Finite Group Databasebeta

← #6491148

Subgroups — #6491148

Order 512.

3288 conjugacy classes of subgroups.

The subgroup lattice has 795 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#533C211yesmaximal, characteristic
2C2×#3249C212yesmaximal, complemented
3#36625C211yesmaximal, characteristic
4#32957C212yesmaximal, complemented
5#32906C212yesmaximal, complemented
6#29691C212yesmaximal, complemented
7#29664C212yesmaximal, complemented
8#25498C214yesmaximal, complemented
9#24380C214yesmaximal
10#24302C212yesmaximal, complemented
11#24212C212yesmaximal, complemented
12#24155C214yesmaximal, complemented
13#21885C212yesmaximal, complemented
14C2×#1797C211yesmaximal, characteristic
15C2×#533—21no—
16C2×#533—21no—
17C2×#533—21no—
18C2×#533—21no—
19C2×#533—216no—
20C2×#533C2211yescharacteristic
21C2×#533C2212yes—
22C2×#533C2212yes—
23C2×#533C2212yes—
24C2×#533C2212yes—
25C22×C4⋊Q8C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C22×#125—21no—
28C22×C22⋊Q8—21no—
29C22×C22⋊Q8C2212yes—
30C22×C4×Q8—21no—
31C22×C4×Q8C2212yes—
32C22×#117—21no—
33C23×C42C2211yescharacteristic
34#3249—216no—
35C2×#477C2214yescomplemented
36C2×#477C2214yescomplemented
37C2×#467C2218yes—
38C2×#462C2214yescomplemented
39C2×#462C2214yescomplemented
40C2×#451C2214yes—
41C22×C4⋊C8C2212yes—
42C22×C22⋊C8C2212yes—
43#2857C2211yescharacteristic
44#2857C2211yescharacteristic
45#2857C2211yescharacteristic
46#2857C2211yescharacteristic
47#2855—21no—
48#2855C2212yes—
49#2851—21no—
50#2851—21no—
51#2848—21no—
52#2848C2212yes—
53C4×C22⋊Q8—21no—
54C4×C22⋊Q8—21no—
55C4×C22⋊Q8C2212yes—
56C4×C22⋊Q8C2212yes—
57#2296—21no—
58#2285C2211yescharacteristic
59#2280—21no—
60#2057C2214yescomplemented
61#2043C2214yescomplemented
62#2036C2218yes—
63#2024C2214yescomplemented
64#2016C2214yescomplemented
65#2001C2218yes—
66#1987C2214yescomplemented
67#1981C2214yescomplemented
68#1892C2218yes—
69#1878C2218yescomplemented
70#1872C2214yes—
71#1863C2218yescomplemented
72#1852C2214yes—
73#1803C2214yescomplemented
74#1803C2214yescomplemented
75#1797C2212yes—
76#1797C2212yes—
77#1797C2212yes—
78#1797C2212yes—
79#1787C2214yes—
80C2×#336C2212yes—
81C23×Q8—21no—
82C23×Q8C2312yes—
83C24×C4D411yescharacteristic
84C24×C4D411yescharacteristic
85C24×C4C2311yescharacteristic
86C22×Q16C2318yes—
87C23×C8C2314yes—
88#533—216no—
89#533—216no—
90#533—216no—
91#533—216no—
92#533—28no—
93#533—28no—
94#533—216no—
95#533—216no—
96#533—28no—
97#533—28no—
98#533D4116yes—
99C2×C4⋊Q8—28no—
100C2×C4⋊Q8—28no—
101C2×C4⋊Q8—21no—
102C2×C4⋊Q8—21no—
103C2×C4⋊Q8—21no—
104C2×C4⋊Q8—21no—
105C2×C4⋊Q8C2311yescharacteristic
106C2×C4⋊Q8C2312yes—
107C2×C4⋊Q8C2312yes—
108C2×C4⋊Q8C2311yescharacteristic
109C2×C4⋊Q8C2312yes—
110C2×C4⋊Q8C2312yes—
111C2×#125—216no—
112C2×#125—22no—
113C2×#125—22no—
114C2×#125—22no—
115C2×#125—22no—
116C2×#125—21no—
117C2×C22⋊Q8—216no—
118C2×C22⋊Q8—22no—
119C2×C22⋊Q8—22no—
120C2×C22⋊Q8—22no—
121C2×C22⋊Q8—22no—
122C2×C22⋊Q8—22no—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8—216no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8C2312yes—
129C2×C22⋊Q8C2312yes—
130C2×C22⋊Q8C2314yes—
131C2×C22⋊Q8C2314yes—
132C2×C22⋊Q8C2312yes—
