Finite Group Databasebeta

← #678084

Subgroups — #678084

Order 512.

2974 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2354C211yesmaximal, characteristic, complemented
2C2×C4×#121C211yesmaximal, characteristic
3#16077C214yesmaximal, complemented
4#15293C214yesmaximal, complemented
5#15219C212yesmaximal
6#15181C212yesmaximal, complemented
7#15138C212yesmaximal, complemented
8#15132C212yesmaximal, complemented
9#14686C211yesmaximal, characteristic, complemented
10#14151C211yesmaximal, characteristic, complemented
11#14030C212yesmaximal, complemented
12#13973C212yesmaximal, complemented
13#13939C212yesmaximal, complemented
14#13911C211yesmaximal, characteristic, complemented
15#13906C211yesmaximal, characteristic, complemented
16#13871C212yesmaximal, complemented
17C4×#380C211yesmaximal, characteristic, complemented
18C22×#121C2211yescharacteristic
19C22×C4×D4C2212yes—
20C22×C4×D4C2211yescharacteristic
21C22×#117C2212yes—
22C23×C42C2211yescharacteristic
23C2×#397C2214yes—
24#2354—28no—
25C4×#121—28no—
26C2×#390C2211yescharacteristic
27C2×#390C2212yes—
28C2×#390C2212yes—
29C2×#389C2211yescharacteristic
30C2×#389C2212yes—
31C2×#389C2212yes—
32C2×#388C2214yes—
33C2×#388C2212yes—
34C2×#386C2212yes—
35C2×#384C2211yescharacteristic
36C2×#384C2211yescharacteristic
37C2×#382C2212yes—
38C2×#380C2212yes—
39C2×#380C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2212yes—
42C2×#380C2211yescharacteristic
43C2×#380C2212yes—
44C2×#380C2212yes—
45C2×#380C2212yes—
46C2×#380C2212yes—
47C2×C4×C4⋊C4C2211yescharacteristic
48C2×C4×C4⋊C4C2212yes—
49C2×C4×C4⋊C4C2211yescharacteristic
50C2×C4×C4⋊C4C2211yescharacteristic
51C2×C4×C22⋊C4C2212yes—
52C2×C4×C22⋊C4C2212yes—
53#1443C2214yes—
54#1442C2214yes—
55#1442C2214yes—
56#1442C2214yes—
57#1441C2214yes—
58#1440C2214yes—
59#1440C2214yes—
60#1440C2214yes—
61#1440C2214yes—
62#1439C2214yes—
63#1439C2214yes—
64#1439C2214yes—
65#1438C2214yes—
66#1438C2214yes—
67#1437C2214yes—
68#1436C2214yes—
69C4⋊#95C2211yescharacteristic
70C4⋊#95C2212yes—
71C4⋊#95C2212yes—
72C4⋊#95C2212yes—
73C4⋊#95C2212yes—
74C4⋊#95C2212yes—
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2211yescharacteristic
80#1434C2214yes—
81#1434C2214yes—
82#1434C2212yes—
83C22⋊#95C2212yes—
84C4×#95C2212yes—
85C23×D4C2311yescharacteristic
86C23×D4C2312yes—
87C24×C4C2312yes—
88C24×C4C2311yescharacteristic
89C24×C4C2311yescharacteristic
90C24×C4C2311yescharacteristic
91C2×#121—24no—
92C2×#121—24no—
93C2×#121—24no—
94C2×C4×D4—28no—
95C2×C4×D4—28no—
96C2×C4×D4—24no—
97C2×C4×D4—24no—
98C2×C4×D4—44no—
99C2×C4×D4D418yes—
100C2×#117—28no—
101C2×#117—28no—
102C2×#117—44no—
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2312yes—
108C22×C4⋊C4C2311yescharacteristic
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2312yes—
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2314yes—
118C22×C22⋊C4C2312yes—
119C22×C22⋊C4C2312yes—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2314yes—
128C22×C22⋊C4C2314yes—
129C22×C22⋊C4C2314yes—
130C22×C42—24no—
131C22×C42—24no—
132C22×C42—24no—
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135C22×C42C2311yescharacteristic
136C22×C42C2312yes—
137C22×C42C2312yes—
138C22×C42C2312yes—
139C22×C42C2314yes—
140C22×C42C2311yescharacteristic
141#397—48no—
142#390—28no—
143#390—24no—
144#390—44no—
145#389—24no—
