Finite Group Databasebeta

← C2×#24194 #6448784

Subgroups — C2×#24194 #6448784

Order 512.

3680 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#559C211yesmaximal, characteristic
2C22×#464C211yesmaximal, characteristic, complemented
3C22×C4×SD16C211yesmaximal, characteristic, complemented
4C2×#2581C211yesmaximal, characteristic, complemented
5#24194C2116yesmaximal, direct product factor
6C2×#2042C211yesmaximal, characteristic, complemented
7C2×#2041C211yesmaximal, characteristic
8C2×#2015C211yesmaximal, characteristic, complemented
9C2×#2014C211yesmaximal, characteristic
10C2×#1984C211yesmaximal, characteristic, complemented
11C2×#1958C211yesmaximal, characteristic, complemented
12C2×#1878C211yesmaximal, characteristic, complemented
13C2×#1877C211yesmaximal, characteristic, complemented
14C2×#1865C211yesmaximal, characteristic, complemented
15C2×#1864C211yesmaximal, characteristic, complemented
16C2×#1804C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×SD16C2211yescharacteristic
20C2×#559—28no—
21C2×#559—24no—
22C2×#559—28no—
23C2×#559C2218yes—
24C22×#127C2211yescharacteristic
25C22×#124—21no—
26C22×#124C2211yescharacteristic
27C22×#124C2211yescharacteristic
28C22×#123—21no—
29C22×#123—21no—
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×D4—21no—
34C22×C4×D4C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36C2×#464—28no—
37C2×#464C2218yescomplemented
38C2×C4×SD16—28no—
39C2×C4×SD16C2218yescomplemented
40C22×#106C2211yescharacteristic
41C22×C4⋊C8C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#102C2211yescharacteristic
47C22×#102C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×#102C2211yescharacteristic
51C22×#102C2211yescharacteristic
52C22×C4×C8C2211yescharacteristic
53#2581—24no—
54#2581C2218yescomplemented
55C2×#400—21no—
56C2×#395—21no—
57C2×#391C2211yescharacteristic
58C2×#391C2211yescharacteristic
59C2×#389C2211yescharacteristic
60C2×#389C2211yescharacteristic
61C2×#387—21no—
62C2×#387—21no—
63C2×#382C2211yescharacteristic
64#2042C2218yescomplemented
65#2041C2218yes—
66#2015C2218yescomplemented
67#2014C2218yes—
68#1984C2218yescomplemented
69#1958C2218yescomplemented
70#1878C2218yescomplemented
71#1877C2218yescomplemented
72#1865C2218yescomplemented
73#1864C2218yescomplemented
74#1804C2218yescomplemented
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8D411yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×Q8C2311yescharacteristic
84C23×D4—21no—
85C23×D4—21no—
86C23×D4C2311yescharacteristic
87C23×D4C2311yescharacteristic
88C24×C4—21no—
89C24×C4—21no—
90C22×Q16—24no—
91C22×Q16—24no—
92C22×Q16—42no—
93C22×Q16C2314yes—
94C22×SD16—24no—
95C22×SD16—24no—
96C22×SD16—24no—
97C22×SD16—24no—
98C22×SD16—24no—
99C22×SD16—42no—
100C22×SD16C2314yes—
101C22×SD16C2314yes—
102C23×C8C2311yescharacteristic
103C23×C8C2311yescharacteristic
104C23×C8C2311yescharacteristic
105C23×C8C2311yescharacteristic
106#559—264no—
107#559—232no—
108#559—232no—
109C2×#127—24no—
110C2×#127—24no—
111C2×#127—22no—
112C2×#127C2314yes—
113C2×#124—216no—
114C2×#124—28no—
115C2×#124—24no—
116C2×#124—24no—
117C2×#124—22no—
118C2×#124—22no—
119C2×#124—24no—
120C2×#124D418yes—
121C2×#124C2314yes—
122C2×#124C2314yes—
123C2×#123—216no—
124C2×#123—216no—
125C2×#123—28no—
126C2×#123—28no—
127C2×C4×Q8—24no—
128C2×C4×Q8—24no—
129C2×C4×Q8—22no—
130C2×C4×Q8—24no—
131C2×C4×Q8—24no—
