Finite Group Databasebeta

← #26119416

Subgroups — #26119416

Order 12032.

402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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#20246693C211yesmaximal, characteristic, complemented
2#20241883C212yesmaximal
3#20241289C212yesmaximal, complemented
4#20241217C211yesmaximal, characteristic, complemented
5C47×#1963C211yesmaximal, characteristic
6#15689176C2212yes—
7#15689065—22no—
8#15689057—22no—
9C4×Dic47⋊C4—22no—
10C4×C4⋊Dic47C2212yes—
11#15688857—22no—
12#15688857—22no—
13C47×#532C2211yescharacteristic
14C47×#423C2211yescharacteristic
15C2×#104×C47—22no—
16C47×#376C2211yescharacteristic
17C2×C4⋊Dic47—22no—
18C2×Dic47⋊C4—22no—
19C2×Dic47⋊C4—22no—
20C2×C4×Dic47—22no—
21C4⋊(C47⋊C8)—22no—
22C22⋊(C47⋊C8)—22no—
23C4×C47⋊C8—22no—
24C47⋊#95—22no—
25C47⋊#95—22no—
26C47⋊#95D412yes—
27C47⋊#95D412yes—
28C2×#41×C47—21no—
29C2×M16×C47—21no—
30C4⋊Q8×C47Q811yescharacteristic
31#127×C47Q811yescharacteristic
32#124×C47—21no—
33#121×C47—22no—
34C4×D4×C47—22no—
35C2×C42×C47D412yes—
36C2×C42×C47C2311yescharacteristic
37C4⋊C8×C47—22no—
38#104×C47—44no—
39#95×C47—22no—
40#41×C47—42no—
41#41×C47—42no—
42C2×Q8×C47—21no—
43C2×D4×C47—21no—
44C2×D4×C47—22no—
45C2×D4×C47—41no—
46C22×C4×C47—22no—
47C22×C4×C47—41no—
48C22×C4×C47C2×D412yes—
49C22×C4×C47C2×D411yescharacteristic
50C22×Dic47—22no—
51C22×Dic47—22no—
52M16×C47—42no—
53C2×C8×C47—41no—
54C4⋊C4×C47—22no—
55C22⋊C4×C47—42no—
56C42×C47—22no—
57C42×C47—22no—
58C42×C47C2×Q811yescharacteristic
59C42×C47#4111yescharacteristic
60C42×C47#4112yes—
61C4⋊Dic47—44no—
62Dic47⋊C4—44no—
63Dic47⋊C4—44no—
64C4×Dic47—42no—
65C4×Dic47—42no—
66C2×C47⋊C8—42no—
67C23×C47—41no—
68C23×C47#12011yescharacteristic
69Q8×C47—42no—
70D4×C47—42no—
71D4×C47—82no—
72D4×C47—82no—
73C2×C4×C47—42no—
74C2×C4×C47—42no—
75C2×C4×C47—42no—
76C2×C4×C47—41no—
77C2×C4×C47—42no—
78C2×C4×C47—81no—
79C2×C4×C47—81no—
80C2×C4×C47C22⋊Q812yes—
81C2×C4×C47C22⋊Q811yescharacteristic
82C2×C4×C47#12412yes—
83C2×C4×C47#12411yescharacteristic
84C2×C4×C47#13512yes—
85C2×C4×C47AGL(1,ℤ/8)12yes—
86C2×Dic47—24no—
87C2×Dic47—42no—
88C2×Dic47—42no—
89C2×Dic47—42no—
90C2×Dic47—42no—
91C2×Dic47—42no—
92C8×C47—81no—
93C47⋊C8—82no—
94#10372—471nomaximal, Sylow
95C22×C47—22no—
96C22×C47—81no—
97C22×C47—82no—
98C22×C47#39311yescharacteristic
99C22×C47#44912yes—
100C4×C47—22no—
101C4×C47—22no—
102C4×C47—82no—
103C4×C47—81no—
104C4×C47#47812yes—
105C4×C47#48811yescharacteristic
106C4×C47#49011yescharacteristic
107Dic47—44no—
108Dic47—82no—
109#2402—471no—
110#1963D4711yescharacteristic
111#1502—472no—
112#1303—472no—
113#1274—471no—
