Finite Group Databasebeta

← #678239

Subgroups — #678239

Order 512.

3382 conjugacy classes of subgroups.

The subgroup lattice has 923 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C2×#2547C211yesmaximal, characteristic, complemented
3C2×#2354C211yesmaximal, characteristic, complemented
4C2×C4×#121C211yesmaximal, characteristic
5#15840C214yesmaximal, complemented
6#15687C214yesmaximal, complemented
7#15226C212yesmaximal, complemented
8#15215C212yesmaximal
9#15183C212yesmaximal, complemented
10#15181C212yesmaximal, complemented
11#14155C211yesmaximal, characteristic, complemented
12#14151C211yesmaximal, characteristic, complemented
13#14142C212yesmaximal, complemented
14#13997C212yesmaximal, complemented
15#13951C212yesmaximal, complemented
16#13871C212yesmaximal, complemented
17C4×#380C211yesmaximal, characteristic, complemented
18C22×C4⋊Q8C2211yescharacteristic
19C22×#124C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×#121C2211yescharacteristic
22C22×C4×D4C2212yes—
23C22×C4×D4C2211yescharacteristic
24C22×#117C2212yes—
25C23×C42C2211yescharacteristic
26#2857—28no—
27#2547—28no—
28C2×#397C2214yes—
29#2354—28no—
30C4×#121—28no—
31C2×#391C2212yes—
32C2×#391C2212yes—
33C2×#391C2212yes—
34C2×#391C2212yes—
35C2×#390C2212yes—
36C2×#390C2211yescharacteristic
37C2×#389C2212yes—
38C2×#389C2212yes—
39C2×#389C2211yescharacteristic
40C2×#389C2212yes—
41C2×#389C2212yes—
42C2×#388C2214yes—
43C2×#388C2212yes—
44C2×#386C2212yes—
45C2×#384C2211yescharacteristic
46C2×#380C2212yes—
47C2×#380C2212yes—
48C2×#380C2211yescharacteristic
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2211yescharacteristic
52C2×#380C2212yes—
53C2×#380C2211yescharacteristic
54C2×C4×C4⋊C4C2212yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yes—
60#1445C2214yes—
61#1445C2214yes—
62#1443C2214yes—
63#1442C2214yes—
64#1441C2214yes—
65#1440C2214yes—
66#1440C2214yes—
67#1439C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1438C2214yes—
73#1438C2214yes—
74#1437C2214yes—
75#1436C2214yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2214yes—
83#1434C2214yes—
84#1434C2212yes—
85C22⋊#95C2212yes—
86C4×#95C2212yes—
87C23×Q8C2312yes—
88C23×D4C2311yescharacteristic
89C23×D4C2312yes—
90C24×C4C2312yes—
91C24×C4C2311yescharacteristic
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C2×C4⋊Q8—24no—
95C2×C4⋊Q8—24no—
96C2×C4⋊Q8—24no—
97C2×#124—28no—
98C2×#124—44no—
99C2×#124—44no—
100C2×C22⋊Q8—28no—
101C2×C22⋊Q8—28no—
102C2×C22⋊Q8—44no—
103C2×#121—24no—
104C2×#121—24no—
105C2×#121—24no—
106C2×C4×D4—28no—
107C2×C4×D4—28no—
108C2×C4×D4—24no—
109C2×C4×D4—24no—
110C2×C4×D4—44no—
111C2×C4×D4D418yes—
112C2×#117—28no—
113C2×#117—28no—
114C2×#117—44no—
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2314yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C42—24no—
143C22×C42—24no—
144C22×C42—24no—
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2312yes—
149C22×C42C2312yes—
150C22×C42C2312yes—
151C22×C42C2314yes—
152C22×C42C2311yescharacteristic
153#397—216no—
154#391—28no—
155#391—28no—
156#391—28no—
157#391—44no—
158#390—24no—
159#390—28no—
160#389—28no—
161#389—28no—
162#389—24no—
163#389—44no—
164#389—44no—
165#388—216no—
166#388—28no—
167#386—28no—
168#384D418yescomplemented
169#380—28no—
170#380—28no—
171#380—24no—
172#380—28no—
173#380—28no—
174#380—28no—
175#380—24no—
176#380—24no—
177C4×C4⋊C4—28no—
178C4×C4⋊C4—24no—
179C4×C4⋊C4—24no—
180C4×C4⋊C4—24no—
181C4×C22⋊C4—28no—
182C4×C22⋊C4—44no—
183C2×#95C2312yes—
184C2×#95C2314yes—
185C2×#95C2314yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2312yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2314yes—
201C2×#95C2312yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C25C2412yes—
207C25C2411yescharacteristic
208C22×Q8—24no—
209C22×Q8—24no—
210C22×Q8—24no—
211C22×Q8—24no—
212C22×Q8—24no—
213C22×Q8—24no—
214C22×Q8—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—24no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—24no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—42no—
