Finite Group Databasebeta

← C2×#20242310 #26188353

Subgroups — C2×#20242310 #26188353

Order 12032.

1696 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1696 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689749C211yesmaximal, characteristic, complemented
2C2×#15689274C212yesmaximal, complemented
3#20242310C218yesmaximal, direct product factor
4C2×#15688859C212yesmaximal, complemented
5C2×#15688847C211yesmaximal, characteristic, complemented
6C2×C47×#392C211yesmaximal, characteristic
7C22×#10625335—22no—
8#15689749—24no—
9#15689749—22no—
10#15689749C2214yescomplemented
11C2×#13094003—21no—
12C2×#13094003C2212yes—
13C2×#13094001—22no—
14C2×#13094001—22no—
15C22×C22⋊Dic47—21no—
16#15689274—24no—
17#15689274C2218yescomplemented
18C2×#13093945—22no—
19C2×C22⋊(C47⋊C8)C2212yes—
20#15688859C2218yescomplemented
21#15688847C2214yescomplemented
22C23×D4×C47—21no—
23C23×D4×C47C2211yescharacteristic
24C22×C22⋊C4×C47—21no—
25C22×C22⋊C4×C47C2211yescharacteristic
26C47×#392—22no—
27C47×#392C2214yes—
28C2×#95×C47C2211yescharacteristic
29C22×Dic94—21no—
30C22×Dic94D412yescomplemented
31C23×Dic47—21no—
32C23×Dic47—21no—
33C2×#10625335—28no—
34C2×#10625335—48no—
35C22×C47⋊C8—22no—
36#13094003—24no—
37#13094003—22no—
38#13094003—22no—
39#13094003—24no—
40#13094003D414yescomplemented
41#13094003C2314yes—
42#13094001—28no—
43#13094001—28no—
44#13094001—28no—
45#13094001—28no—
46C2×C4⋊Dic47—21no—
47C2×C4⋊Dic47D412yescomplemented
48C2×Dic47⋊C4—22no—
49C2×Dic47⋊C4—22no—
50C2×C22⋊Dic47—24no—
51C2×C22⋊Dic47—22no—
52C2×C22⋊Dic47—24no—
53C2×C22⋊Dic47—22no—
54#13093945—28no—
55C22⋊(C47⋊C8)—22no—
56C22⋊(C47⋊C8)C2314yes—
57C25×C47—21no—
58C25×C47D411yescharacteristic
59C22×D4×C47—24no—
60C22×D4×C47—22no—
61C22×D4×C47—22no—
62C22×D4×C47—21no—
63C22×D4×C47—44no—
64C22×D4×C47—44no—
65C22×D4×C47—44no—
66C22×D4×C47—44no—
67C22×D4×C47C2312yes—
68C23×C4×C47—21no—
69C23×C4×C47D411yescharacteristic
70C23×C4×C47C2311yescharacteristic
71C2×C22⋊C4×C47—22no—
72C2×C22⋊C4×C47—22no—
73C2×C22⋊C4×C47—24no—
74C2×C22⋊C4×C47—44no—
75C2×C22⋊C4×C47D412yes—
76C2×C22⋊C4×C47C2312yes—
77#95×C47—21no—
78#95×C47C2312yes—
79C24×C47—21no—
80C24×C47—21no—
81C24×C47—22no—
82C24×C47—24no—
83C24×C47—22no—
84C24×C47—42no—
85C24×C47—42no—
86C24×C47—42no—
87C24×C47—42no—
88C24×C47—42no—
89C24×C47—41no—
90C24×C47—41no—
91C24×C47—42no—
92C24×C47—42no—
93C24×C47SD1614yescomplemented
94C24×C47C2×D411yescharacteristic
95C24×C47C2×D412yes—
96C2×D4×C47—28no—
97C2×D4×C47—24no—
98C2×D4×C47—44no—
99C2×D4×C47—48no—
100C2×D4×C47—44no—
101C2×D4×C47—48no—
102C2×D4×C47—44no—
103C2×D4×C47—48no—
104C2×D4×C47—432no—
105C2×D4×C47—48no—
106C2×D4×C47—42no—
107C22×C4×C47—24no—
108C22×C4×C47—21no—
109C22×C4×C47—22no—
110C22×C4×C47—21no—
111C22×C4×C47—42no—
112C22×C4×C47—42no—
113C22×C4×C47—42no—
