Finite Group Databasebeta

← #26113686

Subgroups — #26113686

Order 12032.

486 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 115 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
2#20248373C211yesmaximal, characteristic
3#20242061C212yesmaximal
4#20241289C212yesmaximal
5C47×#1801C211yesmaximal, characteristic
6C2×#13094024C2211yescharacteristic
7C2×#13094022—21no—
8#15689254—24no—
9#15689180—22no—
10#15689176C2212yes—
11#15689053C414yes—
12#15689028—21no—
13#15689021—22no—
14C4×C4⋊Dic47C2211yescharacteristic
15#15688870—24no—
16C2×C4×Q8×C47C2211yescharacteristic
17C47×#423C2212yes—
18C2×#101×C47—21no—
19C47×#343—21no—
20C22×Dic94—21no—
21#13094024—22no—
22#13094024—22no—
23#13094022—44no—
24C2×C4⋊Dic47—21no—
25C2×C4⋊Dic47—21no—
26C2×C4⋊Dic47C2×C412yes—
27C2×Dic47⋊C4—24no—
28C2×C4×Dic47—21no—
29C4⋊(C47⋊C8)—24no—
30C4⋊(C47⋊C8)D414yes—
31C22⋊(C47⋊C8)—22no—
32#13093935—24no—
33C4×C47⋊C8—22no—
34C47⋊#95—24no—
35C47⋊#95C2×C412yes—
36C22×Q8×C47D411yescharacteristic
37C2×M16×C47—22no—
38C4×Q8×C47—22no—
39C4×Q8×C47—22no—
40C2×C4⋊C4×C47C2×C412yes—
41C2×C4⋊C4×C47D411yescharacteristic
42C2×C42×C47D412yes—
43C2×C42×C47C2311yescharacteristic
44C4⋊C8×C47—22no—
45C4⋊C8×C47—22no—
46#101×C47—42no—
47C2×Q8×C47—22no—
48C2×Q8×C47—22no—
49C2×Q8×C47—21no—
50C2×Q8×C47—21no—
51C22×C4×C47C22⋊C412yes—
52C22×C4×C47C22⋊C412yes—
53C22×C4×C47C22×C411yescharacteristic
54C22×C4×C47C2×D411yescharacteristic
55C22×C4×C47C2×D411yescharacteristic
56C22×Dic47—22no—
57C22×Dic47—22no—
58C2×Dic94—42no—
59C2×Dic94—42no—
60C2×Dic94—41no—
61C2×Dic94—41no—
62M16×C47—42no—
63M16×C47—42no—
64C2×C8×C47—42no—
65C4⋊C4×C47—24no—
66C4⋊C4×C47—22no—
67C42×C47—22no—
68C42×C47—22no—
69C42×C47C2×D412yes—
70C42×C47#4112yes—
71C4⋊Dic47—24no—
72C4⋊Dic47—24no—
73C4⋊Dic47—41no—
74C4⋊Dic47—41no—
75Dic47⋊C4—48no—
76C4×Dic47—42no—
77C2×C47⋊C8—24no—
78C23×C47C2×C22⋊C411yescharacteristic
79Q8×C47—42no—
80Q8×C47—42no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—22no—
86C2×C4×C47—41no—
87C2×C4×C47—42no—
88C2×C4×C47C4×D412yes—
89C2×C4×C47#12011yescharacteristic
90C2×C4×C47#12112yes—
91C2×C4×C47#12311yescharacteristic
92C2×C4×C47AGL(1,ℤ/8)12yes—
93C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
94C2×C4×C47#13711yescharacteristic
95C2×Dic47—24no—
96C2×Dic47—42no—
97C2×Dic47—42no—
98C2×Dic47—42no—
99C2×Dic47—42no—
100C2×Dic47—42no—
101Dic94—82no—
102Dic94—82no—
103C8×C47—82no—
104C47⋊C8—44no—
105#9402—471nomaximal, Sylow
106C22×C47—21no—
107C22×C47—21no—
108C22×C47#38611yescharacteristic
109C22×C47#41711yescharacteristic
110C22×C47#41811yescharacteristic
111C4×C47—21no—
112C4×C47—22no—
113C4×C47—42no—
114C4×C47—42no—
115C4×C47#45612yes—
116C4×C47#46812yes—
117C4×C47#46912yes—
118Dic47—44no—
119Dic47—82no—
120#2983—471no—
121#2546—471no—
122#1801D4711yescharacteristic
123#1546—472no—
124#1303—472no—
125C2×C47—21no—
