Finite Group Databasebeta

← #656999

Subgroups — #656999

Order 512.

4830 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2534C212yesmaximal
2C2×#2486C211yesmaximal, characteristic, complemented
3C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
4C2×C4×#120C211yesmaximal, characteristic
5C22×#380C211yesmaximal, characteristic, complemented
6#15436C214yesmaximal, complemented
7#15390C214yesmaximal, complemented
8#15131C212yesmaximal, complemented
9#15129C212yesmaximal, complemented
10#14935C212yesmaximal, complemented
11#14918C212yesmaximal, complemented
12#14680C211yesmaximal, characteristic, complemented
13#13974C212yesmaximal, complemented
14#13968C212yesmaximal, complemented
15#13907C211yesmaximal, characteristic, complemented
16#13904C211yesmaximal, characteristic, complemented
17#13872C212yesmaximal, complemented
18C25×C4C2211yescharacteristic
19C22×#123C2212yes—
20C22×#120C2211yescharacteristic
21C22×C4×D4C2212yes—
22C22×C4×D4C2212yes—
23C22×C4×D4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic
26C23×C4⋊C4C2211yescharacteristic, complemented
27C23×C22⋊C4C2212yes—
28#2534—216no—
29#2486—28no—
30C2×#398C2212yescomplemented
31C2×#397C2212yescomplemented
32C2×#396C2214yes—
33C2×#394C2214yes—
34D4×C4⋊C4—28no—
35C4×#120—28no—
36C2×#389C2212yescomplemented
37C2×#389C2212yescomplemented
38C2×#389C2212yescomplemented
39C2×#388C2214yes—
40C2×#386C2214yes—
41C2×#386C2212yes—
42C2×#386C2211yescharacteristic
43C2×#385C2212yes—
44C2×#385C2212yes—
45C2×#385C2211yescharacteristic
46C2×#385C2212yescomplemented
47C2×#384C2211yescharacteristic, complemented
48C2×#381C2212yes—
49C2×#381C2212yes—
50C2×#381C2212yes—
51C2×#380—28no—
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×#380C2214yes—
56C2×#380C2212yes—
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2212yes—
60C2×#380C2211yescharacteristic, complemented
61C2×#380C2212yescomplemented
62C2×#379C2212yes—
63C2×#379C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic, complemented
65C2×C4×C22⋊C4C2212yes—
66C2×C4×C22⋊C4C2211yescharacteristic
67C22×#95C2212yes—
68#1445C2214yescomplemented
69#1443C2214yescomplemented
70#1441C2214yescomplemented
71#1441C2214yescomplemented
72#1441C2214yescomplemented
73#1441C2214yescomplemented
74#1441C2214yescomplemented
75#1440C2214yes—
76#1440C2214yes—
77#1440C2214yescomplemented
78#1439C2214yes—
79#1439C2214yes—
80#1436C2214yescomplemented
81C4⋊#95C2212yescomplemented
82C4⋊#95C2212yescomplemented
83C4⋊#95C2212yescomplemented
84C22⋊#95C2214yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C22⋊#95C2214yescomplemented
88C26C2311yescharacteristic
89C23×D4C2312yes—
90C23×D4C2311yescharacteristic
91C24×C4—24no—
92C24×C4—28no—
93C24×C4—24no—
94C24×C4—24no—
95C24×C4—44no—
96C24×C4C2312yes—
97C24×C4C2311yescharacteristic
98C24×C4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C24×C4C2312yes—
104C2×#123—28no—
105C2×#123—28no—
106C2×#123—28no—
107C2×#120—24no—
108C2×#120—24no—
109C2×#120D418yes—
110C2×C4×D4—24no—
111C2×C4×D4—24no—
112C2×C4×D4—28no—
113C2×C4×D4—28no—
114C2×C4×D4—28no—
115C2×C4×D4—28no—
116C2×C4×D4—44no—
117C2×C4×D4—44no—
118C2×C4×D4D418yes—
119C22×C4⋊C4—24no—
120C22×C4⋊C4—24no—
121C22×C4⋊C4—24no—
122C22×C4⋊C4—24no—
123C22×C4⋊C4—44no—
124C22×C4⋊C4—44no—
125C22×C4⋊C4D418yescomplemented
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2312yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C22⋊C4—28no—
142C22×C22⋊C4—28no—
143C22×C22⋊C4—44no—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2311yescharacteristic
