Finite Group Databasebeta

← #874595

Subgroups — #874595

Order 512.

3336 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2499C211yesmaximal, characteristic, complemented
2C2×#2415C211yesmaximal, characteristic
3C2×#2434C211yesmaximal, characteristic, complemented
4C2×#2409C211yesmaximal, characteristic
5#16787C214yesmaximal, complemented
6#15627C214yesmaximal, complemented
7#15497C214yesmaximal
8#15237C211yesmaximal, characteristic, complemented
9#15236C211yesmaximal, characteristic, complemented
10#15180C211yesmaximal, characteristic, complemented
11#15178C211yesmaximal, characteristic, complemented
12#15178C211yesmaximal, characteristic, complemented
13#15150C211yesmaximal, characteristic, complemented
14#14714C211yesmaximal, characteristic, complemented
15#14703C211yesmaximal, characteristic, complemented
16#14541C214yesmaximal, complemented
17#14138C211yesmaximal, characteristic, complemented
18#13922C211yesmaximal, characteristic, complemented
19C4×#390C211yesmaximal, characteristic
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
29#2499—28no—
30#2434—28no—
31#2415—28no—
32#2409—28no—
33C2×#397C2214yes—
34C2×#397C2214yes—
35C2×#397C2212yes—
36C2×#395C2212yes—
37C2×#395C2214yes—
38C2×#394C2212yes—
39C2×#393C2212yes—
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#390C2212yes—
52C2×#389C2212yes—
53C2×#389C2211yescharacteristic
54C2×#388C2212yes—
55C2×#387C2214yes—
56C2×#386C2212yes—
57C2×#385C2212yes—
58C2×#385C2214yes—
59C2×#384C2211yescharacteristic
60C2×#382C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C43C2211yescharacteristic
69#1446C2214yes—
70#1445C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1443C2214yes—
74#1442C2214yes—
75#1442C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1440C2214yes—
79#1440C2214yes—
80#1439C2214yes—
81#1439C2214yes—
82#1437C2212yes—
83#1437C2212yes—
84#1436C2214yes—
85#1436C2214yes—
86C4⋊#95C2212yes—
87C4⋊#95C2214yes—
88C4⋊#95C2211yescharacteristic
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2214yes—
93#1434C2214yes—
94C22⋊#95C2214yes—
95C23×Q8—24no—
96C23×Q8—24no—
97C23×Q8—24no—
98C23×Q8—42no—
99C23×Q8—42no—
100C23×Q8—42no—
101C23×Q8—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×Q8C2311yescharacteristic
105C23×Q8C2312yes—
106C23×D4C2311yescharacteristic
107C24×C4C2311yescharacteristic
108C24×C4C2311yescharacteristic
109C24×C4C2312yes—
110C2×C4⋊Q8—24no—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—42no—
114C2×C4⋊Q8—42no—
115C2×C4⋊Q8—42no—
116C2×C22⋊Q8—24no—
117C2×C22⋊Q8—24no—
118C2×C22⋊Q8—24no—
119C2×C22⋊Q8—24no—
120C2×C22⋊Q8—24no—
121C2×C22⋊Q8—24no—
122C2×C22⋊Q8—24no—
123C2×C22⋊Q8—42no—
124C2×C22⋊Q8—42no—
125C2×C22⋊Q8—42no—
126C2×C22⋊Q8—42no—
127C2×C22⋊Q8—42no—
128C2×C4×D4—42no—
129C2×C4×D4—42no—
130C2×C4×D4D418yes—
131C2×#117—24no—
132C2×#117—24no—
133C2×#117—42no—
134C22×C4⋊C4C2312yes—
135C22×C4⋊C4C2314yes—
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C4⋊C4C2311yescharacteristic
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2314yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2311yescharacteristic
146C22×C4⋊C4C2314yes—
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2312yes—
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2312yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2311yescharacteristic
161C22×C22⋊C4C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2311yescharacteristic
165C22×C42C2312yes—
166C22×C42C2312yes—
167C22×C42C2312yes—
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170#397—28no—
171#397—216no—
172#397—216no—
173#395—28no—
174#395—216no—
175#394—28no—
176#393—28no—
177#391—24no—
178#391—24no—
179#391—24no—
180#391—24no—
181#391—24no—
182#391—42no—
183#391—42no—
184#391—42no—
185#391—42no—
186#391—42no—
187#391D418yescomplemented
188#390—28no—
189#389—28no—
190#389—24no—
191#388—28no—
192#387—216no—
193#386—28no—
194#385—28no—
195#385—216no—
196#384—24no—
197#382—24no—
198#380—24no—
199#380—24no—
200C4×C4⋊C4—42no—
201C4×C22⋊C4—24no—
202C4×C22⋊C4—24no—
203C4×C22⋊C4—42no—
