Finite Group Databasebeta

← #674156

Subgroups — #674156

Order 512.

3214 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2485C212yesmaximal, complemented
2C2×#2354C211yesmaximal, characteristic, complemented
3C2×C4×#121C211yesmaximal, characteristic
4#15400C214yesmaximal, complemented
5#15295C214yesmaximal, complemented
6#15181C212yesmaximal, complemented
7#15136C212yesmaximal, complemented
8#15132C212yesmaximal, complemented
9#15126C212yesmaximal
10#14686C211yesmaximal, characteristic, complemented
11#14151C211yesmaximal, characteristic, complemented
12#14133C212yesmaximal, complemented
13#14129C212yesmaximal, complemented
14#13910C211yesmaximal, characteristic, complemented
15#13906C211yesmaximal, characteristic, complemented
16#13876C212yesmaximal, complemented
17C4×#380C211yesmaximal, characteristic, complemented
18C22×#121C2211yescharacteristic
19C22×C4×D4C2212yes—
20C22×C4×D4C2211yescharacteristic
21C22×#117C2212yes—
22C23×C42C2211yescharacteristic
23#2485—216no—
24C2×#397C2214yes—
25C2×#397C2214yes—
26C2×#394C2214yes—
27#2354—28no—
28C4×#121—28no—
29C2×#390C2212yes—
30C2×#390C2211yescharacteristic
31C2×#390C2212yes—
32C2×#389C2212yes—
33C2×#389C2212yes—
34C2×#389C2212yes—
35C2×#389C2211yescharacteristic
36C2×#389C2212yes—
37C2×#388C2212yes—
38C2×#388C2214yes—
39C2×#388C2214yes—
40C2×#387C2214yes—
41C2×#386C2212yes—
42C2×#384C2211yescharacteristic
43C2×#384C2211yescharacteristic
44C2×#384C2212yes—
45C2×#380C2212yes—
46C2×#380C2212yes—
47C2×#380C2212yes—
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2211yescharacteristic
54C2×C4×C4⋊C4C2212yes—
55C2×C4×C4⋊C4C2211yescharacteristic
56C2×C4×C4⋊C4C2211yescharacteristic
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4C2212yes—
59C2×C4×C22⋊C4C2212yes—
60#1444C2214yes—
61#1443C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1441C2214yes—
65#1440C2214yes—
66#1439C2214yes—
67#1439C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1438C2214yes—
72#1436C2214yes—
73#1436C2214yes—
74C4⋊#95C2212yes—
75C4⋊#95C2211yescharacteristic
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2212yes—
83#1434C2212yes—
84C22⋊#95C2212yes—
85C4×#95C2212yes—
86C23×D4C2311yescharacteristic
87C23×D4C2312yes—
88C24×C4C2311yescharacteristic
89C24×C4C2312yes—
90C24×C4C2311yescharacteristic
91C24×C4C2311yescharacteristic
92C2×#121—24no—
93C2×#121—24no—
94C2×#121—24no—
95C2×C4×D4—28no—
96C2×C4×D4—28no—
97C2×C4×D4—24no—
98C2×C4×D4—24no—
99C2×C4×D4—44no—
100C2×C4×D4D418yes—
101C2×#117—28no—
102C2×#117—28no—
103C2×#117—44no—
104C22×C4⋊C4C2312yes—
105C22×C4⋊C4C2311yescharacteristic
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2314yes—
111C22×C4⋊C4C2312yes—
112C22×C4⋊C4C2311yescharacteristic
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2314yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2312yes—
120C22×C4⋊C4C2314yes—
121C22×C22⋊C4C2312yes—
122C22×C22⋊C4C2314yes—
123C22×C22⋊C4C2312yes—
124C22×C22⋊C4C2312yes—
125C22×C22⋊C4C2312yes—
126C22×C22⋊C4C2312yes—
127C22×C22⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2314yes—
130C22×C22⋊C4C2314yes—
131C22×C22⋊C4C2314yes—
132C22×C22⋊C4C2314yes—
133C22×C42—24no—
134C22×C42—24no—
135C22×C42—24no—
136C22×C42C2311yescharacteristic
137C22×C42C2311yescharacteristic
138C22×C42C2311yescharacteristic
139C22×C42C2312yes—
