Finite Group Databasebeta

← #646945

Subgroups — #646945

Order 512.

2454 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2855C211yesmaximal, characteristic
2C2×C4×C22⋊Q8C211yesmaximal, characteristic
3#17019C214yesmaximal, complemented
4#16987C214yesmaximal
5#15196C211yesmaximal, characteristic, complemented
6#15195C211yesmaximal, characteristic
7#15184C211yesmaximal, characteristic, complemented
8#15184C211yesmaximal, characteristic, complemented
9#15182C211yesmaximal, characteristic
10#15182C211yesmaximal, characteristic
11#15180C211yesmaximal, characteristic, complemented
12#15178C211yesmaximal, characteristic
13#15099C214yesmaximal, complemented
14#14297C214yesmaximal
15#14048C211yesmaximal, characteristic, complemented
16#14024C211yesmaximal, characteristic, complemented
17#14000C211yesmaximal, characteristic, complemented
18#13976C211yesmaximal, characteristic, complemented
19C4×#380C211yesmaximal, characteristic
20C22×C4⋊Q8C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C22⋊Q8C2211yescharacteristic
23C22×C4×Q8C2211yescharacteristic
24C23×C42C2211yescharacteristic
25#2855—28no—
26C4×C22⋊Q8—28no—
27C2×#391C2211yescharacteristic
28C2×#391C2211yescharacteristic
29C2×#391C2211yescharacteristic
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#391C2211yescharacteristic
33C2×#391C2211yescharacteristic
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#389C2211yescharacteristic
38C2×#389C2211yescharacteristic
39C2×#387C2212yes—
40C2×#387C2212yes—
41C2×#387C2212yes—
42C2×#385C2212yes—
43C2×#385C2212yes—
44C2×#384C2211yescharacteristic
45C2×#384C2211yescharacteristic
46C2×#384C2211yescharacteristic
47C2×#381C2212yes—
48C2×#380C2211yescharacteristic
49C2×#380C2211yescharacteristic
50C2×#380C2212yes—
51C2×C4×C4⋊C4C2211yescharacteristic
52C2×C4×C4⋊C4C2212yes—
53C2×C4×C4⋊C4C2211yescharacteristic
54C2×C4×C4⋊C4C2211yescharacteristic
55C2×C4×C22⋊C4C2212yes—
56C2×C4×C22⋊C4C2211yescharacteristic
57C2×C4×C22⋊C4C2211yescharacteristic
58#1444C2214yes—
59#1444C2214yes—
60#1444C2214yes—
61#1442C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1441C2214yes—
65#1441C2214yes—
66#1441C2214yes—
67#1441C2214yes—
68#1441C2214yes—
69#1441C2214yes—
70#1441C2214yes—
71#1441C2214yes—
72#1441C2214yes—
73#1441C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1436C2214yes—
79#1436C2214yes—
80#1436C2214yes—
81#1436C2214yes—
82C4⋊#95C2211yescharacteristic
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2212yes—
89#1434C2212yes—
90C22⋊#95C2212yes—
91C4×#95C2211yescharacteristic
92C4×#95C2211yescharacteristic
93C23×Q8C2311yescharacteristic
94C23×Q8C2311yescharacteristic
95C24×C4C2311yescharacteristic
96C24×C4C2311yescharacteristic
97C24×C4C2311yescharacteristic
98C2×C4⋊Q8—24no—
99C2×C4⋊Q8—42no—
100C2×C4⋊Q8—42no—
101C2×C22⋊Q8—24no—
102C2×C22⋊Q8—24no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—42no—
106C2×C22⋊Q8—42no—
107C2×C4×Q8—24no—
108C2×C4×Q8—42no—
109C2×C4×Q8—42no—
110C22×C4⋊C4C2311yescharacteristic
111C22×C4⋊C4C2311yescharacteristic
112C22×C4⋊C4C2312yes—
