Finite Group Databasebeta

← #26112277

Subgroups — #26112277

Order 12032.

436 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 107 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
1#20252473C211yesmaximal, characteristic
2C4×#13093943C211yesmaximal, characteristic
3#20241990C212yesmaximal
4#20241252C212yesmaximal
5C47×#2634C211yesmaximal, characteristic
6#15689254—24no—
7#15689180—21no—
8#15689180C2212yes—
9#15689176—21no—
10C2×#13093943—21no—
11C4×#10625329C2212yes—
12#15688892—21no—
13#15688865—24no—
14C2×#125×C47C2211yescharacteristic
15C2×C4×Q8×C47C2211yescharacteristic
16C47×#400—21no—
17C47×#400C411yescharacteristic
18C47×#400C411yescharacteristic
19C47×#398C411yescharacteristic
20C47×#398C411yescharacteristic
21C47×#395—21no—
22C47×#387—21no—
23C47×#387—21no—
24C47×#383C2211yescharacteristic
25C2×#10625329—22no—
26C4⋊(C47⋊C8)—22no—
27C4⋊(C47⋊C8)—22no—
28C4⋊(C47⋊C8)—22no—
29#13093943—24no—
30C22⋊(C47⋊C8)—22no—
31#13093935—22no—
32#13093935—22no—
33#13093935D414yes—
34C4×C47⋊C8—22no—
35C4×C47⋊C8—22no—
36C22×Q8×C47D411yescharacteristic
37#125×C47—22no—
38#125×C47—22no—
39C4×Q8×C47—22no—
40C4×Q8×C47—22no—
41C2×C4⋊C4×C47—21no—
42C2×C4⋊C4×C47—21no—
43C2×C4⋊C4×C47—21no—
44C2×C4⋊C4×C47—21no—
45C2×C4⋊C4×C47C2×C411yescharacteristic
46C2×C4⋊C4×C47C2×C411yescharacteristic
47C2×C4⋊C4×C47C2×C411yescharacteristic
48C2×C4⋊C4×C47C2×C411yescharacteristic
49C2×C4⋊C4×C47D411yescharacteristic
50C2×C42×C47D411yescharacteristic
51C2×C42×C47D411yescharacteristic
52C2×C42×C47C2311yescharacteristic
53#95×C47—21no—
54#95×C47—21no—
55#95×C47—21no—
56#95×C47—21no—
57#95×C47—21no—
58#95×C47—21no—
59#95×C47—21no—
60#95×C47—21no—
61#95×C47C2×C411yescharacteristic
62#95×C47C2×C411yescharacteristic
63C2×Q8×C47—22no—
64C2×Q8×C47—22no—
65C2×Q8×C47—41no—
66C22×C4×C47—21no—
67C22×C4×C47—21no—
68C22×C4×C47—21no—
69C22×C4×C47—21no—
70C22×C4×C47C22⋊C411yescharacteristic
71C22×C4×C47C22⋊C411yescharacteristic
72C22×C4×C47C22⋊C411yescharacteristic
73C22×C4×C47C22⋊C411yescharacteristic
74C22×C4×C47C22×C411yescharacteristic
75C22×C4×C47C2×D411yescharacteristic
76C22×C4×C47C2×D411yescharacteristic
77C4⋊C4×C47—22no—
78C4⋊C4×C47—22no—
79C4⋊C4×C47—22no—
80C4⋊C4×C47—22no—
81C4⋊C4×C47—22no—
82C4⋊C4×C47—42no—
83C4⋊C4×C47—42no—
84C4⋊C4×C47—41no—
85C4⋊C4×C47—42no—
86C4⋊C4×C47—41no—
87C42×C47—21no—
88C42×C47—21no—
89C42×C47—21no—
90C42×C47—21no—
91C42×C47C2×D412yes—
92C42×C47#4112yes—
93#10625329—24no—
94#10625329—42no—
95C2×C47⋊C8—24no—
96C2×C47⋊C8—42no—
97C23×C47C2×C22⋊C411yescharacteristic
98Q8×C47—44no—
99C2×C4×C47—21no—
100C2×C4×C47—21no—
101C2×C4×C47—21no—
102C2×C4×C47—21no—
103C2×C4×C47—21no—
104C2×C4×C47—21no—
105C2×C4×C47—21no—
106C2×C4×C47—21no—
107C2×C4×C47—21no—
108C2×C4×C47—41no—
109C2×C4×C47—41no—
110C2×C4×C47—41no—
111C2×C4×C47—41no—
112C2×C4×C47—41no—
113C2×C4×C47—41no—
114C2×C4×C47—41no—
115C2×C4×C47—41no—
116C2×C4×C47—42no—
117C2×C4×C47—41no—
118C2×C4×C47—41no—
119C2×C4×C47—41no—
120C2×C4×C47—41no—
121C2×C4×C47—41no—
122C2×C4×C47—41no—
123C2×C4×C47#10412yes—
124C2×C4×C47C4×D412yes—
125C2×C4×C47#12011yescharacteristic
126C2×C4×C47#12112yes—
127C2×C4×C47#12311yescharacteristic
128C47⋊C8—44no—
129C47⋊C8—44no—
130#9190—471nomaximal, Sylow
131C22×C47—21no—
132C22×C47—21no—
133C22×C47#38611yescharacteristic
134C22×C47C2×#10411yescharacteristic
135C22×C47#42111yescharacteristic
136C4×C47—22no—
