Finite Group Databasebeta

← #637121

Subgroups — #637121

Order 512.

4436 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×#2848C211yesmaximal, characteristic, complemented
2C2×#2417C211yesmaximal, characteristic, complemented
3C2×C4×#120C211yesmaximal, characteristic
4C22×#380C211yesmaximal, characteristic, complemented
5#16561C214yesmaximal, complemented
6#16513C214yesmaximal, complemented
7#15179C212yesmaximal, complemented
8#15177C212yesmaximal, complemented
9#15132C212yesmaximal, complemented
10#15129C212yesmaximal, complemented
11#14820C212yesmaximal, complemented
12#14725C212yesmaximal
13#14275C212yesmaximal, complemented
14#14259C212yesmaximal, complemented
15#14139C211yesmaximal, characteristic, complemented
16#13907C211yesmaximal, characteristic, complemented
17#13872C211yesmaximal, characteristic, complemented
18C25×C4C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Q8C2212yes—
21C22×C22⋊Q8C2211yescharacteristic, complemented
22C22×#120C2211yescharacteristic
23C22×C4×D4C2211yescharacteristic
24C22×C4×D4C2212yes—
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic
27C23×C22⋊C4C2212yes—
28#2848—28no—
29#2417—28no—
30C2×#398C2212yescomplemented
31C2×#397C2214yes—
32C2×#396C2212yescomplemented
33C2×#394C2214yes—
34C4×#120—28no—
35C2×#391C2211yescharacteristic, complemented
36C2×#391C2212yescomplemented
37C2×#389C2211yescharacteristic, complemented
38C2×#389C2212yescomplemented
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#386C2211yescharacteristic
43C2×#385C2214yes—
44C2×#385C2212yes—
45C2×#385C2212yes—
46C2×#385C2211yescharacteristic
47C2×#380—28no—
48C2×#380C2212yes—
49C2×#380C2211yescharacteristic
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2214yes—
55C2×#380C2211yescharacteristic, complemented
56C2×#380C2212yescomplemented
57C2×#379C2212yes—
58C2×#379C2211yescharacteristic
59C2×C4×C22⋊C4C2212yes—
60C2×C4×C22⋊C4C2211yescharacteristic
61C22×#95C2212yes—
62#1444C2214yescomplemented
63#1443C2214yescomplemented
64#1442C2214yescomplemented
65#1442C2214yescomplemented
66#1441C2214yescomplemented
67#1441C2212yescomplemented
68#1441C2214yescomplemented
69#1441C2214yescomplemented
70#1441C2214yescomplemented
71#1440C2214yes—
72#1440C2214yes—
73#1440C2214yes—
74#1440C2214yescomplemented
75#1439C2214yes—
76#1439C2214yes—
77#1439C2212yescomplemented
78#1439C2214yescomplemented
79#1438C2214yes—
80C4⋊#95C2212yescomplemented
81C4⋊#95C2212yescomplemented
82C4⋊#95C2212yescomplemented
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C26C2311yescharacteristic
88C23×Q8C2311yescharacteristic
89C23×D4C2311yescharacteristic
90C23×D4C2312yes—
91C24×C4—24no—
92C24×C4—24no—
93C24×C4—44no—
94C24×C4—44no—
95C24×C4D418yes—
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C24×C4C2311yescharacteristic
101C24×C4C2312yes—
102C24×C4C2312yes—
103C2×C22⋊Q8—28no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—24no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—44no—
109C2×C22⋊Q8—44no—
110C2×C22⋊Q8—44no—
111C2×#120—24no—
112C2×#120—24no—
113C2×#120—24no—
114C2×C4×D4—24no—
115C2×C4×D4—28no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—44no—
119C2×C4×D4—44no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—44no—
122C22×C4⋊C4—44no—
123C22×C4⋊C4D418yescomplemented
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C22⋊C4—28no—
139C22×C22⋊C4—48no—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2311yescharacteristic
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2311yescharacteristic
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2314yes—
157C22×C42C2311yescharacteristic
158C22×C42C2312yes—
159#398—28no—
160#397—48no—
161#396—28no—
162#394—48no—
163#391—24no—
164#391—44no—
165#389—24no—
166#389—44no—
167#386—28no—
168#386—28no—
169#386—28no—
170#386—24no—
171#385—216no—
172#385—28no—
173#385—28no—
174#385—24no—
175#380—28no—
176#380—24no—
177#380—28no—
178#380—24no—
179#380—28no—
180#380—28no—
181#380—216no—
182#380—28no—
183#380—44no—
184#379—28no—
185#379—24no—
186C4×C22⋊C4—28no—
187C4×C22⋊C4—24no—
188C2×#95—28no—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C25—22no—
211C25—22no—
212C25—24no—
213C25—24no—
214C25—22no—
215C25—22no—
216C25—22no—
217C25—22no—
218C25—42no—
219C25—42no—
220C25C2×D414yes—
221C25C2411yescharacteristic
222C25C2412yes—
223C25C2411yescharacteristic
