Finite Group Databasebeta

← C2×#31306 #7504325

Subgroups — C2×#31306 #7504325

Order 512.

3074 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
1C2×#2496C211yesmaximal, characteristic, complemented
2C2×#2435C211yesmaximal, characteristic
3#31306C2116yesmaximal, direct product factor
4C2×#2094C211yesmaximal, characteristic, complemented
5C2×#2065C211yesmaximal, characteristic, complemented
6C2×#2042C211yesmaximal, characteristic, complemented
7C2×#2042C211yesmaximal, characteristic, complemented
8C2×#2035C211yesmaximal, characteristic, complemented
9C2×#2035C211yesmaximal, characteristic, complemented
10C2×#1983C211yesmaximal, characteristic, complemented
11C2×#1959C211yesmaximal, characteristic, complemented
12C2×#1936C211yesmaximal, characteristic, complemented
13C2×#1926C211yesmaximal, characteristic, complemented
14C2×#1924C211yesmaximal, characteristic, complemented
15C2×#1786C211yesmaximal, characteristic
16C2×#1786C211yesmaximal, characteristic
17C24×D4C2211yescharacteristic
18C22×#126—21no—
19C22×#124C2211yescharacteristic
20C22×#124C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×#106C2211yescharacteristic, complemented
23C22×#106C2211yescharacteristic, complemented
24C22×C4⋊C8C2211yescharacteristic, complemented
25C22×#103C2211yescharacteristic, complemented
26C22×#103C2211yescharacteristic, complemented
27C22×#103C2211yescharacteristic, complemented
28C22×#103C2211yescharacteristic, complemented
29C22×#102C2211yescharacteristic
30C22×#102C2211yescharacteristic
31C22×#102C2211yescharacteristic
32C22×#102C2211yescharacteristic
33C22×#102C2211yescharacteristic
34C22×#102C2211yescharacteristic
35C22×#102C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C22×C22⋊C8C2211yescharacteristic
38C22×C22⋊C8C2211yescharacteristic
39C22×#97C2211yescharacteristic, complemented
40#2496—24no—
41#2496C2218yescomplemented
42#2435—24no—
43#2435C2218yes—
44C2×#400—21no—
45C2×#397—21no—
46C2×#394—21no—
47C2×#394—21no—
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#389C2211yescharacteristic, complemented
51C2×#389C2211yescharacteristic, complemented
52C2×#387—21no—
53C2×#384C2211yescharacteristic, complemented
54C2×#380C2211yescharacteristic
55C2×#380C2211yescharacteristic
56C2×#379—21no—
57C2×#379—21no—
58C2×C4×C4⋊C4C2211yescharacteristic, complemented
59C2×C4×C22⋊C4C2211yescharacteristic
60#2094C2218yescomplemented
61#2065C2218yescomplemented
62#2042C2218yescomplemented
63#2042C2218yescomplemented
64#2035C2218yescomplemented
65#2035C2218yescomplemented
66#1983C2218yescomplemented
67#1959C2218yescomplemented
68#1936C2218yescomplemented
69#1926C2218yescomplemented
70#1924C2218yescomplemented
71#1786C2218yes—
72#1786C2218yes—
73C2×#340C2211yescharacteristic, complemented
74C2×#340C2211yescharacteristic, complemented
75C2×#336C2211yescharacteristic, complemented
76C2×#336C2211yescharacteristic, complemented
77C26—21no—
78C23×Q8C2311yescharacteristic
79C23×D4—24no—
80C23×D4—24no—
81C23×D4—21no—
82C23×D4—22no—
83C23×D4—42no—
84C23×D4—42no—
85C23×D4—42no—
86C23×D4—42no—