114C22×C4×C47—42no—
115C22×C4×C47C2×D412yes—
116C22×C4×C47C2×D412yes—
117C22×C4×C47C2×D411yescharacteristic
118C22×C4×C47C2×D412yes—
119C22×C4×C47C2411yescharacteristic
120C22×Dic47—22no—
121C22×Dic47—22no—
122C22×Dic47—24no—
123C22×Dic47—24no—
124C22×Dic47—82no—
125C22×Dic47—82no—
126C2×Dic94—24no—
127C2×Dic94—22no—
128C2×Dic94—44no—
129C2×Dic94—82no—
130C2×Dic94C2×D414yescomplemented
131C22⋊C4×C47—24no—
132C22⋊C4×C47—24no—
133C22⋊C4×C47—48no—
134C22⋊Dic47—28no—
135C22⋊Dic47—24no—
136C22⋊Dic47—24no—
137#10625335—416no—
138C4⋊Dic47—24no—
139C4⋊Dic47—22no—
140C4⋊Dic47C2×D414yescomplemented
141Dic47⋊C4—28no—
142Dic47⋊C4—24no—
143Dic47⋊C4—24no—
144C2×C47⋊C8—24no—
145C2×C47⋊C8—44no—
146C23×C47—22no—
147C23×C47—22no—
148C23×C47—22no—
149C23×C47—24no—
150C23×C47—22no—
151C23×C47—24no—
152C23×C47—24no—
153C23×C47—48no—
154C23×C47—42no—
155C23×C47—42no—
156C23×C47—42no—
157C23×C47—48no—
158C23×C47—42no—
159C23×C47—42no—
160C23×C47—44no—
161C23×C47—48no—
162C23×C47—42no—
163C23×C47—42no—
164C23×C47—42no—
165C23×C47—42no—
166C23×C47—42no—
167C23×C47—44no—
168C23×C47—84no—
169C23×C47—81no—
170C23×C47—81no—
171C23×C47—84no—
172C23×C47—84no—
173C23×C47—82no—
174C23×C47—82no—
175C23×C47—82no—
176C23×C47—82no—
177C23×C47#12011yescharacteristic
178C23×C47#12011yescharacteristic
179C23×C47C2×SD1612yes—
180C23×C47C2×SD1614yescomplemented
181C23×C47#13712yes—
182C23×C47C22×D411yescharacteristic
183D4×C47—28no—
184D4×C47—44no—
185D4×C47—48no—
186D4×C47—432no—
187C2×C4×C47—24no—
188C2×C4×C47—24no—
189C2×C4×C47—22no—
190C2×C4×C47—42no—
191C2×C4×C47—41no—
192C2×C4×C47—41no—
193C2×C4×C47—48no—
194C2×C4×C47—42no—
195C2×C4×C47—42no—
196C2×C4×C47—42no—
197C2×C4×C47—42no—
198C2×C4×C47—81no—
199C2×C4×C47#12012yes—
200C2×C4×C47C22×D412yes—
201C2×Dic47—24no—
202C2×Dic47—24no—
203C2×Dic47—44no—
204C2×Dic47—44no—
205C2×Dic47—84no—
206C2×Dic47—84no—
207Dic94—44no—
208Dic94—82no—
209Dic94—84no—
210C47⋊C8—44no—
211C2×#1596—471nomaximal, Sylow
212C22×C47—24no—
213C22×C47—24no—
214C22×C47—21no—
215C22×C47—21no—
216C22×C47—21no—
217C22×C47—21no—
218C22×C47—24no—
219C22×C47—44no—
220C22×C47—44no—
221C22×C47—44no—
222C22×C47—48no—
223C22×C47—42no—
224C22×C47—42no—
225C22×C47—44no—
226C22×C47—82no—
227C22×C47—84no—
228C22×C47—82no—
229C22×C47—82no—
230C22×C47—88no—
231C22×C47—88no—
232C22×C47—82no—
233C22×C47—82no—
234C22×C47#44812yes—
235C22×C47#44812yes—
236C22×C47#45312yes—
237C22×C47B(4,𝔽2)12yes—
238C22×C47C2×#12011yescharacteristic
239C22×C47C22×SD1611yescharacteristic
240C22×C47C2×#13711yescharacteristic
241C4×C47—22no—
242C4×C47—22no—
243C4×C47—44no—
244C4×C47—42no—
245Dic47—44no—
246Dic47—44no—
247C2×#543—471no—
248C2×#450—472no—
249C2×#392D4711yescharacteristic
250#1596—478no—
251C2×#328—472no—
252C2×#323—471no—
253C2×C47—21no—
254C2×C47—21no—
