Finite Group Databasebeta

← #6440338

Subgroups — #6440338

Order 512.

4474 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3488C211yesmaximal, characteristic
2C2×#3093C211yesmaximal, characteristic, complemented
3C22×#482C211yesmaximal, characteristic, complemented
4#34044C211yesmaximal, characteristic, complemented
5#24017C214yesmaximal, complemented
6#24015C214yesmaximal, complemented
7#24009C214yesmaximal, complemented
8#24008C214yesmaximal, complemented
9#23489C211yesmaximal, characteristic, complemented
10#23488C211yesmaximal, characteristic, complemented
11#23483C211yesmaximal, characteristic, complemented
12#23483C211yesmaximal, characteristic, complemented
13#20912C211yesmaximal, characteristic, complemented
14#20908C211yesmaximal, characteristic, complemented
15#20848C211yesmaximal, characteristic, complemented
16#20847C211yesmaximal, characteristic, complemented
17#20602C211yesmaximal, characteristic, complemented
18#20602C211yesmaximal, characteristic, complemented
19#20581C211yesmaximal, characteristic, complemented
20C22×H(5,𝔽2)C2211yescharacteristic
21C23×#41C2211yescharacteristic
22#3488—28no—
23#3488—28no—
24C2×#550—21no—
25C2×#548—21no—
26C2×#546—21no—
27C2×#546—22no—
28C2×D42—22no—
29C2×D42—21no—
30C2×#537C2211yescharacteristic
31C2×#537C2212yes—
32C2×#535C2211yescharacteristic
33C2×#535C2212yes—
34C2×#525C2212yes—
35C2×#525C2211yescharacteristic
36C22×#121C2212yes—
37C22×#121C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C22×#117C2211yescharacteristic, complemented
40C22×#117C2211yescharacteristic, complemented
41#3093—28no—
42C2×#485C2212yescomplemented
43C2×#485C2212yescomplemented
44C2×#482—28no—
45C2×#482C2214yescomplemented
46C2×#482C2214yescomplemented
47C2×#482C2212yescomplemented
48C2×#482C2212yescomplemented
49C2×#428C2211yescharacteristic, complemented
50C2×#428C2211yescharacteristic, complemented
51C22×#107C2211yescharacteristic, complemented
52C22×#106C2211yescharacteristic, complemented
53C2×#417C2211yescharacteristic, complemented
54C2×#417C2211yescharacteristic, complemented
55C2×#418C2211yescharacteristic, complemented
56C2×#418C2211yescharacteristic, complemented
57C2×#416C2211yescharacteristic, complemented
58C2×#416C2211yescharacteristic, complemented
59C22×#102C2211yescharacteristic, complemented
60C22×#102C2211yescharacteristic, complemented
61C2×#408C2211yescharacteristic
62C2×#408C2211yescharacteristic
63C2×#408C2211yescharacteristic, complemented
64C2×#408C2211yescharacteristic, complemented
65C2×#407C2211yescharacteristic, complemented
66C22×C22⋊C8C2211yescharacteristic, complemented
67#2311C2211yescharacteristic
68#2311C2211yescharacteristic
69#2311C2211yescharacteristic, complemented
70#2311C2211yescharacteristic, complemented
71#2311C2214yescomplemented
72#2310—21no—
73#2309—21no—
74#2308—22no—
75#2297—22no—
76#2297—21no—
77#2297—21no—
78#2280C2214yescomplemented
79#2036C2214yescomplemented
80#2035C2214yescomplemented
81#2034C2214yescomplemented
82#2034C2214yescomplemented
83#2034C2214yescomplemented
84#2033C2214yescomplemented
85#2033C2214yescomplemented
86#2033C2214yescomplemented
87#1875C2212yescomplemented
