Finite Group Databasebeta

← #26103793

Subgroups — #26103793

Order 12032.

252 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 41 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#20244487C211yesmaximal, characteristic
2#20241322C211yesmaximal, characteristic
3C47×#1394C211yesmaximal, characteristic
4C22×#10625337—21no—
5C2×#13094024C411yescharacteristic
6C2×#13093947—21no—
7#15688878C411yescharacteristic
8#15688849—21no—
9C2×#101×C47—21no—
10C47×#391C2211yescharacteristic
11C22×Dic94—21no—
12C2×#10625337—42no—
13C2×#10625337—42no—
14C2×#10625337—41no—
15C2×#10625337—41no—
16C22×C47⋊C8—21no—
17#13094024—42no—
18C2×C4⋊Dic47—41no—
19#13093947—42no—
20C22⋊(C47⋊C8)—41no—
21C22×Q8×C47D411yescharacteristic
22C2×M16×C47—41no—
23C2×C4⋊C4×C47D411yescharacteristic
24C2×C42×C47C2×C411yescharacteristic
25#101×C47—22no—
26#101×C47—41no—
27#95×C47—41no—
28C2×Q8×C47—21no—
29C2×Q8×C47—41no—
30C2×Q8×C47—41no—
31C2×Q8×C47D811yescharacteristic
32C2×Q8×C47SD1611yescharacteristic
33C22×C4×C47—21no—
34C22×C4×C47—21no—
35C22×C4×C47—21no—
36C22×C4×C47C22⋊C411yescharacteristic
37C22×Dic47—41no—
38C2×Dic94—22no—
39C2×Dic94—41no—
40C2×Dic94—41no—
41C2×Dic94—41no—
42C2×Dic94—41no—
43C2×Dic94—41no—
44M16×C47—42no—
45M16×C47—81no—
46C2×C8×C47—81no—
47C4⋊C4×C47—41no—
48C42×C47—41no—
49#10625337—44no—
50#10625337—44no—
51C4⋊Dic47—42no—
52C4⋊Dic47—42no—
53C2×C47⋊C8—22no—
54C2×C47⋊C8—41no—
55C2×C47⋊C8—41no—
56C2×C47⋊C8—81no—
57C23×C47#9911yescharacteristic
58Q8×C47—41no—
59Q8×C47—41no—
60Q8×C47—81no—
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47—22no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47—41no—
71C2×C4×C47—81no—
72C2×C4×C47#10211yescharacteristic
73C2×C4×C47#10411yescharacteristic
74C2×Dic47—42no—
75C2×Dic47—81no—
76C2×Dic47—81no—
77Dic94—42no—
78Dic94—42no—
79Dic94—81no—
80Dic94—81no—
81C8×C47—82no—
82C47⋊C8—42no—
83C47⋊C8—161no—
84#7405—471nomaximal, Sylow
85C22×C47—21no—
86C22×C47—21no—
87C22×C47#32711yescharacteristic
88C22×C47AΣL(1,𝔽16)11yescharacteristic
89C22×C47#35311yescharacteristic
90C4×C47—21no—
91C4×C47—21no—
92C4×C47—42no—
93C4×C47—41no—
94C4×C47—41no—
95C4×C47—81no—
96Dic47—82no—
97#2016—471no—
98#1394D4711yescharacteristic
99#1319—471no—
100C2×C47—21no—
101C2×C47—21no—
102C2×C47#134311yescharacteristic
103C2×C47#140711yescharacteristic
104C2×C47#141111yescharacteristic
105C22×Q16—941no—
106C2×C4⋊Q8—471no—
107C2×#103—941no—
108C2×#101—21no—
109#391C2×D4711yescharacteristic
110#336—471no—
111#324—941no—
112C47#740511yescharacteristic, complemented, Sylow
113C22×Q8—941no—
114C22×Q8C22⋊D4711yescharacteristic
115C2×Q16—1882no—
116C2×Q16—1882no—
117C2×Q16—1881no—
118C2×Q16—1881no—
119C2×M16—41no—
120C22×C8—941no—
121C4⋊Q8—1882no—
122C2×C4⋊C4—1881no—
123C2×C4⋊C4D18811yescharacteristic
124C2×C42C4×D4711yescharacteristic
125#103—1882no—
126#101—22no—
127#101—41no—
128C22⋊C8—1881no—
129#95—41no—
130C2×Q8—21no—
131C2×Q8—41no—
132C2×Q8—41no—
133C2×Q8—942no—
134C2×Q8—1881no—
135C2×Q8—1881no—
136C2×Q8—1881no—
137C2×Q8—1881no—
138C2×Q8—1881no—
139C2×Q8#1062533411yescharacteristic
140C2×Q8#1062533611yescharacteristic
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—1881no—
145C22×C4(C2×D47)⋊C411yescharacteristic
146Q16—1884no—
147Q16—1884no—
148M16—42no—
149M16—81no—
150C2×C8—81no—
151C2×C8—942no—
152C2×C8—3761no—
153C2×C8—1881no—
154C2×C8—1881no—
155C4⋊C4—41no—
156C4⋊C4—1882no—
157C4⋊C4—1882no—
158C42—41no—
159C23#1309393811yescharacteristic
160Q8—41no—
161Q8—41no—
162Q8—81no—
163Q8—3761no—
164Q8—3761no—
165Q8—1882no—
166Q8—1882no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—81no—
178C2×C4—3761no—
179C2×C4—3761no—
180C2×C4—1882no—
181C2×C4#1309394411yescharacteristic
182C2×C4#1309395211yescharacteristic
183C8—82no—
184C8—1882no—
185C8—7521no—
186C22—21no—
187C22—21no—
188C22#1568885611yescharacteristic
189C22#1568890911yescharacteristic
190C22#1568891511yescharacteristic
191C4—21no—
192C4—21no—
193C4—42no—
194C4—41no—
195C4—41no—
196C4—81no—
197C4—3762no—
198C2—21no—
199C2—21no—
200C2#2024138411yescharacteristic
201C2#2024154911yescharacteristic
202C2#2024155611yescharacteristic
subgroupG/H
centerC22#15688915
commutatorC2×C42×C47C2×C4
Frattini#391C2×D47
FittingC47×#1394C2
socleC22×C47#353
prime radicalC23×C47#99
cosocleC47×#391C22
hypercenter#1394D47
hypocenterC47#7405
LCSG ▷ C2×C42×C47 ▷ C22×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #391 ◁ #1394

Complements

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

NH ≅ G/Ntype
112. C47#7405semidirect

Maximal subgroups

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

subgroupindex
#202444872
#202413222
C47×#13942
#740547