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2314yes—
151C22×C22⋊C4C2314yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2314yes—
160C22×C42C2312yes—
161C22×C42C2312yes—
162C22×C42C2311yescharacteristic
163#398—28no—
164#397—28no—
165#396—216no—
166#394—216no—
167#389—28no—
168#389—28no—
169#389—44no—
170#388—216no—
171#386—216no—
172#386—24no—
173#386—28no—
174#385—28no—
175#385—28no—
176#385—28no—
177#385—24no—
178#384—24no—
179#381—28no—
180#381—28no—
181#381—44no—
182#380—24no—
183#380—24no—
184#380—28no—
185#380—28no—
186#380—24no—
187#380—28no—
188#380—28no—
189#380—216no—
190#380—28no—
191#380—44no—
192#379—28no—
193#379—24no—
194C4×C4⋊C4—24no—
195C4×C22⋊C4—24no—
196C4×C22⋊C4—28no—
197C2×#95—28no—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2314yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C25—22no—
219C25—24no—
220C25—22no—
221C25—24no—
222C25—22no—
223C25—22no—
224C25—22no—
225C25—22no—
226C25—42no—
227C25—42no—
228C25C2×D414yes—
229C25C2411yescharacteristic
230C25C2412yes—
231C25C2411yescharacteristic
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—24no—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—42no—
241C22×D4—42no—
242C22×D4C2×D418yes—
243C22×D4C2×D414yes—
244C22×D4C2×D414yes—
245C22×D4#4114yes—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—232no—
249C23×C4—22no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—22no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—22no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—22no—
270C23×C4—24no—
271C23×C4—24no—
272C23×C4—22no—
273C23×C4—24no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—24no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—432no—
283C23×C4—432no—
284C23×C4—44no—
285C23×C4—44no—
286C23×C4—42no—
287C23×C4—44no—
288C23×C4—44no—
289C23×C4—416no—
290C23×C4—416no—
291C23×C4C2×D414yes—
292C23×C4C2×D414yes—
293C23×C4C2×D414yes—
294C23×C4C2×D418yes—
295C23×C4#4118yes—
296C23×C4#4114yes—
297C23×C4C2414yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2414yes—
302C23×C4C2411yescharacteristic
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2411yescharacteristic
309C23×C4C2411yescharacteristic
310C23×C4C2411yescharacteristic
311#123—432no—
312#120—232no—
313C4×D4—232no—
314C4×D4—432no—
315C4×D4—432no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—416no—
344C2×C4⋊C4—416no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—42no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—416no—
350C2×C4⋊C4—44no—
351C2×C4⋊C4—44no—
352C2×C4⋊C4—44no—
353C2×C4⋊C4C2×D414yes—
354C2×C4⋊C4C2×D414yes—
355C2×C4⋊C4C2×D414yes—
356C2×C4⋊C4C2×D418yes—
357C2×C22⋊C4—22no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—28no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—432no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—44no—
402C2×C22⋊C4C2×D414yes—
403C2×C22⋊C4C2×D414yes—
404C2×C22⋊C4C2×D414yes—
405C2×C22⋊C4C2×D418yes—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—42no—
414C2×C42C2×D414yes—
415#95—28no—
416#95—28no—
417#95—24no—
418#95—24no—
419#95—24no—
420#95—24no—
421#95—28no—
422#95—24no—
423#95—24no—
424#95—28no—
425#95—24no—
426#95—28no—
427#95—28no—
428#95—28no—
429#95—28no—
430#95—44no—
431#95—44no—
432#95—44no—
433#95—44no—
434#95—44no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—28no—
440C24—28no—
441C24—216no—
442C24—28no—
443C24—216no—
444C24—22no—
445C24—21no—
446C24—22no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—21no—
455C24—22no—
456C24—22no—
457C24—21no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—28no—
