Finite Group Databasebeta

← #6433580

Subgroups — #6433580

Order 512.

1942 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36625C211yesmaximal, characteristic
2C2×C4×C22⋊Q8C211yesmaximal, characteristic
3#30168C212yesmaximal, complemented
4#30109C212yesmaximal, complemented
5#30013C214yesmaximal, complemented
6#29968C211yesmaximal, characteristic, complemented
7#29953C211yesmaximal, characteristic, complemented
8#29894C212yesmaximal
9#29756C211yesmaximal, characteristic, complemented
10#29715C211yesmaximal, characteristic, complemented
11#29599C212yesmaximal
12#23762C212yesmaximal, complemented
13#23709C214yesmaximal, complemented
14#23577C212yesmaximal, complemented
15#21579C212yesmaximal, complemented
16#21455C212yesmaximal, complemented
17#20715C211yesmaximal, characteristic
18C2×#533C2211yescharacteristic
19C22×C22⋊Q8C2211yescharacteristic
20C22×C4×Q8C2211yescharacteristic
21C23×C42C2211yescharacteristic
22C2×#483C2212yes—
23C2×#451C2212yes—
24C2×#441C2214yescomplemented
25C2×#432C2212yes—
26#2857C2211yescharacteristic
27#2857C2211yescharacteristic
28#2857C2211yescharacteristic
29#2857C2211yescharacteristic
30#2855—21no—
31#2855C2212yes—
32#2851—21no—
33#2851—21no—
34#2848—21no—
35#2848C2212yes—
36C4×C22⋊Q8—21no—
37C4×C22⋊Q8—21no—
38C4×C22⋊Q8—21no—
39C4×C22⋊Q8—21no—
40C4×C22⋊Q8—21no—
41C4×C22⋊Q8—21no—
42C4×C22⋊Q8C2212yes—
43C4×C22⋊Q8C2212yes—
44C4×C22⋊Q8C2212yes—
45C4×C22⋊Q8C2212yes—
46C4×C22⋊Q8C2212yes—
47C4×C22⋊Q8C2212yes—
48#2296—21no—
49C2×#391C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#387—21no—
52C2×#385—21no—
53#2285C2211yescharacteristic
54#2280—21no—
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4—21no—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4—21no—
59#2100C2212yescomplemented
60#2095C2212yescomplemented
61#2088C2214yescomplemented
62#2084C2212yescomplemented
63#2077C2214yes—
64#2075C2214yes—
65#2072C2212yescomplemented
66#2068C2214yescomplemented
67#2066C2214yescomplemented
68#2058C2212yescomplemented
69#2056C2214yescomplemented
70#2043C2212yescomplemented
71#2036C2214yes—
72#2035C2214yes—
73#2035C2214yes—
74#2035C2214yes—
75#2024C2212yescomplemented
76#2016C2212yescomplemented
77#2001C2214yes—
78#2001C2214yes—
79#1928C2214yescomplemented
80#1919C2214yescomplemented
81#1878C2214yescomplemented
82#1872C2212yes—
83#1872C2212yes—
84#1865C2214yescomplemented
85#1853C2212yes—
86#1852C2212yes—
87#1823C2212yes—
88#1817C2212yes—
89#1797C2211yescharacteristic
90#1797C2211yescharacteristic
91#1797C2212yes—
92#1787C2212yes—
93#1779C2212yes—
94#1776C2214yescomplemented
95#1763C2214yescomplemented
96#1763C2214yescomplemented
97#1749C2212yes—
98#1749C2212yes—
99C23×Q8C2311yescharacteristic
100C24×C4D411yescharacteristic
101C24×C4D411yescharacteristic
102C24×C4C2311yescharacteristic
103C22×Q16C2314yes—
104#533—44no—
105C2×C4⋊Q8C2311yescharacteristic
106C2×C4⋊Q8C2311yescharacteristic
107C2×#125—21no—
108C2×C22⋊Q8—24no—
109C2×C22⋊Q8—21no—
110C2×C22⋊Q8—21no—
111C2×C22⋊Q8—21no—
112C2×C22⋊Q8—21no—
113C2×C22⋊Q8—21no—
114C2×C22⋊Q8—24no—
115C2×C22⋊Q8C2312yes—