88#1875C2214yescomplemented
89#1874C2212yescomplemented
90#1874C2214yescomplemented
91#1873C2212yescomplemented
92#1872C2212yescomplemented
93#1854C2214yescomplemented
94#1854C2214yescomplemented
95#1853C2214yescomplemented
96#1852C2214yescomplemented
97#1788C2214yescomplemented
98#1788C2214yescomplemented
99#1786C2214yescomplemented
100#1786C2214yescomplemented
101#1780C2214yescomplemented
102#1779C2214yescomplemented
103#1736C2211yescharacteristic, complemented
104#1736C2211yescharacteristic, complemented
105#1735C2211yescharacteristic, complemented
106#1735C2211yescharacteristic, complemented
107C2×H(5,𝔽2)—24no—
108C2×H(5,𝔽2)—24no—
109C2×H(5,𝔽2)—24no—
110C2×H(5,𝔽2)—24no—
111C2×H(5,𝔽2)—42no—
112C2×H(5,𝔽2)—42no—
113C22×#41—24no—
114C22×#41—24no—
115C22×#41—21no—
116C22×#41—24no—
117C22×#41—24no—
118C22×#41—42no—
119C22×#41—42no—
120C22×#41D411yescharacteristic
121C22×#41D412yes—
122C22×#41D411yescharacteristic
123C22×#41C2311yescharacteristic
124C22×#41C2312yes—
125C22×#41C2311yescharacteristic
126C22×#41C2312yes—
127C22×#41C2311yescharacteristic
128C23×Q8D411yescharacteristic
129C23×D4—22no—
130C23×D4—21no—
131C23×D4—22no—
132C23×D4—21no—
133C23×D4D412yes—
134C23×D4D411yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C24×C4C2312yes—
138C24×C4C2311yescharacteristic
139C22×M16C2311yescharacteristic
140C22×M16C2311yescharacteristic
141C23×C8C2311yescharacteristic
142C23×C8C2311yescharacteristic
143#550—216no—
144#548—216no—
145#546—216no—
146#546—232no—
147D42—232no—
148D42—216no—
149#537—24no—
150#537—28no—
151#537—28no—
152#537—24no—
153#535—24no—
154#535—28no—
155#535—28no—
156#535—24no—
157C2×#127—21no—
158C2×#127—22no—
159C2×#124—21no—
160C2×#124—22no—
161#525—24no—
162#525—28no—
163#525—28no—
164#525D418yes—
165C2×#123—22no—
166C2×#123—21no—
167C2×C22⋊Q8—21no—
168C2×C22⋊Q8—22no—
169C2×C22⋊Q8C2312yes—
170C2×C22⋊Q8C2311yescharacteristic
171C2×C22⋊Q8C2311yescharacteristic
172C2×#121—22no—
173C2×#121—22no—
174C2×#121—22no—
175C2×#121—21no—
176C2×#121—22no—
177C2×#121—22no—
178C2×#121—21no—
179C2×#121—22no—
180C2×#121—21no—
181C2×#121—24no—
182C2×#121—28no—
183C2×#121—28no—
184C2×#121D418yes—
185C2×#121C2312yes—
186C2×#121C2312yes—
187C2×#121C2312yes—
188C2×#121C2312yes—
189C2×#121C2311yescharacteristic
190C2×#121C2311yescharacteristic
191C2×#121C2312yes—
192C2×#120—22no—
193C2×#120—21no—
194C2×#120—22no—
195C2×#120—22no—
196C2×#120—22no—
197#520—24no—
198#520—24no—
199C2×C4×Q8—21no—
200C2×C4×D4—22no—
201C2×C4×D4—21no—
202C2×C4×D4—22no—
203C2×C4×D4—21no—
204C2×C4×D4—22no—
205C2×C4×D4—21no—
206C2×#117—21no—
207C2×#117—21no—
208C2×#117—21no—
209C2×#117—21no—
210C2×#117—24no—
211C2×#117—24no—
212C2×#117—42no—
213C2×#117—42no—
214C2×#117C2311yescharacteristic
215C2×#117C2311yescharacteristic
216C2×#117C2312yes—
217C2×#117C2312yes—
218C2×#117C2312yes—
219C2×#117C2311yescharacteristic
220C2×#117C2312yes—
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2312yes—
226C22×C22⋊C4—22no—
227C22×C22⋊C4—21no—
228C22×C22⋊C4—21no—
229C22×C22⋊C4—21no—
230C22×C42—21no—
231C22×C42—21no—
232#485—28no—
233#485—28no—
234#482—216no—
235#482—216no—
236#482—28no—