465C24—28no—
466C24—48no—
467C24—48no—
468C24—48no—
469C24—48no—
470C24—48no—
471C24—48no—
472C24—48no—
473C24—48no—
474C24—48no—
475C24—44no—
476C24—44no—
477C24—48no—
478C24—44no—
479C24—44no—
480C24—44no—
481C24—44no—
482C24C22×D412yes—
483C24C22×D412yes—
484C24C22×D414yes—
485C24C22×D412yes—
486C24C22×D412yes—
487C24C22×D412yes—
488C24C2×#4112yes—
489C24C2×#4114yes—
490C24C2×#4112yes—
491C24C2×#4112yes—
492C24H(5,𝔽2)12yes—
493C242−1+414yes—
494C242−1+412yes—
495C24C2511yescharacteristic
496C2×D4—28no—
497C2×D4—28no—
498C2×D4—28no—
499C2×D4—28no—
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—216no—
503C2×D4—216no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—48no—
508C2×D4—48no—
509C2×D4#121116yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—28no—
517C22×C4—28no—
518C22×C4—216no—
519C22×C4—216no—
520C22×C4—216no—
521C22×C4—28no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—24no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—216no—
551C22×C4—28no—
552C22×C4—216no—
553C22×C4—216no—
554C22×C4—216no—
555C22×C4—216no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—22no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—24no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—48no—
593C22×C4—48no—
594C22×C4—48no—
595C22×C4—48no—
596C22×C4—4128no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—44no—
604C22×C4—44no—
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×C4—48no—
615C22×C4—48no—
616C22×C4—84no—
617C22×C4—88no—
618C22×C4—88no—
619C22×C4—88no—
620C22×C4—88no—
621C22×C4#121116yes—
622C22×C4C22×D412yes—
623C22×C4C22×D414yes—
624C22×C4C22×D412yes—
625C22×C4C22×D414yes—
626C22×C4C22×D414yes—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D412yes—
633C22×C4C2×#4114yes—
634C22×C4C2×#4112yes—
635C22×C4C2×#4112yes—
636C22×C4C2×#4112yes—
637C22×C4C2×#4114yes—
638C22×C4H(5,𝔽2)14yes—
639C4⋊C4—28no—
640C4⋊C4—28no—
641C4⋊C4—28no—
642C4⋊C4—48no—
643C4⋊C4—48no—
644C4⋊C4—48no—
645C4⋊C4—48no—
646C4⋊C4—48no—
647C4⋊C4—48no—
648C4⋊C4—416no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—48no—
652C4⋊C4—84no—
653C4⋊C4—88no—
654C22⋊C4—28no—
655C22⋊C4—28no—
656C22⋊C4—28no—
657C22⋊C4—216no—
658C22⋊C4—48no—
659C22⋊C4—416no—
660C22⋊C4—416no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—416no—
666C22⋊C4—44no—
667C22⋊C4—48no—
668C22⋊C4—416no—
669C22⋊C4—88no—
670C42—28no—
671C42—48no—
672C42—48no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—22no—
680C23—22no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—232no—
690C23—22no—
691C23—24no—
692C23—24no—
693C23—22no—
694C23—24no—
695C23—22no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—22no—
700C23—24no—
701C23—24no—
702C23—22no—
703C23—24no—
704C23—22no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—24no—
717C23—24no—
718C23—24no—
719C23—24no—
720C23—432no—
721C23—432no—
722C23—416no—
723C23—416no—
724C23—432no—
725C23—416no—
726C23—416no—
727C23—432no—
728C23—416no—
729C23—42no—
730C23—41no—
731C23—416no—
732C23—41no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—41no—
742C23—42no—
743C23—41no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23C2×#12114yes—
757C23C2×#12114yes—
758C23C2×#12114yes—
759C23#53714yes—
760C23D4214yes—
761C23#54718yes—
762C23#54714yes—
763C23#54814yes—
764C23#55314yes—
765C23C23×D411yescharacteristic
766C23C23×D411yescharacteristic
767C23C23×D411yescharacteristic
768C23C22×#4111yescharacteristic
769C23C22×#4111yescharacteristic
770C23C22×#4112yes—
771C23C2×H(5,𝔽2)12yes—
772C23C2×H(5,𝔽2)11yescharacteristic