116C2×C22⋊Q8C2312yes—
117C2×C22⋊Q8C2312yes—
118C2×C22⋊Q8C2312yes—
119C2×C22⋊Q8C2312yes—
120C2×C4×Q8—21no—
121C2×C4×Q8—21no—
122C2×C4×Q8—21no—
123C2×C4×Q8—44no—
124C2×C4×Q8C2312yes—
125C2×C4×Q8C2312yes—
126C2×C4×Q8C2312yes—
127C2×#117—21no—
128C2×#117—21no—
129C22×C4⋊C4—21no—
130C22×C4⋊C4—21no—
131C22×C4⋊C4—21no—
132C22×C4⋊C4C2311yescharacteristic
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C22⋊C4—21no—
136C22×C22⋊C4—21no—
137C22×C42—21no—
138C22×C42—21no—
139C22×C42—44no—
140C22×C42D411yescharacteristic
141C22×C42D411yescharacteristic
142C22×C42D411yescharacteristic
143C22×C42D411yescharacteristic
144C22×C42D411yescharacteristic
145C22×C42D411yescharacteristic
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2311yescharacteristic
152#483—28no—
153#451—28no—
154#441—48no—
155#432—44no—
156C2×#107C2314yes—
157C2×#106C2314yes—
158C2×#106C2314yes—
159C2×C4⋊C8C2312yes—
160C2×C4⋊C8C2312yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×C22⋊C8C2312yes—
168C2×C22⋊C8C2312yes—
169C2×C22⋊C8C2314yes—
170C2×C22⋊C8C2314yes—
171C2×#97C2314yes—
172#391—21no—
173#391—21no—
174#391—21no—
175#391—21no—
176#391C2312yes—
177#391C2312yes—
178#391C2312yes—
179#391C2312yes—
180#389—21no—
181#389—21no—
182#389—21no—
183#389—21no—
184#389—21no—
185#389—21no—
186#389—21no—
187#389—21no—
188#389C2312yes—
189#389C2312yes—
190#389C2312yes—
191#389C2312yes—
192#387—22no—
193#387—22no—
194#387—22no—
195#387—22no—
196#387—22no—
197#387—22no—
198#387—22no—
199#387—22no—
200#385—22no—
201#385—22no—
202#385—22no—
203#385—22no—
204#385—22no—
205#385—22no—
206#385—22no—
207#385—22no—
208#385—22no—
209#385—22no—
210#384C2311yescharacteristic
211#384C2311yescharacteristic
212#382—21no—
213#381—22no—
214#380—21no—
215#380—21no—
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#380C2312yes—
227#380C2312yes—
228#379—22no—
229C4×C4⋊C4—22no—
230C4×C4⋊C4—22no—
231C4×C4⋊C4—22no—
232C4×C4⋊C4—22no—
233C4×C4⋊C4—21no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—22no—
237C4×C4⋊C4—22no—
238C4×C4⋊C4C2312yes—
239C4×C4⋊C4C2312yes—
240C4×C4⋊C4C2312yes—
241C4×C22⋊C4—22no—
242C4×C22⋊C4—22no—
243C4×C22⋊C4—22no—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C2×#95—21no—
248C2×#95—21no—
249C2×#95—21no—
250C2×#95—21no—
251C2×#95—21no—
252#340C2314yes—
253#340C2314yes—
254#340C2314yes—
255#340C2314yes—
256#340C2314yes—
257#340C2314yes—
258#336C2312yes—
259#336C2312yes—
260#336C2314yes—
261C25C2×D411yescharacteristic
262C22×Q8—21no—
263C22×Q8—21no—
264C22×Q8—22no—
265C22×Q8—42no—
266C22×Q8—42no—
267C22×Q8#4114yes—
268C22×Q8C2412yes—
269C22×Q8C2412yes—
270C23×C4—21no—
271C23×C4—21no—
272C23×C4—24no—
273C23×C4—24no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—21no—
277C23×C4—21no—
278C23×C4—42no—
279C23×C4—42no—
280C23×C4—42no—
281C23×C4—42no—
282C23×C4—42no—
283C23×C4—42no—
284C23×C4C2×D411yescharacteristic
285C23×C4C2×D411yescharacteristic
286C23×C4C2×D411yescharacteristic
287C23×C4C2×D411yescharacteristic
288C23×C4C2×D411yescharacteristic
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C2×Q16—28no—
