Finite Group Databasebeta

← C2×#20244742 #26244409

Subgroups — C2×#20244742 #26244409

Order 12032.

1614 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689749C211yesmaximal, characteristic
2C2×#15688998C212yesmaximal
3C2×#15688995C211yesmaximal, characteristic
4#20244742C218yesmaximal, direct product factor
5C2×#15688889C212yesmaximal
6C2×C47×#342C211yesmaximal, characteristic
7C24×Dic47C2211yescharacteristic
8#15689749—24no—
9#15689749—22no—
10#15689749C2214yes—
11C2×#13094003—21no—
12C2×#13094003—21no—
13C2×#13094001—22no—
14C2×#13094001—22no—
15C22×C4⋊Dic47—22no—
16C22×Dic47⋊C4—21no—
17C22×C22⋊Dic47C2212yes—
18C22×C22⋊Dic47C2211yescharacteristic
19#15688998—24no—
20#15688998C2218yes—
21#15688995—22no—
22#15688995C2214yes—
23C2×C47⋊#95—22no—
24C2×C47⋊#95—21no—
25#15688889C2218yes—
26C22×C22⋊C4×C47C2211yescharacteristic
27C22×C22⋊C4×C47C2212yes—
28C47×#342C2214yes—
29C22×Dic94—21no—
30C22×Dic94—21no—
31C23×Dic47—21no—
32C23×Dic47—21no—
33C23×Dic47—22no—
34C23×Dic47—21no—
35C23×Dic47—22no—
36C23×Dic47—44no—
37C23×Dic47D412yes—
38C23×Dic47D412yes—
39C23×Dic47C2312yes—
40#13094003—24no—
41#13094003—24no—
42#13094003—24no—
43#13094003—24no—
44#13094001—28no—
45#13094001—28no—
46#13094001—28no—
47#13094001—28no—
48C2×C4⋊Dic47—21no—
49C2×C4⋊Dic47—21no—
50C2×C4⋊Dic47—28no—
51C2×C4⋊Dic47—48no—
52C2×Dic47⋊C4—22no—
53C2×Dic47⋊C4—22no—
54C2×Dic47⋊C4—24no—
55C2×Dic47⋊C4—44no—
56C2×C22⋊Dic47—22no—
57C2×C22⋊Dic47—22no—
58C2×C22⋊Dic47—21no—
59C2×C22⋊Dic47—22no—
60C2×C22⋊Dic47—22no—
61C2×C22⋊Dic47—22no—
62C2×C22⋊Dic47D414yes—
63C2×C22⋊Dic47Q814yescomplemented
64C2×C22⋊Dic47C2314yes—
65C2×C22⋊Dic47C2312yes—
66C47⋊#95—24no—
67C47⋊#95—28no—
68C25×C47C2311yescharacteristic
69C23×C4×C47—22no—
70C23×C4×C47D411yescharacteristic
71C23×C4×C47D411yescharacteristic
72C2×C22⋊C4×C47—22no—
73C2×C22⋊C4×C47—22no—
74C2×C22⋊C4×C47—22no—
75C2×C22⋊C4×C47—24no—
76C2×C22⋊C4×C47D412yes—
77C2×C22⋊C4×C47Q818yescomplemented
78C2×C22⋊C4×C47C2312yes—
79C2×C22⋊C4×C47C2314yes—
80C24×C47—42no—
81C24×C47—42no—
82C24×C47C2×D411yescharacteristic
83C24×C47C2×D412yes—
84C24×C47C2×D411yescharacteristic
85C24×C47C2×D412yes—
86C24×C47C2×Q814yes—
87C24×C47C2×Q812yes—
88C24×C47#4112yes—
89C24×C47C2411yescharacteristic
90C22×C4×C47—21no—
91C22×C4×C47—21no—
92C22×C4×C47—28no—
93C22×C4×C47—24no—
94C22×C4×C47—21no—
95C22×C4×C47—21no—
96C22×C4×C47—44no—
97C22×C4×C47—44no—
98C22×C4×C47—42no—
99C22×C4×C47—42no—
100C22×C4×C47C2×D412yes—
101C22×C4×C47C2×D412yes—
102C22×Dic47—24no—
103C22×Dic47—28no—
104C22×Dic47—22no—
105C22×Dic47—22no—
106C22×Dic47—24no—
107C22×Dic47—22no—
108C22×Dic47—22no—
109C22×Dic47—24no—
110C22×Dic47—22no—
111C22×Dic47—22no—
112C22×Dic47—44no—
113C22×Dic47—44no—
114C22×Dic47—48no—
115C22×Dic47—42no—
116C22×Dic47—42no—
117C22×Dic47—42no—
118C22×Dic47—44no—
