Finite Group Databasebeta

← #626273

Subgroups — #626273

Order 512.

3316 conjugacy classes of subgroups.

The subgroup lattice has 947 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2414C211yesmaximal, characteristic
2C2×#2417C211yesmaximal, characteristic, complemented
3C2×#2620C211yesmaximal, characteristic, complemented
4C2×#2290C211yesmaximal, characteristic, complemented
5#15599C214yesmaximal, complemented
6#15507C214yesmaximal, complemented
7#15473C214yesmaximal, complemented
8#15375C214yesmaximal, complemented
9#15217C211yesmaximal, characteristic, complemented
10#15215C211yesmaximal, characteristic, complemented
11#15195C211yesmaximal, characteristic, complemented
12#15151C211yesmaximal, characteristic, complemented
13#14702C211yesmaximal, characteristic, complemented
14#14698C211yesmaximal, characteristic, complemented
15#14261C211yesmaximal, characteristic, complemented
16#14260C211yesmaximal, characteristic, complemented
17#14138C211yesmaximal, characteristic, complemented
18#14137C211yesmaximal, characteristic, complemented
19#13795C211yesmaximal, characteristic, complemented
20C22×#124C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×#121C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C23×C4⋊C4C2211yescharacteristic
29C23×C42C2211yescharacteristic
30#2620—28no—
31#2417—28no—
32#2414—28no—
33C2×#398C2212yes—
34C2×#398C2214yes—
35C2×#396C2214yes—
36C2×#396C2212yes—
37C2×#394C2214yes—
38C2×#394C2212yes—
39C2×#392C2212yes—
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2212yes—
48C2×#390C2211yescharacteristic
49C2×#389C2211yescharacteristic
50C2×#389C2211yescharacteristic
51#2290—28no—
52C2×#388C2212yes—
53C2×#388C2212yes—
54C2×#387C2212yes—
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#386C2214yes—
58C2×#386C2214yes—
59C2×#385C2212yes—
60C2×#384C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2212yes—
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×#376C2211yescharacteristic
68#1445C2214yes—
69#1443C2214yes—
70#1442C2214yes—
71#1442C2214yes—
72#1440C2214yes—
73#1440C2214yes—
74#1440C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2214yes—
80#1438C2214yes—
81#1437C2214yes—
82#1436C2214yes—
83#1436C2214yes—
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2214yes—
93C22⋊#95C2214yes—
94C22⋊#95C2214yes—
95C23×Q8C2311yescharacteristic
96C23×D4C2311yescharacteristic
97C23×D4C2312yes—
98C23×D4C2311yescharacteristic
99C23×D4C2312yes—
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C24×C4C2312yes—
104C2×#124—24no—
105C2×#124—42no—
106C2×#124—42no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—24no—
111C2×C22⋊Q8—24no—
112C2×C22⋊Q8—42no—
113C2×#121—24no—
114C2×#121—24no—
115C2×#121—24no—
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—24no—
124C2×#117—42no—
125C2×#117—42no—
126C2×#117—42no—
127C2×#117D418yescomplemented
128C22×C4⋊C4—24no—
129C22×C4⋊C4—24no—
130C22×C4⋊C4—42no—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2311yescharacteristic
154C22×C22⋊C4C2311yescharacteristic
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2314yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2312yes—
164C22×C42—24no—
165C22×C42—42no—
166C22×C42—42no—
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2312yes—
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2312yes—
174#398—28no—
175#398—48no—
176#396—216no—
177#396—28no—
178#394—216no—
179#394—28no—
180#392—28no—
181#391—24no—
182#391—24no—
183#391—24no—
184#391—42no—
185#390—24no—
186#390—28no—
187#390—24no—
188#390—24no—
189#390—42no—
190#389—24no—
191#389—24no—
192#388—28no—
193#388—28no—
194#387—28no—
195#386—28no—
196#386—28no—
197#386—48no—
198#386—48no—
199#385—28no—
200#384—24no—
201#380—24no—
202#380—24no—
203#380—28no—
204C4×C4⋊C4—24no—
205C4×C22⋊C4—24no—
206C4×C22⋊C4—24no—
207#376—24no—
208C2×#95C2312yes—
209C2×#95C2314yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C25C2412yes—
231C25C2411yescharacteristic