227C22×D4—42no—
228C22×D4C2×D414yes—
229C23×C4—22no—
230C23×C4—24no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—24no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—41no—
253C23×C4—41no—
254C23×C4C2×D418yes—
255C23×C4#4114yes—
256C23×C4#4114yes—
257C23×C4C2414yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2412yes—
262C23×C4C2414yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2412yes—
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C4⋊Q8—416no—
273#124—432no—
274C22⋊Q8—432no—
275#121—232no—
276C4×D4—232no—
277C4×D4—432no—
278#117—432no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4C2×D418yes—
319C2×C4⋊C4C2×D414yes—
320C2×C4⋊C4C2×D418yes—
321C2×C4⋊C4C2×D418yes—
322C2×C4⋊C4#4114yes—
323C2×C4⋊C4#4114yes—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—42no—
346C2×C22⋊C4—42no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—42no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4C2×D418yes—
360C2×C42—28no—
361C2×C42—24no—
362C2×C42—24no—
363C2×C42—22no—
364C2×C42—24no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—28no—
371C2×C42—24no—
372C2×C42—24no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—44no—
381C2×C42—416no—
382C2×C42C2×D414yes—
383C2×C42C2×D414yes—
384C2×C42#4114yes—
385#95—24no—
386#95—24no—
387#95—28no—
388#95—24no—
389#95—24no—
390#95—24no—
391#95—28no—
392#95—28no—
393#95—28no—
394#95—28no—
395#95—24no—
396#95—24no—
397#95—28no—
398#95—28no—
399#95—24no—
400#95—42no—
401#95—44no—
402#95—42no—
403#95—42no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408C24—21no—
409C24—21no—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—21no—
416C24—21no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24C22×D414yes—
435C24C2×#4112yes—
436C24C2×#4112yes—
437C242−1+412yes—
438C24C2511yescharacteristic
439C2×Q8—48no—
440C2×Q8—48no—
441C2×Q8—48no—
442C2×Q8—48no—
443C2×Q8—48no—
444C2×Q8—48no—
445C2×Q8—48no—
446C2×D4—216no—
447C2×D4—28no—
448C2×D4—28no—
449C2×D4—28no—
450C2×D4—48no—
451C2×D4—48no—
452C2×D4—48no—
453C2×D4—48no—
454C2×D4—48no—
455C2×D4—48no—
456C2×D4—44no—
457C2×D4—44no—
458C2×D4—44no—
459C2×D4—44no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—28no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—21no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—21no—
506C22×C4—24no—
507C22×C4—216no—
508C22×C4—28no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—216no—
512C22×C4—28no—
513C22×C4—216no—
514C22×C4—28no—
515C22×C4—28no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—44no—
554C22×C4—44no—
555C22×C4—44no—
556C22×C4—44no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—48no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—48no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4C22×D414yes—
570C22×C4C22×D418yes—
571C22×C4C22×D412yes—
572C22×C4C22×D412yes—
573C22×C4C22×D412yes—
574C22×C4C22×D412yes—
575C22×C4C22×D412yes—
576C22×C4C22×D412yes—
577C22×C4C2×#4114yes—
578C22×C4C2×#4112yes—
579C22×C4C2×#4114yes—
580C22×C4C2×#4112yes—
581C22×C4C2×#4112yes—
582C22×C4C2×#4112yes—
583C22×C4C2×#4112yes—
584C22×C4C2×#4112yes—
585C22×C4C2×#4112yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4H(5,𝔽2)12yes—
589C22×C4H(5,𝔽2)12yes—
590C22×C4H(5,𝔽2)12yes—
591C22×C42−1+412yes—
592C22×C42−1+412yes—
593C4⋊C4—28no—
594C4⋊C4—28no—
595C4⋊C4—216no—
596C4⋊C4—216no—
597C4⋊C4—28no—
598C4⋊C4—48no—
599C4⋊C4—48no—
600C4⋊C4—416no—
601C4⋊C4—48no—
602C4⋊C4—48no—
603C4⋊C4—44no—
604C4⋊C4—44no—
605C4⋊C4—44no—
606C4⋊C4—44no—
607C4⋊C4—88no—
608C22⋊C4—216no—
609C22⋊C4—216no—
610C22⋊C4—416no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—416no—
616C22⋊C4—48no—
617C22⋊C4—416no—
618C22⋊C4—416no—
619C22⋊C4—88no—
620C42—416no—
621C42—44no—
622C42—44no—
623C42—44no—
624C42—48no—
625C42—48no—
626C42—48no—
627C42#121116yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23#55614yes—
698C23C23×D411yescharacteristic
