Finite Group Databasebeta

← #119981

Subgroups — #119981

Order 512.

1076 conjugacy classes of subgroups.

The subgroup lattice has 773 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1802C211yesmaximal, characteristic
2C22×D4⋊C8C211yesmaximal, characteristic
3#13906C211yesmaximal, characteristic
4#10849C211yesmaximal, characteristic, complemented
5#10841C211yesmaximal, characteristic, complemented
6C2×#1296C211yesmaximal, characteristic, complemented
7C2×#1279C211yesmaximal, characteristic, complemented
8C22×C4×D4C2211yescharacteristic
9C22×C4⋊C8C2211yescharacteristic
10C22×C4⋊C8C2211yescharacteristic
11C22×#102—21no—
12C22×C4×C8C2211yescharacteristic
13C2×#390—21no—
14C2×#384C2211yescharacteristic
15C2×#384C2211yescharacteristic
16C2×#380—21no—
17C2×#380—21no—
18C2×C4×C4⋊C4C2211yescharacteristic
19#1802—22no—
20#1802C414yescomplemented
21C2×#340—21no—
22C2×#340—22no—
23C2×#340—21no—
24C2×#340—21no—
25C2×D4⋊C8—22no—
26C2×D4⋊C8—22no—
27C2×D4⋊C8—22no—
28#1439—22no—
29C4⋊#95—21no—
30#1296—22no—
31#1279—22no—
32C23×D4D411yescharacteristic
33C24×C4—21no—
34C23×C8—21no—
35C23×C8—21no—
36C23×C8—21no—
37C2×C4×D4—21no—
38C2×C4×D4—21no—
39C2×C4×D4—21no—
40C2×C4×D4—21no—
41C2×C4×D4—21no—
42C2×C4×D4—21no—
43C2×C4×D4—21no—
44C2×C4×D4—21no—
45C2×C4×D4—21no—
46C2×C4×D4—21no—
47C2×C4×D4C2×C412yes—
48C2×C4×D4D412yes—
49C22×C4⋊C4—21no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4D411yescharacteristic
55C22×C4⋊C4D411yescharacteristic
56C22×C4⋊C4D411yescharacteristic
57C22×C4⋊C4D412yes—
58C22×C22⋊C4—21no—
59C22×C22⋊C4—22no—
60C22×C22⋊C4—22no—
61C22×C42—21no—
62C22×C42C2311yescharacteristic
63C2×C4⋊C8—21no—
64C2×C4⋊C8—21no—
65C2×C4⋊C8—21no—
66C2×C4⋊C8—21no—
67C2×C4⋊C8—21no—
68C2×C4⋊C8—21no—
69C2×C4⋊C8—21no—
70C2×C4⋊C8—21no—
71C2×C4⋊C8—21no—
72C2×C4⋊C8—21no—
73C2×C4⋊C8C2×C412yes—
74C2×C4⋊C8D412yes—
75C2×#102—24no—
76C2×#102—42no—
77C2×#102—42no—
78C2×C4×C8—21no—
79C2×C4×C8—21no—
80C2×C4×C8—21no—
81C2×C4×C8—21no—
82C2×C4×C8—21no—
83C2×C4×C8D412yes—
84#390—42no—
85#390—42no—
86#384—21no—
87#384—21no—
88#384—21no—
89#384—21no—
90#384—21no—
91#384—21no—
92#384—21no—
93#384C2×C412yes—
94#380—42no—
95#380—42no—
96#380—42no—
97#380—42no—
98C4×C4⋊C4—21no—
99C4×C4⋊C4—21no—
100C4×C4⋊C4—21no—
101C4×C4⋊C4—21no—
102C2×#95—22no—
103C2×#95—22no—
104C2×#95—21no—
105#340—24no—
106#340—42no—
107#340—44no—
108#340—42no—
109D4⋊C8—28no—
110C25—21no—
111C22×D4—21no—
112C22×D4—21no—
113C22×D4—21no—
114C22×D4—21no—
115C22×D4—21no—
116C22×D4—21no—
117C22×D4—21no—
118C22×D4—21no—
119C22×D4—21no—
120C22×D4—21no—
121C22×D4—21no—
122C22×D4C22⋊C412yes—
123C22×D4SD1612yes—
124C22×D4Q1612yes—
125C23×C4—21no—
126C23×C4—21no—
127C23×C4—21no—
128C23×C4—22no—
129C23×C4—22no—
130C23×C4—22no—
131C23×C4—41no—
132C23×C4—41no—
133C23×C4—41no—
134C23×C4—41no—
135C23×C4—41no—
136C23×C4—41no—
137C23×C4—41no—
138C23×C4—41no—
139C23×C4—41no—
140C23×C4—41no—
141C23×C4—41no—
142C23×C4—41no—
143C23×C4—41no—
144C23×C4C2×D411yescharacteristic
