Finite Group Databasebeta

← #582901

Subgroups — #582901

Order 512.

4018 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2408C211yesmaximal, characteristic
2#14673C212yesmaximal, complemented
3#14645C214yesmaximal, complemented
4#14621C212yesmaximal, complemented
5#14521C212yesmaximal, complemented
6#14366C212yesmaximal, complemented
7#14357C214yesmaximal, complemented
8#14260C212yesmaximal, complemented
9#14137C212yesmaximal, complemented
10#14022C212yesmaximal, complemented
11#13998C212yesmaximal, complemented
12#13993C212yesmaximal, complemented
13#13902C212yesmaximal, complemented
14#13872C211yesmaximal, characteristic, complemented
15#13847C211yesmaximal, characteristic, complemented
16C24×D4C2211yescharacteristic
17C22×#121C2212yes—
18C22×#120C2212yes—
19C22×C4×D4C2211yescharacteristic
20C23×C4⋊C4C2211yescharacteristic, complemented
21#2408C4116yescomplemented
22C2×#394C2212yes—
23C2×#392C2212yes—
24C2×#390C2212yes—
25C2×#390C2212yes—
26C2×#390C2212yes—
27C2×#390C2212yes—
28C2×#390C2212yes—
29C2×#390C2214yescomplemented
30C2×#389C2212yescomplemented
31C2×#388C2214yescomplemented
32C2×#386C2212yes—
33C2×#386C2214yescomplemented
34C2×#386C2214yescomplemented
35C2×#380C2212yes—
36C2×#380C2211yescharacteristic
37C2×#380C2211yescharacteristic, complemented
38C2×#379C2214yes—
39C2×#379C2214yes—
40C2×#379C2212yes—
41C2×C4×C4⋊C4C2211yescharacteristic, complemented
42C2×C4×C4⋊C4C2212yescomplemented
43C2×C4×C22⋊C4C2212yes—
44C2×C4×C22⋊C4C2212yescomplemented
45C2×#376C2211yescharacteristic, complemented
46#1445C2212yescomplemented
47#1443C2214yescomplemented
48#1441C2212yescomplemented
49#1440C2214yescomplemented
50#1440C2214yescomplemented
51#1440C2214yescomplemented
52#1439C2214yes—
53#1439C2211yescharacteristic
54#1439C2211yescharacteristic
55#1439C2212yes—
56#1439C2214yescomplemented
57#1439C2211yescharacteristic, complemented
58#1439C2211yescharacteristic, complemented
59#1439C2214yescomplemented
60#1439C2214yescomplemented
61#1439C2214yescomplemented
62#1439C2214yescomplemented
63#1439C2214yescomplemented
64#1438C2212yes—
65#1438C2214yes—
66#1438C2214yes—
67#1438C2214yescomplemented
68#1437C2214yes—
69#1437C2214yescomplemented
70#1437C2214yescomplemented
71#1436C2214yescomplemented
72C4⋊#95C2212yescomplemented
73C4⋊#95C2212yescomplemented
74C4⋊#95C2212yescomplemented
75C22⋊#95C2212yescomplemented
76C26C2312yes—
77C23×D4—42no—
78C23×D4—42no—
79C23×D4—44no—
80C23×D4—44no—
81C23×D4C2×C418yescomplemented
82C23×D4C2312yes—
83C23×D4C2311yescharacteristic
84C23×D4C2314yes—
85C23×D4C2312yes—
86C24×C4C2311yescharacteristic
87C24×C4C2311yescharacteristic
88C24×C4C2312yes—
89C2×#121—44no—
90C2×#121—44no—
91C2×#121C2×C4116yes—
92C2×#120—44no—
93C2×#120—44no—
94C2×#120C2×C4116yes—
95C2×C4×D4—42no—
96C2×C4×D4—42no—
97C2×C4×D4C2×C418yes—
98C22×C4⋊C4—44no—
99C22×C4⋊C4—42no—
100C22×C4⋊C4C2312yes—
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2311yescharacteristic
103C22×C4⋊C4C2312yes—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2314yes—
106C22×C4⋊C4C2311yescharacteristic
107C22×C4⋊C4C2311yescharacteristic
108C22×C22⋊C4C2312yes—
109C22×C22⋊C4C2312yes—
110C22×C22⋊C4C2312yes—
111C22×C22⋊C4C2314yes—
112C22×C22⋊C4C2314yes—
113C22×C22⋊C4C2314yes—
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⋊C4C2311yescharacteristic
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2311yescharacteristic
127C22×C22⋊C4C2312yes—
128C22×C42C2312yes—
129C22×C42C2312yes—