146#389—44no—
147#389—44no—
148#388—216no—
149#388—28no—
150#386—28no—
151#384—24no—
152#384—24no—
153#382—28no—
154#380—28no—
155#380—24no—
156#380—28no—
157#380—24no—
158#380—24no—
159#380—44no—
160#380—44no—
161#380—44no—
162#380—44no—
163C4×C4⋊C4—28no—
164C4×C4⋊C4—24no—
165C4×C4⋊C4—24no—
166C4×C4⋊C4—24no—
167C4×C22⋊C4—28no—
168C4×C22⋊C4—44no—
169C2×#95C2312yes—
170C2×#95C2314yes—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2312yes—
174C2×#95C2312yes—
175C2×#95C2312yes—
176C2×#95C2312yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2312yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2314yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2314yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C25C2412yes—
194C25C2411yescharacteristic
195C22×D4—24no—
196C22×D4—24no—
197C22×D4—24no—
198C22×D4—24no—
199C22×D4—22no—
200C22×D4—22no—
201C22×D4—24no—
202C22×D4—22no—
203C22×D4—22no—
204C22×D4—22no—
205C22×D4—22no—
206C22×D4—42no—
207C22×D4—42no—
208C22×D4C2×D414yes—
209C23×C4—22no—
210C23×C4—22no—
211C23×C4—22no—
212C23×C4—24no—
213C23×C4—24no—
214C23×C4—24no—
215C23×C4—24no—
216C23×C4—22no—
217C23×C4—22no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—22no—
221C23×C4—22no—
222C23×C4—22no—
223C23×C4—24no—
224C23×C4—22no—
225C23×C4—24no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—22no—
232C23×C4—41no—
233C23×C4—41no—
234C23×C4C2×D418yes—
235C23×C4#4114yes—
236C23×C4#4114yes—
237C23×C4C2414yes—
238C23×C4C2412yes—
239C23×C4C2412yes—
240C23×C4C2414yes—
241C23×C4C2412yes—
242C23×C4C2412yes—
243C23×C4C2412yes—
244C23×C4C2412yes—
245C23×C4C2411yescharacteristic
246C23×C4C2411yescharacteristic
247C23×C4C2412yes—
248C23×C4C2411yescharacteristic
249C23×C4C2411yescharacteristic
250C23×C4C2411yescharacteristic
251C23×C4C2411yescharacteristic
252#121—232no—
253C4×D4—232no—
254C4×D4—432no—
255#117—432no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—24no—
263C2×C4⋊C4—24no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—24no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—22no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—24no—
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—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—42no—
294C2×C4⋊C4—42no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—44no—
297C2×C4⋊C4—44no—
298C2×C4⋊C4C2×D414yes—
299C2×C4⋊C4#4114yes—
300C2×C4⋊C4#4114yes—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—24no—
304C2×C22⋊C4—24no—
305C2×C22⋊C4—24no—
306C2×C22⋊C4—28no—
307C2×C22⋊C4—24no—
308C2×C22⋊C4—24no—
309C2×C22⋊C4—24no—
310C2×C22⋊C4—24no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—28no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—28no—
318C2×C22⋊C4—28no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—42no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—44no—
327C2×C22⋊C4—44no—
328C2×C22⋊C4—44no—
329C2×C22⋊C4—44no—
330C2×C22⋊C4—44no—
331C2×C22⋊C4—44no—
332C2×C22⋊C4—44no—
333C2×C22⋊C4—44no—
334C2×C22⋊C4—44no—
335C2×C22⋊C4—44no—
336C2×C22⋊C4C2×D418yes—
337C2×C42—28no—
338C2×C42—24no—
339C2×C42—22no—
340C2×C42—24no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—28no—
344C2×C42—24no—
345C2×C42—24no—
346C2×C42—24no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—22no—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—24no—
