Finite Group Databasebeta

← #759798

Subgroups — #759798

Order 512.

3770 conjugacy classes of subgroups.

The subgroup lattice has 935 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2547C211yesmaximal, characteristic, complemented
2C2×#2542C211yesmaximal, characteristic, complemented
3C2×#2537C211yesmaximal, characteristic
4C2×#2426C212yesmaximal, complemented
5C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
6#16549C214yesmaximal, complemented
7#15215C212yesmaximal, complemented
8#15179C212yesmaximal, complemented
9#15131C212yesmaximal, complemented
10#15126C212yesmaximal, complemented
11#14778C214yesmaximal, complemented
12#14151C211yesmaximal, characteristic, complemented
13#13998C212yesmaximal, complemented
14#13969C212yesmaximal, complemented
15#13876C212yesmaximal, complemented
16C4×#390C211yesmaximal, characteristic, complemented
17C4×#390C211yesmaximal, characteristic, complemented
18C22×C4⋊Q8C2211yescharacteristic
19C22×#124C2212yes—
20C22×C22⋊Q8C2212yes—
21C22×C22⋊Q8C2212yes—
22C22×#121C2212yes—
23C22×#121C2212yes—
24C22×C4×Q8C2212yes—
25C22×C4×D4C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27#2547—28no—
28#2542—28no—
29#2537—28no—
30#2426—216no—
31C2×#399C2214yes—
32C2×#397C2214yes—
33C2×#396C2214yes—
34C2×#394C2214yes—
35C2×#394C2214yes—
36C4×C4⋊Q8—28no—
37C2×#391C2212yes—
38C2×#391C2212yes—
39C2×#390C2211yescharacteristic
40C2×#390C2212yes—
41C2×#390C2211yescharacteristic
42C2×#390C2214yes—
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#389C2212yes—
46C2×#389C2212yes—
47C2×#389C2212yes—
48C2×#389C2212yes—
49C2×#388C2214yes—
50C2×#384C2212yes—
51C2×#384C2211yescharacteristic
52C2×#380C2212yes—
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×C4×C4⋊C4C2212yes—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C4⋊C4C2212yes—
60C2×C4×C22⋊C4C2212yes—
61C2×C4×C22⋊C4C2212yes—
62C2×C4×C22⋊C4C2212yes—
63C2×C4×C22⋊C4C2212yes—
64C2×C43C2211yescharacteristic
65#1442C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1440C2214yes—
70#1439C2214yes—
71#1439C2214yes—
72#1439C2214yes—
73#1439C2214yes—
74#1438C2214yes—
75#1438C2214yes—
76#1437C2214yes—
77#1437C2212yes—
78#1437C2212yes—
79#1437C2212yes—
80#1437C2212yes—
81#1436C2214yes—
82C4⋊#95C2212yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2212yes—
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C23×Q8C2312yes—
89C23×D4C2311yescharacteristic
90C23×D4C2311yescharacteristic
91C23×D4C2314yes—
92C24×C4C2312yes—
93C24×C4C2312yes—
94C2×C4⋊Q8—24no—
95C2×C4⋊Q8—24no—
96C2×C4⋊Q8D418yescomplemented
97C2×#124—28no—
98C2×#124—28no—
99C2×#124—44no—
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×#121—28no—
107C2×#121—28no—
108C2×#121—28no—
109C2×#121—28no—
110C2×#121—44no—
111C2×#121—44no—
112C2×C4×Q8—28no—
113C2×C4×Q8—28no—
114C2×C4×Q8—44no—
115C2×C4×D4—24no—
116C2×C4×D4—24no—
117C2×C4×D4—24no—
118C2×C4×D4—24no—
119C2×C4×D4—24no—
120C2×C4×D4—24no—
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2311yescharacteristic
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2314yes—
127C22×C4⋊C4C2314yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2312yes—
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2311yescharacteristic
132C22×C4⋊C4C2312yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2314yes—
135C22×C4⋊C4C2312yes—
136C22×C22⋊C4C2312yes—
137C22×C22⋊C4C2312yes—
138C22×C22⋊C4C2312yes—
139C22×C22⋊C4C2312yes—
140C22×C22⋊C4C2314yes—
141C22×C22⋊C4C2314yes—
142C22×C22⋊C4C2314yes—
143C22×C22⋊C4C2314yes—
144C22×C22⋊C4C2314yes—
145C22×C22⋊C4C2314yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2312yes—
