Finite Group Databasebeta

← #6468281

Subgroups — #6468281

Order 512.

1760 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36645C211yesmaximal, characteristic, complemented
2C4×#529C211yesmaximal, characteristic
3#29225C211yesmaximal, characteristic, complemented
4#29213C211yesmaximal, characteristic, complemented
5#29198C212yesmaximal, complemented
6#29184C212yesmaximal, complemented
7#29160C212yesmaximal, complemented
8#29156C212yesmaximal
9#29148C211yesmaximal, characteristic, complemented
10#28520C211yesmaximal, characteristic, complemented
11#24838C212yesmaximal, complemented
12#24835C212yesmaximal
13#23782C212yesmaximal, complemented
14#23780C212yesmaximal, complemented
15#21615C212yesmaximal, complemented
16#21613C212yesmaximal, complemented
17#21406C212yesmaximal
18#20823C212yesmaximal, complemented
19C2×#1767C211yesmaximal, characteristic, complemented
20C2×#533—21no—
21C2×#529C2211yescharacteristic
22C2×#475C2212yes—
23C2×#474C2212yes—
24C22×C4⋊C8C2212yes—
25C22×#97C2212yes—
26#2868C2211yescharacteristic
27#2868C2211yescharacteristic
28#2862—21no—
29#2859—21no—
30#2859C2212yes—
31#2857—21no—
32#2857—21no—
33#2857C2212yes—
34#2857C2212yes—
35C4×C4⋊Q8—21no—
36C4×C4⋊Q8—21no—
37C4×C4⋊Q8C2212yes—
38C4×C4⋊Q8C2212yes—
39C4×#125C2211yescharacteristic
40C4×#125C2211yescharacteristic
41C4×#126—21no—
42C4×#126—21no—
43C4×#124C2211yescharacteristic
44C4×#124C2211yescharacteristic
45C4×C22⋊Q8C2211yescharacteristic
46C4×C22⋊Q8C2211yescharacteristic
47C4×#123—21no—
48C4×#123—21no—
49C4×#121C2211yescharacteristic
50C4×#121C2211yescharacteristic
51#2298—21no—
52#2295C2211yescharacteristic
53#2293C2211yescharacteristic
54#2290—21no—
55#2285—21no—
56#2285C2212yes—
57#2283C2211yescharacteristic
58C42×Q8C2211yescharacteristic
59C42×D4—21no—
60C42×D4C2211yescharacteristic
61C4×#117—21no—
62C2×C43C2211yescharacteristic
63#2100C2212yes—
64#2100C2212yes—
65#2095C2212yes—
66#2094C2212yes—
67#2088C2214yes—
68#2086C2214yes—
69#2067C2214yes—
70#2066C2214yes—
71#2058C2212yes—
72#2057C2212yes—
73#2024C2212yes—
74#2023C2212yes—
75#1992C2212yes—
76#1992C2212yes—
77#1988C2212yes—
78#1988C2212yes—
79#1959C2212yes—
80#1959C2212yes—
81#1948C2212yes—
82#1947C2212yes—
83#1921C2214yes—
84#1920C2214yes—
85#1893C2214yes—
86#1892C2214yes—
87#1864C2214yes—
88#1863C2214yes—
89#1847C2212yes—
90#1847C2212yes—
91#1836C2212yes—
92#1836C2212yes—
93#1808C2214yes—
94#1807C2214yes—
95#1803C2212yes—
96#1802C2212yes—
97#1776C2214yes—
98#1776C2214yes—
99#1767C2212yes—
100#1767C2211yescharacteristic
101#1767C2211yescharacteristic
102#1767C2212yes—
103#1767C2212yes—
104#1763C2214yes—
105#1762C2214yes—
106C2×#336C2212yes—
107C23×C8C2314yes—
108#533—48no—
109C2×C4⋊Q8—21no—
110C2×C4⋊Q8—21no—
111C2×C4⋊Q8—21no—
112C2×C4⋊Q8—21no—
113C2×C4⋊Q8C2312yes—
114C2×C4⋊Q8C2312yes—
115#529—24no—
116#529Q818yescomplemented
117C2×#126—21no—
118C2×#125—22no—
119C2×#125C2311yescharacteristic
120C2×#124C2311yescharacteristic
121C2×#123—21no—
122C2×C22⋊Q8—22no—
123C2×C22⋊Q8—22no—
124C2×C22⋊Q8C2311yescharacteristic
125C2×#121C2311yescharacteristic
126C2×C4×Q8—22no—
127C2×C4×Q8—22no—
128C2×C4×Q8C2311yescharacteristic
129C2×C4×Q8C2311yescharacteristic
130C2×C4×Q8C2311yescharacteristic
