Finite Group Databasebeta

← #873888

Subgroups — #873888

Order 512.

3420 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2857C211yesmaximal, characteristic, complemented
2C2×#2850C211yesmaximal, characteristic
3C2×#2546C211yesmaximal, characteristic, complemented
4C2×#2545C211yesmaximal, characteristic, complemented
5C2×#2426C211yesmaximal, characteristic
6C2×#2429C211yesmaximal, characteristic, complemented
7#16330C214yesmaximal, complemented
8#15387C214yesmaximal, complemented
9#15309C214yesmaximal, complemented
10#15243C211yesmaximal, characteristic, complemented
11#15243C211yesmaximal, characteristic, complemented
12#15237C211yesmaximal, characteristic, complemented
13#15215C211yesmaximal, characteristic
14#15178C211yesmaximal, characteristic, complemented
15#15134C211yesmaximal, characteristic, complemented
16#14562C214yesmaximal, complemented
17#13978C211yesmaximal, characteristic, complemented
18#13976C211yesmaximal, characteristic, complemented
19C4×#385C211yesmaximal, characteristic, complemented
20C22×C4⋊Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×#124C2211yescharacteristic
24C22×#124C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C22×#121C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C23×C42C2211yescharacteristic
33#2857—28no—
34#2850—28no—
35#2546—28no—
36#2545—28no—
37#2429—28no—
38#2426—28no—
39C2×#398C2214yes—
40C2×#398C2212yes—
41C2×#396C2214yes—
42C2×#396C2214yes—
43C2×#396C2212yes—
44C2×#396C2212yes—
45C2×#394C2212yes—
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#390C2211yescharacteristic
54C2×#390C2211yescharacteristic
55C2×#390C2211yescharacteristic
56C2×#390C2212yes—
57C2×#389C2214yes—
58C2×#389C2211yescharacteristic
59C2×#389C2214yes—
60C2×#389C2212yes—
61C2×#389C2211yescharacteristic
62C2×#388C2214yes—
63C2×#388C2212yes—
64C2×#388C2214yes—
65C2×#388C2212yes—
66C2×#386C2214yes—
67C2×#385C2212yes—
68C2×#384C2211yescharacteristic
69C2×#382C2211yescharacteristic
70C2×#380C2214yes—
71C2×C4×C4⋊C4C2211yescharacteristic
72C2×C4×C4⋊C4C2211yescharacteristic
73C2×C4×C22⋊C4C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75#1444C2214yes—
76#1444C2214yes—
77#1443C2214yes—
78#1442C2214yes—
79#1441C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1439C2214yes—
84#1439C2214yes—
85#1439C2214yes—
86#1439C2214yes—
87#1438C2214yes—
88#1436C2214yes—
89#1436C2214yes—
90#1436C2212yes—
91#1436C2212yes—
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C22⋊#95C2212yes—
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×Q8C2311yescharacteristic
100C23×D4C2311yescharacteristic
101C23×D4C2312yes—
102C24×C4C2311yescharacteristic
103C24×C4C2312yes—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8—24no—
107C2×C4⋊Q8—24no—
108C2×C4⋊Q8—24no—
109C2×C4⋊Q8—24no—
110C2×C4⋊Q8—42no—
111C2×C4⋊Q8—42no—
112C2×C4⋊Q8—42no—
113C2×#124—24no—
114C2×#124—24no—
115C2×#124—24no—
116C2×#124—24no—
117C2×#124—42no—
118C2×#124—42no—
119C2×#124—42no—
120C2×#124—42no—
121C2×#124—42no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—24no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8—24no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—42no—
129C2×C22⋊Q8—42no—
130C2×C22⋊Q8—42no—
131C2×#121—24no—
132C2×#121—24no—
133C2×#121—42no—
134C2×C4×Q8—24no—
135C2×C4×Q8—24no—
136C2×C4×Q8—24no—
137C2×C4×Q8—24no—
138C2×C4×Q8—42no—
139C2×C4×Q8—42no—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2311yescharacteristic
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2314yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2312yes—
149C22×C4⋊C4C2314yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2314yes—
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2314yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2314yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2311yescharacteristic
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2314yes—
173C22×C42—24no—
174C22×C42—24no—
175C22×C42—42no—
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178C22×C42C2312yes—
179C22×C42C2312yes—
180C22×C42C2312yes—
181C22×C42C2311yescharacteristic
182C22×C42C2311yescharacteristic
183C22×C42C2311yescharacteristic
184C22×C42C2311yescharacteristic
185#398—28no—
186#398—216no—
187#396—216no—
188#396—28no—
189#396—28no—
190#396—216no—
191#394—28no—
192#391—24no—
193#391—24no—
194#391—24no—
195#391—42no—
196#391—42no—
197#391D418yes—
198#391D418yescomplemented
199#390—24no—
200#390—28no—
201#390—24no—
202#390—24no—
203#389—24no—
204#389—24no—
205#389—216no—
206#389—28no—
207#389—216no—
208#388—28no—
209#388—216no—
210#388—28no—
211#388—216no—
