Finite Group Databasebeta

← #676267

Subgroups — #676267

Order 512.

4506 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic, complemented
2C2×#2857C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊Q8C211yesmaximal, characteristic, complemented
4C2×C4×#121C211yesmaximal, characteristic
5#15985C214yesmaximal, complemented
6#15951C214yesmaximal, complemented
7#15218C212yesmaximal, complemented
8#15216C212yesmaximal, complemented
9#15179C212yesmaximal, complemented
10#15177C212yesmaximal, complemented
11#14161C211yesmaximal, characteristic, complemented
12#14130C212yesmaximal, complemented
13#14018C212yesmaximal, complemented
14#13970C212yesmaximal
15#13926C211yesmaximal, characteristic, complemented
16#13906C211yesmaximal, characteristic, complemented
17#13872C212yesmaximal, complemented
18C2×#554—28no—
19C2×#554—28no—
20C2×#554—28no—
21C22×C4⋊Q8C2211yescharacteristic
22C22×#125C2212yes—
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2212yes—
25C22×C22⋊Q8C2214yes—
26C22×C22⋊Q8C2212yes—
27C22×#121C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×D4C2212yes—
30C22×C4×D4C2212yes—
31C22×C4×D4C2211yescharacteristic
32C23×C4⋊C4C2212yes—
33C23×C42C2211yescharacteristic
34#2857—28no—
35C4×C22⋊Q8—28no—
36C4×#121—28no—
37C2×#391C2212yes—
38C2×#391C2211yescharacteristic
39C2×#391C2212yes—
40C2×#390C2212yes—
41C2×#390C2211yescharacteristic
42C2×#389C2212yes—
43C2×#389C2212yes—
44C2×#389C2211yescharacteristic
45C2×#389C2211yescharacteristic
46C2×#388C2212yes—
47C2×#387C2212yes—
48C2×#386C2212yes—
49C2×#386C2214yes—
50C2×#385C2212yes—
51C2×#385C2214yes—
52C2×#384C2211yescharacteristic
53C2×#380C2212yes—
54C2×#380C2212yes—
55C2×#380C2211yescharacteristic
56C2×#380C2212yes—
57C2×#380C2211yescharacteristic
58C2×#380C2212yes—
59C2×C4×C4⋊C4C2211yescharacteristic
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2212yes—
62C2×C4×C22⋊C4C2212yes—
63C2×C4×C22⋊C4C2212yes—
64#1446C2214yes—
65#1444C2214yes—
66#1444C2214yes—
67#1442C2214yes—
68#1442C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1440C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1438C2214yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C4⋊#95C2212yes—
86C4⋊#95C2212yes—
87C22⋊#95C2214yes—
88C22⋊#95C2214yes—
89C23×Q8C2311yescharacteristic
90C23×Q8C2312yes—
91C23×D4C2312yes—
92C23×D4C2311yescharacteristic
93C24×C4C2312yes—
94C24×C4C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2314yes—
98#554—2128no—
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8D418yescomplemented
102C2×#125—28no—
103C2×#125—28no—
104C2×#125—28no—
105C2×C22⋊Q8—216no—
106C2×C22⋊Q8—28no—
107C2×C22⋊Q8—24no—
108C2×C22⋊Q8—28no—
109C2×C22⋊Q8—24no—
110C2×C22⋊Q8—28no—
111C2×C22⋊Q8—216no—
112C2×C22⋊Q8—28no—
113C2×C22⋊Q8—24no—
114C2×C22⋊Q8—216no—
115C2×C22⋊Q8—44no—
116C2×C22⋊Q8—44no—
117C2×#121—24no—
118C2×#121—24no—
119C2×#121Q818yescomplemented
120C2×C4×Q8—24no—
121C2×C4×Q8—24no—
122C2×C4×Q8D418yescomplemented
123C2×C4×D4—28no—
124C2×C4×D4—28no—
125C2×C4×D4—28no—
126C2×C4×D4—28no—
127C2×C4×D4—28no—
128C2×C4×D4—24no—
129C2×C4×D4—24no—
130C2×C4×D4—44no—
131C2×C4×D4D418yes—
132C22×C4⋊C4—28no—
133C22×C4⋊C4—28no—
134C22×C4⋊C4—28no—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2314yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2312yes—
153C22×C22⋊C4C2314yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2314yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2314yes—
164C22×C42—24no—
165C22×C42—24no—
166C22×C42—24no—
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2312yes—
171C22×C42C2312yes—
172C22×C42C2312yes—
173C22×C42C2311yescharacteristic
174#391—28no—
175#391—24no—
