Finite Group Databasebeta

← #26379111

Subgroups — #26379111

Order 12032.

2486 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246562C214yesmaximal, complemented
2#20246500C214yesmaximal, complemented
3#20246237C218yesmaximal, complemented
4#20246203C218yesmaximal, complemented
5#20245974C212yesmaximal, complemented
6#20245966C212yesmaximal
7#20245786C212yesmaximal, complemented
8C22×#124×C47C211yesmaximal, characteristic
9C2×#13093983C2214yes—
10C22×C22⋊Dic47C2214yes—
11#15689030C2218yescomplemented
12#15689030C2218yescomplemented
13#15689016C22116yescomplemented
14#15689016C22116yescomplemented
15#15689003C2218yes—
16#15689003C2218yes—
17#15688998C22116yescomplemented
18#15688991C2214yescomplemented
19#15688989C2214yescomplemented
20#15688986C2214yes—
21#15688986C2214yes—
22#15688983C2214yes—
23#15688979C2214yes—
24C4×C4⋊Dic47C2214yescomplemented
25C22⋊C4×Dic47C22116yescomplemented
26C4×C22⋊Dic47C2214yes—
27#15688969C2214yescomplemented
28C23×Q8×C47C2211yescharacteristic
29C23×D4×C47C2211yescharacteristic
30C2×#124×C47C4116yescomplemented
31C2×#124×C47C2212yes—
32C2×#124×C47C2214yes—
33C2×#124×C47C2212yes—
34C22×C22⋊C4×C47C2214yes—
35C22×C42×C47C2211yescharacteristic
36C23×Dic47C2318yes—
37#13093983—48no—
38C2×C4⋊Dic47C2318yes—
39C2×C4⋊Dic47C2318yes—
40C2×C22⋊Dic47—48no—
41C2×C22⋊Dic47C2318yes—
42C2×C22⋊Dic47C23116yes—
43C2×C22⋊Dic47C2318yes—
44C2×C4×Dic47C2318yes—
45C2×C4×Dic47C2318yes—
46C47⋊#95C2318yes—
47C47⋊#95C2318yes—
48C47⋊#95C2318yes—
49C47⋊#95C23116yes—
50C47⋊#95C2318yes—
51C25×C47C2312yes—
52C22×Q8×C47—44no—
53C22×Q8×C47C2×C418yescomplemented
54C22×Q8×C47C2312yes—
55C22×Q8×C47C2312yes—
56C22×D4×C47—44no—
57C22×D4×C47C2×C418yes—
58C22×D4×C47C2312yes—
59C22×D4×C47C2312yes—
60C23×C4×C47C2311yescharacteristic
61C23×C4×C47C2312yes—
62C23×C4×C47C2312yes—
63#124×C47C2×C4116yescomplemented
64#124×C47C2×C4132yescomplemented
65#124×C47C2×C4116yescomplemented
66C2×C22⋊C4×C47C2×C4132yescomplemented
67C2×C22⋊C4×C47C2318yes—
68C2×C22⋊C4×C47C2318yes—
69C2×C42×C47C2×C418yescomplemented
70C2×C42×C47C2311yescharacteristic
71C2×C42×C47C2312yes—
72C2×C42×C47C2311yescharacteristic
73C24×C47—28no—
74C24×C47—48no—
75C24×C47C22×C418yes—
76C24×C47C2414yes—
77C24×C47C2411yescharacteristic
78C2×Q8×C47—416no—
79C2×Q8×C47—42no—
80C2×Q8×C47—44no—
81C2×Q8×C47—42no—
82C2×Q8×C47C22×C418yes—
83C2×Q8×C47C22×C418yes—
84C2×D4×C47—416no—
85C2×D4×C47—42no—
86C2×D4×C47—44no—
87C2×D4×C47—42no—
88C2×D4×C47C22×C418yes—
89C2×D4×C47C22×C418yes—
90C22×C4×C47—24no—
91C22×C4×C47—28no—
92C22×C4×C47—44no—
93C22×C4×C47C22×C414yes—
94C22×C4×C47C22×C418yes—
95C22×C4×C47C22×C418yes—
96C22×C4×C47C2412yes—
97C22×C4×C47C2412yes—
98C22×C4×C47C2411yescharacteristic
99C22×C4×C47C2411yescharacteristic
100C22×C4×C47C2414yes—
101C22×Dic47—48no—
102C22×Dic47—416no—
103C22×Dic47C24116yes—
104C22⋊C4×C47C22×C4132yes—
105C22⋊C4×C47C22×C4132yes—
106C42×C47C22×C414yes—
107C42×C47C22×C418yes—
108C42×C47C22×C414yes—
109C22⋊Dic47—216no—
