Finite Group Databasebeta

← #674167

Subgroups — #674167

Order 512.

3742 conjugacy classes of subgroups.

The subgroup lattice has 945 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C2×#2542C211yesmaximal, characteristic, complemented
3C2×#2538C212yesmaximal, complemented
4C2×#2365C211yesmaximal, characteristic, complemented
5C2×C4×#121C211yesmaximal, characteristic
6#15365C214yesmaximal, complemented
7#15335C214yesmaximal, complemented
8#15182C212yesmaximal, complemented
9#15177C212yesmaximal, complemented
10#15141C212yesmaximal, complemented
11#15131C212yesmaximal, complemented
12#14005C212yesmaximal, complemented
13#13998C212yesmaximal
14#13969C212yesmaximal, complemented
15#13910C211yesmaximal, characteristic, complemented
16#13906C211yesmaximal, characteristic, complemented
17C4×#380C211yesmaximal, characteristic, complemented
18C22×C4⋊Q8C2211yescharacteristic
19C22×C22⋊Q8C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×C22⋊Q8C2212yes—
22C22×#121C2211yescharacteristic
23C22×C4×Q8C2212yes—
24C22×C4×D4C2211yescharacteristic
25C22×C4×D4C2212yes—
26C23×C42C2211yescharacteristic
27#2857—28no—
28#2542—28no—
29#2538—216no—
30C2×#399C2214yes—
31C2×#396C2214yes—
32C2×#396C2214yes—
33#2365—28no—
34C4×#121—28no—
35C2×#391C2212yes—
36C2×#391C2212yes—
37C2×#390C2211yescharacteristic
38C2×#390C2212yes—
39C2×#390C2214yes—
40C2×#390C2212yes—
41C2×#389C2212yes—
42C2×#389C2214yes—
43C2×#389C2212yes—
44C2×#389C2212yes—
45C2×#389C2212yes—
46C2×#389C2211yescharacteristic
47C2×#389C2212yes—
48C2×#388C2212yes—
49C2×#387C2214yes—
50C2×#386C2212yes—
51C2×#384C2211yescharacteristic
52C2×#384C2212yes—
53C2×#384C2212yes—
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2212yes—
59C2×#380C2212yes—
60C2×#380C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2212yes—
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2212yes—
66C2×C4×C22⋊C4C2212yes—
67#1444C2214yes—
68#1444C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1438C2214yes—
79#1437C2214yes—
80#1436C2214yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85#1434C2212yes—
86C22⋊#95C2212yes—
87C4×#95C2212yes—
88C23×Q8C2312yes—
89C23×D4C2311yescharacteristic
90C23×D4C2312yes—
91C24×C4C2312yes—
92C24×C4C2311yescharacteristic
93C24×C4C2311yescharacteristic
94C24×C4C2311yescharacteristic
95C2×C4⋊Q8—24no—
96C2×C4⋊Q8—24no—
97C2×C4⋊Q8D418yescomplemented
98C2×C22⋊Q8—28no—
99C2×C22⋊Q8—28no—
100C2×C22⋊Q8—28no—
101C2×C22⋊Q8—28no—
102C2×C22⋊Q8—28no—
103C2×C22⋊Q8—28no—
104C2×C22⋊Q8—44no—
105C2×C22⋊Q8—44no—
106C2×C22⋊Q8—44no—
107C2×#121—24no—
108C2×#121—24no—
109C2×#121Q818yescomplemented
110C2×C4×Q8—28no—
111C2×C4×Q8—28no—
112C2×C4×Q8—44no—
113C2×C4×D4—28no—
114C2×C4×D4—24no—
115C2×C4×D4—28no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—44no—
119C22×C4⋊C4C2311yescharacteristic
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2314yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2314yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2311yescharacteristic
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2311yescharacteristic
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2314yes—
148C22×C22⋊C4C2314yes—
149C22×C22⋊C4C2312yes—
150C22×C42—24no—
151C22×C42—24no—
152C22×C42—24no—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157C22×C42C2312yes—
158C22×C42C2314yes—
159C22×C42C2312yes—
160C22×C42C2311yescharacteristic
161#399—216no—
162#396—216no—
163#396—216no—
164#391—28no—
165#391—28no—
166#390—28no—
167#390—24no—
168#390—216no—
169#390—44no—
