Finite Group Databasebeta

← #4416996

Subgroups — #4416996

Order 512.

3880 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2848C211yesmaximal, characteristic, complemented
2C2×#2847C211yesmaximal, characteristic
3#16893C214yesmaximal, complemented
4#16798C214yesmaximal, complemented
5#16255C214yesmaximal, complemented
6#15236C211yesmaximal, characteristic, complemented
7#15233C211yesmaximal, characteristic, complemented
8#15219C211yesmaximal, characteristic, complemented
9#15215C211yesmaximal, characteristic, complemented
10#15215C211yesmaximal, characteristic, complemented
11#15215C211yesmaximal, characteristic, complemented
12#15195C211yesmaximal, characteristic, complemented
13#15182C211yesmaximal, characteristic, complemented
14#15182C211yesmaximal, characteristic, complemented
15#15150C211yesmaximal, characteristic, complemented
16#15130C211yesmaximal, characteristic, complemented
17#15130C211yesmaximal, characteristic, complemented
18#14622C214yesmaximal, complemented
19C4×#379C211yesmaximal, characteristic, complemented
20C25×C4C2211yescharacteristic
21C22×#124C2211yescharacteristic, complemented
22C22×C22⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×#121C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#120C2212yes—
29#2848—28no—
30#2847—28no—
31C2×#397C2214yes—
32C2×#394C2214yes—
33C2×#394C2214yes—
34C2×#391C2211yescharacteristic, complemented
35C2×#391C2211yescharacteristic, complemented
36C2×#391C2211yescharacteristic, complemented
37C2×#390C2211yescharacteristic, complemented
38C2×#390C2211yescharacteristic, complemented
39C2×#390C2211yescharacteristic, complemented
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#386C2212yes—
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#385C2212yes—
46C2×#384C2211yescharacteristic, complemented
47C2×#384C2211yescharacteristic, complemented
48C2×#382C2211yescharacteristic, complemented
49C2×#380C2211yescharacteristic
50C2×#380C2211yescharacteristic
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#379C2212yes—
56C2×#379C2212yes—
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2211yescharacteristic
60C2×C4×C22⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62C2×C4×C22⋊C4C2211yescharacteristic
63#1445C2214yescomplemented
64#1443C2214yescomplemented
65#1442C2214yescomplemented
66#1442C2214yescomplemented
67#1441C2214yescomplemented
68#1441C2214yescomplemented
69#1440C2214yes—
70#1440C2214yes—
71#1440C2214yescomplemented
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yescomplemented
76#1439C2214yescomplemented
77#1439C2214yescomplemented
78#1439C2214yescomplemented
79#1439C2214yescomplemented
80#1438C2214yes—
81#1438C2214yes—
82#1438C2214yes—
83#1438C2214yes—
84C4⋊#95C2211yescharacteristic, complemented
85C4⋊#95C2211yescharacteristic, complemented
86C4⋊#95C2211yescharacteristic, complemented
87C4⋊#95C2211yescharacteristic, complemented
88C4⋊#95C2211yescharacteristic, complemented
89C4⋊#95C2211yescharacteristic, complemented
90C22⋊#95C2212yes—
91C22⋊#95C2212yes—
92C22⋊#95C2212yes—
93C26C2311yescharacteristic
94C23×Q8C2311yescharacteristic
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C23×D4C2312yes—
98C23×D4C2312yes—
99C24×C4—42no—
100C24×C4—42no—
101C24×C4—42no—
102C24×C4—42no—
103C24×C4—42no—
104C24×C4—42no—
105C24×C4D418yes—
106C24×C4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2311yescharacteristic
111C24×C4C2311yescharacteristic
112C2×#124—42no—
113C2×#124—42no—
114C2×#124—42no—
115C2×C22⋊Q8—24no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—42no—
119C2×C22⋊Q8—42no—
120C2×C22⋊Q8—42no—
121C2×C22⋊Q8—42no—
122C2×C22⋊Q8—42no—
123C2×C22⋊Q8—42no—
124C2×#121—24no—
125C2×#121—24no—
126C2×#121—24no—
127C2×#121—42no—
128C2×#121—42no—
129C2×#121—42no—
130C2×#121—42no—
131C2×#121—42no—
132C2×#121—42no—
133C2×#120—28no—
