Finite Group Databasebeta

← #26134482

Subgroups — #26134482

Order 12032.

438 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252080C211yesmaximal, characteristic
2#20245153C211yesmaximal, characteristic, complemented
3#20245016C211yesmaximal, characteristic, complemented
4#20244998C211yesmaximal, characteristic, complemented
5#20244998C211yesmaximal, characteristic, complemented
6#20244992C211yesmaximal, characteristic, complemented
7C47×#2117C211yesmaximal, characteristic, complemented
8C22×C8×D47C2211yescharacteristic
9#15689630C411yescharacteristic
10C2×#13093964C2211yescharacteristic
11C2×#13093964C2211yescharacteristic
12#15689192—22no—
13C8×C22⋊D47—22no—
14#15689151C411yescharacteristic
15#15689090C411yescharacteristic
16#15689086C411yescharacteristic
17#15689078C2211yescharacteristic
18#15688943—22no—
19#15688907—22no—
20(C2×D47)⋊C16—22no—
21(C2×D47)⋊C16—22no—
22#15688900—22no—
23C2×#131×C47C2211yescharacteristic
24C2×M32×C47C2211yescharacteristic
25C2×M32×C47C2211yescharacteristic
26C47×#350—22no—
27C22×C4×D47C2×C411yescharacteristic
28C2×#10625329C2×C411yescharacteristic
29C22×C47⋊C8C2×C411yescharacteristic
30C2×C8×D47—21no—
31C2×C8×D47—21no—
32C2×C8×D47—21no—
33C2×C8×D47—21no—
34C2×C8×D47—21no—
35C2×C8×D47—21no—
36#13094005—21no—
37#13094000—21no—
38#13093995—21no—
39#13093992—21no—
40C4×C22⋊D47—22no—
41#13093983C2×C411yescharacteristic
42#13093964—21no—
43#13093964—21no—
44#13093964—21no—
45#13093964—21no—
46C2×C47⋊C16—21no—
47C2×C47⋊C16D412yescomplemented
48Dic47⋊C8—22no—
49C22⋊(C47⋊C8)—22no—
50(C2×D47)⋊C8—22no—
51#13093934D412yes—
52C8×Dic47D412yes—
53C2×#41×C47C2×C411yescharacteristic
54#131×C47—21no—
55#131×C47—21no—
56#131×C47—21no—
57#131×C47—21no—
58C2×M16×C47—21no—
59C2×M16×C47C2×C411yescharacteristic
60C22×C8×C47—21no—
61C22×C8×C47C2311yescharacteristic
62M32×C47—21no—
63M32×C47—21no—
64M32×C47—21no—
65M32×C47—21no—
66C2×C16×C47—21no—
67C2×C16×C47D412yescomplemented
68C23×D47M1611yescharacteristic
69#41×C47—21no—
70#41×C47—21no—
71#41×C47—21no—
72#41×C47—21no—
73C2×Q8×C47M1611yescharacteristic
74C2×D4×C47—21no—
75C2×D4×C47M1611yescharacteristic
76C22×C4×C47—21no—
77C22×C4×C47C22×C411yescharacteristic
78C2×C22⋊D47—22no—
79C22×Dic47M1611yescharacteristic
80C2×C4×D47—21no—
81C2×C4×D47—21no—
82C2×C4×D47—21no—
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47—21no—
86M16×C47—21no—
87M16×C47—21no—
88M16×C47—41no—
89M16×C47—41no—
90C2×C8×C47—21no—
91C2×C8×C47—41no—
92C2×C8×C47—41no—
93C2×C8×C47C2×D411yescharacteristic
94C2×C8×C47C2×D411yescharacteristic
95C2×C8×C47C2×D411yescharacteristic
96C2×C8×C47C2×D411yescharacteristic
97C2×C8×C47#4111yescharacteristic
98C2×C8×C47#4111yescharacteristic
99C22⋊Dic47—22no—
100C22⋊Dic47—21no—
101(C2×D47)⋊C4—22no—
102C4⋊Dic47—21no—
103Dic47⋊C4—22no—
104C4×Dic47C22⋊C412yes—
105#10625329—21no—
106#10625329—21no—
107C2×C47⋊C8—21no—
108C2×C47⋊C8—21no—
109C2×C47⋊C8—21no—
