Finite Group Databasebeta

← C2×#20241719 #26182121

Subgroups — C2×#20241719 #26182121

Order 12032.

1326 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093980C211yesmaximal, characteristic
2C2×#15689177C212yesmaximal, complemented
3#20241719C218yesmaximal, direct product factor
4C2×#15688848C212yesmaximal, complemented
5C2×#15688847C211yesmaximal, characteristic
6C2×C47×#323C211yesmaximal, characteristic
7C24×Dic47C411yescharacteristic
8C2×#13093980—22no—
9C2×#13093980—22no—
10C2×#13093980—24no—
11C2×#13093980C414yes—
12C2×#13093980C2214yes—
13C22×Dic47⋊C4C411yescharacteristic
14C22×Dic47⋊C4C2211yescharacteristic
15C22×C22⋊Dic47C411yescharacteristic
16C22×C4×Dic47C411yescharacteristic
17C22×C4×Dic47C2211yescharacteristic
18#15689177—24no—
19#15689177C2218yescomplemented
20C2×Dic47⋊C8—22no—
21C2×C22⋊(C47⋊C8)C2212yes—
22C2×#13093934—22no—
23#15688848C2218yescomplemented
24#15688847C2214yes—
25C22×C22⋊C4×C47C2211yescharacteristic
26C2×C22⋊C8×C47C2212yes—
27C47×#323C2214yes—
28C23×Dic47—24no—
29C23×Dic47—22no—
30C23×Dic47—21no—
31C23×Dic47—21no—
32C23×Dic47—24no—
33C23×Dic47C2×C414yes—
34C23×Dic47C2×C411yescharacteristic
35C23×Dic47C2×C411yescharacteristic
36C23×Dic47C2×C411yescharacteristic
37C23×Dic47C2×C411yescharacteristic
38C22×C47⋊C8—22no—
39#13093980—28no—
40#13093980—28no—
41#13093980—28no—
42#13093980—28no—
43C2×Dic47⋊C4—22no—
44C2×Dic47⋊C4—22no—
45C2×Dic47⋊C4—22no—
46C2×Dic47⋊C4—22no—
47C2×Dic47⋊C4C2×C414yes—
48C2×Dic47⋊C4C2×C412yes—
49C2×Dic47⋊C4C2312yes—
50C2×C22⋊Dic47—22no—
51C2×C22⋊Dic47—22no—
52C2×C22⋊Dic47C2×C414yes—
53C2×C4×Dic47—22no—
54C2×C4×Dic47—21no—
55C2×C4×Dic47—21no—
56C2×C4×Dic47C2×C414yes—
57C2×C4×Dic47C2×C412yes—
58C2×C4×Dic47D412yes—
59C2×C4×Dic47D412yes—
60C2×C4×Dic47D414yes—
61C2×C4×Dic47C2312yes—
62Dic47⋊C8—28no—
63C22⋊(C47⋊C8)—22no—
64C22⋊(C47⋊C8)C2314yes—
65#13093934—28no—
66C25×C47C2×C411yescharacteristic
67C23×C4×C47C2×C411yescharacteristic
68C23×C4×C47C2311yescharacteristic
69C22×C8×C47—22no—
70C2×C22⋊C4×C47—22no—
71C2×C22⋊C4×C47—22no—
72C2×C22⋊C4×C47C2×C412yes—
73C2×C22⋊C4×C47C2312yes—
74C22⋊C8×C47—22no—
75C22⋊C8×C47C2314yes—
76C24×C47—21no—
77C24×C47—21no—
78C24×C47—22no—
79C24×C47—42no—
80C24×C47—42no—
81C24×C47M1614yes—
82C24×C47C22×C411yescharacteristic
83C24×C47C22×C412yes—
84C22×C4×C47—21no—
85C22×C4×C47—21no—
86C22×C4×C47—42no—
87C22×C4×C47—42no—
88C22×C4×C47C22×C412yes—
89C22×C4×C47C22×C411yescharacteristic
90C22×C4×C47C2×D412yes—
91C22×C4×C47C2×D412yes—
92C22×C4×C47C2411yescharacteristic
