Finite Group Databasebeta

← #674424

Subgroups — #674424

Order 512.

4070 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2538C211yesmaximal, characteristic, complemented
2C2×#2538C211yesmaximal, characteristic, complemented
3C2×#2417C212yesmaximal, complemented
4C2×D4×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×#127C211yesmaximal, characteristic
6#15507C214yesmaximal, complemented
7#15309C214yesmaximal, complemented
8#15181C212yesmaximal, complemented
9#15177C212yesmaximal, complemented
10#15141C212yesmaximal, complemented
11#15137C212yesmaximal, complemented
12#14712C211yesmaximal, characteristic, complemented
13#14025C212yesmaximal
14#13920C212yesmaximal, complemented
15#13906C211yesmaximal, characteristic, complemented
16#13872C212yesmaximal, complemented
17C4×#391C211yesmaximal, characteristic, complemented
18C22×#127C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×C4×Q8C2211yescharacteristic
22C22×C4×D4C2211yescharacteristic
23C22×C4×D4C2212yes—
24C22×C4×D4C2212yes—
25C22×C4×D4C2212yes—
26C22×C4×D4C2211yescharacteristic
27C23×C4⋊C4C2212yes—
28#2538—28no—
29#2538—28no—
30#2417—216no—
31C2×#398C2214yes—
32C2×#396C2214yes—
33C2×#396C2214yes—
34C2×#396C2214yes—
35D4×C4⋊C4—28no—
36C4×#127—28no—
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#390C2212yes—
41C2×#390C2211yescharacteristic
42C2×#390C2212yes—
43C2×#390C2212yes—
44C2×#390C2212yes—
45C2×#390C2212yes—
46C2×#389C2212yes—
47C2×#389C2212yes—
48C2×#389C2212yes—
49C2×#389C2212yes—
50C2×#389C2212yes—
51C2×#389C2212yes—
52C2×#386C2214yes—
53C2×#386C2214yes—
54C2×#385C2214yes—
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57C2×#384C2211yescharacteristic
58C2×#380C2212yes—
59C2×#380C2212yes—
60C2×#380C2212yes—
61C2×#380C2212yes—
62C2×#380C2214yes—
63C2×#380C2212yes—
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C43C2211yescharacteristic
66#1444C2214yes—
67#1442C2214yes—
68#1441C2214yes—
69#1439C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1438C2214yes—
76#1438C2214yes—
77#1436C2212yes—
78#1436C2212yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2211yescharacteristic
82C4⋊#95C2212yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2212yes—
85C22⋊#95C2214yes—
86C4×#95C2212yes—
87C4×#95C2212yes—
88C23×Q8C2311yescharacteristic
89C23×D4C2311yescharacteristic
90C23×D4C2312yes—
91C23×D4C2312yes—
92C23×D4C2311yescharacteristic
93C24×C4C2312yes—
94C24×C4C2312yes—
95C24×C4C2314yes—
96C2×#127—24no—
97C2×#127—24no—
98C2×#127Q818yescomplemented
99C2×C22⋊Q8—28no—
100C2×C22⋊Q8—28no—
101C2×C22⋊Q8—28no—
102C2×C22⋊Q8—28no—
103C2×C22⋊Q8—44no—
104C2×C22⋊Q8—44no—
105C2×C4×Q8—24no—
106C2×C4×Q8—24no—
107C2×C4×Q8—24no—
108C2×C4×D4—28no—
109C2×C4×D4—28no—
110C2×C4×D4—28no—
111C2×C4×D4—28no—
112C2×C4×D4—24no—
113C2×C4×D4—24no—
114C2×C4×D4—28no—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4—28no—
118C2×C4×D4—24no—
119C2×C4×D4—44no—
120C2×C4×D4—44no—
121C2×C4×D4—44no—
122C2×C4×D4D418yes—
123C22×C4⋊C4—28no—
124C22×C4⋊C4—28no—
125C22×C4⋊C4—44no—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2311yescharacteristic
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2312yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2314yes—
143C22×C4⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2314yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2314yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2314yes—
