211yesmaximal, characteristic, complemented
14#14700C211yesmaximal, characteristic, complemented
15#14340C211yesmaximal, characteristic, complemented
16#14258C211yesmaximal, characteristic, complemented
17#14257C211yesmaximal, characteristic, complemented
18#13937C211yesmaximal, characteristic, complemented
19#13924C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C22×#123C2212yes—
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×C4×D4C2211yescharacteristic
25C22×#117C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C23×C4⋊C4C2211yescharacteristic
28#2486—28no—
29#2407—28no—
30C2×#398C2212yes—
31C2×#397C2212yes—
32C2×#396C2214yes—
33C2×#394C2212yes—
34C2×#392C2212yes—
35#2311—28no—
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41#2293—28no—
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2212yes—
47C2×#390C2211yescharacteristic
48C2×#389C2211yescharacteristic
49C2×#389C2212yes—
50C2×#389C2211yescharacteristic
51C2×#388C2212yes—
52C2×#388C2212yes—
53C2×#388C2214yes—
54C2×#386C2214yes—
55C2×#386C2212yes—
56C2×#385C2212yes—
57C2×#384C2211yescharacteristic
58C2×#382C2211yescharacteristic
59C2×#381C2212yes—
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2214yes—
63C2×#380C2211yescharacteristic
64C2×#380C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C43C2211yescharacteristic
69#1445C2214yes—
70#1443C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1440C2214yes—
76#1440C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1438C2214yes—
82#1438C2214yes—
83#1438C2214yes—
84#1437C2214yes—
85#1436C2214yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92#1434C2214yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C22×#41—24no—
96C22×#41—24no—
97C22×#41—24no—
98C22×#41—24no—
99C22×#41—24no—
100C22×#41—42no—
101C22×#41—42no—
102C23×Q8C2311yescharacteristic
103C23×D4C2311yescharacteristic
104C23×D4C2312yes—
105C23×D4C2311yescharacteristic
106C23×D4C2312yes—
107C24×C4C2311yescharacteristic
108C24×C4C2312yes—
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C2×#123—28no—
112C2×#123—48no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8—42no—
116C2×#121—24no—
117C2×#121—24no—
118C2×#121—42no—
119C2×C4×D4—24no—
120C2×C4×D4—24no—
121C2×C4×D4D418yes—
122C2×#117—24no—
123C2×#117—42no—
124C2×#117—42no—
125C2×#117—42no—
126C2×#117—42no—
127C2×#117D418yescomplemented
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—24no—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2314yes—
145C22×C4⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2311yescharacteristic
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2312yes—
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166C22×C42C2312yes—
167C22×C42C2312yes—
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171#398—28no—
172#397—28no—
173#396—48no—
174#394—28no—
175#392—28no—
176#391—24no—
177#391—24no—
178#391—24no—
179#391—24no—
180#391—42no—
181#390—24no—
182#390—28no—
183#390—24no—
184#390—24no—
185#390—24no—
186#390—42no—
187#389—28no—
188#389—24no—
189#389—24no—
190#388—28no—
191#388—28no—
192#388—48no—
193#386—216no—
194#386—28no—
195#385—28no—
196#384—42no—
197#382—42no—
198#381—28no—
199#380—24no—
200#380—24no—
201#380—24no—
202#380—24no—
203#380—216no—
204C4×C4⋊C4—24no—
205C4×C22⋊C4—24no—
206C4×C22⋊C4—24no—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C43—24no—
230C25C2411yescharacteristic
231C25C2412yes—
232C25C2411yescharacteristic
233C2×#41—232no—
234C2×#41—416no—
235C2×#41—416no—
236C2×#41—416no—
237C2×#41—416no—
238C2×#41—416no—
239C2×#41—416no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8#4114yes—
247C22×D4—22no—
248C22×D4—24no—
249C22×D4—22no—
250C22×D4—24no—
251C22×D4—24no—
252C22×D4—24no—
253C22×D4—24no—
254C22×D4—24no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—24no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—24no—