176#391—44no—
177#390—24no—
178#390—28no—
179#389—28no—
180#389—28no—
181#389—24no—
182#389—24no—
183#388—28no—
184#387—28no—
185#386—28no—
186#386—48no—
187#385—28no—
188#385—48no—
189#384—24no—
190#380—28no—
191#380—28no—
192#380—24no—
193#380—24no—
194#380—28no—
195#380—44no—
196C4×C4⋊C4—24no—
197C4×C4⋊C4—28no—
198C4×C4⋊C4—24no—
199C4×C22⋊C4—28no—
200C4×C22⋊C4—28no—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2314yes—
221C25C2412yes—
222C25C2411yescharacteristic
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—24no—
226C22×Q8—24no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—22no—
230C22×Q8—22no—
231C22×Q8—42no—
232C22×Q8—42no—
233C22×Q8—42no—
234C22×Q8—42no—
235C22×Q8C2×D414yes—
236C22×Q8C2×D418yes—
237C22×D4—24no—
238C22×D4—24no—
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—22no—
245C22×D4—42no—
246C22×D4—42no—
247C22×D4C2×D414yes—
248C22×D4C2×Q818yes—
249C22×D4C2×Q814yes—
250C22×D4#4114yes—
251C23×C4—22no—
252C23×C4—28no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—22no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—24no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—24no—
266C23×C4—22no—
267C23×C4—24no—
268C23×C4—22no—
269C23×C4—24no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—28no—
274C23×C4—28no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—41no—
278C23×C4—41no—
279C23×C4—44no—
280C23×C4—44no—
281C23×C4—44no—
282C23×C4—44no—
283C23×C4C2×D418yes—
284C23×C4C2×Q814yes—
285C23×C4#4114yes—
286C23×C4C2414yes—
287C23×C4C2412yes—
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2412yes—
291C23×C4C2414yes—
292C23×C4C2412yes—
293C23×C4C2411yescharacteristic
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C23×C4C2411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C4⋊Q8—232no—
302#125—264no—
303C22⋊Q8—232no—
304C22⋊Q8—264no—
305C22⋊Q8—2128no—
306C22⋊Q8—432no—
307#121—232no—
308C4×Q8—232no—
309C4×D4—264no—
310C4×D4—232no—
311C4×D4—432no—
312C2×C4⋊C4—264no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—28no—
317C2×C4⋊C4—28no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—28no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—28no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—28no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4C2×D414yes—
361C2×C4⋊C4C2×D418yes—
362C2×C4⋊C4C2×D418yes—
363C2×C4⋊C4C2×D414yes—
364C2×C4⋊C4C2×D418yes—
365C2×C4⋊C4C2×Q814yes—
366C2×C4⋊C4#4114yes—
367C2×C22⋊C4—28no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—28no—
372C2×C22⋊C4—28no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—42no—
391C2×C22⋊C4—42no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—44no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4C2×D418yes—
399C2×C22⋊C4C2×Q818yes—
400C2×C42—24no—
401C2×C42—24no—
402C2×C42—24no—
403C2×C42—22no—
404C2×C42—24no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—24no—
417C2×C42—416no—
418C2×C42C2×D418yes—
419C2×C42C2×D414yes—
420C2×C42C2×D414yes—
421C2×C42C2×D414yes—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—28no—
431#95—28no—
432#95—28no—
433#95—44no—
434#95—44no—
435#95—44no—
436#95—44no—
437#95—44no—
438#95—44no—
439#95—44no—
440#95—44no—
441#95—44no—
442C24—21no—
443C24—21no—
444C24—22no—
445C24—22no—
446C24—21no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—21no—
451C24—22no—
452C24—21no—
453C24—22no—
454C24—21no—
455C24—22no—
456C24—22no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—22no—
461C24—22no—
462C24—21no—
463C24—22no—
464C24—22no—
465C24—21no—
466C24C22×D414yes—
467C24C22×Q814yes—
468C24C22×Q812yes—
469C24C2×#4114yes—
470C24C2×#4112yes—
471C24H(5,𝔽2)12yes—