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—24no—
228C22×Q8—24no—
229C22×D4—24no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—24no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—42no—
241C22×D4—42no—
242C22×D4#4114yes—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—232no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—432no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—42no—
273C23×C4—44no—
274C23×C4—44no—
275C23×C4—44no—
276C23×C4—44no—
277C23×C4—416no—
278C23×C4—416no—
279C23×C4—432no—
280C23×C4C2×D418yes—
281C23×C4C2×D414yes—
282C23×C4C2×D414yes—
283C23×C4C2×D418yes—
284C23×C4C2×D414yes—
285C23×C4C2×D418yes—
286C23×C4#4114yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2414yes—
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2411yescharacteristic
293C23×C4C2414yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C22⋊Q8—416no—
302C22⋊Q8—432no—
303C22⋊Q8—416no—
304#120—232no—
305C4×D4—432no—
306C4×D4—416no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—28no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—416no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—416no—
339C2×C4⋊C4—44no—
340C2×C4⋊C4—44no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4C2×D414yes—
343C2×C4⋊C4C2×D414yes—
344C2×C4⋊C4C2×D418yes—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—22no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—22no—
352C2×C22⋊C4—22no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—432no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4#4114yes—
395C2×C42—22no—
396C2×C42—24no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—24no—
400C2×C42—24no—
401#95—28no—
402#95—28no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—28no—
408#95—24no—
409#95—24no—
410#95—24no—
411#95—24no—
412#95—28no—
413#95—28no—
414#95—44no—
415#95—44no—
416#95—44no—
417#95—44no—
418#95—44no—
419#95—44no—
420#95—44no—
421#95—44no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—28no—
427C24—28no—
428C24—216no—
429C24—28no—
430C24—216no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—28no—
444C24—28no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—21no—
453C24—21no—
454C24—22no—
455C24—48no—
456C24—48no—
457C24—48no—
458C24—48no—
459C24—48no—
460C24—48no—
461C24—48no—
462C24—48no—
463C24—48no—
464C24—44no—
465C24—44no—
466C24—48no—
467C24—44no—
468C24—44no—
469C24—44no—
470C24—44no—
471C24C22×D414yes—
472C24C22×D412yes—
473C24C22×D412yes—
474C24C2×#4112yes—
475C24C2×#4112yes—
476C24C2×#4112yes—
477C24C2×#4112yes—
478C24H(5,𝔽2)14yes—
479C242−1+414yes—
480C242−1+412yes—
481C242−1+412yes—
482C24C2511yescharacteristic
483C2×Q8—44no—
484C2×Q8—48no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—48no—
488C2×D4—216no—
489C2×D4—28no—
490C2×D4—28no—
491C2×D4—28no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—48no—
500C2×D4—44no—
501C2×D4—44no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—28no—
505C22×C4—216no—
506C22×C4—28no—
507C22×C4—216no—
508C22×C4—28no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—216no—
536C22×C4—216no—
537C22×C4—216no—
538C22×C4—216no—
539C22×C4—216no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—4128no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—44no—
602C22×C4—48no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—48no—
606C22×C4—88no—
607C22×C4—88no—
608C22×C4—88no—
609C22×C4—88no—
610C22×C4#121116yes—
611C22×C4C22×D414yes—
612C22×C4C22×D414yes—
613C22×C4C22×D414yes—
614C22×C4C22×D412yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4114yes—
620C22×C4C2×#4112yes—
621C22×C4C2×#4112yes—
622C22×C4H(5,𝔽2)14yes—
623C22×C4H(5,𝔽2)14yes—
624C4⋊C4—28no—
625C4⋊C4—28no—
626C4⋊C4—48no—
627C4⋊C4—48no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—416no—
631C4⋊C4—44no—
632C4⋊C4—44no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—84no—
637C4⋊C4—88no—
638C22⋊C4—216no—
639C22⋊C4—28no—
640C22⋊C4—416no—
641C22⋊C4—416no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—416no—
646C22⋊C4—44no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—44no—
650C22⋊C4—48no—
651C22⋊C4—416no—
652C22⋊C4—44no—
653C22⋊C4—84no—
654C22⋊C4—88no—
655C42—44no—
656C42—48no—
657C23—22no—
658C23—24no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—232no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—24no—
