Finite Group Databasebeta

← #674387

Subgroups — #674387

Order 512.

4086 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C2×#2546C211yesmaximal, characteristic, complemented
3C2×#2542C212yesmaximal, complemented
4C2×#2542C211yesmaximal, characteristic, complemented
5C2×#2538C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
7C2×C4×#121C211yesmaximal, characteristic
8#15765C214yesmaximal, complemented
9#15505C214yesmaximal, complemented
10#15178C212yesmaximal, complemented
11#15177C212yesmaximal, complemented
12#15148C212yesmaximal, complemented
13#15135C212yesmaximal, complemented
14#13998C212yesmaximal
15#13997C212yesmaximal, complemented
16#13910C212yesmaximal, complemented
17C4⋊C42C211yesmaximal, characteristic, complemented
18C22×C4⋊Q8C2211yescharacteristic
19C22×C4⋊Q8C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×C22⋊Q8C2212yes—
22C22×C22⋊Q8C2212yes—
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2212yes—
25C22×#121C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2212yes—
29C23×C42C2211yescharacteristic
30#2857—28no—
31#2546—28no—
32#2542—28no—
33#2542—216no—
34#2538—28no—
35C2×#399C2214yes—
36C2×#399C2214yes—
37C2×#399C2214yes—
38C2×#398C2214yes—
39C2×#396C2214yes—
40C4×C22⋊Q8—28no—
41C4×#121—28no—
42C2×#391C2212yes—
43C2×#391C2212yes—
44C2×#391C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2212yes—
47C2×#390C2212yes—
48C2×#390C2214yes—
49C2×#389C2212yes—
50C2×#389C2212yes—
51C2×#389C2212yes—
52C2×#389C2212yes—
53C2×#389C2211yescharacteristic
54C2×#389C2212yes—
55C2×#389C2211yescharacteristic
56C2×#388C2212yes—
57C2×#387C2212yes—
58C2×#386C2212yes—
59C2×#385C2212yes—
60C2×#384C2212yes—
61C2×#384C2214yes—
62C2×#384C2211yescharacteristic
63C2×#380C2212yes—
64C2×#380C2212yes—
65C2×#380C2211yescharacteristic
66C2×#380C2211yescharacteristic
67C2×#380C2212yes—
68C2×C4×C4⋊C4C2212yes—
69C2×C4×C4⋊C4C2212yes—
70C2×C4×C4⋊C4C2212yes—
71C2×C4×C4⋊C4C2211yescharacteristic
72C2×C4×C4⋊C4C2211yescharacteristic
73C2×C4×C22⋊C4C2212yes—
74C2×C4×C22⋊C4C2212yes—
75#1445C2214yes—
76#1444C2214yes—
77#1444C2214yes—
78#1444C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1438C2214yes—
85#1437C2214yes—
86#1436C2214yes—
87C4⋊#95C2212yes—
88C4⋊#95C2212yes—
89C4⋊#95C2214yes—
90C23×Q8C2312yes—
91C23×Q8C2311yescharacteristic
92C23×D4C2311yescharacteristic
93C23×D4C2312yes—
94C24×C4C2312yes—
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C2×C4⋊Q8—28no—
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—28no—
102C2×C4⋊Q8—24no—
103C2×C4⋊Q8—44no—
104C2×C22⋊Q8—28no—
105C2×C22⋊Q8—28no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8—28no—
108C2×C22⋊Q8—28no—
109C2×C22⋊Q8—28no—
110C2×C22⋊Q8—28no—
111C2×C22⋊Q8—28no—
112C2×C22⋊Q8—24no—
113C2×C22⋊Q8—28no—
114C2×C22⋊Q8—44no—
115C2×C22⋊Q8—44no—
116C2×C22⋊Q8—44no—
117C2×C22⋊Q8—44no—
118C2×C22⋊Q8D418yescomplemented
119C2×#121—24no—
120C2×#121—24no—
121C2×#121Q818yescomplemented
122C2×C4×Q8—24no—
123C2×C4×Q8—24no—
124C2×C4×Q8—24no—
125C2×C4×D4—28no—
126C2×C4×D4—24no—
127C2×C4×D4—24no—
128C2×C4×D4—28no—
129C2×C4×D4—24no—
130C2×C4×D4—44no—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2314yes—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2314yes—
138C22×C4⋊C4C2314yes—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2314yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2314yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C42—24no—
165C22×C42—24no—
166C22×C42—24no—