204C4×C22⋊C4—42no—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2312yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2312yes—
221C2×#95C2314yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2314yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2314yes—
231C2×#95C2314yes—
232C43—42no—
233C25C2411yescharacteristic
234C25C2411yescharacteristic
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—24no—
241C22×Q8—24no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—24no—
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—42no—
258C22×Q8—42no—
259C22×Q8—42no—
260C22×Q8—42no—
261C22×Q8—416no—
262C22×Q8—416no—
263C22×Q8—416no—
264C22×Q8—416no—
265C22×Q8—416no—
266C22×Q8—416no—
267C22×Q8—416no—
268C22×Q8C2×D414yes—
269C22×Q8#4114yes—
270C22×D4—24no—
271C22×D4—24no—
272C22×D4—41no—
273C22×D4—41no—
274C22×D4C2×D414yes—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—22no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4—42no—
294C23×C4C2×D414yes—
295C23×C4C2×D414yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2412yes—
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2411yescharacteristic
312C23×C4C2411yescharacteristic
313C4⋊Q8—416no—
314C4⋊Q8—416no—
315C22⋊Q8—416no—
316C22⋊Q8—416no—
317C22⋊Q8—416no—
318C22⋊Q8—416no—
319C4×D4—416no—
320#117—416no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—28no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—28no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—41no—
353C2×C4⋊C4—41no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—42no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—42no—
363C2×C4⋊C4C2×D414yes—
364C2×C4⋊C4C2×D414yes—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—28no—
376C2×C22⋊C4—28no—
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—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—42no—
388C2×C22⋊C4—41no—
389C2×C22⋊C4—41no—
390C2×C22⋊C4—41no—
391C2×C22⋊C4—41no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—42no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4C2×D414yes—
400C2×C22⋊C4C2×D414yes—
401C2×C22⋊C4#4118yes—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—24no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—24no—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42—42no—
422C2×C42—42no—
423C2×C42—42no—
424C2×C42C2×D414yes—
425C2×C42C2×D414yes—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—24no—
430#95—28no—
431#95—24no—
432#95—24no—
433#95—28no—
434#95—24no—
435#95—24no—
436#95—28no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—28no—
441#95—28no—
442#95—28no—
443#95—28no—
444#95—42no—
445#95—42no—
446#95—42no—
447#95—44no—
448#95—44no—
449#95—44no—
450#95—44no—
451#95—44no—
452#95C2×D4116yes—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—21no—
458C24—21no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24—21no—
463C24—21no—
464C24—22no—
465C24—21no—
466C24—21no—
467C24—21no—
468C24—21no—
469C24—22no—
470C24—22no—
471C24—22no—
472C24C22×D412yes—
473C24C22×D412yes—
474C24C2×#4114yes—
475C24C2511yescharacteristic
476C2×Q8—28no—
477C2×Q8—28no—
478C2×Q8—28no—
479C2×Q8—28no—
480C2×Q8—28no—
481C2×Q8—28no—
482C2×Q8—48no—
483C2×Q8—48no—
484C2×Q8—48no—
485C2×Q8—48no—
486C2×Q8—48no—
487C2×Q8—48no—
488C2×Q8—4128no—
489C2×Q8—48no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
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×D4—28no—
506C2×D4—28no—
507C2×D4—44no—
508C2×D4—48no—
509C2×D4—48no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—24no—
560C22×C4—22no—
561C22×C4—28no—
562C22×C4—28no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
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—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—24no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—24no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—22no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4C22×D412yes—
617C22×C4C22×D414yes—
618C22×C4C22×D412yes—
619C22×C4C22×D414yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D414yes—
623C22×C4C22×D412yes—
624C22×C4C22×D412yes—
625C22×C4C2×#4114yes—
626C22×C4C2×#4114yes—
627C22×C4C2×#4114yes—
