Finite Group Databasebeta

← C2×#19145779 #25968680

Subgroups — C2×#19145779 #25968680

Order 11008.

1810 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583454C211yesmaximal, characteristic, complemented
2C2×#14583436C211yesmaximal, characteristic
3#19145779C2116yesmaximal, direct product factor
4C2×#14583300C212yesmaximal, complemented
5C2×#14583255C212yesmaximal, complemented
6C2×#14583239C212yesmaximal, complemented
7C2×#14583226C212yesmaximal
8C2×#14583184C211yesmaximal, characteristic, complemented
9C2×#14583186C211yesmaximal, characteristic, complemented
10C2×#14583180C211yesmaximal, characteristic, complemented
11C2×#14582951C211yesmaximal, characteristic, complemented
12C2×C43×#477C211yesmaximal, characteristic, complemented
13#14583454—24no—
14#14583454C2218yescomplemented
15C2×#13063325C2211yescharacteristic
16#14583436—24no—
17#14583436C2218yes—
18C2×#13063320—21no—
19C2×#13063316C2211yescharacteristic
20C2×#13063316C2212yes—
21C2×#13063314C2211yescharacteristic
22C2×#13063310—21no—
23C2×#13063305—21no—
24C2×#13063301—21no—
25C2×#13063301C2211yescharacteristic
26C2×#13063300C2211yescharacteristic
27C2×Q8×Dic43—21no—
28C2×#13063290—21no—
29C2×C4×D172—21no—
30C2×C4×D172C2211yescharacteristic
31C2×#13063283C2212yes—
32C2×#13063282—21no—
33C2×C42×D43C2211yescharacteristic
34#14583300C22116yescomplemented
35#14583255C22116yescomplemented
36#14583239C22116yescomplemented
37#14583226C22116yes—
38#14583186C2218yescomplemented
39#14583184C2218yescomplemented
40#14583180C2218yescomplemented
41#14582951C2218yescomplemented
42C2×#13063259C2212yes—
43C2×#13063256C2212yes—
44C2×#13063256C2212yes—
45C2×C4⋊(C43⋊C8)C2211yescharacteristic
46C2×#13063249C2212yes—
47C2×#13063247C2212yes—
48C2×#13063245C2212yes—
49C2×(C2×D43)⋊C8C2212yes—
50C2×C8×Dic43C2212yes—
51C2×C4⋊Q8×C43C2211yescharacteristic
52C2×C4×Q8×C43C2211yescharacteristic
53C43×#477C2218yescomplemented
54C2×#107×C43C2212yes—
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#103×C43C2212yes—
57C22×Dic86—21no—
58C22×D172—21no—
59C22×D172C2311yescharacteristic
60C22×C4×D43—21no—
61C22×C4×D43D411yescharacteristic
62C22×C4×D43D411yescharacteristic
63C22×C4×D43C2311yescharacteristic
64C22×C43⋊C8C2312yes—
65#13063325—22no—
66#13063325C2314yes—
67#13063320—28no—
68#13063316—22no—
69#13063316—24no—
70#13063316C2314yes—
71#13063316C2318yes—
72#13063314—22no—
73#13063314C2314yes—
74#13063310—28no—
75#13063305—28no—
76#13063301—28no—
77#13063301—22no—
78#13063301C2314yes—
79#13063300—22no—
80#13063300C2314yes—
81Q8×Dic43—28no—
82#13063290—28no—
83C4×D172—28no—
84C4×D172—22no—
85C4×D172C2314yes—
86#13063283—24no—
87#13063283C2318yes—
88#13063282—28no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43C2312yes—
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—22no—
97C2×(C2×D43)⋊C4—22no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×C4×Dic43—22no—
104C2×C4×Dic43D411yescharacteristic
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43C2311yescharacteristic
107C42×D43D414yes—
108C42×D43C2314yes—
109#13063259C2318yes—
110#13063256C2318yes—
111#13063256C2318yes—
112C4⋊(C43⋊C8)C2314yes—
113#13063249C2318yes—
114#13063247C2318yes—
115#13063245C2318yes—
116(C2×D43)⋊C8C2318yes—
117C8×Dic43C2318yes—
