Finite Group Databasebeta

← #4309138

Subgroups — #4309138

Order 512.

4160 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic, complemented
2C2×#2847C211yesmaximal, characteristic
3C2×#2620C211yesmaximal, characteristic, complemented
4C2×#2280C211yesmaximal, characteristic, complemented
5#16661C214yesmaximal, complemented
6#16562C214yesmaximal, complemented
7#16513C214yesmaximal, complemented
8#16255C214yesmaximal, complemented
9#15236C211yesmaximal, characteristic, complemented
10#15219C211yesmaximal, characteristic, complemented
11#15215C211yesmaximal, characteristic, complemented
12#15215C211yesmaximal, characteristic, complemented
13#15195C211yesmaximal, characteristic, complemented
14#15182C211yesmaximal, characteristic, complemented
15#15150C211yesmaximal, characteristic, complemented
16#15130C211yesmaximal, characteristic, complemented
17#14340C211yesmaximal, characteristic, complemented
18#14258C211yesmaximal, characteristic, complemented
19#14257C211yesmaximal, characteristic, complemented
20C25×C4C2211yescharacteristic
21C22×#124C2211yescharacteristic, complemented
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#120C2212yes—
29C22×#117C2211yescharacteristic
30C22×#117C2211yescharacteristic
31#2848—28no—
32#2847—28no—
33#2620—28no—
34C2×#397C2214yes—
35C2×#396C2214yescomplemented
36C2×#394C2214yes—
37C2×#394C2214yes—
38C2×#391C2211yescharacteristic, complemented
39C2×#391C2211yescharacteristic, complemented
40C2×#391C2211yescharacteristic, complemented
41C2×#390C2211yescharacteristic, complemented
42C2×#390C2211yescharacteristic, complemented
43C2×#390C2211yescharacteristic, complemented
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#385C2212yes—
50C2×#384C2211yescharacteristic, complemented
51C2×#384C2211yescharacteristic, complemented
52C2×#382C2211yescharacteristic, complemented
53#2280—28no—
54C2×#381C2212yes—
55C2×#380C2211yescharacteristic
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2212yes—
62C2×#380C2212yes—
63C2×#379C2212yes—
64C2×#379C2212yes—
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2211yescharacteristic
69#1445C2214yescomplemented
70#1442C2214yescomplemented
71#1442C2214yescomplemented
72#1441C2214yescomplemented
73#1441C2214yescomplemented
74#1441C2214yescomplemented
75#1440C2214yes—
76#1440C2214yes—
77#1440C2214yescomplemented
78#1439C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yescomplemented
82#1439C2214yescomplemented
83#1439C2214yescomplemented
84#1439C2214yescomplemented
85#1438C2214yes—
86#1438C2214yes—
87#1438C2214yes—
88#1438C2214yes—
89C4⋊#95C2211yescharacteristic, complemented
90C4⋊#95C2211yescharacteristic, complemented
91C4⋊#95C2211yescharacteristic, complemented
92C4⋊#95C2211yescharacteristic, complemented
93C4⋊#95C2211yescharacteristic, complemented
94C4⋊#95C2211yescharacteristic, complemented
95C26C2311yescharacteristic
96C23×Q8C2311yescharacteristic
97C23×D4C2311yescharacteristic
98C23×D4C2312yes—
99C23×D4C2312yes—
100C23×D4C2312yes—
101C24×C4—24no—
102C24×C4—24no—
103C24×C4—42no—
104C24×C4—42no—
105C24×C4—42no—
106C24×C4—42no—
107C24×C4D418yes—
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C2×#124—24no—