110C2×C47⋊C8C22⋊C412yes—
111C8×D47—41no—
112C8×D47—41no—
113C8×D47—41no—
114C8×D47—41no—
115C16×C47—22no—
116C16×C47—41no—
117C47⋊C16—22no—
118C47⋊C16—41no—
119C23×C47—21no—
120C23×C47C2×M1611yescharacteristic
121C22×D47—21no—
122C22×D47—21no—
123C22×D47—21no—
124C22×D47—42no—
125Q8×C47—21no—
126Q8×C47—21no—
127D4×C47—21no—
128D4×C47—21no—
129D4×C47—41no—
130D4×C47—41no—
131C2×C4×C47—21no—
132C2×C4×C47—41no—
133C2×C4×C47—41no—
134C2×C4×C47C2×C22⋊C411yescharacteristic
135C2×C4×C47C4×D411yescharacteristic
136C2×C4×C47C4×D411yescharacteristic
137C2×C4×C47C2×M1611yescharacteristic
138C2×C4×C47#13111yescharacteristic
139C2×C4×C47#13111yescharacteristic
140C22⋊D47—44no—
141C2×Dic47—22no—
142C2×Dic47—21no—
143C2×Dic47—21no—
144C2×Dic47—21no—
145C4×D47—41no—
146C4×D47—41no—
147C4×D47—41no—
148C4×D47—41no—
149C8×C47—41no—
150C8×C47#12111yescharacteristic
151C8×C47#12111yescharacteristic
152C8×C47#12411yescharacteristic
153C8×C47#12711yescharacteristic
154C47⋊C8—22no—
155C47⋊C8—41no—
156#13200—471nomaximal, Sylow
157C22×C47—41no—
158C22×C47—42no—
159C22×C47—41no—
160C22×C47#40711yescharacteristic
161C22×C47#43511yescharacteristic
162C22×C47#43511yescharacteristic
163C2×D47—22no—
164C2×D47—22no—
165C2×D47—22no—
166C2×D47—41no—
167C2×D47—41no—
168C2×D47—41no—
169C2×D47—41no—
170C4×C47—41no—
171C4×C47#39011yescharacteristic
172C4×C47#40811yescharacteristic
173C4×C47#43511yescharacteristic
174C4×C47#43511yescharacteristic
175Dic47—42no—
176Dic47—41no—
177#2929—471no—
178#2153—471no—
179#2117—471no—
180#2117D4711yescharacteristic, complemented
181#2112—471no—
182#2112—471no—
183#2110—471no—
184C2×C47—21no—
185C2×C47—21no—
186C2×C47—21no—
187C2×C47—81no—
188C2×C47#195511yescharacteristic
189D47—42no—
190C2×#131C2×D4711yescharacteristic
191C23×C8—471no—
192#525—471no—
193C2×M32—471no—
194C2×M32—471no—
195C2×M32C2×D4711yescharacteristic
196C2×M32C2×D4711yescharacteristic
197#435—942no—
198C8×D4—942no—
199#424—471no—
200#408—471no—
201#407—471no—
202#405—471no—
203#364—942no—
204#350—22no—
205#350—942no—
206C22⋊C16—942no—
207C22⋊C16—942no—
208#347—942no—
209C47#1320011yescharacteristic, complemented, Sylow
210C2×#41C4×D4711yescharacteristic
211C23×C4—471no—
212#131—21no—
213#131—21no—
214#131—21no—
215#131—21no—
216C2×M16—21no—
217C2×M16—471no—
218C2×M16C4×D4711yescharacteristic
219C22×C8—21no—
220C22×C8—471no—
221C22×C8—941no—
222C22×C8—941no—
223C22×C8—941no—
224C22×C8—941no—
225C22×C8—941no—
226C22×C8—941no—
227C22×C8C22×D4711yescharacteristic
228#123—941no—
229C22⋊Q8—941no—
230#121—941no—
231#120—941no—
232C4×D4—942no—
233#117—471no—
234M32—21no—
235M32—21no—
236M32—21no—
237M32—21no—
238M32—941no—
239M32—941no—
240M32—941no—
241M32—941no—
242C2×C16—21no—
243C2×C16—472no—
244C2×C16—941no—
245C2×C16C22⋊D4712yescomplemented
246C4⋊C8—942no—
247C22⋊C8—942no—
248C22⋊C8—942no—
249#97—472no—
250C4×C8—472no—
251C24—471no—
252#41—21no—
253#41—21no—
254#41—21no—
