Finite Group Databasebeta

← #530481

Subgroups — #530481

Order 512.

4638 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C4×#120C211yesmaximal, characteristic
3C22×#380C211yesmaximal, characteristic, complemented
4#14680C211yesmaximal, characteristic, complemented
5#14392C214yesmaximal, complemented
6#14391C214yesmaximal, complemented
7#14265C212yesmaximal, complemented
8#13971C212yesmaximal, complemented
9#13967C212yesmaximal
10#13905C212yesmaximal, complemented
11#13881C211yesmaximal, characteristic, complemented
12#13876C212yesmaximal, complemented
13#13875C212yesmaximal, complemented
14#13872C211yesmaximal, characteristic, complemented
15#13872C212yesmaximal, complemented
16C22⋊C4×C4⋊C4C211yesmaximal, characteristic, complemented
17#13784C212yesmaximal, complemented
18C25×C4C2211yescharacteristic
19C22×#120C2211yescharacteristic
20C22×C4×D4C2212yes—
21C22×C4×D4C2211yescharacteristic
22C22×C4×D4C2212yes—
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2211yescharacteristic
25C23×C4⋊C4C2211yescharacteristic, complemented
26C23×C22⋊C4C2212yes—
27D4×C4⋊C4—28no—
28C4×#120C4116yescomplemented
29C2×#389C2212yescomplemented
30C2×#388C2214yes—
31C2×#386C2212yes—
32C2×#386C2214yes—
33C2×#386C2211yescharacteristic
34C2×#386C2212yes—
35C2×#385C2212yes—
36C2×#385C2212yes—
37C2×#385C2211yescharacteristic
38C2×#385C2212yescomplemented
39C2×#384C2211yescharacteristic, complemented
40C2×#382C2212yescomplemented
41C2×#380—28no—
42C2×#380C2212yes—
43C2×#380C2211yescharacteristic
44C2×#380C2212yes—
45C2×#380C2214yes—
46C2×#380C2211yescharacteristic
47C2×#380C2212yes—
48C2×#380C2212yes—
49C2×#380C2211yescharacteristic, complemented
50C2×#380C2212yescomplemented
51C2×#379C2212yes—
52C2×#379C2211yescharacteristic
53C2×C4×C4⋊C4C2211yescharacteristic, complemented
54C2×C4×C4⋊C4C2212yescomplemented
55C2×C4×C22⋊C4C2212yes—
56C2×C4×C22⋊C4C2212yes—
57C2×C4×C22⋊C4C2211yescharacteristic
58C22×#95C2212yes—
59#1445C2214yescomplemented
60#1443C2214yescomplemented
61#1442C2214yescomplemented
62#1442C2214yescomplemented
63#1441C2212yescomplemented
64#1441C2214yescomplemented
65#1440C2214yes—
66#1439C2214yes—
67#1439C2214yes—
68#1439C2212yescomplemented
69#1438C2214yes—
70#1437C2214yes—
71#1437C2214yes—
72#1437C2214yescomplemented
73#1436C2214yescomplemented
74#1436C2214yescomplemented
75C4⋊#95C2212yescomplemented
76C4⋊#95C2212yescomplemented
77C4⋊#95C2212yescomplemented
78#1434C2214yescomplemented
79C22⋊#95C2212yes—
80C22⋊#95C2214yes—
81C22⋊#95C2212yes—
82C22⋊#95C2212yes—
83C22⋊#95C2212yes—
84C22⋊#95C2212yes—
85C22⋊#95C2214yescomplemented
86C26C2311yescharacteristic
87C23×D4C2312yes—
88C23×D4C2311yescharacteristic
89C24×C4—24no—
90C24×C4—24no—
91C24×C4—44no—
92C24×C4—44no—
93C24×C4C2×C418yescomplemented
94C24×C4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2312yes—
98C24×C4C2312yes—
99C24×C4C2311yescharacteristic
100C24×C4C2312yes—
101C24×C4C2312yes—
102C2×#120—24no—
103C2×#120—24no—
104C2×#120C2×C418yes—
105C2×C4×D4—24no—
106C2×C4×D4—24no—
107C2×C4×D4—28no—
108C2×C4×D4—28no—
109C2×C4×D4—44no—
110C2×C4×D4—44no—
111C2×C4×D4—44no—
112C2×C4×D4C2×C418yes—
113C2×C4×D4C2×C4116yescomplemented
114C22×C4⋊C4—24no—
115C22×C4⋊C4—24no—
116C22×C4⋊C4—44no—
117C22×C4⋊C4—44no—
118C22×C4⋊C4—44no—
119C22×C4⋊C4D418yescomplemented
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C22⋊C4—28no—
134C22×C22⋊C4—48no—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2314yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2311yescharacteristic
141C22×C22⋊C4C2311yescharacteristic
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2311yescharacteristic
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C42C2312yes—
