Finite Group Databasebeta

← #617780

Subgroups — #617780

Order 512.

3640 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2415C211yesmaximal, characteristic
2C2×#2434C211yesmaximal, characteristic, complemented
3C2×#2409C211yesmaximal, characteristic
4C2×#2621C211yesmaximal, characteristic, complemented
5C2×#2310C211yesmaximal, characteristic, complemented
6C2×#2293C211yesmaximal, characteristic
7#15632C214yesmaximal, complemented
8#15623C214yesmaximal, complemented
9#15300C214yesmaximal
10#15298C214yesmaximal, complemented
11#15237C211yesmaximal, characteristic, complemented
12#15182C211yesmaximal, characteristic, complemented
13#15180C211yesmaximal, characteristic, complemented
14#15178C211yesmaximal, characteristic, complemented
15#14714C211yesmaximal, characteristic, complemented
16#14703C211yesmaximal, characteristic, complemented
17#14258C211yesmaximal, characteristic, complemented
18#14258C211yesmaximal, characteristic, complemented
19#13879C211yesmaximal, characteristic, complemented
20C24×Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C22⋊Q8C2211yescharacteristic
24C22×C22⋊Q8C2211yescharacteristic
25C22×C22⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×#117C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C22×#117C2211yescharacteristic
31#2621—28no—
32#2434—28no—
33#2415—28no—
34#2409—28no—
35C2×#398C2214yes—
36C2×#397C2214yes—
37C2×#397C2212yes—
38C2×#395C2212yes—
39C2×#395C2214yes—
40C2×#394C2212yes—
41C2×#393C2212yes—
42#2310—28no—
43C2×#391C2214yes—
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55#2293—28no—
56C2×#390C2212yes—
57C2×#389C2212yes—
58C2×#389C2212yes—
59C2×#389C2211yescharacteristic
60C2×#388C2212yes—
61C2×#388C2212yes—
62C2×#388C2212yes—
63C2×#386C2212yes—
64C2×#385C2212yes—
65C2×#385C2214yes—
66C2×#384C2211yescharacteristic
67C2×#382C2211yescharacteristic
68C2×#381C2214yes—
69C2×#380C2211yescharacteristic
70C2×#380C2211yescharacteristic
71C2×C4×C4⋊C4C2211yescharacteristic
72C2×C4×C22⋊C4C2211yescharacteristic
73C2×C4×C22⋊C4C2211yescharacteristic
74C2×C43C2211yescharacteristic
75#1444C2214yes—
76#1443C2214yes—
77#1442C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1441C2214yes—
81#1441C2214yes—
82#1441C2214yes—
83#1440C2214yes—
84#1440C2214yes—
85#1439C2214yes—
86#1439C2214yes—
87#1439C2214yes—
88#1436C2214yes—
89#1436C2214yes—
90C4⋊#95C2214yes—
91C4⋊#95C2214yes—
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95C4⋊#95C2211yescharacteristic
96#1434C2214yes—
97C23×Q8—24no—
98C23×Q8—24no—
99C23×Q8—24no—
100C23×Q8—24no—
101C23×Q8—24no—
102C23×Q8—42no—
103C23×Q8—42no—
104C23×Q8C2311yescharacteristic
105C23×Q8C2311yescharacteristic
106C23×Q8C2311yescharacteristic
107C23×Q8C2312yes—
108C23×D4C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C24×C4C2311yescharacteristic
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—42no—
117C2×C4⋊Q8—42no—
118C2×C22⋊Q8—24no—
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—24no—
127C2×C22⋊Q8—42no—
128C2×C22⋊Q8—42no—
129C2×C22⋊Q8—42no—
130C2×C4×D4—24no—
131C2×C4×D4—24no—
132C2×C4×D4D418yes—
133C2×#117—24no—
134C2×#117—24no—
135C2×#117—24no—
136C2×#117—24no—
137C2×#117—24no—
138C2×#117—24no—
139C2×#117—42no—
140C2×#117—42no—
141C2×#117—42no—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2311yescharacteristic
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2314yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2314yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2311yescharacteristic