132C2×C4×Q8—22no—
133C2×C4×Q8—24no—
134C2×C4×Q8—24no—
135C2×C4×Q8D414yes—
136C2×C4×Q8C2314yes—
137C2×C4×Q8C2314yes—
138C2×C4×Q8C2314yes—
139C2×C4×D4—216no—
140C2×C4×D4—24no—
141C2×C4×D4—28no—
142C2×C4×D4—24no—
143C2×C4×D4—22no—
144C2×C4×D4—22no—
145C2×C4×D4—24no—
146C2×C4×D4D418yes—
147C2×C4×D4C2314yes—
148C2×C4×D4C2314yes—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4D411yescharacteristic
154C22×C4⋊C4D411yescharacteristic
155C22×C4⋊C4D411yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2311yescharacteristic
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C22⋊C4—21no—
161C22×C22⋊C4—21no—
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C22⋊C4—21no—
165C22×C22⋊C4—21no—
166C22×C42—21no—
167C22×C42—21no—
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171#464—232no—
172C4×SD16—232no—
173C2×#106—24no—
174C2×#106C2314yes—
175C2×C4⋊C8—24no—
176C2×C4⋊C8C2314yes—
177C2×#103—24no—
178C2×#103—24no—
179C2×#103—24no—
180C2×#103—42no—
181C2×#103C2314yes—
182C2×#103C2314yes—
183C2×#103C2314yes—
184C2×#103C2314yes—
185C2×#102—24no—
186C2×#102—24no—
187C2×#102—24no—
188C2×#102—42no—
189C2×#102—42no—
190C2×#102—42no—
191C2×#102C2314yes—
192C2×#102C2314yes—
193C2×#102C2314yes—
194C2×#102C2314yes—
195C2×#102C2314yes—
196C2×#102C2314yes—
197C2×C4×C8—24no—
198C2×C4×C8C2314yes—
199#400—28no—
200#395—28no—
201#391—22no—
202#391—22no—
203#391C2314yes—
204#391C2314yes—
205#389—22no—
206#389—22no—
207#389C2314yes—
208#389C2314yes—
209#387—28no—
210#387—28no—
211#382—22no—
212#382C2314yes—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—21no—
216C2×#95—21no—
217C2×#95—21no—
218C2×#95—21no—
219C2×#95—21no—
220C2×#95—21no—
221#340C2314yes—
222#340C2314yes—
223#336C2314yes—
224#336C2314yes—
225#336C2314yes—
226#336C2314yes—
227C25—21no—
228C25—21no—
229C22×Q8—24no—
230C22×Q8—24no—
231C22×Q8—22no—
232C22×Q8—21no—
233C22×Q8—21no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—22no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—42no—
244C22×Q8C2×D414yes—
245C22×Q8C2×D414yes—
246C22×Q8#4114yes—
247C22×Q8C2412yes—
248C22×Q8C2412yes—
249C22×D4—28no—
250C22×D4—28no—
251C22×D4—21no—
252C22×D4—21no—
253C22×D4—22no—
254C22×D4—22no—
255C22×D4—24no—
256C22×D4—24no—
257C22×D4—22no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—44no—
266C22×D4—44no—
267C22×D4—82no—
268C22×D4—82no—
269C22×D4C2×D414yes—
270C22×D4C2×D414yes—
271C22×D4C2412yes—
272C22×D4C2412yes—
273C23×C4—21no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—28no—
277C23×C4—28no—
278C23×C4—24no—
279C23×C4—24no—
280C23×C4—21no—
281C23×C4—21no—
282C23×C4—21no—
283C23×C4—82no—
284C23×C4—82no—
285C23×C4—82no—
286C23×C4—82no—
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2411yescharacteristic
294C2×Q16—28no—
295C2×Q16—28no—
296C2×Q16—44no—
297C2×Q16—416no—
298C2×SD16—232no—
299C2×SD16—28no—
300C2×SD16—28no—
301C2×SD16—28no—
302C2×SD16—28no—
303C2×SD16—28no—
304C2×SD16—44no—
305C2×SD16—416no—
306C22×C8—22no—
307C22×C8—22no—
308C22×C8—22no—
309C22×C8—22no—
310C22×C8—22no—
311C22×C8—22no—
312C22×C8—22no—
313C22×C8—22no—
314C22×C8—22no—
315C22×C8—22no—
316C22×C8—22no—
317C22×C8#4114yes—
318C22×C8C2412yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322#127—216no—
323#127—28no—
324#127—28no—
325#124—264no—
326#124—216no—
327#124—28no—
328#124—28no—
329#124—216no—
330#124—28no—
331#124C2×D4116yes—
