Finite Group Databasebeta

← C2×#25505 #6452056

Subgroups — C2×#25505 #6452056

Order 512.

3694 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#529C211yesmaximal, characteristic
2C22×#470C211yesmaximal, characteristic, complemented
3C22×#468C211yesmaximal, characteristic
4C2×#2855C211yesmaximal, characteristic, complemented
5#25505C2116yesmaximal, direct product factor
6C2×#2059C211yesmaximal, characteristic, complemented
7C2×#2042C211yesmaximal, characteristic, complemented
8C2×#2026C211yesmaximal, characteristic, complemented
9C2×#2015C211yesmaximal, characteristic, complemented
10C2×#1895C211yesmaximal, characteristic
11C2×#1894C211yesmaximal, characteristic, complemented
12C2×#1878C211yesmaximal, characteristic, complemented
13C2×#1877C211yesmaximal, characteristic, complemented
14C2×#1863C211yesmaximal, characteristic, complemented
15C2×#1864C211yesmaximal, characteristic, complemented
16C2×#1728C211yesmaximal, characteristic, complemented
17C23×Q16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C23×M16C2211yescharacteristic
20C23×M16C2211yescharacteristic
21C2×#529—24no—
22C2×#529—28no—
23C2×#529—28no—
24C2×#529C2218yes—
25C22×#126—21no—
26C22×#125C2211yescharacteristic
27C22×#124C2211yescharacteristic
28C22×#123—21no—
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×#121C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C22×C4×D4—21no—
34C22×C4×D4C2211yescharacteristic
35C22×#117—21no—
36C23×C42C2211yescharacteristic
37C2×#470—28no—
38C2×#470C2218yescomplemented
39C2×#468—28no—
40C2×#468C2218yes—
41C22×#107C2211yescharacteristic
42C22×#106C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45C22×#103C2211yescharacteristic
46C22×#103C2211yescharacteristic
47C22×#103C2211yescharacteristic
48C22×#102C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×#102C2211yescharacteristic
51#2855—24no—
52#2855C2218yescomplemented
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#389C2211yescharacteristic
56C2×#389C2211yescharacteristic
57C2×#387—21no—
58C2×#387—21no—
59C2×#385—21no—
60C2×#381—21no—
61C2×#380C2211yescharacteristic
62#2059C2218yescomplemented
63#2042C2218yescomplemented
64#2026C2218yescomplemented
65#2015C2218yescomplemented
66#1895C2218yes—
67#1894C2218yescomplemented
68#1878C2218yescomplemented
69#1877C2218yescomplemented
70#1864C2218yescomplemented
71#1863C2218yescomplemented
72C2×#340C2211yescharacteristic
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76#1728C2218yescomplemented
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C2×#336C2211yescharacteristic
80C2×#336C2211yescharacteristic
81C23×Q8C2311yescharacteristic
82C23×Q8C2311yescharacteristic
83C23×D4—21no—
84C23×D4C2311yescharacteristic
85C24×C4—21no—
86C24×C4D411yescharacteristic
87C24×C4D411yescharacteristic
88C24×C4C2311yescharacteristic
89C22×Q16—24no—
90C22×Q16—24no—
91C22×Q16—42no—
92C22×Q16C2314yes—
93C22×SD16—24no—
94C22×SD16—24no—
95C22×SD16—42no—
96C22×SD16C2314yes—
97C22×M16—24no—
98C22×M16—24no—
99C22×M16—24no—
100C22×M16—24no—
101C22×M16—42no—
102C22×M16—42no—
103C22×M16C2314yes—
104C22×M16C2314yes—
105C23×C8C2311yescharacteristic
106C23×C8C2311yescharacteristic
107C23×C8C2311yescharacteristic
108C23×C8C2311yescharacteristic
109#529—264no—
110#529—232no—
111#529—232no—
112C2×#126—216no—
113C2×#126—28no—
114C2×#125—24no—
115C2×#125—24no—
116C2×#125—22no—
117C2×#125C2314yes—
118C2×#124—24no—
119C2×#124—24no—
120C2×#124—22no—
121C2×#124C2314yes—