156C22×C22⋊C4C2314yes—
157C22×C42C2312yes—
158C22×C42C2312yes—
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2311yescharacteristic
166#398—216no—
167#396—216no—
168#396—216no—
169#396—216no—
170#391—24no—
171#391D418yescomplemented
172#390—24no—
173#390—28no—
174#390—24no—
175#390—28no—
176#390—28no—
177#390—28no—
178#390—44no—
179#389—28no—
180#389—28no—
181#389—28no—
182#389—28no—
183#389—44no—
184#389—44no—
185#386—216no—
186#386—48no—
187#385—216no—
188#384—24no—
189#384—24no—
190#384D418yescomplemented
191#380—28no—
192#380—28no—
193#380—28no—
194#380—28no—
195#380—216no—
196#380—44no—
197C4×C4⋊C4—24no—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C43—24no—
216C25C2412yes—
217C25C2412yes—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8C2×D414yes—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—24no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—24no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—24no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—24no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—24no—
242C22×D4—22no—
243C22×D4—42no—
244C22×D4—42no—
245C22×D4—42no—
246C22×D4—42no—
247C22×D4C2×D414yes—
248C22×D4C2×Q814yes—
249C22×D4C2×Q818yes—
250C22×D4C2×Q818yes—
251C22×D4C2×Q814yes—
252C22×D4#4114yes—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—28no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—28no—
268C23×C4—28no—
269C23×C4—44no—
270C23×C4—44no—
271C23×C4—44no—
272C23×C4—44no—
273C23×C4C2×D418yes—
274C23×C4C2414yes—
275C23×C4C2412yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2414yes—
282C23×C4C2412yes—
283C23×C4C2411yescharacteristic
284C23×C4C2411yescharacteristic
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289#127—232no—
290C22⋊Q8—432no—
291C22⋊Q8—432no—
292C4×Q8—416no—
293C4×D4—232no—
294C4×D4—432no—
295C4×D4—432no—
296C4×D4—432no—
297C4×D4—416no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—24no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—28no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—28no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—432no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4—42no—
341C2×C4⋊C4—44no—
342C2×C4⋊C4—44no—
343C2×C4⋊C4—42no—
344C2×C4⋊C4—42no—
345C2×C4⋊C4—42no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4C2×D414yes—
349C2×C4⋊C4C2×D418yes—
350C2×C4⋊C4C2×D418yes—
351C2×C4⋊C4C2×D414yes—
352C2×C4⋊C4C2×D418yes—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—28no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—44no—
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⋊C4C2×D418yes—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—41no—
412C2×C42—41no—
413C2×C42C2×D414yes—
414C2×C42C2×D414yes—
415C2×C42C2×D414yes—
416C2×C42C2×Q814yes—
417C2×C42#4114yes—
418C2×C42#4114yes—
419#95—24no—
420#95—28no—
421#95—28no—
422#95—28no—
423#95—28no—
424#95—28no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—28no—
429#95—24no—
430#95—42no—
431#95—42no—
432#95—44no—
433#95—44no—
434#95C2×D418yes—
435#95C2×D418yes—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24—22no—
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24C22×D414yes—
463C24C22×Q814yes—
464C24C22×Q814yes—
465C24C2×#4114yes—
466C24C2511yescharacteristic
467C2×Q8—28no—
468C2×Q8—28no—
469C2×Q8—28no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×D4—216no—
475C2×D4—216no—