131C2×C4×D4—21no—
132C2×C4×D4—21no—
133C2×C4×D4—21no—
134C2×C4×D4C2311yescharacteristic
135C2×C4×D4C2311yescharacteristic
136C2×C4×D4C2311yescharacteristic
137C2×#117—22no—
138C2×#117—21no—
139C2×#117—21no—
140C22×C42—21no—
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42C2311yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148#475—28no—
149#474—28no—
150C2×#107C2314yes—
151C2×#107C2314yes—
152C2×#106C2314yes—
153C2×#106C2314yes—
154C2×C4⋊C8—28no—
155C2×C4⋊C8C2312yes—
156C2×C4⋊C8C2314yes—
157C2×C4⋊C8C2312yes—
158C2×#103C2314yes—
159C2×#103C2314yes—
160C2×#102C2314yes—
161C2×#102C2314yes—
162C2×#97—28no—
163C2×#97C2312yes—
164C2×#97C2312yes—
165C2×#97C2314yes—
166#391—22no—
167#391—22no—
168#391—22no—
169#391—22no—
170#391C2311yescharacteristic
171#391C2311yescharacteristic
172#390C2311yescharacteristic
173#390C2311yescharacteristic
174#389—22no—
175#389—22no—
176#389—22no—
177#389—22no—
178#389—22no—
179#389—22no—
180#389C2311yescharacteristic
181#389C2311yescharacteristic
182#389C2311yescharacteristic
183#389C2311yescharacteristic
184#389C2314yes—
185#389C2314yes—
186#388—21no—
187#388—21no—
188#388—21no—
189#388—21no—
190#388—21no—
191#388—21no—
192#388—21no—
193#388—21no—
194#387—21no—
195#387—21no—
196#387—21no—
197#387—21no—
198#387—21no—
199#387—21no—
200#387—21no—
201#387—21no—
202#386—21no—
203#386—21no—
204#385—21no—
205#385—21no—
206#384—21no—
207#384—21no—
208#384—21no—
209#384—21no—
210#384C2312yes—
211#384C2312yes—
212#384C2312yes—
213#384C2312yes—
214#383—21no—
215#382—22no—
216#382—22no—
217#382C2311yescharacteristic
218#382C2311yescharacteristic
219#381—21no—
220#380—22no—
221#380—22no—
222#380—22no—
223#380C2311yescharacteristic
224#380C2314yes—
225#380C2311yescharacteristic
226C4×C4⋊C4—21no—
227C4×C4⋊C4—21no—
228C4×C4⋊C4—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4—21no—
231C4×C4⋊C4—21no—
232C4×C4⋊C4—21no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—22no—
235C4×C4⋊C4—22no—
236C4×C4⋊C4—22no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4C2311yescharacteristic
240C4×C4⋊C4C2311yescharacteristic
241C4×C4⋊C4C2311yescharacteristic
242C4×C4⋊C4C2311yescharacteristic
243C4×C4⋊C4C2314yes—
244C4×C4⋊C4C2311yescharacteristic
245C4×C4⋊C4C2311yescharacteristic
246C4×C22⋊C4—21no—
247C4×C22⋊C4—21no—
248C4×C22⋊C4—21no—
249C4×C22⋊C4—21no—
250C4×C22⋊C4—21no—
251C4×C22⋊C4—21no—
252C4×C22⋊C4—21no—
253C4×C22⋊C4—21no—
254C4×C22⋊C4—21no—
255C4×C22⋊C4—21no—
256C4×C22⋊C4—21no—
257C4×C22⋊C4—21no—
258C4×C22⋊C4—21no—
259#376—21no—
260#376—21no—
261C43—21no—
262C43D411yescharacteristic
263C43D411yescharacteristic
264C43D411yescharacteristic
265C43D411yescharacteristic
266C43C2311yescharacteristic
267C43C2311yescharacteristic
268C43C2311yescharacteristic
269C43C2311yescharacteristic
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#336C2312yes—
279#336C2312yes—
280#336C2314yes—
281C22×Q8—22no—
282C22×Q8—22no—
283C22×Q8C2411yescharacteristic
284C22×D4—21no—
285C22×D4C2411yescharacteristic
286C23×C4—21no—
287C23×C4—21no—
288C23×C4—21no—
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2411yescharacteristic
296C22×C8—28no—
297C22×C8—28no—
298C22×C8—44no—
299C22×C8C2414yes—
300C22×C8C2414yes—
