Finite Group Databasebeta

← #366782

Subgroups — #366782

Order 512.

1614 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2499C211yesmaximal, characteristic
2C2×#1892C211yesmaximal, characteristic
3C2×#1873C211yesmaximal, characteristic
4C2×#1825C211yesmaximal, characteristic
5C2×C8×C22⋊C4C211yesmaximal, characteristic
6C2×#1735C211yesmaximal, characteristic
7#13879C211yesmaximal, characteristic
8#11373C211yesmaximal, characteristic, complemented
9#11372C211yesmaximal, characteristic, complemented
10#11052C211yesmaximal, characteristic, complemented
11#11050C211yesmaximal, characteristic, complemented
12#10926C211yesmaximal, characteristic, complemented
13#10926C211yesmaximal, characteristic, complemented
14#10842C211yesmaximal, characteristic, complemented
15#10841C211yesmaximal, characteristic, complemented
16C24×C8C2211yescharacteristic
17C22×C22⋊Q8C2211yescharacteristic
18C22×#117C2211yescharacteristic
19C22×#117C2211yescharacteristic
20C22×#103C2211yescharacteristic
21C22×#103C2211yescharacteristic
22C22×#103C2211yescharacteristic
23C22×#103C2211yescharacteristic
24C22×C22⋊C8C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26C22×C4×C8C2211yescharacteristic
27#2499—24no—
28#2499C418yescomplemented
29C2×#397—22no—
30C2×#391C2211yescharacteristic
31C2×#391C2211yescharacteristic
32C2×#387—22no—
33C2×#384C2211yescharacteristic
34C2×#384C2211yescharacteristic
35C2×#382C2211yescharacteristic
36C2×#382C2211yescharacteristic
37C2×#380C2211yescharacteristic
38C2×C4×C22⋊C4C2211yescharacteristic
39#1892—24no—
40#1873—24no—
41#1825—24no—
42C8×C22⋊C4—24no—
43#1735—24no—
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#340C2211yescharacteristic
48C2×#340C2211yescharacteristic
49C2×#340C2211yescharacteristic
50C2×#340C2211yescharacteristic
51C2×#340C2211yescharacteristic
52C2×#340C2211yescharacteristic
53C2×#340C2211yescharacteristic
54C2×#340C2211yescharacteristic
55C2×#340C2211yescharacteristic
56C2×#336C2211yescharacteristic
57C2×#336C2211yescharacteristic
58#1439—22no—
59#1436—22no—
60C4⋊#95C2211yescharacteristic
61C4⋊#95C2211yescharacteristic
62C23×Q8C2311yescharacteristic
63C24×C4C2311yescharacteristic
64C23×C8—22no—
65C23×C8—22no—
66C23×C8—22no—
67C23×C8—22no—
68C23×C8—41no—
69C23×C8—41no—
70C23×C8D414yes—
71C23×C8C2311yescharacteristic
72C23×C8C2311yescharacteristic
73C23×C8C2311yescharacteristic
74C23×C8C2311yescharacteristic
75C2×C22⋊Q8—22no—
76C2×C22⋊Q8—22no—
77C2×C22⋊Q8—22no—
78C2×C22⋊Q8—22no—
79C2×C22⋊Q8—22no—
80C2×C22⋊Q8C2×C414yes—
81C2×#117—22no—
82C2×#117—22no—
83C2×#117—22no—
84C2×#117—22no—
85C2×#117—22no—
86C2×#117—22no—
87C2×#117—22no—
88C2×#117—22no—
89C2×#117—22no—
90C2×#117—41no—
91C2×#117—41no—
92C2×#117C2×C414yes—
93C22×C4⋊C4—22no—
94C22×C4⋊C4—21no—
95C22×C4⋊C4—22no—
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2311yescharacteristic
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2311yescharacteristic
101C22×C4⋊C4C2311yescharacteristic
102C22×C4⋊C4C2311yescharacteristic
103C22×C22⋊C4—21no—
104C22×C22⋊C4—21no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4—21no—
107C22×C22⋊C4D412yes—
108C22×C42—21no—
109C22×C42—21no—
110C22×C42C2311yescharacteristic
111C22×C42C2311yescharacteristic
112C2×#103—22no—
113C2×#103—22no—
114C2×#103—22no—
115C2×#103—22no—
116C2×#103—22no—
117C2×#103—22no—
118C2×#103—22no—
119C2×#103—22no—
120C2×#103—41no—