87C23×D4C2311yescharacteristic
88C23×D4C2311yescharacteristic
89C23×D4C2314yes—
90C24×C4C2311yescharacteristic
91C23×C8C2311yescharacteristic
92C23×C8C2311yescharacteristic
93C23×C8C2311yescharacteristic
94C23×C8C2311yescharacteristic
95C2×#126—28no—
96C2×#126—48no—
97C2×#124—24no—
98C2×#124—24no—
99C2×#124—22no—
100C2×#124—22no—
101C2×#124—42no—
102C2×#124—42no—
103C2×#124C2314yes—
104C2×#124C2314yes—
105C2×C22⋊Q8—22no—
106C2×C22⋊Q8—42no—
107C2×C22⋊Q8—42no—
108C2×C22⋊Q8C2314yes—
109C22×C4⋊C4—21no—
110C22×C4⋊C4—21no—
111C22×C4⋊C4—21no—
112C22×C4⋊C4—21no—
113C22×C4⋊C4—21no—
114C22×C4⋊C4C2311yescharacteristic
115C22×C4⋊C4C2311yescharacteristic
116C22×C4⋊C4C2311yescharacteristic
117C22×C4⋊C4C2311yescharacteristic
118C22×C4⋊C4C2311yescharacteristic
119C22×C22⋊C4—21no—
120C22×C22⋊C4—21no—
121C22×C22⋊C4—21no—
122C22×C22⋊C4—21no—
123C22×C22⋊C4—21no—
124C22×C22⋊C4—21no—
125C22×C22⋊C4—21no—
126C22×C22⋊C4—21no—
127C22×C22⋊C4—21no—
128C22×C22⋊C4—21no—
129C22×C22⋊C4—21no—
130C22×C22⋊C4D411yescharacteristic
131C22×C22⋊C4D411yescharacteristic
132C22×C42—21no—
133C22×C42C2311yescharacteristic
134C22×C42C2311yescharacteristic
135C2×#106—42no—
136C2×#106—42no—
137C2×#106C2314yescomplemented
138C2×#106C2314yescomplemented
139C2×C4⋊C8—42no—
140C2×C4⋊C8C2314yescomplemented
141C2×#103—42no—
142C2×#103—42no—
143C2×#103—42no—
144C2×#103—42no—
145C2×#103C2314yescomplemented
146C2×#103C2314yescomplemented
147C2×#103C2314yescomplemented
148C2×#103C2314yescomplemented
149C2×#102—24no—
150C2×#102—24no—
151C2×#102—42no—
152C2×#102—42no—
153C2×#102—42no—
154C2×#102—42no—
155C2×#102—42no—
156C2×#102—42no—
157C2×#102C2314yes—
158C2×#102C2314yes—
159C2×#102C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×#102C2314yes—
163C2×#102C2314yes—
164C2×#102C2314yes—
165C2×C22⋊C8—42no—
166C2×C22⋊C8—42no—
167C2×C22⋊C8C2314yes—
168C2×C22⋊C8C2314yes—
169C2×#97—42no—
170C2×#97C2314yescomplemented
171#400—28no—
172#397—28no—
173#394—28no—
174#394—28no—
175#390—22no—
176#390—22no—
177#390C2314yes—
178#390C2314yes—
179#389—22no—
180#389—22no—
181#389C2314yescomplemented
182#389C2314yescomplemented
183#387—28no—
184#384—22no—
185#384C2314yescomplemented
186#380—22no—
187#380—22no—
188#380C2314yes—
189#380C2314yes—
190#379—28no—
191#379—28no—
192C4×C4⋊C4—22no—
193C4×C4⋊C4C2314yescomplemented
194C4×C22⋊C4D414yes—
195C4×C22⋊C4C2314yes—
196C2×#95—21no—
197C2×#95—21no—
198C2×#95—21no—
199C2×#95—21no—
200C2×#95—21no—
201C2×#95D411yescharacteristic
202C2×#95D411yescharacteristic
203#340C2314yescomplemented
204#340C2314yescomplemented
205#336C2314yescomplemented
206#336C2314yescomplemented
207C25—21no—
208C25—21no—
209C25—24no—
210C25—44no—
211C25—44no—
212C25—44no—
213C25—44no—
214C25—44no—
215C25—82no—
216C25—82no—
217C25C2×D411yescharacteristic
218C22×Q8—21no—
219C22×Q8—22no—
220C22×Q8—22no—
221C22×Q8—22no—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8C2412yes—
226C22×D4—28no—
227C22×D4—28no—
228C22×D4—21no—
229C22×D4—21no—
230C22×D4—24no—
231C22×D4—22no—
232C22×D4—22no—
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—44no—