237#482—28no—
238#428—24no—
239#428—24no—
240C2×#107—24no—
241C2×#107C2314yes—
242C2×#107C2312yes—
243C2×#107C2312yes—
244C2×#106—24no—
245C2×#106C2314yes—
246C2×#106C2312yes—
247C2×#106C2312yes—
248#418—42no—
249#418—42no—
250#417—24no—
251#417—24no—
252#416—42no—
253#416—42no—
254C2×#103C2312yes—
255C2×#103C2312yes—
256C2×#103C2312yes—
257C2×#103C2312yes—
258C2×#102—24no—
259C2×#102—24no—
260C2×#102C2314yes—
261C2×#102C2314yes—
262C2×#102C2312yes—
263C2×#102C2312yes—
264C2×#102C2312yes—
265C2×#102C2312yes—
266C2×#102C2314yes—
267C2×#102C2314yes—
268#408—24no—
269#408—24no—
270#408—42no—
271#408—42no—
272#407—24no—
273C2×C22⋊C8—24no—
274C2×C22⋊C8C2312yes—
275C2×C22⋊C8C2312yes—
276C2×C22⋊C8C2312yes—
277C2×C22⋊C8C2312yes—
278C2×C22⋊C8C2314yes—
279C2×C22⋊C8C2314yes—
280C2×C22⋊C8C2314yes—
281C2×C22⋊C8C2314yes—
282#391—21no—
283#391—21no—
284#391—21no—
285#391—21no—
286#391—24no—
287#390—21no—
288#390—21no—
289#390—21no—
290#390—21no—
291#390—24no—
292#386—22no—
293#386—22no—
294#386—22no—
295#386—22no—
296#386—24no—
297#386—24no—
298#381—24no—
299#380C2314yes—
300#380C2314yes—
301#380C2314yes—
302#380C2314yes—
303#379—24no—
304C4×C22⋊C4—24no—
305C4×C22⋊C4—24no—
306#340C2312yes—
307#340C2314yes—
308#340C2312yes—
309#340C2314yes—
310#340C2312yes—
311#340C2312yes—
312C25—22no—
313C25—21no—
314C25C2×D412yes—
315C25C2×D411yescharacteristic
316H(5,𝔽2)—416no—
317H(5,𝔽2)—416no—
318H(5,𝔽2)—416no—
319H(5,𝔽2)—416no—
320C2×#41—28no—
321C2×#41—24no—
322C2×#41—24no—
323C2×#41—28no—
324C2×#41—24no—
325C2×#41—24no—
326C2×#41—24no—
327C2×#41—28no—
328C2×#41—24no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—22no—
332C2×#41—24no—
333C2×#41—24no—
334C2×#41—22no—
335C2×#41—22no—
336C2×#41—24no—
337C2×#41—24no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41—22no—
346C2×#41—24no—
347C2×#41—24no—
348C2×#41—22no—
349C2×#41—22no—
350C2×#41—42no—
351C2×#41—42no—
352C2×#41—44no—
353C2×#41—42no—
354C2×#41—42no—
355C2×#41—42no—
356C2×#41—42no—
357C2×#41—416no—
358C2×#41—416no—
359C2×#41—416no—
360C2×#41—416no—
361C2×#41—44no—
362C2×#41—44no—
363C2×#41C2×D414yes—
364C2×#41#4114yes—
365C2×#41#4114yes—
366C22×Q8—24no—
367C22×Q8—24no—
368C22×Q8—42no—
369C22×Q8C2×D411yescharacteristic
370C22×Q8C2×D412yes—
371C22×Q8C2×D411yescharacteristic
372C22×Q8C2411yescharacteristic
373C22×D4—216no—
374C22×D4—28no—
375C22×D4—28no—
376C22×D4—22no—
377C22×D4—21no—
378C22×D4—22no—
379C22×D4—21no—
380C22×D4—216no—
381C22×D4—28no—
382C22×D4—22no—
383C22×D4—21no—
384C22×D4—22no—
385C22×D4—22no—
386C22×D4—22no—
387C22×D4—24no—
388C22×D4—28no—
389C22×D4—24no—
390C22×D4—24no—
391C22×D4—24no—
392C22×D4—22no—
393C22×D4—21no—
394C22×D4—22no—
395C22×D4—22no—
396C22×D4—22no—
397C22×D4—24no—
398C22×D4—24no—
399C22×D4—22no—
400C22×D4—22no—
401C22×D4—42no—
402C22×D4—42no—
403C22×D4—42no—
404C22×D4—44no—
405C22×D4—48no—
406C22×D4—44no—
407C22×D4—48no—
408C22×D4—44no—
409C22×D4—84no—
410C22×D4—88no—
411C22×D4C2×D412yes—
412C22×D4C2×D411yescharacteristic
413C22×D4C2×D414yes—
414C22×D4C2×D412yes—
415C22×D4C2×D412yes—
416C22×D4C2×D412yes—
417C22×D4C2×D412yes—
418C22×D4C2×D411yescharacteristic
419C22×D4C2412yes—