115C2×#124—42no—
116C2×#124—42no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—42no—
123C2×C22⋊Q8—42no—
124C2×C22⋊Q8—42no—
125C2×C22⋊Q8—42no—
126C2×#121—24no—
127C2×#121—24no—
128C2×#121—24no—
129C2×#121—24no—
130C2×#121—24no—
131C2×#121—42no—
132C2×#121—42no—
133C2×#121—42no—
134C2×#121—42no—
135C2×#120—28no—
136C2×#120—48no—
137C2×#117—24no—
138C2×#117—42no—
139C2×#117—42no—
140C2×#117—42no—
141C2×#117—42no—
142C2×#117D418yescomplemented
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2314yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2314yes—
155C22×C4⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2314yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2314yes—
176C22×C22⋊C4C2314yes—
177C22×C22⋊C4C2312yes—
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180C22×C42C2311yescharacteristic
181C22×C42C2311yescharacteristic
182#397—48no—
183#396—216no—
184#394—216no—
185#394—48no—
186#391—24no—
187#391—42no—
188#391—42no—
189#390—24no—
190#390—42no—
191#390—42no—
192#386—28no—
193#386—28no—
194#386—28no—
195#385—28no—
196#385—28no—
197#385—28no—
198#384—24no—
199#384—42no—
200#382—42no—
201#381—28no—
202#380—24no—
203#380—24no—
204#380—24no—
205#380—24no—
206#380—24no—
207#380—24no—
208#380—28no—
209#380—28no—
210#379—28no—
211#379—28no—
212C4×C22⋊C4—24no—
213C4×C22⋊C4—24no—
214C4×C22⋊C4—24no—
215C4×C22⋊C4—24no—
216C2×#95C2314yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2314yes—
228C2×#95C2314yes—
229C2×#95C2314yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C25—22no—
237C25—22no—
238C25—24no—
239C25—24no—
240C25—41no—
241C25—41no—
242C25—41no—
243C25—41no—
244C25—42no—
245C25—42no—
246C25C2×D414yes—
247C25C2412yes—
248C25C2411yescharacteristic
249C25C2411yescharacteristic
250C25C2411yescharacteristic
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×D4—24no—
259C22×D4—24no—
260C22×D4—24no—
261C22×D4—24no—
262C22×D4—24no—
263C22×D4—28no—
264C22×D4—28no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—22no—
271C22×D4—22no—
272C22×D4—44no—
273C22×D4—44no—
274C22×D4—42no—
275C22×D4—42no—
276C22×D4—42no—
277C22×D4—42no—
278C22×D4—44no—
279C22×D4—44no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—232no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—22no—
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—22no—
302C23×C4—22no—
303C23×C4—416no—
304C23×C4—416no—
305C23×C4—41no—
306C23×C4—41no—
307C23×C4—41no—
308C23×C4—41no—
309C23×C4—41no—
310C23×C4—41no—
311C23×C4—41no—
312C23×C4—41no—
313C23×C4—41no—
314C23×C4—41no—
315C23×C4—41no—
316C23×C4—41no—
317C23×C4—416no—
318C23×C4—416no—
319C23×C4—416no—
320C23×C4—416no—
321C23×C4C2×D414yes—
322C23×C4C2×D414yes—
323C23×C4C2×D414yes—
324C23×C4C2×D414yes—
325C23×C4C2×D414yes—
326C23×C4C2×D414yes—
327C23×C4C2×D414yes—
328C23×C4#4114yes—
329C23×C4C2412yes—
330C23×C4C2412yes—
331C23×C4C2412yes—
332C23×C4C2412yes—
333C23×C4C2412yes—
334C23×C4C2412yes—
335C23×C4C2412yes—
336C23×C4C2412yes—
337C23×C4C2412yes—
338C23×C4C2412yes—
339C23×C4C2412yes—
340C23×C4C2411yescharacteristic
341C23×C4C2411yescharacteristic
342C23×C4C2411yescharacteristic
343C23×C4C2411yescharacteristic
344#124—416no—
345C22⋊Q8—416no—