303C2×Q16—44no—
304C2×Q16—44no—
305C22×C8C2414yes—
306C22×C8C2414yes—
307C4⋊Q8—42no—
308C4⋊Q8—42no—
309#125—44no—
310C22⋊Q8—28no—
311C22⋊Q8—28no—
312C22⋊Q8—24no—
313C22⋊Q8—24no—
314C22⋊Q8—24no—
315C22⋊Q8—24no—
316C22⋊Q8—24no—
317C22⋊Q8—24no—
318C22⋊Q8—44no—
319C22⋊Q8—44no—
320C22⋊Q8—44no—
321C22⋊Q8—44no—
322C22⋊Q8—44no—
323C4×Q8—28no—
324C4×Q8—28no—
325C4×Q8—44no—
326C4×Q8—44no—
327C4×Q8—44no—
328C4×Q8—44no—
329#117—44no—
330#117—44no—
331C2×C4⋊C4—28no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4#4114yes—
360C2×C4⋊C4C2412yes—
361C2×C4⋊C4C2412yes—
362C2×C4⋊C4C2412yes—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C22⋊C4—28no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—44no—
378C2×C42—24no—
379C2×C42—24no—
380C2×C42—24no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—22no—
387C2×C42—42no—
388C2×C42—42no—
389C2×C42—42no—
390C2×C42—42no—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394C2×C42—42no—
395C2×C42—42no—
396C2×C42—44no—
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×C42C2411yescharacteristic
411C2×C42C2411yescharacteristic
412C2×C42C2411yescharacteristic
413C2×C42C2411yescharacteristic
414#107—44no—
415#106—28no—
416#106—44no—
417C4⋊C8—42no—
418C4⋊C8—42no—
419#103—28no—
420#103—28no—
421#103—44no—
422#103—44no—
423#103—44no—
424#103—44no—
425C22⋊C8—24no—
426C22⋊C8—24no—
427C22⋊C8—44no—
428C22⋊C8—44no—
429#97—28no—
430#95—22no—
431#95—22no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—22no—
455C24—41no—
456C24—41no—
457C24C22×D411yescharacteristic
458C24C22×D411yescharacteristic
459C24C22×D411yescharacteristic
460C2×Q8—24no—
461C2×Q8—22no—
462C2×Q8—22no—
463C2×Q8—22no—
464C2×Q8—24no—
465C2×Q8—24no—
466C2×Q8—24no—
467C2×Q8—24no—
468C2×Q8—48no—
469C2×Q8—42no—
470C2×Q8—42no—
471C2×Q8—48no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—42no—
475C2×Q8C2×#4114yes—
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—24no—
485C22×C4—24no—
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—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
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—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—41no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—41no—
536C22×C4—41no—
537C22×C4—41no—
538C22×C4—41no—
539C22×C4—416no—
540C22×C4—416no—
541C22×C4—48no—
542C22×C4—48no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—42no—
549C22×C4—42no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4#13714yes—
554C22×C4#13714yes—
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D411yescharacteristic
564C22×C4C22×D411yescharacteristic
565C22×C4C22×D411yescharacteristic
566C22×C4C2×#4112yes—
567C22×C4C2×#4112yes—
568C22×C4C2511yescharacteristic
569Q16—416no—
570C2×C8—24no—
571C2×C8—24no—
572C2×C8—24no—
573C2×C8—24no—
574C2×C8—24no—
575C2×C8—24no—
576C4⋊C4—28no—
577C4⋊C4—28no—
578C4⋊C4—24no—
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—24no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—44no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—44no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—44no—