242C22×D4—44no—
243C22×D4—44no—
244C22×D4—44no—
245C22×D4—48no—
246C22×D4—48no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4—44no—
250C22×D4—48no—
251C22×D4—416no—
252C22×D4—416no—
253C22×D4—416no—
254C22×D4—416no—
255C22×D4#4114yes—
256C22×D4#4114yes—
257C22×D4C2412yes—
258C22×D4C2412yes—
259C23×C4—22no—
260C23×C4—22no—
261C23×C4—22no—
262C23×C4—22no—
263C23×C4—22no—
264C23×C4—22no—
265C23×C4—21no—
266C23×C4—21no—
267C23×C4—21no—
268C23×C4—21no—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4C2×D412yes—
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2412yes—
278C23×C4C2411yescharacteristic
279C22×C8—22no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8—22no—
283C22×C8—22no—
284C22×C8—22no—
285C22×C8—22no—
286C22×C8—22no—
287C22×C8—22no—
288C22×C8—22no—
289C22×C8—22no—
290C22×C8—22no—
291C22×C8C2412yes—
292C22×C8C2412yes—
293C22×C8C2412yes—
294C22×C8C2412yes—
295#126—432no—
296#124—28no—
297#124—28no—
298#124—44no—
299#124—44no—
300#124—48no—
301#124—48no—
302C22⋊Q8—44no—
303C22⋊Q8—44no—
304C22⋊Q8—48no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—24no—
316C2×C4⋊C4—24no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—24no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—44no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—44no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4C2412yes—
331C2×C4⋊C4C2412yes—
332C2×C4⋊C4C2412yes—
333C2×C4⋊C4C2412yes—
334C2×C4⋊C4C2412yes—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—42no—
348C2×C22⋊C4—44no—
349C2×C22⋊C4—44no—
350C2×C22⋊C4—44no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—44no—
353C2×C22⋊C4—44no—
354C2×C22⋊C4—44no—
355C2×C22⋊C4—82no—
356C2×C22⋊C4—82no—
357C2×C22⋊C4—82no—
358C2×C22⋊C4—82no—
359C2×C22⋊C4C2×D414yes—
360C2×C22⋊C4C2×D414yes—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—24no—
366C2×C42—44no—
367C2×C42C2×D412yes—
368C2×C42C2×D412yes—
369C2×C42C2412yes—
370C2×C42C2412yes—
371#106—44no—
372#106—44no—
373C4⋊C8—44no—
374#103—44no—
375#103—44no—
376#103—44no—
377#103—44no—
378#102—28no—
379#102—28no—
380#102—44no—
381#102—44no—
382#102—44no—
383#102—44no—
384#102—44no—
385#102—44no—
386C22⋊C8—44no—
387C22⋊C8—44no—
388#97—44no—
389#95—24no—
390#95—24no—
391#95—24no—
392#95—24no—
393#95—24no—
394#95C2×D414yes—
395#95C2×D414yes—
396C24—22no—
397C24—22no—
398C24—22no—
399C24—22no—
400C24—22no—
401C24—22no—
402C24—24no—
403C24—24no—
404C24—22no—
405C24—22no—
406C24—48no—
407C24—48no—
408C24—48no—
409C24—48no—
410C24—432no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24—42no—
421C24—42no—
422C24—42no—
423C24—48no—
424C24—84no—
425C24—84no—
426C24—816no—
427C24—816no—
428C24—816no—
429C24—816no—
430C24—816no—
431C24—816no—
432C24AGL(1,ℤ/8)14yes—
433C24C22×D412yes—
434C24C22×D411yescharacteristic
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—22no—
441C2×Q8—42no—
442C2×Q8—42no—
443C2×Q8—42no—
444C2×Q8—44no—
445C2×Q8—44no—
446C2×Q8—44no—
447C2×Q8—44no—
448C2×D4—28no—
449C2×D4—28no—
450C2×D4—24no—
451C2×D4—24no—
452C2×D4—28no—
453C2×D4—28no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—48no—