134C2×#120—48no—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊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⋊C4C2312yes—
165C22×C22⋊C4C2314yes—
166C22×C22⋊C4C2314yes—
167C22×C22⋊C4C2312yes—
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172#397—48no—
173#394—216no—
174#394—48no—
175#391—42no—
176#391—42no—
177#391—42no—
178#390—42no—
179#390—42no—
180#390—42no—
181#386—28no—
182#386—28no—
183#386—28no—
184#385—28no—
185#385—28no—
186#385—28no—
187#384—42no—
188#384—42no—
189#382—42no—
190#380—24no—
191#380—24no—
192#380—24no—
193#380—24no—
194#380—24no—
195#380—24no—
196#379—28no—
197#379—28no—
198C4×C22⋊C4—42no—
199C4×C22⋊C4—42no—
200C4×C22⋊C4—42no—
201C4×C22⋊C4—42no—
202C4×C22⋊C4—42no—
203C4×C22⋊C4—42no—
204C2×#95C2314yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2314yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C25—24no—
227C25—24no—
228C25—24no—
229C25—41no—
230C25—41no—
231C25—41no—
232C25—41no—
233C25—41no—
234C25—41no—
235C25—42no—
236C25C2×D414yes—
237C25C2412yes—
238C25C2411yescharacteristic
239C25C2411yescharacteristic
240C25C2411yescharacteristic
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×D4—24no—
249C22×D4—24no—
250C22×D4—24no—
251C22×D4—28no—
252C22×D4—28no—
253C22×D4—28no—
254C22×D4—22no—
255C22×D4—22no—
256C22×D4—22no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—44no—
262C22×D4—44no—
263C22×D4—42no—
264C22×D4—42no—
265C22×D4—42no—
266C22×D4—42no—
267C22×D4—42no—
268C22×D4—42no—
269C22×D4—44no—
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—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—416no—
289C23×C4—416no—
290C23×C4—416no—
291C23×C4—41no—
292C23×C4—41no—
293C23×C4—41no—
294C23×C4—41no—
295C23×C4—41no—
296C23×C4—41no—
297C23×C4—41no—
298C23×C4—41no—
299C23×C4—41no—
300C23×C4—41no—
301C23×C4—41no—
302C23×C4—41no—
303C23×C4—41no—
304C23×C4—41no—
305C23×C4—41no—
306C23×C4—41no—
307C23×C4—41no—
308C23×C4—41no—
309C23×C4—416no—
310C23×C4—416no—
311C23×C4—416no—
312C23×C4—416no—
313C23×C4C2×D414yes—
314C23×C4C2×D414yes—
315C23×C4C2×D414yes—
316C23×C4C2×D414yes—
317C23×C4C2×D414yes—
318C23×C4C2×D414yes—
319C23×C4C2412yes—
320C23×C4C2412yes—
321C23×C4C2412yes—
322C23×C4C2412yes—
323C23×C4C2412yes—
324C23×C4C2412yes—
325C23×C4C2412yes—
326C23×C4C2412yes—
327C23×C4C2412yes—
328C23×C4C2411yescharacteristic
329C23×C4C2411yescharacteristic
330C23×C4C2411yescharacteristic
331C23×C4C2412yes—
332C23×C4C2412yes—
333C23×C4C2411yescharacteristic
334#124—416no—
335C22⋊Q8—416no—
336C22⋊Q8—416no—
337C22⋊Q8—416no—
338#121—416no—
339#121—416no—
340#121—416no—
341#120—432no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
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—28no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—42no—
367C2×C4⋊C4—42no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4—44no—
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—24no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
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—28no—
400C2×C22⋊C4—28no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—42no—
408C2×C22⋊C4—42no—
409C2×C22⋊C4—42no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4—42no—
418C2×C22⋊C4—44no—
419C2×C22⋊C4—44no—
420C2×C22⋊C4—44no—
421C2×C22⋊C4—42no—
422C2×C22⋊C4—42no—
423C2×C22⋊C4—42no—
424C2×C22⋊C4—42no—
425C2×C22⋊C4—42no—
426C2×C22⋊C4—42no—
427C2×C22⋊C4—44no—
428C2×C22⋊C4—44no—
429C2×C22⋊C4—44no—
430C2×C22⋊C4—44no—
431C2×C22⋊C4—44no—
432C2×C22⋊C4—44no—
433C2×C22⋊C4—44no—
434C2×C22⋊C4#4118yes—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—24no—
452#95—24no—
453#95—28no—
454#95—44no—
455#95—42no—
456#95—42no—
457#95—42no—
458#95—42no—
459#95—42no—
460#95—42no—
461#95—44no—
462#95—44no—
463#95—44no—
464#95—44no—
465#95—44no—
466#95—44no—
467#95—44no—
468#95—44no—
469C24—22no—
470C24—22no—
471C24—21no—
472C24—21no—
473C24—21no—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24—22no—