130C22×C42C2311yescharacteristic
131C22×C42C2314yes—
132#394C2×C4116yescomplemented
133#392C2×C4116yes—
134#390—44no—
135#390—44no—
136#390—44no—
137#390—44no—
138#390—48no—
139#390C2×C4116yescomplemented
140#389—44no—
141#388—48no—
142#386—48no—
143#386—44no—
144#386—48no—
145#380—44no—
146#380—42no—
147#380C2×C418yescomplemented
148#379—48no—
149#379—48no—
150#379C2×C4116yescomplemented
151C4×C4⋊C4—42no—
152C4×C4⋊C4—44no—
153C4×C22⋊C4—44no—
154C4×C22⋊C4—44no—
155#376—42no—
156C2×#95C2314yes—
157C2×#95C2314yes—
158C2×#95C2314yes—
159C2×#95C2314yes—
160C2×#95C2314yes—
161C2×#95C2314yes—
162C2×#95C2314yes—
163C2×#95C2312yes—
164C2×#95C2314yes—
165C2×#95C2312yes—
166C2×#95C2312yes—
167C2×#95C2312yes—
168C2×#95C2312yes—
169C2×#95C2312yes—
170C2×#95C2314yes—
171C2×#95C2311yescharacteristic
172C2×#95C2312yes—
173C2×#95C2311yescharacteristic
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—28no—
194C22×D4—28no—
195C22×D4—24no—
196C22×D4—24no—
197C22×D4—24no—
198C22×D4—24no—
199C22×D4—24no—
200C22×D4—24no—
201C22×D4—416no—
202C22×D4—432no—
203C22×D4—41no—
204C22×D4—41no—
205C22×D4—44no—
206C22×D4—44no—
207C22×D4—42no—
208C22×D4—42no—
209C22×D4—44no—
210C22×D4—44no—
211C22×D4—44no—
212C22×D4—44no—
213C22×D4—416no—
214C22×D4—432no—
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×C4—24no—
229C23×C4—44no—
230C23×C4—42no—
231C23×C4—44no—
232C23×C4—42no—
233C23×C4C22×C414yes—
234C23×C4C22×C414yes—
235C23×C4C2412yes—
236C23×C4C2414yes—
237C23×C4C2412yes—
238C23×C4C2412yes—
239C23×C4C2414yes—
240C23×C4C2411yescharacteristic
241C23×C4C2411yescharacteristic
242C23×C4C2414yes—
243C23×C4C2411yescharacteristic
244C23×C4C2411yescharacteristic
245C23×C4C2412yes—
246C23×C4C2411yescharacteristic
247#121—432no—
248#120—432no—
249C4×D4—416no—
250C2×C4⋊C4—24no—
251C2×C4⋊C4—24no—
252C2×C4⋊C4—24no—
253C2×C4⋊C4—24no—
254C2×C4⋊C4—24no—
255C2×C4⋊C4—24no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—24no—
258C2×C4⋊C4—24no—
259C2×C4⋊C4—44no—
260C2×C4⋊C4—42no—
261C2×C4⋊C4—42no—
262C2×C4⋊C4—41no—
263C2×C4⋊C4—41no—
264C2×C4⋊C4—41no—
265C2×C4⋊C4—41no—
266C2×C4⋊C4—416no—
267C2×C4⋊C4—44no—
268C2×C4⋊C4—44no—
269C2×C4⋊C4—44no—
270C2×C4⋊C4C22×C418yes—
271C2×C4⋊C4C22×C414yes—
272C2×C22⋊C4—24no—
273C2×C22⋊C4—24no—
274C2×C22⋊C4—24no—
275C2×C22⋊C4—24no—
276C2×C22⋊C4—24no—
277C2×C22⋊C4—24no—
278C2×C22⋊C4—28no—
279C2×C22⋊C4—24no—
280C2×C22⋊C4—28no—
281C2×C22⋊C4—28no—
282C2×C22⋊C4—44no—
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—44no—
291C2×C22⋊C4—42no—
292C2×C22⋊C4—44no—
293C2×C22⋊C4—44no—
294C2×C22⋊C4—44no—
295C2×C22⋊C4—42no—
296C2×C22⋊C4—42no—
297C2×C22⋊C4—42no—
298C2×C22⋊C4—42no—
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—42no—
311C2×C22⋊C4—42no—
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⋊C4—44no—
325C2×C22⋊C4—44no—
326C2×C22⋊C4C22×C414yes—
327C2×C22⋊C4C22×C414yes—
328C2×C22⋊C4C22×C418yes—
329C2×C22⋊C4C22×C4116yes—
330C2×C22⋊C4C22×C4116yes—
331C2×C22⋊C4C22×C4116yes—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—24no—
335C2×C42—24no—
336C2×C42—24no—
337C2×C42—24no—
338C2×C42—24no—
339C2×C42—24no—
340C2×C42—44no—
341C2×C42—44no—
342C2×C42—44no—
343C2×C42C22×C414yes—
344#95—28no—
345#95—41no—
346#95—41no—
347#95—42no—
348#95—42no—
349#95—42no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—44no—
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—21no—
366C24—22no—
367C24—22no—
368C24—22no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—21no—
375C24—22no—