140C22×C42C2312yes—
141C22×C42C2312yes—
142C22×C42C2314yes—
143C22×C42C2311yescharacteristic
144#397—216no—
145#397—48no—
146#394—216no—
147#390—28no—
148#390—24no—
149#390—44no—
150#389—28no—
151#389—28no—
152#389—24no—
153#389—28no—
154#389—44no—
155#388—216no—
156#388—216no—
157#388—28no—
158#387—216no—
159#386—28no—
160#384—24no—
161#384—24no—
162#384—44no—
163#380—28no—
164#380—28no—
165#380—28no—
166#380—24no—
167#380—24no—
168#380—28no—
169#380—44no—
170#380—44no—
171#380D418yescomplemented
172C4×C4⋊C4—28no—
173C4×C4⋊C4—24no—
174C4×C4⋊C4—24no—
175C4×C4⋊C4—24no—
176C4×C22⋊C4—28no—
177C4×C22⋊C4—28no—
178C2×#95C2314yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2314yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2314yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2312yes—
200C25C2412yes—
201C25C2411yescharacteristic
202C22×D4—24no—
203C22×D4—24no—
204C22×D4—24no—
205C22×D4—24no—
206C22×D4—22no—
207C22×D4—22no—
208C22×D4—24no—
209C22×D4—22no—
210C22×D4—22no—
211C22×D4—22no—
212C22×D4—22no—
213C22×D4—42no—
214C22×D4—42no—
215C22×D4C2×D414yes—
216C23×C4—22no—
217C23×C4—24no—
218C23×C4—22no—
219C23×C4—22no—
220C23×C4—24no—
221C23×C4—24no—
222C23×C4—22no—
223C23×C4—22no—
224C23×C4—24no—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—24no—
231C23×C4—22no—
232C23×C4—22no—
233C23×C4—22no—
234C23×C4—22no—
235C23×C4—24no—
236C23×C4—22no—
237C23×C4—22no—
238C23×C4—22no—
239C23×C4—41no—
240C23×C4—41no—
241C23×C4C2×D418yes—
242C23×C4C2×D414yes—
243C23×C4#4114yes—
244C23×C4C2412yes—
245C23×C4C2414yes—
246C23×C4C2414yes—
247C23×C4C2412yes—
248C23×C4C2412yes—
249C23×C4C2412yes—
250C23×C4C2412yes—
251C23×C4C2411yescharacteristic
252C23×C4C2412yes—
253C23×C4C2411yescharacteristic
254C23×C4C2412yes—
255C23×C4C2411yescharacteristic
256C23×C4C2411yescharacteristic
257C23×C4C2411yescharacteristic
258C23×C4C2411yescharacteristic
259#121—232no—
260C4×D4—232no—
261C4×D4—432no—
262#117—432no—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—22no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—22no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—22no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—24no—
276C2×C4⋊C4—24no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—24no—
280C2×C4⋊C4—24no—
281C2×C4⋊C4—28no—
282C2×C4⋊C4—24no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—28no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—44no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—42no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4C2×D414yes—
310C2×C4⋊C4C2×D414yes—
311C2×C4⋊C4C2×D414yes—
312C2×C4⋊C4#4114yes—
313C2×C4⋊C4#4114yes—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—28no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—24no—
324C2×C22⋊C4—24no—
325C2×C22⋊C4—24no—
326C2×C22⋊C4—28no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—28no—
333C2×C22⋊C4—28no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—44no—
338C2×C22⋊C4—42no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—44no—
342C2×C22⋊C4—44no—
343C2×C22⋊C4—44no—
344C2×C22⋊C4—44no—
345C2×C22⋊C4—44no—
346C2×C22⋊C4—44no—
347C2×C22⋊C4—44no—
348C2×C22⋊C4C2×D418yes—
349C2×C22⋊C4C2×D418yes—
350C2×C42—28no—
351C2×C42—28no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—22no—