262C22×D4—22no—
263C22×D4—42no—
264C22×D4—42no—
265C22×D4—42no—
266C22×D4—42no—
267C22×D4—44no—
268C22×D4—44no—
269C22×D4C2×D414yes—
270C22×D4#4114yes—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—22no—
275C23×C4—24no—
276C23×C4—22no—
277C23×C4—24no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—24no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—44no—
292C23×C4—44no—
293C23×C4C2×D414yes—
294C23×C4C2×D414yes—
295C23×C4C2×D414yes—
296C23×C4#4114yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313#123—432no—
314C22⋊Q8—416no—
315#121—416no—
316C4×D4—232no—
317#117—416no—
318#117—416no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—416no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4C2×D414yes—
362C2×C4⋊C4C2×D418yes—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4—44no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4C2×D414yes—
409C2×C22⋊C4C2×D414yes—
410C2×C22⋊C4C2×D418yes—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—24no—
426C2×C42—24no—
427C2×C42—42no—
428C2×C42—42no—
429C2×C42C2×D414yes—
430C2×C42C2×D414yes—
431C2×C42C2×D414yes—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—28no—
439#95—28no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—24no—
445#95—28no—
446#95—44no—
447#95—44no—
448#95—44no—
449#95—44no—
450#95—44no—
451#95—44no—
452#95—44no—
453#95—44no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—21no—
463C24—22no—
464C24—22no—
465C24—21no—
466C24—21no—
467C24—22no—
468C24—21no—
469C24—22no—
470C24—24no—
471C24—21no—
472C24—22no—
473C24—21no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—24no—
478C24—24no—
479C24—24no—
480C24—22no—
481C24—22no—
482C24C22×D412yes—
483C24C22×D412yes—
484C24C22×D412yes—
485C24C2×#4114yes—
486C24C2×#4112yes—
487C24C2511yescharacteristic
488#41—4128no—
489C2×Q8—28no—
490C2×Q8—28no—
491C2×Q8—28no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×D4—216no—
497C2×D4—28no—
498C2×D4—28no—
499C2×D4—28no—
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—44no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—48no—
510C2×D4—48no—
511C2×D4—48no—
512C2×D4—48no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—84no—
518C2×D4—88no—
519C2×D4—88no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—216no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—21no—
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—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—24no—
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—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—24no—
600C22×C4—22no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—22no—
607C22×C4—24no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—88no—
622C22×C4—88no—
623C22×C4#121116yes—
624C22×C4C22×D412yes—
625C22×C4C22×D414yes—
626C22×C4C22×D412yes—
627C22×C4C22×D414yes—
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D412yes—
633C22×C4C2×#4114yes—
634C22×C4C2×#4112yes—
635C22×C4C2×#4112yes—
636C22×C4C2×#4112yes—
637C22×C4C2×#4112yes—
638C22×C4H(5,𝔽2)14yes—
639C22×C4H(5,𝔽2)12yes—
640C22×C4H(5,𝔽2)12yes—
641C22×C42−1+414yes—
642C4⋊C4—28no—
643C4⋊C4—48no—
644C4⋊C4—48no—
645C4⋊C4—48no—
646C4⋊C4—48no—
647C4⋊C4—48no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—48no—
651C4⋊C4—48no—
652C4⋊C4—44no—
653C4⋊C4—44no—
654C4⋊C4—44no—
655C4⋊C4—44no—
656C4⋊C4—88no—
657C22⋊C4—28no—
658C22⋊C4—28no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—416no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—88no—
671C22⋊C4—88no—
672C22⋊C4—84no—
673C22⋊C4—84no—
674C22⋊C4—88no—
675C42—28no—
676C42—28no—
677C42—28no—
678C42—48no—
679C42—48no—
680C42—44no—
681C42—44no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—24no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—24no—
