Finite Group Databasebeta

← #582859

Subgroups — #582859

Order 512.

3956 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2408C211yesmaximal, characteristic
2#14673C212yesmaximal, complemented
3#14632C212yesmaximal, complemented
4#14623C214yesmaximal, complemented
5#14589C212yesmaximal, complemented
6#14366C212yesmaximal, complemented
7#14358C214yesmaximal, complemented
8#14257C212yesmaximal, complemented
9#14141C212yesmaximal, complemented
10#14001C212yesmaximal, complemented
11#13998C212yesmaximal, complemented
12#13973C212yesmaximal, complemented
13#13906C211yesmaximal, characteristic, complemented
14#13902C212yesmaximal, complemented
15#13839C211yesmaximal, characteristic, complemented
16C24×D4C2211yescharacteristic
17C22×#121C2212yes—
18C22×#120C2212yes—
19C22×C4×D4C2211yescharacteristic
20C22×#117C2211yescharacteristic, complemented
21#2408C4116yescomplemented
22C2×#394C2212yes—
23C2×#392C2212yes—
24C2×#390C2212yes—
25C2×#390C2212yes—
26C2×#390C2212yes—
27C2×#390C2212yes—
28C2×#390C2212yes—
29C2×#390C2212yes—
30C2×#390C2214yescomplemented
31C2×#389C2212yescomplemented
32C2×#388C2214yescomplemented
33C2×#388C2214yescomplemented
34C2×#388C2214yescomplemented
35C2×#384C2211yescharacteristic, complemented
36C2×#380C2212yes—
37C2×#380C2211yescharacteristic
38C2×#380C2212yescomplemented
39C2×#379C2214yes—
40C2×#379C2214yes—
41C2×#379C2212yes—
42C2×C4×C4⋊C4C2211yescharacteristic, complemented
43C2×C4×C4⋊C4C2212yescomplemented
44C2×C4×C22⋊C4C2212yes—
45C2×C4×C22⋊C4C2211yescharacteristic, complemented
46#1442C2214yescomplemented
47#1441C2211yescharacteristic, complemented
48#1441C2211yescharacteristic, complemented
49#1440C2212yescomplemented
50#1440C2214yescomplemented
51#1439C2211yescharacteristic
52#1439C2211yescharacteristic
53#1439C2214yes—
54#1439C2212yes—
55#1439C2214yescomplemented
56#1439C2214yescomplemented
57#1439C2212yescomplemented
58#1439C2214yescomplemented
59#1439C2214yescomplemented
60#1439C2214yescomplemented
61#1439C2214yescomplemented
62#1438C2212yes—
63#1438C2214yes—
64#1438C2214yes—
65#1438C2214yescomplemented
66#1438C2214yescomplemented
67#1438C2214yescomplemented
68#1437C2214yes—
69#1437C2214yescomplemented
70#1437C2214yescomplemented
71C4⋊#95C2212yescomplemented
72C4⋊#95C2212yescomplemented
73C4⋊#95C2212yescomplemented
74#1434C2214yescomplemented
75C4×#95C2212yescomplemented
76C26C2312yes—
77C23×D4—42no—
78C23×D4—42no—
79C23×D4—44no—
80C23×D4—44no—
81C23×D4C2×C418yes—
82C23×D4C2312yes—
83C23×D4C2311yescharacteristic
84C23×D4C2312yes—
85C23×D4C2314yes—
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C2×#121—44no—
89C2×#121—44no—
90C2×#121C2×C4116yes—
91C2×#120—44no—
92C2×#120—44no—
93C2×#120C2×C4116yes—
94C2×C4×D4—42no—
95C2×C4×D4—42no—
96C2×C4×D4C2×C418yes—
97C2×#117—44no—
98C2×#117—42no—
99C22×C4⋊C4C2312yes—
100C22×C4⋊C4C2312yes—
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2312yes—
103C22×C4⋊C4C2311yescharacteristic
104C22×C4⋊C4C2311yescharacteristic
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2314yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C22⋊C4C2312yes—