476C2×D4—28no—
477C2×D4—28no—
478C2×D4—28no—
479C2×D4—28no—
480C2×D4—28no—
481C2×D4—216no—
482C2×D4—28no—
483C2×D4—28no—
484C2×D4—28no—
485C2×D4—216no—
486C2×D4—28no—
487C2×D4—48no—
488C2×D4—48no—
489C2×D4—48no—
490C2×D4—48no—
491C2×D4—48no—
492C2×D4—48no—
493C2×D4—48no—
494C2×D4—48no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4C22⋊Q8116yescomplemented
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—21no—
531C22×C4—24no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—216no—
551C22×C4—216no—
552C22×C4—216no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—24no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—416no—
582C22×C4—416no—
583C22×C4—416no—
584C22×C4—48no—
585C22×C4—48no—
586C22×C4—48no—
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—88no—
596C22×C4—88no—
597C22×C4—88no—
598C22×C4—88no—
599C22×C4C22×D414yes—
600C22×C4C22×D418yes—
601C22×C4C22×D414yes—
602C22×C4C22×D412yes—
603C22×C4C22×D414yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×Q812yes—
613C22×C4C22×Q812yes—
614C22×C4C22×Q812yes—
615C22×C4C2×#4112yes—
616C22×C4C2×#4112yes—
617C22×C4C2×#4112yes—
618C22×C4C2×#4112yes—
619C22×C4C2×#4112yes—
620C22×C4C2×#4112yes—
621C22×C4C2×#4112yes—
622C22×C4H(5,𝔽2)12yes—
623C22×C4H(5,𝔽2)12yes—
624C22×C4H(5,𝔽2)12yes—
625C22×C4H(5,𝔽2)12yes—
626C22×C42−1+412yes—
627C22×C42−1+412yes—
628C4⋊C4—28no—
629C4⋊C4—28no—
630C4⋊C4—216no—
631C4⋊C4—216no—
632C4⋊C4—48no—
633C4⋊C4—416no—
634C4⋊C4—48no—
635C4⋊C4—48no—
636C4⋊C4—416no—
637C4⋊C4—416no—
638C4⋊C4—44no—
639C4⋊C4—48no—
640C4⋊C4—44no—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C4⋊C4—44no—
644C4⋊C4—84no—
645C4⋊C4—88no—
646C22⋊C4—216no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—416no—
650C22⋊C4—48no—
651C22⋊C4—48no—
652C22⋊C4—416no—
653C22⋊C4—416no—
654C22⋊C4—48no—
655C22⋊C4—88no—
656C22⋊C4—88no—
657C22⋊C4—88no—
658C22⋊C4—88no—
659C42—28no—
660C42—28no—
661C42—28no—
662C42—44no—
663C42—44no—
664C42—48no—
665C42—44no—
666C42—48no—
667C42#121116yes—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
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—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—42no—
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—
734C23—42no—
735C23—42no—
736C23—42no—
737C23C2×C22⋊Q818yes—
738C23C23×D411yescharacteristic
739C23C23×D411yescharacteristic
740C23C23×D411yescharacteristic
741C23C23×Q811yescharacteristic
742C23C22×#4111yescharacteristic
743C23C22×#4111yescharacteristic
744C23C22×#4111yescharacteristic
745C23C2×H(5,𝔽2)11yescharacteristic
746C23C2×H(5,𝔽2)11yescharacteristic
747C23C2×H(5,𝔽2)11yescharacteristic
748C23C2×H(5,𝔽2)11yescharacteristic
749C23C2×2−1+411yescharacteristic
750C23C2×2−1+411yescharacteristic
751C23#58511yescharacteristic
752C23#58511yescharacteristic
753Q8—416no—
754D4—232no—
755D4—432no—
756D4—432no—
757D4—416no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—28no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—28no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—28no—
789C2×C4—22no—
790C2×C4—24no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—44no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—44no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—432no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—44no—
823C2×C4—42no—
824C2×C4—44no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—44no—
838C2×C4—42no—