152C22×C42C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2314yes—
155#389—28no—
156#388—48no—
157#386—28no—
158#386—48no—
159#386C2×C418yes—
160#386C2×C4116yescomplemented
161#385—28no—
162#385—28no—
163#385C2×C4116yescomplemented
164#385C2×C418yescomplemented
165#384—24no—
166#382—44no—
167#380—24no—
168#380—24no—
169#380—24no—
170#380—28no—
171#380—28no—
172#380—216no—
173#380—44no—
174#380—44no—
175#380—44no—
176#379—44no—
177#379C2×C418yescomplemented
178C4×C4⋊C4—24no—
179C4×C4⋊C4—44no—
180C4×C22⋊C4—44no—
181C4×C22⋊C4C2×C4116yescomplemented
182C4×C22⋊C4C2×C418yescomplemented
183C2×#95—28no—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2314yes—
192C2×#95C2314yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2314yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C25—22no—
206C25—22no—
207C25—24no—
208C25—24no—
209C25—22no—
210C25—22no—
211C25—22no—
212C25—22no—
213C25—42no—
214C25—42no—
215C25C22×C414yes—
216C25C2411yescharacteristic
217C25C2412yes—
218C25C2411yescharacteristic
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—22no—
222C22×D4—22no—
223C22×D4—24no—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—42no—
228C22×D4—42no—
229C22×D4C22×C418yes—
230C22×D4C22×C414yes—
231C22×D4#4114yes—
232C22×D4#4114yes—
233C23×C4—24no—
234C23×C4—24no—
235C23×C4—22no—
236C23×C4—22no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—232no—
240C23×C4—22no—
241C23×C4—24no—
242C23×C4—24no—
243C23×C4—22no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—24no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—432no—
258C23×C4—42no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—44no—
265C23×C4—44no—
266C23×C4—44no—
267C23×C4—44no—
268C23×C4—44no—
269C23×C4—42no—
270C23×C4—44no—
271C23×C4—416no—
272C23×C4—416no—
273C23×C4—432no—
274C23×C4C22×C414yes—
275C23×C4C22×C418yes—
276C23×C4C22×C414yes—
277C23×C4C22×C414yes—
278C23×C4C22×C418yes—
279C23×C4C2×D414yes—
280C23×C4C2×D418yes—
281C23×C4#4114yes—
282C23×C4C2412yes—
283C23×C4C2414yes—
284C23×C4C2412yes—
285C23×C4C2414yes—
286C23×C4C2411yescharacteristic
287C23×C4C2412yes—
288C23×C4C2411yescharacteristic
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296#120—232no—
297C4×D4—232no—
298C4×D4—432no—
299C4×D4—432no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—416no—
320C2×C4⋊C4—416no—
321C2×C4⋊C4—44no—
322C2×C4⋊C4—44no—
323C2×C4⋊C4—44no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—416no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4C22×C414yes—
330C2×C4⋊C4C22×C418yes—
331C2×C4⋊C4C2×D414yes—
332C2×C4⋊C4C2×D414yes—
333C2×C4⋊C4C2×D418yes—
334C2×C22⋊C4—22no—
335C2×C22⋊C4—22no—
336C2×C22⋊C4—22no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—28no—
352C2×C22⋊C4—28no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—28no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—432no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—44no—
374C2×C22⋊C4—44no—
375C2×C22⋊C4C22×C414yes—
376C2×C22⋊C4C22×C414yes—
377C2×C22⋊C4C22×C414yes—
378C2×C22⋊C4C22×C418yes—
379C2×C22⋊C4C22×C414yes—
380C2×C22⋊C4C22×C418yes—
381C2×C22⋊C4C22×C418yes—
382C2×C22⋊C4C22×C418yes—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—42no—
390C2×C42—44no—
391C2×C42—44no—
392C2×C42—44no—
393C2×C42C22×C414yes—
394C2×C42C22×C418yes—
395#95—28no—
396#95—28no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—28no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95—44no—
409#95—44no—
410#95—44no—
411#95—44no—
412#95—44no—
413#95C22×C418yes—
414#95C22×C418yes—
415#95C22×C418yes—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—28no—
421C24—28no—
422C24—216no—
423C24—28no—
