Finite Group Databasebeta

← C2×#26950 #6443527

Subgroups — C2×#26950 #6443527

Order 512.

2884 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#482C211yesmaximal, characteristic, complemented
2C22×#460C211yesmaximal, characteristic, complemented
3C2×#2428C211yesmaximal, characteristic
4C2×#2362C211yesmaximal, characteristic, complemented
5#26950C2116yesmaximal, direct product factor
6C2×#2086C211yesmaximal, characteristic, complemented
7C2×#2041C211yesmaximal, characteristic, complemented
8C2×#2000C211yesmaximal, characteristic, complemented
9C2×#2000C211yesmaximal, characteristic, complemented
10C2×#1973C211yesmaximal, characteristic, complemented
11C2×#1926C211yesmaximal, characteristic, complemented
12C2×#1924C211yesmaximal, characteristic, complemented
13C2×#1877C211yesmaximal, characteristic, complemented
14C2×#1875C211yesmaximal, characteristic, complemented
15C2×#1865C211yesmaximal, characteristic, complemented
16C2×#1762C211yesmaximal, characteristic, complemented
17C23×SD16C2211yescharacteristic
18C23×SD16C2211yescharacteristic
19C22×#127C2211yescharacteristic
20C22×C22⋊Q8C2211yescharacteristic
21C22×#121—21no—
22C22×#121C2211yescharacteristic
23C22×#121C2211yescharacteristic
24C22×C4×Q8C2211yescharacteristic
25C22×C4×D4C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C2×#482—28no—
28C2×#482C2218yescomplemented
29C2×#460—28no—
30C2×#460C2218yescomplemented
31C22×#107C2211yescharacteristic
32C22×#106C2211yescharacteristic
33C22×C4⋊C8C2211yescharacteristic
34C22×#103C2211yescharacteristic
35C22×#103C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×#102C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42C22×C22⋊C8C2211yescharacteristic
43C22×C22⋊C8C2211yescharacteristic
44C22×#97C2211yescharacteristic
45#2428—24no—
46#2428C2218yes—
47C2×#394—21no—
48C2×#392—21no—
49#2362—24no—
50#2362C2218yescomplemented
51C2×#391C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#389C2211yescharacteristic
55C2×#388—21no—
56C2×#388—21no—
57C2×#387—21no—
58C2×#386—21no—
59C2×C4×C4⋊C4—21no—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C22⋊C4C2211yescharacteristic
62#2086C2218yescomplemented
63#2041C2218yescomplemented
64#2000C2218yescomplemented
65#2000C2218yescomplemented
66#1973C2218yescomplemented
67#1926C2218yescomplemented
68#1924C2218yescomplemented
69#1877C2218yescomplemented
70#1875C2218yescomplemented
71#1865C2218yescomplemented
72#1762C2218yescomplemented
73C2×#340C2211yescharacteristic
74C2×#340C2211yescharacteristic
75C2×#340C2211yescharacteristic
76C2×#340C2211yescharacteristic
77C2×#336C2211yescharacteristic
78C2×#336C2211yescharacteristic
79C23×Q8C2311yescharacteristic
80C23×D4—21no—
81C23×D4—21no—
82C23×D4—21no—
83C23×D4—21no—
84C23×D4C2311yescharacteristic
85C23×D4C2311yescharacteristic
86C24×C4—21no—
87C24×C4C2311yescharacteristic
88C22×SD16—24no—
89C22×SD16—24no—
90C22×SD16—24no—
91C22×SD16—24no—
92C22×SD16—42no—
93C22×SD16—42no—
94C22×SD16C2314yes—
95C22×SD16C2314yes—
96C23×C8C2311yescharacteristic
97C23×C8C2311yescharacteristic
98C23×C8C2311yescharacteristic
99C23×C8C2311yescharacteristic
100C2×#127—24no—
101C2×#127—22no—
102C2×#127—42no—
103C2×#127C2314yes—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8—22no—
106C2×C22⋊Q8—24no—
107C2×C22⋊Q8C2314yes—
108C2×#121—22no—
109C2×#121—22no—
110C2×#121—28no—
111C2×#121—24no—
112C2×#121—24no—
113C2×#121—48no—
114C2×#121—42no—
115C2×#121—42no—
116C2×#121C2314yes—
117C2×#121C2314yes—
118C2×C4×Q8—22no—