332#123—264no—
333#123—264no—
334C4×Q8—216no—
335C4×Q8—28no—
336C4×Q8—28no—
337C4×Q8—216no—
338C4×Q8—28no—
339C4×Q8—28no—
340C4×Q8—28no—
341C4×Q8—28no—
342C4×Q8—48no—
343C4×D4—264no—
344C4×D4—216no—
345C4×D4—28no—
346C4×D4—28no—
347C4×D4—216no—
348C4×D4—28no—
349C4×D4C2×D4116yes—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4C2×D414yes—
373C2×C4⋊C4C2×D414yes—
374C2×C4⋊C4C2×D414yes—
375C2×C4⋊C4C2×D414yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C22⋊C4—28no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—28no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C42—28no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—24no—
399C2×C42—44no—
400C2×C42C2×D412yes—
401C2×C42C2×D412yes—
402C2×C42C2×D412yes—
403C2×C42C2×D414yes—
404C2×C42C2×D414yes—
405C2×C42C2412yes—
406C2×C42C2412yes—
407C2×C42C2412yes—
408#106—28no—
409C4⋊C8—28no—
410#103—28no—
411#103—28no—
412#103—28no—
413#103—44no—
414#102—28no—
415#102—28no—
416#102—28no—
417#102—44no—
418#102—44no—
419#102—44no—
420C4×C8—28no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429C24—24no—
430C24—24no—
431C24—22no—
432C24—22no—
433C24—42no—
434C24—42no—
435C24—42no—
436C24—42no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24—42no—
444C24—42no—
445C24C22×D411yescharacteristic
446C2×Q8—28no—
447C2×Q8—24no—
448C2×Q8—24no—
449C2×Q8—28no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—28no—
453C2×Q8—28no—
454C2×Q8—28no—
455C2×Q8—28no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—44no—
465C2×Q8—416no—
466C2×Q8—42no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8C22×D414yes—
475C2×Q8C2×#4114yes—
476C2×D4—216no—
477C2×D4—216no—
478C2×D4—24no—
479C2×D4—24no—
480C2×D4—28no—
481C2×D4—28no—
482C2×D4—28no—
483C2×D4—28no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—432no—
495C2×D4—48no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—48no—
505C2×D4—84no—
506C2×D4—84no—
507C2×D4—816no—
508C2×D4C22×D414yes—
509C2×D4C22×D414yes—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—24no—
520C22×C4—22no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—216no—
532C22×C4—216no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—816no—
552C22×C4—84no—
553C22×C4—84no—
554C22×C4—84no—
555C22×C4—84no—
556C22×C4—816no—
557C22×C4#12014yes—
558C22×C4#12014yes—
559C22×C4#13514yes—
560C22×C4C22×D412yes—
561C22×C4C22×D412yes—
562C22×C4C22×D412yes—
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C22×D412yes—
566C22×C4C22×D411yescharacteristic
567C22×C4C22×D412yes—
568C22×C4C22×D412yes—
569C22×C4C2×#4112yes—
570C22×C4C2×#4112yes—
571C22×C4H(5,𝔽2)12yes—
572C22×C42−1+412yes—
573C22×C4C2511yescharacteristic
574Q16—416no—
575SD16—232no—
576SD16—416no—
577C2×C8—28no—
578C2×C8—22no—
579C2×C8—22no—
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—44no—
590C2×C8—44no—
591C2×C8—44no—
592C2×C8C2×#4114yes—
593C4⋊C4—216no—
594C4⋊C4—28no—
595C4⋊C4—24no—
596C4⋊C4—28no—
597C4⋊C4—28no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—48no—
606C4⋊C4—42no—
607C4⋊C4—48no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4—48no—
611C4⋊C4C22×D414yes—
612C22⋊C4—216no—
613C22⋊C4—216no—
614C22⋊C4—216no—
615C22⋊C4—216no—
616C22⋊C4—216no—
617C22⋊C4—216no—
618C42—216no—
619C42—24no—
620C42—24no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—48no—
626C42#12018yes—
627C42C22×D414yes—