121C2×#103—41no—
122C2×#103—41no—
123C2×#103—41no—
124C2×C22⋊C8—22no—
125C2×C22⋊C8—22no—
126C2×C22⋊C8D414yes—
127C2×C4×C8—22no—
128C2×C4×C8—22no—
129C2×C4×C8—22no—
130C2×C4×C8—22no—
131C2×C4×C8—41no—
132C2×C4×C8—41no—
133#397—216no—
134#391—22no—
135#391—22no—
136#391C2×C414yes—
137#391C2×C414yes—
138#387—216no—
139#384—22no—
140#384—22no—
141#384—41no—
142#384C2×C414yes—
143#382—22no—
144#382—22no—
145#382—41no—
146#382C2×C414yes—
147#380—22no—
148#380—22no—
149C4×C22⋊C4C2×C414yes—
150C4×C22⋊C4D414yes—
151C2×#95—22no—
152C2×#95—22no—
153C2×#95—22no—
154C2×#95—22no—
155C2×#95—21no—
156C2×#95—22no—
157C2×#95—22no—
158C2×#95D412yes—
159#340—22no—
160#340—22no—
161#340—22no—
162#340—22no—
163#340—22no—
164#340—22no—
165#340—22no—
166#340—22no—
167#340—22no—
168#340—22no—
169#340—22no—
170#340—22no—
171#336—22no—
172#336—22no—
173C25C2×D411yescharacteristic
174C22×Q8—21no—
175C22×Q8—21no—
176C22×Q8—21no—
177C22×Q8—21no—
178C22×Q8—21no—
179C22×Q8—21no—
180C22×Q8—21no—
181C22×Q8—21no—
182C22×Q8—21no—
183C22×Q8—21no—
184C22×Q8—21no—
185C22×Q8—21no—
186C22×Q8—21no—
187C22×Q8C22×C412yes—
188C23×C4—21no—
189C23×C4—21no—
190C23×C4—21no—
191C23×C4—21no—
192C23×C4—21no—
193C23×C4—21no—
194C23×C4—21no—
195C23×C4—21no—
196C23×C4—21no—
197C23×C4—21no—
198C23×C4—21no—
199C23×C4—21no—
200C23×C4—21no—
201C23×C4—21no—
202C23×C4—21no—
203C23×C4—21no—
204C23×C4C22×C412yes—
205C23×C4C2×D412yes—
206C23×C4C2×D411yescharacteristic
207C23×C4C2×D412yes—
208C23×C4C2×D412yes—
209C23×C4C2×D412yes—
210C23×C4C2×D412yes—
211C23×C4#4112yes—
212C23×C4#4112yes—
213C23×C4C2411yescharacteristic
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—28no—
219C22×C8—21no—
220C22×C8—21no—
221C22×C8—21no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—21no—
231C22×C8—21no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—28no—
238C22×C8—44no—
239C22×C8—44no—
240C22×C8—44no—
241C22×C8—44no—
242C22×C8—44no—
243C22×C8C2×D412yes—
244C22×C8C2×D412yes—
245C22×C8C2×D412yes—
246C22×C8C2×D412yes—
247C22×C8#4112yes—
248C22×C8#4112yes—
249C22⋊Q8—28no—
250C22⋊Q8—28no—
251C22⋊Q8—44no—
252C22⋊Q8—44no—
253#117—28no—
254#117—28no—
255#117—28no—
256#117—44no—
257#117—44no—
258#117—44no—
259#117—44no—
260#117—44no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—28no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—44no—
303C2×C4⋊C4—44no—
304C2×C4⋊C4—44no—
305C2×C4⋊C4—44no—
306C2×C4⋊C4—82no—
307C2×C4⋊C4C22×C412yes—
308C2×C4⋊C4C22×C412yes—
309C2×C4⋊C4C22×C412yes—
310C2×C4⋊C4#4112yes—
311C2×C4⋊C4#4112yes—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—24no—
316C2×C22⋊C4—42no—
317C2×C22⋊C4—42no—
318C2×C22⋊C4—42no—
319C2×C22⋊C4—42no—
320C2×C22⋊C4—42no—
321C2×C22⋊C4—42no—
322C2×C22⋊C4—42no—
323C2×C22⋊C4—42no—
324C2×C22⋊C4—82no—
325C2×C22⋊C4C22⋊C418yes—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—24no—
335C2×C42—42no—
336C2×C42—42no—
337C2×C42—42no—
338C2×C42—42no—
339C2×C42—42no—
340C2×C42C22×C412yes—
341C2×C42C22×C412yes—
342C2×C42C2×D412yes—
343C2×C42C2×D412yes—
344#103—44no—
345#103—44no—
346#103—44no—
347#103—44no—
348C22⋊C8—28no—
349C4×C8—44no—
350C4×C8—44no—
351#95—28no—
352#95—28no—
353#95—28no—
354#95—44no—
355#95—42no—
356#95—44no—
357#95—82no—
358#95C22⋊C418yes—
359C24—21no—
360C24—21no—
361C24—21no—
362C24—21no—
363C24—22no—
364C24—22no—
365C24—22no—
366C24—22no—
367C24C2×C22⋊C412yes—
368C24#12412yes—