346C22⋊Q8—416no—
347C22⋊Q8—416no—
348#121—416no—
349#121—416no—
350#121—416no—
351#120—432no—
352#117—416no—
353#117—416no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—28no—
379C2×C4⋊C4—42no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—42no—
386C2×C4⋊C4—42no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—44no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4C2×D418yes—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—28no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—28no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—24no—
421C2×C22⋊C4—28no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—42no—
425C2×C22⋊C4—42no—
426C2×C22⋊C4—44no—
427C2×C22⋊C4—44no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4—44no—
433C2×C22⋊C4—44no—
434C2×C22⋊C4—42no—
435C2×C22⋊C4—42no—
436C2×C22⋊C4—42no—
437C2×C22⋊C4—42no—
438C2×C22⋊C4—42no—
439C2×C22⋊C4—42no—
440C2×C22⋊C4—42no—
441C2×C22⋊C4—42no—
442C2×C22⋊C4—44no—
443C2×C22⋊C4—44no—
444C2×C22⋊C4—44no—
445C2×C22⋊C4—44no—
446C2×C22⋊C4—44no—
447C2×C22⋊C4—44no—
448C2×C22⋊C4—44no—
449C2×C22⋊C4—44no—
450C2×C22⋊C4—44no—
451C2×C22⋊C4—44no—
452C2×C22⋊C4C2×D418yes—
453C2×C42—22no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—22no—
459C2×C42—22no—
460C2×C42—22no—
461C2×C42—22no—
462C2×C42—22no—
463C2×C42C2×D414yes—
464C2×C42C2×D414yes—
465#95—24no—
466#95—24no—
467#95—24no—
468#95—24no—
469#95—24no—
470#95—24no—
471#95—24no—
472#95—24no—
473#95—24no—
474#95—24no—
475#95—28no—
476#95—44no—
477#95—44no—
478#95—44no—
479#95—44no—
480#95—44no—
481#95—44no—
482#95—44no—
483#95—44no—
484#95—44no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—21no—
492C24—21no—
493C24—21no—
494C24—21no—
495C24—21no—
496C24—21no—
497C24—22no—
498C24—22no—
499C24—21no—
500C24—21no—
501C24—21no—
502C24—21no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—28no—
512C24—28no—
513C24—28no—
514C24—22no—
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—24no—
522C24—24no—
523C24—24no—
524C24—24no—
525C24—44no—
526C24—44no—
527C24—44no—
528C24—44no—
529C24—48no—
530C24—48no—
531C24—48no—
532C24—48no—
533C24—48no—
534C24—48no—
535C24—44no—
536C24—44no—
537C24—44no—
538C24—44no—
539C24—48no—
540C24—48no—
541C24—48no—
542C24—48no—
543C24—48no—
544C24—48no—
545C24C22×D412yes—
546C24C22×D412yes—
547C24C22×D412yes—
548C24C22×D412yes—
549C24C2×#4112yes—
550C24H(5,𝔽2)14yes—
551C242−1+414yes—
552C24C2511yescharacteristic
553C2×Q8—44no—
554C2×Q8—44no—
555C2×Q8—44no—
556C2×Q8—44no—
557C2×Q8—44no—
558C2×Q8—44no—
559C2×Q8—44no—
560C2×D4—48no—
561C2×D4—48no—
562C2×D4—48no—
563C2×D4—48no—
564C2×D4—48no—
565C2×D4—48no—
566C2×D4—48no—
567C2×D4—48no—
568C2×D4—48no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—44no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—44no—
576C2×D4—88no—
577C2×D4—88no—
578C2×D4—88no—
579C2×D4—88no—
580C2×D4—88no—
581C2×D4—88no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—28no—
587C22×C4—28no—
588C22×C4—28no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—28no—
618C22×C4—28no—
619C22×C4—28no—
620C22×C4—28no—
621C22×C4—28no—
622C22×C4—28no—
623C22×C4—28no—
624C22×C4—28no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—24no—