484C24—22no—
485C24—21no—
486C24—21no—
487C24—21no—
488C24—21no—
489C24—21no—
490C24—21no—
491C24—22no—
492C24—22no—
493C24—22no—
494C24—22no—
495C24—22no—
496C24—28no—
497C24—28no—
498C24—28no—
499C24—22no—
500C24—24no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—24no—
508C24—24no—
509C24—24no—
510C24—44no—
511C24—44no—
512C24—44no—
513C24—44no—
514C24—48no—
515C24—48no—
516C24—48no—
517C24—48no—
518C24—48no—
519C24—48no—
520C24—48no—
521C24—48no—
522C24—48no—
523C24—48no—
524C24—48no—
525C24—48no—
526C24—44no—
527C24—44no—
528C24—44no—
529C24—44no—
530C24C22×D412yes—
531C24C22×D412yes—
532C24C22×D412yes—
533C24C2×#4114yes—
534C24H(5,𝔽2)14yes—
535C242−1+414yes—
536C24C2511yescharacteristic
537C2×Q8—44no—
538C2×Q8—44no—
539C2×Q8—44no—
540C2×Q8—44no—
541C2×Q8—44no—
542C2×Q8—44no—
543C2×Q8—44no—
544C2×D4—48no—
545C2×D4—48no—
546C2×D4—48no—
547C2×D4—48no—
548C2×D4—48no—
549C2×D4—48no—
550C2×D4—48no—
551C2×D4—48no—
552C2×D4—48no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—44no—
560C2×D4—88no—
561C2×D4—88no—
562C2×D4—88no—
563C2×D4—88no—
564C2×D4—88no—
565C2×D4—88no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—28no—
599C22×C4—28no—
600C22×C4—28no—
601C22×C4—28no—
602C22×C4—28no—
603C22×C4—28no—
604C22×C4—28no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—24no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—24no—
622C22×C4—24no—
623C22×C4—24no—
624C22×C4—22no—
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—24no—
637C22×C4—24no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—24no—
651C22×C4—22no—
652C22×C4—24no—
653C22×C4—24no—
654C22×C4—22no—
655C22×C4—24no—
656C22×C4—44no—
657C22×C4—44no—
658C22×C4—44no—
659C22×C4—44no—
660C22×C4—44no—
661C22×C4—44no—
662C22×C4—44no—
663C22×C4—44no—
664C22×C4—44no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—44no—
668C22×C4—44no—
669C22×C4—44no—
670C22×C4—44no—
671C22×C4—44no—
672C22×C4—44no—
673C22×C4—44no—
674C22×C4—44no—
675C22×C4—44no—
676C22×C4—44no—
677C22×C4—4128no—
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×C4C22×D412yes—
691C22×C4C22×D412yes—
692C22×C4C22×D412yes—
693C22×C4C22×D412yes—
694C22×C4C2×#4114yes—
695C22×C4C2×#4114yes—
696C22×C4H(5,𝔽2)12yes—
697C22×C4H(5,𝔽2)12yes—
698C22×C4H(5,𝔽2)12yes—
699C22×C4H(5,𝔽2)12yes—
700C22×C4H(5,𝔽2)12yes—
701C22×C4H(5,𝔽2)12yes—
702C4⋊C4—48no—
703C4⋊C4—48no—
704C4⋊C4—48no—
705C4⋊C4—44no—
706C4⋊C4—44no—
707C4⋊C4—44no—
708C4⋊C4—44no—
709C4⋊C4—44no—
710C4⋊C4—44no—
711C4⋊C4—88no—
712C4⋊C4—88no—
713C22⋊C4—48no—
714C22⋊C4—48no—
715C22⋊C4—48no—
716C22⋊C4—48no—
717C22⋊C4—48no—
718C22⋊C4—48no—
719C22⋊C4—48no—
720C22⋊C4—48no—
721C22⋊C4—48no—
722C22⋊C4—48no—
723C22⋊C4—48no—
724C22⋊C4—48no—
725C22⋊C4—48no—
726C22⋊C4—48no—
727C22⋊C4—48no—
728C22⋊C4—416no—
729C22⋊C4—48no—
730C22⋊C4—48no—
731C22⋊C4—48no—
732C22⋊C4—88no—
733C22⋊C4—88no—
734C22⋊C4—88no—
735C42—44no—
736C42—44no—
737C42—44no—
738C42—44no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—22no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—24no—
764C23—24no—
765C23—24no—
766C23—24no—
767C23—24no—
768C23—24no—
769C23—24no—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—416no—
776C23—416no—
777C23—416no—
778C23—416no—
779C23—416no—
780C23—416no—
781C23—416no—
782C23—432no—
783C23—432no—
784C23—432no—
785C23—432no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—44no—
824C23—44no—
825C23—44no—
826C23—44no—
827C23—44no—
828C23—44no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—44no—
834C23—44no—
835C23—44no—
836C23—44no—
837C23—44no—
838C23—44no—
839C23#53214yes—
840C23#53514yes—
841C23#53614yes—
842C23C23×D411yescharacteristic
843C23C22×#4112yes—
844C23C2×H(5,𝔽2)11yescharacteristic
845C23C2×H(5,𝔽2)11yescharacteristic
846C23C2×H(5,𝔽2)11yescharacteristic
847C23C2×H(5,𝔽2)11yescharacteristic
848C23C2×H(5,𝔽2)11yescharacteristic
849C23C2×H(5,𝔽2)11yescharacteristic