133C2×C4×Q8—216no—
134C2×C4×Q8—216no—
135C2×C4×Q8—22no—
136C2×C4×Q8—22no—
137C2×C4×Q8—22no—
138C2×C4×Q8—22no—
139C2×C4×Q8—22no—
140C2×C4×Q8—22no—
141C2×C4×Q8—21no—
142C2×C4×Q8C2312yes—
143C2×C4×Q8C2314yes—
144C2×C4×Q8C2314yes—
145C2×#117—216no—
146C2×#117—22no—
147C2×#117—22no—
148C2×#117—22no—
149C2×#117—22no—
150C2×#117—21no—
151C2×#117—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—22no—
156C22×C4⋊C4—22no—
157C22×C4⋊C4C2312yes—
158C22×C22⋊C4—22no—
159C22×C42—22no—
160C22×C42—28no—
161C22×C42D411yescharacteristic
162C22×C42D411yescharacteristic
163C22×C42D411yescharacteristic
164C22×C42D411yescharacteristic
165C22×C42D411yescharacteristic
166C22×C42D411yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173#477—216no—
174#477—216no—
175#467—232no—
176#462—216no—
177#462—216no—
178#451—48no—
179C2×#107C2318yes—
180C2×C4⋊C8—28no—
181C2×C4⋊C8C2314yes—
182C2×C4⋊C8C2314yes—
183C2×#103C2318yes—
184C2×#103C2318yes—
185C2×#103C2318yes—
186C2×#103C2318yes—
187C2×C22⋊C8—44no—
188C2×C22⋊C8C2314yes—
189C2×C22⋊C8C2314yes—
190#391—21no—
191#391—21no—
192#391C2312yes—
193#391C2312yes—
194#389—21no—
195#389—21no—
196#389—21no—
197#389—21no—
198#389—21no—
199#389—21no—
200#389C2312yes—
201#389C2312yes—
202#387—22no—
203#387—22no—
204#387—22no—
205#387—22no—
206#385—22no—
207#385—22no—
208#385—22no—
209#385—22no—
210#385—22no—
211#385—22no—
212#384C2311yescharacteristic
213#384C2311yescharacteristic
214#382—21no—
215#381—22no—
216#380—21no—
217#380—21no—
218#380—21no—
219#380—21no—
220#380—21no—
221#380—21no—
222#380—21no—
223#380C2312yes—
224#380C2312yes—
225#380C2312yes—
226#379—22no—
227C4×C4⋊C4—21no—
228C4×C4⋊C4—22no—
229C4×C4⋊C4—22no—
230C4×C4⋊C4C2312yes—
231C4×C22⋊C4—22no—
232C4×C22⋊C4—22no—
233#340C2318yes—
234#340C2318yes—
235#336C2314yes—
236#336C2314yes—
237C25C2×D411yescharacteristic
238C22×Q8—28no—
239C22×Q8—28no—
240C22×Q8—22no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—21no—
244C22×Q8—24no—
245C22×Q8—24no—
246C22×Q8—44no—
247C22×Q8—44no—
248C22×Q8—44no—
249C22×Q8C2412yes—
250C22×Q8C2414yes—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—22no—
254C23×C4—22no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—42no—
262C23×C4Q1618yescomplemented
263C23×C4C2×D411yescharacteristic
264C23×C4C2×D411yescharacteristic
265C23×C4C2×D411yescharacteristic
266C23×C4C2×D411yescharacteristic
267C23×C4C2×D411yescharacteristic
268C23×C4C2×D411yescharacteristic
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2411yescharacteristic
279C23×C4C2411yescharacteristic
280C23×C4C2411yescharacteristic
281C2×Q16—216no—
282C2×Q16—48no—
283C2×Q16—48no—
284C22×C8—28no—
285C22×C8—44no—
286C22×C8—44no—
287C22×C8C2418yes—
288C4⋊Q8—28no—
289C4⋊Q8—28no—
290C4⋊Q8—28no—
291C4⋊Q8—28no—
292C4⋊Q8—28no—
293C4⋊Q8—28no—
294C4⋊Q8—24no—
295C4⋊Q8—24no—
296C4⋊Q8—24no—
297C4⋊Q8—24no—
298C4⋊Q8C2×D418yes—
299C4⋊Q8C2×D418yes—
300#125—216no—
301#125—216no—
302#125—216no—
303#125—216no—
304#125—44no—
305C22⋊Q8—216no—
306C22⋊Q8—216no—
307C22⋊Q8—216no—
308C22⋊Q8—216no—
309C22⋊Q8—216no—
310C22⋊Q8—28no—
311C22⋊Q8—216no—
312C22⋊Q8—28no—
313C22⋊Q8—28no—
314C22⋊Q8—28no—
315C22⋊Q8—24no—
316C22⋊Q8—24no—