212#386—216no—
213#385—28no—
214#384—24no—
215#382—24no—
216#380—216no—
217C4×C4⋊C4—24no—
218C4×C4⋊C4—24no—
219C4×C22⋊C4—42no—
220C4×C22⋊C4D418yes—
221C2×#95C2312yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2312yes—
225C2×#95C2314yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2312yes—
234C2×#95C2312yes—
235C2×#95C2314yes—
236C2×#95C2312yes—
237C2×#95C2314yes—
238C2×#95C2314yes—
239C2×#95C2311yescharacteristic
240C2×#95C2314yes—
241C2×#95C2314yes—
242C2×#95C2311yescharacteristic
243C25C2412yes—
244C25C2411yescharacteristic
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
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—22no—
263C22×Q8—22no—
264C22×Q8C2×D414yes—
265C22×Q8C2×D414yes—
266C22×D4—24no—
267C22×D4—28no—
268C22×D4—22no—
269C22×D4—22no—
270C22×D4—24no—
271C22×D4—22no—
272C22×D4—22no—
273C22×D4—22no—
274C22×D4—22no—
275C22×D4—22no—
276C22×D4—42no—
277C22×D4—44no—
278C23×C4—24no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—24no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—24no—
286C23×C4—22no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4C2×D414yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2412yes—
308C23×C4C2411yescharacteristic
309C4⋊Q8—416no—
310C4⋊Q8—416no—
311C4⋊Q8—416no—
312#124—416no—
313#124—416no—
314#124—416no—
315C22⋊Q8—416no—
316C22⋊Q8—416no—
317C22⋊Q8—416no—
318#121—416no—
319C4×Q8—416no—
320C4×Q8—416no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—28no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—28no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—28no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—24no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—42no—
360C2×C4⋊C4—42no—
361C2×C4⋊C4—42no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—42no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—44no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—42no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4C2×D414yes—
371C2×C4⋊C4C2×D414yes—
372C2×C4⋊C4#4118yes—
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—24no—
381C2×C22⋊C4—24no—
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—24no—
390C2×C22⋊C4—28no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—28no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—28no—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—42no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—42no—
404C2×C22⋊C4—42no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—42no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4—44no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—42no—
411C2×C22⋊C4—44no—
412C2×C22⋊C4C2×D414yes—
413C2×C22⋊C4C2×D414yes—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—24no—
423C2×C42—24no—
424C2×C42—24no—
425C2×C42—24no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—24no—
429C2×C42—24no—
430C2×C42—22no—
431C2×C42—22no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—416no—
435C2×C42—42no—
436C2×C42—42no—
437C2×C42—42no—
438C2×C42C2×D414yes—
439C2×C42C2×D414yes—
440C2×C42C2×D414yes—
441C2×C42C2×D414yes—
442#95—24no—
443#95—24no—
444#95—28no—
445#95—28no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—28no—
450#95—24no—
451#95—24no—
452#95—24no—
453#95—28no—
454#95—24no—
455#95—42no—
456#95—44no—
457#95—42no—
458#95—44no—
459#95—44no—
460#95C2×D414yes—
461#95C2×D414yes—
462#95C2×D4116yes—
463#95C2×D4116yes—
464C24—21no—
465C24—21no—
466C24—22no—
467C24—21no—
468C24—21no—
469C24—21no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—24no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—24no—
481C24—24no—
482C24—22no—
483C24—24no—
484C24C22×D412yes—
485C242−1+414yes—
486C24C2511yescharacteristic
487C2×Q8—28no—
488C2×Q8—28no—
489C2×Q8—28no—
490C2×Q8—28no—
491C2×Q8—28no—
492C2×Q8—28no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×D4—48no—
509C2×D4—416no—
510C2×D4—48no—
511C2×D4—44no—
512C2×D4—44no—
513C2×D4—44no—
514C2×D4—44no—
515C2×D4—44no—
516C2×D4—44no—
517C2×D4—44no—
518C2×D4—84no—
519C2×D4—88no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—21no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—216no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—28no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—24no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—24no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—48no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—48no—
614C22×C4—44no—
615C22×C4C22×D414yes—
616C22×C4C22×D412yes—
617C22×C4C22×D414yes—
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D414yes—
