Finite Group Databasebeta

← #26136644

Subgroups — #26136644

Order 12032.

318 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 79 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#20245073C212yesmaximal
2#20241561C214yesmaximal, complemented
3C47×#3142C211yesmaximal, characteristic
4#15689107—22no—
5#15688922C2214yes—
6#15688920—22no—
7C47×#532C2211yescharacteristic
8C2×#125×C47C411yescharacteristic
9C47×#491C2212yes—
10C47×#490C412yes—
11C47×#488—22no—
12C47×#417—22no—
13C4×M16×C47C411yescharacteristic
14C2×#10625329—42no—
15#13093943—24no—
16#13093941—42no—
17C2×#41×C47D412yes—
18C2×M16×C47—21no—
19C4⋊Q8×C47C2311yescharacteristic
20#127×C47C2×C411yescharacteristic
21#125×C47—21no—
22#125×C47—41no—
23#125×C47C2×C412yes—
24#124×C47D412yes—
25#121×C47—41no—
26C4×D4×C47—41no—
27C2×C4⋊C4×C47—21no—
28C2×C4⋊C4×C47—41no—
29C2×C42×C47C2×C411yescharacteristic
30#103×C47—24no—
31#102×C47—24no—
32#97×C47C2×C412yes—
33C4×C8×C47—21no—
34#41×C47—42no—
35#41×C47—42no—
36C2×Q8×C47C2×D412yes—
37C2×D4×C47—22no—
38C2×D4×C47—41no—
39C2×D4×C47C22⋊C412yes—
40C22×C4×C47—21no—
41C22×C4×C47—22no—
42C22×C4×C47—41no—
43C22×C4×C47C22⋊C411yescharacteristic
44M16×C47—42no—
45C2×C8×C47—22no—
46C4⋊C4×C47—22no—
47C4⋊C4×C47—41no—
48C4⋊C4×C47—42no—
49C4⋊C4×C47—42no—
50C4⋊C4×C47—41no—
51C22⋊C4×C47—42no—
52C42×C47—21no—
53C42×C47C22⋊C411yescharacteristic
54C42×C47C22×C411yescharacteristic
55#10625329—44no—
56#10625329—82no—
57C2×C47⋊C8—82no—
58C23×C47—22no—
59C23×C47#9911yescharacteristic
60Q8×C47—42no—
61D4×C47—42no—
62D4×C47—82no—
63D4×C47—82no—
64C2×C4×C47—22no—
65C2×C4×C47—22no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—42no—
69C2×C4×C47—42no—
70C2×C4×C47—42no—
71C2×C4×C47—81no—
72C2×C4×C47—82no—
73C2×C4×C47#9911yescharacteristic
74C2×C4×C47C2×C22⋊C411yescharacteristic
75C8×C47—42no—
76C47⋊C8—84no—
77#13600—471nomaximal, Sylow
78C22×C47—21no—
79C22×C47—41no—
80C22×C47—42no—
81C22×C47—82no—
82C22×C47C2×#9911yescharacteristic
83C4×C47—21no—
84C4×C47—41no—
85C4×C47—41no—
86C4×C47—42no—
87C4×C47—82no—
88C4×C47#35412yes—
89#3142D4711yescharacteristic
90#2132—472no—
91#1413—474no—
92C2×C47—21no—
93C2×C47—41no—
94C2×C47—82no—
95C2×C47C2×#35411yescharacteristic
96#532C2×D4711yescharacteristic
97C2×#125Dic4711yescharacteristic
98#491C2×D4712yes—
99#490Dic4712yes—
100#488—22no—
101#417—22no—
102#413—942no—
103C4×M16Dic4711yescharacteristic
104#356—474no—
105#355—942no—
106C47#1360011yescharacteristic, complemented, Sylow
107C2×#41C22⋊D4712yes—
108C2×M16—21no—
109C2×M16—1882no—
110C4⋊Q8C22×D4711yescharacteristic
111#127C2×Dic4711yescharacteristic
112#125—21no—
113#125—41no—
114#125C2×Dic4712yes—
115#124C22⋊D4712yes—
116#121—41no—
117C4×D4—41no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—41no—
120C2×C42C2×Dic4711yescharacteristic
121#103—24no—
122#102—24no—
123#101—944no—
124#100—1882no—
125#97C2×Dic4712yes—
126C4×C8—21no—
127#41—42no—
128#41—42no—
129C2×Q8C2×C22⋊D4712yes—
130C2×D4—22no—
131C2×D4—41no—
132C2×D4C22⋊Dic4712yes—
133C22×C4—21no—
134C22×C4—22no—
135C22×C4—41no—
136C22×C4C22⋊Dic4711yescharacteristic
137M16—42no—
138M16—3762no—
139M16—1884no—
140C2×C8—22no—
141C2×C8—3762no—
142C4⋊C4—22no—
143C4⋊C4—41no—
144C4⋊C4—42no—
145C4⋊C4—42no—
146C4⋊C4—41no—
147C22⋊C4—42no—
148C42—21no—
149C42C22⋊Dic4711yescharacteristic
150C42C22×Dic4711yescharacteristic
151C23—22no—
152C23#1309393911yescharacteristic
153Q8—42no—
154D4—42no—
155D4—82no—
156D4—82no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—81no—
165C2×C4—82no—
166C2×C4#1309393911yescharacteristic
167C2×C4C2×C22⋊Dic4711yescharacteristic
168C8—42no—
169C8—3764no—
170C22—21no—
171C22—41no—
172C22—42no—
173C22—82no—
174C22C2×#1309393911yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—42no—
179C4—82no—
180C4#1568891812yes—
181C2—21no—
182C2—41no—
183C2—82no—
184C2C2×#1568891811yescharacteristic
subgroupG/H
centerC2C2×#15688918
commutatorC42×C47C22×C4
FrattiniC4⋊Q8C22×D47
FittingC47×#3142C2
socleC2×C47C2×#354
prime radicalC47×#532C22
cosocleC4⋊Q8×C47C23
hypercenter#3142D47
hypocenterC47#13600
LCSG ▷ C42×C47 ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #3142

Complements

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

NH ≅ G/Ntype
2. #20241561C2semidirect
106. C47#13600semidirect

Maximal subgroups

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

subgroupindex
#202450732
#202415612
C47×#31422
#1360047