Finite Group Databasebeta

← #1394091

Subgroups — #1394091

Order 512.

4518 conjugacy classes of subgroups.

The subgroup lattice has 961 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2541C211yesmaximal, characteristic, complemented
2C2×#2428C212yesmaximal, complemented
3C2×#2619C212yesmaximal, complemented
4C2×#2354C211yesmaximal, characteristic, complemented
5#16516C212yesmaximal, complemented
6#16502C212yesmaximal, complemented
7#16291C214yesmaximal, complemented
8#16260C214yesmaximal, complemented
9#15142C211yesmaximal, characteristic, complemented
10#15130C212yesmaximal, complemented
11#15127C211yesmaximal, characteristic, complemented
12#15124C212yesmaximal, complemented
13#15123C211yesmaximal, characteristic, complemented
14#14886C212yesmaximal, complemented
15#13998C212yesmaximal, complemented
16#13918C211yesmaximal, characteristic, complemented
17C4×#394C211yesmaximal, characteristic, complemented
18C22×#127C2212yes—
19C22×#127C2212yes—
20C22×#127C2211yescharacteristic
21C22×#121C2212yes—
22C22×#121C2214yes—
23C22×#121C2212yes—
24C22×#121C2212yes—
25C22×C4×D4C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×#117C2212yes—
28#2619—216no—
29#2541—28no—
30#2428—216no—
31C2×#394C2212yes—
32C2×#394C2214yes—
33C2×#394C2214yes—
34C2×#394C2212yes—
35C2×#394C2214yes—
36C2×#394C2211yescharacteristic
37C2×#392C2212yes—
38C2×#392C2214yes—
39C2×#392C2212yes—
40C2×#392C2214yes—
41C2×#392C2214yes—
42C2×#392C2214yes—
43C2×#392C2212yes—
44C2×#392C2214yes—
45#2354—28no—
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2212yes—
49C2×#390C2212yes—
50C2×#390C2214yes—
51C2×#390C2212yes—
52C2×#390C2212yes—
53C2×#389C2212yes—
54C2×#388C2212yes—
55C2×#388C2212yes—
56C2×#386C2214yes—
57C2×#384C2211yescharacteristic
58C2×#382C2212yes—
59C2×#380C2212yes—
60C2×#380C2212yes—
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2212yes—
65C2×C4×C22⋊C4C2212yes—
66#1442C2211yescharacteristic
67#1442C2214yes—
68#1441C2211yescharacteristic
69#1440C2212yes—
70#1439C2212yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2212yes—
74#1439C2214yes—
75#1438C2214yes—
76#1438C2214yes—
77#1438C2214yes—
78#1438C2212yes—
79#1438C2212yes—
80#1438C2211yescharacteristic
81#1438C2214yes—
82#1437C2214yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2212yes—
85#1434C2212yes—
86C4×#95C2211yescharacteristic
87C23×D4C2312yes—
88C23×D4C2311yescharacteristic
89C23×D4C2314yes—
90C23×D4C2312yes—
91C23×D4C2314yes—
92C23×D4C2314yes—
93C23×D4C2314yes—
94C23×D4C2314yes—
95C23×D4C2311yescharacteristic
96C23×D4C2312yes—
97C24×C4C2312yes—
98C24×C4C2312yes—
99C2×#127—28no—
100C2×#127—28no—
101C2×#127—28no—
102C2×#127—24no—
103C2×#127—44no—
104C2×#127—44no—
105C2×#127—44no—
106C2×#127—44no—
107C2×#121—28no—
108C2×#121—216no—
109C2×#121—28no—
110C2×#121—28no—
111C2×#121—28no—
112C2×#121—28no—
113C2×#121—216no—
114C2×#121—48no—
115C2×#121—44no—
116C2×#121—44no—
117C2×#121—44no—
118C2×#121—44no—
119C2×C4×D4—24no—
120C2×C4×D4—24no—
121C2×C4×D4—24no—
122C2×C4×D4—44no—
123C2×C4×D4D418yescomplemented
124C2×#117—28no—
125C2×#117—28no—
126C2×#117—44no—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2314yes—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2314yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2312yes—
157C22×C42C2312yes—
158C22×C42C2311yescharacteristic
159C22×C42C2312yes—
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163#394—28no—
164#394—216no—
165#394—216no—
166#394—48no—
167#394—44no—
