Finite Group Databasebeta

← #674190

Subgroups — #674190

Order 512.

3686 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×#2487C212yesmaximal, complemented
2C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C4×#127C211yesmaximal, characteristic
4#15358C214yesmaximal, complemented
5#15329C214yesmaximal, complemented
6#15181C212yesmaximal, complemented
7#15181C212yesmaximal, complemented
8#15148C212yesmaximal, complemented
9#15146C212yesmaximal, complemented
10#14712C211yesmaximal, characteristic, complemented
11#14025C212yesmaximal
12#14018C212yesmaximal, complemented
13#13906C211yesmaximal, characteristic, complemented
14#13906C211yesmaximal, characteristic, complemented
15#13906C211yesmaximal, characteristic, complemented
16#13872C212yesmaximal, complemented
17C4×#389C211yesmaximal, characteristic, complemented
18C22×#127C2211yescharacteristic
19C22×C4×D4C2211yescharacteristic
20C22×C4×D4C2212yes—
21C22×C4×D4C2212yes—
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C23×C4⋊C4C2212yes—
25#2487—216no—
26C2×#400C2214yes—
27C2×#399C2214yes—
28D4×C4⋊C4—28no—
29C4×#127—28no—
30C2×#390C2211yescharacteristic
31C2×#390C2212yes—
32C2×#390C2211yescharacteristic
33C2×#390C2212yes—
34C2×#390C2212yes—
35C2×#390C2212yes—
36C2×#390C2212yes—
37C2×#389C2212yes—
38C2×#389C2211yescharacteristic
39C2×#389C2212yes—
40C2×#389C2212yes—
41C2×#389C2212yes—
42C2×#389C2211yescharacteristic
43C2×#386C2214yes—
44C2×#386C2214yes—
45C2×#385C2214yes—
46C2×#385C2214yes—
47C2×#384C2211yescharacteristic
48C2×#384C2211yescharacteristic
49C2×#384C2211yescharacteristic
50C2×#380C2212yes—
51C2×#380C2212yes—
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#380C2212yes—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2212yes—
60C2×C43C2211yescharacteristic
61#1442C2214yes—
62#1442C2214yes—
63#1441C2214yes—
64#1439C2214yes—
65#1439C2214yes—
66#1439C2214yes—
67#1439C2214yes—
68#1439C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1438C2214yes—
73#1438C2214yes—
74#1436C2212yes—
75#1436C2212yes—
76C4⋊#95C2212yes—
77C4⋊#95C2212yes—
78C4⋊#95C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2211yescharacteristic
81C4⋊#95C2212yes—
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2212yes—
84C22⋊#95C2214yes—
85C4×#95C2212yes—
86C23×D4C2311yescharacteristic
87C23×D4C2312yes—
88C23×D4C2312yes—
89C23×D4C2311yescharacteristic
90C24×C4C2312yes—
91C24×C4C2312yes—
92C24×C4C2314yes—
93C2×#127—24no—
94C2×#127—24no—
95C2×#127Q818yes—
96C2×C4×D4—28no—
97C2×C4×D4—28no—
98C2×C4×D4—28no—
99C2×C4×D4—24no—
100C2×C4×D4—28no—
101C2×C4×D4—24no—
102C2×C4×D4—24no—
103C2×C4×D4—28no—
104C2×C4×D4—24no—
105C2×C4×D4—24no—
106C2×C4×D4—44no—
107C2×C4×D4—44no—
108C2×C4×D4—44no—
109C2×C4×D4—44no—
110C2×C4×D4D418yes—
111C22×C4⋊C4—28no—
112C22×C4⋊C4—28no—
113C22×C4⋊C4—44no—
114C22×C4⋊C4C2312yes—
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2312yes—
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2311yescharacteristic
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2314yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2311yescharacteristic
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C22⋊C4C2312yes—
135C22×C22⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2314yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2314yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C42C2312yes—
146C22×C42C2312yes—
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154#400—216no—
155#399—216no—
156#390—24no—
157#390—28no—
158#390—24no—
159#390—28no—
160#390—28no—
161#390—44no—
162#390—44no—
163#389—28no—
164#389—28no—
165#389—24no—
166#389—44no—
167#389—44no—
168#389D418yescomplemented
169#386—216no—
170#386—48no—
171#385—216no—
172#385—216no—
173#384—24no—
174#384—24no—
175#384—24no—
176#380—28no—
177#380—28no—
178#380—28no—
179#380—28no—
180#380—44no—
181#380—44no—
182#380—44no—
183C4×C4⋊C4—24no—
184C4×C4⋊C4—24no—
185C4×C4⋊C4—44no—
186C2×#95C2314yes—
187C2×#95C2314yes—
188C2×#95C2314yes—
189C2×#95C2314yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2312yes—
204C43—24no—
205C25C2412yes—
206C25C2412yes—
207C22×D4—24no—
208C22×D4—24no—
209C22×D4—24no—
210C22×D4—24no—
211C22×D4—22no—
212C22×D4—24no—
213C22×D4—22no—
214C22×D4—22no—
215C22×D4—24no—
216C22×D4—22no—
217C22×D4—22no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—22no—
221C22×D4—24no—
222C22×D4—22no—
223C22×D4—22no—
224C22×D4—24no—
225C22×D4—42no—
226C22×D4—42no—