645C22×C4—24no—
646C22×C4—24no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—24no—
666C22×C4—22no—
667C22×C4—24no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—44no—
677C22×C4—44no—
678C22×C4—44no—
679C22×C4—44no—
680C22×C4—44no—
681C22×C4—44no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—4128no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—44no—
700C22×C4—44no—
701C22×C4—44no—
702C22×C4—44no—
703C22×C4#121116yes—
704C22×C4C22×D414yes—
705C22×C4C22×D412yes—
706C22×C4C22×D412yes—
707C22×C4C22×D414yes—
708C22×C4C22×D412yes—
709C22×C4C22×D412yes—
710C22×C4C22×D412yes—
711C22×C4C22×D412yes—
712C22×C4C2×#4112yes—
713C22×C4C2×#4112yes—
714C22×C4H(5,𝔽2)12yes—
715C22×C4H(5,𝔽2)12yes—
716C22×C4H(5,𝔽2)12yes—
717C22×C4H(5,𝔽2)12yes—
718C4⋊C4—48no—
719C4⋊C4—48no—
720C4⋊C4—48no—
721C4⋊C4—48no—
722C4⋊C4—44no—
723C4⋊C4—44no—
724C4⋊C4—48no—
725C4⋊C4—44no—
726C4⋊C4—44no—
727C4⋊C4—44no—
728C4⋊C4—44no—
729C4⋊C4—88no—
730C4⋊C4—88no—
731C22⋊C4—48no—
732C22⋊C4—48no—
733C22⋊C4—48no—
734C22⋊C4—48no—
735C22⋊C4—48no—
736C22⋊C4—48no—
737C22⋊C4—48no—
738C22⋊C4—416no—
739C22⋊C4—48no—
740C22⋊C4—48no—
741C22⋊C4—48no—
742C22⋊C4—48no—
743C22⋊C4—48no—
744C22⋊C4—48no—
745C22⋊C4—48no—
746C22⋊C4—48no—
747C22⋊C4—48no—
748C22⋊C4—48no—
749C22⋊C4—48no—
750C22⋊C4—88no—
751C22⋊C4—88no—
752C22⋊C4—88no—
753C42—28no—
754C42—28no—
755C42—44no—
756C42—44no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—24no—
791C23—24no—
792C23—24no—
793C23—24no—
794C23—24no—
795C23—416no—
796C23—416no—
797C23—416no—
798C23—416no—
799C23—416no—
800C23—416no—
801C23—416no—
802C23—432no—
803C23—432no—
804C23—432no—
805C23—432no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—44no—
846C23—44no—
847C23—44no—
848C23—44no—
849C23—44no—
850C23—44no—
851C23—44no—
852C23—44no—
853C23—44no—
854C23—44no—
855C23—44no—
856C23—44no—
857C23C2×#12114yes—
858C23#53514yes—
859C23#53614yes—
860C23C23×D411yescharacteristic
861C23C23×D411yescharacteristic
862C23C22×#4111yescharacteristic
863C23C2×H(5,𝔽2)11yescharacteristic
864C23C2×H(5,𝔽2)11yescharacteristic
865C23C2×H(5,𝔽2)11yescharacteristic
866C23C2×H(5,𝔽2)11yescharacteristic
867C23C2×H(5,𝔽2)12yes—
868C23C2×2−1+412yes—
869C23#58512yes—
870C23#58512yes—
871Q8—88no—
872D4—816no—
873D4—816no—
874D4—816no—
875D4—88no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—232no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—416no—
896C2×C4—416no—
897C2×C4—416no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—416no—
915C2×C4—416no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—42no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—42no—
927C2×C4—42no—
928C2×C4—42no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—44no—
946C2×C4—44no—
947C2×C4—42no—
948C2×C4—42no—
949C2×C4—44no—
950C2×C4—44no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—44no—
954C2×C4—44no—
955C2×C4—44no—
956C2×C4—42no—
957C2×C4—44no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—44no—
963C2×C4—44no—
964C2×C4—44no—
965C2×C4—42no—
966C2×C4—44no—
967C2×C4C2×#12114yes—
968C2×C4C2×#12114yes—
969C2×C4#53414yes—
970C2×C4#53414yes—
971C2×C4#53414yes—
972C2×C4#53514yes—
973C2×C4#53814yes—