118C22×Q8×C43—21no—
119C22×Q8×C43C2311yescharacteristic
120C22×C8×C43C2312yes—
121C4⋊Q8×C43—22no—
122C4⋊Q8×C43C2314yes—
123C4×Q8×C43—22no—
124C4×Q8×C43C2314yes—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2312yes—
129C2×C42×C43—21no—
130C2×C42×C43C2311yescharacteristic
131#107×C43C2318yes—
132C4⋊C8×C43C2314yes—
133#103×C43C2318yes—
134C23×D43—21no—
135C23×D43C2×D411yescharacteristic
136C2×Q8×C43—21no—
137C2×Q8×C43—24no—
138C2×Q8×C43—22no—
139C2×Q8×C43—22no—
140C2×Q8×C43—44no—
141C2×Q8×C43C2412yes—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—22no—
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2411yescharacteristic
148C22×Dic43—22no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×D172—21no—
154C2×D172—24no—
155C2×D172—22no—
156C2×D172—22no—
157C2×D172—44no—
158C2×D172C2412yes—
159C2×C4×D43—24no—
160C2×C4×D43—22no—
161C2×C4×D43—22no—
162C2×C4×D43—24no—
163C2×C4×D43—42no—
164C2×C4×D43—44no—
165C2×C4×D43C2×D412yes—
166C2×C4×D43C2×D414yes—
167C2×C4×D43C2×D414yes—
168C2×C4×D43C2412yes—
169C2×Dic86—24no—
170C2×Dic86—44no—
171C2×C8×C43—24no—
172C2×C8×C43C2414yes—
173C4⋊C4×C43—24no—
174C4⋊C4×C43—24no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43C2414yes—
178C4⋊C4×C43C2412yes—
179C42×C43—24no—
180C42×C43C2×D412yes—
181C42×C43C2412yes—
182(C2×D43)⋊C4—24no—
183(C2×D43)⋊C4—24no—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—24no—
186(C2×D43)⋊C4—28no—
187(C2×D43)⋊C4—24no—
188C4⋊Dic43—24no—
189C4⋊Dic43—22no—
190C4⋊Dic43—21no—
191C4⋊Dic43—24no—
192C4⋊Dic43—28no—
193C4⋊Dic43C2414yes—
194C4⋊Dic43C2412yes—
195Dic43⋊C4—24no—
196Dic43⋊C4—24no—
197Dic43⋊C4—28no—
198C4×Dic43—28no—
199C4×Dic43C2×D412yes—
200C4×Dic43C2×D414yes—
201C4×Dic43C2×D414yes—
202C4×Dic43C2412yes—
203C2×C43⋊C8—24no—
204C2×C43⋊C8C2414yes—
205C23×C43C22×D411yescharacteristic
206C22×D43—22no—
207C22×D43—22no—
208C22×D43—22no—
209C22×D43—22no—
210C22×D43—42no—
211C22×D43—42no—
212C22×D43—42no—
213C22×D43C22×D412yes—
214Q8×C43—22no—
215Q8×C43—22no—
216Q8×C43—48no—
217Q8×C43—42no—
218C2×C4×C43—22no—
219C2×C4×C43—24no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—44no—
225C2×C4×C43#13514yes—
226C2×C4×C43C22×D412yes—
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D412yes—
229C2×C4×C432−1+412yes—
230C2×C4×C432−1+412yes—
231C2×C4×C43C2511yescharacteristic
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—24no—
236C2×Dic43—22no—
237C2×Dic43—44no—
238C2×Dic43—42no—
239C2×Dic43C22×D412yes—
240C2×Dic43C22×D412yes—
241C2×Dic43C22×D412yes—
242D172—22no—
243D172—22no—
244D172—48no—
245D172—42no—
246C4×D43—24no—
247C4×D43—28no—
248C4×D43—22no—
249C4×D43—22no—
250C4×D43—44no—
251C4×D43—48no—
252Dic86—48no—
253C8×C43—24no—
254C43⋊C8—24no—
255C2×#3233—431nomaximal, Sylow
256C22×C43#53612yes—
257C22×C43C2×#13512yes—
258C22×C43#57512yes—
259C22×C43C23×D411yescharacteristic
260C2×D43—22no—
261C2×D43—22no—
262C2×D43—22no—
263C2×D43—44no—
264C2×D43—42no—
265C2×D43—42no—
266C2×D43—42no—
267C2×D43—84no—
268C4×C43—22no—
269C4×C43—42no—
270C4×C43—42no—
271C4×C43—44no—
272C4×C43#53612yes—
273C4×C43C2×#13514yes—
274C4×C43C2×2−1+411yescharacteristic
275C4×C43C2×2−1+411yescharacteristic
276Dic43—22no—
277Dic43—22no—
278Dic43—22no—
279Dic43—44no—
280Dic43—42no—
281C2×#533—431no—
