Finite Group Databasebeta

← #6493726

Subgroups — #6493726

Order 512.

1949 conjugacy classes of subgroups.

The subgroup lattice has 879 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36621C211yesmaximal, characteristic
2C2×#2285C211yesmaximal, characteristic, complemented
3#33150C212yesmaximal, complemented
4#33110C212yesmaximal, complemented
5#29944C212yesmaximal, complemented
6#29928C212yesmaximal, complemented
7#27864C212yesmaximal, complemented
8#27863C212yesmaximal, complemented
9#27681C211yesmaximal, characteristic, complemented
10#27678C211yesmaximal, characteristic, complemented
11#27648C211yesmaximal, characteristic, complemented
12#27645C211yesmaximal, characteristic, complemented
13#27628C212yesmaximal, complemented
14#27624C212yesmaximal, complemented
15#24557C212yesmaximal
16#24556C212yesmaximal, complemented
17#21963C212yesmaximal, complemented
18#21890C212yesmaximal, complemented
19#20626C211yesmaximal, characteristic, complemented
20C2×#529C2211yescharacteristic
21C22×#117—21no—
22C23×C42C2211yescharacteristic
23C2×#484C2212yes—
24C2×#481C2212yes—
25C2×#423C2212yes—
26C2×#407C2212yes—
27#2855C2211yescharacteristic
28#2854C2211yescharacteristic
29#2853—21no—
30#2852—21no—
31#2852—21no—
32#2851C2211yescharacteristic
33#2851C2211yescharacteristic
34#2850C2211yescharacteristic
35#2850C2211yescharacteristic
36#2849—21no—
37#2848C2211yescharacteristic
38#2847C2211yescharacteristic
39C4×C22⋊Q8C2211yescharacteristic
40C4×C22⋊Q8C2211yescharacteristic
41C4×#123—21no—
42C4×#121C2211yescharacteristic
43C4×#121C2211yescharacteristic
44C4×#120—21no—
45#2290—21no—
46#2290—21no—
47#2285—21no—
48#2285—21no—
49#2285—21no—
50#2285—21no—
51#2285C2212yes—
52#2285C2212yes—
53#2285C2212yes—
54#2285C2212yes—
55C2×#384C2211yescharacteristic
56C2×#384C2211yescharacteristic
57#2283C2211yescharacteristic
58C2×#382—21no—
59C2×#380—21no—
60C2×#380C2212yes—
61C2×C4×C4⋊C4—21no—
62C2×C4×C4⋊C4C2212yes—
63#2100C2212yescomplemented
64#2100C2212yescomplemented
65#2095C2212yescomplemented
66#2094C2212yescomplemented
67#2084C2212yescomplemented
68#2083C2212yescomplemented
69#2077C2214yes—
70#2075C2214yes—
71#2072C2212yescomplemented
72#2071C2212yescomplemented
73#2035C2214yes—
74#2033C2214yes—
75#1989C2214yescomplemented
76#1983C2214yescomplemented
77#1949C2214yescomplemented
78#1949C2214yescomplemented
79#1948C2212yescomplemented
80#1948C2212yescomplemented
81#1947C2212yescomplemented
82#1947C2212yescomplemented
83#1927C2214yescomplemented
84#1925C2214yescomplemented
85#1920C2214yescomplemented
86#1918C2214yescomplemented
87#1895C2214yes—
88#1894C2214yes—
89#1874C2212yes—
90#1872C2212yes—
91#1853C2212yes—
92#1852C2212yes—
93#1824C2212yes—
94#1824C2212yes—
95#1809C2214yes—
96#1809C2214yes—
97#1803C2212yescomplemented
98#1803C2212yescomplemented
99#1802C2212yescomplemented
100#1802C2212yescomplemented
101#1797C2211yescharacteristic
102#1797C2211yescharacteristic
103#1797C2212yes—
104#1797C2212yes—
105#1797C2212yes—
106#1728C2212yes—
107C24×C4D411yescharacteristic
108C24×C4D411yescharacteristic
109C24×C4C2311yescharacteristic
110C22×M16C2314yes—
111#529—28no—
112C2×#126—21no—
113C2×#125C2311yescharacteristic
114C2×#124C2311yescharacteristic
115C2×#123—21no—
116C2×#123—21no—
117C2×C22⋊Q8C2311yescharacteristic
118C2×C22⋊Q8C2311yescharacteristic
119C2×C22⋊Q8C2311yescharacteristic
120C2×#121C2311yescharacteristic
121C2×#121C2311yescharacteristic
122C2×#121C2311yescharacteristic
123C2×#120—21no—
124C2×C4×Q8C2311yescharacteristic
125C2×C4×D4—21no—
126C2×C4×D4—21no—
127C2×C4×D4—21no—
128C2×C4×D4C2311yescharacteristic
129C2×#117—22no—
130C2×#117—22no—
131C2×#117—22no—
132C2×#117—22no—
133C2×#117—21no—
134C2×#117—48no—
135C22×C4⋊C4—21no—
136C22×C4⋊C4—21no—
137C22×C4⋊C4—21no—