420C22×D4C2411yescharacteristic
421C23×C4—22no—
422C23×C4—22no—
423C23×C4—22no—
424C23×C4—22no—
425C23×C4—22no—
426C23×C4—21no—
427C23×C4—22no—
428C23×C4—21no—
429C23×C4—24no—
430C23×C4—24no—
431C23×C4—24no—
432C23×C4—24no—
433C23×C4—22no—
434C23×C4—21no—
435C23×C4—21no—
436C23×C4—42no—
437C23×C4—42no—
438C23×C4C2×D412yes—
439C23×C4C2×D412yes—
440C23×C4C2×D412yes—
441C23×C4C2×D411yescharacteristic
442C23×C4C2×D411yescharacteristic
443C23×C4C2×D411yescharacteristic
444C23×C4C2×D414yes—
445C23×C4C2×D414yes—
446C23×C4C2412yes—
447C23×C4C2411yescharacteristic
448C23×C4C2411yescharacteristic
449C23×C4C2412yes—
450C23×C4C2411yescharacteristic
451C2×M16—22no—
452C2×M16—22no—
453C2×M16—22no—
454C2×M16—22no—
455C2×M16—22no—
456C2×M16—22no—
457C22×C8—22no—
458C22×C8—22no—
459C22×C8—22no—
460C22×C8—22no—
461C22×C8—22no—
462C22×C8—22no—
463C22×C8C2412yes—
464C22×C8C2412yes—
465C22×C8C2412yes—
466C22×C8C2412yes—
467#127—216no—
468#127—28no—
469#124—216no—
470#124—28no—
471#123—216no—
472#123—28no—
473C22⋊Q8—28no—
474C22⋊Q8—216no—
475C22⋊Q8—24no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—24no—
479C22⋊Q8C2×D414yes—
480C22⋊Q8C2×D414yes—
481#121—216no—
482#121—216no—
483#121—216no—
484#121—216no—
485#121—216no—
486#121—28no—
487#121—216no—
488#121—24no—
489#121—24no—
490#121—24no—
491#121—28no—
492#121—28no—
493#121—24no—
494#121—22no—
495#121—24no—
496#121—22no—
497#121—24no—
498#121—24no—
499#121—24no—
500#121C2×D414yes—
501#121C2×D418yes—
502#121C2×D418yes—
503#121C2×D414yes—
504#120—216no—
505#120—216no—
506#120—216no—
507#120—216no—
508#120—28no—
509C4×Q8—28no—
510C4×D4—216no—
511C4×D4—28no—
512C4×D4—216no—
513C4×D4—216no—
514C4×D4—28no—
515C4×D4—28no—
516#117—22no—
517#117—24no—
518#117—24no—
519#117—24no—
520#117—24no—
521#117—24no—
522#117—24no—
523#117—22no—
524#117—22no—
525#117—22no—
526#117—22no—
527#117—42no—
528#117—42no—
529#117—44no—
530#117—44no—
531#117—44no—
532#117—44no—
533#117C2×D414yes—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—24no—
541C2×C4⋊C4—24no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—42no—
550C2×C4⋊C4—42no—
551C2×C4⋊C4C2×D414yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2411yescharacteristic
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2411yescharacteristic
559C2×C22⋊C4—216no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—28no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—24no—
580C2×C22⋊C4—24no—
581C2×C22⋊C4—24no—
582C2×C22⋊C4—44no—
583C2×C22⋊C4—44no—
584C2×C42—22no—
585C2×C42—21no—
586C2×C42—22no—
587C2×C42—22no—
588C2×C42—22no—
589C2×C42—21no—
590C2×C42—21no—
591C2×C42—44no—
592C2×C42—44no—
593#107—28no—
594#107—24no—
595#107—24no—
596#106—28no—
597#106—24no—
598#106—24no—
599#103—24no—
600#103—24no—
601#103—42no—
602#103—42no—
603#102—28no—
604#102—28no—
605#102—24no—
606#102—24no—
607#102—42no—
608#102—42no—
609#102—44no—
610#102—44no—
611C22⋊C8—24no—
612C22⋊C8—24no—
613C22⋊C8—24no—
614C22⋊C8—24no—
615C22⋊C8—28no—
616C22⋊C8—28no—
617C22⋊C8—44no—
618C22⋊C8—44no—
619#95—24no—
620#95—24no—
621#95—24no—
622#95—24no—
623C24—22no—
624C24—22no—
625C24—28no—
626C24—21no—
627C24—22no—
628C24—24no—
