Finite Group Databasebeta

← #674259

Subgroups — #674259

Order 512.

3410 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2420C212yesmaximal
2C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C4×#121C211yesmaximal, characteristic
4#15929C214yesmaximal, complemented
5#15383C214yesmaximal, complemented
6#15225C212yesmaximal, complemented
7#15183C212yesmaximal, complemented
8#15132C212yesmaximal, complemented
9#15129C212yesmaximal, complemented
10#14686C211yesmaximal, characteristic, complemented
11#14151C211yesmaximal, characteristic, complemented
12#13916C212yesmaximal, complemented
13#13911C211yesmaximal, characteristic, complemented
14#13906C211yesmaximal, characteristic, complemented
15#13904C212yesmaximal, complemented
16#13872C212yesmaximal, complemented
17C4×#380C211yesmaximal, characteristic, complemented
18C22×#121C2211yescharacteristic
19C22×C4×D4C2212yes—
20C22×C4×D4C2212yes—
21C22×C4×D4C2211yescharacteristic
22C23×C4⋊C4C2212yes—
23C23×C42C2211yescharacteristic
24#2420—216no—
25C2×#397C2214yes—
26C2×#394C2214yes—
27D4×C4⋊C4—28no—
28C4×#121—28no—
29C2×#390C2212yes—
30C2×#390C2211yescharacteristic
31C2×#389C2212yes—
32C2×#389C2212yes—
33C2×#389C2211yescharacteristic
34C2×#389C2212yes—
35C2×#388C2212yes—
36C2×#386C2212yes—
37C2×#386C2214yes—
38C2×#385C2214yes—
39C2×#384C2211yescharacteristic
40C2×#384C2211yescharacteristic
41C2×#382C2212yes—
42C2×#381C2214yes—
43C2×#381C2214yes—
44C2×#380C2211yescharacteristic
45C2×#380C2212yes—
46C2×#380C2211yescharacteristic
47C2×#380C2211yescharacteristic
48C2×#380C2212yes—
49C2×#380C2212yes—
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2212yes—
58#1445C2214yes—
59#1445C2214yes—
60#1443C2214yes—
61#1442C2214yes—
62#1442C2214yes—
63#1441C2214yes—
64#1441C2214yes—
65#1441C2214yes—
66#1440C2214yes—
67#1440C2214yes—
68#1440C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71C4⋊#95C2212yes—
72C4⋊#95C2211yescharacteristic
73C4⋊#95C2212yes—
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2212yes—
82#1434C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2214yes—
85C4×#95C2212yes—
86C23×D4C2312yes—
87C23×D4C2311yescharacteristic
88C24×C4C2311yescharacteristic
89C24×C4C2312yes—
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C24×C4C2314yes—
93C2×#121—24no—
94C2×#121—24no—
95C2×#121D418yes—
96C2×C4×D4—28no—
97C2×C4×D4—28no—
98C2×C4×D4—28no—
99C2×C4×D4—28no—
100C2×C4×D4—28no—
101C2×C4×D4—24no—
102C2×C4×D4—24no—
103C2×C4×D4—44no—
104C2×C4×D4D418yes—
105C22×C4⋊C4—28no—
106C22×C4⋊C4—28no—
107C22×C4⋊C4—44no—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2312yes—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2314yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C42—24no—
136C22×C42—24no—
137C22×C42—24no—
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2312yes—
142C22×C42C2312yes—
143C22×C42C2312yes—
144C22×C42C2311yescharacteristic
145#397—216no—
146#394—216no—
147#390—28no—
148#390—24no—
149#389—28no—
150#389—28no—
151#389—24no—
152#389—44no—
153#388—28no—
154#386—216no—
155#386—28no—
156#385—216no—
157#384—24no—
158#384—24no—
159#382—28no—
160#381—216no—
161#381—48no—
162#380—28no—
163#380—28no—
164#380—24no—
165#380—24no—
166#380—24no—
167#380—44no—
168#380—44no—
169#380—44no—
170#380—44no—
171C4×C4⋊C4—24no—
172C4×C4⋊C4—24no—
173C4×C4⋊C4—24no—
