Finite Group Databasebeta

← #516864

Subgroups — #516864

Order 512.

3554 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2487C211yesmaximal, characteristic
2C22×#389C211yesmaximal, characteristic, complemented
3C2×C42×D4C211yesmaximal, characteristic
4#14699C212yesmaximal, complemented
5#14697C212yesmaximal, complemented
6#14318C212yesmaximal, complemented
7#14317C212yesmaximal, complemented
8#14242C212yesmaximal, complemented
9#14230C212yesmaximal, complemented
10#14130C211yesmaximal, characteristic, complemented
11#14045C212yesmaximal, complemented
12#14039C212yesmaximal, complemented
13#14015C212yesmaximal
14#13973C212yesmaximal, complemented
15#13924C211yesmaximal, characteristic, complemented
16#13872C211yesmaximal, characteristic
17#13784C212yesmaximal
18#13782C212yesmaximal, complemented
19C4×#380C211yesmaximal, characteristic, complemented
20C22×C4×D4C2211yescharacteristic
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2212yes—
26C23×C42C2211yescharacteristic
27C23×C42C2211yescharacteristic
28#2487C4116yescomplemented
29C2×#400C2212yes—
30C2×#399C2212yes—
31C2×#389—28no—
32C2×#389C2212yes—
33C2×#389C2212yes—
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#389C2212yes—
38C2×#387C2214yes—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#385C2212yes—
42C2×#385C2214yes—
43C2×#385C2212yes—
44C2×#380C2211yescharacteristic
45C2×#380C2212yes—
46C2×#380C2211yescharacteristic
47C2×#380C2212yes—
48C42×D4—28no—
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C22⋊C4C2211yescharacteristic
54C2×C4×C22⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2212yes—
60C22×#95C2212yes—
61C2×C43C2211yescharacteristic
62#1445C2212yes—
63#1445C2212yes—
64#1444C2212yes—
65#1444C2214yes—
66#1442C2212yes—
67#1442C2214yes—
68#1441C2212yes—
69#1441C2214yes—
70#1439C2212yes—
71#1439C2214yes—
72#1437C2214yes—
73#1436C2214yes—
74#1436C2214yes—
75#1436C2214yes—
76#1436C2214yes—
77#1436C2214yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2214yes—
84#1434C2214yes—
85#1434C2214yes—
86#1434C2212yes—
87C22⋊#95C2212yes—
88C22⋊#95C2212yes—
89C22⋊#95C2212yes—
90C22⋊#95C2212yes—
91C22⋊#95C2214yes—
92C22⋊#95C2212yes—
93C4×#95C2212yes—
94C23×D4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2312yes—
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2311yescharacteristic
103C2×C4×D4—24no—
104C2×C4×D4—24no—
105C2×C4×D4—24no—
106C2×C4×D4—24no—
107C2×C4×D4—24no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C2×C4×D4C2×C418yes—
111C2×C4×D4Q818yes—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—28no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—44no—
117C22×C4⋊C4—48no—
118C22×C4⋊C4C2×C418yescomplemented
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2314yes—
132C22×C22⋊C4C2311yescharacteristic
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2311yescharacteristic
135C22×C22⋊C4C2311yescharacteristic
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2311yescharacteristic
138C22×C22⋊C4C2311yescharacteristic
139C22×C22⋊C4C2311yescharacteristic
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C42—24no—
143C22×C42—44no—
144C22×C42—44no—
145C22×C42D418yes—
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2314yes—
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160#400C2×C4116yescomplemented
161#399C2×C4116yescomplemented
162#389—28no—
163#389—28no—
164#389—28no—
165#389—28no—
166#389—44no—
167#389C2×C4116yescomplemented
168#387—48no—
169#386—28no—
170#386C2×C4116yes—
171#385—28no—
172#385—48no—
173#385C2×C4116yescomplemented
174#380—24no—
175#380—44no—
176#380C2×C4116yescomplemented
177#380C2×C418yescomplemented
178C4×C4⋊C4—24no—
179C4×C4⋊C4—24no—
180C4×C4⋊C4—24no—
181C4×C4⋊C4—44no—
182C4×C22⋊C4—24no—
183C4×C22⋊C4—24no—
184C4×C22⋊C4—24no—
185C4×C22⋊C4—28no—
186C4×C22⋊C4—24no—
187C4×C22⋊C4—24no—
188C4×C22⋊C4—24no—
189C2×#95—28no—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2311yescharacteristic
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2311yescharacteristic
199C2×#95C2311yescharacteristic
200C2×#95C2311yescharacteristic
201C2×#95C2311yescharacteristic
202C2×#95C2311yescharacteristic
