Finite Group Databasebeta

← #26120345

Subgroups — #26120345

Order 12032.

408 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 81 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#20243541C211yesmaximal, characteristic, complemented
2#20242083C212yesmaximal, complemented
3#20241896C212yesmaximal, complemented
4#20241258C211yesmaximal, characteristic, complemented
5C47×#3245C211yesmaximal, characteristic
6#15689180C2212yes—
7C2×C4⋊(C47⋊C8)C2211yescharacteristic
8C2×Dic47⋊C8—22no—
9#15688969C2211yescharacteristic
10#15688872—22no—
11#15688867—22no—
12#15688857—24no—
13C47×#532C2212yes—
14C47×#474—22no—
15C47×#466—22no—
16C47×#459—22no—
17C2×C4⋊C8×C47C2211yescharacteristic
18C22×C47⋊C8—21no—
19C2×C4×Dic47—21no—
20C4⋊(C47⋊C8)—22no—
21C4⋊(C47⋊C8)—22no—
22Dic47⋊C8—44no—
23C22⋊(C47⋊C8)—22no—
24#13093935—22no—
25C47⋊#95—21no—
26C47⋊#95D412yes—
27C2×#41×C47—22no—
28C2×D8×C47—22no—
29C22×C8×C47D412yes—
30C4⋊Q8×C47D412yes—
31#127×C47D412yes—
32#124×C47—22no—
33#121×C47—22no—
34#121×C47—22no—
35C4×D4×C47—22no—
36C4×D4×C47—22no—
37C2×C42×C47C2311yescharacteristic
38#107×C47—22no—
39C4⋊C8×C47—22no—
40#102×C47—24no—
41#41×C47—84no—
42C2×Q8×C47—22no—
43C2×D4×C47—22no—
44C2×D4×C47—22no—
45C2×D4×C47—22no—
46C2×D4×C47—42no—
47C22×C4×C47—42no—
48C22×C4×C47C2×D411yescharacteristic
49C22×C4×C47C2×D411yescharacteristic
50C22×C4×C47#4111yescharacteristic
51C22×Dic47—22no—
52D8×C47—82no—
53C2×C8×C47—22no—
54C2×C8×C47—42no—
55C4⋊C4×C47—22no—
56C4⋊C4×C47—22no—
57C22⋊C4×C47—42no—
58C22⋊C4×C47—42no—
59C42×C47C2×D412yes—
60C42×C47#4112yes—
61C4×Dic47—22no—
62C4×Dic47—22no—
63C2×C47⋊C8—42no—
64C2×C47⋊C8—41no—
65C2×C47⋊C8—42no—
66C23×C47—42no—
67C23×C47#12111yescharacteristic
68Q8×C47—82no—
69D4×C47—42no—
70D4×C47—42no—
71D4×C47—82no—
72D4×C47—82no—
73D4×C47—84no—
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—41no—
78C2×C4×C47—42no—
79C2×C4×C47—84no—
80C2×C4×C47#12011yescharacteristic
81C2×C4×C47#12112yes—
82C2×C4×C47#12312yes—
83C2×C4×C47#12411yescharacteristic
84C2×Dic47—24no—
85C2×Dic47—42no—
86C2×Dic47—42no—
87C8×C47—42no—
88C47⋊C8—82no—
89C47⋊C8—81no—
90#10512—471nomaximal, Sylow
91C22×C47—21no—
92C22×C47—21no—
93C22×C47—82no—
94C22×C47—82no—
95C22×C47—82no—
96C22×C47#39411yescharacteristic
97C22×C47#47212yes—
98C4×C47—22no—
99C4×C47—21no—
100C4×C47—22no—
101C4×C47—82no—
102C4×C47#45311yescharacteristic
103C4×C47#45611yescharacteristic
104Dic47—44no—
105#3245D4711yescharacteristic
106#1843—471no—
107#1551—472no—
108#1505—472no—
109#1290—471no—
110C2×C47—22no—
111C2×C47—162no—
112C2×C47#203911yescharacteristic
113C2×C47#204511yescharacteristic
114C2×C47#205311yescharacteristic
115#532C2×D4712yes—
116#474—22no—
117#466—22no—
118#459—22no—
119#432—472no—
120C2×C4⋊C8—471no—
121C2×C4⋊C8—942no—
122C2×C4⋊C8C2×D4711yescharacteristic
123#376—471no—
124#333—942no—
125#331—942no—
126#327—944no—
127C47#1051211yescharacteristic, complemented, Sylow
128C2×#41—22no—
129C2×D8—22no—
130C22×C8—941no—
131C22×C8C22⋊D4712yes—
132C4⋊Q8C22⋊D4712yes—
133#127C22⋊D4712yes—
134#124—22no—
135#121—22no—
136#121—22no—
137C4×D4—22no—
138C4×D4—22no—
139C2×C42—941no—
140C2×C42C22×D4711yescharacteristic
141#107—22no—
142C4⋊C8—22no—
143C4⋊C8—942no—
144C4⋊C8—942no—
145C4⋊C8—1884no—
146#102—24no—
147C22⋊C8—942no—
148#97—942no—
149#95—472no—
150#95—941no—
151#41—84no—
152C2×Q8—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4—42no—
157C22×C4—42no—
158C22×C4—942no—
159C22×C4D4×D4711yescharacteristic
160C22×C4#1062535211yescharacteristic
161C22×C4C2×C22⋊D4711yescharacteristic
162D8—82no—
163C2×C8—22no—
164C2×C8—42no—
165C2×C8—1882no—
166C2×C8—1881no—
167C2×C8—1882no—
168C4⋊C4—22no—
169C4⋊C4—22no—
170C22⋊C4—42no—
171C22⋊C4—42no—
172C42—942no—
173C42—942no—
174C42#1062535212yes—
175C42C2×C22⋊D4712yes—
176C23—42no—
177C23#1309399511yescharacteristic
178Q8—82no—
179D4—42no—
180D4—42no—
181D4—82no—
182D4—82no—
183D4—84no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—84no—
190C2×C4—944no—
191C2×C4—1882no—
192C2×C4—1882no—
193C2×C4#1309399311yescharacteristic
194C2×C4#1309399612yes—
195C2×C4#1309400512yes—
196C2×C4#1309401111yescharacteristic
197C8—42no—
198C8—3762no—
199C8—3761no—
200C22—21no—
201C22—21no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22#1568903711yescharacteristic
206C22#1568939012yes—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—1884no—
212C4#1568929111yescharacteristic
213C4#1568930611yescharacteristic
214C2—22no—
215C2—162no—
216C2#2024460911yescharacteristic
217C2#2024464111yescharacteristic
218C2#2024469111yescharacteristic
subgroupG/H
centerC22#15689037
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
Fitting, prime radicalC47×#3245C2
socleC22×C47#394
hypercenter#3245D47
hypocenterC47#10512
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #20243541C2semidirect
2. #20242083C2semidirect
3. #20241896C2semidirect
4. #20241258C2semidirect
127. C47#10512semidirect

Maximal subgroups

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

subgroupindex
#202435412
#202420832
#202418962
#202412582
C47×#32452
#1051247