629C24—24no—
630C24—24no—
631C24—42no—
632C24—42no—
633C24—44no—
634C24—42no—
635C24—44no—
636C24—44no—
637C24—44no—
638C24—42no—
639C24—42no—
640C24—82no—
641C24—84no—
642C24—82no—
643C24—84no—
644C24#12014yes—
645C24C22×D412yes—
646C24C22×D411yescharacteristic
647C24C22×D411yescharacteristic
648C24C22×D412yes—
649C24C22×D411yescharacteristic
650#41—28no—
651#41—28no—
652#41—28no—
653#41—28no—
654#41—28no—
655#41—28no—
656#41—48no—
657#41—48no—
658#41—48no—
659#41—48no—
660#41—432no—
661#41—416no—
662#41—48no—
663#41—48no—
664#41—416no—
665#41—48no—
666#41—48no—
667#41—432no—
668#41—44no—
669#41—44no—
670#41—44no—
671#41—44no—
672#41—44no—
673#41—44no—
674C2×Q8—22no—
675C2×Q8—24no—
676C2×Q8—22no—
677C2×Q8—24no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—22no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—42no—
687C2×Q8—416no—
688C2×Q8#12314yes—
689C2×Q8C22×D412yes—
690C2×D4—24no—
691C2×D4—24no—
692C2×D4—28no—
693C2×D4—28no—
694C2×D4—28no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—24no—
701C2×D4—24no—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—24no—
708C2×D4—28no—
709C2×D4—22no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—22no—
713C2×D4—24no—
714C2×D4—22no—
715C2×D4—22no—
716C2×D4—22no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—22no—
720C2×D4—21no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—416no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—44no—
738C2×D4—432no—
739C2×D4—464no—
740C2×D4—432no—
741C2×D4—44no—
742C2×D4—48no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—44no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—82no—
753C2×D4—84no—
754C2×D4—84no—
755C2×D4—84no—
756C2×D4—84no—
757C2×D4—816no—
758C2×D4—832no—
759C2×D4#12318yes—
760C2×D4#12314yes—
761C2×D4C22×D412yes—
762C2×D4C22×D414yes—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—28no—
770C22×C4—28no—
771C22×C4—28no—
772C22×C4—28no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—28no—
786C22×C4—24no—
787C22×C4—24no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—28no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4—48no—
815C22×C4—48no—
816C22×C4—44no—
817C22×C4—44no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—44no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—82no—
824C22×C4—82no—
825C22×C4—82no—
826C22×C4—82no—
827C22×C4—82no—
828C22×C4—84no—
829C22×C4#12014yes—
830C22×C4#12014yes—
831C22×C4#12014yes—
832C22×C4C22×D412yes—
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D412yes—
836C22×C4C22×D412yes—
837C22×C4C22×D412yes—
838C22×C4C22×D412yes—
839C22×C4C22×D412yes—
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D412yes—
842C22×C4C22×D412yes—
843C22×C4C2×#4114yes—
844C22×C4C2×#4114yes—
845C22×C4C2×#4112yes—
846C22×C4C2×#4112yes—
847C22×C4H(5,𝔽2)12yes—
848C22×C4H(5,𝔽2)12yes—
849C22×C4C2511yescharacteristic
850M16—44no—
851M16—44no—
852C2×C8—22no—
853C2×C8—22no—
854C2×C8—22no—
855C2×C8—22no—
856C2×C8—22no—
857C2×C8—22no—
858C2×C8—22no—
859C2×C8—22no—
860C2×C8—22no—
861C2×C8—22no—
862C2×C8—22no—
863C2×C8—22no—
864C2×C8—44no—