110C22⋊Dic47—48no—
111C22⋊Dic47—416no—
112C4⋊Dic47—48no—
113C4⋊Dic47—48no—
114C4×Dic47—48no—
115C4×Dic47—48no—
116C23×C47—24no—
117C23×C47—24no—
118C23×C47—24no—
119C23×C47—216no—
120C23×C47—216no—
121C23×C47—416no—
122C23×C47—816no—
123C23×C47C23×C418yes—
124C23×C47C23×C412yes—
125C23×C47H(5,𝔽2)14yes—
126C23×C47C2511yescharacteristic
127Q8×C47—48no—
128Q8×C47—48no—
129D4×C47—48no—
130D4×C47—48no—
131C2×C4×C47—28no—
132C2×C4×C47—216no—
133C2×C4×C47—24no—
134C2×C4×C47—24no—
135C2×C4×C47—22no—
136C2×C4×C47—22no—
137C2×C4×C47—24no—
138C2×C4×C47—24no—
139C2×C4×C47—48no—
140C2×C4×C47C23×C414yes—
141C2×C4×C47C23×C414yes—
142C2×C4×C47C23×C412yes—
143C2×C4×C47C23×C412yes—
144C2×C4×C47C23×C418yes—
145C2×Dic47—216no—
146C2×Dic47—216no—
147C2×Dic47—216no—
148C2×Dic47—816no—
149#34366—471nomaximal, Sylow
150C22×C47—24no—
151C22×C47—28no—
152C22×C47—28no—
153C22×C47—216no—
154C22×C47—48no—
155C22×C47—48no—
156C22×C47—816no—
157C22×C47#51814yes—
158C22×C47C24×C411yescharacteristic
159C22×C47C2×H(5,𝔽2)12yes—
160C22×C47#58514yes—
161C4×C47—22no—
162C4×C47—22no—
163C4×C47—28no—
164C4×C47—24no—
165C4×C47—24no—
166Dic47—416no—
167C22×#124D4711yescharacteristic
168#2379—474no—
169#2372—474no—
170#2342—478no—
171#2337—478no—
172#2310—472no—
173#2308—472no—
174#2283—472no—
175C2×C47—24no—
176C2×C47—48no—
177C2×C47C2×#51811yescharacteristic
178C2×C47#342812yes—
179C2×C47#354514yes—
180C23×Q8C2×D4711yescharacteristic
181C23×D4C2×D4711yescharacteristic
182C2×#124Dic47116yescomplemented
183C2×#124C2×D4714yes—
184C2×#124C2×D4712yes—
185C2×#124C2×D4712yes—
186C2×#117—474no—
187C22×C22⋊C4—474no—
188C22×C22⋊C4C2×D4714yes—
189C22×C42C2×D4711yescharacteristic
190#391—478no—
191#391—478no—
192#388—4716no—
193#388—4716no—
194#386—478no—
195#386—478no—
196#385—4716no—
197#383—474no—
198#382—474no—
199#381—474no—
200#381—474no—
201#380—474no—
202#379—474no—
203C4×C4⋊C4—474no—
204C4×C22⋊C4—474no—
205C4×C22⋊C4—4716no—
206#376—474no—
207C47#3436611yescharacteristic, complemented, Sylow
208C25C22×D4712yes—
209C22×Q8—44no—
210C22×Q8C2×Dic4718yescomplemented
211C22×Q8C22×D4712yes—
212C22×Q8C22×D4712yes—
213C22×D4—44no—
214C22×D4C2×Dic4718yes—
215C22×D4C22×D4712yes—
216C22×D4C22×D4712yes—
217C23×C4—478no—
218C23×C4C22×D4712yes—
219C23×C4C22×D4711yescharacteristic
220C23×C4C22×D4712yes—
221#124C2×Dic47132yescomplemented
222#124C2×Dic47116yescomplemented
223#124C2×Dic47116yescomplemented
224#117—1888no—
225C2×C4⋊C4—478no—
226C2×C4⋊C4—478no—
227C2×C22⋊C4—478no—
228C2×C22⋊C4—478no—
229C2×C22⋊C4—4716no—
230C2×C22⋊C4—1888no—
231C2×C22⋊C4C2×Dic47132yescomplemented
232C2×C22⋊C4C22×D4718yes—
233C2×C22⋊C4C22×D4718yes—
234C2×C42—478no—
235C2×C42—478no—
236C2×C42C2×Dic4718yescomplemented
237C2×C42C22×D4711yescharacteristic
238C2×C42C22×D4712yes—
239C2×C42C22×D4711yescharacteristic
240#95—478no—
241#95—478no—
242#95—4716no—
243#95—478no—
244#95—478no—
245C24—28no—
246C24—48no—
247C24C22×Dic4718yes—
248C24C23×D4714yes—
249C24C23×D4711yescharacteristic