170#389—28no—
171#389—28no—
172#389—28no—
173#389—24no—
174#389—28no—
175#389—216no—
176#389—44no—
177#388—28no—
178#387—216no—
179#386—28no—
180#384—28no—
181#384—28no—
182#384—24no—
183#380—28no—
184#380—28no—
185#380—28no—
186#380—24no—
187#380—24no—
188#380—44no—
189#380D418yescomplemented
190C4×C4⋊C4—28no—
191C4×C4⋊C4—24no—
192C4×C4⋊C4—24no—
193C4×C4⋊C4D418yes—
194C4×C22⋊C4—28no—
195C4×C22⋊C4—44no—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2314yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C25C2412yes—
216C25C2411yescharacteristic
217C22×Q8—24no—
218C22×Q8—24no—
219C22×Q8—24no—
220C22×Q8—24no—
221C22×Q8—24no—
222C22×Q8—24no—
223C22×Q8C2×D418yes—
224C22×D4—24no—
225C22×D4—24no—
226C22×D4—24no—
227C22×D4—22no—
228C22×D4—22no—
229C22×D4—22no—
230C22×D4—24no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—42no—
235C22×D4—42no—
236C22×D4C2×Q814yes—
237C22×D4C2×Q818yes—
238C23×C4—22no—
239C23×C4—22no—
240C23×C4—22no—
241C23×C4—22no—
242C23×C4—22no—
243C23×C4—22no—
244C23×C4—22no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—22no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—22no—
251C23×C4—22no—
252C23×C4—22no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—22no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—22no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—41no—
263C23×C4—41no—
264C23×C4C2×D414yes—
265C23×C4C2×Q814yes—
266C23×C4C2414yes—
267C23×C4C2412yes—
268C23×C4C2412yes—
269C23×C4C2412yes—
270C23×C4C2414yes—
271C23×C4C2412yes—
272C23×C4C2412yes—
273C23×C4C2411yescharacteristic
274C23×C4C2411yescharacteristic
275C23×C4C2412yes—
276C23×C4C2411yescharacteristic
277C23×C4C2411yescharacteristic
278C23×C4C2412yes—
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C4⋊Q8—232no—
282C22⋊Q8—432no—
283C22⋊Q8—432no—
284C22⋊Q8—432no—
285#121—232no—
286C4×Q8—432no—
287C4×D4—432no—
288C4×D4—416no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—22no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—22no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—28no—
310C2×C4⋊C4—28no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—28no—
313C2×C4⋊C4—28no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—28no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—28no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—44no—
332C2×C4⋊C4—44no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4—44no—
337C2×C4⋊C4C2×D414yes—
338C2×C4⋊C4C2×D414yes—
339C2×C4⋊C4C2×D418yes—
340C2×C4⋊C4C2×D418yes—
341C2×C4⋊C4C2×D414yes—
342C2×C4⋊C4C2×D414yes—
343C2×C4⋊C4C2×Q814yes—
344C2×C4⋊C4#4114yes—
345C2×C4⋊C4#4114yes—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—24no—
349C2×C22⋊C4—28no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—28no—
358C2×C22⋊C4—28no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—28no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—44no—
372C2×C22⋊C4—44no—
373C2×C22⋊C4—42no—
374C2×C22⋊C4—42no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—44no—
377C2×C22⋊C4—44no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—44no—
380C2×C22⋊C4C2×D418yes—
381C2×C22⋊C4C2×Q818yes—
382C2×C42—24no—
383C2×C42—24no—
384C2×C42—28no—
385C2×C42—28no—
386C2×C42—22no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—24no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—44no—
402C2×C42—416no—
403C2×C42C2×D418yes—
404C2×C42C2×D414yes—
405C2×C42C2×D414yes—
406C2×C42#4114yes—
407#95—24no—
408#95—24no—
409#95—24no—
410#95—28no—
411#95—24no—
412#95—28no—
413#95—28no—
