Finite Group Databasebeta

← #657608

Subgroups — #657608

Order 512.

4326 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic
2C2×#2857C211yesmaximal, characteristic, complemented
3C2×#2502C211yesmaximal, characteristic, complemented
4C2×#2417C211yesmaximal, characteristic
5#15848C214yesmaximal, complemented
6#15614C214yesmaximal, complemented
7#15191C211yesmaximal, characteristic, complemented
8#15182C211yesmaximal, characteristic, complemented
9#15178C211yesmaximal, characteristic, complemented
10#15143C211yesmaximal, characteristic, complemented
11#14758C214yesmaximal, complemented
12#14139C211yesmaximal, characteristic, complemented
13#14139C211yesmaximal, characteristic, complemented
14#14024C211yesmaximal, characteristic, complemented
15#13976C211yesmaximal, characteristic, complemented
16#13975C214yesmaximal
17#13880C211yesmaximal, characteristic, complemented
18C4×#386C211yesmaximal, characteristic
19C2×C4⋊#95C211yesmaximal, characteristic, complemented
20C2×#554—28no—
21C2×#554—28no—
22C2×#554—28no—
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×#125C2212yes—
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2212yes—
29C22×C22⋊Q8C2212yes—
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×D4C2212yes—
34C22×C4×D4C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36C23×C4⋊C4C2211yescharacteristic
37C23×C4⋊C4C2211yescharacteristic
38C23×C42C2211yescharacteristic
39#2857—28no—
40#2502—28no—
41#2417—28no—
42C2×#398C2212yes—
43C2×#398C2214yes—
44C2×#396C2212yes—
45C2×#395C2214yes—
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#389C2214yes—
54C2×#389C2211yescharacteristic
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#385C2214yes—
58C2×#385C2214yes—
59C2×#384C2211yescharacteristic
60C2×#384C2211yescharacteristic
61C2×#384C2211yescharacteristic
62C2×#380C2214yes—
63C2×#380C2211yescharacteristic
64C2×#380C2212yes—
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C22×#95C2214yes—
69#1446C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1444C2214yes—
74#1442C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1439C2214yes—
80#1439C2214yes—
81#1437C2212yes—
82#1436C2214yes—
83#1436C2214yes—
84#1436C2212yes—
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2214yes—
92C22⋊#95C2214yes—
93C22⋊#95C2214yes—
94C22⋊#95C2212yes—
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×Q8C2312yes—
100C23×D4C2311yescharacteristic
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103C24×C4C2312yes—
104C24×C4C2311yescharacteristic
105C24×C4C2312yes—
106C24×C4C2312yes—
107#554—2128no—
108C2×C4⋊Q8—24no—
109C2×C4⋊Q8—24no—
110C2×C4⋊Q8—24no—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—42no—
114C2×#125—28no—
115C2×#125—28no—
116C2×#125—28no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—28no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8—28no—
127C2×C22⋊Q8—28no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—28no—
131C2×C22⋊Q8—28no—
132C2×C22⋊Q8—28no—
133C2×C22⋊Q8—42no—
134C2×C22⋊Q8D418yes—
135C2×C4×Q8—24no—
136C2×C4×Q8—24no—
137C2×C4×Q8—24no—
138C2×C4×D4—28no—
139C2×C4×D4—28no—
140C2×C4×D4—24no—
141C2×C4×D4—24no—
142C2×C4×D4—28no—
143C2×C4×D4D418yes—
144C22×C4⋊C4—24no—
145C22×C4⋊C4—24no—
146C22×C4⋊C4—24no—
147C22×C4⋊C4—24no—
148C22×C4⋊C4—24no—
149C22×C4⋊C4—24no—
150C22×C4⋊C4—24no—
151C22×C4⋊C4—42no—
152C22×C4⋊C4D418yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2314yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2314yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2314yes—
