Finite Group Databasebeta

← C2×#24907922 #35406192

Subgroups — C2×#24907922 #35406192

Order 21248.

2066 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581751C211yesmaximal, characteristic, complemented
2C22×#14581707C212yesmaximal
3C2×#19127564C211yesmaximal, characteristic, complemented
4#24907922C218yesmaximal, direct product factor
5C2×#19127468C212yesmaximal, complemented
6C22×#123×C83C211yesmaximal, characteristic
7C2×#14581751—28no—
8C2×#14581751—22no—
9C2×#14581751C2214yescomplemented
10C22×C4⋊Dic83—21no—
11C22×C22⋊Dic83C2212yes—
12C22×C22⋊Dic83C2212yes—
13C22×C4×Dic83—21no—
14C2×#14581707—28no—
15C2×#14581707C2218yes—
16#19127564—22no—
17#19127564C2214yescomplemented
18C2×C83⋊#95—22no—
19#19127468C2218yescomplemented
20C23×D4×C83C2211yescharacteristic
21C24×C4×C83C2211yescharacteristic
22C2×#123×C83—22no—
23C2×#123×C83—21no—
24C2×#123×C83—21no—
25C2×#123×C83—22no—
26C2×#123×C83—22no—
27C2×#123×C83C414yescomplemented
28C2×#123×C83C2214yes—
29C22×C4⋊C4×C83C412yescomplemented
30C22×C22⋊C4×C83C412yescomplemented
31C22×C22⋊C4×C83C2211yescharacteristic
32C23×Dic83—22no—
33C23×Dic83—22no—
34#14581751—216no—
35#14581751—216no—
36C2×C4⋊Dic83—28no—
37C2×C4⋊Dic83—24no—
38C2×C22⋊Dic83—24no—
39C2×C22⋊Dic83—22no—
40C2×C22⋊Dic83—24no—
41C2×C22⋊Dic83—22no—
42C2×C22⋊Dic83—24no—
43C2×C22⋊Dic83D418yes—
44C2×C22⋊Dic83C2314yes—
45C2×C22⋊Dic83C2314yes—
46C2×C4×Dic83—28no—
47C2×C4×Dic83—24no—
48#14581707—216no—
49C83⋊#95—28no—
50C25×C83C2×C411yescharacteristic
51C25×C83C2311yescharacteristic
52C22×D4×C83—21no—
53C22×D4×C83—21no—
54C22×D4×C83—21no—
55C22×D4×C83—21no—
56C22×D4×C83—24no—
57C22×D4×C83—24no—
58C22×D4×C83C2×C412yes—
59C22×D4×C83C2312yes—
60C23×C4×C83—24no—
61C23×C4×C83—24no—
62C23×C4×C83C2×C411yescharacteristic
63C23×C4×C83C2×C412yes—
64C23×C4×C83C2×C412yes—
65C23×C4×C83C2×C412yes—
66C23×C4×C83D412yes—
67C23×C4×C83D411yescharacteristic
68C23×C4×C83D411yescharacteristic
69C23×C4×C83D412yes—
70C23×C4×C83D412yes—
71C23×C4×C83C2312yes—
72#123×C83—24no—
73#123×C83—24no—
74#123×C83—28no—
75#123×C83—28no—
76#123×C83—24no—
77#123×C83—24no—
78C2×C4⋊C4×C83—24no—
79C2×C4⋊C4×C83—22no—
80C2×C4⋊C4×C83—22no—
81C2×C4⋊C4×C83C2×C418yescomplemented
82C2×C22⋊C4×C83—21no—
83C2×C22⋊C4×C83—21no—
84C2×C22⋊C4×C83—21no—
85C2×C22⋊C4×C83—21no—
86C2×C22⋊C4×C83—24no—
87C2×C22⋊C4×C83—22no—
88C2×C22⋊C4×C83—22no—
89C2×C22⋊C4×C83C2×C412yes—
90C2×C22⋊C4×C83C2×C418yescomplemented
91C2×C22⋊C4×C83C2312yes—
92C22×Dic83—28no—
93C22×Dic83—24no—
94C22×Dic83—24no—
95C22×Dic83—48no—
96C22×Dic83—48no—
97C22×Dic83—44no—
98C4⋊Dic83—216no—
99C22⋊Dic83—28no—
100C22⋊Dic83—24no—