424C24—216no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—21no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—21no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—28no—
446C24—28no—
447C24—48no—
448C24—48no—
449C24—48no—
450C24—48no—
451C24—48no—
452C24—48no—
453C24—48no—
454C24—48no—
455C24—48no—
456C24—44no—
457C24—44no—
458C24—48no—
459C24—44no—
460C24—44no—
461C24—44no—
462C24—44no—
463C24C23×C412yes—
464C24C23×C414yes—
465C24C23×C412yes—
466C24C22×D412yes—
467C24C2×#4112yes—
468C24C2×#4112yes—
469C24C2×#4112yes—
470C24C2×#4112yes—
471C24C2×#4112yes—
472C24H(5,𝔽2)14yes—
473C24H(5,𝔽2)12yes—
474C242−1+414yes—
475C242−1+412yes—
476C24C2511yescharacteristic
477C2×D4—28no—
478C2×D4—28no—
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—216no—
484C2×D4—216no—
485C2×D4—48no—
486C2×D4—48no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4#117116yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—216no—
498C22×C4—28no—
499C22×C4—28no—
500C22×C4—216no—
501C22×C4—28no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—216no—
537C22×C4—28no—
538C22×C4—216no—
539C22×C4—216no—
540C22×C4—216no—
541C22×C4—216no—
542C22×C4—216no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—24no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—24no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—24no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—4128no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—48no—
582C22×C4—44no—
583C22×C4—48no—
584C22×C4—44no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—84no—
593C22×C4—88no—
594C22×C4—88no—
595C22×C4—88no—
596C22×C4—88no—
597C22×C4—88no—
598C22×C4—88no—
599C22×C4C4×D4116yes—
600C22×C4C23×C412yes—
601C22×C4C23×C414yes—
602C22×C4C23×C414yes—
603C22×C4C23×C414yes—
604C22×C4C23×C412yes—
605C22×C4C23×C412yes—
606C22×C4C23×C412yes—
607C22×C4C23×C412yes—
608C22×C4C22×D414yes—
609C22×C4C22×D414yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C2×#4112yes—
613C22×C4C2×#4112yes—
614C22×C4C2×#4112yes—
615C22×C4C2×#4112yes—
616C22×C4H(5,𝔽2)14yes—
617C22×C4H(5,𝔽2)14yes—
618C4⋊C4—28no—
619C4⋊C4—28no—
620C4⋊C4—28no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—48no—
626C4⋊C4—44no—
627C4⋊C4—44no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—84no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—216no—
634C22⋊C4—28no—
635C22⋊C4—216no—
636C22⋊C4—28no—
637C22⋊C4—48no—
638C22⋊C4—48no—
639C22⋊C4—416no—
640C22⋊C4—416no—
641C22⋊C4—48no—
642C22⋊C4—48no—
643C22⋊C4—48no—
644C22⋊C4—88no—
645C22⋊C4—88no—
646C22⋊C4—88no—
647C42—28no—
648C42—216no—
649C42—48no—
650C42—88no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—22no—
657C23—22no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—232no—
668C23—24no—
669C23—22no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—24no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—432no—
699C23—432no—
700C23—416no—
701C23—432no—
702C23—416no—
703C23—416no—
704C23—432no—
705C23—416no—
706C23—416no—
707C23—416no—
708C23—41no—
709C23—42no—
710C23—42no—
711C23—41no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23C2×#11714yes—
735C23C2×#11714yes—
736C23C2×C4×D414yes—
737C23#52018yes—
738C23#52014yes—
739C23#54614yes—
740C23#54814yes—
741C23#55214yes—
742C23#55314yes—
743C23C24×C411yescharacteristic
744C23C23×D411yescharacteristic
745C23C22×#4111yescharacteristic
746C23C22×#4111yescharacteristic
747C23C22×#4111yescharacteristic
748C23C2×H(5,𝔽2)12yes—
749C23C2×H(5,𝔽2)12yes—
750C23C2×H(5,𝔽2)11yescharacteristic
751C23C2×H(5,𝔽2)12yes—
752C23C2×2−1+411yescharacteristic
753C23C2×2−1+412yes—
754D4—232no—