113C22×C4⋊C4C2311yescharacteristic
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2312yes—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2314yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2312yes—
124C22×C4⋊C4C2314yes—
125C22×C4⋊C4C2314yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C22⋊C4C2312yes—
129C22×C22⋊C4C2312yes—
130C22×C22⋊C4C2312yes—
131C22×C22⋊C4C2312yes—
132C22×C22⋊C4C2312yes—
133C22×C22⋊C4C2312yes—
134C22×C42—42no—
135C22×C42—42no—
136C22×C42D418yes—
137C22×C42C2311yescharacteristic
138C22×C42C2311yescharacteristic
139C22×C42C2311yescharacteristic
140C22×C42C2311yescharacteristic
141C22×C42C2311yescharacteristic
142C22×C42C2311yescharacteristic
143C22×C42C2312yes—
144C22×C42C2312yes—
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147#391—24no—
148#391—24no—
149#391—24no—
150#391—24no—
151#391—24no—
152#391—42no—
153#391—42no—
154#391—42no—
155#391—42no—
156#389—24no—
157#389—24no—
158#389—24no—
159#387—28no—
160#387—28no—
161#387—28no—
162#385—28no—
163#385—28no—
164#384—24no—
165#384—42no—
166#384—42no—
167#381—28no—
168#380—24no—
169#380—24no—
170#380Q8116yescomplemented
171C4×C4⋊C4—28no—
172C4×C4⋊C4—24no—
173C4×C4⋊C4—42no—
174C4×C4⋊C4—42no—
175C4×C22⋊C4—28no—
176C4×C22⋊C4—42no—
177C4×C22⋊C4—42no—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2314yes—
181C2×#95C2314yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2314yes—
199C2×#95C2314yes—
200C2×#95C2314yes—
201C2×#95C2314yes—
202C2×#95C2314yes—
203C2×#95C2314yes—
204C2×#95C2314yes—
205C2×#95C2314yes—
206C2×#95C2314yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C25C2411yescharacteristic
211C22×Q8—22no—
212C22×Q8—22no—
213C22×Q8—22no—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8—22no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8#4114yes—
225C23×C4—22no—
226C23×C4—22no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4—22no—
230C23×C4—22no—
231C23×C4—42no—
232C23×C4—42no—
233C23×C4—42no—
234C23×C4—41no—
235C23×C4—41no—
236C23×C4—41no—
237C23×C4—41no—
238C23×C4C2×D414yes—
239C23×C4C2×D414yes—
240C23×C4C2×D414yes—
241C23×C4C2×Q818yes—
242C23×C4C2412yes—
243C23×C4C2412yes—
244C23×C4C2412yes—
245C23×C4C2412yes—
246C23×C4C2412yes—
247C23×C4C2412yes—
248C23×C4C2411yescharacteristic
249C23×C4C2411yescharacteristic
250C23×C4C2411yescharacteristic
251C23×C4C2412yes—
252C23×C4C2412yes—
253C23×C4C2412yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2411yescharacteristic
258C23×C4C2411yescharacteristic
259C23×C4C2411yescharacteristic
260C4⋊Q8—416no—
261C22⋊Q8—232no—
262C22⋊Q8—416no—
263C4×Q8—416no—
264C2×C4⋊C4—24no—
265C2×C4⋊C4—22no—
266C2×C4⋊C4—24no—
267C2×C4⋊C4—24no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4—24no—
271C2×C4⋊C4—24no—
272C2×C4⋊C4—22no—
273C2×C4⋊C4—22no—
274C2×C4⋊C4—24no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—24no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—28no—
291C2×C4⋊C4—42no—
292C2×C4⋊C4—42no—
293C2×C4⋊C4—44no—
294C2×C4⋊C4—44no—
295C2×C4⋊C4—44no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—44no—