376C24—21no—
377C24—22no—
378C24—22no—
379C24—24no—
380C24—24no—
381C24—24no—
382C24—24no—
383C24—24no—
384C24—24no—
385C24—24no—
386C24—24no—
387C24—24no—
388C24—24no—
389C24—24no—
390C24—24no—
391C24—24no—
392C24—24no—
393C24—216no—
394C24—48no—
395C24—416no—
396C24—48no—
397C24—416no—
398C24—48no—
399C24—416no—
400C24—48no—
401C24—88no—
402C24—84no—
403C24—84no—
404C24—84no—
405C24—84no—
406C24—88no—
407C24—88no—
408C24—88no—
409C24—84no—
410C24—88no—
411C24—84no—
412C24—88no—
413C24—88no—
414C24—88no—
415C24—88no—
416C24C23×C418yes—
417C24C23×C412yes—
418C24C23×C412yes—
419C24H(5,𝔽2)12yes—
420C24H(5,𝔽2)12yes—
421C24H(5,𝔽2)12yes—
422C242−1+412yes—
423C24C2511yescharacteristic
424C2×D4—28no—
425C2×D4—28no—
426C2×D4—232no—
427C2×D4—216no—
428C2×D4—216no—
429C2×D4—216no—
430C2×D4—44no—
431C2×D4—48no—
432C2×D4—416no—
433C2×D4—416no—
434C2×D4—416no—
435C2×D4—44no—
436C2×D4—44no—
437C2×D4—44no—
438C2×D4—44no—
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—24no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—216no—
484C22×C4—216no—
485C22×C4—24no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—24no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—44no—
521C22×C4—48no—
522C22×C4—44no—
523C22×C4—48no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—48no—
527C22×C4—84no—
528C22×C4—88no—
529C22×C4—84no—
530C22×C4—88no—
531C22×C4C23×C412yes—
532C22×C4C23×C418yes—
533C22×C4C23×C412yes—
534C22×C4C23×C412yes—
535C22×C4C23×C412yes—
536C22×C4C23×C412yes—
537C22×C4H(5,𝔽2)14yes—
538C22×C4H(5,𝔽2)12yes—
539C22×C4H(5,𝔽2)14yes—
540C22×C4H(5,𝔽2)12yes—
541C22×C4H(5,𝔽2)14yes—
542C4⋊C4—216no—
543C4⋊C4—44no—
544C4⋊C4—44no—
545C4⋊C4—44no—
546C4⋊C4—48no—
547C4⋊C4—48no—
548C4⋊C4—48no—
549C4⋊C4—88no—
550C22⋊C4—416no—
551C22⋊C4—44no—
552C22⋊C4—44no—
553C22⋊C4—416no—
554C22⋊C4—48no—
555C22⋊C4—416no—
556C22⋊C4—48no—
557C22⋊C4—48no—
558C22⋊C4—48no—
559C22⋊C4—48no—
560C22⋊C4—88no—
561C22⋊C4—88no—
562C22⋊C4—84no—
563C22⋊C4—88no—
564C22⋊C4—88no—
565C22⋊C4—88no—
566C22⋊C4—88no—
567C22⋊C4—88no—
568C22⋊C4—88no—
569C22⋊C4—88no—
570C42—28no—
571C42—48no—
572C42—48no—
573C42—88no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—24no—
578C23—24no—
579C23—22no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—24no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—28no—
599C23—28no—
600C23—28no—
601C23—28no—
602C23—28no—
603C23—28no—
604C23—28no—
605C23—41no—
606C23—42no—
607C23—41no—
608C23—42no—
609C23—41no—
610C23—41no—
611C23—42no—
612C23—41no—
613C23—41no—
614C23—42no—
615C23—41no—
616C23—41no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—42no—
622C23—42no—
623C23—42no—
624C23—42no—
625C23—432no—
626C23—44no—
627C23—44no—
628C23—44no—
629C23—44no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—816no—
655C23—832no—
656C23—816no—
657C23—832no—
658C23—816no—
659C23—832no—
660C23—832no—
661C23—816no—
662C23—816no—
663C23—816no—
664C23#51814yes—
665C23#52014yes—
666C23C24×C411yescharacteristic
667C23C2×H(5,𝔽2)12yes—
668C23C2×H(5,𝔽2)11yescharacteristic
669C23C2×H(5,𝔽2)11yescharacteristic
670C23C2×H(5,𝔽2)12yes—
671C23C2×H(5,𝔽2)11yescharacteristic
672C23C2×H(5,𝔽2)11yescharacteristic
673C23C2×H(5,𝔽2)11yescharacteristic
674C23C2×H(5,𝔽2)12yes—
675C23C2×2−1+411yescharacteristic
676C23#58512yes—
677D4—416no—
678D4—432no—
679D4—432no—
680D4—832no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—24no—
685C2×C4—28no—
686C2×C4—28no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—22no—