621C22×C4C22×D414yes—
622C22×C4C22×D414yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C22×D414yes—
626C22×C4C22×D412yes—
627C22×C4C22×D412yes—
628C22×C4C22×D412yes—
629C22×C4C2×#4114yes—
630C22×C4C2×#4114yes—
631C22×C4C2×#4114yes—
632C22×C4H(5,𝔽2)12yes—
633C22×C4H(5,𝔽2)12yes—
634C22×C4H(5,𝔽2)12yes—
635C22×C42−1+414yes—
636C22×C42−1+412yes—
637C4⋊C4—28no—
638C4⋊C4—28no—
639C4⋊C4—216no—
640C4⋊C4—416no—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C4⋊C4—48no—
644C4⋊C4—48no—
645C4⋊C4—48no—
646C4⋊C4—48no—
647C4⋊C4—48no—
648C4⋊C4—416no—
649C4⋊C4—48no—
650C4⋊C4—416no—
651C4⋊C4—48no—
652C4⋊C4—44no—
653C4⋊C4—44no—
654C4⋊C4—84no—
655C22⋊C4—28no—
656C22⋊C4—28no—
657C22⋊C4—416no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—416no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—416no—
667C22⋊C4—48no—
668C22⋊C4—416no—
669C22⋊C4—84no—
670C42—28no—
671C42—28no—
672C42—28no—
673C42—28no—
674C42—48no—
675C42—48no—
676C42—48no—
677C42—44no—
678C42—44no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—24no—
684C23—24no—
685C23—22no—
686C23—22no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—41no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—44no—
710C23—44no—
711C23—44no—
712C23—44no—
713C23—42no—
714C23—42no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—42no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23#53614yes—
725C23C23×D411yescharacteristic
726C23C23×D411yescharacteristic
727C23C23×D411yescharacteristic
728C23C22×#4112yes—
729C23C2×H(5,𝔽2)11yescharacteristic
730C23C2×H(5,𝔽2)11yescharacteristic
731C23C2×H(5,𝔽2)11yescharacteristic
732C23C2×2−1+412yes—
733C23C2×2−1+411yescharacteristic
734C23C2×2−1+412yes—
735C23#58512yes—
736Q8—416no—
737Q8—416no—
738Q8—88no—
739D4—816no—
740D4—88no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—24no—
771C2×C4—28no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—28no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—24no—
779C2×C4—432no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—41no—
789C2×C4—42no—
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—44no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—44no—
812C2×C4—416no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—44no—
824C2×C4—44no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—44no—
828C2×C4—42no—
829C2×C4—44no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4#53214yes—
838C2×C4#53714yes—
839C2×C4#53714yes—
840C2×C4#53714yes—
841C2×C4D4214yes—
842C2×C4D4214yes—
843C2×C4D4214yes—
844C2×C4#54818yes—
845C2×C4#56014yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—44no—
853C22—42no—
854C22—44no—
855C22—44no—
856C22—44no—
857C22—82no—
858C22—82no—
859C22—82no—
860C22—82no—
861C22—82no—
862C22—84no—
863C22—82no—
864C22—84no—
865C22—82no—
866C22—84no—
867C22—84no—
868C22C2×#53211yescharacteristic
869C22C2×#53611yescharacteristic
870C22C2×#53711yescharacteristic
871C22C2×#53711yescharacteristic
872C22C2×#53711yescharacteristic
873C22C2×D4211yescharacteristic
874C22C2×D4211yescharacteristic
875C22C2×D4211yescharacteristic
876C22C2×#54812yes—
877C22D4×#4112yes—
878C22#348612yes—
879C22#348912yes—
880C22#349911yescharacteristic
881C22#350011yescharacteristic
882C22#351112yes—
883C22#351712yes—
884C22#352012yes—
885C22#352312yes—
886C22C2×#56011yescharacteristic
887C22#354112yes—
888C22#355212yes—
889C22#355512yes—
890C22#356112yes—
891C4—24no—
892C4—28no—
893C4—42no—
894C4—44no—
895C4—42no—
896C4—42no—
897C4—44no—
898C4—42no—
899C4—44no—
900C4—44no—
901C4—44no—
902C4—44no—
903C4—82no—
904C4—82no—
905C4—82no—
906C4—82no—
907C4#267518yes—
908C2—44no—
909C2—162no—
910C2#3524111yescharacteristic
911C2#3612211yescharacteristic
912C2#3612511yescharacteristic
913C2#3738911yescharacteristic
914C2#3767511yescharacteristic
915C2#3767611yescharacteristic
916C2#3912712yes—
917C2#3987912yes—
918C2#4562812yes—
919C2C2×#267511yescharacteristic
920C2#5900512yes—
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
3. C2×#2546C2semidirect
4. C2×#2545C2semidirect
6. C2×#2429C2semidirect
7. #16330C2semidirect
8. #15387C2semidirect
9. #15309C2semidirect
10. #15243C2semidirect
11. #15243C2semidirect
12. #15237C2semidirect
14. #15178C2semidirect
15. #15134C2semidirect
16. #14562C2semidirect
17. #13978C2semidirect
18. #13976C2semidirect
19. C4×#385C2semidirect
198. #391D4semidirect

Maximal subgroups

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

subgroupindex
C2×#28572
C2×#28502
C2×#25462
C2×#25452
C2×#24262
C2×#24292
#163302
#153872
#153092
#152432
#152372
#152152
#151782
#151342
#145622
#139782
#139762
C4×#3852