227C22×D4—42no—
228C22×D4—42no—
229C22×D4C2×D414yes—
230C22×D4C2×Q814yes—
231C22×D4C2×Q818yes—
232C22×D4C2×Q818yes—
233C22×D4C2×Q814yes—
234C22×D4#4114yes—
235C23×C4—24no—
236C23×C4—24no—
237C23×C4—24no—
238C23×C4—24no—
239C23×C4—24no—
240C23×C4—24no—
241C23×C4—28no—
242C23×C4—24no—
243C23×C4—24no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—24no—
247C23×C4—24no—
248C23×C4—24no—
249C23×C4—28no—
250C23×C4—44no—
251C23×C4—44no—
252C23×C4—44no—
253C23×C4—44no—
254C23×C4—44no—
255C23×C4C2×D418yes—
256C23×C4C2414yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2414yes—
260C23×C4C2412yes—
261C23×C4C2411yescharacteristic
262C23×C4C2412yes—
263C23×C4C2412yes—
264C23×C4C2412yes—
265C23×C4C2411yescharacteristic
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271#127—232no—
272C4×D4—232no—
273C4×D4—432no—
274C4×D4—432no—
275C4×D4—432no—
276C4×D4—416no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—24no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—28no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—432no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—42no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4C2×D414yes—
329C2×C4⋊C4C2×D414yes—
330C2×C4⋊C4C2×D414yes—
331C2×C4⋊C4C2×D418yes—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—28no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—28no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—42no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C2×C22⋊C4—42no—
356C2×C22⋊C4—44no—
357C2×C22⋊C4—44no—
358C2×C22⋊C4—44no—
359C2×C22⋊C4—44no—
360C2×C22⋊C4—44no—
361C2×C22⋊C4—44no—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—44no—
364C2×C22⋊C4—44no—
365C2×C22⋊C4—44no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4C2×D418yes—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—24no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—22no—
386C2×C42—24no—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—41no—
391C2×C42—41no—
392C2×C42C2×D414yes—
393C2×C42C2×D414yes—
394C2×C42C2×Q814yes—
395C2×C42#4114yes—
396C2×C42#4114yes—
397C2×C42#4114yes—
398#95—24no—
399#95—28no—
400#95—28no—
401#95—28no—
402#95—28no—
403#95—28no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95—28no—
408#95—24no—
409#95—42no—
410#95—42no—
411#95—44no—
412#95—44no—
413#95—44no—
414#95—44no—
415#95C2×D418yes—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—22no—
420C24—22no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24C22×D414yes—
443C24C22×Q814yes—
444C24C22×Q814yes—
445C24C2×#4114yes—
446C24C2511yescharacteristic
447C2×D4—216no—
448C2×D4—216no—
449C2×D4—28no—
450C2×D4—28no—
451C2×D4—28no—
452C2×D4—216no—
453C2×D4—28no—
454C2×D4—28no—
455C2×D4—28no—
456C2×D4—28no—
457C2×D4—216no—
458C2×D4—28no—
459C2×D4—28no—
460C2×D4—48no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—48no—
469C2×D4—48no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4C22⋊Q8116yes—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—216no—
518C22×C4—216no—
519C22×C4—216no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—24no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—24no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—416no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—416no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—88no—
569C22×C4—88no—
570C22×C4—88no—
571C22×C4—88no—
572C22×C4—88no—
573C22×C4C22×D414yes—
574C22×C4C22×D414yes—
575C22×C4C22×D414yes—
576C22×C4C22×D412yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×Q812yes—
583C22×C4C22×Q812yes—
584C22×C4C22×Q812yes—
585C22×C4C2×#4112yes—
586C22×C4C2×#4112yes—
587C22×C4C2×#4112yes—
588C22×C4C2×#4112yes—
589C22×C4C2×#4112yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4112yes—
594C22×C4C2×#4112yes—
595C22×C4H(5,𝔽2)12yes—
596C22×C4H(5,𝔽2)12yes—
597C22×C4H(5,𝔽2)12yes—
598C22×C4H(5,𝔽2)12yes—
599C22×C4H(5,𝔽2)12yes—
600C22×C42−1+412yes—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—28no—
604C4⋊C4—48no—
605C4⋊C4—416no—
606C4⋊C4—48no—
607C4⋊C4—48no—
608C4⋊C4—48no—
609C4⋊C4—48no—
610C4⋊C4—44no—
611C4⋊C4—48no—
612C4⋊C4—44no—
613C4⋊C4—48no—
614C4⋊C4—44no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C4⋊C4—84no—
618C4⋊C4—88no—
619C22⋊C4—216no—
620C22⋊C4—48no—
621C22⋊C4—48no—
622C22⋊C4—416no—
623C22⋊C4—48no—
624C22⋊C4—48no—
625C22⋊C4—416no—
626C22⋊C4—48no—
627C22⋊C4—88no—
628C22⋊C4—88no—
629C22⋊C4—88no—
630C22⋊C4—88no—
631C22⋊C4—88no—