255C2×C47—22no—
256C2×C47—44no—
257C2×C47—84no—
258C2×C47#159614yescomplemented
259C2×C47C2×#44811yescharacteristic
260C2×C47C2×#45311yescharacteristic
261C2×C47C2×B(4,𝔽2)11yescharacteristic
262C23×D4—21no—
263C23×D4C2×D4711yescharacteristic
264C22×SD16—942no—
265#543—474no—
266#543—944no—
267#543—942no—
268C2×C22⋊Q8—472no—
269C2×C22⋊Q8—942no—
270C2×C22⋊Q8—942no—
271C2×C22⋊Q8—941no—
272C22×C22⋊C4—21no—
273C22×C22⋊C4—941no—
274C22×C22⋊C4C2×D4711yescharacteristic
275#450—478no—
276#450—944no—
277C2×#102—942no—
278C2×C22⋊C8—472no—
279#392—22no—
280#392C2×D4714yes—
281C2×#95C2×D4711yescharacteristic
282#328—478no—
283#323—474no—
284C47C2×#159611yescharacteristic, complemented, Sylow
285C25—21no—
286C25C22⋊D4711yescharacteristic
287C22×Q8—472no—
288C22×Q8—941no—
289C22×D4—24no—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—21no—
293C22×D4—44no—
294C22×D4—44no—
295C22×D4—44no—
296C22×D4—44no—
297C22×D4C22×D4712yes—
298C23×C4—21no—
299C23×C4—941no—
300C23×C4—941no—
301C23×C4C22⋊D4711yescharacteristic
302C23×C4C22×D4711yescharacteristic
303C2×SD16—948no—
304C2×SD16—1888no—
305C22×C8—942no—
306C22⋊Q8—474no—
307C22⋊Q8—474no—
308C22⋊Q8—948no—
309C22⋊Q8—948no—
310C22⋊Q8—948no—
311C22⋊Q8—948no—
312C22⋊Q8—944no—
313C22⋊Q8—942no—
314C22⋊Q8—942no—
315C22⋊Q8—944no—
316C2×C4⋊C4—472no—
317C2×C4⋊C4—942no—
318C2×C4⋊C4—941no—
319C2×C4⋊C4—942no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—24no—
323C2×C22⋊C4—44no—
324C2×C22⋊C4—942no—
325C2×C22⋊C4—944no—
326C2×C22⋊C4—942no—
327C2×C22⋊C4—944no—
328C2×C22⋊C4C22⋊D4712yes—
329C2×C22⋊C4C22×D4712yes—
330#102—948no—
331C22⋊C8—474no—
332C22⋊C8—942no—
333#95—21no—
334#95C22×D4712yes—
335C24—21no—
336C24—21no—
337C24—22no—
338C24—24no—
339C24—22no—
340C24—42no—
341C24—42no—
342C24—42no—
343C24—42no—
344C24—42no—
345C24—41no—
346C24—41no—
347C24—42no—
348C24—42no—
349C24#1062533514yescomplemented
350C24C2×C22⋊D4711yescharacteristic
351C24C2×C22⋊D4712yes—
352C2×Q8—474no—
353C2×Q8—944no—
354C2×Q8—942no—
355C2×Q8—3762no—
356C2×Q8—1884no—
357C2×D4—28no—
358C2×D4—24no—
359C2×D4—44no—
360C2×D4—48no—
361C2×D4—44no—
362C2×D4—48no—
363C2×D4—44no—
364C2×D4—48no—
365C2×D4—432no—
366C2×D4—48no—
367C2×D4—42no—
368C22×C4—24no—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—21no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—944no—
377C22×C4—944no—
378C22×C4—942no—
379C22×C4—942no—
380C22×C4—3762no—
381C22×C4—3762no—
382C22×C4D4×D4712yes—
383C22×C4D4×D4712yes—
384C22×C4C2×C22⋊D4712yes—
385C22×C4C2×C22⋊D4711yescharacteristic
386C22×C4C23×D4711yescharacteristic
387SD16—18816no—
388C2×C8—944no—
389C2×C8—1884no—
390C4⋊C4—474no—
391C4⋊C4—948no—
392C4⋊C4—944no—
393C4⋊C4—944no—
394C4⋊C4—942no—
395C4⋊C4—944no—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C22⋊C4—48no—
399C22⋊C4—948no—
400C22⋊C4—944no—