317C22⋊Q8—44no—
318C22⋊Q8—44no—
319C22⋊Q8—44no—
320C22⋊Q8—44no—
321C22⋊Q8C2×D4116yes—
322C4×Q8—216no—
323C4×Q8—216no—
324C4×Q8—216no—
325C4×Q8—216no—
326C4×Q8—216no—
327C4×Q8—28no—
328C4×Q8—28no—
329C4×Q8—216no—
330C4×Q8—28no—
331C4×Q8—28no—
332C4×Q8—44no—
333C4×Q8C2×D4116yes—
334#117—216no—
335#117—216no—
336#117—216no—
337#117—216no—
338#117—44no—
339#117—44no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—28no—
342C2×C4⋊C4—216no—
343C2×C4⋊C4—216no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—24no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—28no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4C2412yes—
371C2×C4⋊C4C2412yes—
372C2×C4⋊C4C2412yes—
373C2×C4⋊C4C2414yes—
374C2×C22⋊C4—216no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C42—216no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—24no—
387C2×C42—24no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D418yes—
412C2×C42C2411yescharacteristic
413C2×C42C2411yescharacteristic
414C2×C42C2411yescharacteristic
415C2×C42C2411yescharacteristic
416#107—216no—
417C4⋊C8—28no—
418C4⋊C8—28no—
419#103—216no—
420#103—216no—
421#103—48no—
422#103—48no—
423C22⋊C8—28no—
424C22⋊C8—44no—
425#95—22no—
426#95—22no—
427#95—22no—
428#95—22no—
429#95—22no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435C24—22no—
436C24—22no—
437C24—22no—
438C24—22no—
439C24—41no—
440C24—41no—
441C24C2×Q1614yes—
442C24C22×D411yescharacteristic
443C24C22×D411yescharacteristic
444C24C22×D411yescharacteristic
445C2×Q8—28no—
446C2×Q8—28no—
447C2×Q8—28no—
448C2×Q8—24no—
449C2×Q8—24no—
450C2×Q8—24no—
451C2×Q8—22no—
452C2×Q8—24no—
453C2×Q8—22no—
454C2×Q8—24no—
455C2×Q8—24no—
456C2×Q8—24no—
457C2×Q8—416no—
458C2×Q8—416no—
459C2×Q8—432no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—44no—
468C2×Q8—44no—
469C2×Q8C22×D418yes—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—232no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4—416no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4#12014yes—
532C22×C4#12014yes—
533C22×C4C2×Q1614yes—
534C22×C4C2×Q1614yes—
535C22×C4C2×Q1614yes—
536C22×C4C2×Q1614yes—
537C22×C4C2×Q1614yes—
538C22×C4C2×Q1614yes—
539C22×C4#13714yes—
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D414yes—
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4H(5,𝔽2)12yes—
553C22×C42−1+412yes—
554C22×C4C2511yescharacteristic
555Q16—816no—
556C2×C8—28no—
557C2×C8—28no—
558C2×C8—28no—
559C2×C8—88no—
560C4⋊C4—28no—
561C4⋊C4—28no—
562C4⋊C4—216no—
563C4⋊C4—216no—
564C4⋊C4—28no—
565C4⋊C4—28no—
566C4⋊C4—28no—
567C4⋊C4—28no—
568C4⋊C4—28no—
569C4⋊C4—216no—
570C4⋊C4—216no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—24no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—44no—
583C4⋊C4—44no—
584C4⋊C4—42no—
585C4⋊C4—44no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—44no—
589C4⋊C4C22×D418yes—
590C22⋊C4—216no—
591C22⋊C4—216no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C42—216no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—216no—
610C42—22no—
611C42—22no—
612C42—44no—
613C42—44no—
614C42#12014yes—
615C42#12014yes—
616C42C22×D414yes—