93C22×Dic47—216no—
94C22×Dic47—28no—
95C22×Dic47—28no—
96C22×Dic47—21no—
97C22×Dic47—21no—
98C22×Dic47—28no—
99C22×Dic47—22no—
100C22×Dic47—22no—
101C22×Dic47—22no—
102C22×Dic47—24no—
103C22×Dic47—24no—
104C22×Dic47—28no—
105C22×Dic47—21no—
106C22×Dic47—21no—
107C22×Dic47—42no—
108C22×Dic47—42no—
109C22×Dic47C22⋊C412yes—
110C22×Dic47C22⋊C411yescharacteristic
111C22×Dic47C22⋊C411yescharacteristic
112C22×Dic47C22⋊C412yes—
113C22×Dic47C22⋊C412yes—
114C22×Dic47M1614yes—
115C22×Dic47C22×C412yes—
116C22×Dic47C22×C412yes—
117C22×Dic47C22×C412yes—
118C22×Dic47C22×C412yes—
119C2×C8×C47—24no—
120C2×C8×C47—44no—
121C22⋊C4×C47—24no—
122C22⋊C4×C47—24no—
123C22⋊Dic47—28no—
124Dic47⋊C4—24no—
125Dic47⋊C4—24no—
126Dic47⋊C4—28no—
127C4×Dic47—24no—
128C4×Dic47—24no—
129C4×Dic47C22⋊C414yes—
130C4×Dic47C22⋊C414yes—
131C4×Dic47C2×D414yes—
132C4×Dic47C2×D414yes—
133C2×C47⋊C8—24no—
134C2×C47⋊C8—44no—
135C23×C47—22no—
136C23×C47—22no—
137C23×C47—22no—
138C23×C47—22no—
139C23×C47—24no—
140C23×C47—24no—
141C23×C47—48no—
142C23×C47—42no—
143C23×C47—42no—
144C23×C47—42no—
145C23×C47—42no—
146C23×C47—48no—
147C23×C47—42no—
148C23×C47—42no—
149C23×C47C2×C22⋊C411yescharacteristic
150C23×C47C2×C22⋊C411yescharacteristic
151C23×C47C2×M1612yes—
152C23×C47C2×M1612yes—
153C23×C47C2×M1614yes—
154C23×C47C23×C411yescharacteristic
155C2×C4×C47—24no—
156C2×C4×C47—22no—
157C2×C4×C47—41no—
158C2×C4×C47—42no—
159C2×C4×C47—41no—
160C2×C4×C47—42no—
161C2×C4×C47—42no—
162C2×C4×C47—42no—
163C2×C4×C47C2×C22⋊C412yes—
164C2×C4×C47C22×D412yes—
165C2×Dic47—216no—
166C2×Dic47—216no—
167C2×Dic47—22no—
168C2×Dic47—22no—
169C2×Dic47—22no—
170C2×Dic47—22no—
171C2×Dic47—24no—
172C2×Dic47—22no—
173C2×Dic47—22no—
174C2×Dic47—24no—
175C2×Dic47—24no—
176C2×Dic47—24no—
177C2×Dic47—22no—
178C2×Dic47—42no—
179C2×Dic47—42no—
180C2×Dic47—42no—
181C2×Dic47—42no—
182C2×Dic47—42no—
183C2×Dic47C2×C22⋊C412yes—
184C2×Dic47C2×C22⋊C412yes—
185C2×Dic47C2×C22⋊C414yes—
186C2×Dic47C2×M1614yes—
187C8×C47—44no—
188C47⋊C8—44no—
189C2×#1464—471nomaximal, Sylow
190C22×C47—21no—
191C22×C47—21no—
192C22×C47—21no—
193C22×C47—21no—
194C22×C47—24no—
195C22×C47—24no—
196C22×C47—24no—
197C22×C47—44no—
198C22×C47—44no—
199C22×C47—48no—
200C22×C47—42no—
201C22×C47—42no—
202C22×C47—48no—
203C22×C47#40712yes—
204C22×C47#40712yes—
205C22×C47#41012yes—
206C22×C47#41312yes—
207C22×C47C22×C22⋊C411yescharacteristic
208C22×C47C22×M1611yescharacteristic
209C22×C47C22×M1611yescharacteristic
210C4×C47—22no—
211C4×C47—22no—