699C23C23×D411yescharacteristic
700C23C22×#4111yescharacteristic
701C23C22×#4111yescharacteristic
702C23C22×#4111yescharacteristic
703C23C22×#4111yescharacteristic
704C23C22×#4111yescharacteristic
705C23C2×H(5,𝔽2)11yescharacteristic
706C23C2×H(5,𝔽2)11yescharacteristic
707C23C2×H(5,𝔽2)11yescharacteristic
708C23C2×2−1+411yescharacteristic
709C23C2×2−1+411yescharacteristic
710C23C2×2−1+411yescharacteristic
711C23#58511yescharacteristic
712C23#58511yescharacteristic
713Q8—816no—
714D4—432no—
715D4—416no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—24no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—28no—
728C2×C4—22no—
729C2×C4—28no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—28no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—416no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—42no—
760C2×C4—44no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—416no—
773C2×C4—416no—
774C2×C4—432no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
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—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4C2×#12114yes—
811C2×C4C2×#12114yes—
812C2×C4C2×#12114yes—
813C2×C4#52514yes—
814C2×C4#52914yes—
815C2×C4#53514yes—
816C2×C4#54214yes—
817C2×C4#54614yes—
818C2×C4#54614yes—
819C2×C4#54614yes—
820C2×C4#54714yes—
821C2×C4#54814yes—
822C2×C4#55014yes—
823C2×C4#55314yes—
824C2×C4#55514yes—
825C22—24no—
826C22—24no—
827C22—24no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—82no—
848C22—82no—
849C22—82no—
850C22—82no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22C22×#12111yescharacteristic
856C22C2×#52511yescharacteristic
857C22C2×#52911yescharacteristic
858C22C2×#53511yescharacteristic
859C22C2×#54211yescharacteristic
860C22C2×#54611yescharacteristic
861C22C2×#54611yescharacteristic
862C22C2×#54611yescharacteristic
863C22C2×#54711yescharacteristic
864C22C2×#54811yescharacteristic
865C22C2×#55011yescharacteristic
866C22C2×#55311yescharacteristic
867C22C2×#55511yescharacteristic
868C22C2×#55611yescharacteristic
869C22#347511yescharacteristic
870C22#348011yescharacteristic
871C22#348211yescharacteristic
872C22#348511yescharacteristic
873C22#348611yescharacteristic
874C22#348911yescharacteristic
875C22#348911yescharacteristic
876C22#349511yescharacteristic
877C22#349511yescharacteristic
878C22#350611yescharacteristic
879C22#350611yescharacteristic
880C22#350911yescharacteristic
881C22#351111yescharacteristic
882C22#351711yescharacteristic
883C22#351811yescharacteristic
884C22#352011yescharacteristic
885C22#352011yescharacteristic
886C22#354611yescharacteristic
887C22#354711yescharacteristic
888C22#354811yescharacteristic
889C22#355211yescharacteristic
890C4—24no—
891C4—42no—
892C4—44no—
893C4—44no—
894C4—42no—
895C4—42no—
896C4—48no—
897C4—44no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—84no—
902C4—82no—
903C4#241418yes—
904C4#242718yes—
905C2—44no—
906C2—84no—
907C2C2×#242711yescharacteristic
908C2C2×#241411yescharacteristic
909C2#3563311yescharacteristic
910C2#3616111yescharacteristic
911C2#3631511yescharacteristic
912C2#3640511yescharacteristic
913C2#3658611yescharacteristic
914C2#3892011yescharacteristic
915C2#3894011yescharacteristic
916C2#3947111yescharacteristic
917C2#3973711yescharacteristic
918C2#5903311yescharacteristic
919C2#5904011yescharacteristic
920C2#5905011yescharacteristic
921C2#5913411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2857C2semidirect
2. C2×#2547C2semidirect
3. C2×#2354C2semidirect
5. #15840C2semidirect
6. #15687C2semidirect
7. #15226C2semidirect
9. #15183C2semidirect
10. #15181C2semidirect
11. #14155C2semidirect
12. #14151C2semidirect
13. #14142C2semidirect
14. #13997C2semidirect
15. #13951C2semidirect
16. #13871C2semidirect
17. C4×#380C2semidirect
168. #384D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25472
C2×#23542
C2×C4×#1212
#158402
#156872
#152262
#152152
#151832
#151812
#141552
#141512
#141422
#139972
#139512
#138712
C4×#3802