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2312yes—
171C22×C42C2314yes—
172C22×C42C2312yes—
173C22×C42C2312yes—
174C22×C42C2311yescharacteristic
175#399—216no—
176#399—216no—
177#399—216no—
178#398—216no—
179#396—216no—
180#391—28no—
181#391—24no—
182#391—28no—
183#390—28no—
184#390—24no—
185#390—216no—
186#390—28no—
187#389—28no—
188#389—28no—
189#389—28no—
190#389—28no—
191#389—28no—
192#389—24no—
193#389—24no—
194#388—28no—
195#387—28no—
196#386—28no—
197#385—28no—
198#384—216no—
199#384—28no—
200#384D418yescomplemented
201#380—28no—
202#380—28no—
203#380—28no—
204#380—24no—
205#380—24no—
206C4×C4⋊C4—28no—
207C4×C4⋊C4—28no—
208C4×C4⋊C4—28no—
209C4×C4⋊C4D418yes—
210C4×C4⋊C4D418yescomplemented
211C4×C22⋊C4—28no—
212C4×C22⋊C4—28no—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2312yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2312yes—
221C2×#95C2314yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2314yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C25C2412yes—
230C25C2411yescharacteristic
231C22×Q8—22no—
232C22×Q8—22no—
233C22×Q8—22no—
234C22×Q8—24no—
235C22×Q8—24no—
236C22×Q8—24no—
237C22×Q8—24no—
238C22×Q8—22no—
239C22×Q8—24no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—24no—
243C22×Q8—24no—
244C22×Q8C2×D414yes—
245C22×D4—24no—
246C22×D4—24no—
247C22×D4—24no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—24no—
252C22×D4—22no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—42no—
256C22×D4—42no—
257C22×D4C2×Q814yes—
258C22×D4C2×Q818yes—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—24no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—24no—
281C23×C4—24no—
282C23×C4—24no—
283C23×C4—41no—
284C23×C4—41no—
285C23×C4C2×D414yes—
286C23×C4C2×Q814yes—
287C23×C4C2414yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2414yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C4⋊Q8—432no—
303C4⋊Q8—416no—
304C22⋊Q8—232no—
305C22⋊Q8—432no—
306C22⋊Q8—432no—
307C22⋊Q8—432no—
308C22⋊Q8—432no—
309#121—232no—
310C4×Q8—416no—
311C4×D4—432no—
312C4×D4—416no—
313C2×C4⋊C4—24no—
314C2×C4⋊C4—24no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—22no—
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—28no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—28no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—28no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—44no—
364C2×C4⋊C4C2×D414yes—
365C2×C4⋊C4C2×D418yes—
366C2×C4⋊C4C2×D418yes—
367C2×C4⋊C4C2×D414yes—
368C2×C4⋊C4C2×D418yes—
369C2×C4⋊C4C2×D418yes—
370C2×C4⋊C4C2×D414yes—
371C2×C4⋊C4C2×D414yes—
372C2×C4⋊C4C2×D414yes—
373C2×C4⋊C4C2×Q814yes—
374C2×C4⋊C4#4114yes—
375C2×C4⋊C4#4114yes—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—28no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4C2×D418yes—
411C2×C22⋊C4C2×Q818yes—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—24no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—28no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—28no—
430C2×C42—44no—
431C2×C42—416no—
432C2×C42C2×D418yes—
433C2×C42C2×D418yes—
434C2×C42C2×D414yes—
435C2×C42C2×D414yes—
436C2×C42C2×D414yes—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—28no—
444#95—28no—
445#95—28no—
446#95—28no—
447#95—28no—
448#95—28no—
449#95—28no—
450#95—44no—
451#95C2×D418yes—
452#95C2×D418yes—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—21no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24C22×D412yes—
480C24C22×Q814yes—
481C24C22×Q812yes—