174C4×C22⋊C4—28no—
175C4×C22⋊C4—28no—
176C2×#95C2314yes—
177C2×#95C2312yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C25C2412yes—
201C25C2411yescharacteristic
202C22×D4—24no—
203C22×D4—24no—
204C22×D4—24no—
205C22×D4—24no—
206C22×D4—22no—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4—22no—
210C22×D4—42no—
211C22×D4—42no—
212C22×D4C2×D418yes—
213C22×D4C2×D414yes—
214C22×D4C2×D414yes—
215C22×D4#4114yes—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—24no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—24no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—24no—
231C23×C4—22no—
232C23×C4—24no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—28no—
238C23×C4—28no—
239C23×C4—28no—
240C23×C4—22no—
241C23×C4—28no—
242C23×C4—22no—
243C23×C4—41no—
244C23×C4—41no—
245C23×C4—44no—
246C23×C4—44no—
247C23×C4—44no—
248C23×C4C2×D418yes—
249C23×C4C2×D414yes—
250C23×C4#4114yes—
251C23×C4C2414yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2414yes—
257C23×C4C2412yes—
258C23×C4C2411yescharacteristic
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2412yes—
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2411yescharacteristic
265C23×C4C2411yescharacteristic
266#121—232no—
267C4×D4—232no—
268C4×D4—432no—
269C4×D4—432no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—28no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—432no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—42no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4C2×D414yes—
317C2×C4⋊C4C2×D414yes—
318C2×C4⋊C4#4114yes—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—28no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—28no—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—42no—
341C2×C22⋊C4—42no—
342C2×C22⋊C4—42no—
343C2×C22⋊C4—42no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4C2×D418yes—
351C2×C22⋊C4C2×D418yes—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—22no—
356C2×C42—24no—
357C2×C42—22no—
358C2×C42—22no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—24no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—24no—
369C2×C42—24no—
370C2×C42—416no—
371C2×C42C2×D414yes—
372C2×C42#4114yes—
373C2×C42#4114yes—
374#95—24no—
375#95—24no—
376#95—24no—
377#95—24no—
378#95—24no—
379#95—24no—
380#95—28no—
381#95—28no—
382#95—28no—
383#95—28no—
384#95—28no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—28no—
389#95—24no—
390#95—42no—
391#95—44no—
392#95—44no—
393#95—44no—
394#95—44no—
395#95—44no—
396#95—44no—
397#95—44no—
398C24—21no—
399C24—21no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—21no—
404C24—22no—
405C24—21no—
406C24—21no—
407C24—22no—
408C24—21no—
409C24—21no—
410C24—22no—
411C24—22no—
412C24—21no—
413C24—21no—
414C24—21no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—21no—
419C24—22no—
420C24—22no—
421C24—21no—
422C24C22×D414yes—
423C24C22×D414yes—
424C24C22×D412yes—
425C24C2×#4114yes—
426C24C2×#4112yes—
427C242−1+412yes—
428C24C2511yescharacteristic
429C2×D4—216no—
430C2×D4—216no—
431C2×D4—28no—
432C2×D4—28no—
433C2×D4—28no—
434C2×D4—28no—
435C2×D4—28no—
436C2×D4—28no—
437C2×D4—48no—
438C2×D4—48no—
439C2×D4—48no—
440C2×D4—48no—
441C2×D4—48no—
442C2×D4#121116yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—28no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—28no—