282C2×#529—431no—
283#3233—4316no—
284C2×#499—432no—
285C2×#488—432no—
286C2×#485—432no—
287C2×#482—432no—
288C2×#477D4311yescharacteristic, complemented
289C2×#475—431no—
290C2×#476—431no—
291C2×#474—431no—
292C2×#431—431no—
293C2×C43#323314yescomplemented
294C2×C43C2×#53611yescharacteristic
295C2×C43C22×#13511yescharacteristic
296C2×C43C2×#57511yescharacteristic
297D43—42no—
298D43—82no—
299#533—438no—
300#533—864no—
301C2×C4⋊Q8—431no—
302C2×C4⋊Q8C2×D4311yescharacteristic
303#529—438no—
304#529—864no—
305C2×#126—861no—
306C2×#125—432no—
307C2×#125—431no—
308C2×#124—431no—
309C2×#123—861no—
310C2×C22⋊Q8—431no—
311C2×C22⋊Q8—861no—
312C2×C22⋊Q8—861no—
313C2×#121—431no—
314C2×C4×Q8—861no—
315C2×C4×Q8—861no—
316C2×C4×Q8C2×D4311yescharacteristic
317C2×C4×D4—431no—
318C2×C4×D4—861no—
319C2×#117—432no—
320C2×#117—861no—
321C22×C42—431no—
322#499—4316no—
323#488—4316no—
324#485—4316no—
325#482—4316no—
326#477C2×D4318yescomplemented
327#476—438no—
328#475—438no—
329#474—438no—
330#431—438no—
331C2×#107—432no—
332C2×#107C2×D4312yes—
333C2×#106—432no—
334C2×#106—432no—
335C2×C4⋊C8—431no—
336C2×C4⋊C8C2×D4311yescharacteristic
337C2×#103—432no—
338C2×#103C2×D4312yes—
339C2×#102—432no—
340C2×#102—432no—
341C2×C22⋊C8—432no—
342C2×C4×C8—432no—
343C43C2×#323311yescharacteristic, complemented, Sylow
344C22×Q8—21no—
345C22×Q8—861no—
346C22×Q8C22×D4311yescharacteristic
347C22×D4—431no—
348C22×D4—861no—
349C23×C4—431no—
350C23×C4—431no—
351C23×C4—431no—
352C23×C4—861no—
353C22×C8—432no—
354C22×C8C22×D4312yes—
355C4⋊Q8—22no—
356C4⋊Q8—434no—
357C4⋊Q8—862no—
358C4⋊Q8C22×D4314yes—
359#126—868no—
360#125—434no—
361#125—438no—
362#125—862no—
363#125—864no—
364#124—434no—
365#124—862no—
366#123—868no—
367C22⋊Q8—434no—
368C22⋊Q8—868no—
369C22⋊Q8—862no—
370C22⋊Q8—868no—
371#121—434no—
372#121—862no—
373C4×Q8—22no—
374C4×Q8—868no—
375C4×Q8—868no—
376C4×Q8C22×D4314yes—
377C4×D4—434no—
378C4×D4—868no—
379C4×D4—862no—
380#117—438no—
381#117—868no—
382#117—864no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—432no—
386C2×C4⋊C4—431no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4—861no—
390C2×C4⋊C4—862no—
391C2×C4⋊C4—862no—
392C2×C4⋊C4—861no—
393C2×C4⋊C4C22×D4312yes—
394C2×C4⋊C4C22×D4311yescharacteristic
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C22⋊C4—861no—
398C2×C22⋊C4—862no—
399C2×C22⋊C4—861no—
400C2×C22⋊C4—861no—
401C2×C42—21no—
402C2×C42—431no—
403C2×C42—431no—
404C2×C42—431no—
405C2×C42—434no—
406C2×C42—434no—
407C2×C42—862no—
408C2×C42C22×D4311yescharacteristic
409#107—438no—
410#107C22×D4318yes—
411#106—438no—
412#106—438no—
413C4⋊C8—434no—
414C4⋊C8C22×D4314yes—
415#103—438no—
416#103C22×D4318yes—
417#102—438no—
418#102—438no—
419C22⋊C8—438no—
420C4×C8—438no—
421C24—431no—
422C24—861no—
423C2×Q8—21no—
424C2×Q8—24no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—44no—
428C2×Q8—864no—
429C2×Q8—1724no—
430C2×Q8C23×D4312yes—
431C2×D4—432no—
432C2×D4—864no—
433C2×D4—861no—
434C2×D4—862no—
435C2×D4—862no—
436C2×D4—1724no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—431no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—432no—
444C22×C4—434no—
445C22×C4—432no—
446C22×C4—434no—
447C22×C4—864no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—861no—