145C23×C4C2×D411yescharacteristic
146C23×C4C2×D411yescharacteristic
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—22no—
150C22×C8—22no—
151C22×C8—22no—
152C22×C8—41no—
153C22×C8—41no—
154C22×C8—41no—
155C22×C8—41no—
156C22×C8—41no—
157C22×C8—41no—
158C22×C8—41no—
159C22×C8—41no—
160C22×C8—41no—
161C22×C8—41no—
162C22×C8—41no—
163C22×C8—41no—
164C22×C8—41no—
165C22×C8—41no—
166C22×C8—41no—
167C22×C8—41no—
168C4×D4—22no—
169C4×D4—22no—
170C4×D4—22no—
171C4×D4—22no—
172C4×D4—22no—
173C4×D4—22no—
174C4×D4—22no—
175C4×D4—22no—
176C4×D4—41no—
177C4×D4—41no—
178C4×D4—41no—
179C4×D4—41no—
180C4×D4—41no—
181C4×D4—41no—
182C4×D4—41no—
183C4×D4—41no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—42no—
205C2×C4⋊C4—42no—
206C2×C4⋊C4—42no—
207C2×C4⋊C4—42no—
208C2×C4⋊C4—41no—
209C2×C4⋊C4—41no—
210C2×C4⋊C4—41no—
211C2×C4⋊C4—41no—
212C2×C4⋊C4—41no—
213C2×C4⋊C4—41no—
214C2×C4⋊C4—41no—
215C2×C4⋊C4—41no—
216C2×C4⋊C4—41no—
217C2×C4⋊C4—41no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4—41no—
221C2×C4⋊C4—41no—
222C2×C4⋊C4—41no—
223C2×C4⋊C4—41no—
224C2×C4⋊C4—41no—
225C2×C4⋊C4—41no—
226C2×C4⋊C4—41no—
227C2×C4⋊C4—41no—
228C2×C4⋊C4—41no—
229C2×C4⋊C4—41no—
230C2×C4⋊C4—41no—
231C2×C4⋊C4C22⋊C412yes—
232C2×C4⋊C4D812yes—
233C2×C4⋊C4SD1612yes—
234C2×C22⋊C4—22no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—41no—
237C2×C22⋊C4—41no—
238C2×C22⋊C4—41no—
239C2×C22⋊C4—41no—
240C2×C22⋊C4—44no—
241C2×C22⋊C4—44no—
242C2×C22⋊C4—44no—
243C2×C22⋊C4—44no—
244C2×C22⋊C4—82no—
245C2×C22⋊C4—82no—
246C2×C42—41no—
247C2×C42—41no—
248C2×C42—41no—
249C2×C42—41no—
250C2×C42—41no—
251C2×C42—41no—
252C2×C42C22×C411yescharacteristic
253C2×C42C2×D411yescharacteristic
254C2×C42C2×D411yescharacteristic
255C2×C42C2×D411yescharacteristic
256C2×C42#4111yescharacteristic
257C2×C42#4111yescharacteristic
258C2×C42#4111yescharacteristic
259C2×C42#4111yescharacteristic
260C2×C42#4111yescharacteristic
261C2×C42#4111yescharacteristic
262C2×C42#4111yescharacteristic
263C2×C42#4111yescharacteristic
264C4⋊C8—22no—
265C4⋊C8—22no—
266C4⋊C8—22no—
267C4⋊C8—22no—
268C4⋊C8—41no—
269C4⋊C8—41no—
270C4⋊C8—41no—
271C4⋊C8—41no—
272#102—48no—
273C4×C8—22no—
274C4×C8—22no—
275C4×C8—41no—
276C4×C8—41no—
277#95—44no—
278#95—44no—
279#95—41no—
280#95—41no—
281C24—22no—
282C24—22no—
283C24—22no—
284C24—41no—
285C24—41no—
286C24—41no—
287C24—41no—
288C24—41no—
289C24—41no—
290C24—41no—
291C24—41no—
292C24—41no—
293C24—41no—
294C24—41no—
295C24—41no—
296C24#12011yescharacteristic
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—22no—
301C2×D4—22no—
302C2×D4—22no—
303C2×D4—22no—
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4#10314yes—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—42no—
359C22×C4—42no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—42no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—81no—
371C22×C4—81no—
372C22×C4—81no—
373C22×C4—81no—
374C22×C4—81no—
375C22×C4—81no—
376C22×C4—81no—
