Finite Group Databasebeta

← #26102968

Subgroups — #26102968

Order 12032.

204 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 45 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#20244711C211yesmaximal, characteristic
2#20241328C211yesmaximal, characteristic
3C47×#1290C211yesmaximal, characteristic
4C22×Dic188C411yescharacteristic
5C2×#13093949—21no—
6#15689029—21no—
7C22⋊(C47⋊C16)—21no—
8#15688886C411yescharacteristic
9C47×#432—21no—
10C2×C4⋊C8×C47C2211yescharacteristic
11C22×Dic94—21no—
12C2×Dic188—41no—
13C2×Dic188—42no—
14C2×C4⋊Dic47—21no—
15C2×C47⋊C16—41no—
16#13093949—42no—
17C47⋊#95—41no—
18C47⋊#95—41no—
19C22×C8×C47C2×C411yescharacteristic
20C22×C8×C47D411yescharacteristic
21C2×C42×C47D411yescharacteristic
22C4⋊C8×C47—41no—
23C4⋊C8×C47—41no—
24C22⋊C8×C47—41no—
25#97×C47—22no—
26C22×C4×C47C22⋊C411yescharacteristic
27C22×C4×C47D811yescharacteristic
28C22×C4×C47SD1611yescharacteristic
29C22×Dic47—41no—
30C22×Dic47—41no—
31C2×Dic94—22no—
32C2×Dic94—41no—
33C2×Dic94—41no—
34C2×Dic94—41no—
35C2×Dic94—41no—
36C2×Dic94—41no—
37C2×C8×C47—21no—
38C2×C8×C47—21no—
39C2×C8×C47—41no—
40C2×C8×C47—41no—
41C2×C8×C47—42no—
42C42×C47—21no—
43C42×C47—21no—
44C4⋊Dic47—41no—
45C4⋊Dic47—41no—
46Dic188—42no—
47Dic188—42no—
48C47⋊C16—81no—
49C23×C47#10211yescharacteristic
50C2×C4×C47—21no—
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47—41no—
57C2×C4×C47#9911yescharacteristic
58C2×C4×C47#10411yescharacteristic
59C2×Dic47—42no—
60C2×Dic47—81no—
61C2×Dic47—81no—
62C2×Dic47—81no—
63C2×Dic47—81no—
64C2×Dic47—81no—
65Dic94—42no—
66Dic94—42no—
67Dic94—81no—
68Dic94—81no—
69C8×C47—41no—
70C8×C47—41no—
71C8×C47—82no—
72#7082—471nomaximal, Sylow
73C22×C47—21no—
74C22×C47—21no—
75C22×C47#32711yescharacteristic
76C22×C47#35911yescharacteristic
77C22×C47#36211yescharacteristic
78C4×C47—21no—
79C4×C47—41no—
80C4×C47—41no—
81C4×C47AΣL(1,𝔽16)11yescharacteristic
82C4×C47#35511yescharacteristic
83Dic47—82no—
84Dic47—161no—
85#2056—471no—
86#1322—471no—
87#1290D4711yescharacteristic
88C2×C47—21no—
89C2×C47—21no—
90C2×C47#134011yescharacteristic
91C2×C47#134511yescharacteristic
92C2×C47#135011yescharacteristic
93C22×Q16—471no—
94#432—21no—
95C2×C4⋊C8C2×D4711yescharacteristic
96C2×#103—941no—
97#391—941no—
98C22⋊C16—941no—
99#340—471no—
100C47#708211yescharacteristic, complemented, Sylow
101C22×Q8—941no—
102C2×Q16—1881no—
103C2×Q16—1882no—
104C22×C8C4×D4711yescharacteristic
105C22×C8D18811yescharacteristic
106C2×C4⋊C4—941no—
107C2×C42C22⋊D4711yescharacteristic
108C2×C16—1881no—
109C4⋊C8—41no—
110C4⋊C8—41no—
111#103—1882no—
112C22⋊C8—41no—
113#97—22no—
114#95—1881no—
115#95—1881no—
116C2×Q8—942no—
117C2×Q8—1881no—
118C2×Q8—1881no—
119C2×Q8—1881no—
120C2×Q8—1881no—
121C2×Q8—1881no—
122C22×C4—1881no—
123C22×C4—1881no—
124C22×C4(C2×D47)⋊C411yescharacteristic
125C22×C4#1062533411yescharacteristic
126C22×C4#1062533611yescharacteristic
127Q16—1882no—
128Q16—1882no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—41no—
132C2×C8—41no—
133C2×C8—42no—
134C4⋊C4—1881no—
135C4⋊C4—1881no—
136C42—21no—
137C42—21no—
138C16—3761no—
139C23#1309394411yescharacteristic
140Q8—3761no—
141Q8—3761no—
142Q8—1882no—
143Q8—1882no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—3761no—
152C2×C4—3761no—
153C2×C4—3761no—
154C2×C4—3761no—
155C2×C4—3761no—
156C2×C4—1882no—
157C2×C4#1309393811yescharacteristic
158C2×C4#1309395211yescharacteristic
159C8—41no—
160C8—41no—
161C8—82no—
162C22—21no—
163C22—21no—
164C22#1568885611yescharacteristic
165C22#1568892911yescharacteristic
166C22#1568893811yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—3762no—
171C4—7521no—
172C4#1568891111yescharacteristic
173C4#1568891911yescharacteristic
174C2—21no—
175C2—21no—
176C2#2024137511yescharacteristic
177C2#2024139011yescharacteristic
178C2#2024140511yescharacteristic
subgroupG/H
centerC22#15688856
commutatorC22×C8×C47C2×C4
FrattiniC2×C4⋊C8C2×D47
FittingC47×#1290C2
socleC22×C47#327
prime radicalC23×C47#102
cosocleC2×C4⋊C8×C47C22
hypercenter#1290D47
hypocenterC47#7082
LCSG ▷ C22×C8×C47 ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #1290

Complements

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

NH ≅ G/Ntype
100. C47#7082semidirect

Maximal subgroups

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

subgroupindex
#202447112
#202413282
C47×#12902
#708247