354C2×C42—24no—
355C2×C42—24no—
356C2×C42—24no—
357C2×C42—44no—
358C2×C42—416no—
359C2×C42C2×D414yes—
360C2×C42#4114yes—
361C2×C42#4114yes—
362#95—24no—
363#95—24no—
364#95—28no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—28no—
370#95—24no—
371#95—28no—
372#95—28no—
373#95—28no—
374#95—24no—
375#95—42no—
376#95—44no—
377#95—44no—
378#95—42no—
379#95—42no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95—44no—
386C24—21no—
387C24—21no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—21no—
392C24—21no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—22no—
403C24—22no—
404C24—22no—
405C24—22no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24C22×D414yes—
413C24C2×#4112yes—
414C24C2×#4112yes—
415C242−1+412yes—
416C24C2511yescharacteristic
417C2×D4—216no—
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—28no—
421C2×D4—48no—
422C2×D4—48no—
423C2×D4—48no—
424C2×D4—48no—
425C2×D4—48no—
426C2×D4—48no—
427C2×D4—44no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—44no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—28no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—21no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—216no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—216no—
476C22×C4—28no—
477C22×C4—216no—
478C22×C4—28no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—48no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—48no—
535C22×C4—44no—
536C22×C4—48no—
537C22×C4—44no—
538C22×C4—48no—
539C22×C4—44no—
540C22×C4—44no—
541C22×C4C22×D414yes—
542C22×C4C22×D412yes—
543C22×C4C22×D412yes—
544C22×C4C22×D412yes—
545C22×C4C2×#4112yes—
546C22×C4C2×#4114yes—
547C22×C4C2×#4112yes—
548C22×C4C2×#4114yes—
549C22×C4C2×#4112yes—
550C22×C4C2×#4112yes—
551C22×C4C2×#4112yes—
552C22×C4C2×#4112yes—
553C22×C4C2×#4112yes—
554C22×C4C2×#4112yes—
555C22×C4C2×#4112yes—
556C22×C4C2×#4112yes—
557C22×C4C2×#4112yes—
558C22×C4C2×#4112yes—
559C22×C4H(5,𝔽2)12yes—
560C22×C4H(5,𝔽2)12yes—
561C22×C4H(5,𝔽2)12yes—
562C22×C4H(5,𝔽2)12yes—
563C22×C42−1+412yes—
564C4⋊C4—28no—
565C4⋊C4—28no—
566C4⋊C4—28no—
567C4⋊C4—48no—
568C4⋊C4—48no—
569C4⋊C4—44no—
570C4⋊C4—48no—
571C4⋊C4—44no—
572C4⋊C4—48no—
573C4⋊C4—44no—
574C4⋊C4—48no—
575C4⋊C4—44no—
576C4⋊C4—84no—
577C4⋊C4—84no—
578C4⋊C4—88no—
579C22⋊C4—216no—
580C22⋊C4—216no—
581C22⋊C4—48no—
582C22⋊C4—48no—
583C22⋊C4—416no—
584C22⋊C4—48no—
585C22⋊C4—48no—
586C22⋊C4—48no—
587C22⋊C4—88no—
588C22⋊C4—88no—
589C22⋊C4—88no—
590C22⋊C4—88no—
591C42—416no—
592C42—44no—
593C42—44no—
594C42—44no—
595C42—48no—
596C42—48no—
597C42—48no—
598C42#123116yes—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—24no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—24no—
623C23—24no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23#55614yes—
669C23C23×D411yescharacteristic
670C23C22×#4111yescharacteristic
671C23C22×#4111yescharacteristic
672C23C22×#4111yescharacteristic
673C23C22×#4111yescharacteristic
674C23C22×#4111yescharacteristic
675C23C22×#4111yescharacteristic
676C23C2×H(5,𝔽2)11yescharacteristic
677C23C2×H(5,𝔽2)11yescharacteristic
678C23C2×H(5,𝔽2)11yescharacteristic
679C23C2×H(5,𝔽2)11yescharacteristic
680C23C2×2−1+411yescharacteristic
681C23C2×2−1+411yescharacteristic
682C23#58511yescharacteristic
683C23#58511yescharacteristic
684D4—432no—