974C2×C4#53814yes—
975C22—24no—
976C22—24no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—24no—
983C22—24no—
984C22—464no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—42no—
989C22—42no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—44no—
994C22—44no—
995C22—44no—
996C22—44no—
997C22—44no—
998C22—44no—
999C22—44no—
1000C22—44no—
1001C22—44no—
1002C22—44no—
1003C22—44no—
1004C22—44no—
1005C22—42no—
1006C22—42no—
1007C22—42no—
1008C22—42no—
1009C22—82no—
1010C22—82no—
1011C22—82no—
1012C22—82no—
1013C22—84no—
1014C22—84no—
1015C22—84no—
1016C22—84no—
1017C22—82no—
1018C22—82no—
1019C22—82no—
1020C22C22×#12111yescharacteristic
1021C22C2×#53411yescharacteristic
1022C22C2×#53411yescharacteristic
1023C22C2×#53411yescharacteristic
1024C22C2×#53511yescharacteristic
1025C22C2×#53511yescharacteristic
1026C22C2×#53611yescharacteristic
1027C22#344911yescharacteristic
1028C22#344911yescharacteristic
1029C22C2×#53811yescharacteristic
1030C22C2×#53811yescharacteristic
1031C22#348812yes—
1032C22#348912yes—
1033C22#349412yes—
1034C22#349512yes—
1035C22#353612yes—
1036C22#353612yes—
1037C22#353912yes—
1038C22#354012yes—
1039C22#354112yes—
1040C22#354112yes—
1041C22#354212yes—
1042C22#354212yes—
1043C4—24no—
1044C4—44no—
1045C4—44no—
1046C4—42no—
1047C4—42no—
1048C4—82no—
1049C4—82no—
1050C4—82no—
1051C4—82no—
1052C4—82no—
1053C4—82no—
1054C4—82no—
1055C4—82no—
1056C4—82no—
1057C4#261718yes—
1058C2—44no—
1059C2—44no—
1060C2—44no—
1061C2—162no—
1062C2C2×#261711yescharacteristic
1063C2#3525211yescharacteristic
1064C2#3530611yescharacteristic
1065C2#3726812yes—
1066C2#3727112yes—
1067C2#3728212yes—
1068C2#3728512yes—
1069C2#3744811yescharacteristic
1070C2#3744911yescharacteristic
1071C2#3745111yescharacteristic
1072C2#3745511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2847C2
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×#2848C2semidirect
3. C2×#2620C2semidirect
4. C2×#2280C2semidirect
5. #16661C2semidirect
6. #16562C2semidirect
7. #16513C2semidirect
8. #16255C2semidirect
9. #15236C2semidirect
10. #15219C2semidirect
11. #15215C2semidirect
12. #15215C2semidirect
13. #15195C2semidirect
14. #15182C2semidirect
15. #15150C2semidirect
16. #15130C2semidirect
17. #14340C2semidirect
18. #14258C2semidirect
19. #14257C2semidirect
21. C22×#124C22semidirect
35. C2×#396C22semidirect
38. C2×#391C22semidirect
39. C2×#391C22semidirect
40. C2×#391C22semidirect
41. C2×#390C22semidirect
42. C2×#390C22semidirect
43. C2×#390C22semidirect
50. C2×#384C22semidirect
51. C2×#384C22semidirect
52. C2×#382C22semidirect
69. #1445C22semidirect
70. #1442C22semidirect
71. #1442C22semidirect
72. #1441C22semidirect
73. #1441C22semidirect
74. #1441C22semidirect
77. #1440C22semidirect
81. #1439C22semidirect
82. #1439C22semidirect
83. #1439C22semidirect
84. #1439C22semidirect
89. C4⋊#95C22semidirect
90. C4⋊#95C22semidirect
91. C4⋊#95C22semidirect
92. C4⋊#95C22semidirect
93. C4⋊#95C22semidirect
94. C4⋊#95C22semidirect
142. C2×#117D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#28472
C2×#26202
C2×#22802
#166612
#165622
#165132
#162552
#152362
#152192
#152152
#151952
#151822
#151502
#151302
#143402
#142582
#142572