126C2×C47—21no—
127C2×C47#188611yescharacteristic
128C2×C47#189511yescharacteristic
129C2×C47#191511yescharacteristic
130C2×C4⋊Q8—471no—
131C2×C4⋊Q8—941no—
132C2×C4×Q8C2×D4711yescharacteristic
133#446—944no—
134#432—942no—
135#431—472no—
136#423C2×D4712yes—
137C2×#101—21no—
138#398—474no—
139#391—941no—
140#389—942no—
141C4×C4⋊C4—471no—
142#343—21no—
143#332—944no—
144C47#940211yescharacteristic, complemented, Sylow
145C22×Q8—941no—
146C22×Q8C22⋊D4711yescharacteristic
147C2×M16—22no—
148C4⋊Q8—942no—
149C4⋊Q8—942no—
150C4⋊Q8—1884no—
151C4×Q8—22no—
152C4×Q8—22no—
153C2×C4⋊C4—472no—
154C2×C4⋊C4—941no—
155C2×C4⋊C4—944no—
156C2×C4⋊C4—941no—
157C2×C4⋊C4C4×D4712yes—
158C2×C4⋊C4C22⋊D4711yescharacteristic
159C2×C42—941no—
160C2×C42D18812yes—
161C2×C42C22×D4711yescharacteristic
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—474no—
165C4⋊C8—944no—
166#101—42no—
167C22⋊C8—942no—
168#97—944no—
169C4×C8—942no—
170#95—472no—
171#95—944no—
172C2×Q8—22no—
173C2×Q8—22no—
174C2×Q8—21no—
175C2×Q8—21no—
176C2×Q8—1882no—
177C2×Q8—1882no—
178C2×Q8—1881no—
179C2×Q8—1881no—
180C22×C4—942no—
181C22×C4—942no—
182C22×C4(C2×D47)⋊C412yes—
183C22×C4(C2×D47)⋊C412yes—
184C22×C4C2×C4×D4711yescharacteristic
185C22×C4C2×D18811yescharacteristic
186C22×C4C2×C22⋊D4711yescharacteristic
187M16—42no—
188M16—42no—
189C2×C8—42no—
190C2×C8—944no—
191C4⋊C4—24no—
192C4⋊C4—22no—
193C4⋊C4—944no—
194C4⋊C4—944no—
195C4⋊C4—1888no—
196C4⋊C4—1881no—
197C4⋊C4—1881no—
198C42—22no—
199C42—22no—
200C42—1882no—
201C42D4×D4712yes—
202C42#1062535212yes—
203C23C2×(C2×D47)⋊C411yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—3762no—
207Q8—3762no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—944no—
216C2×C4—1882no—
217C2×C4—1882no—
218C2×C4—1882no—
219C2×C4—1882no—
220C2×C4—1882no—
221C2×C4(C22⋊D47)⋊C412yes—
222C2×C4#1309399411yescharacteristic
223C2×C4#1309399612yes—
224C2×C4#1309400811yescharacteristic
225C2×C4#1309404912yes—
226C2×C4#1309405011yescharacteristic
227C2×C4#1309405511yescharacteristic
228C8—82no—
229C8—1884no—
230C22—21no—
231C22—21no—
232C22#1568900011yescharacteristic
233C22#1568912211yescharacteristic
234C22#1568912711yescharacteristic
235C4—21no—
236C4—22no—
237C4—42no—
238C4—42no—
239C4—3762no—
240C4—1884no—
241C4#1568930812yes—
242C4#1568937112yes—
243C4#1568937412yes—
244C2—21no—
245C2—21no—
246C2#2024377911yescharacteristic
247C2#2024382411yescharacteristic
248C2#2024393811yescharacteristic
subgroupG/H
centerC22#15689000
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1801C2
socleC22×C47#386
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1801D47
hypocenterC47#9402
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
144. C47#9402semidirect

Maximal subgroups

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

subgroupindex
#202524732
#202483732
#202420612
#202412892
C47×#18012
#940247