685D4—416no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—416no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—416no—
736C2×C4—432no—
737C2×C4—416no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—44no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—44no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4C2×#12314yes—
781C2×C4C2×#12314yes—
782C2×C4C2×#12314yes—
783C2×C4#52514yes—
784C2×C4#52914yes—
785C2×C4#53714yes—
786C2×C4#54014yes—
787C2×C4#54614yes—
788C2×C4#54614yes—
789C2×C4#55214yes—
790C2×C4#55314yes—
791C2×C4#55314yes—
792C2×C4#55514yes—
793C2×C4#55514yes—
794C2×C4#55614yes—
795C22—24no—
796C22—24no—
797C22—24no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—44no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22—44no—
816C22—44no—
817C22—82no—
818C22—82no—
819C22—82no—
820C22—82no—
821C22—82no—
822C22—82no—
823C22—82no—
824C22—82no—
825C22C22×#12311yescharacteristic
826C22C2×#52511yescharacteristic
827C22C2×#52911yescharacteristic
828C22C2×#53711yescharacteristic
829C22C2×#54011yescharacteristic
830C22C2×#54611yescharacteristic
831C22C2×#54611yescharacteristic
832C22C2×#55211yescharacteristic
833C22C2×#55311yescharacteristic
834C22C2×#55311yescharacteristic
835C22C2×#55511yescharacteristic
836C22C2×#55511yescharacteristic
837C22C2×#55611yescharacteristic
838C22C2×#55611yescharacteristic
839C22#347511yescharacteristic
840C22#348011yescharacteristic
841C22#348311yescharacteristic
842C22#348811yescharacteristic
843C22#348911yescharacteristic
844C22#349211yescharacteristic
845C22#349311yescharacteristic
846C22#349411yescharacteristic
847C22#349511yescharacteristic
848C22#350611yescharacteristic
849C22#350611yescharacteristic
850C22#350811yescharacteristic
851C22#351111yescharacteristic
852C22#351511yescharacteristic
853C22#351711yescharacteristic
854C22#352011yescharacteristic
855C22#352011yescharacteristic
856C22#354611yescharacteristic
857C22#354711yescharacteristic
858C22#354911yescharacteristic
859C22#355211yescharacteristic
860C4—24no—
861C4—44no—
862C4—44no—
863C4—42no—
864C4—42no—
865C4—42no—
866C4—44no—
867C4—82no—
868C4—82no—
869C4—84no—
870C4—84no—
871C4—82no—
872C4—82no—
873C4#242018yes—
874C4#248518yes—
875C2—44no—
876C2—84no—
877C2C2×#242011yescharacteristic
878C2C2×#248511yescharacteristic
879C2#3551611yescharacteristic
880C2#3616111yescharacteristic
881C2#3641011yescharacteristic
882C2#3645911yescharacteristic
883C2#3658611yescharacteristic
884C2#3890811yescharacteristic
885C2#3915611yescharacteristic
886C2#3946911yescharacteristic
887C2#3973511yescharacteristic
888C2#5922711yescharacteristic
889C2#5922811yescharacteristic
890C2#5923311yescharacteristic
891C2#5930211yescharacteristic
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×#2354C2semidirect
3. #16077C2semidirect
4. #15293C2semidirect
6. #15181C2semidirect
7. #15138C2semidirect
8. #15132C2semidirect
9. #14686C2semidirect
10. #14151C2semidirect
11. #14030C2semidirect
12. #13973C2semidirect
13. #13939C2semidirect
14. #13911C2semidirect
15. #13906C2semidirect
16. #13871C2semidirect
17. C4×#380C2semidirect

Maximal subgroups

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

subgroupindex
C2×#23542
C2×C4×#1212
#160772
#152932
#152192
#151812
#151382
#151322
#146862
#141512
#140302
#139732
#139392
#139112
#139062
#138712
C4×#3802