109C22×C22⋊C4C2314yes—
110C22×C22⋊C4C2314yes—
111C22×C22⋊C4C2314yes—
112C22×C22⋊C4C2314yes—
113C22×C22⋊C4C2312yes—
114C22×C22⋊C4C2312yes—
115C22×C22⋊C4C2312yes—
116C22×C22⋊C4C2314yes—
117C22×C22⋊C4C2314yes—
118C22×C22⋊C4C2314yes—
119C22×C22⋊C4C2314yes—
120C22×C22⋊C4C2314yes—
121C22×C22⋊C4C2314yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2311yescharacteristic
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2311yescharacteristic
127C22×C22⋊C4C2312yes—
128C22×C42C2312yes—
129C22×C42C2312yes—
130C22×C42C2311yescharacteristic
131C22×C42C2314yes—
132C22×C42C2312yes—
133#394C2×C4116yes—
134#392C2×C4116yes—
135#390—48no—
136#390—44no—
137#390—44no—
138#390—44no—
139#390—44no—
140#390—44no—
141#390C2×C4116yes—
142#389—44no—
143#388—48no—
144#388—48no—
145#388—48no—
146#384—42no—
147#380—44no—
148#380—44no—
149#380C2×C418yes—
150#379—48no—
151#379—48no—
152#379C2×C4116yes—
153C4×C4⋊C4—42no—
154C4×C4⋊C4—44no—
155C4×C22⋊C4—44no—
156C4×C22⋊C4—42no—
157C2×#95C2312yes—
158C2×#95C2312yes—
159C2×#95C2312yes—
160C2×#95C2312yes—
161C2×#95C2312yes—
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2314yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2311yescharacteristic
170C2×#95C2312yes—
171C2×#95C2314yes—
172C2×#95C2311yescharacteristic
173C2×#95C2312yes—
174C2×#95C2312yes—
175C25—24no—
176C25—24no—
177C25—44no—
178C25—44no—
179C25—42no—
180C25—42no—
181C25—42no—
182C25—42no—
183C25—44no—
184C25—44no—
185C25C22×C418yes—
186C25C2414yes—
187C25C2411yescharacteristic
188C25C2411yescharacteristic
189C22×D4—22no—
190C22×D4—22no—
191C22×D4—22no—
192C22×D4—22no—
193C22×D4—24no—
194C22×D4—24no—
195C22×D4—24no—
196C22×D4—24no—
197C22×D4—24no—
198C22×D4—24no—
199C22×D4—416no—
200C22×D4—432no—
201C22×D4—41no—
202C22×D4—41no—
203C22×D4—44no—
204C22×D4—44no—
205C22×D4—42no—
206C22×D4—42no—
207C22×D4—44no—
208C22×D4—44no—
209C22×D4—44no—
210C22×D4—44no—
211C22×D4—44no—
212C22×D4—44no—
213C22×D4—432no—
214C22×D4—416no—
215C22×D4—416no—
216C22×D4C22×C418yes—
217C22×D4C22×C414yes—
218C22×D4C22×C4116yes—
219C22×D4C22×C418yes—
220C23×C4—22no—
221C23×C4—24no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—22no—
225C23×C4—24no—
226C23×C4—24no—
227C23×C4—24no—
228C23×C4C22×C414yes—
229C23×C4C22×C414yes—
230C23×C4C2414yes—
231C23×C4C2412yes—
232C23×C4C2414yes—
233C23×C4C2412yes—
234C23×C4C2412yes—
235C23×C4C2411yescharacteristic
236C23×C4C2411yescharacteristic
237C23×C4C2414yes—
238C23×C4C2411yescharacteristic
239C23×C4C2412yes—
240C23×C4C2411yescharacteristic
241C23×C4C2411yescharacteristic
242#121—432no—
243#120—432no—
244C4×D4—416no—
245#117—416no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—24no—
248C2×C4⋊C4—24no—
249C2×C4⋊C4—24no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—42no—
256C2×C4⋊C4—42no—
257C2×C4⋊C4—41no—
258C2×C4⋊C4—41no—
259C2×C4⋊C4—41no—
260C2×C4⋊C4—41no—
261C2×C4⋊C4—42no—
262C2×C4⋊C4—42no—
263C2×C4⋊C4—44no—
264C2×C4⋊C4—44no—
265C2×C4⋊C4—44no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4—44no—
268C2×C4⋊C4C22×C418yes—
269C2×C4⋊C4C22×C414yes—