850C23C2×H(5,𝔽2)12yes—
851C23C2×2−1+412yes—
852C23#58512yes—
853Q8—88no—
854D4—816no—
855D4—816no—
856D4—816no—
857D4—88no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—416no—
874C2×C4—416no—
875C2×C4—416no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—416no—
897C2×C4—416no—
898C2×C4—416no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—42no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—42no—
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—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—42no—
918C2×C4—42no—
919C2×C4—42no—
920C2×C4—44no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—44no—
927C2×C4—44no—
928C2×C4—44no—
929C2×C4—44no—
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—44no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—44no—
946C2×C4—44no—
947C2×C4—44no—
948C2×C4—42no—
949C2×C4—44no—
950C2×C4#53414yes—
951C2×C4#53414yes—
952C2×C4#53414yes—
953C2×C4#56014yes—
954C2×C4#56014yes—
955C2×C4#56014yes—
956C2×C4H(3,𝔽4)14yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—24no—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—464no—
967C22—42no—
968C22—42no—
969C22—44no—
970C22—44no—
971C22—44no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—42no—
986C22—44no—
987C22—44no—
988C22—44no—
989C22—42no—
990C22—42no—
991C22—82no—
992C22—82no—
993C22—84no—
994C22—84no—
995C22—82no—
996C22—84no—
997C22—82no—
998C22—82no—
999C22—82no—
1000C22—84no—
1001C22—82no—
1002C22C2×#53211yescharacteristic
1003C22C2×#53411yescharacteristic
1004C22C2×#53411yescharacteristic
1005C22C2×#53411yescharacteristic
1006C22C2×#53511yescharacteristic
1007C22C2×#53611yescharacteristic
1008C22#344911yescharacteristic
1009C22#350512yes—
1010C22#350612yes—
1011C22#351912yes—
1012C22#351912yes—
1013C22#352012yes—
1014C22#352012yes—
1015C22C2×#56011yescharacteristic
1016C22C2×#56011yescharacteristic
1017C22C2×#56011yescharacteristic
1018C22C2×H(3,𝔽4)11yescharacteristic
1019C22#353612yes—
1020C22#353612yes—
1021C22#354112yes—
1022C22#354112yes—
1023C22#354212yes—
1024C22#354212yes—
1025C4—44no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—44no—
1030C4—82no—
1031C4—82no—
1032C4—82no—
1033C4—82no—
1034C4—82no—
1035C4—82no—
1036C4—82no—
1037C4—82no—
1038C4—82no—
1039C4#281218yes—
1040C2—44no—
1041C2—44no—
1042C2—44no—
1043C2—162no—
1044C2#3503211yescharacteristic
1045C2#3507811yescharacteristic
1046C2#3508511yescharacteristic
1047C2C2×#281211yescharacteristic
1048C2#3744811yescharacteristic
1049C2#3744911yescharacteristic
1050C2#3745111yescharacteristic
1051C2#4559812yes—
1052C2#4560112yes—
1053C2#4562312yes—
1054C2#4564612yes—
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. #16893C2semidirect
4. #16798C2semidirect
5. #16255C2semidirect
6. #15236C2semidirect
7. #15233C2semidirect
8. #15219C2semidirect
9. #15215C2semidirect
10. #15215C2semidirect
11. #15215C2semidirect
12. #15195C2semidirect
13. #15182C2semidirect
14. #15182C2semidirect
15. #15150C2semidirect
16. #15130C2semidirect
17. #15130C2semidirect
18. #14622C2semidirect
19. C4×#379C2semidirect
21. C22×#124C22semidirect
34. C2×#391C22semidirect
35. C2×#391C22semidirect
36. C2×#391C22semidirect
37. C2×#390C22semidirect
38. C2×#390C22semidirect
39. C2×#390C22semidirect
46. C2×#384C22semidirect
47. C2×#384C22semidirect
48. C2×#382C22semidirect
63. #1445C22semidirect
64. #1443C22semidirect
65. #1442C22semidirect
66. #1442C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
71. #1440C22semidirect
75. #1439C22semidirect
76. #1439C22semidirect
77. #1439C22semidirect
78. #1439C22semidirect
79. #1439C22semidirect
84. C4⋊#95C22semidirect
85. C4⋊#95C22semidirect
86. C4⋊#95C22semidirect
87. C4⋊#95C22semidirect
88. C4⋊#95C22semidirect
89. C4⋊#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#28472
#168932
#167982
#162552
#152362
#152332
#152192
#152152
#151952
#151822
#151502
#151302
#146222
C4×#3792