Finite Group Databasebeta

← #521339

Subgroups — #521339

Order 512.

5198 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2315C211yesmaximal, characteristic, complemented
2C22×#386C211yesmaximal, characteristic
3C2×#2280C211yesmaximal, characteristic, complemented
4#14680C211yesmaximal, characteristic, complemented
5#14391C214yesmaximal, complemented
6#14373C214yesmaximal, complemented
7#14347C211yesmaximal, characteristic, complemented
8#14338C211yesmaximal, characteristic, complemented
9#14064C214yesmaximal, complemented
10#13988C214yesmaximal, complemented
11#13883C212yesmaximal, complemented
12#13873C212yesmaximal, complemented
13#13867C212yesmaximal
14C22⋊C42C212yesmaximal, complemented
15#13778C211yesmaximal, characteristic, complemented
16C24×D4C2211yescharacteristic
17C25×C4C2211yescharacteristic
18C22×#117C2212yescomplemented
19C23×C22⋊C4C2212yes—
20C23×C22⋊C4C2211yescharacteristic
21C23×C22⋊C4C2211yescharacteristic
22C23×C22⋊C4C2211yescharacteristic
23#2315—28no—
24C2×#388C2214yescomplemented
25C2×#386C4116yescomplemented
26C2×#386C2214yes—
27C2×#386C2214yes—
28C2×#386C2212yes—
29C2×#386C2212yes—
30C2×#386C2212yes—
31C2×#386C2212yes—
32C2×#385C2214yescomplemented
33C2×#385C2214yescomplemented
34#2280—28no—
35C2×#381C2212yescomplemented
36C2×#380C2211yescharacteristic
37C2×#380C2212yes—
38C2×#380C2211yescharacteristic
39C2×#380C2211yescharacteristic
40C2×#380C2211yescharacteristic
41C2×#380C2212yescomplemented
42C2×#380C2212yescomplemented
43C2×#380C2212yescomplemented
44C2×#379C2212yes—
45C2×#379C2212yes—
46C2×#379C2212yes—
47C2×C4×C22⋊C4C2212yes—
48C2×C4×C22⋊C4C2212yes—
49C2×C4×C22⋊C4C2212yescomplemented
50C2×C4×C22⋊C4C2214yescomplemented
51C22×#95C2211yescharacteristic
52C22×#95C2211yescharacteristic
53#1443C2214yescomplemented
54#1442C2214yescomplemented
55#1442C2214yescomplemented
56#1442C2214yescomplemented
57#1440C2214yescomplemented
58#1439C2214yescomplemented
59#1439C2214yescomplemented
60#1439C2214yescomplemented
61#1438C2214yes—
62#1438C2214yes—
63#1437C2214yescomplemented
64#1437C2214yescomplemented
65#1437C2214yescomplemented
66#1436C2214yescomplemented
67#1436C2214yescomplemented
68#1436C2214yescomplemented
69#1434C2214yescomplemented
70C22⋊#95C2212yes—
71C22⋊#95C2212yes—
72C22⋊#95C2212yes—
73C22⋊#95C2212yes—
74C22⋊#95C2212yes—
75C22⋊#95C2214yescomplemented
76C22⋊#95C2212yescomplemented
77C22⋊#95C2212yescomplemented
78C26C2311yescharacteristic
79C26C2311yescharacteristic
80C23×D4—24no—
81C23×D4—24no—
82C23×D4—44no—
83C23×D4—44no—
84C23×D4C2×C418yes—
85C23×D4C2312yes—
86C23×D4C2312yes—
87C24×C4—24no—
88C24×C4—24no—
89C24×C4—44no—
90C24×C4—44no—
91C24×C4C2×C418yescomplemented
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2314yes—
97C24×C4C2311yescharacteristic
98C24×C4C2311yescharacteristic
99C24×C4C2311yescharacteristic
100C24×C4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C2×#117—28no—
103C2×#117—44no—
104C2×#117—44no—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2314yes—
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C22⋊C4—24no—
111C22×C22⋊C4—24no—
112C22×C22⋊C4—28no—
113C22×C22⋊C4—28no—
114C22×C22⋊C4—44no—
115C22×C22⋊C4—44no—
116C22×C22⋊C4—44no—
117C22×C22⋊C4C2×C418yes—
118C22×C22⋊C4C2×C418yes—
119C22×C22⋊C4C2×C418yescomplemented
120C22×C22⋊C4C2312yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2312yes—
123C22×C22⋊C4C2314yes—
124C22×C22⋊C4C2314yes—
125C22×C22⋊C4C2314yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C22⋊C4C2314yes—
134C22×C22⋊C4C2314yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C42C2314yes—
138C22×C42C2314yes—
139#388—48no—
140#386—48no—
141#386—48no—
142#386C2×C4116yescomplemented
143#386C2×C4116yescomplemented
144#386C2×C4116yescomplemented
145#386C2×C4116yescomplemented
146#385—216no—
147#385—216no—
148#381—28no—
149#380—24no—