270C2×C22⋊C4—28no—
271C2×C22⋊C4—28no—
272C2×C22⋊C4—24no—
273C2×C22⋊C4—24no—
274C2×C22⋊C4—24no—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—28no—
277C2×C22⋊C4—28no—
278C2×C22⋊C4—28no—
279C2×C22⋊C4—44no—
280C2×C22⋊C4—42no—
281C2×C22⋊C4—42no—
282C2×C22⋊C4—42no—
283C2×C22⋊C4—42no—
284C2×C22⋊C4—42no—
285C2×C22⋊C4—41no—
286C2×C22⋊C4—41no—
287C2×C22⋊C4—41no—
288C2×C22⋊C4—41no—
289C2×C22⋊C4—42no—
290C2×C22⋊C4—42no—
291C2×C22⋊C4—44no—
292C2×C22⋊C4—44no—
293C2×C22⋊C4—42no—
294C2×C22⋊C4—42no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—44no—
297C2×C22⋊C4—44no—
298C2×C22⋊C4—44no—
299C2×C22⋊C4—44no—
300C2×C22⋊C4—44no—
301C2×C22⋊C4—44no—
302C2×C22⋊C4—44no—
303C2×C22⋊C4—44no—
304C2×C22⋊C4—44no—
305C2×C22⋊C4—44no—
306C2×C22⋊C4—44no—
307C2×C22⋊C4—44no—
308C2×C22⋊C4—44no—
309C2×C22⋊C4—44no—
310C2×C22⋊C4—44no—
311C2×C22⋊C4—44no—
312C2×C22⋊C4—44no—
313C2×C22⋊C4—44no—
314C2×C22⋊C4—44no—
315C2×C22⋊C4—44no—
316C2×C22⋊C4—44no—
317C2×C22⋊C4—44no—
318C2×C22⋊C4—44no—
319C2×C22⋊C4—44no—
320C2×C22⋊C4—44no—
321C2×C22⋊C4—44no—
322C2×C22⋊C4—44no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4C22×C4116yes—
325C2×C22⋊C4C22×C414yes—
326C2×C22⋊C4C22×C414yes—
327C2×C22⋊C4C22×C418yes—
328C2×C22⋊C4C22×C4116yes—
329C2×C22⋊C4C22×C4116yes—
330C2×C42—22no—
331C2×C42—22no—
332C2×C42—24no—
333C2×C42—24no—
334C2×C42—24no—
335C2×C42—24no—
336C2×C42—24no—
337C2×C42—24no—
338C2×C42—24no—
339C2×C42—28no—
340C2×C42—42no—
341C2×C42—44no—
342C2×C42—44no—
343C2×C42—42no—
344C2×C42C22×C414yes—
345#95—24no—
346#95—24no—
347#95—24no—
348#95—42no—
349#95—44no—
350#95—42no—
351#95—41no—
352#95—41no—
353#95—42no—
354#95—42no—
355#95—44no—
356#95—44no—
357#95—44no—
358#95—44no—
359#95—44no—
360#95—44no—
361#95—44no—
362#95C22×C418yes—
363C24—22no—
364C24—22no—
365C24—22no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—22no—
371C24—24no—
372C24—22no—
373C24—24no—
374C24—24no—
375C24—24no—
376C24—21no—
377C24—24no—
378C24—21no—
379C24—21no—
380C24—22no—
381C24—22no—
382C24—24no—
383C24—24no—
384C24—24no—
385C24—24no—
386C24—24no—
387C24—24no—
388C24—21no—
389C24—21no—
390C24—21no—
391C24—24no—
392C24—24no—
393C24—22no—
394C24—24no—
395C24—216no—
396C24—48no—
397C24—416no—
398C24—48no—
399C24—416no—
400C24—48no—
401C24—416no—
402C24—48no—
403C24—88no—
404C24—84no—
405C24—84no—
406C24—84no—
407C24—84no—
408C24—88no—
409C24—88no—
410C24—88no—
411C24—88no—
412C24—88no—
413C24—88no—
414C24—88no—
415C24—84no—
416C24—88no—
417C24—84no—
418C24C23×C418yes—
419C24C23×C412yes—
420C24C23×C412yes—
421C24H(5,𝔽2)12yes—
422C242−1+412yes—
423C24C2511yescharacteristic
424C2×D4—28no—
425C2×D4—28no—
426C2×D4—216no—
427C2×D4—216no—
428C2×D4—216no—
429C2×D4—44no—
430C2×D4—48no—
431C2×D4—416no—
432C2×D4—44no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—44no—
436C2×D4—416no—
437C2×D4—416no—
438C2×D4—416no—
439C2×D4—48no—
440C2×D4—416no—
441C2×D4—48no—
442C2×D4—4128no—
443C2×D4—48no—
444C2×D4—48no—
445C2×D4—48no—
446C2×D4—48no—
447C2×D4—88no—
448C2×D4—88no—
449C2×D4—88no—
450C2×D4—88no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—216no—