377C22×C4—81no—
378C22×C4—81no—
379C22×C4—81no—
380C22×C4—81no—
381C22×C4—81no—
382C22×C4—81no—
383C22×C4—81no—
384C22×C4—81no—
385C22×C4—81no—
386C22×C4—81no—
387C22×C4—81no—
388C22×C4—81no—
389C22×C4—81no—
390C22×C4—81no—
391C22×C4—81no—
392C22×C4C2×C22⋊C411yescharacteristic
393C22×C4C4×D411yescharacteristic
394C22×C4C4×D411yescharacteristic
395C22×C4#12111yescharacteristic
396C22×C4#12111yescharacteristic
397C22×C4#12111yescharacteristic
398C22×C4#12111yescharacteristic
399C22×C4#12111yescharacteristic
400C22×C4#12111yescharacteristic
401C22×C4#12111yescharacteristic
402C22×C4#12111yescharacteristic
403C22×C4#12311yescharacteristic
404C22×C4#12311yescharacteristic
405C22×C4#12311yescharacteristic
406C22×C4#12311yescharacteristic
407C22×C4#12311yescharacteristic
408C22×C4#12411yescharacteristic
409C22×C4#12411yescharacteristic
410C22×C4C2×D811yescharacteristic
411C22×C4C2×SD1611yescharacteristic
412C22×C4C2×SD1611yescharacteristic
413C22×C4C2×Q1611yescharacteristic
414C22×C4#13511yescharacteristic
415C22×C4#13511yescharacteristic
416C22×C4#13511yescharacteristic
417C22×C4#13511yescharacteristic
418C22×C4AGL(1,ℤ/8)11yescharacteristic
419C22×C4AGL(1,ℤ/8)11yescharacteristic
420C22×C4AGL(1,ℤ/8)11yescharacteristic
421C22×C4AGL(1,ℤ/8)11yescharacteristic
422C22×C4AGL(1,ℤ/8)11yescharacteristic
423C22×C4AGL(1,ℤ/8)11yescharacteristic
424C22×C4#13711yescharacteristic
425C22×C4#13711yescharacteristic
426C2×C8—24no—
427C2×C8—42no—
428C2×C8—42no—
429C2×C8—42no—
430C2×C8—42no—
431C2×C8—42no—
432C2×C8—42no—
433C2×C8—42no—
434C2×C8—42no—
435C2×C8—42no—
436C2×C8—42no—
437C2×C8—42no—
438C2×C8—42no—
439C2×C8—81no—
440C2×C8—81no—
441C2×C8—81no—
442C2×C8—81no—
443C2×C8—81no—
444C2×C8—81no—
445C2×C8—81no—
446C2×C8—81no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—44no—
454C4⋊C4—44no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—42no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—42no—
465C4⋊C4—82no—
466C4⋊C4—82no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4—81no—
474C4⋊C4—81no—
475C4⋊C4—81no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C22⋊C4—42no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—88no—
484C22⋊C4—88no—
485C42—81no—
486C42—81no—
487C42—81no—
488C42—81no—
489C42#11711yescharacteristic
490C42#11711yescharacteristic
491C42C4×D411yescharacteristic
492C42C4×D411yescharacteristic
493C42#12011yescharacteristic
494C42#12311yescharacteristic
495C42#12311yescharacteristic
496C42#12311yescharacteristic
497C42#12311yescharacteristic
498C42#12311yescharacteristic
499C42#12411yescharacteristic
500C42#12411yescharacteristic
501C42#12611yescharacteristic
502C42#12611yescharacteristic
503C42#12611yescharacteristic
504C42#12611yescharacteristic
505C23—24no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—81no—
525C23—81no—
526C23—81no—
527C23—81no—
528C23—81no—
529C23—81no—
530C23—81no—
531C23—81no—
532C23—81no—
533C23—81no—
534C23—81no—
535C23—81no—
536C23—81no—