465C2×D4—48no—
466C2×D4—48no—
467C2×D4—416no—
468C2×D4—416no—
469C2×D4—416no—
470C2×D4—432no—
471C2×D4—464no—
472C2×D4—416no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—44no—
476C2×D4—44no—
477C2×D4—42no—
478C2×D4—42no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4C2×#4114yes—
482C2×D4C2×#4114yes—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—24no—
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—22no—
512C22×C4—22no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4—44no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—42no—
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—42no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4C22×D412yes—
536C22×C4C22×D412yes—
537C22×C4C22×D412yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D411yescharacteristic
541C22×C4C2×#4112yes—
542C22×C4C2×#4112yes—
543C22×C4H(5,𝔽2)12yes—
544C22×C4H(5,𝔽2)12yes—
545C22×C4H(5,𝔽2)12yes—
546C22×C4H(5,𝔽2)12yes—
547C22×C4C2511yescharacteristic
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—44no—
561C2×C8—44no—
562C2×C8—44no—
563C2×C8—44no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—48no—
575C4⋊C4—48no—
576C4⋊C4—48no—
577C4⋊C4—48no—
578C4⋊C4—48no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C22⋊C4—28no—
585C22⋊C4—44no—
586C22⋊C4—48no—
587C22⋊C4—48no—
588C22⋊C4—48no—
589C22⋊C4—48no—
590C22⋊C4—48no—
591C22⋊C4—48no—
592C22⋊C4—48no—
593C22⋊C4—84no—
594C22⋊C4—84no—
595C22⋊C4—84no—
596C22⋊C4—84no—
597C42—24no—
598C42—24no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—48no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—28no—
608C23—28no—
609C23—28no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—24no—
614C23—24no—
615C23—44no—
616C23—44no—
617C23—44no—
618C23—44no—
619C23—432no—
620C23—42no—
621C23—42no—
622C23—48no—
623C23—48no—
624C23—42no—
625C23—42no—
626C23—48no—
627C23—48no—
628C23—48no—
629C23—42no—
630C23—42no—
631C23—48no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—816no—
639C23—816no—
640C23—816no—
641C23—816no—
642C23—816no—
643C23—8128no—
644C23—816no—
645C23—84no—
646C23—84no—
647C23—84no—
648C23—84no—
649C23—84no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23#53512yes—
654C23#54612yes—
655C23#54612yes—
656C23C2×AGL(1,ℤ/8)14yes—
657C23C2×AGL(1,ℤ/8)12yes—
658C23#57512yes—
659C23#57712yes—
660C23#57712yes—
661C23C23×D411yescharacteristic
662Q8—42no—
663Q8—42no—
664Q8—42no—
665Q8—42no—
666Q8—84no—
667D4—24no—
668D4—24no—
669D4—24no—
670D4—24no—
671D4—432no—
672D4—42no—
673D4—42no—
674D4—48no—
675D4—48no—
676D4—42no—
677D4—42no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—48no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
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—84no—
722C2×C4—84no—
723C2×C4—84no—
724C2×C4—84no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4#53512yes—
728C2×C4#53814yes—
729C2×C4#53814yes—
730C2×C4#54612yes—
731C2×C4#54612yes—
732C2×C4#55114yes—
733C2×C4#56014yes—
734C2×C4C22×#4111yescharacteristic
735C2×C4C22×#4111yescharacteristic