472C24C2511yescharacteristic
473C2×Q8—28no—
474C2×Q8—216no—
475C2×Q8—28no—
476C2×Q8—28no—
477C2×Q8—48no—
478C2×Q8—48no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—84no—
484C2×Q8—84no—
485C2×Q8—84no—
486C2×Q8—84no—
487C2×D4—216no—
488C2×D4—216no—
489C2×D4—28no—
490C2×D4—28no—
491C2×D4—28no—
492C2×D4—28no—
493C2×D4—28no—
494C2×D4—28no—
495C2×D4—48no—
496C2×D4—48no—
497C2×D4—48no—
498C2×D4—48no—
499C2×D4—48no—
500C2×D4C22⋊Q8116yescomplemented
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—28no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—22no—
560C22×C4—232no—
561C22×C4—216no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—216no—
566C22×C4—216no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—24no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—48no—
600C22×C4—44no—
601C22×C4—48no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—48no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—48no—
608C22×C4—44no—
609C22×C4—88no—
610C22×C4—88no—
611C22×C4—88no—
612C22×C4—88no—
613C22×C4—88no—
614C22×C4—88no—
615C22×C4C22×D414yes—
616C22×C4C22×D414yes—
617C22×C4C22×D418yes—
618C22×C4C22×D414yes—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×Q812yes—
629C22×C4C22×Q814yes—
630C22×C4C22×Q812yes—
631C22×C4C2×#4114yes—
632C22×C4C2×#4112yes—
633C22×C4C2×#4112yes—
634C22×C4C2×#4112yes—
635C22×C4C2×#4112yes—
636C22×C4H(5,𝔽2)12yes—
637C22×C4H(5,𝔽2)12yes—
638C22×C42−1+412yes—
639C22×C42−1+412yes—
640C22×C42−1+412yes—
641C4⋊C4—232no—
642C4⋊C4—216no—
643C4⋊C4—232no—
644C4⋊C4—28no—
645C4⋊C4—216no—
646C4⋊C4—28no—
647C4⋊C4—216no—
648C4⋊C4—216no—
649C4⋊C4—28no—
650C4⋊C4—28no—
651C4⋊C4—48no—
652C4⋊C4—48no—
653C4⋊C4—416no—
654C4⋊C4—48no—
655C4⋊C4—44no—
656C4⋊C4—44no—
657C4⋊C4—48no—
658C4⋊C4—48no—
659C22⋊C4—232no—
660C22⋊C4—216no—
661C22⋊C4—216no—
662C22⋊C4—216no—
663C22⋊C4—416no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—416no—
669C22⋊C4—88no—
670C42—216no—
671C42—44no—
672C42—44no—
673C42—44no—
674C42—48no—
675C42—48no—
676C42#120116yes—
677C23—24no—
678C23—22no—
679C23—22no—
680C23—24no—
681C23—22no—
682C23—24no—
683C23—24no—
684C23—22no—
685C23—24no—
686C23—24no—
687C23—22no—
688C23—22no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—22no—
693C23—24no—
694C23—24no—
695C23—22no—
696C23—24no—
697C23—22no—
698C23—22no—
699C23—24no—
700C23—22no—
701C23—24no—
702C23—22no—
703C23—24no—
704C23—22no—
705C23—24no—
706C23—22no—
707C23—22no—
708C23—24no—
709C23—24no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—41no—
714C23—42no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—41no—
719C23—42no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—42no—
724C23—41no—
725C23—42no—
726C23—41no—
727C23—42no—
728C23—41no—
729C23—41no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—41no—
735C23—42no—
736C23—41no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—41no—
741C23—42no—
742C23—41no—
743C23—41no—
744C23—42no—
745C23C2×C22⋊Q818yes—
746C23#55414yescomplemented
747C23C23×D411yescharacteristic
748C23C23×D411yescharacteristic
749C23C23×D411yescharacteristic
750C23C23×Q811yescharacteristic
751C23C22×#4111yescharacteristic
752C23C22×#4111yescharacteristic
753C23C22×#4111yescharacteristic
754C23C2×H(5,𝔽2)11yescharacteristic
755C23C2×H(5,𝔽2)11yescharacteristic
756C23C2×H(5,𝔽2)11yescharacteristic
757C23C2×2−1+411yescharacteristic
758C23C2×2−1+411yescharacteristic
759C23C2×2−1+411yescharacteristic
760C23#58511yescharacteristic
761C23#58511yescharacteristic
762Q8—416no—
763Q8—816no—
764D4—232no—
765D4—432no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—28no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—28no—
