Finite Group Databasebeta

← C2×#20245038 #26369010

Subgroups — C2×#20245038 #26369010

Order 12032.

1406 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689107C211yesmaximal, characteristic, complemented
2C2×#15689097C211yesmaximal, characteristic, complemented
3#20245038C218yesmaximal, direct product factor
4C2×#15688910C214yesmaximal, complemented
5C2×C47×#535C211yesmaximal, characteristic
6C22×#10625329—21no—
7C2×#13093983—21no—
8#15689107—22no—
9#15689107C2214yescomplemented
10C2×#13093943—21no—
11C2×#13093941C2212yes—
12#15689097—22no—
13#15689097C2214yescomplemented
14C2×#13093939—21no—
15C2×#13093939C2212yes—
16#15688910C22116yescomplemented
17C22×#41×C47C2211yescharacteristic
18C23×D4×C47C411yescharacteristic, complemented
19C47×#535—22no—
20C47×#535—22no—
21C47×#535C414yescomplemented
22C47×#535C2214yes—
23C2×#127×C47—21no—
24C2×#124×C47—21no—
25C2×#121×C47—21no—
26C2×#121×C47—21no—
27C2×#120×C47C412yescomplemented
28C2×#120×C47C2212yes—
29C2×#117×C47C411yescharacteristic, complemented
30C2×#10625329—22no—
31C2×#10625329—24no—
32C2×#10625329—41no—
33C2×#10625329—42no—
34C22×C47⋊C8—41no—
35#13093983—24no—
36#13093983—42no—
37C2×C4⋊Dic47—41no—
38C2×C22⋊Dic47—22no—
39C2×C4×Dic47—41no—
40#13093943—24no—
41#13093941—22no—
42#13093941C2314yes—
43#13093939—24no—
44#13093939—22no—
45#13093939C2314yes—
46C25×C47C2×C412yes—
47C2×#41×C47—41no—
48C2×#41×C47—41no—
49C2×#41×C47—42no—
50C2×#41×C47C2×C412yes—
51C2×#41×C47D412yes—
52C2×#41×C47D412yes—
53C2×#41×C47C2312yes—
54C22×Q8×C47D411yescharacteristic
55C22×D4×C47—22no—
56C22×D4×C47—22no—
57C22×D4×C47—21no—
58C22×D4×C47—21no—
59C22×D4×C47—22no—
60C22×D4×C47—41no—
61C22×D4×C47—41no—
62C22×D4×C47—42no—
63C22×D4×C47C2×C411yescharacteristic
64C22×D4×C47C2×C414yescomplemented
65C22×D4×C47D411yescharacteristic
66C22×D4×C47C2311yescharacteristic
67C23×C4×C47C2×C411yescharacteristic
68C23×C4×C47D411yescharacteristic
69C23×C4×C47D411yescharacteristic
70#127×C47—24no—
71#127×C47—24no—
72#124×C47—24no—
73#124×C47—24no—
74#121×C47—24no—
75#121×C47—24no—
76#121×C47—24no—
77#121×C47—24no—
78#120×C47—24no—
79#120×C47—22no—
80#120×C47—22no—
81#120×C47C2×C414yes—
82#120×C47C2×C418yescomplemented
83#120×C47C2314yes—
84#117×C47—22no—
85#117×C47C2×C414yescomplemented
86C2×C4⋊C4×C47—21no—
87C2×C22⋊C4×C47—22no—
88C2×C22⋊C4×C47—22no—
89C2×C22⋊C4×C47C2×C412yes—
90C2×C42×C47—21no—
91C24×C47—22no—
92C24×C47—22no—
93C24×C47—42no—
94C24×C47—42no—
95C24×C47—84no—
96C24×C47C22⋊C411yescharacteristic
97C24×C47C22×C411yescharacteristic
98C24×C47C22×C414yes—
99C24×C47C2×D411yescharacteristic
100#41×C47—42no—
101#41×C47—42no—
102#41×C47—42no—
103#41×C47—42no—
104#41×C47—42no—
105#41×C47—42no—
106#41×C47—42no—
107#41×C47—42no—
108C2×Q8×C47—41no—
109C2×Q8×C47—41no—
110C2×Q8×C47C22⋊C412yes—
111C2×Q8×C47C2×D412yes—
112C2×D4×C47—24no—
113C2×D4×C47—28no—
114C2×D4×C47—24no—
115C2×D4×C47—24no—
116C2×D4×C47—24no—
117C2×D4×C47—41no—
118C2×D4×C47—41no—
119C2×D4×C47—41no—
120C2×D4×C47—41no—
121C2×D4×C47—41no—
122C2×D4×C47—41no—
123C2×D4×C47—42no—
124C2×D4×C47—42no—
125C2×D4×C47—44no—
126C2×D4×C47—44no—
127C2×D4×C47—44no—
128C2×D4×C47—44no—
129C2×D4×C47—42no—
130C2×D4×C47—41no—
131C2×D4×C47—41no—