138C22×C4⋊C4—21no—
139C22×C4⋊C4C2312yes—
140C22×C4⋊C4C2312yes—
141C22×C22⋊C4—22no—
142C22×C42—28no—
143C22×C42—22no—
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42D411yescharacteristic
147C22×C42D411yescharacteristic
148C22×C42D411yescharacteristic
149C22×C42D411yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#484—44no—
157#481—44no—
158C2×#107C2314yes—
159C2×#107C2314yes—
160C2×#106C2314yes—
161C2×#106C2314yes—
162#423—28no—
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170#407—44no—
171C2×C22⋊C8C2312yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2314yes—
174#391C2311yescharacteristic
175#391C2311yescharacteristic
176#390C2311yescharacteristic
177#390C2311yescharacteristic
178#389C2311yescharacteristic
179#389C2311yescharacteristic
180#389C2311yescharacteristic
181#389C2311yescharacteristic
182#388—21no—
183#388—21no—
184#388—21no—
185#388—21no—
186#388—21no—
187#388—21no—
188#388—21no—
189#388—21no—
190#387—21no—
191#387—21no—
192#387—21no—
193#387—21no—
194#387—21no—
195#387—21no—
196#387—21no—
197#387—21no—
198#386—21no—
199#386—21no—
200#386—21no—
201#386—21no—
202#386—21no—
203#386—21no—
204#386—21no—
205#386—21no—
206#386—21no—
207#386—21no—
208#385—21no—
209#385—21no—
210#385—21no—
211#385—21no—
212#385—21no—
213#385—21no—
214#385—21no—
215#385—21no—
216#385—21no—
217#385—21no—
218#384—21no—
219#384—21no—
220#384—21no—
221#384—21no—
222#384C2312yes—
223#384C2312yes—
224#384C2312yes—
225#384C2312yes—
226#383—21no—
227#382—22no—
228#382—22no—
229#382—22no—
230#382—22no—
231#382C2311yescharacteristic
232#382C2311yescharacteristic
233#381—21no—
234#381—21no—
235#380—22no—
236#380—22no—
237#380—22no—
238#380—22no—
239#380—22no—
240#380—22no—
241#380C2311yescharacteristic
242#380C2311yescharacteristic
243#380C2314yes—
244#380C2311yescharacteristic
245#380C2314yes—
246#380C2311yescharacteristic
247#380C2311yescharacteristic
248#380C2311yescharacteristic
249#379—21no—
250C4×C4⋊C4—22no—
251C4×C4⋊C4—22no—
252C4×C4⋊C4—22no—
253C4×C4⋊C4—22no—
254C4×C4⋊C4—22no—
255C4×C4⋊C4—22no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4C2314yes—
259C4×C4⋊C4C2311yescharacteristic
260C4×C4⋊C4C2311yescharacteristic
261C4×C4⋊C4C2314yes—
262C4×C22⋊C4—21no—
263C4×C22⋊C4—21no—
264C4×C22⋊C4—21no—
265C4×C22⋊C4—21no—
266C4×C22⋊C4—21no—
267#376—21no—
268C2×#95—22no—
269C2×#95—22no—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#340C2314yes—
278#336C2312yes—
279#336C2312yes—
280#336C2314yes—
281C25C2×D411yescharacteristic
282C22×Q8C2411yescharacteristic
283C22×D4—21no—
284C22×D4—21no—
285C22×D4—21no—
286C22×D4C2411yescharacteristic
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—24no—
291C23×C4—24no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—22no—
295C23×C4—22no—
296C23×C4—21no—
297C23×C4—42no—
298C23×C4—42no—
299C23×C4—42no—
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2×D411yescharacteristic
305C23×C4C2×D411yescharacteristic
306C23×C4C2×D411yescharacteristic
307C23×C4C2×D411yescharacteristic
308C23×C4C2×D411yescharacteristic
309C23×C4C2×D411yescharacteristic
310C23×C4C2×D411yescharacteristic
311C23×C4C2×D411yescharacteristic
312C23×C4C2×D411yescharacteristic
313C23×C4C2×D411yescharacteristic
314C23×C4C2×D411yescharacteristic
315C23×C4C2411yescharacteristic
316C23×C4C2411yescharacteristic
317C23×C4C2411yescharacteristic
318C2×M16—28no—
319C2×M16—44no—
320C2×M16—44no—
321C22×C8C2414yes—
322C22×C8C2414yes—
323#126—44no—
324#125—24no—
325#124—24no—
326#123—44no—
327#123—44no—
328C22⋊Q8—24no—
329C22⋊Q8—22no—
330C22⋊Q8—22no—
331C22⋊Q8—42no—
332#121—24no—
333#121—22no—
334#121—22no—
335#121—42no—
336#120—44no—
337C4×Q8—24no—
338C4×D4—24no—
339C4×D4—44no—
340C4×D4—44no—
341C4×D4—44no—
342#117—48no—
343#117—48no—
344#117—48no—
345#117—48no—