212C4×C47—42no—
213Dic47—22no—
214Dic47—22no—
215Dic47—24no—
216Dic47—24no—
217Dic47—42no—
218C22×#117—471no—
219C2×#432—472no—
220#1464—478no—
221C2×#324—472no—
222C2×#323—471no—
223C2×#323D4711yescharacteristic
224C2×C47—21no—
225C2×C47—21no—
226C2×C47—22no—
227C2×C47—44no—
228C2×C47#146414yescomplemented
229C2×C47C2×#40711yescharacteristic
230C2×C47C2×#41011yescharacteristic
231C2×C47C2×#41311yescharacteristic
232C24×C4—471no—
233C2×#117—474no—
234C2×#117—474no—
235C2×#117—942no—
236C2×#117—942no—
237C2×#117—944no—
238C22×C4⋊C4—471no—
239C22×C4⋊C4—471no—
240C22×C22⋊C4—471no—
241C22×C22⋊C4C2×D4711yescharacteristic
242C22×C42—471no—
243C22×C42—471no—
244#432—478no—
245#432—944no—
246C2×C4⋊C8—942no—
247C2×C22⋊C8—472no—
248C2×C22⋊C8C2×D4712yes—
249C2×#97—942no—
250#324—478no—
251#323—474no—
252#323C2×D4714yes—
253C47C2×#146411yescharacteristic, complemented, Sylow
254C25C4×D4711yescharacteristic
255C23×C4—471no—
256C23×C4—471no—
257C23×C4—471no—
258C23×C4—474no—
259C23×C4—471no—
260C23×C4—942no—
261C23×C4—941no—
262C23×C4—941no—
263C23×C4—944no—
264C23×C4—944no—
265C23×C4C4×D4711yescharacteristic
266C23×C4C22×D4711yescharacteristic
267C22×C8—22no—
268C22×C8—942no—
269#117—948no—
270#117—948no—
271#117—948no—
272#117—948no—
273C2×C4⋊C4—474no—
274C2×C4⋊C4—472no—
275C2×C4⋊C4—472no—
276C2×C4⋊C4—942no—
277C2×C4⋊C4—942no—
278C2×C4⋊C4—942no—
279C2×C4⋊C4—942no—
280C2×C22⋊C4—22no—
281C2×C22⋊C4—22no—
282C2×C22⋊C4—474no—
283C2×C22⋊C4—942no—
284C2×C22⋊C4—942no—
285C2×C22⋊C4C4×D4712yes—
286C2×C22⋊C4C22×D4712yes—
287C2×C42—472no—
288C2×C42—472no—
289C2×C42—472no—
290C2×C42—474no—
291C2×C42—472no—
292C2×C42—474no—
293C2×C42—942no—
294C2×C42—941no—
295C2×C42—941no—
296C4⋊C8—948no—
297C22⋊C8—22no—
298C22⋊C8—474no—
299C22⋊C8—942no—
300C22⋊C8C22×D4714yes—
301#97—948no—
302C24—21no—
303C24—21no—
304C24—22no—
305C24—42no—
306C24—42no—
307C24#1062532414yes—
308C24C2×C4×D4711yescharacteristic
309C24C2×C4×D4712yes—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—42no—
313C22×C4—42no—
314C22×C4—472no—
315C22×C4—471no—
316C22×C4—471no—
317C22×C4—472no—
318C22×C4—474no—
319C22×C4—472no—
320C22×C4—472no—
321C22×C4—472no—
322C22×C4—472no—
323C22×C4—472no—
324C22×C4—944no—
325C22×C4—944no—
326C22×C4—948no—
327C22×C4—9416no—
328C22×C4—948no—
329C22×C4—948no—
330C22×C4—941no—
331C22×C4—941no—
332C22×C4—942no—
333C22×C4—948no—
334C22×C4—942no—
335C22×C4—942no—
336C22×C4—941no—
337C22×C4—941no—
338C22×C4—1882no—
339C22×C4—1882no—
340C22×C4C2×C4×D4712yes—