173C22×C4⋊C4C2314yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C42—24no—
185C22×C42—24no—
186C22×C42—42no—
187C22×C42C2311yescharacteristic
188C22×C42C2312yes—
189C22×C42C2311yescharacteristic
190C22×C42C2311yescharacteristic
191C22×C42C2312yes—
192C22×C42C2311yescharacteristic
193C22×C42C2311yescharacteristic
194#398—28no—
195#398—216no—
196#396—28no—
197#395—48no—
198#391—24no—
199#391—24no—
200#391—24no—
201#391—24no—
202#391—24no—
203#391—24no—
204#391—42no—
205#389—216no—
206#389—24no—
207#386—28no—
208#386Q8116yescomplemented
209#385—216no—
210#385—48no—
211#384—24no—
212#384—24no—
213#384—24no—
214#380—24no—
215#380—216no—
216#380—28no—
217C4×C22⋊C4—24no—
218C4×C22⋊C4—24no—
219C4×C22⋊C4—42no—
220C2×#95—48no—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2312yes—
224C2×#95C2312yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2314yes—
229C2×#95C2312yes—
230C2×#95C2314yes—
231C2×#95C2312yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2312yes—
237C2×#95C2314yes—
238C2×#95C2314yes—
239C2×#95C2314yes—
240C2×#95C2312yes—
241C2×#95C2314yes—
242C2×#95C2312yes—
243C2×#95C2312yes—
244C25C2411yescharacteristic
245C25C2411yescharacteristic
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—24no—
249C22×Q8—24no—
250C22×Q8—24no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8—44no—
263C22×Q8—44no—
264C22×Q8C2×D414yes—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—24no—
268C22×D4C2×D414yes—
269C22×D4C2×Q818yes—
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—24no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—24no—
284C23×C4—22no—
285C23×C4—24no—
286C23×C4—22no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—28no—
291C23×C4—24no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4—42no—
295C23×C4—44no—
296C23×C4—44no—
297C23×C4—44no—
298C23×C4—44no—
299C23×C4—44no—
300C23×C4C2×D414yes—
301C23×C4C2×D414yes—
302C23×C4C2×D414yes—
303C23×C4C2×D414yes—
304C23×C4C2×D418yes—
305C23×C4C2×Q818yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2412yes—
317C23×C4C2412yes—
318C23×C4C2412yes—
319C23×C4C2411yescharacteristic
320C23×C4C2411yescharacteristic
321C23×C4C2412yes—
322C23×C4C2411yescharacteristic
323C4⋊Q8—232no—
324C4⋊Q8—416no—
325#125—264no—
326C22⋊Q8—232no—
327C22⋊Q8—264no—
328C22⋊Q8—264no—
329C22⋊Q8—232no—
330C22⋊Q8—416no—
331C22⋊Q8—416no—
332C4×Q8—232no—
333C4×D4—264no—
334C4×D4—232no—
335C2×C4⋊C4—232no—
336C2×C4⋊C4—232no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—24no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—28no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—24no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—24no—
377C2×C4⋊C4—28no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—28no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—28no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—416no—
384C2×C4⋊C4—42no—
385C2×C4⋊C4—44no—
386C2×C4⋊C4—42no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—44no—
389C2×C4⋊C4—44no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4—44no—
392C2×C4⋊C4—44no—
393C2×C4⋊C4C2×D414yes—
394C2×C4⋊C4C2×D414yes—
395C2×C4⋊C4C2×D418yes—
396C2×C4⋊C4C2×D414yes—
397C2×C4⋊C4C2×D414yes—
398C2×C4⋊C4C2×D418yes—
399C2×C4⋊C4#4114yes—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—22no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—24no—
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—42no—
420C2×C22⋊C4—42no—
421C2×C22⋊C4—42no—
422C2×C22⋊C4—44no—
423C2×C22⋊C4C2×D418yes—
424C2×C22⋊C4C2×D414yes—
425C2×C22⋊C4C2×D414yes—
426C2×C22⋊C4C2×Q818yes—
427C2×C22⋊C4C2×Q818yes—