168#394D418yescomplemented
169#392—28no—
170#392—216no—
171#392—216no—
172#392—28no—
173#392—216no—
174#392—44no—
175#392—48no—
176#392—48no—
177#390—24no—
178#390—216no—
179#390—24no—
180#390—28no—
181#390—28no—
182#390—44no—
183#390—44no—
184#389—28no—
185#388—28no—
186#388—28no—
187#386—216no—
188#384—24no—
189#382—28no—
190#380—28no—
191#380—44no—
192C4×C4⋊C4—24no—
193C4×C4⋊C4—24no—
194C4×C4⋊C4D418yescomplemented
195C4×C22⋊C4—28no—
196C4×C22⋊C4—44no—
197C2×#95C2311yescharacteristic
198C2×#95C2312yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C2×#95C2311yescharacteristic
205C2×#95C2312yes—
206C2×#95C2311yescharacteristic
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2311yescharacteristic
213C2×#95C2312yes—
214C25C2414yes—
215C25C2412yes—
216C25C2412yes—
217C22×D4—28no—
218C22×D4—28no—
219C22×D4—28no—
220C22×D4—28no—
221C22×D4—28no—
222C22×D4—28no—
223C22×D4—22no—
224C22×D4—22no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—28no—
229C22×D4—28no—
230C22×D4—28no—
231C22×D4—28no—
232C22×D4—24no—
233C22×D4—24no—
234C22×D4—22no—
235C22×D4—24no—
236C22×D4—28no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—22no—
240C22×D4—24no—
241C22×D4—24no—
242C22×D4—24no—
243C22×D4—24no—
244C22×D4—24no—
245C22×D4—28no—
246C22×D4—42no—
247C22×D4—42no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—44no—
252C22×D4—44no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4—44no—
256C22×D4—44no—
257C22×D4—44no—
258C22×D4—44no—
259C22×D4—44no—
260C22×D4—44no—
261C22×D4—44no—
262C22×D4—44no—
263C22×D4—44no—
264C22×D4—44no—
265C22×D4—44no—
266C22×D4—44no—
267C22×D4—44no—
268C22×D4—42no—
269C22×D4—44no—
270C22×D4—44no—
271C22×D4—44no—
272C22×D4—44no—
273C22×D4—44no—
274C22×D4—44no—
275C22×D4—44no—
276C22×D4—42no—
277C22×D4C2×D414yes—
278C22×D4C2×D414yes—
279C23×C4—24no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—24no—
284C23×C4—24no—
285C23×C4—24no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4C2×D418yes—
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2412yes—
296C23×C4C2414yes—
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2411yescharacteristic
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C23×C4C2411yescharacteristic
307#127—432no—
308#127—416no—
309#127—432no—
310#121—464no—
311#121—432no—
312#121—432no—
313#121—432no—
314C4×D4—232no—
315C4×D4—416no—
316#117—432no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—28no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—41no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4C2×D414yes—
339C2×C4⋊C4C2×D414yes—
340C2×C4⋊C4C2×D414yes—
341C2×C4⋊C4C2×D414yes—
342C2×C4⋊C4#4114yes—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—28no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—28no—
354C2×C22⋊C4—28no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—28no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—44no—
384C2×C22⋊C4—44no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4C2×D418yes—
399C2×C22⋊C4C2×D418yes—
400C2×C22⋊C4C2×D418yes—
401C2×C42—24no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—22no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—42no—
414C2×C42C2×D418yes—
415C2×C42C2×D414yes—
416C2×C42C2×D414yes—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—22no—
421#95—22no—
422#95—28no—
423#95—24no—
424#95—28no—
425#95—24no—
426#95—22no—
427#95—28no—
428#95—42no—
429#95—42no—
430#95—44no—
431#95—42no—
432#95C2×D418yes—
433#95C2×D414yes—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—24no—