482C242−1+412yes—
483C24C2511yescharacteristic
484C2×Q8—28no—
485C2×Q8—28no—
486C2×Q8—28no—
487C2×Q8—48no—
488C2×Q8—44no—
489C2×Q8—48no—
490C2×Q8—44no—
491C2×Q8—48no—
492C2×Q8—48no—
493C2×Q8—48no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—48no—
497C2×Q8—48no—
498C2×D4—216no—
499C2×D4—216no—
500C2×D4—28no—
501C2×D4—28no—
502C2×D4—28no—
503C2×D4—48no—
504C2×D4—48no—
505C2×D4—48no—
506C2×D4—48no—
507C2×D4—48no—
508C2×D4—44no—
509C2×D4—44no—
510C2×D4—44no—
511C2×D4—44no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—28no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—24no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—24no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—24no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—22no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4—44no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—44no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—48no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4C22×D414yes—
616C22×C4C22×D414yes—
617C22×C4C22×D418yes—
618C22×C4C22×D414yes—
619C22×C4C22×D412yes—
620C22×C4C22×D414yes—
621C22×C4C22×D414yes—
622C22×C4C22×D414yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C22×D412yes—
630C22×C4C22×D412yes—
631C22×C4C22×D412yes—
632C22×C4C22×D412yes—
633C22×C4C22×Q812yes—
634C22×C4C22×Q814yes—
635C22×C4C22×Q812yes—
636C22×C4C2×#4114yes—
637C22×C4C2×#4114yes—
638C22×C4C2×#4112yes—
639C22×C4C2×#4112yes—
640C22×C4H(5,𝔽2)12yes—
641C22×C4H(5,𝔽2)12yes—
642C22×C42−1+412yes—
643C22×C42−1+412yes—
644C22×C42−1+412yes—
645C4⋊C4—216no—
646C4⋊C4—28no—
647C4⋊C4—28no—
648C4⋊C4—216no—
649C4⋊C4—216no—
650C4⋊C4—48no—
651C4⋊C4—48no—
652C4⋊C4—48no—
653C4⋊C4—416no—
654C4⋊C4—416no—
655C4⋊C4—416no—
656C4⋊C4—416no—
657C4⋊C4—416no—
658C4⋊C4—416no—
659C4⋊C4—44no—
660C4⋊C4—48no—
661C4⋊C4—44no—
662C4⋊C4—48no—
663C4⋊C4—48no—
664C4⋊C4#121116yescomplemented
665C4⋊C4C22⋊Q8116yescomplemented
666C22⋊C4—216no—
667C22⋊C4—216no—
668C22⋊C4—48no—
669C22⋊C4—48no—
670C22⋊C4—416no—
671C22⋊C4—48no—
672C22⋊C4—48no—
673C22⋊C4—416no—
674C22⋊C4—416no—
675C22⋊C4—416no—
676C22⋊C4—48no—
677C22⋊C4—88no—
678C42—216no—
679C42—216no—
680C42—416no—
681C42—44no—
682C42—44no—
683C42—44no—
684C42—48no—
685C42#127116yes—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—24no—
710C23—24no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—41no—
726C23—41no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—42no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23D4×Q814yes—
756C23C23×D411yescharacteristic
757C23C23×D411yescharacteristic
758C23C23×D411yescharacteristic
759C23C23×D411yescharacteristic
760C23C23×Q811yescharacteristic
761C23C22×#4111yescharacteristic
762C23C22×#4111yescharacteristic
763C23C2×H(5,𝔽2)11yescharacteristic
764C23C2×H(5,𝔽2)11yescharacteristic
765C23C2×2−1+411yescharacteristic
766C23C2×2−1+411yescharacteristic
767C23C2×2−1+411yescharacteristic
768C23C2×2−1+411yescharacteristic
769C23#58511yescharacteristic
770C23#58511yescharacteristic
771Q8—416no—
772Q8—816no—
773D4—432no—
774D4—416no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—28no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—22no—
803C2×C4—24no—
804C2×C4—24no—
805C2×C4—28no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—28no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—416no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—42no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—44no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—44no—