301C4⋊Q8—24no—
302C4⋊Q8—24no—
303C4⋊Q8—44no—
304C4⋊Q8—44no—
305C4⋊Q8—44no—
306C4⋊Q8—44no—
307C4⋊Q8—44no—
308#126—28no—
309#125—22no—
310#125—48no—
311#125C2×Q814yes—
312#124—22no—
313#124C2×Q814yes—
314#123—28no—
315C22⋊Q8—22no—
316C22⋊Q8—48no—
317C22⋊Q8—48no—
318C22⋊Q8C2×Q814yes—
319#121—22no—
320#121C2×Q814yes—
321C4×Q8—22no—
322C4×Q8—24no—
323C4×Q8—42no—
324C4×Q8—48no—
325C4×Q8—48no—
326C4×Q8C2×Q814yes—
327C4×D4—28no—
328C4×D4—22no—
329C4×D4—24no—
330C4×D4—42no—
331C4×D4—44no—
332C4×D4—44no—
333C4×D4C2×Q814yes—
334#117—28no—
335#117—44no—
336#117—48no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4C2411yescharacteristic
360C2×C4⋊C4C2411yescharacteristic
361C2×C4⋊C4C2411yescharacteristic
362C2×C4⋊C4C2411yescharacteristic
363C2×C4⋊C4C2414yes—
364C2×C4⋊C4C2414yes—
365C2×C4⋊C4C2411yescharacteristic
366C2×C4⋊C4C2411yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C42—24no—
382C2×C42—24no—
383C2×C42—21no—
384C2×C42—24no—
385C2×C42—24no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42—21no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—42no—
397C2×C42—44no—
398C2×C42C2×D411yescharacteristic
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×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×Q814yes—
421C2×C42#4114yes—
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428#107—28no—
429#107—44no—
430#106—28no—
431#106—44no—
432C4⋊C8—28no—
433C4⋊C8—24no—
434C4⋊C8#4118yes—
435#103—28no—
436#103—44no—
437#102—28no—
438#102—44no—
439#97—28no—
440#97—24no—
441#97—24no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—24no—
463#95—24no—
464#95—24no—
465#95—24no—
466C24—21no—
467C24C22×D411yescharacteristic
468C2×Q8—21no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8C22×Q812yes—
478C2×D4—24no—
479C2×D4—22no—
480C2×D4—21no—
481C2×D4—22no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4C22×Q812yes—
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—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—24no—
504C22×C4—24no—
505C22×C4—41no—
506C22×C4—41no—
507C22×C4—41no—
508C22×C4—41no—
509C22×C4—41no—
510C22×C4—41no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—42no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4C22⋊Q814yes—
520C22×C4C22⋊Q814yes—
521C22×C4AGL(1,ℤ/8)14yes—
522C22×C4#13714yes—
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C22×D411yescharacteristic
526C22×C4C22×D411yescharacteristic
527C22×C4C22×D411yescharacteristic
528C22×C4C22×D411yescharacteristic
529C22×C4C22×D411yescharacteristic
530C22×C4C22×D411yescharacteristic
531C22×C4C22×D411yescharacteristic
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D411yescharacteristic
534C22×C4C22×D411yescharacteristic
535C22×C4C22×D411yescharacteristic
536C22×C4C22×Q812yes—
537C22×C4C2×#4112yes—
538C22×C4C2511yescharacteristic
539C2×C8—24no—
540C2×C8—24no—
541C2×C8—24no—
542C2×C8—24no—
543C2×C8—24no—
544C2×C8—416no—
545C2×C8C2×#4118yes—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—42no—
561C4⋊C4—44no—
562C4⋊C4—44no—
563C4⋊C4—42no—
564C4⋊C4—48no—
565C4⋊C4—44no—
566C4⋊C4—44no—
567C4⋊C4—44no—
568C4⋊C4—44no—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4—42no—
572C4⋊C4—44no—
573C4⋊C4—42no—
