Finite Group Databasebeta

← #26104548

Subgroups — #26104548

Order 12032.

468 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 127 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#20243137C211yesmaximal, characteristic
2#20243137C211yesmaximal, characteristic
3#20241211C214yesmaximal
4C4×C4⋊Q8×C47C211yesmaximal, characteristic
5C2×#13093935—21no—
6C2×#13093935—21no—
7#15688878—21no—
8#15688878—21no—
9#15688878C2212yes—
10#15688878C2212yes—
11C2×C4⋊Q8×C47C411yescharacteristic
12C2×C4×Q8×C47—21no—
13C47×#391—21no—
14C47×#389—21no—
15C47×#389C2212yes—
16C47×#384C411yescharacteristic
17C4×C4⋊C4×C47—21no—
18C4×C4⋊C4×C47C412yes—
19C43×C47C2211yescharacteristic
20C22×C47⋊C8—22no—
21C22×C47⋊C8—22no—
22#13093935—24no—
23#13093935—24no—
24C22×Q8×C47—21no—
25C4⋊Q8×C47—24no—
26C4×Q8×C47—44no—
27C2×C4⋊C4×C47—21no—
28C2×C4⋊C4×C47—21no—
29C2×C4⋊C4×C47—21no—
30C2×C4⋊C4×C47—22no—
31C2×C4⋊C4×C47C2×C412yes—
32C2×C4⋊C4×C47C2×C412yes—
33C2×C42×C47—22no—
34C2×C42×C47C2×C411yescharacteristic
35C2×C42×C47C2×C411yescharacteristic
36C2×C42×C47D411yescharacteristic
37C2×C42×C47D411yescharacteristic
38C2×C42×C47D411yescharacteristic
39C2×C42×C47D411yescharacteristic
40C2×C42×C47C2311yescharacteristic
41#95×C47—22no—
42#95×C47—22no—
43C2×Q8×C47—24no—
44C2×Q8×C47—42no—
45C2×Q8×C47—42no—
46C22×C4×C47—22no—
47C22×C4×C47—22no—
48C22×C4×C47C22⋊C411yescharacteristic
49C22×C4×C47C22⋊C411yescharacteristic
50C22×C4×C47C22⋊C411yescharacteristic
51C22×C4×C47C22⋊C411yescharacteristic
52C22×C4×C47C22×C411yescharacteristic
53C22×C4×C47C2×D411yescharacteristic
54C22×C4×C47C2×D411yescharacteristic
55C4⋊C4×C47—24no—
56C4⋊C4×C47—22no—
57C4⋊C4×C47—42no—
58C4⋊C4×C47—42no—
59C4⋊C4×C47—42no—
60C4⋊C4×C47—44no—
61C4⋊C4×C47M1614yes—
62C42×C47—22no—
63C42×C47—22no—
64C42×C47—22no—
65C42×C47—22no—
66C42×C47—22no—
67C42×C47—22no—
68C42×C47—41no—
69C42×C47—44no—
70C2×C47⋊C8—24no—
71C2×C47⋊C8—24no—
72C2×C47⋊C8—42no—
73C2×C47⋊C8—42no—
74C2×C47⋊C8—42no—
75C2×C47⋊C8—42no—
76C23×C47C2×C22⋊C411yescharacteristic
77Q8×C47—48no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47—21no—
86C2×C4×C47—21no—
87C2×C4×C47—21no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—24no—
91C2×C4×C47—21no—
92C2×C4×C47—21no—
93C2×C4×C47—21no—
94C2×C4×C47—42no—
95C2×C4×C47—42no—
96C2×C4×C47—42no—
97C2×C4×C47—42no—
98C2×C4×C47—42no—
99C2×C4×C47#10112yes—
100C2×C4×C47#10412yes—
101C2×C4×C47#10412yes—
102C2×C4×C47C2×M1612yes—
103C2×C4×C47AGL(1,ℤ/8)12yes—
104C2×C4×C47#13712yes—
105C47⋊C8—44no—
106C47⋊C8—44no—
107#7638—471nomaximal, Sylow
108C22×C47#40711yescharacteristic
109C22×C47#41011yescharacteristic
110C22×C47C2×#10111yescharacteristic
111C22×C47#41811yescharacteristic
112C22×C47#41911yescharacteristic
113C22×C47C2×#10411yescharacteristic
114C22×C47C2×#10411yescharacteristic
115C4×C47—22no—
116C4×C47—22no—
117C4×C47—22no—
118C4×C47—22no—
119C4×C47—22no—
120C4×C47—22no—
121C4×C47—44no—
122C4×C47—41no—
123C4×C47—82no—
124C4×C4⋊Q8D4711yescharacteristic
125#1745—471no—
126#1745—471no—
127#1271—474no—
128C2×C47#146711yescharacteristic