119C22×Dic47—41no—
120C22×Dic47—42no—
121C22×Dic47—41no—
122C22×Dic47—44no—
123C22×Dic47—44no—
124C22×Dic47C2×D414yes—
125C22×Dic47C2×D414yes—
126C2×Dic94—24no—
127C2×Dic94—24no—
128C2×Dic94—82no—
129C2×Dic94—82no—
130C22⋊C4×C47—24no—
131C22⋊C4×C47—28no—
132C22⋊C4×C47—24no—
133C22⋊C4×C47—24no—
134C22⋊C4×C47C2×Q818yescomplemented
135C22⋊Dic47—24no—
136C22⋊Dic47—24no—
137C22⋊Dic47—24no—
138C22⋊Dic47—24no—
139C22⋊Dic47—24no—
140C22⋊Dic47—22no—
141C22⋊Dic47C2×Q814yescomplemented
142C4⋊Dic47—24no—
143C4⋊Dic47—24no—
144C4⋊Dic47—416no—
145Dic47⋊C4—28no—
146Dic47⋊C4—28no—
147Dic47⋊C4—48no—
148C23×C47—22no—
149C23×C47—24no—
150C23×C47—22no—
151C23×C47—24no—
152C23×C47—41no—
153C23×C47—42no—
154C23×C47—41no—
155C23×C47—41no—
156C23×C47—42no—
157C23×C47—48no—
158C23×C47—44no—
159C23×C47—44no—
160C23×C47—41no—
161C23×C47#12011yescharacteristic
162C23×C47#12012yes—
163C23×C47#12011yescharacteristic
164C23×C47C22⋊Q814yes—
165C23×C47C22⋊Q814yes—
166C23×C47C22⋊Q812yes—
167C23×C47C22⋊Q812yes—
168C23×C47C4⋊Q814yes—
169C23×C47C4⋊Q814yes—
170C23×C47C4⋊Q812yes—
171C23×C47C4⋊Q812yes—
172C23×C47C22×D412yes—
173C23×C47C22×D411yescharacteristic
174C23×C47C22×Q811yescharacteristic
175C23×C47C22×Q812yes—
176C23×C47C2×#4111yescharacteristic
177C2×C4×C47—22no—
178C2×C4×C47—22no—
179C2×C4×C47—28no—
180C2×C4×C47—44no—
181C2×C4×C47—416no—
182C2×C4×C47—44no—
183C2×C4×C47—42no—
184C2×C4×C47—42no—
185C2×C4×C47—42no—
186C2×C4×C47—42no—
187C2×C4×C47—81no—
188C2×C4×C47—81no—
189C2×Dic47—24no—
190C2×Dic47—28no—
191C2×Dic47—24no—
192C2×Dic47—24no—
193C2×Dic47—24no—
194C2×Dic47—42no—
195C2×Dic47—48no—
196C2×Dic47—42no—
197C2×Dic47—42no—
198C2×Dic47—44no—
199C2×Dic47—48no—
200C2×Dic47—44no—
201C2×Dic47—42no—
202C2×Dic47—44no—
203C2×Dic47—44no—
204C2×Dic47—44no—
205C2×Dic47—44no—
206C2×Dic47—44no—
207C2×Dic47—82no—
208C2×Dic47—82no—
209Dic94—84no—
210Dic94—84no—
211C2×#2062—471nomaximal, Sylow
212C22×C47—24no—
213C22×C47—28no—
214C22×C47—28no—
215C22×C47—24no—
216C22×C47—22no—
217C22×C47—21no—
218C22×C47—22no—
219C22×C47—21no—
220C22×C47—22no—
221C22×C47—21no—
222C22×C47—22no—
223C22×C47—21no—
224C22×C47—44no—
225C22×C47—42no—
226C22×C47—44no—
227C22×C47—42no—
228C22×C47—41no—
229C22×C47—42no—
230C22×C47—41no—
231C22×C47#39512yes—
232C22×C47#39514yes—
233C22×C47#39512yes—
234C22×C47B(4,𝔽2)12yes—
235C22×C47#45812yes—
236C22×C47C2×#12011yescharacteristic
237C22×C47C2×C22⋊Q812yes—
238C22×C47C2×C22⋊Q811yescharacteristic
239C22×C47C2×C4⋊Q812yes—
240C22×C47C2×C4⋊Q811yescharacteristic
241C4×C47—48no—
242C4×C47—42no—
243C4×C47—42no—
244Dic47—44no—
245Dic47—44no—
246Dic47—44no—
247Dic47—44no—
248C2×#543—471no—
249C2×#385—471no—
250C2×#385—472no—
251#2062—478no—
252C2×#342—472no—
253C2×#342D4711yescharacteristic
254C2×C47—21no—
255C2×C47—22no—
256C2×C47—22no—
257C2×C47—21no—
258C2×C47—22no—