301C2×C4⋊C4—44no—
302C2×C4⋊C4—42no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—44no—
307C2×C4⋊C4—44no—
308C2×C4⋊C4—44no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4C2×Q818yes—
313C2×C4⋊C4C2×Q818yes—
314C2×C4⋊C4#4114yes—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—24no—
317C2×C22⋊C4—24no—
318C2×C22⋊C4—24no—
319C2×C22⋊C4—24no—
320C2×C22⋊C4—24no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—44no—
325C2×C22⋊C4—42no—
326C2×C22⋊C4—42no—
327C2×C22⋊C4—42no—
328C2×C22⋊C4—42no—
329C2×C22⋊C4C2×Q818yes—
330C2×C22⋊C4C2×Q818yes—
331C2×C42—22no—
332C2×C42—22no—
333C2×C42—22no—
334C2×C42—22no—
335C2×C42—24no—
336C2×C42—24no—
337C2×C42—22no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42—22no—
342C2×C42—22no—
343C2×C42—22no—
344C2×C42—22no—
345C2×C42—22no—
346C2×C42—22no—
347C2×C42—22no—
348C2×C42—22no—
349C2×C42—416no—
350C2×C42—42no—
351C2×C42—42no—
352C2×C42—41no—
353C2×C42—41no—
354C2×C42—41no—
355C2×C42—41no—
356C2×C42—44no—
357C2×C42C2×D414yes—
358C2×C42C2×D414yes—
359C2×C42C2×D414yes—
360C2×C42C2×D414yes—
361#95—24no—
362#95—24no—
363#95—24no—
364#95—24no—
365#95—24no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—24no—
371#95—24no—
372#95—24no—
373#95—28no—
374#95—28no—
375#95—42no—
376#95—44no—
377#95—44no—
378#95—44no—
379#95—44no—
380#95—44no—
381#95—44no—
382#95—42no—
383#95—42no—
384#95—42no—
385#95—42no—
386#95—42no—
387#95—44no—
388#95—44no—
389#95—44no—
390#95—44no—
391#95C2×Q818yes—
392#95C2×Q818yes—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—21no—
398C24—21no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24C22×D412yes—
403C24C22×Q814yes—
404C24C2511yescharacteristic
405C2×Q8—28no—
406C2×Q8—28no—
407C2×Q8—28no—
408C2×Q8—44no—
409C2×Q8—44no—
410C2×Q8—44no—
411C2×Q8—44no—
412C2×Q8—44no—
413C2×Q8—44no—
414C2×Q8—44no—
415C2×Q8—44no—
416C2×Q8—44no—
417C2×Q8—44no—
418C2×Q8—44no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—28no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
501C22×C4—24no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—24no—
507C22×C4—24no—
508C22×C4—44no—
509C22×C4—44no—
510C22×C4—44no—
511C22×C4—44no—
512C22×C4—44no—
513C22×C4—48no—
514C22×C4—48no—
515C22×C4—48no—
516C22×C4—48no—
517C22×C4—44no—
518C22×C4—44no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4C4⋊Q8116yescomplemented
522C22×C4C22×D412yes—
523C22×C4C22×D412yes—
524C22×C4C22×D412yes—
525C22×C4C22×D412yes—
526C22×C4C22×D412yes—
527C22×C4C22×D412yes—
528C22×C4C22×Q814yes—
529C22×C4C22×Q814yes—
530C22×C4C22×Q814yes—
531C22×C4C22×Q814yes—
532C22×C4C22×Q814yes—
533C22×C4C22×Q814yes—
534C22×C4C2×#4114yes—
535C22×C4C2×#4114yes—
536C22×C4C2×#4112yes—
537C22×C4C2×#4112yes—
538C22×C4H(5,𝔽2)12yes—
539C22×C4H(5,𝔽2)12yes—
540C22×C4H(5,𝔽2)12yes—
541C22×C42−1+412yes—
542C4⋊C4—216no—
543C4⋊C4—28no—
544C4⋊C4—48no—
545C4⋊C4—48no—
546C4⋊C4—48no—
547C4⋊C4—48no—
548C4⋊C4—48no—
549C4⋊C4—48no—
550C4⋊C4—48no—
551C4⋊C4—416no—
552C4⋊C4—44no—
553C4⋊C4—44no—
554C4⋊C4—44no—
555C4⋊C4—44no—
556C4⋊C4—44no—
557C4⋊C4—88no—
558C4⋊C4—88no—