150#380—24no—
151#380—24no—
152#380—28no—
153#380—28no—
154#380—44no—
155#380—44no—
156#380D418yescomplemented
157#379—28no—
158#379—28no—
159#379—44no—
160C4×C22⋊C4—28no—
161C4×C22⋊C4—28no—
162C4×C22⋊C4—48no—
163C4×C22⋊C4—44no—
164C2×#95C2×C418yescomplemented
165C2×#95C2×C418yescomplemented
166C2×#95C2314yes—
167C2×#95C2312yes—
168C2×#95C2312yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2312yes—
172C2×#95C2314yes—
173C2×#95C2314yes—
174C2×#95C2314yes—
175C2×#95C2314yes—
176C2×#95C2314yes—
177C2×#95C2314yes—
178C2×#95C2314yes—
179C2×#95C2314yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C25—22no—
188C25—22no—
189C25—24no—
190C25—24no—
191C25—22no—
192C25—22no—
193C25—22no—
194C25—22no—
195C25—22no—
196C25—22no—
197C25—22no—
198C25—22no—
199C25—42no—
200C25—42no—
201C25—42no—
202C25—42no—
203C25—42no—
204C25—42no—
205C25C22×C414yes—
206C25C22×C414yes—
207C25#4114yes—
208C25#4114yes—
209C25C2412yes—
210C25C2411yescharacteristic
211C25C2411yescharacteristic
212C25C2411yescharacteristic
213C22×D4—232no—
214C22×D4—24no—
215C22×D4—24no—
216C22×D4—24no—
217C22×D4—24no—
218C22×D4—28no—
219C22×D4—28no—
220C22×D4—44no—
221C22×D4—44no—
222C22×D4—416no—
223C22×D4—416no—
224C22×D4—432no—
225C22×D4—432no—
226C22×D4C22×C418yes—
227C22×D4C22×C418yes—
228C23×C4—24no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—24no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—232no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—28no—
251C23×C4—28no—
252C23×C4—416no—
253C23×C4—416no—
254C23×C4—42no—
255C23×C4—42no—
256C23×C4—42no—
257C23×C4—42no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—44no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—44no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4—44no—
272C23×C4—432no—
273C23×C4—432no—
274C23×C4C22×C414yes—
275C23×C4C22×C414yes—
276C23×C4C22×C414yes—
277C23×C4C22×C414yes—
278C23×C4C22×C414yes—
279C23×C4C22×C414yes—
280C23×C4C22×C414yes—
281C23×C4C22×C414yes—
282C23×C4C22×C414yes—
283C23×C4C2×D414yes—
284C23×C4#4114yes—
285C23×C4C2414yes—
286C23×C4C2414yes—
287C23×C4C2414yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2414yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296#117—432no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4C2×D418yescomplemented
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—232no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—28no—
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—28no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—28no—
336C2×C22⋊C4—28no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—416no—
341C2×C22⋊C4—416no—
342C2×C22⋊C4—432no—
343C2×C22⋊C4—44no—
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⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—44no—
356C2×C22⋊C4C22×C418yes—
357C2×C22⋊C4C22×C418yes—
358C2×C22⋊C4C22×C418yes—
359C2×C22⋊C4C22×C418yes—
360C2×C22⋊C4C22×C418yes—
361C2×C22⋊C4C22×C418yes—
362C2×C22⋊C4C2×D418yes—
363C2×C42—28no—
364C2×C42—28no—
365C2×C42—44no—
366C2×C42—44no—
367C2×C42—44no—
368C2×C42—44no—
369#95—28no—
370#95—24no—
371#95—28no—
372#95—24no—
373#95—24no—
374#95—28no—
375#95—44no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—44no—
383#95—44no—
384#95—44no—
385#95C22×C418yes—
386#95C22×C418yes—
387#95C22×C418yes—
388#95C22×C418yes—
389#95C2×D418yescomplemented
390C24—22no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—216no—
395C24—216no—
396C24—28no—
397C24—28no—
398C24—28no—
399C24—22no—
400C24—21no—
401C24—21no—
402C24—22no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—24no—
410C24—21no—
411C24—21no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—24no—
417C24—24no—
418C24—22no—
419C24—22no—
420C24—21no—
421C24—21no—
422C24—22no—
423C24—22no—
424C24—24no—
425C24—28no—
426C24—28no—
427C24—28no—
428C24—28no—
429C24—28no—