122C2×#123—216no—
123C2×#123—28no—
124C2×C22⋊Q8—24no—
125C2×C22⋊Q8—22no—
126C2×C22⋊Q8—22no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8D418yes—
130C2×C22⋊Q8C2314yes—
131C2×C22⋊Q8C2314yes—
132C2×#121—24no—
133C2×#121—22no—
134C2×#121D418yes—
135C2×#121C2314yes—
136C2×C4×Q8—24no—
137C2×C4×Q8—24no—
138C2×C4×Q8—22no—
139C2×C4×Q8C2314yes—
140C2×C4×D4—216no—
141C2×C4×D4—24no—
142C2×C4×D4—28no—
143C2×C4×D4—24no—
144C2×C4×D4—22no—
145C2×C4×D4C2314yes—
146C2×#117—216no—
147C2×#117—28no—
148C22×C4⋊C4—21no—
149C22×C4⋊C4—21no—
150C22×C4⋊C4—21no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
167C22×C42—24no—
168C22×C42—24no—
169C22×C42—21no—
170C22×C42D414yes—
171C22×C42D411yescharacteristic
172C22×C42D411yescharacteristic
173C22×C42C2314yes—
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176#470—232no—
177#468—232no—
178C2×#107—24no—
179C2×#107C2314yes—
180C2×#106—24no—
181C2×#106C2314yes—
182C2×#103—24no—
183C2×#103—24no—
184C2×#103—24no—
185C2×#103—24no—
186C2×#103—42no—
187C2×#103C2314yes—
188C2×#103C2314yes—
189C2×#103C2314yes—
190C2×#103C2314yes—
191C2×#103C2314yes—
192C2×#102—24no—
193C2×#102—24no—
194C2×#102—42no—
195C2×#102C2314yes—
196C2×#102C2314yes—
197C2×#102C2314yes—
198#391—22no—
199#391—22no—
200#391C2314yes—
201#391C2314yes—
202#389—22no—
203#389—22no—
204#389C2314yes—
205#389C2314yes—
206#387—28no—
207#387—28no—
208#385—28no—
209#381—28no—
210#380—22no—
211#380C2314yes—
212C2×#95—21no—
213C2×#95—21no—
214C2×#95—21no—
215C2×#95—21no—
216C2×#95—21no—
217C2×#95—21no—
218C2×#95—21no—
219#340C2314yes—
220#340C2314yes—
221#340C2314yes—
222#340C2314yes—
223#336C2314yes—
224#336C2314yes—
225#336C2314yes—
226#336C2314yes—
227C25—21no—
228C25C2×D411yescharacteristic
229C22×Q8—22no—
230C22×Q8—21no—
231C22×Q8—21no—
232C22×Q8—22no—
233C22×Q8—22no—
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×Q8C2×D414yes—
243C22×Q8C2412yes—
244C22×Q8C2412yes—
245C22×D4—28no—
246C22×D4—24no—
247C22×D4—21no—
248C22×D4—22no—
249C22×D4—22no—
250C22×D4—22no—
251C22×D4—22no—
252C22×D4—22no—
253C22×D4—44no—
254C22×D4—44no—
255C22×D4C2×D414yes—
256C22×D4C2412yes—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—28no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—24no—
268C23×C4—24no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—42no—
276C23×C4—44no—
277C23×C4—44no—
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D414yes—
282C23×C4C2×D412yes—
283C23×C4C2×D411yescharacteristic
284C23×C4C2×D414yes—
285C23×C4C2×D414yes—
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D414yes—
288C23×C4C2412yes—
289C23×C4C2411yescharacteristic
290C2×Q16—28no—
291C2×Q16—28no—
292C2×Q16—44no—
293C2×Q16—416no—
294C2×SD16—28no—
295C2×SD16—28no—
296C2×SD16—44no—
297C2×SD16—416no—
298C2×M16—28no—
299C2×M16—28no—
300C2×M16—28no—
301C2×M16—28no—
302C2×M16—44no—
303C2×M16—44no—
304C2×M16—416no—
305C2×M16—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#4114yes—
317C22×C8#4114yes—
318C22×C8C2412yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322#126—264no—
323#125—216no—
324#125—28no—
325#125—28no—
326#124—216no—
327#124—28no—
328#124—28no—
329#123—264no—
330C22⋊Q8—216no—
331C22⋊Q8—28no—
332C22⋊Q8—28no—
333C22⋊Q8—28no—
334C22⋊Q8—48no—
335C22⋊Q8C2×D4116yes—
336#121—216no—
337#121—28no—
338#121C2×D4116yes—
339C4×Q8—216no—
340C4×Q8—28no—
341C4×Q8—28no—
342C4×D4—264no—
343C4×D4—216no—
344C4×D4—28no—
345C4×D4—28no—
346#117—264no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—28no—