346#117—44no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
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⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4C2414yes—
375C2×C4⋊C4C2414yes—
376C2×C4⋊C4C2411yescharacteristic
377C2×C4⋊C4C2411yescharacteristic
378C2×C4⋊C4C2411yescharacteristic
379C2×C4⋊C4C2411yescharacteristic
380C2×C4⋊C4C2411yescharacteristic
381C2×C4⋊C4C2411yescharacteristic
382C2×C22⋊C4—24no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—48no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—24no—
407C2×C42—24no—
408C2×C42—24no—
409C2×C42—24no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—24no—
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—48no—
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42C2×D411yescharacteristic
430C2×C42C2×D411yescharacteristic
431C2×C42C2×D411yescharacteristic
432C2×C42C2×D411yescharacteristic
433C2×C42#4118yes—
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436C2×C42C2411yescharacteristic
437C2×C42C2411yescharacteristic
438#107—44no—
439#107—44no—
440#106—44no—
441#106—44no—
442C4⋊C8—24no—
443C4⋊C8—24no—
444C4⋊C8—28no—
445#103—44no—
446#103—44no—
447#102—44no—
448#102—44no—
449C22⋊C8—24no—
450C22⋊C8—24no—
451C22⋊C8—44no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475#95—21no—
476C24—22no—
477C24—22no—
478C24—22no—
479C24—22no—
480C24—22no—
481C24—21no—
482C24—41no—
483C24—41no—
484C24C22×D411yescharacteristic
485C24C22×D411yescharacteristic
486C24C22×D411yescharacteristic
487C2×Q8—22no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—22no—
491C2×D4—22no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—22no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C22×C4—232no—
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—22no—
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—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—41no—
555C22×C4—41no—
556C22×C4—41no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—41no—
561C22×C4—41no—
562C22×C4—41no—
563C22×C4—41no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—416no—
567C22×C4—44no—
568C22×C4—44no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—44no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4#12314yes—
577C22×C4#12314yes—
578C22×C4AGL(1,ℤ/8)14yes—
579C22×C4#13714yes—
580C22×C4C22×D411yescharacteristic
581C22×C4C22×D411yescharacteristic
582C22×C4C22×D411yescharacteristic
583C22×C4C22×D411yescharacteristic
584C22×C4C22×D411yescharacteristic
585C22×C4C22×D411yescharacteristic
586C22×C4C22×D411yescharacteristic
587C22×C4C22×D411yescharacteristic
588C22×C4C22×D411yescharacteristic
589C22×C4C22×D411yescharacteristic
590C22×C4C22×D411yescharacteristic
591C22×C4C2×#4114yes—
592C22×C4H(5,𝔽2)12yes—
593C22×C42−1+412yes—
594C22×C4C2511yescharacteristic
595M16—88no—
596C2×C8—24no—
597C2×C8—24no—
598C2×C8—24no—
599C2×C8—24no—
600C2×C8—24no—
601C2×C8—24no—
602C4⋊C4—22no—
603C4⋊C4—22no—
604C4⋊C4—24no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—24no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—24no—
611C4⋊C4—22no—
612C4⋊C4—24no—
613C4⋊C4—22no—
614C4⋊C4—44no—
615C4⋊C4—44no—
616C4⋊C4—44no—
617C4⋊C4—44no—
618C4⋊C4—44no—
619C4⋊C4—44no—
620C4⋊C4—42no—
621C4⋊C4—42no—
622C4⋊C4—42no—
623C4⋊C4—42no—
624C4⋊C4—42no—
625C4⋊C4—42no—
626C4⋊C4—44no—
627C4⋊C4—42no—
628C4⋊C4—44no—
629C4⋊C4—44no—
630C4⋊C4—42no—
631C4⋊C4—42no—
632C4⋊C4—44no—
633C4⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—48no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—48no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C42—22no—
656C42—22no—
657C42—22no—
658C42—22no—
659C42—22no—
660C42—22no—
661C42—22no—
662C42—22no—
663C42—22no—
664C42—22no—
665C42—22no—
666C42—22no—
667C42—48no—
668C42—42no—