537C23—81no—
538C23—81no—
539C23—81no—
540C23#38611yescharacteristic
541C23#39411yescharacteristic
542C23#39411yescharacteristic
543C23#44711yescharacteristic
544C23#44911yescharacteristic
545C23#44911yescharacteristic
546C23#44911yescharacteristic
547C23#45011yescharacteristic
548C23#45011yescharacteristic
549C23#45111yescharacteristic
550C23#45211yescharacteristic
551C23#45311yescharacteristic
552C23#45411yescharacteristic
553C23#45511yescharacteristic
554C23#45611yescharacteristic
555D4—24no—
556D4—24no—
557D4—42no—
558D4—42no—
559D4—42no—
560D4—42no—
561D4—42no—
562D4—42no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—81no—
585C2×C4—81no—
586C2×C4—81no—
587C2×C4—81no—
588C2×C4—81no—
589C2×C4—81no—
590C2×C4—81no—
591C2×C4—81no—
592C2×C4—81no—
593C2×C4—81no—
594C2×C4—81no—
595C2×C4—81no—
596C2×C4—82no—
597C2×C4—82no—
598C2×C4—82no—
599C2×C4—82no—
600C2×C4—82no—
601C2×C4—82no—
602C2×C4—82no—
603C2×C4—82no—
604C2×C4—82no—
605C2×C4—82no—
606C2×C4—82no—
607C2×C4—82no—
608C2×C4—82no—
609C2×C4—82no—
610C2×C4—82no—
611C2×C4—82no—
612C2×C4—82no—
613C2×C4—82no—
614C2×C4—161no—
615C2×C4—161no—
616C2×C4—161no—
617C2×C4—161no—
618C2×C4#38111yescharacteristic
619C2×C4#38611yescharacteristic
620C2×C4#38811yescharacteristic
621C2×C4#38811yescharacteristic
622C2×C4#38811yescharacteristic
623C2×C4#38811yescharacteristic
624C2×C4#39411yescharacteristic
625C2×C4#39411yescharacteristic
626C2×C4#39711yescharacteristic
627C2×C4#39711yescharacteristic
628C2×C4#39711yescharacteristic
629C2×C4#39711yescharacteristic
630C2×C4C2×#10311yescharacteristic
631C2×C4#41611yescharacteristic
632C2×C4#41711yescharacteristic
633C2×C4#41811yescharacteristic
634C2×C4C4×D811yescharacteristic
635C2×C4C4×SD1611yescharacteristic
636C2×C4#44011yescharacteristic
637C2×C4#44211yescharacteristic
638C2×C4#45911yescharacteristic
639C2×C4#45911yescharacteristic
640C2×C4#46011yescharacteristic
641C2×C4#46111yescharacteristic
642C2×C4#46311yescharacteristic
643C2×C4#46311yescharacteristic
644C2×C4#46311yescharacteristic
645C2×C4#46411yescharacteristic
646C2×C4#46511yescharacteristic
647C2×C4#46511yescharacteristic
648C2×C4#46511yescharacteristic
649C2×C4#46611yescharacteristic
650C2×C4#46711yescharacteristic
651C2×C4#46711yescharacteristic
652C2×C4#46811yescharacteristic
653C2×C4#46811yescharacteristic
654C2×C4#46811yescharacteristic
655C2×C4#46911yescharacteristic
656C2×C4#46911yescharacteristic
657C2×C4#46911yescharacteristic
658C2×C4#48011yescharacteristic
659C2×C4#48111yescharacteristic
660C2×C4#48111yescharacteristic
661C2×C4#48111yescharacteristic
662C2×C4#48211yescharacteristic
663C2×C4#48211yescharacteristic
664C2×C4#48211yescharacteristic
665C2×C4#48211yescharacteristic
666C2×C4#48211yescharacteristic
667C2×C4#48211yescharacteristic
668C2×C4#48311yescharacteristic
669C2×C4#48411yescharacteristic
670C2×C4#48411yescharacteristic
671C2×C4#48411yescharacteristic
672C2×C4#48511yescharacteristic