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C43—24no—
216C25C2411yescharacteristic
217C25C2411yescharacteristic
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4C22×C414yes—
223C22×D4C2×Q814yes—
224C22×D4#4114yes—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4—24no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—44no—
246C23×C4—42no—
247C23×C4—42no—
248C23×C4—44no—
249C23×C4—42no—
250C23×C4—42no—
251C23×C4—42no—
252C23×C4—42no—
253C23×C4—44no—
254C23×C4—44no—
255C23×C4C22×C414yes—
256C23×C4C22×C414yes—
257C23×C4C22×C418yes—
258C23×C4C2×D414yes—
259C23×C4C2×D414yes—
260C23×C4C2×D414yes—
261C23×C4C2×Q814yes—
262C23×C4C2×Q814yes—
263C23×C4#4114yes—
264C23×C4#4114yes—
265C23×C4C2414yes—
266C23×C4C2414yes—
267C23×C4C2411yescharacteristic
268C23×C4C2414yes—
269C23×C4C2414yes—
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C23×C4C2411yescharacteristic
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2411yescharacteristic
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C4×D4—232no—
283C4×D4—232no—
284C4×D4—232no—
285C2×C4⋊C4—232no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—28no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—416no—
317C2×C4⋊C4—432no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4—44no—
320C2×C4⋊C4C22×C418yes—
321C2×C4⋊C4C22×C418yes—
322C2×C4⋊C4C22×C414yes—
323C2×C4⋊C4C22×C418yes—
324C2×C4⋊C4C22×C4116yes—
325C2×C4⋊C4C2×Q814yes—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—22no—
328C2×C22⋊C4—22no—
329C2×C22⋊C4—22no—
330C2×C22⋊C4—22no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4C22×C414yes—
350C2×C22⋊C4C22×C414yes—
351C2×C22⋊C4C22×C418yes—
352C2×C22⋊C4C22×C4116yes—
353C2×C22⋊C4C2×Q814yes—
354C2×C22⋊C4C2×Q814yes—
355C2×C22⋊C4#4114yes—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—24no—
364C2×C42—24no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—24no—
374C2×C42—28no—
375C2×C42—416no—
376C2×C42—416no—
377C2×C42—42no—
378C2×C42—42no—
379C2×C42—42no—
380C2×C42—42no—
381C2×C42—42no—
382C2×C42—44no—
383C2×C42—44no—
384C2×C42C22×C414yes—
385C2×C42C2×D414yes—
386C2×C42C2×D414yes—
387C2×C42C2×D414yes—
388C2×C42C2×D414yes—
389C2×C42C2×Q814yes—
390#95—28no—
391#95—28no—
392#95—22no—
393#95—22no—
394#95—22no—
395#95—22no—
396#95—22no—
397#95—22no—
398#95—28no—
399#95—24no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95—44no—
412#95C22×C4116yes—
413#95C22×C418yes—
414#95C22×C4116yes—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—21no—
420C24—21no—
421C24—21no—
422C24—21no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24C23×C412yes—
428C24C23×C412yes—
429C24C22×D412yes—
430C24C22×Q812yes—
431C24C22×Q812yes—
432C24C2×#4112yes—
433C24C2×#4112yes—
434C24C2×#4112yes—
435C24C2×#4112yes—
436C24C2×#4112yes—
437C24C2511yescharacteristic
438C2×D4—28no—
439C2×D4—28no—
440C2×D4—28no—
441C2×D4—28no—
442C2×D4—28no—
443C2×D4—28no—
444C2×D4C4×Q8116yes—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—216no—
459C22×C4—28no—
460C22×C4—28no—
461C22×C4—216no—
462C22×C4—28no—
463C22×C4—216no—
464C22×C4—28no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—28no—
506C22×C4—216no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—416no—
526C22×C4—44no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4—48no—
540C22×C4—416no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—44no—
544C22×C4—48no—
545C22×C4—48no—
546C22×C4—48no—
547C22×C4—48no—
548C22×C4—88no—
549C22×C4—88no—
550C22×C4C4×D4116yes—
551C22×C4C22⋊Q8116yes—
552C22×C4C23×C412yes—
553C22×C4C23×C418yes—
554C22×C4C23×C418yes—
555C22×C4C23×C412yes—
556C22×C4C23×C412yes—
557C22×C4C23×C412yes—
558C22×C4C23×C412yes—
559C22×C4C22×D412yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×Q812yes—
566C22×C4C22×Q812yes—
567C22×C4C22×Q812yes—
568C22×C4C22×Q812yes—
569C22×C4C22×Q812yes—
570C22×C4C2×#4112yes—
571C22×C4C2×#4112yes—
572C22×C4C2×#4112yes—
573C22×C4C2×#4112yes—
574C22×C4C2×#4112yes—
575C22×C4C2×#4112yes—
576C22×C4C2×#4112yes—
577C22×C4H(5,𝔽2)14yes—
578C22×C4H(5,𝔽2)14yes—
579C22×C42−1+414yes—
580C4⋊C4—28no—
581C4⋊C4—216no—
582C4⋊C4—216no—
583C4⋊C4—28no—