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C42C2312yes—
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2312yes—
156C22×C42C2311yescharacteristic
157C22×C42C2314yes—
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2311yescharacteristic
161C22×C42C2311yescharacteristic
162#399—216no—
163#397—216no—
164#396—216no—
165#394—216no—
166#394—216no—
167#391—28no—
168#391—28no—
169#390—24no—
170#390—28no—
171#390—24no—
172#390—216no—
173#390—24no—
174#390D418yescomplemented
175#389—28no—
176#389—28no—
177#389—28no—
178#389—44no—
179#388—216no—
180#384—28no—
181#384D418yes—
182#380—28no—
183#380—28no—
184#380—28no—
185#380—28no—
186C4×C4⋊C4—28no—
187C4×C4⋊C4—28no—
188C4×C4⋊C4—24no—
189C4×C4⋊C4—24no—
190C4×C22⋊C4—28no—
191C4×C22⋊C4—28no—
192C4×C22⋊C4—44no—
193C4×C22⋊C4—44no—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C43—24no—
213C25C2412yes—
214C25C2412yes—
215C22×Q8—24no—
216C22×Q8—24no—
217C22×Q8—24no—
218C22×Q8—24no—
219C22×Q8—24no—
220C22×Q8—24no—
221C22×Q8C2×D418yes—
222C22×D4—28no—
223C22×D4—28no—
224C22×D4—22no—
225C22×D4—22no—
226C22×D4—22no—
227C22×D4—22no—
228C22×D4—28no—
229C22×D4—22no—
230C22×D4—22no—
231C22×D4—22no—
232C22×D4—22no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—44no—
238C22×D4—44no—
239C22×D4—44no—
240C22×D4—44no—
241C22×D4C2×D414yes—
242C22×D4#4114yes—
243C23×C4—24no—
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×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2412yes—
261C23×C4C2414yes—
262C23×C4C2412yes—
263C23×C4C2411yescharacteristic
264C23×C4C2414yes—
265C23×C4C2412yes—
266C23×C4C2411yescharacteristic
267C23×C4C2411yescharacteristic
268C23×C4C2411yescharacteristic
269C23×C4C2411yescharacteristic
270C23×C4C2411yescharacteristic
271C23×C4C2411yescharacteristic
272C4⋊Q8—232no—
273#124—432no—
274C22⋊Q8—432no—
275C22⋊Q8—432no—
276#121—432no—
277#121—432no—
278C4×Q8—432no—
279C4×D4—416no—
280C4×D4—416no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—24no—
285C2×C4⋊C4—24no—
286C2×C4⋊C4—24no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—24no—
290C2×C4⋊C4—24no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—28no—
298C2×C4⋊C4—28no—
299C2×C4⋊C4—28no—
300C2×C4⋊C4—28no—
301C2×C4⋊C4—28no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—22no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—28no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4—44no—
317C2×C4⋊C4—44no—
318C2×C4⋊C4—44no—
319C2×C4⋊C4C2×D418yes—
320C2×C4⋊C4C2×D418yes—
321C2×C4⋊C4C2×D414yes—
322C2×C4⋊C4C2×D418yes—
323C2×C4⋊C4C2×D418yes—
324C2×C4⋊C4C2×D418yes—
325C2×C4⋊C4#4114yes—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—28no—
329C2×C22⋊C4—28no—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—28no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—28no—
339C2×C22⋊C4—28no—
340C2×C22⋊C4—28no—
341C2×C22⋊C4—28no—
342C2×C22⋊C4—28no—
343C2×C22⋊C4—28no—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—24no—
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—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—42no—
359C2×C22⋊C4—42no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
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—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4C2×D418yes—
373C2×C22⋊C4C2×D418yes—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—28no—
382C2×C42—28no—
383C2×C42—24no—
384C2×C42—24no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—22no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—24no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—44no—