702C23—22no—
703C23—24no—
704C23—22no—
705C23—22no—
706C23—28no—
707C23—28no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—41no—
718C23—41no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—44no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—41no—
727C23—41no—
728C23—44no—
729C23—42no—
730C23—42no—
731C23—44no—
732C23—42no—
733C23—44no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—44no—
738C23—42no—
739C23—44no—
740C23—42no—
741C23—42no—
742C23—44no—
743C23—42no—
744C23—42no—
745C23—44no—
746C23—44no—
747C23—42no—
748C23—42no—
749C23—44no—
750C23C2×#12114yes—
751C23C23×D411yescharacteristic
752C23C23×D411yescharacteristic
753C23C22×#4111yescharacteristic
754C23C22×#4111yescharacteristic
755C23C22×#4111yescharacteristic
756C23C2×H(5,𝔽2)11yescharacteristic
757C23C2×H(5,𝔽2)11yescharacteristic
758C23C2×H(5,𝔽2)12yes—
759C23C2×2−1+412yes—
760C23#58512yes—
761C23#58512yes—
762Q8—416no—
763D4—416no—
764D4—432no—
765D4—416no—
766D4—816no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—232no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—432no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
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—416no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—44no—
836C2×C4—44no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—44no—
851C2×C4—44no—
852C2×C4—42no—
853C2×C4—44no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—44no—
857C2×C4—816no—
858C2×C4C2×#12114yes—
859C2×C4C2×#12114yes—
860C2×C4#52514yes—
861C2×C4#53414yes—
862C2×C4#53514yes—
863C2×C4#54614yes—
864C2×C4#54614yes—
865C2×C4#55114yes—
866C2×C4#55114yes—
867C22—24no—
868C22—24no—
869C22—24no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—44no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—44no—
883C22—42no—
884C22—44no—
885C22—42no—
886C22—48no—
887C22—42no—
888C22—48no—
889C22—42no—
890C22—82no—
891C22—82no—
892C22—82no—
893C22—84no—
894C22—82no—
895C22—82no—
896C22—84no—
897C22—82no—
898C22—82no—
899C22—82no—
900C22C22×#12111yescharacteristic
901C22C2×#52511yescharacteristic
902C22C2×#53411yescharacteristic
903C22C2×#53511yescharacteristic
904C22#344911yescharacteristic
905C22#346112yes—
906C22C2×#54611yescharacteristic
907C22C2×#54611yescharacteristic
908C22C2×#55111yescharacteristic
909C22C2×#55111yescharacteristic
910C22#348812yes—
911C22#348912yes—
912C22#349412yes—
913C22#349911yescharacteristic
914C22#350011yescharacteristic
915C22#351612yes—
916C22#351712yes—
917C22#352012yes—
918C22#352112yes—
919C22#354612yes—
920C22#354712yes—
921C22#354812yes—
922C22#355112yes—
923C4—24no—
924C4—24no—
925C4—42no—
926C4—44no—
927C4—44no—
928C4—44no—
929C4—44no—
930C4—42no—
931C4—82no—
932C4—82no—
933C4—82no—
934C4—82no—
935C4—82no—
936C4—82no—
937C4—82no—
938C4#253418yes—
939C2—44no—
940C2—84no—
941C2—82no—
942C2C2×#253411yescharacteristic
943C2#3525211yescharacteristic
944C2#3530811yescharacteristic
945C2#3552112yes—
946C2#3727212yes—
947C2#3820012yes—
948C2#3820512yes—
949C2#3894611yescharacteristic
950C2#3894711yescharacteristic
951C2#3895111yescharacteristic
952C2#3895611yescharacteristic
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×#2486C2semidirect
3. C2×#2311C2semidirect
4. C2×#2293C2semidirect
5. #15921C2semidirect
6. #15687C2semidirect
7. #15436C2semidirect
8. #15272C2semidirect
9. #15237C2semidirect
10. #15219C2semidirect
11. #15182C2semidirect
12. #15134C2semidirect
13. #14703C2semidirect
14. #14700C2semidirect
15. #14340C2semidirect
16. #14258C2semidirect
17. #14257C2semidirect
18. #13937C2semidirect
19. #13924C2semidirect
127. C2×#117D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24862
C2×#24072
C2×#23112
C2×#22932
#159212
#156872
#154362
#152722
#152372
#152192
#151822
#151342
#147032
#147002
#143402
#142582
#142572
#139372
#139242