132C2×D4×C47—84no—
133C2×D4×C47—84no—
134C2×D4×C47C22⋊C412yes—
135C2×D4×C47C22⋊C412yes—
136C2×D4×C47C22×C411yescharacteristic
137C2×D4×C47C22×C412yes—
138C2×D4×C47C2×D411yescharacteristic
139C2×D4×C47C2×D412yes—
140C2×D4×C47C2×D411yescharacteristic
141C2×D4×C47C2411yescharacteristic
142C22×C4×C47—22no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—22no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47C22⋊C411yescharacteristic
153C22×C4×C47C22⋊C411yescharacteristic
154C22×C4×C47C22⋊C412yes—
155C22×C4×C47C22⋊C412yes—
156C22×C4×C47C22⋊C412yes—
157C22×C4×C47C22⋊C411yescharacteristic
158C22×C4×C47C22×C412yes—
159C22×C4×C47C2×D412yes—
160C22×C4×C47C2×D411yescharacteristic
161C22×C4×C47C2×D412yes—
162C22×Dic47—42no—
163C4⋊C4×C47—24no—
164C22⋊C4×C47—22no—
165C22⋊C4×C47—24no—
166C22⋊C4×C47—28no—
167C22⋊C4×C47—24no—
168C22⋊C4×C47C22×C414yes—
169C42×C47—24no—
170C22⋊Dic47—24no—
171C22⋊Dic47—42no—
172C4⋊Dic47—44no—
173C4×Dic47—44no—
174#10625329—24no—
175#10625329—42no—
176#10625329—44no—
177C2×C47⋊C8—42no—
178C2×C47⋊C8—44no—
179C23×C47—21no—
180C23×C47—21no—
181C23×C47—21no—
182C23×C47—21no—
183C23×C47—21no—
184C23×C47—21no—
185C23×C47—24no—
186C23×C47—42no—
187C23×C47—42no—
188C23×C47—42no—
189C23×C47—44no—
190C23×C47—44no—
191C23×C47—44no—
192C23×C47—44no—
193C23×C47—42no—
194C23×C47—42no—
195C23×C47—84no—
196C23×C47—84no—
197C23×C47—88no—
198C23×C47—88no—
199C23×C47C2×C22⋊C411yescharacteristic
200C23×C47C2×C22⋊C411yescharacteristic
201C23×C47C2×C22⋊C411yescharacteristic
202C23×C47C2×C22⋊C412yes—
203C23×C47C23×C411yescharacteristic
204C23×C47C22×D411yescharacteristic
205Q8×C47—42no—
206Q8×C47—42no—
207D4×C47—42no—
208D4×C47—42no—
209D4×C47—42no—
210D4×C47—41no—
211D4×C47—41no—
212D4×C47—42no—
213D4×C47—41no—
214D4×C47—41no—
215D4×C47—48no—
216D4×C47—44no—
217D4×C47—44no—
218D4×C47—84no—
219D4×C47—88no—
220D4×C47—84no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—22no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—22no—
232C2×C4×C47—22no—
233C2×C4×C47—22no—
234C2×C4×C47—22no—
235C2×C4×C47—22no—
236C2×C4×C47—22no—
237C2×C4×C47—22no—
238C2×C4×C47—22no—
239C2×C4×C47—24no—
240C2×C4×C47—44no—
241C2×C4×C47#9912yes—
242C2×C4×C47#9911yescharacteristic
243C2×C4×C47#9911yescharacteristic
244C2×C4×C47C2×C22⋊C412yes—
245C2×C4×C47C2×C22⋊C412yes—
246C2×C4×C47C2×C22⋊C411yescharacteristic
247C2×C4×C47C2×C22⋊C412yes—
248C2×C4×C47C22×D411yescharacteristic
249C2×Dic47—44no—
250C2×Dic47—84no—
251C47⋊C8—44no—
252C2×#2122—471nomaximal, Sylow
253C22×C47—22no—
254C22×C47—21no—
255C22×C47—21no—
256C22×C47—21no—
257C22×C47—22no—
258C22×C47—21no—
259C22×C47—42no—
260C22×C47—41no—
261C22×C47—41no—
262C22×C47—41no—
263C22×C47—41no—
264C22×C47—42no—
265C22×C47—44no—
266C22×C47—44no—
267C22×C47—42no—
268C22×C47—42no—
269C22×C47—42no—
270C22×C47—44no—
271C22×C47—81no—
272C22×C47—81no—
273C22×C47—84no—
274C22×C47—88no—
275C22×C47—88no—
276C22×C47—84no—
277C22×C47C2×#9911yescharacteristic
278C22×C47C2×#9911yescharacteristic
279C22×C47C22×C22⋊C411yescharacteristic
280C4×C47—21no—
281C4×C47—22no—
282C4×C47—21no—
283C4×C47—22no—
284C4×C47—44no—
285C4×C47C2×#9912yes—
286C4×C47C2×#9912yes—
287Dic47—84no—
288C2×#535D4711yescharacteristic