430C24—28no—
431C24—28no—
432C24—28no—
433C24—44no—
434C24—44no—
435C24—44no—
436C24—44no—
437C24—44no—
438C24—48no—
439C24—48no—
440C24—44no—
441C24—48no—
442C24—48no—
443C24—48no—
444C24—48no—
445C24—48no—
446C24—48no—
447C24—48no—
448C24—48no—
449C24—48no—
450C24—48no—
451C24—48no—
452C24—48no—
453C24—44no—
454C24—44no—
455C24—44no—
456C24—44no—
457C24—84no—
458C24—84no—
459C24—84no—
460C24—84no—
461C24—84no—
462C24—84no—
463C24—84no—
464C24—84no—
465C24#117116yescomplemented
466C24C23×C414yes—
467C24C23×C412yes—
468C24C23×C412yes—
469C24C23×C412yes—
470C24C22×D412yes—
471C24C2×#4114yes—
472C24C2×#4114yes—
473C24C2×#4112yes—
474C24C2×#4112yes—
475C24C2×#4112yes—
476C24H(5,𝔽2)14yes—
477C24H(5,𝔽2)14yes—
478C24H(5,𝔽2)12yes—
479C242−1+412yes—
480C24C2511yescharacteristic
481C2×D4—216no—
482C2×D4—216no—
483C2×D4—216no—
484C2×D4—216no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—416no—
488C2×D4—416no—
489C2×D4—416no—
490C2×D4—416no—
491C2×D4—4128no—
492C22×C4—216no—
493C22×C4—216no—
494C22×C4—28no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—28no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—24no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—24no—
529C22×C4—28no—
530C22×C4—28no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—44no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—44no—
561C22×C4—44no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—4128no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—416no—
582C22×C4—48no—
583C22×C4—48no—
584C22×C4—416no—
585C22×C4—88no—
586C22×C4—88no—
587C22×C4—84no—
588C22×C4—88no—
589C22×C4—84no—
590C22×C4—84no—
591C22×C4—84no—
592C22×C4—88no—
593C22×C4—88no—
594C22×C4C4×D4116yes—
595C22×C4C23×C414yes—
596C22×C4C23×C414yes—
597C22×C4C23×C414yes—
598C22×C4C23×C412yes—
599C22×C4C23×C412yes—
600C22×C4C23×C412yes—
601C22×C4C23×C412yes—
602C22×C4C22×D418yes—
603C22×C4C22×D412yes—
604C22×C4C22×D412yes—
605C22×C4C2×#4112yes—
606C22×C4C2×#4112yes—
607C22×C4H(5,𝔽2)14yes—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—84no—
611C4⋊C4—84no—
612C4⋊C4—88no—
613C22⋊C4—216no—
614C22⋊C4—216no—
615C22⋊C4—216no—
616C22⋊C4—216no—
617C22⋊C4—216no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—416no—
621C22⋊C4—416no—
622C22⋊C4—416no—
623C22⋊C4—416no—
624C22⋊C4—48no—
625C22⋊C4—48no—
626C22⋊C4—48no—
627C22⋊C4—88no—
628C22⋊C4—88no—
629C22⋊C4—88no—
630C42—416no—
631C42—88no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—232no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23—22no—
664C23—24no—
665C23—22no—
666C23—22no—
667C23—28no—
668C23—28no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—28no—
676C23—24no—
677C23—28no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—232no—
688C23—416no—
689C23—416no—
690C23—416no—
691C23—416no—
692C23—416no—
693C23—416no—
694C23—416no—
695C23—432no—
696C23—432no—
697C23—432no—
698C23—432no—
699C23—416no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—42no—
713C23—44no—
714C23—44no—
715C23—42no—
716C23—42no—
717C23—44no—
718C23—42no—
719C23—44no—
720C23—44no—
721C23—42no—
722C23—42no—
723C23—44no—
724C23—42no—
725C23—44no—
726C23—44no—
727C23—42no—
728C23—816no—
729C23—816no—
730C23—88no—
731C23—88no—
732C23—816no—
733C23—816no—
734C23—88no—
735C23—88no—
736C23C2×#11718yes—
737C23C2×#11714yes—
738C23C2×C4×D414yes—
739C23#51814yes—
740C23#51814yes—
741C23#52014yes—
742C23#54614yes—
743C23#54814yes—
744C23#55214yes—
745C23#55314yes—
746C23C24×C411yescharacteristic
747C23C23×D411yescharacteristic
748C23C22×#4111yescharacteristic
749C23C22×#4111yescharacteristic
750C23C22×#4111yescharacteristic
751C23C2×H(5,𝔽2)12yes—
752C23C2×H(5,𝔽2)12yes—
753C23C2×H(5,𝔽2)12yes—
754C23C2×H(5,𝔽2)11yescharacteristic
755C23C2×2−1+411yescharacteristic
756C23#58512yes—
757D4—432no—
758D4—432no—