401C22⋊C4—944no—
402C23—22no—
403C23—22no—
404C23—24no—
405C23—22no—
406C23—24no—
407C23—22no—
408C23—24no—
409C23—48no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—42no—
414C23—42no—
415C23—44no—
416C23—48no—
417C23—48no—
418C23—42no—
419C23—42no—
420C23—44no—
421C23—42no—
422C23—42no—
423C23—42no—
424C23—81no—
425C23—81no—
426C23—84no—
427C23—82no—
428C23—84no—
429C23—84no—
430C23—82no—
431C23—82no—
432C23—82no—
433C23#1309399211yescharacteristic
434C23#1309399211yescharacteristic
435C23C2×#1062533512yes—
436C23C2×#1062533514yescomplemented
437C23#1309405412yes—
438C23C22×C22⋊D4711yescharacteristic
439Q8—3762no—
440Q8—3764no—
441Q8—1884no—
442D4—28no—
443D4—44no—
444D4—48no—
445D4—432no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—22no—
449C2×C4—42no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—48no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—81no—
458C2×C4—944no—
459C2×C4—944no—
460C2×C4—3764no—
461C2×C4—3764no—
462C2×C4—1884no—
463C2×C4—1884no—
464C2×C4#1309399212yes—
465C2×C4C2×D4×D4712yes—
466C8—1884no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—24no—
472C22—24no—
473C22—24no—
474C22—44no—
475C22—44no—
476C22—44no—
477C22—42no—
478C22—42no—
479C22—48no—
480C22—44no—
481C22—82no—
482C22—84no—
483C22—82no—
484C22—82no—
485C22—88no—
486C22—82no—
487C22—88no—
488C22—82no—
489C22#1568926112yes—
490C22#1568926112yes—
491C22#1568929012yes—
492C22#1568930912yes—
493C22C2×#1309399211yescharacteristic
494C22C22×#1062533511yescharacteristic
495C22C2×#1309405411yescharacteristic
496C4—22no—
497C4—22no—
498C4—44no—
499C4—42no—
500C4—1884no—
501C4—1884no—
502C2—21no—
503C2—21no—
504C2—22no—
505C2—44no—
506C2—84no—
507C2#2024231014yesdirect product factor
508C2C2×#1568926111yescharacteristic
509C2C2×#1568929011yescharacteristic
510C2C2×#1568930911yescharacteristic
subgroupG/H
centerC23#13093992
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
Fitting, prime radicalC2×C47×#392C2
socleC23×C47#120
hypercenterC2×#392D47
hypocenterC47C2×#1596
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×#15689749C2semidirect
2. C2×#15689274C2semidirect
3. #20242310C2direct (N × H)
4. C2×#15688859C2semidirect
5. C2×#15688847C2semidirect
10. #15689749C22semidirect
17. #15689274C22semidirect
20. #15688859C22semidirect
21. #15688847C22semidirect
30. C22×Dic94D4semidirect
40. #13094003D4semidirect
47. C2×C4⋊Dic47D4semidirect
93. C24×C47SD16semidirect
130. C2×Dic94C2×D4semidirect
140. C4⋊Dic47C2×D4semidirect
180. C23×C47C2×SD16semidirect
258. C2×C47#1596semidirect
284. C47C2×#1596semidirect
349. C24#10625335semidirect
436. C23C2×#10625335semidirect
507. C2#20242310direct (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×#156892742
#202423102
C2×#156888592
C2×#156888472
C2×C47×#3922
C2×#159647