101C22⋊Dic83—24no—
102C22⋊Dic83—24no—
103C22⋊Dic83—44no—
104C22⋊Dic83C2×D418yes—
105C4×Dic83—216no—
106C24×C83—21no—
107C24×C83—21no—
108C24×C83—24no—
109C24×C83—44no—
110C24×C83—44no—
111C24×C83C22×C411yescharacteristic
112C24×C83C22×C412yes—
113C24×C83C22×C411yescharacteristic
114C24×C83C2×D414yes—
115C24×C83C2×D411yescharacteristic
116C24×C83C2×D411yescharacteristic
117C24×C83C2×D411yescharacteristic
118C24×C83C2×D411yescharacteristic
119C24×C83#4114yes—
120C24×C83C2411yescharacteristic
121C2×D4×C83—22no—
122C2×D4×C83—22no—
123C2×D4×C83—28no—
124C2×D4×C83—22no—
125C2×D4×C83—22no—
126C2×D4×C83—24no—
127C2×D4×C83—24no—
128C2×D4×C83—42no—
129C2×D4×C83—42no—
130C2×D4×C83—44no—
131C2×D4×C83—44no—
132C2×D4×C83—42no—
133C2×D4×C83—42no—
134C22×C4×C83—28no—
135C22×C4×C83—28no—
136C22×C4×C83—22no—
137C22×C4×C83—22no—
138C22×C4×C83—24no—
139C22×C4×C83—28no—
140C22×C4×C83—28no—
141C22×C4×C83—22no—
142C22×C4×C83—22no—
143C22×C4×C83—24no—
144C22×C4×C83—24no—
145C22×C4×C83—24no—
146C22×C4×C83—22no—
147C22×C4×C83—22no—
148C22×C4×C83—21no—
149C22×C4×C83—21no—
150C22×C4×C83—24no—
151C22×C4×C83—44no—
152C22×C4×C83C22⋊C414yes—
153C22×C4×C83C22⋊C412yes—
154C22×C4×C83C22⋊C412yes—
155C22×C4×C83C22⋊C412yes—
156C22×C4×C83C22⋊C412yes—
157C22×C4×C83C22⋊C414yes—
158C22×C4×C83C22×C412yes—
159C22×C4×C83C22×C414yes—
160C22×C4×C83C22×C414yes—
161C22×C4×C83C2×D414yes—
162C22×C4×C83C2×D412yes—
163C22×C4×C83C2×D412yes—
164C4⋊C4×C83—28no—
165C4⋊C4×C83—28no—
166C22⋊C4×C83—22no—
167C22⋊C4×C83—22no—
168C22⋊C4×C83—22no—
169C22⋊C4×C83—22no—
170C22⋊C4×C83—28no—
171C22⋊C4×C83—28no—
172C23×C83—24no—
173C23×C83—24no—
174C23×C83—24no—
175C23×C83—22no—
176C23×C83—24no—
177C23×C83—42no—
178C23×C83—48no—
179C23×C83—42no—
180C23×C83—42no—
181C23×C83—48no—
182C23×C83—42no—
183C23×C83—44no—
184C23×C83—44no—
185C23×C83—42no—
186C23×C83—42no—
187C23×C83—44no—
188C23×C83—88no—
189C23×C83C2×C22⋊C411yescharacteristic
190C23×C83C2×C22⋊C411yescharacteristic
191C23×C83C2×C22⋊C411yescharacteristic
192C23×C83C2×C22⋊C411yescharacteristic
193C23×C83C4×D414yes—
194C23×C83C4×D414yes—
195C23×C83#12012yes—
196C23×C83#12012yes—
197C23×C83#12114yes—
198C23×C83#12114yes—
199C23×C83#12312yes—
200C23×C83#12312yes—
201C23×C83C23×C411yescharacteristic
202C23×C83C22×D412yes—
203C23×C83C22×D411yescharacteristic
204C23×C83C22×D411yescharacteristic
205C23×C83C2×#4112yes—
206D4×C83—42no—
207D4×C83—44no—
208D4×C83—42no—
209D4×C83—44no—
210D4×C83—44no—
211C2×C4×C83—28no—
212C2×C4×C83—22no—
213C2×C4×C83—22no—
214C2×C4×C83—28no—
215C2×C4×C83—22no—
216C2×C4×C83—22no—
217C2×C4×C83—28no—
218C2×C4×C83—24no—