168C22×C22⋊C4C2311yescharacteristic
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C42C2311yescharacteristic
173C22×C42C2312yes—
174C22×C42C2312yes—
175C22×C42C2312yes—
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180#398—216no—
181#397—28no—
182#397—216no—
183#395—28no—
184#395—216no—
185#394—28no—
186#393—28no—
187#391—24no—
188#391—24no—
189#391—24no—
190#391—24no—
191#391—24no—
192#391—24no—
193#391—24no—
194#391—24no—
195#391—24no—
196#391—216no—
197#391—42no—
198#391D418yescomplemented
199#390—28no—
200#389—28no—
201#389—24no—
202#389—28no—
203#388—28no—
204#388—28no—
205#388—28no—
206#386—28no—
207#385—28no—
208#385—216no—
209#384—42no—
210#382—24no—
211#381—216no—
212#380—24no—
213#380—24no—
214C4×C4⋊C4—24no—
215C4×C22⋊C4—24no—
216C4×C22⋊C4D418yes—
217C2×#95C2312yes—
218C2×#95C2312yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2314yes—
222C2×#95C2312yes—
223C2×#95C2312yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2312yes—
235C2×#95C2312yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C2×#95C2314yes—
239C2×#95C2314yes—
240C2×#95C2312yes—
241C2×#95C2314yes—
242C43—24no—
243C25C2411yescharacteristic
244C25C2411yescharacteristic
245C22×Q8—232no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—24no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—24no—
256C22×Q8—24no—
257C22×Q8—24no—
258C22×Q8—24no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8—42no—
271C22×Q8—42no—
272C22×Q8—416no—
273C22×Q8—416no—
274C22×Q8—416no—
275C22×Q8—416no—
276C22×Q8—416no—
277C22×Q8—416no—
278C22×Q8C2×D414yes—
279C22×Q8#4114yes—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—24no—
283C22×D4—42no—
284C22×D4C2×D414yes—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—24no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—24no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—24no—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4—24no—
299C23×C4—24no—
300C23×C4—42no—
301C23×C4—42no—
302C23×C4C2×D414yes—
303C23×C4C2×D414yes—
304C23×C4C2×D414yes—
305C23×C4#4114yes—
306C23×C4C2412yes—
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2412yes—
313C23×C4C2412yes—
314C23×C4C2412yes—
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2412yes—
318C23×C4C2412yes—
319C23×C4C2411yescharacteristic
320C23×C4C2412yes—
321C23×C4C2411yescharacteristic
322C23×C4C2411yescharacteristic
323C4⋊Q8—416no—
324C4⋊Q8—416no—
325C22⋊Q8—416no—
326C22⋊Q8—416no—
327C22⋊Q8—416no—
328C22⋊Q8—416no—
329C4×D4—232no—
330#117—416no—
331#117—416no—
332#117—416no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—24no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—28no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—24no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—28no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4—28no—
370C2×C4⋊C4—28no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—42no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4C2×D414yes—
382C2×C4⋊C4C2×D414yes—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—24no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4—24no—
403C2×C22⋊C4—24no—
404C2×C22⋊C4—24no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—24no—
407C2×C22⋊C4—24no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—44no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—42no—
412C2×C22⋊C4—42no—
413C2×C22⋊C4—42no—
414C2×C22⋊C4—42no—