759C2×C4—232no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—28no—
785C2×C4—28no—
786C2×C4—28no—
787C2×C4—416no—
788C2×C4—416no—
789C2×C4—416no—
790C2×C4—416no—
791C2×C4—416no—
792C2×C4—416no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—44no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—44no—
812C2×C4—44no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—44no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—88no—
827C2×C4—88no—
828C2×C4—832no—
829C2×C4C2×C4×D414yes—
830C2×C4C2×C4×D414yes—
831C2×C4#51814yes—
832C22—24no—
833C22—28no—
834C22—28no—
835C22—24no—
836C22—24no—
837C22—28no—
838C22—28no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—28no—
843C22—28no—
844C22—24no—
845C22—24no—
846C22—24no—
847C22—24no—
848C22—28no—
849C22—24no—
850C22—24no—
851C22—464no—
852C22—42no—
853C22—42no—
854C22—44no—
855C22—44no—
856C22—48no—
857C22—44no—
858C22—44no—
859C22—48no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—44no—
864C22—42no—
865C22—44no—
866C22—48no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—48no—
872C22—42no—
873C22—44no—
874C22—42no—
875C22—44no—
876C22—832no—
877C22#235218yes—
878C22C22×#11711yescharacteristic
879C22C22×C4×D411yescharacteristic
880C22C2×#51811yescharacteristic
881C22C2×#51811yescharacteristic
882C22C2×#51811yescharacteristic
883C22C2×#52011yescharacteristic
884C22#342811yescharacteristic
885C22#345912yes—
886C22#345912yes—
887C22C2×#54611yescharacteristic
888C22C2×#54811yescharacteristic
889C22C2×#55211yescharacteristic
890C22C2×#55311yescharacteristic
891C22#348412yes—
892C22#348812yes—
893C22#349012yes—
894C22#349012yes—
895C22#349012yes—
896C22#349412yes—
897C22#353412yes—
898C22#353512yes—
899C22#353612yes—
900C22#353712yes—
901C4—24no—
902C4—24no—
903C4—24no—
904C4—44no—
905C4—48no—
906C4—44no—
907C4—42no—
908C4—44no—
909C4—84no—
910C4—84no—
911C4—84no—
912C2—28no—
913C2—44no—
914C2—44no—
915C2—48no—
916C2#3405711yescharacteristic
917C2C2×#235211yescharacteristic
918C2#3417611yescharacteristic
919C2#3419811yescharacteristic
920C2#3420411yescharacteristic
921C2#3437611yescharacteristic
922C2#3437911yescharacteristic
923C2#3774412yes—
924C2#3775212yes—
925C2#3793212yes—
926C2#3794012yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC24×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2315C2semidirect
3. C2×#2280C2semidirect
4. #14680C2semidirect
5. #14391C2semidirect
6. #14373C2semidirect
7. #14347C2semidirect
8. #14338C2semidirect
9. #14064C2semidirect
10. #13988C2semidirect
11. #13883C2semidirect
12. #13873C2semidirect
14. C22⋊C42C2semidirect
15. #13778C2semidirect
18. C22×#117C22semidirect
24. C2×#388C22semidirect
25. C2×#386C4semidirect
32. C2×#385C22semidirect
33. C2×#385C22semidirect
35. C2×#381C22semidirect
41. C2×#380C22semidirect
42. C2×#380C22semidirect
43. C2×#380C22semidirect
49. C2×C4×C22⋊C4C22semidirect
50. C2×C4×C22⋊C4C22semidirect
53. #1443C22semidirect
54. #1442C22semidirect
55. #1442C22semidirect
56. #1442C22semidirect
57. #1440C22semidirect
58. #1439C22semidirect
59. #1439C22semidirect
60. #1439C22semidirect
63. #1437C22semidirect
64. #1437C22semidirect
65. #1437C22semidirect
66. #1436C22semidirect
67. #1436C22semidirect
68. #1436C22semidirect
69. #1434C22semidirect
75. C22⋊#95C22semidirect
76. C22⋊#95C22semidirect
77. C22⋊#95C22semidirect
91. C24×C4C2×C4semidirect
119. C22×C22⋊C4C2×C4semidirect
142. #386C2×C4semidirect
143. #386C2×C4semidirect
144. #386C2×C4semidirect
145. #386C2×C4semidirect
156. #380D4semidirect
164. C2×#95C2×C4semidirect
165. C2×#95C2×C4semidirect
311. C2×C4⋊C4C2×D4semidirect
389. #95C2×D4semidirect
465. C24#117semidirect

Maximal subgroups

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

subgroupindex
C2×#23152
C22×#3862
C2×#22802
#146802
#143912
#143732
#143472
#143382
#140642
#139882
#138832
#138732
#138672
C22⋊C422
#137782