250C2×Q8—416no—
251C2×Q8—42no—
252C2×Q8—44no—
253C2×Q8—42no—
254C2×Q8C22×Dic4718yes—
255C2×Q8C22×Dic4718yes—
256C2×D4—416no—
257C2×D4—42no—
258C2×D4—44no—
259C2×D4—42no—
260C2×D4C22×Dic4718yes—
261C2×D4C22×Dic4718yes—
262C22×C4—28no—
263C22×C4—24no—
264C22×C4—44no—
265C22×C4—4716no—
266C22×C4—1888no—
267C22×C4—18816no—
268C22×C4C22×Dic4714yes—
269C22×C4C22×Dic4718yes—
270C22×C4C22×Dic4718yes—
271C22×C4C23×D4711yescharacteristic
272C22×C4C23×D4711yescharacteristic
273C22×C4C23×D4712yes—
274C22×C4C23×D4714yes—
275C22×C4C23×D4712yes—
276C4⋊C4—1888no—
277C4⋊C4—1888no—
278C22⋊C4—9416no—
279C22⋊C4—18816no—
280C22⋊C4—1888no—
281C22⋊C4C22×Dic47132yes—
282C22⋊C4C22×Dic47132yes—
283C42—1888no—
284C42—1888no—
285C42C22×Dic4714yes—
286C42C22×Dic4718yes—
287C42C22×Dic4714yes—
288C23—24no—
289C23—24no—
290C23—24no—
291C23—216no—
292C23—216no—
293C23—416no—
294C23—816no—
295C23C23×Dic4718yes—
296C23C23×Dic4712yes—
297C23#1309406914yes—
298C23C24×D4711yescharacteristic
299Q8—48no—
300Q8—48no—
301D4—48no—
302D4—48no—
303C2×C4—28no—
304C2×C4—216no—
305C2×C4—24no—
306C2×C4—24no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—24no—
310C2×C4—24no—
311C2×C4—48no—
312C2×C4—9416no—
313C2×C4—9416no—
314C2×C4—9416no—
315C2×C4—37616no—
316C2×C4C23×Dic4714yes—
317C2×C4C23×Dic4714yes—
318C2×C4C23×Dic4712yes—
319C2×C4C23×Dic4712yes—
320C2×C4C23×Dic4718yes—
321C22—24no—
322C22—28no—
323C22—28no—
324C22—216no—
325C22—48no—
326C22—48no—
327C22—816no—
328C22#1568959814yes—
329C22C24×Dic4711yescharacteristic
330C22C2×#1309406912yes—
331C22#1568995914yes—
332C4—22no—
333C4—22no—
334C4—28no—
335C4—24no—
336C4—24no—
337C4—18816no—
338C2—24no—
339C2—48no—
340C2C2×#1568959811yescharacteristic
341C2#2025659112yes—
342C2#2025774514yes—
subgroupG/H
center, FrattiniC23C24×D47
commutatorC22×C47C24×C4
FittingC22×#124×C47C2
socle, cosocleC23×C47C25
prime radicalC23×D4×C47C22
hypercenterC22×#124D47
hypocenterC47#34366
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. #20246562C2semidirect
2. #20246500C2semidirect
3. #20246237C2semidirect
4. #20246203C2semidirect
5. #20245974C2semidirect
7. #20245786C2semidirect
11. #15689030C22semidirect
12. #15689030C22semidirect
13. #15689016C22semidirect
14. #15689016C22semidirect
17. #15688998C22semidirect
18. #15688991C22semidirect
19. #15688989C22semidirect
24. C4×C4⋊Dic47C22semidirect
25. C22⋊C4×Dic47C22semidirect
27. #15688969C22semidirect
30. C2×#124×C47C4semidirect
53. C22×Q8×C47C2×C4semidirect
63. #124×C47C2×C4semidirect
64. #124×C47C2×C4semidirect
65. #124×C47C2×C4semidirect
66. C2×C22⋊C4×C47C2×C4semidirect
69. C2×C42×C47C2×C4semidirect
182. C2×#124Dic47semidirect
207. C47#34366semidirect
210. C22×Q8C2×Dic47semidirect
221. #124C2×Dic47semidirect
222. #124C2×Dic47semidirect
223. #124C2×Dic47semidirect
231. C2×C22⋊C4C2×Dic47semidirect
236. C2×C42C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
#202465622
#202465002
#202462372
#202462032
#202459742
#202459662
#202457862
C22×#124×C472
#3436647