414#95—28no—
415#95—28no—
416#95—24no—
417#95—28no—
418#95—24no—
419#95—42no—
420#95—42no—
421#95—42no—
422#95—44no—
423#95—44no—
424#95C2×D418yes—
425#95C2×D418yes—
426C24—21no—
427C24—21no—
428C24—21no—
429C24—21no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—21no—
435C24—21no—
436C24—21no—
437C24—21no—
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—
452C24C22×D412yes—
453C24C22×Q814yes—
454C24C22×Q812yes—
455C242−1+412yes—
456C24C2511yescharacteristic
457C2×Q8—216no—
458C2×Q8—216no—
459C2×Q8—216no—
460C2×Q8—48no—
461C2×Q8—48no—
462C2×Q8—48no—
463C2×Q8—48no—
464C2×D4—216no—
465C2×D4—216no—
466C2×D4—28no—
467C2×D4—28no—
468C2×D4—28no—
469C2×D4—48no—
470C2×D4—48no—
471C2×D4—48no—
472C2×D4—48no—
473C2×D4—48no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—44no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—22no—
486C22×C4—28no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—24no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—24no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—44no—
563C22×C4—44no—
564C22×C4—44no—
565C22×C4—44no—
566C22×C4—44no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—44no—
574C22×C4—44no—
575C22×C4—44no—
576C22×C4—48no—
577C22×C4—48no—
578C22×C4—48no—
579C22×C4—48no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—48no—
583C22×C4C22×D414yes—
584C22×C4C22×D414yes—
585C22×C4C22×D418yes—
586C22×C4C22×D412yes—
587C22×C4C22×D414yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D414yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×Q812yes—
597C22×C4C22×Q814yes—
598C22×C4C22×Q812yes—
599C22×C4C2×#4114yes—
600C22×C4C2×#4112yes—
601C22×C4C2×#4114yes—
602C22×C4C2×#4112yes—
603C22×C4C2×#4112yes—
604C22×C4C2×#4112yes—
605C22×C4C2×#4112yes—
606C22×C4H(5,𝔽2)12yes—
607C22×C4H(5,𝔽2)12yes—
608C22×C4H(5,𝔽2)12yes—
609C22×C42−1+412yes—
610C22×C42−1+412yes—
611C4⋊C4—216no—
612C4⋊C4—216no—
613C4⋊C4—28no—
614C4⋊C4—28no—
615C4⋊C4—28no—
616C4⋊C4—28no—
617C4⋊C4—416no—
618C4⋊C4—48no—
619C4⋊C4—416no—
620C4⋊C4—416no—
621C4⋊C4—416no—
622C4⋊C4—416no—
623C4⋊C4—48no—
624C4⋊C4—44no—
625C4⋊C4—48no—
626C4⋊C4—44no—
627C4⋊C4—48no—
628C4⋊C4—88no—
629C4⋊C4C22⋊Q8116yescomplemented
630C22⋊C4—216no—
631C22⋊C4—48no—
632C22⋊C4—48no—
633C22⋊C4—48no—
634C22⋊C4—416no—
635C22⋊C4—416no—
636C22⋊C4—48no—
637C22⋊C4—48no—
638C22⋊C4—416no—
639C22⋊C4—48no—
640C22⋊C4—88no—
641C22⋊C4—88no—
642C42—216no—
643C42—416no—
644C42—44no—
645C42—44no—
646C42—44no—
647C42—48no—
648C42—48no—
649C42#121116yes—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
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—
710C23—42no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23D4×Q814yes—
720C23C23×D411yescharacteristic
721C23C23×D411yescharacteristic
722C23C23×D411yescharacteristic
723C23C23×Q811yescharacteristic
724C23C22×#4111yescharacteristic
725C23C22×#4111yescharacteristic
726C23C22×#4111yescharacteristic
727C23C2×H(5,𝔽2)11yescharacteristic
728C23C2×H(5,𝔽2)11yescharacteristic
729C23C2×H(5,𝔽2)11yescharacteristic
730C23C2×2−1+411yescharacteristic
731C23C2×2−1+411yescharacteristic
732C23C2×2−1+411yescharacteristic
733C23#58511yescharacteristic
734C23#58511yescharacteristic
735Q8—432no—
736D4—432no—
737D4—416no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—28no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—28no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—28no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—416no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—44no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—44no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—416no—