482C22×C4—216no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—48no—
519C22×C4—44no—
520C22×C4—48no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4C23×C412yes—
525C22×C4C23×C418yes—
526C22×C4C23×C412yes—
527C22×C4C23×C412yes—
528C22×C4C23×C412yes—
529C22×C4C23×C412yes—
530C22×C4H(5,𝔽2)14yes—
531C22×C4H(5,𝔽2)12yes—
532C22×C4H(5,𝔽2)12yes—
533C22×C4H(5,𝔽2)12yes—
534C22×C4H(5,𝔽2)14yes—
535C22×C4H(5,𝔽2)12yes—
536C22×C4H(5,𝔽2)14yes—
537C4⋊C4—216no—
538C4⋊C4—44no—
539C4⋊C4—44no—
540C4⋊C4—44no—
541C4⋊C4—48no—
542C4⋊C4—48no—
543C4⋊C4—84no—
544C4⋊C4—84no—
545C4⋊C4—88no—
546C22⋊C4—232no—
547C22⋊C4—416no—
548C22⋊C4—44no—
549C22⋊C4—44no—
550C22⋊C4—48no—
551C22⋊C4—416no—
552C22⋊C4—48no—
553C22⋊C4—48no—
554C22⋊C4—48no—
555C22⋊C4—48no—
556C22⋊C4—88no—
557C22⋊C4—88no—
558C22⋊C4—88no—
559C22⋊C4—88no—
560C22⋊C4—88no—
561C22⋊C4—88no—
562C22⋊C4—88no—
563C22⋊C4—88no—
564C22⋊C4—88no—
565C22⋊C4—88no—
566C42—28no—
567C42—48no—
568C42—48no—
569C42—84no—
570C42—88no—
571C23—22no—
572C23—22no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—28no—
584C23—22no—
585C23—28no—
586C23—24no—
587C23—22no—
588C23—28no—
589C23—28no—
590C23—22no—
591C23—28no—
592C23—28no—
593C23—24no—
594C23—28no—
595C23—41no—
596C23—42no—
597C23—41no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—41no—
604C23—41no—
605C23—432no—
606C23—41no—
607C23—42no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23—41no—
612C23—44no—
613C23—41no—
614C23—41no—
615C23—42no—
616C23—44no—
617C23—44no—
618C23—44no—
619C23—44no—
620C23—44no—
621C23—44no—
622C23—41no—
623C23—41no—
624C23—42no—
625C23—44no—
626C23—44no—
627C23—42no—
628C23—44no—
629C23—44no—
630C23—42no—
631C23—44no—
632C23—44no—
633C23—42no—
634C23—44no—
635C23—44no—
636C23—42no—
637C23—42no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—42no—
645C23—44no—
646C23—41no—
647C23—41no—
648C23—44no—
649C23—42no—
650C23—44no—
651C23—44no—
652C23—816no—
653C23—832no—
654C23—816no—
655C23—832no—
656C23—816no—
657C23—816no—
658C23—832no—
659C23—816no—
660C23—816no—
661C23—832no—
662C23#52014yes—
663C23C24×C411yescharacteristic
664C23C2×H(5,𝔽2)11yescharacteristic
665C23C2×H(5,𝔽2)12yes—
666C23C2×H(5,𝔽2)11yescharacteristic
667C23C2×H(5,𝔽2)12yes—
668C23C2×H(5,𝔽2)11yescharacteristic
669C23C2×H(5,𝔽2)11yescharacteristic
670C23C2×H(5,𝔽2)11yescharacteristic
671C23C2×H(5,𝔽2)12yes—
672C23C2×2−1+411yescharacteristic
673C23#58512yes—
674D4—416no—
675D4—432no—
676D4—432no—
677D4—832no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—28no—
686C2×C4—24no—
687C2×C4—28no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—28no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—44no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—41no—
710C2×C4—44no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—416no—
714C2×C4—416no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—44no—
734C2×C4—44no—
735C2×C4—42no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—42no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4#51814yes—
751C2×C4#51814yes—
752C2×C4#51818yes—
753C2×C4#56018yes—