415C2×C22⋊C4—42no—
416C2×C22⋊C4—42no—
417C2×C22⋊C4C2×D414yes—
418C2×C22⋊C4C2×D414yes—
419C2×C22⋊C4C2×D418yes—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—24no—
430C2×C42—24no—
431C2×C42—22no—
432C2×C42—24no—
433C2×C42—24no—
434C2×C42—22no—
435C2×C42—24no—
436C2×C42—24no—
437C2×C42—24no—
438C2×C42—42no—
439C2×C42—42no—
440C2×C42C2×D414yes—
441C2×C42C2×D414yes—
442C2×C42C2×D414yes—
443C2×C42C2×D414yes—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—28no—
449#95—28no—
450#95—28no—
451#95—28no—
452#95—24no—
453#95—24no—
454#95—28no—
455#95—28no—
456#95—24no—
457#95—24no—
458#95—24no—
459#95—24no—
460#95—24no—
461#95—28no—
462#95—28no—
463#95—44no—
464#95—44no—
465#95—44no—
466#95—44no—
467#95C2×D418yes—
468#95C2×D4116yes—
469C24—21no—
470C24—21no—
471C24—21no—
472C24—21no—
473C24—22no—
474C24—22no—
475C24—22no—
476C24—22no—
477C24—21no—
478C24—21no—
479C24—21no—
480C24—21no—
481C24—21no—
482C24—21no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24C22×D412yes—
488C24C22×D412yes—
489C24C22×D412yes—
490C24C2×#4112yes—
491C24C2511yescharacteristic
492C2×Q8—216no—
493C2×Q8—28no—
494C2×Q8—28no—
495C2×Q8—28no—
496C2×Q8—28no—
497C2×Q8—28no—
498C2×Q8—28no—
499C2×Q8—48no—
500C2×Q8—48no—
501C2×Q8—48no—
502C2×Q8—48no—
503C2×Q8—48no—
504C2×Q8—4128no—
505C2×Q8—48no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8—44no—
509C2×Q8—44no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—44no—
514C2×Q8—44no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8—44no—
518C2×Q8—44no—
519C2×Q8—44no—
520C2×Q8—44no—
521C2×D4—28no—
522C2×D4—28no—
523C2×D4—44no—
524C2×D4—48no—
525C2×D4—48no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—28no—
538C22×C4—28no—
539C22×C4—28no—
540C22×C4—28no—
541C22×C4—28no—
542C22×C4—28no—
543C22×C4—216no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
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—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—24no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—24no—
611C22×C4—22no—
612C22×C4—24no—
613C22×C4—24no—
614C22×C4—24no—
615C22×C4—24no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—48no—
620C22×C4—48no—
621C22×C4—48no—
622C22×C4—48no—
623C22×C4—48no—
624C22×C4—48no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4—44no—
628C22×C4—44no—
629C22×C4#121116yes—
630C22×C4C22×D412yes—
631C22×C4C22×D414yes—
632C22×C4C22×D414yes—
633C22×C4C22×D414yes—
634C22×C4C22×D414yes—
635C22×C4C22×D412yes—
636C22×C4C22×D412yes—
637C22×C4C22×D412yes—
638C22×C4C22×D412yes—
639C22×C4C22×D414yes—
640C22×C4C22×D412yes—
641C22×C4C22×D412yes—
642C22×C4C22×D412yes—
643C22×C4C2×#4114yes—
644C22×C4C2×#4112yes—
645C22×C4C2×#4112yes—
646C22×C4C2×#4112yes—
647C22×C4H(5,𝔽2)12yes—
648C22×C4H(5,𝔽2)12yes—
649C22×C42−1+414yes—
650C22×C42−1+414yes—
651C22×C42−1+414yes—
652C4⋊C4—28no—
653C4⋊C4—28no—
654C4⋊C4—48no—
655C4⋊C4—48no—
656C4⋊C4—48no—
657C4⋊C4—48no—
658C4⋊C4—48no—
659C4⋊C4—48no—
660C4⋊C4—416no—
661C4⋊C4—416no—
662C4⋊C4—44no—
663C4⋊C4—48no—
664C4⋊C4—48no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—44no—
668C4⋊C4—88no—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—216no—
672C22⋊C4—48no—
673C22⋊C4—48no—
674C22⋊C4—48no—
675C22⋊C4—48no—
676C22⋊C4—48no—
677C22⋊C4—48no—
678C22⋊C4—48no—
679C22⋊C4—48no—
680C22⋊C4—48no—
681C22⋊C4—48no—
682C42—28no—
683C42—28no—
684C42—28no—
685C42—28no—
686C42—48no—
687C42—48no—
688C42—48no—
689C42—44no—
690C23—22no—