485C22×C4—216no—
486C22×C4—28no—
487C22×C4—216no—
488C22×C4—28no—
489C22×C4—216no—
490C22×C4—28no—
491C22×C4—28no—
492C22×C4—28no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—24no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—416no—
541C22×C4—416no—
542C22×C4—416no—
543C22×C4—44no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—48no—
547C22×C4—44no—
548C22×C4—48no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—44no—
556C22×C4—416no—
557C22×C4—88no—
558C22×C4—88no—
559C22×C4—88no—
560C22×C4C22×D412yes—
561C22×C4C22×D414yes—
562C22×C4C22×D414yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D412yes—
567C22×C4C2×#4112yes—
568C22×C4C2×#4114yes—
569C22×C4C2×#4112yes—
570C22×C4C2×#4112yes—
571C22×C4C2×#4112yes—
572C22×C4C2×#4112yes—
573C22×C4C2×#4112yes—
574C22×C4C2×#4112yes—
575C22×C4C2×#4112yes—
576C22×C4C2×#4112yes—
577C22×C4C2×#4112yes—
578C22×C4H(5,𝔽2)12yes—
579C22×C4H(5,𝔽2)12yes—
580C22×C4H(5,𝔽2)12yes—
581C22×C42−1+412yes—
582C22×C42−1+412yes—
583C4⋊C4—28no—
584C4⋊C4—28no—
585C4⋊C4—28no—
586C4⋊C4—416no—
587C4⋊C4—48no—
588C4⋊C4—48no—
589C4⋊C4—44no—
590C4⋊C4—48no—
591C4⋊C4—44no—
592C4⋊C4—48no—
593C4⋊C4—48no—
594C4⋊C4—44no—
595C4⋊C4—44no—
596C4⋊C4—84no—
597C4⋊C4—84no—
598C4⋊C4—88no—
599C22⋊C4—216no—
600C22⋊C4—216no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—48no—
604C22⋊C4—48no—
605C22⋊C4—416no—
606C22⋊C4—48no—
607C22⋊C4—88no—
608C22⋊C4—88no—
609C22⋊C4—88no—
610C42—48no—
611C42—44no—
612C42—44no—
613C42—44no—
614C42—48no—
615C42—48no—
616C42#123116yes—
617C23—22no—
618C23—24no—
619C23—22no—
620C23—24no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—22no—
625C23—22no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—22no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—22no—
634C23—22no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—22no—
639C23—24no—
640C23—22no—
641C23—22no—
642C23—24no—
643C23—22no—
644C23—22no—
645C23—24no—
646C23—22no—
647C23—22no—
648C23—24no—
649C23—22no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—42no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—42no—
662C23—41no—
663C23—42no—
664C23—41no—
665C23—41no—
666C23—42no—
667C23—41no—
668C23—42no—
669C23—41no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—41no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—41no—
684C23—42no—
685C23C2×#12118yes—
686C23#54714yes—
687C23C23×D411yescharacteristic
688C23C23×D411yescharacteristic
689C23C22×#4111yescharacteristic
690C23C22×#4111yescharacteristic
691C23C22×#4111yescharacteristic
692C23C22×#4111yescharacteristic
693C23C22×#4111yescharacteristic
694C23C2×H(5,𝔽2)11yescharacteristic
695C23C2×H(5,𝔽2)11yescharacteristic
696C23C2×H(5,𝔽2)11yescharacteristic
697C23C2×2−1+411yescharacteristic
698C23C2×2−1+411yescharacteristic
699C23C2×2−1+411yescharacteristic
700C23#58511yescharacteristic
701C23#58511yescharacteristic
702D4—232no—
703D4—432no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—416no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—432no—
754C2×C4—416no—
755C2×C4—416no—
756C2×C4—42no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—44no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—44no—
768C2×C4—42no—
769C2×C4—44no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—42no—