755D4—432no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—232no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—432no—
787C2×C4—416no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4—42no—
810C2×C4—416no—
811C2×C4—432no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—42no—
815C2×C4—44no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—44no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—44no—
835C2×C4—44no—
836C2×C4—816no—
837C2×C4—816no—
838C2×C4—816no—
839C2×C4C2×#11714yes—
840C2×C4C2×C4×D414yes—
841C2×C4C2×C4×D414yes—
842C2×C4#51818yes—
843C2×C4#53414yes—
844C2×C4#53514yes—
845C2×C4#53818yes—
846C22—24no—
847C22—28no—
848C22—28no—
849C22—28no—
850C22—24no—
851C22—24no—
852C22—24no—
853C22—28no—
854C22—24no—
855C22—24no—
856C22—28no—
857C22—24no—
858C22—28no—
859C22—28no—
860C22—28no—
861C22—464no—
862C22—44no—
863C22—42no—
864C22—44no—
865C22—44no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—44no—
870C22—44no—
871C22—42no—
872C22—42no—
873C22—44no—
874C22—42no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—42no—
880C22—44no—
881C22—42no—
882C22—44no—
883C22#235218yes—
884C22C22×#11711yescharacteristic
885C22C22×C4×D411yescharacteristic
886C22C2×#51812yes—
887C22C2×#52011yescharacteristic
888C22C2×#52012yes—
889C22C2×#53411yescharacteristic
890C22C2×#53511yescharacteristic
891C22C2×#53812yes—
892C22C2×#54611yescharacteristic
893C22C2×#54811yescharacteristic
894C22C2×#55211yescharacteristic
895C22C2×#55311yescharacteristic
896C22#348411yescharacteristic
897C22#348611yescharacteristic
898C22#349212yes—
899C22#351912yes—
900C22#351912yes—
901C22#352012yes—
902C22#352012yes—
903C22#353612yes—
904C22#353612yes—
905C22#353712yes—
906C22#353812yes—
907C4—24no—
908C4—24no—
909C4—42no—
910C4—44no—
911C4—44no—
912C4—44no—
913C4—42no—
914C4—44no—
915C4—44no—
916C4—84no—
917C4—84no—
918C4—82no—
919C4—82no—
920C4#232118yes—
921C2—28no—
922C2—44no—
923C2—48no—
924C2C2×#232111yescharacteristic
925C2C2×#235211yescharacteristic
926C2#3419412yes—
927C2#3420011yescharacteristic
928C2#3436012yes—
929C2#3890411yescharacteristic
930C2#3890511yescharacteristic
931C2#3892812yes—
932C2#3912011yescharacteristic
933C2#3912111yescharacteristic
934C2#3914412yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#120C22
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×D4×C4⋊C4C2semidirect
3. C22×#380C2semidirect
4. #14680C2semidirect
5. #14392C2semidirect
6. #14391C2semidirect
7. #14265C2semidirect
8. #13971C2semidirect
10. #13905C2semidirect
11. #13881C2semidirect
12. #13876C2semidirect
13. #13875C2semidirect
14. #13872C2semidirect
15. #13872C2semidirect
16. C22⋊C4×C4⋊C4C2semidirect
17. #13784C2semidirect
25. C23×C4⋊C4C22semidirect
28. C4×#120C4semidirect
29. C2×#389C22semidirect
38. C2×#385C22semidirect
39. C2×#384C22semidirect
40. C2×#382C22semidirect
49. C2×#380C22semidirect
50. C2×#380C22semidirect
53. C2×C4×C4⋊C4C22semidirect
54. C2×C4×C4⋊C4C22semidirect
59. #1445C22semidirect
60. #1443C22semidirect
61. #1442C22semidirect
62. #1442C22semidirect
63. #1441C22semidirect
64. #1441C22semidirect
68. #1439C22semidirect
72. #1437C22semidirect
73. #1436C22semidirect
74. #1436C22semidirect
75. C4⋊#95C22semidirect
76. C4⋊#95C22semidirect
77. C4⋊#95C22semidirect
78. #1434C22semidirect
85. C22⋊#95C22semidirect
93. C24×C4C2×C4semidirect
113. C2×C4×D4C2×C4semidirect
119. C22×C4⋊C4D4semidirect
160. #386C2×C4semidirect
163. #385C2×C4semidirect
164. #385C2×C4semidirect
177. #379C2×C4semidirect
181. C4×C22⋊C4C2×C4semidirect
182. C4×C22⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C4⋊C42
C2×C4×#1202
C22×#3802
#146802
#143922
#143912
#142652
#139712
#139672
#139052
#138812
#138762
#138752
#138722
C22⋊C4×C4⋊C42
#137842