428C2×C22⋊C4C2×Q818yes—
429C2×C42—24no—
430C2×C42—24no—
431C2×C42—24no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—24no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—24no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42—416no—
448C2×C42—42no—
449C2×C42C2×D414yes—
450C2×C42#4114yes—
451#95—24no—
452#95—24no—
453#95—28no—
454#95—28no—
455#95—24no—
456#95—28no—
457#95—28no—
458#95—24no—
459#95—24no—
460#95—24no—
461#95—28no—
462#95—28no—
463#95—28no—
464#95—24no—
465#95—44no—
466#95—44no—
467#95—42no—
468#95—42no—
469#95—44no—
470#95—44no—
471#95—44no—
472#95C2×Q818yes—
473#95C2×Q818yes—
474C24—21no—
475C24—21no—
476C24—21no—
477C24—22no—
478C24—21no—
479C24—22no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24—21no—
484C24—22no—
485C24—21no—
486C24—21no—
487C24—22no—
488C24—22no—
489C24C22×D412yes—
490C24C22×D412yes—
491C24C22×D412yes—
492C24C22×D412yes—
493C24C22×Q814yes—
494C24C22×Q814yes—
495C242−1+414yes—
496C24C2511yescharacteristic
497C2×Q8—216no—
498C2×Q8—28no—
499C2×Q8—28no—
500C2×Q8—28no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8—44no—
509C2×Q8—44no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—88no—
513C2×Q8—88no—
514C2×Q8—84no—
515C2×Q8—84no—
516C2×D4—28no—
517C2×D4—28no—
518C2×D4—216no—
519C2×D4—216no—
520C2×D4C4⋊Q8116yescomplemented
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—28no—
533C22×C4—28no—
534C22×C4—28no—
535C22×C4—28no—
536C22×C4—28no—
537C22×C4—28no—
538C22×C4—216no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—24no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—216no—
590C22×C4—216no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—28no—
594C22×C4—216no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—22no—
607C22×C4—24no—
608C22×C4—22no—
609C22×C4—24no—
610C22×C4—22no—
611C22×C4—24no—
612C22×C4—48no—
613C22×C4—416no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—416no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—48no—
625C22×C4—88no—
626C22×C4—88no—
627C22×C4—88no—
628C22×C4—84no—
629C22×C4—84no—
630C22×C4—84no—
631C22×C4—84no—
632C22×C4—84no—
633C22×C4—88no—
634C22×C4#120116yes—
635C22×C4C22×D414yes—
636C22×C4C22×D414yes—
637C22×C4C22×D412yes—
638C22×C4C22×D414yes—
639C22×C4C22×D412yes—
640C22×C4C22×D414yes—
641C22×C4C22×D412yes—
642C22×C4C22×D412yes—
643C22×C4C22×D412yes—
644C22×C4C22×D412yes—
645C22×C4C22×D412yes—
646C22×C4C22×D412yes—
647C22×C4C22×D412yes—
648C22×C4C22×Q814yes—
649C22×C4C22×Q814yes—
650C22×C4C22×Q814yes—
651C22×C4C22×Q814yes—
652C22×C4C22×Q814yes—
653C22×C4C2×#4114yes—
654C22×C4C2×#4114yes—
655C22×C4C2×#4112yes—
656C22×C4C2×#4112yes—
657C22×C4H(5,𝔽2)14yes—
658C22×C4H(5,𝔽2)12yes—
659C22×C42−1+412yes—
660C4⋊C4—216no—
661C4⋊C4—216no—
662C4⋊C4—216no—
663C4⋊C4—216no—
664C4⋊C4—28no—
665C4⋊C4—216no—
666C4⋊C4—28no—
667C4⋊C4—28no—
668C4⋊C4—28no—
669C4⋊C4—216no—
670C4⋊C4—28no—
671C4⋊C4—416no—
672C4⋊C4—48no—
673C4⋊C4—48no—
674C4⋊C4—416no—
675C4⋊C4—44no—
676C4⋊C4—48no—
677C4⋊C4—44no—
678C4⋊C4—88no—
679C4⋊C4—88no—
680C4⋊C4—84no—
681C22⋊C4—216no—
682C22⋊C4—216no—
683C22⋊C4—28no—
684C22⋊C4—216no—
685C22⋊C4—28no—
686C22⋊C4—216no—
687C22⋊C4—48no—
688C22⋊C4—48no—
689C22⋊C4—48no—
690C22⋊C4—84no—
691C42—216no—
692C42—28no—
693C42—28no—
694C42—48no—
695C42—44no—
696C42—44no—
697C42—44no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—24no—
705C23—24no—
706C23—24no—
707C23—24no—
708C23—24no—
709C23—22no—
710C23—22no—
711C23—24no—
712C23—24no—
713C23—24no—
714C23—24no—
715C23—24no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—24no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—22no—