865C2×C8—44no—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—22no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4—44no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4C22×D412yes—
886C4⋊C4C22×D414yes—
887C4⋊C4C22×D412yes—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—28no—
893C22⋊C4—24no—
894C22⋊C4—24no—
895C22⋊C4—24no—
896C22⋊C4—24no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—24no—
900C22⋊C4—44no—
901C22⋊C4—44no—
902C22⋊C4—44no—
903C22⋊C4—42no—
904C22⋊C4—42no—
905C22⋊C4—84no—
906C22⋊C4—84no—
907C22⋊C4—84no—
908C22⋊C4—84no—
909C42—28no—
910C42—24no—
911C42—44no—
912C42—44no—
913C42—44no—
914C42—42no—
915C42—42no—
916C23—22no—
917C23—22no—
918C23—24no—
919C23—22no—
920C23—22no—
921C23—24no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—21no—
926C23—21no—
927C23—21no—
928C23—21no—
929C23—22no—
930C23—28no—
931C23—24no—
932C23—24no—
933C23—22no—
934C23—24no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—44no—
939C23—44no—
940C23—48no—
941C23—48no—
942C23—416no—
943C23—42no—
944C23—44no—
945C23—44no—
946C23—42no—
947C23—42no—
948C23—41no—
949C23—42no—
950C23—41no—
951C23—48no—
952C23—84no—
953C23—84no—
954C23—88no—
955C23—84no—
956C23—84no—
957C23—84no—
958C23—88no—
959C23—88no—
960C23—88no—
961C23—164no—
962C23—164no—
963C23—168no—
964C23—168no—
965C23C2×#12012yes—
966C23C2×#12012yes—
967C23C2×#12012yes—
968C23C2×#12314yes—
969C23C2×#12312yes—
970C23#53412yes—
971C23C23×D411yescharacteristic
972Q8—28no—
973Q8—22no—
974Q8—22no—
975Q8—48no—
976Q8—44no—
977Q8—41no—
978Q8—41no—
979D4—216no—
980D4—28no—
981D4—24no—
982D4—24no—
983D4—22no—
984D4—22no—
985D4—48no—
986D4—48no—
987D4—416no—
988D4—48no—
989D4—416no—
990D4—416no—
991D4—48no—
992D4—48no—
993D4—48no—
994D4—48no—
995D4—44no—
996D4—41no—
997D4—41no—
998D4—42no—
999D4—42no—
1000D4—84no—
1001D4—88no—
1002D4—88no—
1003D4—88no—
1004D4—88no—
1005C2×C4—28no—
1006C2×C4—22no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—28no—
1013C2×C4—28no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—48no—
1034C2×C4—48no—
1035C2×C4—48no—
1036C2×C4—416no—
1037C2×C4—42no—
1038C2×C4—44no—
1039C2×C4—42no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—48no—
1043C2×C4—42no—
1044C2×C4—42no—
1045C2×C4—42no—
1046C2×C4—42no—
1047C2×C4—42no—
1048C2×C4—42no—
1049C2×C4—44no—
1050C2×C4—42no—
1051C2×C4—42no—
1052C2×C4—44no—
1053C2×C4—42no—
1054C2×C4—42no—
1055C2×C4—42no—
1056C2×C4—42no—
1057C2×C4—84no—
1058C2×C4—88no—
1059C2×C4—84no—
1060C2×C4—84no—
1061C2×C4—88no—
1062C2×C4C2×#12012yes—
1063C2×C4C2×#12012yes—
1064C2×C4C2×#12012yes—
1065C2×C4C2×#12314yes—
1066C2×C4C2×#12312yes—
1067C2×C4#53412yes—
1068C2×C4#54614yes—
1069C2×C4#54614yes—
1070C2×C4#54614yes—
1071C2×C4#54614yes—
1072C2×C4C23×D411yescharacteristic
1073C2×C4C23×D411yescharacteristic
1074C2×C4C22×#4111yescharacteristic
1075C2×C4C22×#4111yescharacteristic
1076C2×C4C2×H(5,𝔽2)11yescharacteristic
1077C2×C4C2×H(5,𝔽2)11yescharacteristic
1078C8—42no—
1079C8—42no—
1080C8—42no—
1081C8—42no—
1082C22—24no—
1083C22—24no—
1084C22—22no—
1085C22—22no—
1086C22—22no—
1087C22—22no—
1088C22—24no—
1089C22—28no—
1090C22—22no—
1091C22—22no—
1092C22—22no—
1093C22—22no—
1094C22—42no—
1095C22—42no—