632C42—28no—
633C42—28no—
634C42—28no—
635C42—44no—
636C42—44no—
637C42—44no—
638C42—48no—
639C42—48no—
640C42#123116yes—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—24no—
665C23—24no—
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—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23C2×C22⋊Q818yes—
711C23C23×D411yescharacteristic
712C23C23×D411yescharacteristic
713C23C23×Q811yescharacteristic
714C23C22×#4111yescharacteristic
715C23C22×#4111yescharacteristic
716C23C22×#4111yescharacteristic
717C23C22×#4111yescharacteristic
718C23C2×H(5,𝔽2)11yescharacteristic
719C23C2×H(5,𝔽2)11yescharacteristic
720C23C2×H(5,𝔽2)11yescharacteristic
721C23C2×H(5,𝔽2)11yescharacteristic
722C23C2×H(5,𝔽2)11yescharacteristic
723C23C2×2−1+411yescharacteristic
724C23#58511yescharacteristic
725C23#58511yescharacteristic
726D4—232no—
727D4—432no—
728D4—432no—
729D4—416no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—432no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—44no—
795C2×C4—42no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4—44no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—44no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—44no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—44no—
819C2×C4—832no—
820C2×C4—816no—
821C2×C4C2×C22⋊Q814yes—
822C2×C4C2×#12314yes—
823C2×C4C2×#12314yes—
824C2×C4C2×#12314yes—
825C2×C4#53214yes—
826C2×C4#53514yes—
827C2×C4#54014yes—
828C2×C4D4214yes—
829C2×C4#54614yes—
830C2×C4D4×Q814yes—
831C2×C4#55014yes—
832C2×C4#55314yes—
833C2×C4#55314yes—
834C2×C4#55414yes—
835C2×C4#55414yes—
836C2×C4#55414yes—
837C2×C4#55914yes—
838C22—28no—
839C22—28no—
840C22—28no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—44no—
852C22—44no—
853C22—44no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—44no—
858C22—44no—
859C22—44no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22—82no—
868C22C22×C22⋊Q811yescharacteristic
869C22C22×#12311yescharacteristic
870C22C2×#53211yescharacteristic
871C22C2×#53511yescharacteristic
872C22C2×#54011yescharacteristic
873C22C2×D4211yescharacteristic
874C22C2×#54611yescharacteristic
875C22C2×D4×Q811yescharacteristic
876C22C2×#55011yescharacteristic
877C22D4×#4111yescharacteristic
878C22C2×#55311yescharacteristic
879C22C2×#55311yescharacteristic
880C22C2×#55411yescharacteristic
881C22C2×#55411yescharacteristic
882C22C2×#55411yescharacteristic
883C22#347511yescharacteristic
884C22C2×#55911yescharacteristic
885C22#348811yescharacteristic
886C22#348911yescharacteristic
887C22#349611yescharacteristic
888C22#349811yescharacteristic
889C22#350111yescharacteristic
890C22#350111yescharacteristic
891C22#350611yescharacteristic
892C22#350611yescharacteristic
893C22#350711yescharacteristic
894C22#351111yescharacteristic
895C22#351111yescharacteristic
896C22#351211yescharacteristic
897C22#351911yescharacteristic
898C22#352011yescharacteristic
899C22#354611yescharacteristic
900C22#354611yescharacteristic
901C22#354811yescharacteristic
902C22#354911yescharacteristic
903C4—24no—
904C4—24no—
905C4—24no—
906C4—42no—
907C4—44no—
908C4—44no—
909C4—42no—
910C4—44no—
911C4—82no—
912C4—84no—
913C4—82no—
914C4—82no—
915C4—84no—
916C4#244518yes—
917C4#248718yescomplemented
918C2—48no—
919C2—84no—
920C2C2×#244511yescharacteristic
921C2C2×#248711yescharacteristic
922C2#3551711yescharacteristic
923C2D4×C22⋊Q811yescharacteristic
924C2#3615411yescharacteristic
925C2#3646811yescharacteristic
926C2#3655911yescharacteristic
927C2#3919111yescharacteristic
928C2#3934211yescharacteristic
929C2#3947111yescharacteristic
930C2#3963411yescharacteristic
931C2#5967811yescharacteristic
932C2#5968011yescharacteristic
933C2#5982311yescharacteristic
934C2#5986411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#127C22
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×#2487C2semidirect
2. C2×D4×C4⋊C4C2semidirect
4. #15358C2semidirect
5. #15329C2semidirect
6. #15181C2semidirect
7. #15181C2semidirect
8. #15148C2semidirect
9. #15146C2semidirect
10. #14712C2semidirect
12. #14018C2semidirect
13. #13906C2semidirect
14. #13906C2semidirect
15. #13906C2semidirect
16. #13872C2semidirect
17. C4×#389C2semidirect
168. #389D4semidirect
917. C4#2487semidirect

Maximal subgroups

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

subgroupindex
C2×#24872
C2×D4×C4⋊C42
C2×C4×#1272
#153582
#153292
#151812
#151482
#151462
#147122
#140252
#140182
#139062
#138722
C4×#3892