219C2×C4×C83—24no—
220C2×C4×C83—28no—
221C2×C4×C83—24no—
222C2×C4×C83—24no—
223C2×C4×C83—24no—
224C2×C4×C83—22no—
225C2×C4×C83—24no—
226C2×C4×C83—44no—
227C2×C4×C83—42no—
228C2×C4×C83—42no—
229C2×C4×C83—44no—
230C2×C4×C83—44no—
231C2×C4×C83C2×C22⋊C414yes—
232C2×C4×C83C2×C22⋊C414yes—
233C2×Dic83—28no—
234C2×Dic83—48no—
235C2×Dic83—416no—
236C2×Dic83—48no—
237C2×Dic83—44no—
238C2×Dic83—88no—
239C22×C83—22no—
240C22×C83—22no—
241C22×C83—22no—
242C22×C83—22no—
243C22×C83—22no—
244C22×C83—22no—
245C22×C83—24no—
246C22×C83—28no—
247C22×C83—28no—
248C22×C83—24no—
249C22×C83—44no—
250C22×C83—42no—
251C22×C83—44no—
252C22×C83—42no—
253C22×C83—42no—
254C22×C83—42no—
255C22×C83—44no—
256C22×C83—42no—
257C22×C83—84no—
258C22×C83—84no—
259C22×C83—84no—
260C22×C83#38612yes—
261C22×C83#38612yes—
262C22×C83#38612yes—
263C22×C83#38612yes—
264C22×C83#41014yes—
265C22×C83C22×C22⋊C411yescharacteristic
266C22×C83C2×C4×D412yes—
267C22×C83C2×#12011yescharacteristic
268C22×C83C2×#12112yes—
269C22×C83C2×#12311yescharacteristic
270C4×C83—24no—
271C4×C83—24no—
272C4×C83—44no—
273C4×C83—42no—
274Dic83—48no—
275Dic83—84no—
276C2×#1899—831nomaximal, Sylow
277C2×C83—21no—
278C2×C83—22no—
279C2×C83—22no—
280C2×C83—22no—
281C2×C83—21no—
282C2×C83—22no—
283C2×C83—22no—
284C2×C83—82no—
285C2×C83#189914yescomplemented
286C2×C83C2×#38611yescharacteristic
287C2×C83C2×#41012yes—
288C22×#123D8311yescharacteristic
289C22×#117—831no—
290C22×#99—832no—
291C2×#381—831no—
292#1899—838no—
293C2×#342—832no—
294C83C2×#189911yescharacteristic, complemented, Sylow
295C23×D4C2×D8311yescharacteristic
296C24×C4C2×D8311yescharacteristic
297C2×#123—21no—
298C2×#123—22no—
299C2×#123—22no—
300C2×#123—22no—
301C2×#123—21no—
302C2×#123Dic8314yescomplemented
303C2×#123C2×D8314yes—
304C2×#117—834no—
305C2×#117—1668no—
306C2×#117—1662no—
307C22×C4⋊C4—1661no—
308C22×C4⋊C4Dic8312yescomplemented
309C22×C22⋊C4—832no—
310C22×C22⋊C4—832no—
311C22×C22⋊C4Dic8312yescomplemented
312C22×C22⋊C4C2×D8311yescharacteristic
313C22×C42—1661no—
314C2×#99—838no—
315C2×#99—1668no—
316#381—834no—
317#381—1662no—
318C2×#95—1662no—
319#342—838no—
320C25C2×Dic8311yescharacteristic
321C25C22×D8311yescharacteristic
322C22×D4—24no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—24no—
328C22×D4C2×Dic8312yes—
329C22×D4C22×D8312yes—
330C23×C4—24no—
331C23×C4—24no—
332C23×C4—1662no—
333C23×C4—1662no—
334C23×C4C2×Dic8311yescharacteristic
335C23×C4C2×Dic8312yes—
336C23×C4C2×Dic8312yes—
337C23×C4C2×Dic8312yes—
338C23×C4C22⋊D8311yescharacteristic
339C23×C4C22⋊D8312yes—
340C23×C4C22⋊D8312yes—
341C23×C4C22⋊D8312yes—