447C24—22no—
448C24—24no—
449C24—24no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—24no—
457C24—22no—
458C24—24no—
459C24—24no—
460C24—24no—
461C24—24no—
462C24—24no—
463C24—24no—
464C24—24no—
465C24—24no—
466C24—24no—
467C24—24no—
468C24—24no—
469C24—24no—
470C24—24no—
471C24—24no—
472C24—24no—
473C24C22×D414yes—
474C24C22×D414yes—
475C24C2511yescharacteristic
476C2×D4—28no—
477C2×D4—216no—
478C2×D4—28no—
479C2×D4—48no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—48no—
483C2×D4—416no—
484C2×D4—416no—
485C2×D4—416no—
486C2×D4—416no—
487C2×D4—416no—
488C2×D4—416no—
489C2×D4—416no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—416no—
494C2×D4—416no—
495C2×D4—416no—
496C2×D4—416no—
497C2×D4—416no—
498C2×D4—48no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—48no—
502C2×D4—48no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4—88no—
510C2×D4—88no—
511C2×D4—88no—
512C2×D4—88no—
513C2×D4—88no—
514C2×D4—84no—
515C2×D4—88no—
516C2×D4—88no—
517C2×D4—84no—
518C2×D4—88no—
519C2×D4—88no—
520C2×D4—88no—
521C2×D4—88no—
522C2×D4—88no—
523C2×D4—88no—
524C2×D4—88no—
525C2×D4—88no—
526C2×D4—88no—
527C2×D4—88no—
528C2×D4—88no—
529C2×D4—88no—
530C2×D4—88no—
531C2×D4—88no—
532C2×D4—88no—
533C2×D4—88no—
534C2×D4—88no—
535C2×D4—88no—
536C2×D4—88no—
537C2×D4—88no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—216no—
577C22×C4—216no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—24no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—24no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4C22×D414yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D414yes—
618C22×C4C22×D412yes—
619C22×C4C22×D414yes—
620C22×C4C22×D414yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C2×#4114yes—
628C22×C4C2×#4112yes—
629C22×C4H(5,𝔽2)14yes—
630C22×C4H(5,𝔽2)12yes—
631C22×C4H(5,𝔽2)12yes—
632C22×C4H(5,𝔽2)14yes—
633C22×C4H(5,𝔽2)14yes—
634C4⋊C4—28no—
635C4⋊C4—28no—
636C4⋊C4—44no—
637C4⋊C4—48no—
638C4⋊C4—416no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C4⋊C4—48no—
642C4⋊C4—84no—
643C4⋊C4#121116yes—
644C22⋊C4—216no—
645C22⋊C4—216no—
646C22⋊C4—48no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—48no—
651C22⋊C4—416no—
652C22⋊C4—416no—
653C22⋊C4—416no—
654C22⋊C4—48no—
655C22⋊C4—416no—
656C22⋊C4—88no—
657C22⋊C4—88no—
658C22⋊C4—88no—
659C22⋊C4—84no—
660C22⋊C4—84no—
661C22⋊C4—88no—
662C22⋊C4—88no—
663C22⋊C4—88no—
664C42—28no—
665C42—28no—
666C42—216no—
667C42—48no—
668C42—44no—
669C42—48no—
670C23—24no—
671C23—28no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—28no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—44no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—44no—
701C23—42no—
702C23—42no—
703C23—44no—
704C23—42no—
705C23—44no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—44no—
714C23—44no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—44no—
719C23—42no—
720C23—44no—
721C23—42no—
722C23—42no—
723C23—44no—
724C23—42no—
725C23—44no—
726C23—42no—
727C23—42no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23—44no—
750C23—44no—
751C23—44no—
752C23—44no—
753C23—44no—
754C23—44no—
755C23—44no—
756C23—44no—
757C23—44no—
758C23—44no—
759C23—44no—
760C23—44no—
761C23—44no—
762C23—44no—
763C23C23×D411yescharacteristic
764C23C23×D411yescharacteristic
765C23C23×D411yescharacteristic
766C23C22×#4111yescharacteristic
767C23C2×H(5,𝔽2)12yes—
768C23C2×H(5,𝔽2)12yes—
769C23C2×H(5,𝔽2)11yescharacteristic
770C23C2×H(5,𝔽2)11yescharacteristic