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—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—44no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—416no—
718C2×C4—416no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—44no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—44no—
730C2×C4—42no—
731C2×C4—44no—
732C2×C4—44no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—44no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—44no—
753C2×C4—42no—
754C2×C4—816no—
755C2×C4#51814yes—
756C2×C4#51818yes—
757C2×C4#56014yes—
758C2×C4#56018yes—
759C2×C4H(3,𝔽4)14yes—
760C22—24no—
761C22—24no—
762C22—28no—
763C22—28no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—48no—
783C22—48no—
784C22—48no—
785C22—48no—
786C22—48no—
787C22—48no—
788C22—48no—
789C22—864no—
790C22—84no—
791C22—84no—
792C22—84no—
793C22—84no—
794C22—84no—
795C22—84no—
796C22—84no—
797C22—84no—
798C22C2×#51811yescharacteristic
799C22C2×#51812yes—
800C22C2×#51811yescharacteristic
801C22C2×#52011yescharacteristic
802C22C4×H(5,𝔽2)12yes—
803C22C2×#56011yescharacteristic
804C22C2×#56012yes—
805C22C2×H(3,𝔽4)11yescharacteristic
806C22#353611yescharacteristic
807C22#353611yescharacteristic
808C22#353612yes—
809C22#353711yescharacteristic
810C22#353711yescharacteristic
811C22#353711yescharacteristic
812C22#353712yes—
813C22#354011yescharacteristic
814C22#354212yes—
815C22#354212yes—
816C22#354312yes—
817C22#354312yes—
818C22#354612yes—
819C22#355812yes—
820C22#356112yes—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—42no—
825C4—48no—
826C4—44no—
827C4—82no—
828C4—82no—
829C4—84no—
830C4—82no—
831C4—84no—
832C4#237518yes—
833C2—44no—
834C2—44no—
835C2—88no—
836C2C2×#237511yescharacteristic
837C2#3437911yescharacteristic
838C2#3441111yescharacteristic
839C2#3447112yes—
840C2#3447612yes—
841C2#5297112yes—
842C2#5298112yes—
843C2#5298611yescharacteristic
844C2#5298811yescharacteristic
845C2#5299011yescharacteristic
846C2#5310311yescharacteristic
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. #14645C2semidirect
4. #14621C2semidirect
5. #14521C2semidirect
6. #14366C2semidirect
7. #14357C2semidirect
8. #14260C2semidirect
9. #14137C2semidirect
10. #14022C2semidirect
11. #13998C2semidirect
12. #13993C2semidirect
13. #13902C2semidirect
14. #13872C2semidirect
15. #13847C2semidirect
20. C23×C4⋊C4C22semidirect
21. #2408C4semidirect
29. C2×#390C22semidirect
30. C2×#389C22semidirect
31. C2×#388C22semidirect
33. C2×#386C22semidirect
34. C2×#386C22semidirect
37. C2×#380C22semidirect
41. C2×C4×C4⋊C4C22semidirect
42. C2×C4×C4⋊C4C22semidirect
44. C2×C4×C22⋊C4C22semidirect
45. C2×#376C22semidirect
46. #1445C22semidirect
47. #1443C22semidirect
48. #1441C22semidirect
49. #1440C22semidirect
50. #1440C22semidirect
51. #1440C22semidirect
56. #1439C22semidirect
57. #1439C22semidirect
58. #1439C22semidirect
59. #1439C22semidirect
60. #1439C22semidirect
61. #1439C22semidirect
62. #1439C22semidirect
63. #1439C22semidirect
67. #1438C22semidirect
69. #1437C22semidirect
70. #1437C22semidirect
71. #1436C22semidirect
72. C4⋊#95C22semidirect
73. C4⋊#95C22semidirect
74. C4⋊#95C22semidirect
75. C22⋊#95C22semidirect
81. C23×D4C2×C4semidirect
132. #394C2×C4semidirect
139. #390C2×C4semidirect
147. #380C2×C4semidirect
150. #379C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24082
#146732
#146452
#146212
#145212
#143662
#143572
#142602
#141372
#140222
#139982
#139932
#139022
#138722
#138472