259C2×C47—24no—
260C2×C47#206214yescomplemented
261C2×C47C2×#39511yescharacteristic
262C2×C47C2×B(4,𝔽2)11yescharacteristic
263C2×C47C2×#45811yescharacteristic
264C24×C4—471no—
265#543—474no—
266#543—944no—
267#543—942no—
268C2×C22⋊Q8—942no—
269C2×C22⋊Q8—942no—
270C2×C22⋊Q8—941no—
271C2×C22⋊Q8—941no—
272C22×C4⋊C4—942no—
273C22×C4⋊C4—941no—
274C22×C22⋊C4—471no—
275C22×C22⋊C4—472no—
276C22×C22⋊C4C2×D4711yescharacteristic
277C22×C22⋊C4C2×D4712yes—
278#385—474no—
279#385—478no—
280#385—944no—
281#385—942no—
282C2×#95—942no—
283C2×#95—941no—
284#342—478no—
285#342C2×D4714yes—
286C47C2×#206211yescharacteristic, complemented, Sylow
287C25C22×D4711yescharacteristic
288C22×Q8—941no—
289C22×Q8—941no—
290C23×C4—22no—
291C23×C4—472no—
292C23×C4—472no—
293C23×C4—472no—
294C23×C4—941no—
295C23×C4—941no—
296C23×C4—942no—
297C23×C4—941no—
298C23×C4—942no—
299C23×C4—1884no—
300C23×C4D18811yescharacteristic
301C23×C4D18811yescharacteristic
302C22⋊Q8—948no—
303C22⋊Q8—948no—
304C22⋊Q8—948no—
305C22⋊Q8—948no—
306C22⋊Q8—944no—
307C22⋊Q8—944no—
308C22⋊Q8—944no—
309C22⋊Q8—944no—
310C2×C4⋊C4—942no—
311C2×C4⋊C4—942no—
312C2×C4⋊C4—941no—
313C2×C4⋊C4—941no—
314C2×C4⋊C4—948no—
315C2×C4⋊C4—944no—
316C2×C4⋊C4—1884no—
317C2×C4⋊C4—1888no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—22no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—474no—
323C2×C22⋊C4—472no—
324C2×C22⋊C4—474no—
325C2×C22⋊C4—474no—
326C2×C22⋊C4—942no—
327C2×C22⋊C4—942no—
328C2×C22⋊C4—941no—
329C2×C22⋊C4—942no—
330C2×C22⋊C4—942no—
331C2×C22⋊C4—942no—
332C2×C22⋊C4Dic9418yescomplemented
333C2×C22⋊C4D18812yes—
334C2×C22⋊C4C22×D4712yes—
335C2×C22⋊C4C22×D4714yes—
336#95—948no—
337#95—944no—
338C24—42no—
339C24—42no—
340C24C2×Dic9414yes—
341C24C2×D18811yescharacteristic
342C24C2×D18811yescharacteristic
343C24D4×D4712yes—
344C24D4×D4712yes—
345C24#1062535212yes—
346C24Q8×D4712yes—
347C24C23×D4711yescharacteristic
348C2×Q8—944no—
349C2×Q8—944no—
350C2×Q8—3762no—
351C2×Q8—3762no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—28no—
355C22×C4—24no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—44no—
359C22×C4—44no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—474no—
363C22×C4—474no—
364C22×C4—942no—
365C22×C4—942no—
366C22×C4—944no—
367C22×C4—948no—
368C22×C4—942no—
369C22×C4—942no—
370C22×C4—944no—
371C22×C4—944no—
372C22×C4—942no—
373C22×C4—942no—
374C22×C4—1884no—
375C22×C4—1884no—
376C22×C4—1888no—
377C22×C4—1884no—
378C22×C4—1884no—
379C22×C4—1882no—
380C22×C4—1882no—
381C22×C4—1882no—
382C22×C4—1884no—
383C22×C4—1882no—
384C22×C4—1881no—
385C22×C4—1881no—
386C22×C4C2×D18812yes—
387C22×C4C2×D18812yes—
388C4⋊C4—948no—
389C4⋊C4—948no—
390C4⋊C4—944no—
391C4⋊C4—944no—
392C4⋊C4—1888no—
393C4⋊C4—18816no—
394C22⋊C4—24no—
395C22⋊C4—28no—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C22⋊C4—474no—