369C24#12712yes—
370C24C22×D411yescharacteristic
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8—22no—
375C2×Q8—22no—
376C2×Q8—22no—
377C2×Q8—41no—
378C2×Q8—41no—
379C2×Q8—41no—
380C2×Q8—41no—
381C2×Q8—41no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—41no—
386C2×Q8—41no—
387C2×Q8—41no—
388C2×Q8—41no—
389C2×Q8—41no—
390C2×Q8—41no—
391C2×Q8—41no—
392C2×Q8—41no—
393C2×Q8—41no—
394C2×Q8—41no—
395C2×Q8—41no—
396C2×Q8—41no—
397C2×Q8—41no—
398C2×Q8—41no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
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—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—42no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—42no—
479C22×C4C2×C22⋊C414yes—
480C22×C4C2×C22⋊C412yes—
481C22×C4C2×C22⋊C414yes—
482C22×C4C4×D414yes—
483C22×C4C4×D414yes—
484C22×C4#12114yes—
485C22×C4#12114yes—
486C22×C4#12412yes—
487C22×C4#12712yes—
488C22×C4#13514yes—
489C22×C4#13514yes—
490C22×C4C23×C411yescharacteristic
491C22×C4C22×D411yescharacteristic
492C22×C4C22×D411yescharacteristic
493C22×C4C22×D411yescharacteristic
494C22×C4C2×#4111yescharacteristic
495C22×C4C2×#4111yescharacteristic
496C22×C4C2×#4111yescharacteristic
497C22×C4C2×#4111yescharacteristic
498C22×C4C2×#4111yescharacteristic
499C22×C4C2×#4111yescharacteristic
500C22×C4H(5,𝔽2)11yescharacteristic
501C22×C4H(5,𝔽2)11yescharacteristic
502C22×C42−1+411yescharacteristic
503C22×C42−1+411yescharacteristic
504C2×C8—22no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8—22no—
514C2×C8—22no—
515C2×C8—22no—
516C2×C8—22no—
517C2×C8—22no—
518C2×C8—22no—
519C2×C8—416no—
520C2×C8—41no—
521C2×C8—41no—
522C2×C8—41no—
523C2×C8—41no—
524C2×C8—41no—
525C2×C8—41no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—41no—
529C2×C8—41no—
530C2×C8—41no—
531C2×C8—41no—
532C2×C8#12314yes—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—41no—
544C4⋊C4—41no—
545C4⋊C4—41no—
546C4⋊C4—41no—
547C4⋊C4—41no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4—41no—
551C4⋊C4—41no—
552C4⋊C4—41no—
553C4⋊C4—48no—
554C4⋊C4—416no—
555C4⋊C4—41no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4—41no—
559C4⋊C4—41no—
560C4⋊C4—41no—
561C4⋊C4—41no—
562C4⋊C4—41no—
563C4⋊C4—88no—
564C22⋊C4—216no—
565C22⋊C4—48no—
566C22⋊C4—48no—
567C22⋊C4—48no—
568C22⋊C4—84no—
569C42—22no—
570C42—22no—
571C42—22no—
572C42—22no—
573C42—22no—
574C42—22no—
575C42—22no—
576C42—22no—
577C42—48no—
578C42—48no—
579C23—22no—
580C23—22no—
581C23—24no—
582C23—24no—
583C23—22no—
584C23—22no—
585C23—24no—
586C23—24no—
587C23—22no—
588C23—22no—
589C23—22no—
590C23—22no—
591C23—22no—
592C23—22no—
593C23—42no—
594C23—42no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23#39014yes—
602C23C22×C22⋊C411yescharacteristic
603C23C2×#12411yescharacteristic
604C23C2×#12711yescharacteristic
605C23#54611yescharacteristic
606C23#54611yescharacteristic
607C23#54711yescharacteristic
608C23#54711yescharacteristic
609C23C2×#13512yes—
610C23C2×#13512yes—
611C23#57712yes—
612C23#57812yes—
613Q8—42no—
614Q8—42no—
615Q8—42no—
616Q8—42no—
617Q8—81no—
618Q8—81no—
619Q8—81no—
620Q8—81no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—24no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—24no—
632C2×C4—22no—
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—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—44no—
654C2×C4—44no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—82no—