341C22×C4C2×C4×D4711yescharacteristic
342C22×C4D4×D4712yes—
343C22×C4D4×D4712yes—
344C22×C4C23×D4711yescharacteristic
345C2×C8—24no—
346C2×C8—44no—
347C2×C8—944no—
348C2×C8—1884no—
349C4⋊C4—948no—
350C4⋊C4—944no—
351C4⋊C4—944no—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—948no—
355C42—474no—
356C42—474no—
357C42—474no—
358C42—474no—
359C42—944no—
360C42—944no—
361C23—22no—
362C23—22no—
363C23—22no—
364C23—24no—
365C23—24no—
366C23—22no—
367C23—48no—
368C23—42no—
369C23—42no—
370C23—48no—
371C23—42no—
372C23—42no—
373C23—42no—
374C23—42no—
375C23C22⋊C4×D4711yescharacteristic
376C23C22⋊C4×D4711yescharacteristic
377C23M16×D4712yes—
378C23C2×#1062532412yes—
379C23C2×#1062532414yes—
380C23C22×C4×D4711yescharacteristic
381C2×C4—24no—
382C2×C4—22no—
383C2×C4—41no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—472no—
390C2×C4—472no—
391C2×C4—474no—
392C2×C4—474no—
393C2×C4—9416no—
394C2×C4—9416no—
395C2×C4—942no—
396C2×C4—944no—
397C2×C4—944no—
398C2×C4—942no—
399C2×C4—942no—
400C2×C4—944no—
401C2×C4—944no—
402C2×C4—942no—
403C2×C4—942no—
404C2×C4—942no—
405C2×C4—942no—
406C2×C4—1882no—
407C2×C4—1882no—
408C2×C4—1882no—
409C2×C4—1882no—
410C2×C4—1882no—
411C2×C4C22⋊C4×D4712yes—
412C2×C4C2×D4×D4712yes—
413C8—44no—
414C8—1884no—
415C22—24no—
416C22—24no—
417C22—21no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—24no—
422C22—44no—
423C22—48no—
424C22—44no—
425C22—48no—
426C22—42no—
427C22—42no—
428C22#1568908512yes—
429C22#1568908512yes—
430C22#1568909512yes—
431C22#1568910412yes—
432C22C2×C22⋊C4×D4711yescharacteristic
433C22C2×M16×D4711yescharacteristic
434C22C22×#1062532411yescharacteristic
435C4—22no—
436C4—22no—
437C4—42no—
438C4—942no—
439C4—942no—
440C4—944no—
441C4—944no—
442C4—1882no—
443C2—22no—
444C2—21no—
445C2—21no—
446C2—44no—
447C2#2024171914yesdirect product factor
448C2C2×#1568908511yescharacteristic
449C2C2×#1568909511yescharacteristic
450C2C2×#1568910411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#323C2
socleC23×C47C2×C22⋊C4
prime radicalC25×C47C2×C4
cosocleC22×C4×C47C24
hypercenterC2×#323D47
hypocenterC47C2×#1464
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×#15689177C2semidirect
3. #20241719C2direct (N × H)
4. C2×#15688848C2semidirect
19. #15689177C22semidirect
23. #15688848C22semidirect
228. C2×C47#1464semidirect
253. C47C2×#1464semidirect
447. C2#20241719direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130939802
C2×#156891772
#202417192
C2×#156888482
C2×#156888472
C2×C47×#3232
C2×#146447