754C2×C4#56014yes—
755C2×C4H(3,𝔽4)14yes—
756C22—24no—
757C22—28no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—44no—
762C22—42no—
763C22—44no—
764C22—42no—
765C22—42no—
766C22—44no—
767C22—42no—
768C22—48no—
769C22—42no—
770C22—48no—
771C22—42no—
772C22—48no—
773C22—44no—
774C22—48no—
775C22—48no—
776C22—44no—
777C22—48no—
778C22—48no—
779C22—864no—
780C22—81no—
781C22—84no—
782C22—81no—
783C22—84no—
784C22—82no—
785C22—84no—
786C22—84no—
787C22—81no—
788C22—84no—
789C22—81no—
790C22—84no—
791C22—82no—
792C22—84no—
793C22—84no—
794C22C2×#51811yescharacteristic
795C22C2×#51812yes—
796C22C2×#51811yescharacteristic
797C22C2×#52011yescharacteristic
798C22C4×H(5,𝔽2)12yes—
799C22C2×#56011yescharacteristic
800C22C2×#56012yes—
801C22C2×H(3,𝔽4)11yescharacteristic
802C22#353611yescharacteristic
803C22#353612yes—
804C22#353611yescharacteristic
805C22#353711yescharacteristic
806C22#353711yescharacteristic
807C22#354212yes—
808C22#354212yes—
809C22#354312yes—
810C22#354312yes—
811C22#354612yes—
812C22#354612yes—
813C22#354912yes—
814C22#354911yescharacteristic
815C22#355111yescharacteristic
816C22#356112yes—
817C4—24no—
818C4—42no—
819C4—42no—
820C4—42no—
821C4—48no—
822C4—44no—
823C4—82no—
824C4—82no—
825C4—84no—
826C4—82no—
827C4—84no—
828C4#237518yes—
829C2—44no—
830C2—82no—
831C2—88no—
832C2C2×#237511yescharacteristic
833C2#3437911yescharacteristic
834C2#3441511yescharacteristic
835C2#3447612yes—
836C2#3449312yes—
837C2#5296711yescharacteristic
838C2#5296911yescharacteristic
839C2#5298112yes—
840C2#5301511yescharacteristic
841C2#5301811yescharacteristic
842C2#5310212yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2408C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #14673C2semidirect
3. #14632C2semidirect
4. #14623C2semidirect
5. #14589C2semidirect
6. #14366C2semidirect
7. #14358C2semidirect
8. #14257C2semidirect
9. #14141C2semidirect
10. #14001C2semidirect
11. #13998C2semidirect
12. #13973C2semidirect
13. #13906C2semidirect
14. #13902C2semidirect
15. #13839C2semidirect
20. C22×#117C22semidirect
21. #2408C4semidirect
30. C2×#390C22semidirect
31. C2×#389C22semidirect
32. C2×#388C22semidirect
33. C2×#388C22semidirect
34. C2×#388C22semidirect
35. C2×#384C22semidirect
38. C2×#380C22semidirect
42. C2×C4×C4⋊C4C22semidirect
43. C2×C4×C4⋊C4C22semidirect
45. C2×C4×C22⋊C4C22semidirect
46. #1442C22semidirect
47. #1441C22semidirect
48. #1441C22semidirect
49. #1440C22semidirect
50. #1440C22semidirect
55. #1439C22semidirect
56. #1439C22semidirect
57. #1439C22semidirect
58. #1439C22semidirect
59. #1439C22semidirect
60. #1439C22semidirect
61. #1439C22semidirect
65. #1438C22semidirect
66. #1438C22semidirect
67. #1438C22semidirect
69. #1437C22semidirect
70. #1437C22semidirect
71. C4⋊#95C22semidirect
72. C4⋊#95C22semidirect
73. C4⋊#95C22semidirect
74. #1434C22semidirect
75. C4×#95C22semidirect

Maximal subgroups

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

subgroupindex
C2×#24082
#146732
#146322
#146232
#145892
#143662
#143582
#142572
#141412
#140012
#139982
#139732
#139062
#139022
#138392