601C4⋊C4—44no—
602C4⋊C4—44no—
603C4⋊C4—42no—
604C4⋊C4—44no—
605C4⋊C4C2×#4114yes—
606C22⋊C4—28no—
607C22⋊C4—28no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—41no—
626C42—41no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—44no—
632C42—44no—
633C42—44no—
634C42—44no—
635C42—44no—
636C42—44no—
637C42H(5,𝔽2)14yes—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—28no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—44no—
656C23—44no—
657C23—44no—
658C23—44no—
659C23—44no—
660C23—44no—
661C23#52512yes—
662C23C2×#13712yes—
663C23C2×#13712yes—
664C23#57512yes—
665C23#57512yes—
666C23C23×D411yescharacteristic
667Q8—28no—
668Q8—48no—
669Q8—44no—
670Q8—44no—
671Q8—44no—
672Q8—84no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—48no—
719C2×C4—48no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—84no—
747C2×C4—84no—
748C2×C4#52512yes—
749C2×C4#53412yes—
750C2×C4#53412yes—
751C2×C4C2×#13712yes—
752C2×C4C2×#13712yes—
753C2×C4C2×#13712yes—
754C2×C4C2×#13712yes—
755C2×C4C22×#4111yescharacteristic
756C2×C4C22×#4111yescharacteristic
757C2×C4C2×H(5,𝔽2)12yes—
758C2×C4#58512yes—
759C8—44no—
760C8—44no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—416no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22#311614yes—
783C22C2×#52511yescharacteristic
784C22C2×#53411yescharacteristic
785C22#344911yescharacteristic
786C22C22×#13711yescharacteristic
787C22C22×#13711yescharacteristic
788C22C2×#57511yescharacteristic
789C22C2×#57511yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—22no—
795C4—22no—
796C4—22no—
797C4—41no—
798C4—41no—
799C4—44no—
800C4—41no—
801C4—41no—
802C4—44no—
803C4—82no—
804C4—82no—
805C4—82no—
806C4—82no—
807C4—82no—
808C4—82no—
809C4#345912yes—
810C4#346012yes—
811C2—24no—
812C2—42no—
813C2—42no—
814C2#3456211yescharacteristic
815C2C2×#311611yescharacteristic
816C2#6056011yescharacteristic
817C2#6075111yescharacteristic
818C2#6075111yescharacteristic
819C2#6095911yescharacteristic
820C2#6097111yescharacteristic
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
3. #30168C2semidirect
4. #30109C2semidirect
5. #30013C2semidirect
6. #29968C2semidirect
7. #29953C2semidirect
9. #29756C2semidirect
10. #29715C2semidirect
12. #23762C2semidirect
13. #23709C2semidirect
14. #23577C2semidirect
15. #21579C2semidirect
16. #21455C2semidirect
24. C2×#441C22semidirect
59. #2100C22semidirect
60. #2095C22semidirect
61. #2088C22semidirect
62. #2084C22semidirect
65. #2072C22semidirect
66. #2068C22semidirect
67. #2066C22semidirect
68. #2058C22semidirect
69. #2056C22semidirect
70. #2043C22semidirect
75. #2024C22semidirect
76. #2016C22semidirect
79. #1928C22semidirect
80. #1919C22semidirect
81. #1878C22semidirect
84. #1865C22semidirect
94. #1776C22semidirect
95. #1763C22semidirect
96. #1763C22semidirect

Maximal subgroups

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

subgroupindex
#366252
C2×C4×C22⋊Q82
#301682
#301092
#300132
#299682
#299532
#298942
#297562
#297152
#295992
#237622
#237092
#235772
#215792
#214552
#207152