114C2×C47—22no—
115C2×C47—161no—
116C2×C47#202511yescharacteristic
117C2×C47#203112yes—
118#532C2×D4711yescharacteristic
119#431—472no—
120#423C2×D4711yescharacteristic
121C2×#104—22no—
122#400—942no—
123#398—942no—
124C4×C4⋊C4—472no—
125C4×C4⋊C4—942no—
126#376C2×D4711yescharacteristic
127#327—942no—
128#327—942no—
129C47#1037211yescharacteristic, complemented, Sylow
130C2×#41—21no—
131C2×M16—21no—
132C4⋊Q8Dic9411yescharacteristic
133#127Dic9411yescharacteristic
134#124—21no—
135#121—22no—
136C4×D4—22no—
137C2×C4⋊C4—942no—
138C2×C4⋊C4—942no—
139C2×C4⋊C4—942no—
140C2×C42—942no—
141C2×C42C22⋊D4712yes—
142C2×C42C22×D4711yescharacteristic
143C4⋊C8—22no—
144C4⋊C8—942no—
145#104—44no—
146C22⋊C8—942no—
147C4×C8—942no—
148#95—22no—
149#95—472no—
150#95—472no—
151#95—942no—
152#95—942no—
153#41—42no—
154#41—42no—
155C2×Q8—21no—
156C2×D4—22no—
157C2×D4—21no—
158C2×D4—41no—
159C22×C4—22no—
160C22×C4—41no—
161C22×C4—942no—
162C22×C4—942no—
163C22×C4D4×D4712yes—
164C22×C4C2×C22⋊D4711yescharacteristic
165M16—42no—
166C2×C8—41no—
167C2×C8—1882no—
168C4⋊C4—22no—
169C4⋊C4—1884no—
170C4⋊C4—1884no—
171C4⋊C4—1884no—
172C22⋊C4—42no—
173C42—22no—
174C42—22no—
175C42—1882no—
176C42—1882no—
177C42C2×Dic9411yescharacteristic
178C42#1062535011yescharacteristic
179C42#1062535212yes—
180C23—41no—
181C23#1309399211yescharacteristic
182Q8—42no—
183D4—42no—
184D4—82no—
185D4—82no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—41no—
191C2×C4—81no—
192C2×C4—81no—
193C2×C4—944no—
194C2×C4—1882no—
195C2×C4—1882no—
196C2×C4—1882no—
197C2×C4—1882no—
198C2×C4—1882no—
199C2×C4#1309400112yes—
200C2×C4#1309400311yescharacteristic
201C2×C4#1309401012yes—
202C2×C4#1309401111yescharacteristic
203C2×C4#1309404412yes—
204C2×C4#1309405012yes—
205C8—81no—
206C8—3762no—
207C22—22no—
208C22—81no—
209C22—82no—
210C22#1568903511yescharacteristic
211C22#1568926612yes—
212C4—22no—
213C4—22no—
214C4—82no—
215C4—81no—
216C4—3762no—
217C4—1884no—
218C4#1568942312yes—
219C4#1568947711yescharacteristic
220C4#1568948711yescharacteristic
221C2—22no—
222C2—161no—
223C2#2024453411yescharacteristic
224C2#2024455812yes—
subgroupG/H
centerC2×C4#13094011
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1963C2
socleC22×C47#393
prime radicalC47×#532C22
hypercenter#1963D47
hypocenterC47#10372
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
1. #20246693C2semidirect
3. #20241289C2semidirect
4. #20241217C2semidirect
129. C47#10372semidirect

Maximal subgroups

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

subgroupindex
#202466932
#202418832
#202412892
#202412172
C47×#19632
#1037247