628C22×C4C2×#4112yes—
629C22×C4H(5,𝔽2)12yes—
630C22×C4H(5,𝔽2)12yes—
631C22×C4H(5,𝔽2)12yes—
632C22×C4H(5,𝔽2)12yes—
633C22×C42−1+414yes—
634C22×C42−1+414yes—
635C22×C42−1+414yes—
636C4⋊C4—28no—
637C4⋊C4—44no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—48no—
642C4⋊C4—416no—
643C4⋊C4—48no—
644C4⋊C4—416no—
645C4⋊C4—44no—
646C4⋊C4—48no—
647C4⋊C4—44no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—416no—
651C22⋊C4—216no—
652C22⋊C4—44no—
653C22⋊C4—44no—
654C22⋊C4—48no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4—48no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C42—28no—
665C42—28no—
666C42—48no—
667C42—48no—
668C42—48no—
669C42—44no—
670C42—44no—
671C42—44no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—24no—
677C23—24no—
678C23—22no—
679C23—22no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—42no—
695C23—42no—
696C23—41no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—42no—
712C23—41no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23#53214yes—
718C23C23×D411yescharacteristic
719C23C23×D411yescharacteristic
720C23C22×#4112yes—
721C23C22×#4111yescharacteristic
722C23C2×H(5,𝔽2)11yescharacteristic
723C23C2×H(5,𝔽2)11yescharacteristic
724C23C2×H(5,𝔽2)11yescharacteristic
725C23C2×H(5,𝔽2)11yescharacteristic
726C23C2×2−1+412yes—
727C23C2×2−1+412yes—
728C23C2×2−1+412yes—
729Q8—432no—
730Q8—416no—
731Q8—416no—
732Q8—88no—
733D4—416no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—24no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—28no—
762C2×C4—24no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—432no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
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—44no—
797C2×C4—416no—
798C2×C4—416no—
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—44no—
817C2×C4—44no—
818C2×C4—44no—
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—44no—
829C2×C4—44no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4#53414yes—
834C2×C4#53514yes—
835C2×C4#53614yes—
836C2×C4#53814yes—
837C2×C4D4214yes—
838C2×C4#54614yes—
839C2×C4#54614yes—
840C2×C4#54818yes—
841C2×C4#56014yes—
842C22—24no—
843C22—24no—
844C22—24no—
845C22—44no—
846C22—42no—
847C22—42no—
848C22—44no—
849C22—42no—
850C22—42no—
851C22—44no—
852C22—44no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—42no—
859C22—42no—
860C22—82no—
861C22—82no—
862C22—82no—
863C22—82no—
864C22C2×#53211yescharacteristic
865C22C2×#53411yescharacteristic
866C22C2×#53511yescharacteristic
867C22C2×#53611yescharacteristic
868C22C2×#53811yescharacteristic
869C22C2×D4211yescharacteristic
870C22C2×#54611yescharacteristic
871C22C2×#54611yescharacteristic
872C22C2×#54812yes—
873C22#348212yes—
874C22#349912yes—
875C22#349911yescharacteristic
876C22#349911yescharacteristic
877C22#351112yes—
878C22#352012yes—
879C22#352012yes—
880C22#352012yes—
881C22#352312yes—
882C22C2×#56011yescharacteristic
883C22#353812yes—
884C22#355012yes—
885C22#355012yes—
886C22#355212yes—
887C4—28no—
888C4—24no—
889C4—42no—
890C4—44no—
891C4—42no—
892C4—42no—
893C4—44no—
894C4—44no—
895C4—44no—
896C4—44no—
897C4—82no—
898C4—82no—
899C4—82no—
900C4—82no—
901C4—82no—
902C4—82no—
903C4#267818yes—
904C2—44no—
905C2—82no—
906C2#3508511yescharacteristic
907C2#3612211yescharacteristic
908C2#3637611yescharacteristic
909C2#3738611yescharacteristic
910C2#3895411yescharacteristic
911C2#3916712yes—
912C2#3936011yescharacteristic
913C2#4019012yes—
914C2#4567712yes—
915C2C2×#267811yescharacteristic
916C2#5965112yes—
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
1. C2×#2499C2semidirect
3. C2×#2434C2semidirect
5. #16787C2semidirect
6. #15627C2semidirect
8. #15237C2semidirect
9. #15236C2semidirect
10. #15180C2semidirect
11. #15178C2semidirect
12. #15178C2semidirect
13. #15150C2semidirect
14. #14714C2semidirect
15. #14703C2semidirect
16. #14541C2semidirect
17. #14138C2semidirect
18. #13922C2semidirect
187. #391D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24992
C2×#24152
C2×#24342
C2×#24092
#167872
#156272
#154972
#152372
#152362
#151802
#151782
#151502
#147142
#147032
#145412
#141382
#139222
C4×#3902