399C22⋊C4—944no—
400C22⋊C4—944no—
401C22⋊C4—944no—
402C22⋊C4—944no—
403C22⋊C4—944no—
404C22⋊C4—942no—
405C22⋊C4C2×Dic9418yescomplemented
406C23—22no—
407C23—24no—
408C23—22no—
409C23—24no—
410C23—41no—
411C23—42no—
412C23—41no—
413C23—48no—
414C23—41no—
415C23—42no—
416C23—44no—
417C23—44no—
418C23—41no—
419C23#1309399412yes—
420C23#1309399411yescharacteristic
421C23#1309399411yescharacteristic
422C23#1309400114yes—
423C23#1309400114yes—
424C23#1309400412yes—
425C23#1309400412yes—
426C23#1309402314yes—
427C23#1309402314yes—
428C23#1309402412yes—
429C23#1309402412yes—
430C23C2×D4×D4712yes—
431C23C22×D18811yescharacteristic
432C23C2×Q8×D4711yescharacteristic
433C23C22×Dic9412yes—
434C23C2×#1062535211yescharacteristic
435Q8—3764no—
436Q8—3764no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—28no—
440C2×C4—44no—
441C2×C4—416no—
442C2×C4—44no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—948no—
450C2×C4—944no—
451C2×C4—944no—
452C2×C4—944no—
453C2×C4—944no—
454C2×C4—3762no—
455C2×C4—3762no—
456C2×C4—1882no—
457C2×C4—1888no—
458C2×C4—1882no—
459C2×C4—1884no—
460C2×C4—1882no—
461C2×C4—1884no—
462C2×C4—1888no—
463C2×C4—1884no—
464C2×C4—1884no—
465C2×C4—1884no—
466C2×C4—1882no—
467C2×C4—1884no—
468C2×C4—1884no—
469C22—28no—
470C22—24no—
471C22—28no—
472C22—24no—
473C22—22no—
474C22—21no—
475C22—21no—
476C22—22no—
477C22—22no—
478C22—21no—
479C22—21no—
480C22—22no—
481C22—44no—
482C22—42no—
483C22—44no—
484C22—42no—
485C22—41no—
486C22—42no—
487C22—41no—
488C22#1568904414yes—
489C22#1568904412yes—
490C22#1568904412yes—
491C22#1568931112yes—
492C22#1568931412yes—
493C22C2×#1309399411yescharacteristic
494C22C2×#1309400112yes—
495C22C2×#1309400411yescharacteristic
496C22C2×#1309402312yes—
497C22C2×#1309402411yescharacteristic
498C4—48no—
499C4—42no—
500C4—42no—
501C4—1884no—
502C4—1884no—
503C4—1884no—
504C4—1884no—
505C2—22no—
506C2—21no—
507C2—24no—
508C2—22no—
509C2—22no—
510C2—21no—
511C2#2024474214yesdirect product factor
512C2C2×#1568904411yescharacteristic
513C2C2×#1568931111yescharacteristic
514C2C2×#1568931411yescharacteristic
subgroupG/H
centerC23#13093994
commutator, cosocleC24×C47C24
FrattiniC24C23×D47
FittingC2×C47×#342C2
socleC23×C47#120
prime radicalC25×C47C23
hypercenterC2×#342D47
hypocenterC47C2×#2062
LCSG ▷ C24×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
4. #20244742C2direct (N × H)
63. C2×C22⋊Dic47Q8semidirect
77. C2×C22⋊C4×C47Q8semidirect
134. C22⋊C4×C47C2×Q8semidirect
141. C22⋊Dic47C2×Q8semidirect
260. C2×C47#2062semidirect
286. C47C2×#2062semidirect
332. C2×C22⋊C4Dic94semidirect
405. C22⋊C4C2×Dic94semidirect
511. C2#20244742direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156897492
C2×#156889982
C2×#156889952
#202447422
C2×#156888892
C2×C47×#3422
C2×#206247