119C2×C4×Q8—24no—
120C2×C4×Q8—42no—
121C2×C4×Q8C2314yes—
122C2×C4×D4—24no—
123C2×C4×D4—22no—
124C2×C4×D4—42no—
125C2×C4×D4C2314yes—
126C2×#117—22no—
127C2×#117—24no—
128C2×#117—42no—
129C2×#117C2314yes—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4—21no—
133C22×C4⋊C4—21no—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2311yescharacteristic
138C22×C4⋊C4C2311yescharacteristic
139C22×C22⋊C4—21no—
140C22×C22⋊C4—21no—
141C22×C22⋊C4—21no—
142C22×C22⋊C4—21no—
143C22×C22⋊C4—21no—
144C22×C22⋊C4—21no—
145C22×C22⋊C4—21no—
146C22×C22⋊C4D411yescharacteristic
147C22×C22⋊C4D411yescharacteristic
148C22×C42—21no—
149C22×C42—21no—
150C22×C42—21no—
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153#482—232no—
154#460—232no—
155C2×#107—24no—
156C2×#107C2314yes—
157C2×#106—24no—
158C2×#106C2314yes—
159C2×C4⋊C8—24no—
160C2×C4⋊C8C2314yes—
161C2×#103—24no—
162C2×#103—42no—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#102—24no—
166C2×#102—24no—
167C2×#102—24no—
168C2×#102—24no—
169C2×#102—42no—
170C2×#102D418yescomplemented
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×#102C2314yes—
175C2×#102C2314yes—
176C2×#102C2314yes—
177C2×C22⋊C8—24no—
178C2×C22⋊C8—42no—
179C2×C22⋊C8C2314yes—
180C2×C22⋊C8C2314yes—
181C2×#97—42no—
182C2×#97C2314yes—
183#394—28no—
184#392—28no—
185#391—22no—
186#391C2314yes—
187#390—22no—
188#390C2314yes—
189#389—22no—
190#389—22no—
191#389C2314yes—
192#389C2314yes—
193#388—28no—
194#388—28no—
195#387—28no—
196#386—28no—
197C4×C4⋊C4—22no—
198C4×C4⋊C4—28no—
199C4×C4⋊C4C2314yes—
200C4×C22⋊C4D414yes—
201C4×C22⋊C4C2314yes—
202C2×#95—21no—
203C2×#95—21no—
204C2×#95—21no—
205C2×#95—21no—
206C2×#95—21no—
207C2×#95D411yescharacteristic
208C2×#95D411yescharacteristic
209#340C2314yes—
210#340C2314yes—
211#340C2314yes—
212#340C2314yes—
213#336C2314yes—
214#336C2314yes—
215C25—21no—
216C25—21no—
217C25C2×D411yescharacteristic
218C22×Q8—21no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8#4114yes—
225C22×Q8C2412yes—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4—21no—
229C22×D4—22no—
230C22×D4—21no—
231C22×D4—24no—
232C22×D4—24no—
233C22×D4—22no—
234C22×D4—22no—
235C22×D4—22no—
236C22×D4—22no—
237C22×D4—22no—
238C22×D4—22no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4—44no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—44no—
251C22×D4—82no—
252C22×D4—82no—
253C22×D4—82no—
254C22×D4—82no—
255C22×D4C2×D414yes—
256C22×D4C2412yes—
257C22×D4C2412yes—
258C23×C4—21no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—21no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—22no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—24no—
271C23×C4—44no—
272C23×C4—44no—
273C23×C4—82no—
274C23×C4C2×D412yes—
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2412yes—
281C23×C4C2411yescharacteristic
282C2×SD16—28no—
283C2×SD16—28no—
284C2×SD16—28no—
285C2×SD16—28no—
286C2×SD16—44no—
287C2×SD16—44no—
288C2×SD16—416no—
289C2×SD16—416no—
290C22×C8—22no—
291C22×C8—22no—
292C22×C8—22no—
293C22×C8—22no—
294C22×C8—22no—
295C22×C8—22no—
296C22×C8—22no—
297C22×C8—22no—
298C22×C8—22no—
299C22×C8—22no—
300C22×C8—22no—
301C22×C8C2×D414yes—
302C22×C8C2412yes—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C22×C8C2412yes—
306#127—28no—
307#127—44no—
308#127—48no—
309C22⋊Q8—216no—
310C22⋊Q8—28no—
311C22⋊Q8—28no—
312#121—28no—
313#121—28no—
314#121—432no—
315#121—44no—
316#121—44no—
317#121—48no—
318#121—48no—
319C4×Q8—28no—
320C4×Q8—44no—
321C4×Q8—48no—