617C42C22×D414yes—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—28no—
630C23—28no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—44no—
635C23—44no—
636C23—44no—
637C23—44no—
638C23—44no—
639C23C2×#12012yes—
640C23#53712yes—
641C23C22×Q1612yes—
642C23C22×Q1612yes—
643C23C22×Q1612yes—
644C23C2×#13712yes—
645C23#57512yes—
646C23C23×D411yescharacteristic
647Q8—28no—
648Q8—28no—
649Q8—416no—
650Q8—416no—
651Q8—416no—
652Q8—44no—
653Q8—44no—
654Q8—44no—
655Q8—44no—
656Q8—84no—
657C2×C4—28no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—28no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—28no—
678C2×C4—28no—
679C2×C4—28no—
680C2×C4—28no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—28no—
684C2×C4—28no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—44no—
697C2×C4—416no—
698C2×C4—416no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—44no—
702C2×C4—44no—
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#451116yescomplemented
718C2×C4C2×#12012yes—
719C2×C4C2×#12012yes—
720C2×C4C2×#12012yes—
721C2×C4C2×#12012yes—
722C2×C4C2×#12012yes—
723C2×C4#53712yes—
724C2×C4C22×Q1612yes—
725C2×C4C22×Q1612yes—
726C2×C4C22×Q1612yes—
727C2×C4C22×Q1612yes—
728C2×C4C2×#13712yes—
729C2×C4C2×#13712yes—
730C2×C4#57512yes—
731C2×C4C23×D412yes—
732C2×C4C2×H(5,𝔽2)11yescharacteristic
733C2×C4C2×2−1+411yescharacteristic
734C2×C4#58512yes—
735C8—48no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—416no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22C2×#45114yes—
757C22#324914yescomplemented
758C22C22×#12011yescharacteristic
759C22C2×#53711yescharacteristic
760C22#344911yescharacteristic
761C22C23×Q1611yescharacteristic
762C22C22×#13711yescharacteristic
763C22C2×#57511yescharacteristic
764C22C2×#57511yescharacteristic
765C4—22no—
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—22no—
771C4—22no—
772C4—41no—
773C4—48no—
774C4—41no—
775C4—48no—
776C4—82no—
777C4—82no—
778C4—82no—
779C4—82no—
780C4C2×#45114yes—
781C4C2×#45114yes—
782C4#348812yes—
783C4#348912yes—
784C2—24no—
785C2—24no—
786C2—42no—
787C2#3525111yescharacteristic
788C2C22×#45111yescharacteristic
789C2#6035911yescharacteristic
790C2C2×#324911yescharacteristic
791C2#6091811yescharacteristic
792C2#6094311yescharacteristic
793C2#6096311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3249C2semidirect
4. #32957C2semidirect
5. #32906C2semidirect
6. #29691C2semidirect
7. #29664C2semidirect
8. #25498C2semidirect
10. #24302C2semidirect
11. #24212C2semidirect
12. #24155C2semidirect
13. #21885C2semidirect
35. C2×#477C22semidirect
36. C2×#477C22semidirect
38. C2×#462C22semidirect
39. C2×#462C22semidirect
60. #2057C22semidirect
61. #2043C22semidirect
63. #2024C22semidirect
64. #2016C22semidirect
66. #1987C22semidirect
67. #1981C22semidirect
69. #1878C22semidirect
71. #1863C22semidirect
73. #1803C22semidirect
74. #1803C22semidirect
262. C23×C4Q16semidirect
717. C2×C4#451semidirect
757. C22#3249semidirect

Maximal subgroups

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

subgroupindex
C22×#5332
C2×#32492
#366252
#329572
#329062
#296912
#296642
#254982
#243802
#243022
#242122
#241552
#218852
C2×#17972