129C2×C47#149011yescharacteristic
130C2×C47#149111yescharacteristic
131C2×C47#150511yescharacteristic
132C2×C47#150611yescharacteristic
133C2×C47#152611yescharacteristic
134C2×C47#155611yescharacteristic
135C2×C4⋊Q8Dic4711yescharacteristic
136C2×C4×Q8—21no—
137C2×#97—941no—
138C2×#97—941no—
139#391—21no—
140#389—21no—
141#389C2×D4712yes—
142#384Dic4711yescharacteristic
143C4×C4⋊C4—21no—
144C4×C4⋊C4Dic4712yes—
145C43C2×D4711yescharacteristic
146#336—472no—
147#336—472no—
148#336—941no—
149#336—941no—
150C47#763811yescharacteristic, complemented, Sylow
151C22×Q8—21no—
152C22×C8—942no—
153C22×C8—942no—
154C4⋊Q8—24no—
155C4×Q8—44no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4C2×Dic4712yes—
161C2×C4⋊C4C2×Dic4712yes—
162C2×C42—22no—
163C2×C42C2×Dic4711yescharacteristic
164C2×C42C2×Dic4711yescharacteristic
165C2×C42C22⋊D4711yescharacteristic
166C2×C42C22⋊D4711yescharacteristic
167C2×C42C22⋊D4711yescharacteristic
168C2×C42C22⋊D4711yescharacteristic
169C2×C42C22×D4711yescharacteristic
170#97—944no—
171#97—944no—
172#95—22no—
173#95—22no—
174C2×Q8—24no—
175C2×Q8—42no—
176C2×Q8—42no—
177C22×C4—22no—
178C22×C4—22no—
179C22×C4C22⋊Dic4711yescharacteristic
180C22×C4C22⋊Dic4711yescharacteristic
181C22×C4C22⋊Dic4711yescharacteristic
182C22×C4C22⋊Dic4711yescharacteristic
183C22×C4C22×Dic4711yescharacteristic
184C22×C4C2×C22⋊D4711yescharacteristic
185C22×C4C2×C22⋊D4711yescharacteristic
186C2×C8—944no—
187C2×C8—944no—
188C2×C8—1882no—
189C2×C8—1882no—
190C2×C8—1882no—
191C2×C8—1882no—
192C4⋊C4—24no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—44no—
198C4⋊C4#1062532914yes—
199C42—22no—
200C42—22no—
201C42—22no—
202C42—22no—
203C42—22no—
204C42—22no—
205C42—41no—
206C42—44no—
207C23C2×C22⋊Dic4711yescharacteristic
208Q8—48no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—24no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4#1309394312yes—
231C2×C4#1309395112yes—
232C2×C4#1309395112yes—
233C2×C4C2×#1062532912yes—
234C2×C4#1309405012yes—
235C2×C4#1309405512yes—
236C8—1884no—
237C8—1884no—
238C22#1568908711yescharacteristic
239C22#1568909711yescharacteristic
240C22C2×#1309394311yescharacteristic
241C22#1568912811yescharacteristic
242C22#1568913211yescharacteristic
243C22C2×#1309395111yescharacteristic
244C22C2×#1309395111yescharacteristic
245C4—22no—
246C4—22no—
247C4—22no—
248C4—22no—
249C4—22no—
250C4—22no—
251C4—41no—
252C4—44no—
253C4—82no—
254C2#2024173211yescharacteristic
255C2#2024183111yescharacteristic
256C2#2024183511yescharacteristic
257C2#2024189611yescharacteristic
258C2#2024190011yescharacteristic
259C2#2024198311yescharacteristic
260C2#2024210511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC4×C4⋊Q8×C47C2
socle, prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenterC4×C4⋊Q8D47
hypocenterC47#7638
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C43 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
150. C47#7638semidirect

Maximal subgroups

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

subgroupindex
#202431372
#202412112
C4×C4⋊Q8×C472
#763847