781C2×C4—44no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—44no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—832no—
799C2×C4C2×#12114yes—
800C2×C4C2×#12314yes—
801C2×C4C2×#12314yes—
802C2×C4C2×#12314yes—
803C2×C4#52914yes—
804C2×C4#53614yes—
805C2×C4#54014yes—
806C2×C4#54614yes—
807C2×C4#54614yes—
808C2×C4#54714yes—
809C2×C4#54714yes—
810C2×C4#55214yes—
811C2×C4#55214yes—
812C2×C4#55314yes—
813C2×C4#55514yes—
814C22—24no—
815C22—24no—
816C22—28no—
817C22—28no—
818C22—24no—
819C22—28no—
820C22—44no—
821C22—42no—
822C22—44no—
823C22—44no—
824C22—42no—
825C22—42no—
826C22—44no—
827C22—44no—
828C22—42no—
829C22—44no—
830C22—42no—
831C22—44no—
832C22—42no—
833C22—42no—
834C22—44no—
835C22—42no—
836C22—44no—
837C22—42no—
838C22—44no—
839C22—42no—
840C22—42no—
841C22—44no—
842C22—44no—
843C22—42no—
844C22C22×#12111yescharacteristic
845C22C22×#12311yescharacteristic
846C22C2×#52911yescharacteristic
847C22C2×#53611yescharacteristic
848C22C2×#54011yescharacteristic
849C22C2×#54611yescharacteristic
850C22C2×#54611yescharacteristic
851C22C2×#54711yescharacteristic
852C22C2×#54711yescharacteristic
853C22C2×#54711yescharacteristic
854C22D4×#4111yescharacteristic
855C22C2×#55211yescharacteristic
856C22C2×#55211yescharacteristic
857C22C2×#55311yescharacteristic
858C22C2×#55511yescharacteristic
859C22#347511yescharacteristic
860C22#348111yescharacteristic
861C22#348811yescharacteristic
862C22#348911yescharacteristic
863C22#349211yescharacteristic
864C22#349311yescharacteristic
865C22#349411yescharacteristic
866C22#349511yescharacteristic
867C22#349611yescharacteristic
868C22#349811yescharacteristic
869C22#350711yescharacteristic
870C22#351111yescharacteristic
871C22#351411yescharacteristic
872C22#351811yescharacteristic
873C22#352011yescharacteristic
874C22#352311yescharacteristic
875C22#354711yescharacteristic
876C22#354811yescharacteristic
877C22#355211yescharacteristic
878C22#355411yescharacteristic
879C4—24no—
880C4—44no—
881C4—44no—
882C4—42no—
883C4—44no—
884C4—42no—
885C4—42no—
886C4—82no—
887C4—82no—
888C4—82no—
889C4—84no—
890C4—82no—
891C4—84no—
892C4#242018yescomplemented
893C4#248618yes—
894C2—44no—
895C2—48no—
896C2C2×#242011yescharacteristic
897C2C2×#248611yescharacteristic
898C2#3551611yescharacteristic
899C2#3611611yescharacteristic
900C2#3615311yescharacteristic
901C2#3625811yescharacteristic
902C2#3630111yescharacteristic
903C2#3891111yescharacteristic
904C2#3893011yescharacteristic
905C2#3935211yescharacteristic
906C2#3947011yescharacteristic
907C2#5922911yescharacteristic
908C2#5923511yescharacteristic
909C2#5925711yescharacteristic
910C2#5930411yescharacteristic
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
2. C2×D4×C4⋊C4C2semidirect
4. #15929C2semidirect
5. #15383C2semidirect
6. #15225C2semidirect
7. #15183C2semidirect
8. #15132C2semidirect
9. #15129C2semidirect
10. #14686C2semidirect
11. #14151C2semidirect
12. #13916C2semidirect
13. #13911C2semidirect
14. #13906C2semidirect
15. #13904C2semidirect
16. #13872C2semidirect
17. C4×#380C2semidirect
892. C4#2420semidirect

Maximal subgroups

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

subgroupindex
C2×#24202
C2×D4×C4⋊C42
C2×C4×#1212
#159292
#153832
#152252
#151832
#151322
#151292
#146862
#141512
#139162
#139112
#139062
#139042
#138722
C4×#3802