349C2×C4⋊C4—28no—
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—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—24no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4C2×D414yes—
375C2×C4⋊C4C2×D414yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—28no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—44no—
395C2×C42—28no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—216no—
399C2×C42—24no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—28no—
405C2×C42—28no—
406C2×C42C2×D414yes—
407C2×C42C2×D412yes—
408C2×C42C2×D412yes—
409C2×C42C2×D414yes—
410C2×C42C2412yes—
411C2×C42C2412yes—
412#107—28no—
413#106—28no—
414#103—28no—
415#103—28no—
416#103—28no—
417#103—28no—
418#103—44no—
419#102—28no—
420#102—28no—
421#102—44no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—22no—
435C24—24no—
436C24—22no—
437C24—42no—
438C24—42no—
439C24—42no—
440C24—42no—
441C24—42no—
442C24—42no—
443C24#12014yes—
444C24C22×D412yes—
445C24C22×D411yescharacteristic
446C2×Q8—24no—
447C2×Q8—22no—
448C2×Q8—28no—
449C2×Q8—28no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—42no—
461C2×Q8—42no—
462C2×Q8—42no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—44no—
466C2×Q8—44no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—44no—
471C2×Q8C22×D414yes—
472C2×D4—216no—
473C2×D4—24no—
474C2×D4—28no—
475C2×D4—28no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—432no—
482C2×D4—48no—
483C2×D4—48no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4C22×D414yes—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—28no—
496C22×C4—28no—
497C22×C4—28no—
498C22×C4—28no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—216no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—28no—
508C22×C4—28no—
509C22×C4—24no—
510C22×C4—24no—
511C22×C4—24no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—28no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—416no—
530C22×C4—432no—
531C22×C4—48no—
532C22×C4—416no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—42no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—48no—
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—42no—
552C22×C4#12014yes—
553C22×C4#12018yes—
554C22×C4#13714yes—
555C22×C4C22×D412yes—
556C22×C4C22×D412yes—
557C22×C4C22×D412yes—
558C22×C4C22×D412yes—
559C22×C4C22×D414yes—
560C22×C4C22×D414yes—
561C22×C4C22×D412yes—
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D412yes—
564C22×C4C22×D412yes—
565C22×C4C2×#4112yes—
566C22×C4C2×#4112yes—
567C22×C4H(5,𝔽2)12yes—
568C22×C42−1+412yes—
569C22×C4C2511yescharacteristic
570Q16—416no—
571SD16—416no—
572M16—416no—
573M16—416no—
574C2×C8—28no—
575C2×C8—28no—
576C2×C8—22no—
577C2×C8—22no—
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—44no—
587C2×C8—44no—
588C2×C8C2×#4114yes—
589C2×C8C2×#4114yes—
590C4⋊C4—216no—
591C4⋊C4—216no—
592C4⋊C4—216no—
593C4⋊C4—216no—
594C4⋊C4—24no—
595C4⋊C4—24no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—48no—
605C4⋊C4—48no—
606C4⋊C4—42no—
607C4⋊C4—48no—
608C4⋊C4—42no—
609C4⋊C4—42no—
610C4⋊C4C22×D414yes—
611C4⋊C4C22×D414yes—
612C22⋊C4—216no—
613C22⋊C4—216no—
614C22⋊C4—216no—
615C22⋊C4—216no—
616C22⋊C4—216no—
617C22⋊C4—48no—
618C22⋊C4—48no—
619C42—216no—
620C42—28no—
621C42—24no—
622C42—24no—
623C42—28no—
624C42—22no—
625C42—22no—
626C42—22no—
627C42—22no—
628C23—22no—
629C23—22no—
630C23—28no—
631C23—28no—
632C23—28no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—42no—