773C23C2×2−1+411yescharacteristic
774C23C2×2−1+412yes—
775C23#58512yes—
776D4—232no—
777D4—432no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—22no—
788C2×C4—232no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—432no—
806C2×C4—416no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—416no—
826C2×C4—432no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—44no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—44no—
858C2×C4—816no—
859C2×C4—816no—
860C2×C4—816no—
861C2×C4C2×#12114yes—
862C2×C4C2×#12114yes—
863C2×C4C2×#12114yes—
864C2×C4#52514yes—
865C2×C4#53414yes—
866C2×C4#54618yes—
867C2×C4#55118yes—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—28no—
872C22—28no—
873C22—28no—
874C22—24no—
875C22—24no—
876C22—28no—
877C22—24no—
878C22—28no—
879C22—28no—
880C22—28no—
881C22—28no—
882C22—24no—
883C22—464no—
884C22—44no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22—44no—
892C22—44no—
893C22—44no—
894C22—44no—
895C22—44no—
896C22—42no—
897C22—44no—
898C22—42no—
899C22—44no—
900C22—44no—
901C22—44no—
902C22—44no—
903C22—42no—
904C22—44no—
905C22#241618yes—
906C22C22×#12111yescharacteristic
907C22C22×#12111yescharacteristic
908C22C2×#52511yescharacteristic
909C22C2×#53411yescharacteristic
910C22C2×#53711yescharacteristic
911C22C2×D4211yescharacteristic
912C22C2×#54612yes—
913C22C2×#54712yes—
914C22C2×#54711yescharacteristic
915C22C2×#54811yescharacteristic
916C22C2×#55112yes—
917C22C2×#55311yescharacteristic
918C22#347512yes—
919C22#348511yescharacteristic
920C22#348611yescharacteristic
921C22#348912yes—
922C22#349212yes—
923C22#349512yes—
924C22#349512yes—
925C22#349612yes—
926C22#352012yes—
927C22#353812yes—
928C22#354212yes—
929C4—24no—
930C4—24no—
931C4—42no—
932C4—44no—
933C4—42no—
934C4—44no—
935C4—44no—
936C4—44no—
937C4—82no—
938C4—84no—
939C4—84no—
940C4—82no—
941C4—82no—
942C4#253418yescomplemented
943C2—28no—
944C2—44no—
945C2—48no—
946C2C2×#241611yescharacteristic
947C2C2×#253411yescharacteristic
948C2#3563311yescharacteristic
949C2#3610311yescharacteristic
950C2#3615312yes—
951C2#3651611yescharacteristic
952C2#3783712yes—
953C2#3912111yescharacteristic
954C2#3933811yescharacteristic
955C2#5919812yes—
956C2#5920612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#120C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2486C2semidirect
3. C2×D4×C4⋊C4C2semidirect
5. C22×#380C2semidirect
6. #15436C2semidirect
7. #15390C2semidirect
8. #15131C2semidirect
9. #15129C2semidirect
10. #14935C2semidirect
11. #14918C2semidirect
12. #14680C2semidirect
13. #13974C2semidirect
14. #13968C2semidirect
15. #13907C2semidirect
16. #13904C2semidirect
17. #13872C2semidirect
26. C23×C4⋊C4C22semidirect
30. C2×#398C22semidirect
31. C2×#397C22semidirect
36. C2×#389C22semidirect
37. C2×#389C22semidirect
38. C2×#389C22semidirect
46. C2×#385C22semidirect
47. C2×#384C22semidirect
60. C2×#380C22semidirect
61. C2×#380C22semidirect
64. C2×C4×C4⋊C4C22semidirect
68. #1445C22semidirect
69. #1443C22semidirect
70. #1441C22semidirect
71. #1441C22semidirect
72. #1441C22semidirect
73. #1441C22semidirect
74. #1441C22semidirect
77. #1440C22semidirect
80. #1436C22semidirect
81. C4⋊#95C22semidirect
82. C4⋊#95C22semidirect
83. C4⋊#95C22semidirect
87. C22⋊#95C22semidirect
125. C22×C4⋊C4D4semidirect
942. C4#2534semidirect

Maximal subgroups

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

subgroupindex
C2×#25342
C2×#24862
C2×D4×C4⋊C42
C2×C4×#1202
C22×#3802
#154362
#153902
#151312
#151292
#149352
#149182
#146802
#139742
#139682
#139072
#139042
#138722