584C4⋊C4—216no—
585C4⋊C4—28no—
586C4⋊C4—416no—
587C4⋊C4—48no—
588C4⋊C4—416no—
589C4⋊C4—48no—
590C4⋊C4—416no—
591C4⋊C4—48no—
592C4⋊C4—88no—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—216no—
596C22⋊C4—28no—
597C22⋊C4—28no—
598C22⋊C4—28no—
599C22⋊C4—28no—
600C22⋊C4—416no—
601C22⋊C4—48no—
602C22⋊C4—88no—
603C42—28no—
604C42—28no—
605C42—28no—
606C42—28no—
607C42—28no—
608C42—44no—
609C42—44no—
610C42—44no—
611C42—44no—
612C42—44no—
613C42—44no—
614C42—44no—
615C42—44no—
616C42—88no—
617C23—24no—
618C23—24no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—22no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23C2×C4×D414yes—
656C23C2×C4×Q814yes—
657C23C2×C4×Q814yes—
658C23C4×#4114yes—
659C23C2×C22⋊Q814yes—
660C23#52514yes—
661C23#52914yes—
662C23#53314yes—
663C23C24×C411yescharacteristic
664C23C23×D411yescharacteristic
665C23C23×Q811yescharacteristic
666C23C22×#4111yescharacteristic
667C23C22×#4111yescharacteristic
668C23C22×#4111yescharacteristic
669C23C22×#4111yescharacteristic
670C23C2×H(5,𝔽2)12yes—
671C23C2×H(5,𝔽2)12yes—
672C23C2×2−1+412yes—
673C23#58512yes—
674D4—232no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—232no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—24no—
704C2×C4—28no—
705C2×C4—28no—
706C2×C4—24no—
707C2×C4—28no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—416no—
720C2×C4—416no—
721C2×C4—416no—
722C2×C4—416no—
723C2×C4—432no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—44no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—44no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—42no—
744C2×C4—44no—
745C2×C4—42no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—416no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—816no—
768C2×C4C2×C4×D414yes—
769C2×C4C2×C4×D414yes—
770C2×C4C2×C4×Q814yes—
771C2×C4#52018yes—
772C2×C4C2×C22⋊Q814yes—
773C2×C4C2×C22⋊Q814yes—
774C2×C4#53414yes—
775C2×C4#53514yes—
776C2×C4#53614yes—
777C2×C4#53918yes—
778C22—24no—
779C22—24no—
780C22—28no—
781C22—28no—
782C22—24no—
783C22—24no—
784C22—24no—
785C22—28no—
786C22—24no—
787C22—28no—
788C22—28no—
789C22—24no—
790C22—42no—
791C22—42no—
792C22—44no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—44no—
797C22—42no—
798C22—44no—
799C22C4×C22⋊Q818yes—
800C22C22×C4×D411yescharacteristic
801C22C22×C4×Q811yescharacteristic
802C22C2×C4×#4111yescharacteristic
803C22C2×#52012yes—
804C22C4×H(5,𝔽2)12yes—
805C22C22×C22⋊Q811yescharacteristic
806C22C2×#52511yescharacteristic
807C22C2×#52911yescharacteristic
808C22C2×#53311yescharacteristic
809C22C2×#53411yescharacteristic
810C22C2×#53511yescharacteristic
811C22C2×#53611yescharacteristic
812C22#344911yescharacteristic
813C22C2×#53912yes—
814C22#346012yes—
815C22#350112yes—
816C22#350312yes—
817C22#350512yes—
818C22#351112yes—
819C22#351512yes—
820C22#351512yes—
821C22#351912yes—
822C22#351912yes—
823C4—24no—
824C4—24no—
825C4—24no—
826C4—24no—
827C4—24no—
828C4—42no—
829C4—42no—
830C4—42no—
831C4—48no—
832C4—42no—
833C4—48no—
834C4—42no—
835C4—42no—
836C4—42no—
837C4—84no—
838C4—84no—
839C4#232218yes—
840C2—28no—
841C2—44no—
842C2C2×C4×C22⋊Q811yescharacteristic
843C2C2×#232211yescharacteristic
844C2C4×#53511yescharacteristic
845C2#3432312yes—
846C2#3433212yes—
847C2#3501011yescharacteristic
848C2#3501712yes—
849C2#3502912yes—
850C2#3507611yescharacteristic
851C2#3513811yescharacteristic
852C2#3527911yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×#389C2semidirect
4. #14699C2semidirect
5. #14697C2semidirect
6. #14318C2semidirect
7. #14317C2semidirect
8. #14242C2semidirect
9. #14230C2semidirect
10. #14130C2semidirect
11. #14045C2semidirect
12. #14039C2semidirect
14. #13973C2semidirect
15. #13924C2semidirect
18. #13782C2semidirect
19. C4×#380C2semidirect
28. #2487C4semidirect
118. C22×C4⋊C4C2×C4semidirect
160. #400C2×C4semidirect
161. #399C2×C4semidirect
167. #389C2×C4semidirect
173. #385C2×C4semidirect
176. #380C2×C4semidirect
177. #380C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24872
C22×#3892
C2×C42×D42
#146992
#146972
#143182
#143172
#142422
#142302
#141302
#140452
#140392
#140152
#139732
#139242
#138722
#137842
#137822
C4×#3802