669C42—48no—
670C42—42no—
671C42—42no—
672C42#12314yes—
673C42#12314yes—
674C42C2×#4114yes—
675C42C2×#4114yes—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—28no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—44no—
694C23—44no—
695C23—44no—
696C23—44no—
697C23—44no—
698C23—44no—
699C23—41no—
700C23—41no—
701C23—41no—
702C23—41no—
703C23—41no—
704C23—41no—
705C23—41no—
706C23C2×#12312yes—
707C23#53712yes—
708C23C2×AGL(1,ℤ/8)12yes—
709C23C2×#13712yes—
710C23#57512yes—
711C23C23×D411yescharacteristic
712Q8—42no—
713Q8—42no—
714D4—42no—
715D4—42no—
716D4—84no—
717D4—84no—
718D4—84no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—28no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—28no—
740C2×C4—28no—
741C2×C4—28no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—44no—
759C2×C4—44no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—44no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—44no—
773C2×C4—44no—
774C2×C4—44no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—41no—
789C2×C4—88no—
790C2×C4—88no—
791C2×C4—84no—
792C2×C4C2×#12312yes—
793C2×C4C2×#12312yes—
794C2×C4C2×#12312yes—
795C2×C4C2×#12312yes—
796C2×C4C2×#12312yes—
797C2×C4#53712yes—
798C2×C4C2×AGL(1,ℤ/8)12yes—
799C2×C4C2×AGL(1,ℤ/8)12yes—
800C2×C4C2×#13712yes—
801C2×C4C2×#13712yes—
802C2×C4#57512yes—
803C2×C4C22×#4112yes—
804C2×C4C2×H(5,𝔽2)11yescharacteristic
805C2×C4C2×2−1+411yescharacteristic
806C2×C4#58512yes—
807C8—44no—
808C8—44no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—22no—
821C22—416no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—81no—
831C22—81no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22#325214yes—
838C22C22×#12311yescharacteristic
839C22C2×#53711yescharacteristic
840C22#344911yescharacteristic
841C22C22×AGL(1,ℤ/8)11yescharacteristic
842C22C22×#13711yescharacteristic
843C22C2×#57511yescharacteristic
844C22C2×#57511yescharacteristic
845C4—22no—
846C4—22no—
847C4—22no—
848C4—22no—
849C4—22no—
850C4—22no—
851C4—22no—
852C4—22no—
853C4—41no—
854C4—41no—
855C4—84no—
856C4—81no—
857C4—81no—
858C4—81no—
859C4—81no—
860C4—81no—
861C4—81no—
862C4—81no—
863C4—84no—
864C4#309214yes—
865C4#349412yes—
866C4#349512yes—
867C2—24no—
868C2—42no—
869C2—42no—
870C2—161no—
871C2#3526311yescharacteristic
872C2C2×#309211yescharacteristic
873C2#6051111yescharacteristic
874C2C2×#325211yescharacteristic
875C2#6091611yescharacteristic
876C2#6094911yescharacteristic
877C2#6096611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2847C22
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×#2285C2semidirect
3. #33150C2semidirect
4. #33110C2semidirect
5. #29944C2semidirect
6. #29928C2semidirect
7. #27864C2semidirect
8. #27863C2semidirect
9. #27681C2semidirect
10. #27678C2semidirect
11. #27648C2semidirect
12. #27645C2semidirect
13. #27628C2semidirect
14. #27624C2semidirect
16. #24556C2semidirect
17. #21963C2semidirect
18. #21890C2semidirect
19. #20626C2semidirect
63. #2100C22semidirect
64. #2100C22semidirect
65. #2095C22semidirect
66. #2094C22semidirect
67. #2084C22semidirect
68. #2083C22semidirect
71. #2072C22semidirect
72. #2071C22semidirect
75. #1989C22semidirect
76. #1983C22semidirect
77. #1949C22semidirect
78. #1949C22semidirect
79. #1948C22semidirect
80. #1948C22semidirect
81. #1947C22semidirect
82. #1947C22semidirect
83. #1927C22semidirect
84. #1925C22semidirect
85. #1920C22semidirect
86. #1918C22semidirect
97. #1803C22semidirect
98. #1803C22semidirect
99. #1802C22semidirect
100. #1802C22semidirect

Maximal subgroups

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

subgroupindex
#366212
C2×#22852
#331502
#331102
#299442
#299282
#278642
#278632
#276812
#276782
#276482
#276452
#276282
#276242
#245572
#245562
#219632
#218902
#206262