736C2×C4C2×H(5,𝔽2)11yescharacteristic
737C2×C4C2×H(5,𝔽2)11yescharacteristic
738C2×C4C2×H(5,𝔽2)11yescharacteristic
739C2×C4C2×H(5,𝔽2)11yescharacteristic
740C8—42no—
741C8—42no—
742C8—42no—
743C8—42no—
744C22—24no—
745C22—24no—
746C22—24no—
747C22—416no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—44no—
758C22—864no—
759C22—816no—
760C22—816no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22#268514yes—
770C22#321314yes—
771C22#322214yes—
772C22#330614yes—
773C22#330614yes—
774C22#331114yes—
775C22#332314yes—
776C22C2×#53511yescharacteristic
777C22C2×#54611yescharacteristic
778C22C2×#54611yescharacteristic
779C22C22×AGL(1,ℤ/8)11yescharacteristic
780C22C2×#57511yescharacteristic
781C22C2×#57711yescharacteristic
782C22C2×#57711yescharacteristic
783C4—42no—
784C4—42no—
785C4—42no—
786C4—42no—
787C4—42no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4#268514yes—
795C4C2×#53811yescharacteristic
796C4C2×#53811yescharacteristic
797C4C2×#55111yescharacteristic
798C4C2×#56011yescharacteristic
799C2—44no—
800C2—84no—
801C2—84no—
802C2#3130618yesdirect product factor
803C2C2×#268511yescharacteristic
804C2C2×#321311yescharacteristic
805C2C2×#322211yescharacteristic
806C2C2×#330611yescharacteristic
807C2C2×#330611yescharacteristic
808C2C2×#331111yescharacteristic
809C2C2×#332311yescharacteristic
subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24×D4C22
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. C2×#2496C2semidirect
3. #31306C2direct (N × H)
4. C2×#2094C2semidirect
5. C2×#2065C2semidirect
6. C2×#2042C2semidirect
7. C2×#2042C2semidirect
8. C2×#2035C2semidirect
9. C2×#2035C2semidirect
10. C2×#1983C2semidirect
11. C2×#1959C2semidirect
12. C2×#1936C2semidirect
13. C2×#1926C2semidirect
14. C2×#1924C2semidirect
22. C22×#106C22semidirect
23. C22×#106C22semidirect
24. C22×C4⋊C8C22semidirect
25. C22×#103C22semidirect
26. C22×#103C22semidirect
27. C22×#103C22semidirect
28. C22×#103C22semidirect
39. C22×#97C22semidirect
41. #2496C22semidirect
50. C2×#389C22semidirect
51. C2×#389C22semidirect
53. C2×#384C22semidirect
58. C2×C4×C4⋊C4C22semidirect
60. #2094C22semidirect
61. #2065C22semidirect
62. #2042C22semidirect
63. #2042C22semidirect
64. #2035C22semidirect
65. #2035C22semidirect
66. #1983C22semidirect
67. #1959C22semidirect
68. #1936C22semidirect
69. #1926C22semidirect
70. #1924C22semidirect
73. C2×#340C22semidirect
74. C2×#340C22semidirect
75. C2×#336C22semidirect
76. C2×#336C22semidirect
137. C2×#106C23semidirect
138. C2×#106C23semidirect
140. C2×C4⋊C8C23semidirect
145. C2×#103C23semidirect
146. C2×#103C23semidirect
147. C2×#103C23semidirect
148. C2×#103C23semidirect
170. C2×#97C23semidirect
181. #389C23semidirect
182. #389C23semidirect
185. #384C23semidirect
193. C4×C4⋊C4C23semidirect
203. #340C23semidirect
204. #340C23semidirect
205. #336C23semidirect
206. #336C23semidirect
802. C2#31306direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#24962
C2×#24352
#313062
C2×#20942
C2×#20652
C2×#20422
C2×#20352
C2×#19832
C2×#19592
C2×#19362
C2×#19262
C2×#19242
C2×#17862