342C23×C4C22⋊D8311yescharacteristic
343C23×C4C22×D8312yes—
344#123—24no—
345#123—28no—
346#123—24no—
347#123—28no—
348#123—24no—
349#123—24no—
350#117—16616no—
351#117—16616no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—1668no—
356C2×C4⋊C4—1664no—
357C2×C4⋊C4C2×Dic8318yescomplemented
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—24no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—838no—
366C2×C22⋊C4—834no—
367C2×C22⋊C4—834no—
368C2×C22⋊C4—1662no—
369C2×C22⋊C4—1664no—
370C2×C22⋊C4—1664no—
371C2×C22⋊C4—1664no—
372C2×C22⋊C4—1662no—
373C2×C22⋊C4C2×Dic8312yes—
374C2×C22⋊C4C2×Dic8318yescomplemented
375C2×C22⋊C4C22×D8312yes—
376C2×C42—1668no—
377C2×C42—1664no—
378#99—16616no—
379#95—1668no—
380C24—21no—
381C24—21no—
382C24—24no—
383C24—44no—
384C24—44no—
385C24C22×Dic8311yescharacteristic
386C24C22×Dic8312yes—
387C24C22×Dic8311yescharacteristic
388C24D4×D8314yes—
389C24C2×C22⋊D8311yescharacteristic
390C24C2×C22⋊D8311yescharacteristic
391C24C2×C22⋊D8311yescharacteristic
392C24C2×C22⋊D8311yescharacteristic
393C24#1305058914yes—
394C24C23×D8311yescharacteristic
395C2×D4—24no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—24no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—28no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—44no—
405C2×D4—44no—
406C2×D4—42no—
407C2×D4—42no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—24no—
411C22×C4—28no—
412C22×C4—28no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—28no—
419C22×C4—28no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—24no—
425C22×C4—44no—
426C22×C4—3328no—
427C22×C4—3328no—
428C22×C4—3324no—
429C22×C4—1664no—
430C22×C4—1668no—
431C22×C4—1664no—
432C22×C4C22⋊Dic8314yes—
433C22×C4C22⋊Dic8312yes—
434C22×C4C22⋊Dic8314yes—
435C22×C4C22⋊Dic8312yes—
436C22×C4C22⋊Dic8312yes—
437C22×C4C22⋊Dic8312yes—
438C22×C4C22×Dic8312yes—
439C22×C4C22×Dic8314yes—
440C22×C4C22×Dic8314yes—
441C22×C4C2×C22⋊D8314yes—
442C22×C4C2×C22⋊D8312yes—
443C22×C4C2×C22⋊D8312yes—
444C4⋊C4—28no—
445C4⋊C4—28no—
446C4⋊C4—16616no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—28no—
452C22⋊C4—28no—
453C22⋊C4—3324no—
454C22⋊C4—838no—
455C22⋊C4—1664no—
456C22⋊C4—1664no—
457C22⋊C4—1668no—
458C22⋊C4—1664no—
459C42—16616no—
460C23—24no—
461C23—24no—
462C23—24no—
463C23—22no—
464C23—24no—
465C23—42no—
466C23—48no—
467C23—42no—
468C23—42no—
469C23—48no—
470C23—42no—
471C23—44no—
472C23—44no—
473C23—42no—
474C23—42no—
475C23—44no—
476C23—88no—
477C23C2×C22⋊Dic8311yescharacteristic
478C23C2×C22⋊Dic8311yescharacteristic
479C23C2×C22⋊Dic8311yescharacteristic
480C23C2×C22⋊Dic8311yescharacteristic