289C2×#413—471no—
290C2×#410—471no—
291#2122—478no—
292C2×AΣL(1,𝔽16)—474no—
293C2×C47—21no—
294C2×C47—21no—
295C2×C47—41no—
296C2×C47—41no—
297C2×C47—41no—
298C2×C47—41no—
299C2×C47—42no—
300C2×C47—84no—
301C2×C47#212212yescomplemented
302C2×C47C22×#9911yescharacteristic
303C22×#41C2×D4711yescharacteristic
304C23×D4Dic4711yescharacteristic, complemented
305C22×M16—941no—
306#535—22no—
307#535—22no—
308#535Dic4714yescomplemented
309#535C2×D4714yes—
310C2×#127—21no—
311C2×#124—21no—
312C2×#121—21no—
313C2×#121—21no—
314C2×#120Dic4712yescomplemented
315C2×#120C2×D4712yes—
316C2×#117—941no—
317C2×#117Dic4711yescharacteristic, complemented
318#413—474no—
319#413—942no—
320C2×#101—941no—
321C2×#100—472no—
322#410—474no—
323#410—942no—
324C2×#99—472no—
325C2×#99—941no—
326AΣL(1,𝔽16)—4716no—
327C47C2×#212211yescharacteristic, complemented, Sylow
328C25C2×Dic4712yes—
329C2×#41—41no—
330C2×#41—41no—
331C2×#41—42no—
332C2×#41C2×Dic4712yes—
333C2×#41C22⋊D4712yes—
334C2×#41C22⋊D4712yes—
335C2×#41C22×D4712yes—
336C22×Q8C22⋊D4711yescharacteristic
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—21no—
340C22×D4—22no—
341C22×D4—21no—
342C22×D4—42no—
343C22×D4—41no—
344C22×D4—41no—
345C22×D4C2×Dic4711yescharacteristic
346C22×D4C2×Dic4714yescomplemented
347C22×D4C22⋊D4711yescharacteristic
348C22×D4C22×D4711yescharacteristic
349C23×C4C2×Dic4711yescharacteristic
350C23×C4C22⋊D4711yescharacteristic
351C23×C4C22⋊D4711yescharacteristic
352C2×M16—942no—
353C2×M16—944no—
354C2×M16—1881no—
355C2×M16—1882no—
356C22×C8—1881no—
357#127—24no—
358#127—24no—
359#124—24no—
360#124—24no—
361#121—24no—
362#121—24no—
363#121—24no—
364#121—24no—
365#120—24no—
366#120—22no—
367#120—22no—
368#120C2×Dic4714yes—
369#120C2×Dic4718yescomplemented
370#120C22×D4714yes—
371#117—22no—
372#117—944no—
373#117—1882no—
374#117C2×Dic4714yescomplemented
375C2×C4⋊C4—21no—
376C2×C4⋊C4—1881no—
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—942no—
380C2×C22⋊C4C2×Dic4712yes—
381C2×C42—21no—
382C2×C42—1881no—
383#101—944no—
384#100—474no—
385#100—942no—
386#99—474no—
387#99—942no—
388#99—944no—
389C24—22no—
390C24—22no—
391C24—42no—
392C24—42no—
393C24—84no—
394C24C22⋊Dic4711yescharacteristic
395C24C22×Dic4711yescharacteristic
396C24C22×Dic4714yes—
397C24C2×C22⋊D4711yescharacteristic
398#41—42no—
399#41—42no—
400#41—42no—
401#41—42no—
402#41—42no—
403#41—42no—
404#41—42no—
405#41—42no—
406C2×Q8—41no—
407C2×Q8—41no—
408C2×Q8C22⋊Dic4712yes—
409C2×Q8C2×C22⋊D4712yes—
410C2×D4—24no—
411C2×D4—28no—
412C2×D4—24no—
413C2×D4—24no—
414C2×D4—24no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—44no—
427C2×D4—42no—
428C2×D4—41no—
429C2×D4—41no—
430C2×D4—84no—
431C2×D4—84no—
432C2×D4C22⋊Dic4712yes—
433C2×D4C22⋊Dic4712yes—
434C2×D4C22×Dic4711yescharacteristic
435C2×D4C22×Dic4712yes—
436C2×D4C2×C22⋊D4711yescharacteristic
437C2×D4C2×C22⋊D4712yes—
438C2×D4C2×C22⋊D4711yescharacteristic
439C2×D4C23×D4711yescharacteristic
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—1882no—
451C22×C4C22⋊Dic4711yescharacteristic
452C22×C4C22⋊Dic4711yescharacteristic
453C22×C4C22⋊Dic4712yes—
454C22×C4C22⋊Dic4712yes—
455C22×C4C22⋊Dic4712yes—
456C22×C4C22⋊Dic4711yescharacteristic