843C2×C4—416no—
844C2×C4—416no—
845C2×C4—44no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—44no—
854C2×C4—42no—
855C2×C4—44no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—816no—
867C2×C4C2×#12118yes—
868C2×C4C2×#12114yes—
869C2×C4C2×C22⋊Q818yes—
870C2×C4C2×C22⋊Q814yes—
871C2×C4C2×#12714yes—
872C2×C4C2×#12714yes—
873C2×C4C2×#12714yes—
874C2×C4#53514yes—
875C2×C4#53614yes—
876C2×C4D4214yes—
877C2×C4D4214yes—
878C2×C4#54714yes—
879C2×C4#54714yes—
880C2×C4D4×Q814yes—
881C2×C4D4×Q814yes—
882C2×C4#55014yes—
883C2×C4#55014yes—
884C22—24no—
885C22—24no—
886C22—24no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—44no—
900C22—44no—
901C22—44no—
902C22—44no—
903C22—44no—
904C22—44no—
905C22—44no—
906C22—82no—
907C22—82no—
908C22—82no—
909C22—82no—
910C22—82no—
911C22—82no—
912C22—82no—
913C22—82no—
914C22C22×#12111yescharacteristic
915C22C22×C22⋊Q811yescharacteristic
916C22C22×#12711yescharacteristic
917C22C2×#53511yescharacteristic
918C22C2×#53611yescharacteristic
919C22C2×D4211yescharacteristic
920C22C2×D4211yescharacteristic
921C22C2×#54711yescharacteristic
922C22C2×#54711yescharacteristic
923C22C2×D4×Q811yescharacteristic
924C22C2×D4×Q811yescharacteristic
925C22C2×D4×Q811yescharacteristic
926C22C2×#55011yescharacteristic
927C22C2×#55011yescharacteristic
928C22D4×#4111yescharacteristic
929C22Q8×#4111yescharacteristic
930C22#348211yescharacteristic
931C22#348511yescharacteristic
932C22#348611yescharacteristic
933C22#348911yescharacteristic
934C22#348911yescharacteristic
935C22#348911yescharacteristic
936C22#348911yescharacteristic
937C22#349711yescharacteristic
938C22#349911yescharacteristic
939C22#350111yescharacteristic
940C22#350311yescharacteristic
941C22#351511yescharacteristic
942C22#351711yescharacteristic
943C22#352011yescharacteristic
944C22#352311yescharacteristic
945C22#354711yescharacteristic
946C22#355011yescharacteristic
947C22#355211yescharacteristic
948C22#355411yescharacteristic
949C4—24no—
950C4—28no—
951C4—28no—
952C4—44no—
953C4—42no—
954C4—42no—
955C4—44no—
956C4—42no—
957C4—44no—
958C4—48no—
959C4—82no—
960C4—82no—
961C4—84no—
962C4#254118yes—
963C4#254218yescomplemented
964C2—44no—
965C2—84no—
966C2C2×#254111yescharacteristic
967C2C2×#254211yescharacteristic
968C2#3563411yescharacteristic
969C2D4×C22⋊Q811yescharacteristic
970C2#3625911yescharacteristic
971C2#3644511yescharacteristic
972C2Q8×#12111yescharacteristic
973C2#3892011yescharacteristic
974C2#3913911yescharacteristic
975C2#3934311yescharacteristic
976C2#3959611yescharacteristic
977C2#5905211yescharacteristic
978C2#5905511yescharacteristic
979C2#5906611yescharacteristic
980C2#5912711yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#2857C2semidirect
2. C2×#2546C2semidirect
3. C2×#2542C2semidirect
4. C2×#2542C2semidirect
5. C2×#2538C2semidirect
6. C2×C4×C22⋊Q8C2semidirect
8. #15765C2semidirect
9. #15505C2semidirect
10. #15178C2semidirect
11. #15177C2semidirect
12. #15148C2semidirect
13. #15135C2semidirect
15. #13997C2semidirect
16. #13910C2semidirect
17. C4⋊C42C2semidirect
118. C2×C22⋊Q8D4semidirect
121. C2×#121Q8semidirect
200. #384D4semidirect
210. C4×C4⋊C4D4semidirect
664. C4⋊C4#121semidirect
665. C4⋊C4C22⋊Q8semidirect
963. C4#2542semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25462
C2×#25422
C2×#25382
C2×C4×C22⋊Q82
C2×C4×#1212
#157652
#155052
#151782
#151772
#151482
#151352
#139982
#139972
#139102
C4⋊C422