322C4×D4—28no—
323C4×D4—44no—
324C4×D4—48no—
325#117—28no—
326#117—44no—
327#117—48no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—44no—
346C2×C4⋊C4—44no—
347C2×C4⋊C4—44no—
348C2×C4⋊C4C2×D414yes—
349C2×C4⋊C4#4114yes—
350C2×C4⋊C4#4114yes—
351C2×C4⋊C4C2412yes—
352C2×C4⋊C4C2412yes—
353C2×C4⋊C4C2412yes—
354C2×C4⋊C4C2412yes—
355C2×C4⋊C4C2412yes—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—24no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—44no—
367C2×C22⋊C4—44no—
368C2×C22⋊C4—44no—
369C2×C22⋊C4—44no—
370C2×C22⋊C4—44no—
371C2×C22⋊C4—82no—
372C2×C22⋊C4C2×D414yes—
373C2×C22⋊C4C2×D414yes—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—44no—
382C2×C42—44no—
383C2×C42—44no—
384C2×C42C2×D412yes—
385C2×C42C2×D412yes—
386C2×C42C2412yes—
387C2×C42C2412yes—
388#107—28no—
389#106—28no—
390C4⋊C8—28no—
391#103—28no—
392#103—44no—
393#102—28no—
394#102—28no—
395#102—28no—
396#102—28no—
397#102—44no—
398#102C2×D4116yescomplemented
399C22⋊C8—28no—
400C22⋊C8—44no—
401#97—44no—
402#95—24no—
403#95—24no—
404#95—24no—
405#95—24no—
406#95—24no—
407#95C2×D414yes—
408#95C2×D414yes—
409C24—22no—
410C24—22no—
411C24—24no—
412C24—22no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—42no—
424C24—42no—
425C24—42no—
426C24—42no—
427C24—42no—
428C24—42no—
429C24—42no—
430C24—42no—
431C24—42no—
432C24C22×D412yes—
433C24C22×D411yescharacteristic
434C2×Q8—24no—
435C2×Q8—22no—
436C2×Q8—28no—
437C2×Q8—28no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—22no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—42no—
445C2×Q8—42no—
446C2×Q8C2×#4114yes—
447C2×D4—28no—
448C2×D4—24no—
449C2×D4—28no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—48no—
462C2×D4—48no—
463C2×D4—48no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—48no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—44no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—44no—
476C2×D4—42no—
477C2×D4—44no—
478C2×D4—44no—
479C2×D4—48no—
480C2×D4—84no—
481C2×D4—84no—
482C2×D4—816no—
483C2×D4—84no—
484C2×D4—84no—
485C2×D4—816no—
486C2×D4—816no—
487C2×D4—816no—
488C2×D4C22×D414yes—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—42no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—84no—
543C22×C4—816no—
544C22×C4AGL(1,ℤ/8)14yes—
545C22×C4C22×D412yes—
546C22×C4C22×D412yes—
547C22×C4C22×D412yes—
548C22×C4C22×D412yes—
549C22×C4C22×D412yes—
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D412yes—
552C22×C4C2×#4112yes—
553C22×C4C2×#4112yes—
554C22×C4C2×#4112yes—
555C22×C4H(5,𝔽2)12yes—
556C22×C4H(5,𝔽2)12yes—
557C22×C4C2511yescharacteristic
558SD16—416no—
559SD16—416no—
560C2×C8—28no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—44no—
573C2×C8—44no—
574C2×C8—44no—
575C2×C8C22×D414yes—
576C4⋊C4—216no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—48no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—48no—
591C4⋊C4—48no—
592C4⋊C4C22×D414yes—
593C4⋊C4C2×#4114yes—
594C4⋊C4C2×#4114yes—
595C22⋊C4—216no—
596C22⋊C4—28no—
597C22⋊C4—44no—
598C22⋊C4—48no—
599C22⋊C4—48no—
600C22⋊C4—48no—
601C22⋊C4—48no—
602C22⋊C4—48no—
603C22⋊C4—84no—
604C42—24no—
605C42—24no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—48no—
611C42—48no—
612C42—48no—
613C23—22no—
614C23—22no—
615C23—24no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—44no—
622C23—44no—
623C23—42no—
624C23—42no—
625C23—44no—
626C23—48no—
627C23—44no—
628C23—48no—
629C23—48no—
630C23—44no—
631C23—44no—
632C23—42no—