355C2×C42—24no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—24no—
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—44no—
371C2×C42—416no—
372C2×C42C2×D414yes—
373C2×C42#4114yes—
374C2×C42#4114yes—
375#95—24no—
376#95—24no—
377#95—28no—
378#95—24no—
379#95—24no—
380#95—28no—
381#95—28no—
382#95—28no—
383#95—28no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—28no—
389#95—28no—
390#95—28no—
391#95—24no—
392#95—42no—
393#95—44no—
394#95—44no—
395#95—44no—
396#95C2×D418yes—
397C24—21no—
398C24—21no—
399C24—21no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24C22×D414yes—
424C24C22×D412yes—
425C24C2×#4112yes—
426C242−1+412yes—
427C24C2511yescharacteristic
428C2×D4—216no—
429C2×D4—28no—
430C2×D4—28no—
431C2×D4—28no—
432C2×D4—48no—
433C2×D4—48no—
434C2×D4—48no—
435C2×D4—48no—
436C2×D4—48no—
437C2×D4—48no—
438C2×D4—44no—
439C2×D4—44no—
440C2×D4—44no—
441C2×D4—44no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—28no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—216no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—216no—
499C22×C4—28no—
500C22×C4—28no—
501C22×C4—216no—
502C22×C4—28no—
503C22×C4—28no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—24no—
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—48no—
541C22×C4—44no—
542C22×C4—44no—
543C22×C4—48no—
544C22×C4—48no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—48no—
548C22×C4—44no—
549C22×C4—44no—
550C22×C4C22×D412yes—
551C22×C4C22×D414yes—
552C22×C4C22×D414yes—
553C22×C4C22×D414yes—
554C22×C4C22×D412yes—
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C22×D412yes—
558C22×C4C2×#4112yes—
559C22×C4C2×#4114yes—
560C22×C4C2×#4114yes—
561C22×C4C2×#4112yes—
562C22×C4C2×#4112yes—
563C22×C4C2×#4112yes—
564C22×C4C2×#4112yes—
565C22×C4C2×#4112yes—
566C22×C4C2×#4112yes—
567C22×C4C2×#4112yes—
568C22×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C4H(5,𝔽2)12yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C4H(5,𝔽2)12yes—
573C22×C42−1+412yes—
574C22×C42−1+412yes—
575C4⋊C4—28no—
576C4⋊C4—28no—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—28no—
580C4⋊C4—416no—
581C4⋊C4—48no—
582C4⋊C4—48no—
583C4⋊C4—44no—
584C4⋊C4—48no—
585C4⋊C4—48no—
586C4⋊C4—44no—
587C4⋊C4—48no—
588C4⋊C4—84no—
589C4⋊C4—84no—
590C4⋊C4—88no—
591C4⋊C4—88no—
592C22⋊C4—216no—
593C22⋊C4—216no—
594C22⋊C4—216no—
595C22⋊C4—48no—
596C22⋊C4—48no—
597C22⋊C4—416no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—88no—
601C22⋊C4—88no—
602C22⋊C4—88no—
603C22⋊C4—88no—
604C42—416no—
605C42—44no—
606C42—44no—
607C42—44no—
608C42—48no—
609C42—48no—
610C42—48no—
611C42#123116yes—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
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—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23#54714yes—
682C23C23×D411yescharacteristic
683C23C23×D411yescharacteristic
684C23C22×#4111yescharacteristic
685C23C22×#4111yescharacteristic
686C23C22×#4111yescharacteristic
687C23C22×#4111yescharacteristic
688C23C22×#4111yescharacteristic
689C23C2×H(5,𝔽2)11yescharacteristic
690C23C2×H(5,𝔽2)11yescharacteristic
691C23C2×H(5,𝔽2)11yescharacteristic
692C23C2×2−1+411yescharacteristic
693C23C2×2−1+411yescharacteristic
694C23C2×2−1+411yescharacteristic
695C23#58511yescharacteristic
696C23#58511yescharacteristic
697D4—432no—