791C2×C4—22no—
792C2×C4—28no—
793C2×C4—22no—
794C2×C4—24no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—416no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—44no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—432no—
837C2×C4—416no—
838C2×C4—416no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—44no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—44no—
860C2×C4—832no—
861C2×C4C2×#12014yes—
862C2×C4C2×#12014yes—
863C2×C4C2×#12014yes—
864C2×C4C2×C22⋊Q814yes—
865C2×C4#52514yes—
866C2×C4#53614yes—
867C2×C4#53714yes—
868C2×C4#54614yes—
869C2×C4#54714yes—
870C2×C4#54814yes—
871C2×C4#54814yes—
872C2×C4#54814yes—
873C2×C4D4×Q814yes—
874C2×C4D4×Q814yes—
875C2×C4#55014yes—
876C22—24no—
877C22—24no—
878C22—28no—
879C22—28no—
880C22—28no—
881C22—24no—
882C22—44no—
883C22—44no—
884C22—42no—
885C22—44no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—44no—
890C22—44no—
891C22—42no—
892C22—42no—
893C22—44no—
894C22—42no—
895C22—44no—
896C22—44no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—44no—
901C22—44no—
902C22—42no—
903C22—44no—
904C22—44no—
905C22—42no—
906C22C22×#12011yescharacteristic
907C22C22×C22⋊Q811yescharacteristic
908C22C2×#52511yescharacteristic
909C22C2×#53611yescharacteristic
910C22C2×#53711yescharacteristic
911C22C2×#54611yescharacteristic
912C22C2×#54711yescharacteristic
913C22C2×#54811yescharacteristic
914C22C2×#54811yescharacteristic
915C22C2×#54811yescharacteristic
916C22C2×D4×Q811yescharacteristic
917C22C2×D4×Q811yescharacteristic
918C22C2×#55011yescharacteristic
919C22C2×#55411yescharacteristic
920C22#347511yescharacteristic
921C22Q8×#4111yescharacteristic
922C22#348111yescharacteristic
923C22#348411yescharacteristic
924C22#348511yescharacteristic
925C22#348811yescharacteristic
926C22#348811yescharacteristic
927C22#348811yescharacteristic
928C22#348811yescharacteristic
929C22#350111yescharacteristic
930C22#350311yescharacteristic
931C22#350711yescharacteristic
932C22#351111yescharacteristic
933C22#351511yescharacteristic
934C22#351511yescharacteristic
935C22#351911yescharacteristic
936C22#352211yescharacteristic
937C22#354411yescharacteristic
938C22#354711yescharacteristic
939C22#354811yescharacteristic
940C22#355511yescharacteristic
941C4—24no—
942C4—44no—
943C4—42no—
944C4—44no—
945C4—44no—
946C4—42no—
947C4—44no—
948C4—42no—
949C4—44no—
950C4—48no—
951C4—82no—
952C4—84no—
953C4—82no—
954C4#240718yes—
955C4#240918yes—
956C2—44no—
957C2—48no—
958C2C2×#240911yescharacteristic
959C2C2×#240711yescharacteristic
960C2#3551211yescharacteristic
961C2#3615411yescharacteristic
962C2#3627511yescharacteristic
963C2#3649211yescharacteristic
964C2#3654411yescharacteristic
965C2#3892111yescharacteristic
966C2#3912611yescharacteristic
967C2#3947011yescharacteristic
968C2#3959811yescharacteristic
969C2#5905211yescharacteristic
970C2#5905711yescharacteristic
971C2#5907911yescharacteristic
972C2#5913611yescharacteristic
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. C22×#554C2semidirect
2. C2×#2857C2semidirect
3. C2×C4×C22⋊Q8C2semidirect
5. #15985C2semidirect
6. #15951C2semidirect
7. #15218C2semidirect
8. #15216C2semidirect
9. #15179C2semidirect
10. #15177C2semidirect
11. #14161C2semidirect
12. #14130C2semidirect
13. #14018C2semidirect
15. #13926C2semidirect
16. #13906C2semidirect
17. #13872C2semidirect
101. C2×C4⋊Q8D4semidirect
119. C2×#121Q8semidirect
122. C2×C4×Q8D4semidirect
500. C2×D4C22⋊Q8semidirect
746. C23#554semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#28572
C2×C4×C22⋊Q82
C2×C4×#1212
#159852
#159512
#152182
#152162
#151792
#151772
#141612
#141302
#140182
#139702
#139262
#139062
#138722