696C23—24no—
697C23—432no—
698C23—432no—
699C23—416no—
700C23—416no—
701C23—416no—
702C23—432no—
703C23—416no—
704C23—416no—
705C23—432no—
706C23—416no—
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—41no—
724C23—41no—
725C23—42no—
726C23—41no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23C2×#12114yes—
742C23#52514yes—
743C23#53614yes—
744C23#53718yes—
745C23#54714yes—
746C23#54814yes—
747C23#55214yes—
748C23#55614yes—
749C23C23×D411yescharacteristic
750C23C23×D411yescharacteristic
751C23C22×#4111yescharacteristic
752C23C22×#4111yescharacteristic
753C23C22×#4111yescharacteristic
754C23C2×H(5,𝔽2)12yes—
755C23C2×H(5,𝔽2)12yes—
756C23C2×H(5,𝔽2)12yes—
757C23C2×2−1+411yescharacteristic
758C23C2×2−1+411yescharacteristic
759C23C2×2−1+412yes—
760Q8—88no—
761D4—432no—
762D4—416no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—232no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—432no—
784C2×C4—416no—
785C2×C4—41no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—44no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—432no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—44no—
807C2×C4—42no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—44no—
812C2×C4—41no—
813C2×C4—44no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—44no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—44no—
821C2×C4—42no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—44no—
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—816no—
844C2×C4—816no—
845C2×C4—88no—
846C2×C4C2×#12114yes—
847C2×C4C2×#12114yes—
848C2×C4#53418yes—
849C2×C4#53414yes—
850C2×C4#53514yes—
851C2×C4#53818yes—
852C22—24no—
853C22—28no—
854C22—24no—
855C22—28no—
856C22—28no—
857C22—24no—
858C22—24no—
859C22—24no—
860C22—28no—
861C22—24no—
862C22—28no—
863C22—28no—
864C22—28no—
865C22—464no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—44no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—81no—
884C22—81no—
885C22—82no—
886C22—81no—
887C22—82no—
888C22—81no—
889C22#241518yes—
890C22C22×#12111yescharacteristic
891C22C2×#52511yescharacteristic
892C22C2×#53411yescharacteristic
893C22C2×#53412yes—
894C22C2×#53511yescharacteristic
895C22C2×#53611yescharacteristic
896C22C2×#53712yes—
897C22C2×#53812yes—
898C22C2×#54711yescharacteristic
899C22C2×#54811yescharacteristic
900C22C2×#55211yescharacteristic
901C22C2×#55611yescharacteristic
902C22#348411yescharacteristic
903C22#348611yescharacteristic
904C22#349212yes—
905C22#351912yes—
906C22#351912yes—
907C22#352012yes—
908C22#352012yes—
909C22#353612yes—
910C22#353612yes—
911C22#353812yes—
912C22#353812yes—
913C4—24no—
914C4—44no—
915C4—44no—
916C4—44no—
917C4—42no—
918C4—44no—
919C4—84no—
920C4—82no—
921C4—81no—
922C4—82no—
923C4—84no—
924C4—81no—
925C4—82no—
926C4#261718yes—
927C2—28no—
928C2—48no—
929C2—82no—
930C2C2×#261711yescharacteristic
931C2C2×#241511yescharacteristic
932C2#3507712yes—
933C2#3522311yescharacteristic
934C2#3744212yes—
935C2#3891611yescharacteristic
936C2#3891711yescharacteristic
937C2#3892812yes—
938C2#3912011yescharacteristic
939C2#3912111yescharacteristic
940C2#3915412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
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
2. C2×#2417C2semidirect
4. C22×#380C2semidirect
5. #16561C2semidirect
6. #16513C2semidirect
7. #15179C2semidirect
8. #15177C2semidirect
9. #15132C2semidirect
10. #15129C2semidirect
11. #14820C2semidirect
13. #14275C2semidirect
14. #14259C2semidirect
15. #14139C2semidirect
16. #13907C2semidirect
17. #13872C2semidirect
21. C22×C22⋊Q8C22semidirect
30. C2×#398C22semidirect
32. C2×#396C22semidirect
35. C2×#391C22semidirect
36. C2×#391C22semidirect
37. C2×#389C22semidirect
38. C2×#389C22semidirect
55. C2×#380C22semidirect
56. C2×#380C22semidirect
62. #1444C22semidirect
63. #1443C22semidirect
64. #1442C22semidirect
65. #1442C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
68. #1441C22semidirect
69. #1441C22semidirect
70. #1441C22semidirect
74. #1440C22semidirect
77. #1439C22semidirect
78. #1439C22semidirect
80. C4⋊#95C22semidirect
81. C4⋊#95C22semidirect
82. C4⋊#95C22semidirect
123. C22×C4⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28482
C2×#24172
C2×C4×#1202
C22×#3802
#165612
#165132
#151792
#151772
#151322
#151292
#148202
#147252
#142752
#142592
#141392
#139072
#138722