397C2×C42—41no—
398C2×C42—41no—
399C2×C42C2×D414yes—
400C2×C42C2×D414yes—
401C2×C42C2×D414yes—
402C2×C42#4114yes—
403C2×C42#4114yes—
404#95—24no—
405#95—24no—
406#95—28no—
407#95—28no—
408#95—24no—
409#95—24no—
410#95—28no—
411#95—28no—
412#95—28no—
413#95—28no—
414#95—24no—
415#95—24no—
416#95—44no—
417#95—42no—
418#95—42no—
419#95—42no—
420#95—42no—
421#95—44no—
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—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24C22×D414yes—
451C24C2×#4114yes—
452C24C2511yescharacteristic
453C2×Q8—216no—
454C2×Q8—216no—
455C2×Q8—216no—
456C2×Q8—48no—
457C2×Q8—48no—
458C2×Q8—48no—
459C2×Q8—48no—
460C2×D4—28no—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—28no—
464C2×D4—28no—
465C2×D4—28no—
466C2×D4—416no—
467C2×D4—416no—
468C2×D4—416no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—44no—
474C2×D4—44no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—88no—
478C2×D4—88no—
479C2×D4—88no—
480C2×D4—88no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—24no—
513C22×C4—21no—
514C22×C4—24no—
515C22×C4—24no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—24no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4C22×D418yes—
574C22×C4C22×D412yes—
575C22×C4C22×D418yes—
576C22×C4C22×D414yes—
577C22×C4C22×D412yes—
578C22×C4C22×D412yes—
579C22×C4C22×D412yes—
580C22×C4C22×D412yes—
581C22×C4C22×D412yes—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C2×#4112yes—
586C22×C4C2×#4114yes—
587C22×C4C2×#4112yes—
588C22×C4C2×#4112yes—
589C22×C4C2×#4112yes—
590C22×C4C2×#4112yes—
591C22×C4C2×#4112yes—
592C22×C4C2×#4112yes—
593C22×C4C2×#4112yes—
594C22×C4H(5,𝔽2)12yes—
595C22×C4H(5,𝔽2)12yes—
596C22×C4H(5,𝔽2)12yes—
597C22×C42−1+412yes—
598C22×C42−1+412yes—
599C22×C42−1+412yes—
600C4⋊C4—216no—
601C4⋊C4—216no—
602C4⋊C4—216no—
603C4⋊C4—28no—
604C4⋊C4—216no—
605C4⋊C4—28no—
606C4⋊C4—48no—
607C4⋊C4—416no—
608C4⋊C4—416no—
609C4⋊C4—416no—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—44no—
613C4⋊C4—44no—
614C4⋊C4—88no—
615C22⋊C4—216no—
616C22⋊C4—48no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C22⋊C4—416no—
620C22⋊C4—416no—
621C22⋊C4—48no—
622C22⋊C4—48no—
623C22⋊C4—416no—
624C22⋊C4—416no—
625C22⋊C4—416no—
626C22⋊C4—416no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C42—28no—
632C42—28no—
633C42—28no—
634C42—416no—
635C42—44no—
636C42—48no—
637C42—44no—
638C42—48no—
639C42—44no—
640C42#121116yes—
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—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
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—
710C23—42no—
711C23C23×D411yescharacteristic
712C23C23×D411yescharacteristic
713C23C23×D411yescharacteristic
714C23C22×#4111yescharacteristic
715C23C22×#4111yescharacteristic
716C23C22×#4111yescharacteristic
717C23C22×#4111yescharacteristic
718C23C2×H(5,𝔽2)11yescharacteristic
719C23C2×H(5,𝔽2)11yescharacteristic
720C23C2×H(5,𝔽2)11yescharacteristic
721C23C2×2−1+411yescharacteristic
722C23C2×2−1+411yescharacteristic
723C23C2×2−1+411yescharacteristic
724C23#58511yescharacteristic
725C23#58511yescharacteristic
726Q8—432no—
727D4—416no—
728D4—416no—
729D4—832no—
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—28no—
743C2×C4—22no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—28no—
749C2×C4—28no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—24no—
755C2×C4—28no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—24no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—44no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—44no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—44no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—41no—