232C25C2411yescharacteristic
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—28no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—24no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—42no—
257C22×D4—42no—
258C22×D4—44no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4C2×D414yes—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—42no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—44no—
283C23×C4—44no—
284C23×C4C2×D414yes—
285C23×C4C2×D414yes—
286C23×C4C2×D414yes—
287C23×C4#4114yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2412yes—
296C23×C4C2411yescharacteristic
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304#124—416no—
305C22⋊Q8—416no—
306C22⋊Q8—416no—
307#121—416no—
308#121—416no—
309C4×D4—232no—
310#117—416no—
311#117—416no—
312C2×C4⋊C4—22no—
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—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—416no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—42no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—44no—
349C2×C4⋊C4—44no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4C2×D414yes—
353C2×C4⋊C4C2×D418yes—
354C2×C4⋊C4#4114yes—
355C2×C4⋊C4#4114yes—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
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⋊C4C2×D414yes—
404C2×C22⋊C4C2×D414yes—
405C2×C22⋊C4C2×D418yes—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—24no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—24no—
416C2×C42—24no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—416no—
422C2×C42—42no—
423C2×C42—42no—
424C2×C42—42no—
425C2×C42C2×D414yes—
426C2×C42C2×D414yes—
427C2×C42C2×D414yes—
428#95—24no—
429#95—24no—
430#95—24no—
431#95—24no—
432#95—24no—
433#95—24no—
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—28no—
440#95—28no—
441#95—28no—
442#95—28no—
443#95—44no—
444#95—44no—
445#95—44no—
446#95—44no—
447#95—44no—
448#95—44no—
449#95—44no—
450C24—21no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—22no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—22no—
461C24—21no—
462C24—22no—
463C24—22no—
464C24—22no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—24no—
473C24—22no—
474C24—22no—
475C24—24no—
476C24—24no—
477C24—24no—
478C24C22×D412yes—
479C24C22×D412yes—
480C24C22×D412yes—
481C24C2×#4112yes—
482C242−1+414yes—
483C24C2511yescharacteristic
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×D4—28no—
492C2×D4—28no—
493C2×D4—44no—
494C2×D4—48no—
495C2×D4—416no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—416no—
499C2×D4—48no—
500C2×D4—48no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—44no—
505C2×D4—44no—
506C2×D4—44no—
507C2×D4—44no—
508C2×D4—84no—
509C2×D4—88no—
510C2×D4—88no—
511C2×D4—84no—
512C2×D4—84no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—28no—
518C22×C4—28no—
519C22×C4—28no—
520C22×C4—28no—
521C22×C4—28no—
522C22×C4—28no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—24no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—24no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
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—24no—
585C22×C4—24no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—24no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—22no—
599C22×C4—24no—
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—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—48no—
613C22×C4—88no—
614C22×C4—84no—
615C22×C4—88no—
616C22×C4#121116yes—
617C22×C4C22×D412yes—
618C22×C4C22×D414yes—
619C22×C4C22×D412yes—
620C22×C4C22×D414yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C2×#4114yes—
627C22×C4C2×#4114yes—
628C22×C4C2×#4112yes—
629C22×C4C2×#4112yes—
630C22×C4C2×#4112yes—
631C22×C4C2×#4112yes—
632C22×C4H(5,𝔽2)14yes—
633C22×C4H(5,𝔽2)12yes—
634C22×C4H(5,𝔽2)12yes—
635C4⋊C4—28no—
636C4⋊C4—28no—
637C4⋊C4—28no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—48no—
642C4⋊C4—44no—
643C4⋊C4—44no—
644C4⋊C4—48no—