771C23C2×H(5,𝔽2)12yes—
772C23#58511yescharacteristic
773C23#58512yes—
774D4—416no—
775D4—416no—
776D4—832no—
777D4—816no—
778D4—832no—
779D4—832no—
780D4—832no—
781D4—816no—
782D4—832no—
783D4—816no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—22no—
805C2×C4—24no—
806C2×C4—24no—
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—22no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—432no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—41no—
825C2×C4—44no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—44no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—44no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—44no—
847C2×C4—44no—
848C2×C4—41no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—44no—
854C2×C4—42no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—42no—
858C2×C4—44no—
859C2×C4—816no—
860C2×C4C2×#12118yes—
861C2×C4C2×#12114yes—
862C2×C4#53514yes—
863C2×C4#53518yes—
864C2×C4#53514yes—
865C2×C4#54018yes—
866C2×C4D4214yes—
867C2×C4D4214yes—
868C22—44no—
869C22—44no—
870C22—48no—
871C22—44no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—48no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—44no—
880C22—82no—
881C22—82no—
882C22—82no—
883C22—84no—
884C22—82no—
885C22—82no—
886C22—82no—
887C22—82no—
888C22—82no—
889C22—82no—
890C22—82no—
891C22—82no—
892C22—82no—
893C22—84no—
894C22—84no—
895C22—84no—
896C22—84no—
897C22—84no—
898C22—84no—
899C22—84no—
900C22—84no—
901C22—84no—
902C22—84no—
903C22—84no—
904C22—84no—
905C22—84no—
906C22—84no—
907C22—84no—
908C22—84no—
909C22C22×#12111yescharacteristic
910C22C2×#53511yescharacteristic
911C22C2×#53511yescharacteristic
912C22C2×#53512yes—
913C22C2×#54012yes—
914C22C2×D4211yescharacteristic
915C22C2×D4211yescharacteristic
916C22D4×#4111yescharacteristic
917C22#348711yescharacteristic
918C22#348811yescharacteristic
919C22#348812yes—
920C22#349612yes—
921C22#349611yescharacteristic
922C22#349812yes—
923C22#349811yescharacteristic
924C22#351712yes—
925C22#351911yescharacteristic
926C22#354212yes—
927C22#354212yes—
928C22#354312yes—
929C22#354612yes—
930C22#354912yes—
931C22#356212yes—
932C4—24no—
933C4—24no—
934C4—28no—
935C4—42no—
936C4—44no—
937C4—42no—
938C4—44no—
939C4—44no—
940C4—42no—
941C4—82no—
942C4—84no—
943C4—82no—
944C4—81no—
945C4#261918yescomplemented
946C2—84no—
947C2—84no—
948C2—164no—
949C2C2×#261911yescharacteristic
950C2#3602911yescharacteristic
951C2D4×#12111yescharacteristic
952C2#3933911yescharacteristic
953C2#3934212yes—
954C2#3936111yescharacteristic
955C2#3940212yes—
956C2#4243812yes—
957C2#4257812yes—
958C2#4288911yescharacteristic
959C2#4296311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
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×#2541C2semidirect
2. C2×#2428C2semidirect
3. C2×#2619C2semidirect
4. C2×#2354C2semidirect
5. #16516C2semidirect
6. #16502C2semidirect
7. #16291C2semidirect
8. #16260C2semidirect
9. #15142C2semidirect
10. #15130C2semidirect
11. #15127C2semidirect
12. #15124C2semidirect
13. #15123C2semidirect
14. #14886C2semidirect
15. #13998C2semidirect
16. #13918C2semidirect
17. C4×#394C2semidirect
123. C2×C4×D4D4semidirect
168. #394D4semidirect
194. C4×C4⋊C4D4semidirect
945. C4#2619semidirect

Maximal subgroups

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

subgroupindex
C2×#25412
C2×#24282
C2×#26192
C2×#23542
#165162
#165022
#162912
#162602
#151422
#151302
#151272
#151242
#151232
#148862
#139982
#139182
C4×#3942