Finite Group Databasebeta

← #26137062

Subgroups — #26137062

Order 12032.

220 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×#15688962C211yesmaximal, characteristic, complemented
2C2×#15688961C211yesmaximal, characteristic, complemented
3#20245636C211yesmaximal, characteristic
4#20245246C211yesmaximal, characteristic, complemented
5Dic47⋊C32C211yesmaximal, characteristic, complemented
6#20241565C211yesmaximal, characteristic, complemented
7C47×#1415C211yesmaximal, characteristic, complemented
8C2×Dic376C2211yescharacteristic
9C2×D752C2211yescharacteristic
10C2×#13093965—21no—
11#15689498—21no—
12#15689217—21no—
13#15688962—22no—
14#15688961—22no—
15C2×C47⋊C32C2211yescharacteristic
16#15688926—21no—
17C16×Dic47C2211yescharacteristic
18C2×D16×C47C2211yescharacteristic
19C2×C32×C47C2211yescharacteristic
20C47×#366C2211yescharacteristic
21C2×Dic188—21no—
22C2×D376—21no—
23C2×#10625334—41no—
24#13094020—41no—
25#13093989—41no—
26Dic376—21no—
27Dic376D412yescomplemented
28D752—21no—
29D752—21no—
30#13093965—42no—
31C2×C47⋊C16D411yescharacteristic
32#13093947—41no—
33C8×Dic47D411yescharacteristic
34C47⋊C32—21no—
35C2×D8×C47—21no—
36D16×C47—21no—
37D16×C47—21no—
38C2×C16×C47C2311yescharacteristic
39#107×C47—21no—
40C32×C47—21no—
41C2×D4×C47—41no—
42C2×C22⋊D47—81no—
43C2×C22⋊D47—81no—
44C2×D188—41no—
45C2×Dic94—41no—
46D8×C47—41no—
47D8×C47—41no—
48C2×C8×C47C2×D411yescharacteristic
49C4⋊C4×C47—41no—
50#10625334—82no—
51Dic47⋊C4—81no—
52C4×Dic47—81no—
53C4×Dic47D811yescharacteristic
54C2×C47⋊C8D811yescharacteristic
55Dic188—22no—
56Dic188—41no—
57D376—41no—
58D376—41no—
59C16×C47C2×D411yescharacteristic
60C16×C47#4111yescharacteristic
61C47⋊C16—21no—
62C23×C47—81no—
63C22×D47—81no—
64D4×C47—81no—
65D4×C47—81no—
66C2×C4×C47—81no—
67C2×C4×C47C2×D811yescharacteristic
68C22⋊D47—162no—
69C22⋊D47—162no—
70C2×Dic47—81no—
71C2×Dic47D1611yescharacteristic
72C2×Dic47D1611yescharacteristic
73D188—81no—
74D188—81no—
75Dic94—42no—
76Dic94—81no—
77C8×C47#12111yescharacteristic
78C8×C47AGL(1,ℤ/8)11yescharacteristic
79C47⋊C8—21no—
80#13686—471nomaximal, Sylow
81C22×C47—161no—
82C22×C47—161no—
83C22×C47—161no—
84C22×C47C2×D1611yescharacteristic
85C2×D47—161no—
86C2×D47—161no—
87C2×D47—161no—
88C4×C47—161no—
89C4×C47#45911yescharacteristic
90C4×C47#50911yescharacteristic
91Dic47—21no—
92Dic47—82no—
93Dic47SD6412yescomplemented
94C2×SD64—471no—
95C2×SD64—471no—
96#2246—471no—
97C4×Q32—471no—
98C4⋊C32—471no—
99#1415—471no—
100#1415D4711yescharacteristic, complemented
101C2×C47—321no—
102C2×C47#220611yescharacteristic
103C2×C47C2×SD6411yescharacteristic
104C2×C47#226311yescharacteristic
105D47—321no—
106C2×Q32—471no—
107C2×D16—471no—
108C2×D16—941no—
109C2×D16C2×D4711yescharacteristic
110#493—941no—
111C4×Q16—941no—
112SD64—942no—
113SD64—942no—
114C2×C32—471no—
115C2×C32C2×D4711yescharacteristic
116#366C2×D4711yescharacteristic
117#358—941no—
118C4×C16—471no—
119C47#1368611yescharacteristic, complemented, Sylow
120C2×Q16—941no—
121C2×D8—21no—
122C2×D8—941no—
123C2×D8—1881no—
124#127—1881no—
125C4×Q8—1881no—
126Q32—472no—
127Q32—941no—
128D16—21no—
129D16—21no—
130D16—941no—
131D16—941no—
132D16—1882no—
133C2×C16—471no—
134C2×C16C22×D4711yescharacteristic
135#107—21no—
136#103—1881no—
137C4×C8—471no—
138C32—21no—
139C32—941no—
140C2×Q8—1881no—
141C2×D4—41no—
142C2×D4—3761no—
143C2×D4—3761no—
144C2×D4—1881no—
145Q16—942no—
146Q16—1881no—
147D8—41no—
148D8—41no—
149D8—3762no—
150D8—1881no—
151D8—1881no—
152C2×C8—471no—
153C2×C8D4×D4711yescharacteristic
154C4⋊C4—41no—
155C4⋊C4—3761no—
156C42—471no—
157C42—3761no—
158C16—941no—
159C16#1062535011yescharacteristic
160C16D4×D4711yescharacteristic
161C23—81no—
162C23—3761no—
163Q8—3761no—
164Q8—1882no—
165D4—81no—
166D4—81no—
167D4—3761no—
168D4—3761no—
169D4—7522no—
170D4—7522no—
171C2×C4—81no—
172C2×C4—471no—
173C2×C4—471no—
174C2×C4—3761no—
175C2×C4D8×D4711yescharacteristic
176C8—941no—
177C8#1309399711yescharacteristic
178C8#1309405111yescharacteristic
179C22—161no—
180C22—161no—
181C22—161no—
182C22—7521no—
183C22—7521no—
184C22—7521no—
185C22D16×D4711yescharacteristic
186C4—161no—
187C4—472no—
188C4—941no—
189C4—3762no—
190C4#1568931711yescharacteristic
191C4#1568956011yescharacteristic
192C2—321no—
193C2—15041no—
194C2#2024542211yescharacteristic
195C2SD64×D4711yescharacteristic
196C2#2024569911yescharacteristic
subgroupG/H
centerC22D16×D47
commutator, cosocleC2×C16×C47C23
FrattiniC2×C16C22×D47
FittingC47×#1415C2
socleC22×C47C2×D16
prime radical#20245636C2
hypercenter#1415D47
hypocenterC47#13686
LCSG ▷ C2×C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1415

Complements

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

NH ≅ G/Ntype
1. C2×#15688962C2semidirect
2. C2×#15688961C2semidirect
4. #20245246C2semidirect
5. Dic47⋊C32C2semidirect
6. #20241565C2semidirect
7. C47×#1415C2semidirect
27. Dic376D4semidirect
93. Dic47SD64semidirect
100. #1415D47semidirect
119. C47#13686semidirect

Maximal subgroups

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

subgroupindex
C2×#156889622
C2×#156889612
#202456362
#202452462
Dic47⋊C322
#202415652
C47×#14152
#1368647