673C2×C4#48511yescharacteristic
674C2×C4#48611yescharacteristic
675C2×C4#48811yescharacteristic
676C2×C4#48911yescharacteristic
677C2×C4#49011yescharacteristic
678C8—44no—
679C8—82no—
680C8—82no—
681C22—44no—
682C22—44no—
683C22—44no—
684C22—82no—
685C22—82no—
686C22—82no—
687C22—82no—
688C22—82no—
689C22—82no—
690C22—82no—
691C22—82no—
692C22—82no—
693C22—82no—
694C22—82no—
695C22—82no—
696C22#144011yescharacteristic
697C22#162111yescharacteristic
698C22#162411yescharacteristic
699C22#162511yescharacteristic
700C22#162811yescharacteristic
701C22#162911yescharacteristic
702C22#163211yescharacteristic
703C22#163511yescharacteristic
704C22#163711yescharacteristic
705C22#163911yescharacteristic
706C22#164211yescharacteristic
707C22#164411yescharacteristic
708C22#164611yescharacteristic
709C22#164911yescharacteristic
710C22#165011yescharacteristic
711C22#165411yescharacteristic
712C22#165411yescharacteristic
713C22#187211yescharacteristic
714C22#187511yescharacteristic
715C22#187711yescharacteristic
716C22#187911yescharacteristic
717C22#188211yescharacteristic
718C22#188311yescharacteristic
719C22#203311yescharacteristic
720C22#203411yescharacteristic
721C22#203411yescharacteristic
722C22#203411yescharacteristic
723C22#203611yescharacteristic
724C22#203611yescharacteristic
725C22#203711yescharacteristic
726C22#203811yescharacteristic
727C22#203911yescharacteristic
728C22#204011yescharacteristic
729C22#204111yescharacteristic
730C22#204211yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—21no—
735C4—82no—
736C4—82no—
737C4—82no—
738C4—162no—
739C4—162no—
740C4#182411yescharacteristic
741C4#182511yescharacteristic
742C4#189211yescharacteristic
743C4#189511yescharacteristic
744C4#192511yescharacteristic
745C4#192611yescharacteristic
746C4#193411yescharacteristic
747C4#193611yescharacteristic
748C4#205411yescharacteristic
749C4#205511yescharacteristic
750C4#207111yescharacteristic
751C4#207311yescharacteristic
752C4#207611yescharacteristic
753C4#207611yescharacteristic
754C4#207711yescharacteristic
755C4#207711yescharacteristic
756C2—84no—
757C2#897311yescharacteristic
758C2#898011yescharacteristic
759C2#898111yescharacteristic
760C2#898811yescharacteristic
761C2#1040911yescharacteristic
762C2#1041311yescharacteristic
763C2#1041711yescharacteristic
764C2#1042111yescharacteristic
765C2#1043111yescharacteristic
766C2#1043211yescharacteristic
767C2#1043411yescharacteristic
768C2#1043611yescharacteristic
769C2#1118911yescharacteristic
770C2#1119511yescharacteristic
771C2#1120011yescharacteristic
subgroupG/H
center, socleC24#120
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC23×D4D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #10849C2semidirect
5. #10841C2semidirect
6. C2×#1296C2semidirect
7. C2×#1279C2semidirect
20. #1802C4semidirect

Maximal subgroups

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

subgroupindex
C2×#18022
C22×D4⋊C82
#139062
#108492
#108412
C2×#12962
C2×#12792