725C23—22no—
726C23—24no—
727C23—24no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23—42no—
736C23—42no—
737C23—42no—
738C23C2×#12014yes—
739C23C2×C4⋊Q814yes—
740C23C2×C4⋊Q814yes—
741C23#53614yes—
742C23D4×Q818yes—
743C23D4×Q818yes—
744C23C23×D411yescharacteristic
745C23C23×D411yescharacteristic
746C23C23×D411yescharacteristic
747C23C23×Q812yes—
748C23C22×#4111yescharacteristic
749C23C22×#4111yescharacteristic
750C23C2×H(5,𝔽2)11yescharacteristic
751C23C2×H(5,𝔽2)12yes—
752C23C2×2−1+412yes—
753C23C2×2−1+411yescharacteristic
754C23#58512yes—
755Q8—416no—
756Q8—816no—
757Q8—88no—
758D4—232no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—232no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—22no—
784C2×C4—24no—
785C2×C4—22no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—24no—
790C2×C4—24no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—24no—
801C2×C4—28no—
802C2×C4—432no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—44no—
824C2×C4—42no—
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—42no—
834C2×C4—42no—
835C2×C4—44no—
836C2×C4—42no—
837C2×C4—416no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—816no—
856C2×C4—816no—
857C2×C4—816no—
858C2×C4C2×#12014yes—
859C2×C4C2×#12014yes—
860C2×C4C2×C4⋊Q814yes—
861C2×C4#53214yes—
862C2×C4#53714yes—
863C2×C4#54614yes—
864C2×C4#54614yes—
865C2×C4#54714yes—
866C2×C4#54714yes—
867C2×C4#55418yescomplemented
868C22—24no—
869C22—28no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—28no—
875C22—28no—
876C22—24no—
877C22—28no—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—44no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—44no—
886C22—44no—
887C22—42no—
888C22—44no—
889C22#243418yes—
890C22C22×#12011yescharacteristic
891C22C22×C4⋊Q811yescharacteristic
892C22C2×#53211yescharacteristic
893C22C2×#53611yescharacteristic
894C22C2×#53711yescharacteristic
895C22C2×#54611yescharacteristic
896C22C2×#54611yescharacteristic
897C22C2×#54711yescharacteristic
898C22C2×#54711yescharacteristic
899C22C2×D4×Q812yes—
900C22C2×D4×Q812yes—
901C22C2×#55412yes—
902C22Q8×#4112yes—
903C22#348812yes—
904C22#349512yes—
905C22#349612yes—
906C22#349811yescharacteristic
907C22#350011yescharacteristic
908C22#350112yes—
909C22#350312yes—
910C22#352012yes—
911C22#353612yes—
912C22#356312yes—
913C4—24no—
914C4—28no—
915C4—24no—
916C4—44no—
917C4—42no—
918C4—44no—
919C4—44no—
920C4—44no—
921C4—44no—
922C4—42no—
923C4—44no—
924C4—44no—
925C4—44no—
926C4—82no—
927C4—82no—
928C4—82no—
929C4#243018yes—
930C2—28no—
931C2—44no—
932C2C2×#243411yescharacteristic
933C2C2×#243011yescharacteristic
934C2#3551311yescharacteristic
935C2#3618011yescharacteristic
936C2#3627611yescharacteristic
937C2#3656112yes—
938C2#3786511yescharacteristic
939C2#3807811yescharacteristic
940C2#3961412yes—
941C2#5901612yes—
942C2#5911312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC23×D4C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2857C2semidirect
3. C2×#2502C2semidirect
5. #15848C2semidirect
6. #15614C2semidirect
7. #15191C2semidirect
8. #15182C2semidirect
9. #15178C2semidirect
10. #15143C2semidirect
11. #14758C2semidirect
12. #14139C2semidirect
13. #14139C2semidirect
14. #14024C2semidirect
15. #13976C2semidirect
17. #13880C2semidirect
19. C2×C4⋊#95C2semidirect
208. #386Q8semidirect
520. C2×D4C4⋊Q8semidirect
867. C2×C4#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×#25022
C2×#24172
#158482
#156142
#151912
#151822
#151782
#151432
#147582
#141392
#140242
#139762
#139752
#138802
C4×#3862
C2×C4⋊#952