574C4⋊C4—48no—
575C4⋊C4—44no—
576C4⋊C4—42no—
577C4⋊C4—42no—
578C4⋊C4C22×Q812yes—
579C4⋊C4C22×Q812yes—
580C22⋊C4—24no—
581C22⋊C4—24no—
582C22⋊C4—24no—
583C22⋊C4—24no—
584C22⋊C4—24no—
585C22⋊C4—42no—
586C22⋊C4—42no—
587C22⋊C4—48no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C42—24no—
595C42—22no—
596C42—22no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—41no—
613C42—41no—
614C42—41no—
615C42—41no—
616C42—41no—
617C42—41no—
618C42—42no—
619C42—42no—
620C42—42no—
621C42—48no—
622C42—42no—
623C42—42no—
624C42—42no—
625C42—42no—
626C42—42no—
627C42C22⋊Q814yes—
628C42C22⋊Q814yes—
629C42C22×Q812yes—
630C42C22×Q812yes—
631C42C2×#4112yes—
632C42C2×#4112yes—
633C42C2×#4114yes—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23C2×C22⋊Q812yes—
646C23C2×AGL(1,ℤ/8)12yes—
647C23C2×#13712yes—
648C23C23×D411yescharacteristic
649Q8—24no—
650Q8—42no—
651Q8—88no—
652Q8—88no—
653D4—24no—
654D4—48no—
655D4—42no—
656C2×C4—28no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—28no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—21no—
684C2×C4—21no—
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—48no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—44no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—44no—
706C2×C4—41no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—84no—
719C2×C4—84no—
720C2×C4C2×C22⋊Q812yes—
721C2×C4C2×C22⋊Q812yes—
722C2×C4C2×C22⋊Q812yes—
723C2×C4C2×C22⋊Q812yes—
724C2×C4C2×C22⋊Q812yes—
725C2×C4#53212yes—
726C2×C4#53212yes—
727C2×C4C2×AGL(1,ℤ/8)12yes—
728C2×C4C2×AGL(1,ℤ/8)12yes—
729C2×C4C2×#13712yes—
730C2×C4C2×#13712yes—
731C2×C4#57512yes—
732C2×C4#57512yes—
733C2×C4C23×Q811yescharacteristic
734C2×C4C22×#4111yescharacteristic
735C2×C4C22×#4112yes—
736C2×C4#58512yes—
737C8—28no—
738C8—44no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22#307914yes—
753C22C22×C22⋊Q811yescharacteristic
754C22C2×#53211yescharacteristic
755C22#344911yescharacteristic
756C22C22×AGL(1,ℤ/8)11yescharacteristic
757C22C22×#13711yescharacteristic
758C22C2×#57511yescharacteristic
759C22C2×#57511yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—41no—
771C4—41no—
772C4—42no—
773C4—42no—
774C4—42no—
775C4—81no—
776C4—84no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4—84no—
781C4#318014yes—
782C4#347512yes—
783C4Q8×#4112yes—
784C2—24no—
785C2—82no—
786C2#3494711yescharacteristic
787C2C2×#307911yescharacteristic
788C2#6048411yescharacteristic
789C2C2×#318011yescharacteristic
790C2#6070111yescharacteristic
791C2#6096011yescharacteristic
792C2#6096211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36645C2semidirect
3. #29225C2semidirect
4. #29213C2semidirect
5. #29198C2semidirect
6. #29184C2semidirect
7. #29160C2semidirect
9. #29148C2semidirect
10. #28520C2semidirect
11. #24838C2semidirect
13. #23782C2semidirect
14. #23780C2semidirect
15. #21615C2semidirect
16. #21613C2semidirect
18. #20823C2semidirect
19. C2×#1767C2semidirect
116. #529Q8semidirect

Maximal subgroups

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

subgroupindex
#366452
C4×#5292
#292252
#292132
#291982
#291842
#291602
#291562
#291482
#285202
#248382
#248352
#237822
#237802
#216152
#216132
#214062
#208232
C2×#17672