645C4⋊C4—44no—
646C4⋊C4—44no—
647C4⋊C4—88no—
648C4⋊C4—84no—
649C4⋊C4—84no—
650C22⋊C4—28no—
651C22⋊C4—28no—
652C22⋊C4—48no—
653C22⋊C4—48no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—416no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—88no—
663C22⋊C4—84no—
664C22⋊C4—88no—
665C22⋊C4—88no—
666C22⋊C4—84no—
667C22⋊C4—84no—
668C42—28no—
669C42—28no—
670C42—28no—
671C42—48no—
672C42—48no—
673C42—44no—
674C42—44no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—24no—
701C23—41no—
702C23—41no—
703C23—42no—
704C23—41no—
705C23—41no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—44no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—42no—
733C23—42no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23C2×#12114yes—
743C23#53614yes—
744C23C23×D411yescharacteristic
745C23C23×D411yescharacteristic
746C23C22×#4111yescharacteristic
747C23C22×#4111yescharacteristic
748C23C22×#4111yescharacteristic
749C23C2×H(5,𝔽2)11yescharacteristic
750C23C2×H(5,𝔽2)11yescharacteristic
751C23C2×H(5,𝔽2)12yes—
752C23C2×2−1+412yes—
753C23#58512yes—
754C23#58512yes—
755Q8—88no—
756D4—416no—
757D4—816no—
758D4—816no—
759D4—88no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—232no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—28no—
786C2×C4—28no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—432no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—44no—
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—44no—
816C2×C4—416no—
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—44no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—44no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—816no—
852C2×C4C2×#12114yes—
853C2×C4C2×#12114yes—
854C2×C4#53214yes—
855C2×C4#53414yes—
856C2×C4#54614yes—
857C2×C4#54614yes—
858C2×C4#55314yes—
859C2×C4#55314yes—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—42no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—44no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—44no—
881C22—44no—
882C22—82no—
883C22—84no—
884C22—84no—
885C22—84no—
886C22—82no—
887C22—82no—
888C22—82no—
889C22—82no—
890C22—82no—
891C22—82no—
892C22—84no—
893C22C22×#12111yescharacteristic
894C22C2×#53211yescharacteristic
895C22C2×#53411yescharacteristic
896C22C2×#53611yescharacteristic
897C22#344911yescharacteristic
898C22#346012yes—
899C22C2×#54611yescharacteristic
900C22C2×#54611yescharacteristic
901C22C2×#55311yescharacteristic
902C22C2×#55311yescharacteristic
903C22#348812yes—
904C22#348912yes—
905C22#349512yes—
906C22#349811yescharacteristic
907C22#350011yescharacteristic
908C22#351412yes—
909C22#351612yes—
910C22#352012yes—
911C22#352412yes—
912C22#353612yes—
913C22#353912yes—
914C22#354112yes—
915C22#354212yes—
916C4—24no—
917C4—42no—
918C4—44no—
919C4—44no—
920C4—44no—
921C4—42no—
922C4—44no—
923C4—44no—
924C4—42no—
925C4—82no—
926C4—82no—
927C4—82no—
928C4—82no—
929C4—82no—
930C4—82no—
931C4#254318yes—
932C2—44no—
933C2—44no—
934C2—162no—
935C2C2×#254311yescharacteristic
936C2#3525611yescharacteristic
937C2#3530611yescharacteristic
938C2#3556812yes—
939C2#3726812yes—
940C2#3807811yescharacteristic
941C2#3808511yescharacteristic
942C2#3809011yescharacteristic
943C2#3809311yescharacteristic
944C2#3905512yes—
945C2#3905712yes—
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
2. C2×#2417C2semidirect
3. C2×#2620C2semidirect
4. C2×#2290C2semidirect
5. #15599C2semidirect
6. #15507C2semidirect
7. #15473C2semidirect
8. #15375C2semidirect
9. #15217C2semidirect
10. #15215C2semidirect
11. #15195C2semidirect
12. #15151C2semidirect
13. #14702C2semidirect
14. #14698C2semidirect
15. #14261C2semidirect
16. #14260C2semidirect
17. #14138C2semidirect
18. #14137C2semidirect
19. #13795C2semidirect
127. C2×#117D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24142
C2×#24172
C2×#26202
C2×#22902
#155992
#155072
#154732
#153752
#152172
#152152
#151952
#151512
#147022
#146982
#142612
#142602
#141382
#141372
#137952