559C4⋊C4—88no—
560C22⋊C4—216no—
561C22⋊C4—48no—
562C22⋊C4—48no—
563C22⋊C4—48no—
564C22⋊C4—48no—
565C22⋊C4—48no—
566C42—28no—
567C42—28no—
568C42—44no—
569C42—44no—
570C42—48no—
571C42—48no—
572C42—44no—
573C42—44no—
574C42—44no—
575C42—44no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—42no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23C2×C4⋊Q814yes—
599C23C23×D411yescharacteristic
600C23C23×Q812yes—
601C23C22×#4111yescharacteristic
602C23C22×#4111yescharacteristic
603C23C2×H(5,𝔽2)11yescharacteristic
604C23C2×H(5,𝔽2)11yescharacteristic
605C23C2×H(5,𝔽2)11yescharacteristic
606C23C2×2−1+411yescharacteristic
607C23#58512yes—
608C23#58512yes—
609C23#58512yes—
610Q8—416no—
611Q8—88no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—24no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—24no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—28no—
646C2×C4—416no—
647C2×C4—416no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—44no—
665C2×C4—42no—
666C2×C4—42no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—416no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4#52514yes—
713C2×C4C2×C4⋊Q814yes—
714C2×C4C2×C4⋊Q814yes—
715C2×C4#53414yes—
716C2×C4#53714yes—
717C2×C4#53814yes—
718C2×C4#53914yes—
719C2×C4#54014yes—
720C2×C4#54214yes—
721C22—24no—
722C22—24no—
723C22—24no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—44no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—42no—
732C22C2×#52511yescharacteristic
733C22C22×C4⋊Q811yescharacteristic
734C22C2×#53411yescharacteristic
735C22C2×#53711yescharacteristic
736C22#344911yescharacteristic
737C22#344911yescharacteristic
738C22#344911yescharacteristic
739C22C2×#53811yescharacteristic
740C22C2×#53911yescharacteristic
741C22C2×#54011yescharacteristic
742C22C2×#54211yescharacteristic
743C22Q8×#4112yes—
744C22Q8×#4112yes—
745C22#350112yes—
746C22#350112yes—
747C22#350112yes—
748C22#350212yes—
749C22#352112yes—
750C22#352412yes—
751C22#353912yes—
752C22#354012yes—
753C22#355112yes—
754C22#355712yes—
755C4—24no—
756C4—24no—
757C4—42no—
758C4—42no—
759C4—44no—
760C4—44no—
761C4—44no—
762C4—44no—
763C4—44no—
764C4—42no—
765C4—44no—
766C4—82no—
767C4—82no—
768C4—82no—
769C4—82no—
770C4—82no—
771C4—82no—
772C4#263018yes—
773C2—44no—
774C2C2×#263011yescharacteristic
775C2#3495311yescharacteristic
776C2#3501111yescharacteristic
777C2#3517311yescharacteristic
778C2#3521111yescharacteristic
779C2#3745511yescharacteristic
780C2#3754211yescharacteristic
781C2#3966412yes—
782C2#3966512yes—
783C2#3966612yes—
784C2#3966712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #17019C2semidirect
5. #15196C2semidirect
7. #15184C2semidirect
8. #15184C2semidirect
11. #15180C2semidirect
13. #15099C2semidirect
15. #14048C2semidirect
16. #14024C2semidirect
17. #14000C2semidirect
18. #13976C2semidirect
170. #380Q8semidirect
521. C22×C4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28552
C2×C4×C22⋊Q82
#170192
#169872
#151962
#151952
#151842
#151822
#151802
#151782
#150992
#142972
#140482
#140242
#140002
#139762
C4×#3802