808C2×C4—416no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—44no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—44no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—44no—
821C2×C4—44no—
822C2×C4—42no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—42no—
830C2×C4—816no—
831C2×C4C2×#12114yes—
832C2×C4C2×#12114yes—
833C2×C4C2×#12114yes—
834C2×C4C2×C22⋊Q818yes—
835C2×C4C2×C22⋊Q814yes—
836C2×C4#53214yes—
837C2×C4#53714yes—
838C2×C4#54014yes—
839C2×C4D4214yes—
840C2×C4D4214yes—
841C2×C4#54614yes—
842C2×C4D4×Q814yes—
843C2×C4#55014yes—
844C2×C4#55014yes—
845C2×C4#55414yes—
846C2×C4#55614yes—
847C22—24no—
848C22—24no—
849C22—24no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—42no—
862C22—44no—
863C22—44no—
864C22—44no—
865C22—44no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—82no—
870C22—82no—
871C22—82no—
872C22—82no—
873C22—82no—
874C22—82no—
875C22—82no—
876C22—82no—
877C22C22×#12111yescharacteristic
878C22C22×C22⋊Q811yescharacteristic
879C22C2×#53211yescharacteristic
880C22C2×#53711yescharacteristic
881C22C2×#54011yescharacteristic
882C22C2×D4211yescharacteristic
883C22C2×D4211yescharacteristic
884C22C2×#54611yescharacteristic
885C22C2×D4×Q811yescharacteristic
886C22C2×D4×Q811yescharacteristic
887C22C2×#55011yescharacteristic
888C22C2×#55011yescharacteristic
889C22D4×#4111yescharacteristic
890C22C2×#55411yescharacteristic
891C22C2×#55611yescharacteristic
892C22Q8×#4111yescharacteristic
893C22#348211yescharacteristic
894C22#348611yescharacteristic
895C22#348711yescharacteristic
896C22#348911yescharacteristic
897C22#348911yescharacteristic
898C22#349511yescharacteristic
899C22#349511yescharacteristic
900C22#349611yescharacteristic
901C22#349911yescharacteristic
902C22#350111yescharacteristic
903C22#350311yescharacteristic
904C22#351711yescharacteristic
905C22#351811yescharacteristic
906C22#352011yescharacteristic
907C22#352011yescharacteristic
908C22#354611yescharacteristic
909C22#354711yescharacteristic
910C22#354811yescharacteristic
911C22#355211yescharacteristic
912C4—24no—
913C4—28no—
914C4—42no—
915C4—42no—
916C4—42no—
917C4—48no—
918C4—44no—
919C4—44no—
920C4—44no—
921C4—44no—
922C4—82no—
923C4—84no—
924C4—82no—
925C4#242818yes—
926C4#253818yescomplemented
927C2—44no—
928C2—84no—
929C2C2×#242811yescharacteristic
930C2C2×#253811yescharacteristic
931C2#3566111yescharacteristic
932C2D4×C22⋊Q811yescharacteristic
933C2#3644511yescharacteristic
934C2#3647311yescharacteristic
935C2#3656111yescharacteristic
936C2#3913611yescharacteristic
937C2#3915611yescharacteristic
938C2#3934011yescharacteristic
939C2#3960611yescharacteristic
940C2#5903611yescharacteristic
941C2#5904011yescharacteristic
942C2#5905111yescharacteristic
943C2#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×#2542C2semidirect
3. C2×#2538C2semidirect
4. C2×#2365C2semidirect
6. #15365C2semidirect
7. #15335C2semidirect
8. #15182C2semidirect
9. #15177C2semidirect
10. #15141C2semidirect
11. #15131C2semidirect
12. #14005C2semidirect
14. #13969C2semidirect
15. #13910C2semidirect
16. #13906C2semidirect
17. C4×#380C2semidirect
97. C2×C4⋊Q8D4semidirect
109. C2×#121Q8semidirect
189. #380D4semidirect
629. C4⋊C4C22⋊Q8semidirect
926. C4#2538semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#25422
C2×#25382
C2×#23652
C2×C4×#1212
#153652
#153352
#151822
#151772
#151412
#151312
#140052
#139982
#139692
#139102
#139062
C4×#3802