787C2×C4—44no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
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—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—816no—
820C2×C4—816no—
821C2×C4C2×#12114yes—
822C2×C4C2×#12114yes—
823C2×C4C2×#12114yes—
824C2×C4#52914yes—
825C2×C4#53214yes—
826C2×C4#54014yes—
827C2×C4#54214yes—
828C2×C4D4214yes—
829C2×C4D4214yes—
830C2×C4#54614yes—
831C2×C4#54614yes—
832C2×C4#54714yes—
833C2×C4#54814yes—
834C2×C4#54814yes—
835C2×C4#55014yes—
836C2×C4#55014yes—
837C22—44no—
838C22—44no—
839C22—44no—
840C22—44no—
841C22—44no—
842C22—44no—
843C22—44no—
844C22—44no—
845C22—44no—
846C22—44no—
847C22—44no—
848C22—44no—
849C22—44no—
850C22—44no—
851C22—82no—
852C22—82no—
853C22—82no—
854C22—82no—
855C22—82no—
856C22—82no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22—82no—
865C22—82no—
866C22—82no—
867C22C22×#12111yescharacteristic
868C22C2×#52911yescharacteristic
869C22C2×#53211yescharacteristic
870C22C2×#54011yescharacteristic
871C22C2×#54211yescharacteristic
872C22#346111yescharacteristic
873C22#346111yescharacteristic
874C22C2×D4211yescharacteristic
875C22C2×D4211yescharacteristic
876C22C2×#54611yescharacteristic
877C22C2×#54611yescharacteristic
878C22C2×#54711yescharacteristic
879C22C2×#54811yescharacteristic
880C22C2×#54811yescharacteristic
881C22C2×#55011yescharacteristic
882C22C2×#55011yescharacteristic
883C22D4×#4111yescharacteristic
884C22#347511yescharacteristic
885C22#348211yescharacteristic
886C22#348511yescharacteristic
887C22#348611yescharacteristic
888C22#349611yescharacteristic
889C22#349711yescharacteristic
890C22#349711yescharacteristic
891C22#349911yescharacteristic
892C22#350611yescharacteristic
893C22#351111yescharacteristic
894C22#351411yescharacteristic
895C22#351811yescharacteristic
896C22#352011yescharacteristic
897C22#352011yescharacteristic
898C22#354611yescharacteristic
899C22#354711yescharacteristic
900C22#354811yescharacteristic
901C22#355211yescharacteristic
902C4—24no—
903C4—24no—
904C4—44no—
905C4—48no—
906C4—42no—
907C4—48no—
908C4—42no—
909C4—44no—
910C4—42no—
911C4—82no—
912C4—82no—
913C4—82no—
914C4—82no—
915C4#242618yescomplemented
916C4#242818yes—
917C2—84no—
918C2—84no—
919C2C2×#242811yescharacteristic
920C2C2×#242611yescharacteristic
921C2#3493211yescharacteristic
922C2#3515311yescharacteristic
923C2#3517011yescharacteristic
924C2#3519611yescharacteristic
925C2#3762711yescharacteristic
926C2#5903511yescharacteristic
927C2#5904011yescharacteristic
928C2#5905011yescharacteristic
929C2#5912511yescharacteristic
930C2#5941011yescharacteristic
931C2#5942111yescharacteristic
932C2#5965411yescharacteristic
933C2#5981511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2537C2
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×#2547C2semidirect
2. C2×#2542C2semidirect
4. C2×#2426C2semidirect
5. C2×C4×C4⋊Q8C2semidirect
6. #16549C2semidirect
7. #15215C2semidirect
8. #15179C2semidirect
9. #15131C2semidirect
10. #15126C2semidirect
11. #14778C2semidirect
12. #14151C2semidirect
13. #13998C2semidirect
14. #13969C2semidirect
15. #13876C2semidirect
16. C4×#390C2semidirect
17. C4×#390C2semidirect
96. C2×C4⋊Q8D4semidirect
174. #390D4semidirect
915. C4#2426semidirect

Maximal subgroups

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

subgroupindex
C2×#25472
C2×#25422
C2×#25372
C2×#24262
C2×C4×C4⋊Q82
#165492
#152152
#151792
#151312
#151262
#147782
#141512
#139982
#139692
#138762
C4×#3902