839C2×C4—44no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—832no—
848C2×C4—816no—
849C2×C4C2×#12114yes—
850C2×C4C2×#12114yes—
851C2×C4C2×#12114yes—
852C2×C4C2×C22⋊Q814yes—
853C2×C4#53214yes—
854C2×C4#53714yes—
855C2×C4#54014yes—
856C2×C4D4214yes—
857C2×C4D4214yes—
858C2×C4#54614yes—
859C2×C4#54614yes—
860C2×C4D4×Q814yes—
861C2×C4D4×Q814yes—
862C2×C4#55014yes—
863C2×C4#55214yes—
864C2×C4#55414yes—
865C2×C4#55414yes—
866C22—28no—
867C22—28no—
868C22—28no—
869C22—44no—
870C22—44no—
871C22—44no—
872C22—44no—
873C22—44no—
874C22—44no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—44no—
880C22—44no—
881C22—44no—
882C22—44no—
883C22—44no—
884C22—44no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—82no—
889C22—82no—
890C22—82no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—82no—
895C22—82no—
896C22C22×#12111yescharacteristic
897C22C22×C22⋊Q811yescharacteristic
898C22C2×#53211yescharacteristic
899C22C2×#53711yescharacteristic
900C22C2×#54011yescharacteristic
901C22C2×D4211yescharacteristic
902C22C2×D4211yescharacteristic
903C22C2×#54611yescharacteristic
904C22C2×#54611yescharacteristic
905C22C2×D4×Q811yescharacteristic
906C22C2×D4×Q811yescharacteristic
907C22C2×#55011yescharacteristic
908C22D4×#4111yescharacteristic
909C22C2×#55211yescharacteristic
910C22C2×#55411yescharacteristic
911C22C2×#55411yescharacteristic
912C22#347511yescharacteristic
913C22#348811yescharacteristic
914C22#348911yescharacteristic
915C22#349611yescharacteristic
916C22#349711yescharacteristic
917C22#349711yescharacteristic
918C22#349811yescharacteristic
919C22#350111yescharacteristic
920C22#350111yescharacteristic
921C22#350711yescharacteristic
922C22#351111yescharacteristic
923C22#351111yescharacteristic
924C22#351211yescharacteristic
925C22#351911yescharacteristic
926C22#352011yescharacteristic
927C22#354611yescharacteristic
928C22#354611yescharacteristic
929C22#354811yescharacteristic
930C22#355011yescharacteristic
931C4—24no—
932C4—24no—
933C4—24no—
934C4—48no—
935C4—44no—
936C4—42no—
937C4—44no—
938C4—44no—
939C4—42no—
940C4—82no—
941C4—82no—
942C4—84no—
943C4—82no—
944C4#241718yescomplemented
945C4#242818yes—
946C2—48no—
947C2—84no—
948C2C2×#242811yescharacteristic
949C2C2×#241711yescharacteristic
950C2#3556411yescharacteristic
951C2D4×C22⋊Q811yescharacteristic
952C2#3615411yescharacteristic
953C2#3627011yescharacteristic
954C2#3655911yescharacteristic
955C2#3897511yescharacteristic
956C2#3934111yescharacteristic
957C2#3946811yescharacteristic
958C2#3963411yescharacteristic
959C2#5941011yescharacteristic
960C2#5941211yescharacteristic
961C2#5981711yescharacteristic
962C2#5982311yescharacteristic
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×#2538C2semidirect
2. C2×#2538C2semidirect
3. C2×#2417C2semidirect
4. C2×D4×C4⋊C4C2semidirect
6. #15507C2semidirect
7. #15309C2semidirect
8. #15181C2semidirect
9. #15177C2semidirect
10. #15141C2semidirect
11. #15137C2semidirect
12. #14712C2semidirect
14. #13920C2semidirect
15. #13906C2semidirect
16. #13872C2semidirect
17. C4×#391C2semidirect
98. C2×#127Q8semidirect
171. #391D4semidirect
190. #384D4semidirect
501. C2×D4C22⋊Q8semidirect
944. C4#2417semidirect

Maximal subgroups

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

subgroupindex
C2×#25382
C2×#24172
C2×D4×C4⋊C42
C2×C4×#1272
#155072
#153092
#151812
#151772
#151412
#151372
#147122
#140252
#139202
#139062
#138722
C4×#3912