481C23D4×Dic8314yes—
482C23D4×Dic8314yes—
483C23#1458176012yes—
484C23#1458176012yes—
485C23#1458176414yes—
486C23#1458176414yes—
487C23#1458177312yes—
488C23#1458177312yes—
489C23C23×Dic8311yescharacteristic
490C23C2×D4×D8312yes—
491C23C22×C22⋊D8311yescharacteristic
492C23C22×C22⋊D8311yescharacteristic
493C23C2×#1305058912yes—
494D4—44no—
495D4—44no—
496D4—42no—
497D4—44no—
498D4—42no—
499C2×C4—28no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—28no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—28no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—28no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—33216no—
520C2×C4—3328no—
521C2×C4—3328no—
522C2×C4—3324no—
523C2×C4—6648no—
524C2×C4—1668no—
525C2×C4C2×C22⋊Dic8314yes—
526C2×C4C2×C22⋊Dic8314yes—
527C22—24no—
528C22—28no—
529C22—28no—
530C22—24no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—42no—
538C22—44no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—44no—
543C22—42no—
544C22—44no—
545C22—84no—
546C22—84no—
547C22—84no—
548C22#1912758112yes—
549C22#1912758112yes—
550C22#1912758112yes—
551C22#1912758112yes—
552C22#1912767514yes—
553C22C22×C22⋊Dic8311yescharacteristic
554C22C2×D4×Dic8312yes—
555C22C2×#1458176011yescharacteristic
556C22C2×#1458176412yes—
557C22C2×#1458177311yescharacteristic
558C4—24no—
559C4—24no—
560C4—42no—
561C4—44no—
562C4—3328no—
563C4—6644no—
564C2—21no—
565C2—22no—
566C2—22no—
567C2—22no—
568C2—22no—
569C2—22no—
570C2—21no—
571C2—82no—
572C2#2490792214yesdirect product factor
573C2C2×#1912758111yescharacteristic
574C2C2×#1912767512yes—
subgroupG/H
centerC23C2×C22⋊Dic83
commutatorC23×C83C23×C4
FrattiniC24C23×D83
FittingC22×#123×C83C2
socleC23×C83C2×C22⋊C4
prime radicalC23×D4×C83C22
cosocleC24×C83C24
hypercenterC22×#123D83
hypocenterC83C2×#1899
LCSG ▷ C23×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×#14581751C2semidirect
3. C2×#19127564C2semidirect
4. #24907922C2direct (N × H)
5. C2×#19127468C2semidirect
9. C2×#14581751C22semidirect
17. #19127564C22semidirect
19. #19127468C22semidirect
27. C2×#123×C83C4semidirect
29. C22×C4⋊C4×C83C4semidirect
30. C22×C22⋊C4×C83C4semidirect
81. C2×C4⋊C4×C83C2×C4semidirect
90. C2×C22⋊C4×C83C2×C4semidirect
285. C2×C83#1899semidirect
294. C83C2×#1899semidirect
302. C2×#123Dic83semidirect
308. C22×C4⋊C4Dic83semidirect
311. C22×C22⋊C4Dic83semidirect
357. C2×C4⋊C4C2×Dic83semidirect
374. C2×C22⋊C4C2×Dic83semidirect
572. C2#24907922direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817512
C22×#145817072
C2×#191275642
#249079222
C2×#191274682
C22×#123×C832
C2×#189983