452C22×C4—864no—
453C22×C4—1722no—
454C22×C4—1724no—
455C22×C4D4×D4311yescharacteristic
456C22×C4D4×D4311yescharacteristic
457C22×C4C23×D4311yescharacteristic
458C2×C8—24no—
459C2×C8—434no—
460C2×C8—864no—
461C2×C8C23×D4314yes—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—434no—
467C4⋊C4—432no—
468C4⋊C4—864no—
469C4⋊C4—864no—
470C4⋊C4—864no—
471C4⋊C4—868no—
472C4⋊C4—868no—
473C4⋊C4—862no—
474C4⋊C4—861no—
475C4⋊C4—864no—
476C4⋊C4C23×D4314yes—
477C4⋊C4C23×D4312yes—
478C22⋊C4—864no—
479C22⋊C4—864no—
480C22⋊C4—864no—
481C22⋊C4—868no—
482C22⋊C4—864no—
483C22⋊C4—864no—
484C42—24no—
485C42—434no—
486C42—434no—
487C42—432no—
488C42—432no—
489C42—868no—
490C42D4×D4312yes—
491C42C23×D4312yes—
492C23—432no—
493C23—862no—
494C23—862no—
495C23—862no—
496C23—862no—
497C23—1722no—
498C23—1722no—
499C23—1722no—
500C23C2×D4×D4311yescharacteristic
501Q8—22no—
502Q8—22no—
503Q8—48no—
504Q8—42no—
505Q8—1728no—
506D4—862no—
507D4—862no—
508D4—1728no—
509D4—1722no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—42no—
515C2×C4—44no—
516C2×C4—42no—
517C2×C4—432no—
518C2×C4—432no—
519C2×C4—432no—
520C2×C4—862no—
521C2×C4—862no—
522C2×C4—862no—
523C2×C4—868no—
524C2×C4—864no—
525C2×C4—862no—
526C2×C4—862no—
527C2×C4—864no—
528C2×C4—862no—
529C2×C4—1724no—
530C2×C4—1722no—
531C2×C4—1724no—
532C2×C4—1728no—
533C2×C4#1306334814yes—
534C2×C4C2×D4×D4312yes—
535C2×C4C2×D4×D4312yes—
536C2×C4C2×D4×D4311yescharacteristic
537C2×C4#1306337212yes—
538C2×C4#1306337312yes—
539C2×C4C24×D4311yescharacteristic
540C8—24no—
541C8—864no—
542C22—862no—
543C22—862no—
544C22—862no—
545C22—3444no—
546C22—1722no—
547C22—1722no—
548C22—1722no—
549C22—1724no—
550C22#1458347212yes—
551C22C2×#1306334812yes—
552C22#1458369512yes—
553C22C22×D4×D4311yescharacteristic
554C4—22no—
555C4—42no—
556C4—44no—
557C4—42no—
558C4—862no—
559C4—862no—
560C4—862no—
561C4—1722no—
562C4—1724no—
563C4#1458347212yes—
564C4C2×#1306334814yes—
565C4C2×#1306337211yescharacteristic
566C4C2×#1306337311yescharacteristic
567C2—3442no—
568C2—1722no—
569C2#1914577914yesdirect product factor
570C2C2×#1458347211yescharacteristic
571C2C22×#1306334811yescharacteristic
572C2C2×#1458369511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#477C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenterC2×#477D43
hypocenterC43C2×#3233
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
1. C2×#14583454C2semidirect
3. #19145779C2direct (N × H)
4. C2×#14583300C2semidirect
5. C2×#14583255C2semidirect
6. C2×#14583239C2semidirect
8. C2×#14583184C2semidirect
9. C2×#14583186C2semidirect
10. C2×#14583180C2semidirect
11. C2×#14582951C2semidirect
12. C2×C43×#477C2semidirect
14. #14583454C22semidirect
34. #14583300C22semidirect
35. #14583255C22semidirect
36. #14583239C22semidirect
38. #14583186C22semidirect
39. #14583184C22semidirect
40. #14583180C22semidirect
41. #14582951C22semidirect
53. C43×#477C22semidirect
288. C2×#477D43semidirect
293. C2×C43#3233semidirect
326. #477C2×D43semidirect
343. C43C2×#3233semidirect
569. C2#19145779direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834542
C2×#145834362
#191457792
C2×#145833002
C2×#145832552
C2×#145832392
C2×#145832262
C2×#145831842
C2×#145831862
C2×#145831802
C2×#145829512
C2×C43×#4772
C2×#323343