691C23—24no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—24no—
700C23—24no—
701C23—22no—
702C23—22no—
703C23—24no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—42no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—42no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—42no—
733C23—42no—
734C23—42no—
735C23C2×#12114yes—
736C23C23×D411yescharacteristic
737C23C23×D411yescharacteristic
738C23C23×D411yescharacteristic
739C23C22×#4111yescharacteristic
740C23C22×#4111yescharacteristic
741C23C2×H(5,𝔽2)11yescharacteristic
742C23C2×H(5,𝔽2)11yescharacteristic
743C23C2×2−1+412yes—
744C23C2×2−1+412yes—
745C23C2×2−1+412yes—
746C23#58512yes—
747Q8—432no—
748Q8—416no—
749Q8—416no—
750Q8—88no—
751D4—416no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—232no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—28no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—432no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—41no—
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—44no—
815C2×C4—416no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
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—44no—
837C2×C4—42no—
838C2×C4—44no—
839C2×C4—44no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—44no—
845C2×C4—44no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—44no—
849C2×C4—44no—
850C2×C4C2×#12114yes—
851C2×C4C2×#12114yes—
852C2×C4#52514yes—
853C2×C4#53618yes—
854C2×C4#53614yes—
855C2×C4#53814yes—
856C2×C4D4214yes—
857C2×C4D4214yes—
858C2×C4#54614yes—
859C2×C4#54614yes—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—44no—
864C22—42no—
865C22—42no—
866C22—44no—
867C22—44no—
868C22—44no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—82no—
879C22—82no—
880C22—82no—
881C22—82no—
882C22C22×#12111yescharacteristic
883C22C2×#52511yescharacteristic
884C22C2×#53611yescharacteristic
885C22C2×#53612yes—
886C22#344911yescharacteristic
887C22C2×#53811yescharacteristic
888C22C2×D4211yescharacteristic
889C22C2×D4211yescharacteristic
890C22C2×#54611yescharacteristic
891C22C2×#54611yescharacteristic
892C22#348912yes—
893C22#349512yes—
894C22#349712yes—
895C22#349911yescharacteristic
896C22#349911yescharacteristic
897C22#349912yes—
898C22#350912yes—
899C22#351612yes—
900C22#352312yes—
901C22#354712yes—
902C22#355012yes—
903C22#355212yes—
904C22#356112yes—
905C4—24no—
906C4—28no—
907C4—24no—
908C4—42no—
909C4—44no—
910C4—44no—
911C4—44no—
912C4—44no—
913C4—44no—
914C4—42no—
915C4—82no—
916C4—82no—
917C4—82no—
918C4—82no—
919C4—82no—
920C4—82no—
921C4#242418yes—
922C2—44no—
923C2—82no—
924C2C2×#242411yescharacteristic
925C2#3530611yescharacteristic
926C2#3531611yescharacteristic
927C2#3567112yes—
928C2#3740012yes—
929C2#3802712yes—
930C2#3894611yescharacteristic
931C2#3895411yescharacteristic
932C2#3934312yes—
933C2#3935611yescharacteristic
934C2#3936011yescharacteristic
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×#2434C2semidirect
4. C2×#2621C2semidirect
5. C2×#2310C2semidirect
7. #15632C2semidirect
8. #15623C2semidirect
10. #15298C2semidirect
11. #15237C2semidirect
12. #15182C2semidirect
13. #15180C2semidirect
14. #15178C2semidirect
15. #14714C2semidirect
16. #14703C2semidirect
17. #14258C2semidirect
18. #14258C2semidirect
19. #13879C2semidirect
198. #391D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24152
C2×#24342
C2×#24092
C2×#26212
C2×#23102
C2×#22932
#156322
#156232
#153002
#152982
#152372
#151822
#151802
#151782
#147142
#147032
#142582
#138792