137C4×C47—22no—
138C4×C47—21no—
139C4×C47—21no—
140C4×C47—22no—
141C4×C47—41no—
142C4×C47—41no—
143C4×C47—41no—
144C4×C47—81no—
145C4×C47—81no—
146C4×C47—81no—
147C4×C47—81no—
148#2983—471no—
149#2634D4711yescharacteristic
150C4×#101—471no—
151#1528—472no—
152#1288—472no—
153C2×C47—21no—
154C2×C47—21no—
155C2×C47#187111yescharacteristic
156C2×C47#191211yescharacteristic
157C2×C47#191511yescharacteristic
158C2×#125C2×D4711yescharacteristic
159C2×C4×Q8C2×D4711yescharacteristic
160#446—944no—
161#432—472no—
162#432—941no—
163#431—941no—
164C2×#101—941no—
165C4×M16—472no—
166#400—21no—
167#400Dic4711yescharacteristic
168#400Dic4711yescharacteristic
169#398Dic4711yescharacteristic
170#398Dic4711yescharacteristic
171#395—21no—
172#387—21no—
173#387—21no—
174#383C2×D4711yescharacteristic
175#343—941no—
176#330—944no—
177C47#919011yescharacteristic, complemented, Sylow
178C22×Q8C22⋊D4711yescharacteristic
179C2×M16—942no—
180#125—22no—
181#125—22no—
182C4×Q8—22no—
183C4×Q8—22no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4C2×Dic4711yescharacteristic
189C2×C4⋊C4C2×Dic4711yescharacteristic
190C2×C4⋊C4C2×Dic4711yescharacteristic
191C2×C4⋊C4C2×Dic4711yescharacteristic
192C2×C4⋊C4C22⋊D4711yescharacteristic
193C2×C42C22⋊D4711yescharacteristic
194C2×C42C22⋊D4711yescharacteristic
195C2×C42C22×D4711yescharacteristic
196C4⋊C8—942no—
197C4⋊C8—942no—
198C4⋊C8—942no—
199#101—944no—
200C22⋊C8—942no—
201#97—474no—
202#97—942no—
203#97—942no—
204C4×C8—942no—
205C4×C8—942no—
206#95—21no—
207#95—21no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95C2×Dic4711yescharacteristic
215#95C2×Dic4711yescharacteristic
216C2×Q8—22no—
217C2×Q8—22no—
218C2×Q8—41no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4C22⋊Dic4711yescharacteristic
224C22×C4C22⋊Dic4711yescharacteristic
225C22×C4C22⋊Dic4711yescharacteristic
226C22×C4C22⋊Dic4711yescharacteristic
227C22×C4C22×Dic4711yescharacteristic
228C22×C4C2×C22⋊D4711yescharacteristic
229C22×C4C2×C22⋊D4711yescharacteristic
230M16—944no—
231M16—1882no—
232C2×C8—944no—
233C2×C8—1882no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C4⋊C4—41no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42D4×D4712yes—
249C42#1062535212yes—
250C23C2×C22⋊Dic4711yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4#1309395112yes—
277C2×C4D4×Dic4712yes—
278C2×C4#1309399211yescharacteristic
279C2×C4#1309399612yes—
280C2×C4#1309400511yescharacteristic
281C8—1884no—
282C8—1884no—
283C22—21no—
284C22—21no—
285C22#1568900311yescharacteristic
286C22C2×#1309395111yescharacteristic
287C22#1568914011yescharacteristic
288C4—21no—
289C4—21no—
290C4—22no—
291C4—22no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—81no—
297C4—81no—
298C4—81no—
299C4—81no—
300C2—21no—
301C2—21no—
302C2#2024369111yescharacteristic
303C2#2024392611yescharacteristic
304C2#2024394111yescharacteristic
subgroupG/H
centerC22#15689003
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2634C2
socleC22×C47#386
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#2634D47
hypocenterC47#9190
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2634

Complements

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

NH ≅ G/Ntype
177. C47#9190semidirect

Maximal subgroups

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

subgroupindex
#202524732
C4×#130939432
#202419902
#202412522
C47×#26342
#919047