628C42C22×D414yes—
629C23—24no—
630C23—24no—
631C23—48no—
632C23—48no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—48no—
638C23—48no—
639C23—48no—
640C23—48no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23C2×#12012yes—
658C23#54812yes—
659C23#55012yes—
660C23C2×#13512yes—
661C23#57512yes—
662C23#57712yes—
663C23#57712yes—
664C23C23×D411yescharacteristic
665Q8—24no—
666Q8—24no—
667Q8—24no—
668Q8—24no—
669Q8—416no—
670Q8—48no—
671Q8—48no—
672Q8—42no—
673Q8—42no—
674Q8—42no—
675Q8—42no—
676D4—24no—
677D4—24no—
678D4—24no—
679D4—24no—
680D4—432no—
681D4—48no—
682D4—48no—
683D4—42no—
684D4—42no—
685D4—42no—
686D4—42no—
687D4—816no—
688C2×C4—22no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—48no—
710C2×C4—48no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—48no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—816no—
731C2×C4—816no—
732C2×C4—84no—
733C2×C4—84no—
734C2×C4—84no—
735C2×C4C2×#12014yes—
736C2×C4C2×#12014yes—
737C2×C4C2×#12012yes—
738C2×C4#52514yes—
739C2×C4#53714yes—
740C2×C4#54614yes—
741C2×C4#54714yes—
742C2×C4#54812yes—
743C2×C4#55012yes—
744C2×C4C2×#13514yes—
745C2×C4C23×D411yescharacteristic
746C2×C4C23×D411yescharacteristic
747C2×C4C22×#4111yescharacteristic
748C2×C4C22×#4111yescharacteristic
749C2×C4C2×H(5,𝔽2)11yescharacteristic
750C2×C4C2×2−1+411yescharacteristic
751C8—24no—
752C8—42no—
753C8—42no—
754C8—42no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—82no—
762C22—82no—
763C22—816no—
764C22—816no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22#240714yes—
772C22#300214yes—
773C22#300914yes—
774C22#336514yes—
775C22#337114yes—
776C22#339414yes—
777C22#340114yes—
778C22C22×#12011yescharacteristic
779C22C2×#54811yescharacteristic
780C22C2×#55011yescharacteristic
781C22C22×#13511yescharacteristic
782C22C2×#57511yescharacteristic
783C22C2×#57711yescharacteristic
784C22C2×#57711yescharacteristic
785C4—24no—
786C4—24no—
787C4—24no—
788C4—44no—
789C4—44no—
790C4—42no—
791C4—42no—
792C4—42no—
793C4—44no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4#240714yes—
798C4C2×#52511yescharacteristic
799C4C2×#53711yescharacteristic
800C4C2×#54611yescharacteristic
801C4C2×#54711yescharacteristic
802C2—84no—
803C2—84no—
804C2#2419418yesdirect product factor
805C2C2×#240711yescharacteristic
806C2C2×#300211yescharacteristic
807C2C2×#300911yescharacteristic
808C2C2×#336511yescharacteristic
809C2C2×#337111yescharacteristic
810C2C2×#339411yescharacteristic
811C2C2×#340111yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#464C2semidirect
3. C22×C4×SD16C2semidirect
4. C2×#2581C2semidirect
5. #24194C2direct (N × H)
6. C2×#2042C2semidirect
8. C2×#2015C2semidirect
10. C2×#1984C2semidirect
11. C2×#1958C2semidirect
12. C2×#1878C2semidirect
13. C2×#1877C2semidirect
14. C2×#1865C2semidirect
15. C2×#1864C2semidirect
16. C2×#1804C2semidirect
37. C2×#464C22semidirect
39. C2×C4×SD16C22semidirect
54. #2581C22semidirect
64. #2042C22semidirect
66. #2015C22semidirect
68. #1984C22semidirect
69. #1958C22semidirect
70. #1878C22semidirect
71. #1877C22semidirect
72. #1865C22semidirect
73. #1864C22semidirect
74. #1804C22semidirect
804. C2#24194direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5592
C22×#4642
C22×C4×SD162
C2×#25812
#241942
C2×#20422
C2×#20412
C2×#20152
C2×#20142
C2×#19842
C2×#19582
C2×#18782
C2×#18772
C2×#18652
C2×#18642
C2×#18042