643C23—42no—
644C23—48no—
645C23—48no—
646C23—48no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23C2×#12014yes—
656C23C2×#12012yes—
657C23#53212yes—
658C23#53712yes—
659C23C2×#13712yes—
660C23#57512yes—
661C23#57512yes—
662C23#57512yes—
663C23C23×D411yescharacteristic
664Q8—24no—
665Q8—24no—
666Q8—48no—
667Q8—42no—
668Q8—42no—
669Q8—42no—
670Q8—42no—
671Q8—42no—
672Q8—42no—
673Q8—84no—
674D4—24no—
675D4—24no—
676D4—432no—
677D4—48no—
678D4—42no—
679D4—42no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—28no—
684C2×C4—28no—
685C2×C4—22no—
686C2×C4—216no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—416no—
704C2×C4—432no—
705C2×C4—416no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—48no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—48no—
712C2×C4—44no—
713C2×C4—48no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
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—84no—
731C2×C4—84no—
732C2×C4—84no—
733C2×C4—84no—
734C2×C4C2×#12014yes—
735C2×C4C2×#12012yes—
736C2×C4#53212yes—
737C2×C4#53712yes—
738C2×C4#54614yes—
739C2×C4#54614yes—
740C2×C4#54714yes—
741C2×C4#54714yes—
742C2×C4C2×#13714yes—
743C2×C4C23×D411yescharacteristic
744C2×C4C23×D411yescharacteristic
745C2×C4C22×#4111yescharacteristic
746C2×C4C22×#4111yescharacteristic
747C2×C4C2×H(5,𝔽2)11yescharacteristic
748C2×C4C2×2−1+411yescharacteristic
749C8—24no—
750C8—24no—
751C8—42no—
752C8—42no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—416no—
759C22—42no—
760C22—42no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—82no—
765C22—82no—
766C22—816no—
767C22—82no—
768C22—82no—
769C22#243014yes—
770C22#300514yes—
771C22#300714yes—
772C22#317214yes—
773C22#318314yes—
774C22#325214yes—
775C22#325614yes—
776C22C22×#12011yescharacteristic
777C22C2×#53211yescharacteristic
778C22C2×#53711yescharacteristic
779C22C22×#13711yescharacteristic
780C22C2×#57511yescharacteristic
781C22C2×#57511yescharacteristic
782C22C2×#57511yescharacteristic
783C4—24no—
784C4—24no—
785C4—44no—
786C4—42no—
787C4—42no—
788C4—44no—
789C4—42no—
790C4—44no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4#243014yes—
796C4C2×#54611yescharacteristic
797C4C2×#54611yescharacteristic
798C4C2×#54711yescharacteristic
799C4C2×#54711yescharacteristic
800C2—44no—
801C2—84no—
802C2#2550518yesdirect product factor
803C2C2×#243011yescharacteristic
804C2C2×#300511yescharacteristic
805C2C2×#300711yescharacteristic
806C2C2×#317211yescharacteristic
807C2C2×#318311yescharacteristic
808C2C2×#325211yescharacteristic
809C2C2×#325611yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C22×#470C2semidirect
4. C2×#2855C2semidirect
5. #25505C2direct (N × H)
6. C2×#2059C2semidirect
7. C2×#2042C2semidirect
8. C2×#2026C2semidirect
9. C2×#2015C2semidirect
11. C2×#1894C2semidirect
12. C2×#1878C2semidirect
13. C2×#1877C2semidirect
14. C2×#1863C2semidirect
15. C2×#1864C2semidirect
16. C2×#1728C2semidirect
38. C2×#470C22semidirect
52. #2855C22semidirect
62. #2059C22semidirect
63. #2042C22semidirect
64. #2026C22semidirect
65. #2015C22semidirect
67. #1894C22semidirect
68. #1878C22semidirect
69. #1877C22semidirect
70. #1864C22semidirect
71. #1863C22semidirect
76. #1728C22semidirect
802. C2#25505direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5292
C22×#4702
C22×#4682
C2×#28552
#255052
C2×#20592
C2×#20422
C2×#20262
C2×#20152
C2×#18952
C2×#18942
C2×#18782
C2×#18772
C2×#18632
C2×#18642
C2×#17282