662C2×C4—82no—
663C2×C4—82no—
664C2×C4—81no—
665C2×C4—81no—
666C2×C4—81no—
667C2×C4—81no—
668C2×C4—81no—
669C2×C4—81no—
670C2×C4—81no—
671C2×C4—81no—
672C2×C4—81no—
673C2×C4—81no—
674C2×C4—81no—
675C2×C4—81no—
676C2×C4—81no—
677C2×C4—82no—
678C2×C4—82no—
679C2×C4—81no—
680C2×C4—82no—
681C2×C4—82no—
682C2×C4—81no—
683C2×C4—81no—
684C2×C4—81no—
685C2×C4—81no—
686C2×C4—81no—
687C2×C4—82no—
688C2×C4—82no—
689C2×C4—81no—
690C2×C4#39014yes—
691C2×C4#41618yes—
692C2×C4C2×C4×D411yescharacteristic
693C2×C4C2×C4×D411yescharacteristic
694C2×C4C4×#4111yescharacteristic
695C2×C4C4×#4111yescharacteristic
696C2×C4#52011yescharacteristic
697C2×C4#52011yescharacteristic
698C2×C4C2×#12111yescharacteristic
699C2×C4C2×#12111yescharacteristic
700C2×C4C2×#12311yescharacteristic
701C2×C4#52511yescharacteristic
702C2×C4#52911yescharacteristic
703C2×C4#52911yescharacteristic
704C2×C4#53411yescharacteristic
705C2×C4#53611yescharacteristic
706C2×C4#53911yescharacteristic
707C2×C4#53911yescharacteristic
708C2×C4#54611yescharacteristic
709C2×C4#54611yescharacteristic
710C2×C4#54611yescharacteristic
711C2×C4#54611yescharacteristic
712C2×C4#54711yescharacteristic
713C2×C4#54711yescharacteristic
714C2×C4#54711yescharacteristic
715C2×C4#54711yescharacteristic
716C2×C4#55111yescharacteristic
717C2×C4#55111yescharacteristic
718C2×C4#55211yescharacteristic
719C2×C4#55211yescharacteristic
720C8—24no—
721C8—42no—
722C8—42no—
723C8—42no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—42no—
728C22—42no—
729C22—44no—
730C22—44no—
731C22—42no—
732C22—42no—
733C22—44no—
734C22—44no—
735C22C2×#39011yescharacteristic
736C22#233911yescharacteristic
737C22#233911yescharacteristic
738C22#248811yescharacteristic
739C22#248811yescharacteristic
740C22#250111yescharacteristic
741C22#253911yescharacteristic
742C22C2×#41612yes—
743C22#289812yes—
744C22#313112yes—
745C22#313712yes—
746C22#314711yescharacteristic
747C22#314711yescharacteristic
748C22#315411yescharacteristic
749C22#315611yescharacteristic
750C22#329612yes—
751C22#330012yes—
752C22#330212yes—
753C22#330412yes—
754C22#333612yes—
755C22#333712yes—
756C22#334012yes—
757C22#334212yes—
758C4—24no—
759C4—28no—
760C4—44no—
761C4—82no—
762C4—82no—
763C4—82no—
764C4—82no—
765C4—82no—
766C4—82no—
767C4—161no—
768C4—161no—
769C4C4×#12311yescharacteristic
770C4#232211yescharacteristic
771C4#235911yescharacteristic
772C4#235911yescharacteristic
773C4#241211yescharacteristic
774C4#241311yescharacteristic
775C4#242511yescharacteristic
776C4#242511yescharacteristic
777C2—44no—
778C2#1399611yescharacteristic
779C2#2119511yescharacteristic
780C2#2120511yescharacteristic
781C2#2248612yes—
782C2#2249012yes—
783C2#2769812yes—
784C2#2770012yes—
785C2#2792511yescharacteristic
786C2#2792711yescharacteristic
787C2#2833811yescharacteristic
788C2#2834011yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutatorC22×C4C23×C4
Frattini, cosocleC23×C4C24
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
8. #11373C2semidirect
9. #11372C2semidirect
10. #11052C2semidirect
11. #11050C2semidirect
12. #10926C2semidirect
13. #10926C2semidirect
14. #10842C2semidirect
15. #10841C2semidirect
28. #2499C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24992
C2×#18922
C2×#18732
C2×#18252
C2×C8×C22⋊C42
C2×#17352
#138792
#113732
#113722
#110522
#110502
#109262
#108422
#108412