1096C22—44no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—44no—
1102C22—42no—
1103C22—44no—
1104C22—42no—
1105C22—44no—
1106C22—42no—
1107C22—42no—
1108C22—44no—
1109C22—44no—
1110C22—42no—
1111C22—42no—
1112C22—88no—
1113C22—816no—
1114C22—84no—
1115C22—82no—
1116C22—84no—
1117C22—82no—
1118C22—168no—
1119C22—1616no—
1120C22#240514yes—
1121C22C22×#12011yescharacteristic
1122C22C22×#12311yescharacteristic
1123C22C2×#53411yescharacteristic
1124C22#358412yes—
1125C22#358512yes—
1126C4—22no—
1127C4—22no—
1128C4—24no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—44no—
1133C4—42no—
1134C4—82no—
1135C4—82no—
1136C4—82no—
1137C4—82no—
1138C4#240514yes—
1139C4C2×#54611yescharacteristic
1140C4C2×#54611yescharacteristic
1141C4C2×#54611yescharacteristic
1142C4C2×#54611yescharacteristic
1143C2—24no—
1144C2—42no—
1145C2—42no—
1146C2—44no—
1147C2—82no—
1148C2—84no—
1149C2—82no—
1150C2C2×#240511yescharacteristic
1151C2#6036611yescharacteristic
1152C2#6036711yescharacteristic
1153C2#6052312yes—
1154C2#6076712yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3488C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3093C2semidirect
3. C22×#482C2semidirect
4. #34044C2semidirect
5. #24017C2semidirect
6. #24015C2semidirect
7. #24009C2semidirect
8. #24008C2semidirect
9. #23489C2semidirect
10. #23488C2semidirect
11. #23483C2semidirect
12. #23483C2semidirect
13. #20912C2semidirect
14. #20908C2semidirect
15. #20848C2semidirect
16. #20847C2semidirect
17. #20602C2semidirect
18. #20602C2semidirect
19. #20581C2semidirect
39. C22×#117C22semidirect
40. C22×#117C22semidirect
42. C2×#485C22semidirect
43. C2×#485C22semidirect
45. C2×#482C22semidirect
46. C2×#482C22semidirect
47. C2×#482C22semidirect
48. C2×#482C22semidirect
49. C2×#428C22semidirect
50. C2×#428C22semidirect
51. C22×#107C22semidirect
52. C22×#106C22semidirect
53. C2×#417C22semidirect
54. C2×#417C22semidirect
55. C2×#418C22semidirect
56. C2×#418C22semidirect
57. C2×#416C22semidirect
58. C2×#416C22semidirect
59. C22×#102C22semidirect
60. C22×#102C22semidirect
63. C2×#408C22semidirect
64. C2×#408C22semidirect
65. C2×#407C22semidirect
66. C22×C22⋊C8C22semidirect
69. #2311C22semidirect
70. #2311C22semidirect
71. #2311C22semidirect
78. #2280C22semidirect
79. #2036C22semidirect
80. #2035C22semidirect
81. #2034C22semidirect
82. #2034C22semidirect
83. #2034C22semidirect
84. #2033C22semidirect
85. #2033C22semidirect
86. #2033C22semidirect
87. #1875C22semidirect
88. #1875C22semidirect
89. #1874C22semidirect
90. #1874C22semidirect
91. #1873C22semidirect
92. #1872C22semidirect
93. #1854C22semidirect
94. #1854C22semidirect
95. #1853C22semidirect
96. #1852C22semidirect
97. #1788C22semidirect
98. #1788C22semidirect
99. #1786C22semidirect
100. #1786C22semidirect
101. #1780C22semidirect
102. #1779C22semidirect
103. #1736C22semidirect
104. #1736C22semidirect
105. #1735C22semidirect
106. #1735C22semidirect

Maximal subgroups

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

subgroupindex
C2×#34882
C2×#30932
C22×#4822
#340442
#240172
#240152
#240092
#240082
#234892
#234882
#234832
#209122
#209082
#208482
#208472
#206022
#205812