698D4—416no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—416no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—416no—
763C2×C4—432no—
764C2×C4—416no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—42no—
768C2×C4—44no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4C2×#12314yes—
794C2×C4C2×#12314yes—
795C2×C4C2×#12314yes—
796C2×C4#52514yes—
797C2×C4#53214yes—
798C2×C4#53714yes—
799C2×C4#54214yes—
800C2×C4D4214yes—
801C2×C4#54714yes—
802C2×C4#54714yes—
803C2×C4#55214yes—
804C2×C4#55314yes—
805C2×C4#55314yes—
806C2×C4#55514yes—
807C2×C4#55614yes—
808C22—24no—
809C22—24no—
810C22—24no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—42no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—44no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22—82no—
835C22—82no—
836C22—82no—
837C22—82no—
838C22C22×#12311yescharacteristic
839C22C2×#52511yescharacteristic
840C22C2×#53211yescharacteristic
841C22C2×#53711yescharacteristic
842C22C2×#54211yescharacteristic
843C22C2×D4211yescharacteristic
844C22C2×#54711yescharacteristic
845C22C2×#54711yescharacteristic
846C22C2×#54711yescharacteristic
847C22D4×#4111yescharacteristic
848C22C2×#55211yescharacteristic
849C22C2×#55311yescharacteristic
850C22C2×#55311yescharacteristic
851C22C2×#55511yescharacteristic
852C22C2×#55611yescharacteristic
853C22#347511yescharacteristic
854C22#348311yescharacteristic
855C22#348811yescharacteristic
856C22#348911yescharacteristic
857C22#349211yescharacteristic
858C22#349311yescharacteristic
859C22#349411yescharacteristic
860C22#349511yescharacteristic
861C22#349711yescharacteristic
862C22#349811yescharacteristic
863C22#350611yescharacteristic
864C22#351111yescharacteristic
865C22#351411yescharacteristic
866C22#351811yescharacteristic
867C22#352011yescharacteristic
868C22#352311yescharacteristic
869C22#354611yescharacteristic
870C22#354811yescharacteristic
871C22#355211yescharacteristic
872C22#355511yescharacteristic
873C4—24no—
874C4—44no—
875C4—44no—
876C4—44no—
877C4—44no—
878C4—42no—
879C4—44no—
880C4—42no—
881C4—42no—
882C4—82no—
883C4—82no—
884C4—84no—
885C4—84no—
886C4#242218yes—
887C4#248518yescomplemented
888C2—44no—
889C2—84no—
890C2C2×#242211yescharacteristic
891C2C2×#248511yescharacteristic
892C2#3551611yescharacteristic
893C2#3610011yescharacteristic
894C2#3618611yescharacteristic
895C2#3627311yescharacteristic
896C2#3641111yescharacteristic
897C2#3892311yescharacteristic
898C2#3894011yescharacteristic
899C2#3934111yescharacteristic
900C2#3947911yescharacteristic
901C2#5921211yescharacteristic
902C2#5921811yescharacteristic
903C2#5924411yescharacteristic
904C2#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
1. C2×#2485C2semidirect
2. C2×#2354C2semidirect
4. #15400C2semidirect
5. #15295C2semidirect
6. #15181C2semidirect
7. #15136C2semidirect
8. #15132C2semidirect
10. #14686C2semidirect
11. #14151C2semidirect
12. #14133C2semidirect
13. #14129C2semidirect
14. #13910C2semidirect
15. #13906C2semidirect
16. #13876C2semidirect
17. C4×#380C2semidirect
171. #380D4semidirect
887. C4#2485semidirect

Maximal subgroups

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

subgroupindex
C2×#24852
C2×#23542
C2×C4×#1212
#154002
#152952
#151812
#151362
#151322
#151262
#146862
#141512
#141332
#141292
#139102
#139062
#138762
C4×#3802