633C23—44no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23#52512yes—
656C23D4212yes—
657C23#54612yes—
658C23C2×AGL(1,ℤ/8)12yes—
659C23#57512yes—
660C23#57712yes—
661C23#57712yes—
662C23C23×D411yescharacteristic
663Q8—24no—
664Q8—24no—
665Q8—42no—
666Q8—42no—
667Q8—48no—
668D4—24no—
669D4—24no—
670D4—42no—
671D4—42no—
672D4—42no—
673D4—42no—
674D4—42no—
675D4—42no—
676D4—48no—
677D4—816no—
678D4—816no—
679D4—816no—
680D4—816no—
681D4—84no—
682C2×C4—22no—
683C2×C4—28no—
684C2×C4—22no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—48no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—48no—
706C2×C4—44no—
707C2×C4—48no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—48no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—48no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—816no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4#52512yes—
732C2×C4#53214yes—
733C2×C4#54014yes—
734C2×C4D4212yes—
735C2×C4#54614yes—
736C2×C4#54612yes—
737C2×C4#55314yes—
738C2×C4C2×AGL(1,ℤ/8)14yes—
739C2×C4C23×D411yescharacteristic
740C2×C4C22×#4111yescharacteristic
741C2×C4C22×#4111yescharacteristic
742C2×C4C22×#4111yescharacteristic
743C2×C4C2×H(5,𝔽2)11yescharacteristic
744C2×C4C2×H(5,𝔽2)11yescharacteristic
745C8—24no—
746C8—42no—
747C8—42no—
748C8—42no—
749C22—42no—
750C22—44no—
751C22—44no—
752C22—42no—
753C22—42no—
754C22—44no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—88no—
760C22—816no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—168no—
773C22#246414yes—
774C22#311514yes—
775C22#312614yes—
776C22#326514yes—
777C22#326714yes—
778C22#331714yes—
779C22#332414yes—
780C22C2×#52511yescharacteristic
781C22C2×D4211yescharacteristic
782C22C2×#54611yescharacteristic
783C22C22×AGL(1,ℤ/8)11yescharacteristic
784C22C2×#57511yescharacteristic
785C22C2×#57711yescharacteristic
786C22C2×#57711yescharacteristic
787C4—24no—
788C4—42no—
789C4—44no—
790C4—42no—
791C4—44no—
792C4—44no—
793C4—42no—
794C4—42no—
795C4—44no—
796C4—82no—
797C4—82no—
798C4#246414yes—
799C4C2×#53211yescharacteristic
800C4C2×#54011yescharacteristic
801C4C2×#54611yescharacteristic
802C4C2×#55311yescharacteristic
803C2—82no—
804C2—84no—
805C2—162no—
806C2#2695018yesdirect product factor
807C2C2×#246411yescharacteristic
808C2C2×#311511yescharacteristic
809C2C2×#312611yescharacteristic
810C2C2×#326511yescharacteristic
811C2C2×#326711yescharacteristic
812C2C2×#331711yescharacteristic
813C2C2×#332411yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#2428C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#482C2semidirect
2. C22×#460C2semidirect
4. C2×#2362C2semidirect
5. #26950C2direct (N × H)
6. C2×#2086C2semidirect
7. C2×#2041C2semidirect
8. C2×#2000C2semidirect
9. C2×#2000C2semidirect
10. C2×#1973C2semidirect
11. C2×#1926C2semidirect
12. C2×#1924C2semidirect
13. C2×#1877C2semidirect
14. C2×#1875C2semidirect
15. C2×#1865C2semidirect
16. C2×#1762C2semidirect
28. C2×#482C22semidirect
30. C2×#460C22semidirect
50. #2362C22semidirect
62. #2086C22semidirect
63. #2041C22semidirect
64. #2000C22semidirect
65. #2000C22semidirect
66. #1973C22semidirect
67. #1926C22semidirect
68. #1924C22semidirect
69. #1877C22semidirect
70. #1875C22semidirect
71. #1865C22semidirect
72. #1762C22semidirect
170. C2×#102D4semidirect
398. #102C2×D4semidirect
806. C2#26950direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#4822
C22×#4602
C2×#24282
C2×#23622
#269502
C2×#20862
C2×#20412
C2×#20002
C2×#19732
C2×#19262
C2×#19242
C2×#18772
C2×#18752
C2×#18652
C2×#17622