457C22×C4C22×Dic4712yes—
458C22×C4C2×C22⋊D4712yes—
459C22×C4C2×C22⋊D4711yescharacteristic
460C22×C4C2×C22⋊D4712yes—
461M16—944no—
462M16—1882no—
463M16—1884no—
464C2×C8—1882no—
465C2×C8—1884no—
466C4⋊C4—24no—
467C4⋊C4—1884no—
468C22⋊C4—22no—
469C22⋊C4—24no—
470C22⋊C4—28no—
471C22⋊C4—24no—
472C22⋊C4—944no—
473C22⋊C4—1882no—
474C22⋊C4C22×Dic4714yes—
475C42—24no—
476C42—1884no—
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—24no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—44no—
488C23—44no—
489C23—44no—
490C23—44no—
491C23—42no—
492C23—42no—
493C23—84no—
494C23—84no—
495C23—88no—
496C23—88no—
497C23C2×C22⋊Dic4711yescharacteristic
498C23C2×C22⋊Dic4711yescharacteristic
499C23C2×C22⋊Dic4711yescharacteristic
500C23C2×C22⋊Dic4712yes—
501C23C23×Dic4711yescharacteristic
502C23C22×C22⋊D4711yescharacteristic
503Q8—42no—
504Q8—42no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—41no—
509D4—41no—
510D4—42no—
511D4—41no—
512D4—41no—
513D4—48no—
514D4—44no—
515D4—44no—
516D4—84no—
517D4—88no—
518D4—84no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—44no—
539C2×C4—3764no—
540C2×C4—1884no—
541C2×C4#1309393912yes—
542C2×C4#1309393911yescharacteristic
543C2×C4#1309393911yescharacteristic
544C2×C4C2×C22⋊Dic4712yes—
545C2×C4C2×C22⋊Dic4712yes—
546C2×C4C2×C22⋊Dic4711yescharacteristic
547C2×C4C2×C22⋊Dic4712yes—
548C2×C4C22×C22⋊D4711yescharacteristic
549C8—1884no—
550C22—22no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—22no—
555C22—21no—
556C22—42no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—42no—
562C22—44no—
563C22—44no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—44no—
568C22—81no—
569C22—81no—
570C22—84no—
571C22—88no—
572C22—88no—
573C22—84no—
574C22C2×#1309393911yescharacteristic
575C22C2×#1309393911yescharacteristic
576C22C22×C22⋊Dic4711yescharacteristic
577C4—21no—
578C4—22no—
579C4—21no—
580C4—22no—
581C4—44no—
582C4—3764no—
583C4C2×#1309393912yes—
584C4C2×#1309393912yes—
585C2—21no—
586C2—21no—
587C2—41no—
588C2—41no—
589C2—41no—
590C2—41no—
591C2—42no—
592C2—84no—
593C2#2024503812yesdirect product factor
594C2C22×#1309393911yescharacteristic
subgroupG/H
centerC22C2×#13093939
commutatorC23×C47C23×C4
FrattiniC2×D4C23×D47
Fitting, prime radicalC2×C47×#535C2
socleC22×C47C2×#99
cosocleC2×D4×C47C24
hypercenterC2×#535D47
hypocenterC47C2×#2122
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#15689107C2semidirect
2. C2×#15689097C2semidirect
3. #20245038C2direct (N × H)
4. C2×#15688910C2semidirect
9. #15689107C22semidirect
13. #15689097C22semidirect
16. #15688910C22semidirect
18. C23×D4×C47C4semidirect
21. C47×#535C4semidirect
27. C2×#120×C47C4semidirect
29. C2×#117×C47C4semidirect
64. C22×D4×C47C2×C4semidirect
82. #120×C47C2×C4semidirect
85. #117×C47C2×C4semidirect
301. C2×C47#2122semidirect
304. C23×D4Dic47semidirect
308. #535Dic47semidirect
314. C2×#120Dic47semidirect
317. C2×#117Dic47semidirect
327. C47C2×#2122semidirect
346. C22×D4C2×Dic47semidirect
369. #120C2×Dic47semidirect
374. #117C2×Dic47semidirect
593. C2#20245038direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156891072
C2×#156890972
#202450382
C2×#156889102
C2×C47×#5352
C2×#212247