255#41—21no—
256C2×Q8#1062532411yescharacteristic
257C2×D4—21no—
258C2×D4—942no—
259C2×D4#1062532411yescharacteristic
260C22×C4—21no—
261C22×C4—471no—
262C22×C4—941no—
263C22×C4—941no—
264C22×C4—941no—
265C22×C4—941no—
266C22×C4—941no—
267C22×C4—941no—
268C22×C4C2×C4×D4711yescharacteristic
269M16—21no—
270M16—21no—
271M16—41no—
272M16—41no—
273M16—941no—
274M16—941no—
275C2×C8—21no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—472no—
279C2×C8—941no—
280C2×C8—941no—
281C2×C8—941no—
282C2×C8—1881no—
283C2×C8—1881no—
284C2×C8—1881no—
285C2×C8—1881no—
286C2×C8#1062535011yescharacteristic
287C2×C8D4×D4711yescharacteristic
288C2×C8D4×D4711yescharacteristic
289C2×C8D4×D4711yescharacteristic
290C2×C8#1062535211yescharacteristic
291C2×C8C2×C22⋊D4711yescharacteristic
292C4⋊C4—942no—
293C4⋊C4—941no—
294C22⋊C4—942no—
295C22⋊C4—942no—
296C22⋊C4—941no—
297C42—472no—
298C16—22no—
299C16—41no—
300C16—942no—
301C16—1881no—
302C23—21no—
303C23—941no—
304C23—941no—
305C23—941no—
306C23—1882no—
307C23M16×D4711yescharacteristic
308Q8—21no—
309Q8—21no—
310D4—21no—
311D4—21no—
312D4—41no—
313D4—41no—
314D4—1884no—
315C2×C4—21no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—942no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—941no—
322C2×C4—1881no—
323C2×C4—1881no—
324C2×C4—1881no—
325C2×C4—1881no—
326C2×C4C22⋊C4×D4711yescharacteristic
327C2×C4(C22⋊D47)⋊C411yescharacteristic
328C2×C4C4×C22⋊D4711yescharacteristic
329C2×C4C2×#1062532411yescharacteristic
330C2×C4#1309403011yescharacteristic
331C2×C4#1309403211yescharacteristic
332C8—41no—
333C8—942no—
334C8—1881no—
335C8#1309399611yescharacteristic
336C8#1309399711yescharacteristic
337C8#1309401011yescharacteristic
338C8#1309402011yescharacteristic
339C22—41no—
340C22—42no—
341C22—41no—
342C22—942no—
343C22—942no—
344C22—942no—
345C22—1881no—
346C22—1881no—
347C22—1881no—
348C22—1881no—
349C22#1568908511yescharacteristic
350C22#1568919211yescharacteristic
351C22#1568919711yescharacteristic
352C4—41no—
353C4—1882no—
354C4—1881no—
355C4#1568902311yescharacteristic
356C4#1568908811yescharacteristic
357C4#1568919111yescharacteristic
358C4#1568919411yescharacteristic
359C2—21no—
360C2—21no—
361C2—21no—
362C2—81no—
363C2—1882no—
364C2#2024418411yescharacteristic
subgroupG/H
centerC8#13094020
commutatorC22×C4×C47C22×C4
FrattiniC22×C8C22×D47
FittingC47×#2117C2
socleC2×C47#1955
prime radical#15689630C4
cosocleC22×C8×C47C23
hypercenter#2117D47
hypocenterC47#13200
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
2. #20245153C2semidirect
3. #20245016C2semidirect
4. #20244998C2semidirect
5. #20244998C2semidirect
6. #20244992C2semidirect
7. C47×#2117C2semidirect
47. C2×C47⋊C16D4semidirect
67. C2×C16×C47D4semidirect
180. #2117D47semidirect
209. C47#13200semidirect
245. C2×C16C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
#202520802
#202451532
#202450162
#202449982
#202449922
C47×#21172
#1320047