Finite Group Databasebeta

← #26128290

Subgroups — #26128290

Order 12032.

212 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 69 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#20245254C211yesmaximal, characteristic
2#20242301C211yesmaximal, characteristic
3#20242296C211yesmaximal, characteristic, complemented
4#20241357C211yesmaximal, characteristic, complemented
5#20241354C211yesmaximal, characteristic
6#20241308C211yesmaximal, characteristic, complemented
7C47×#1368C211yesmaximal, characteristic, complemented
8C2×#13093969C411yescharacteristic
9#15689250—21no—
10C4×Dic188C2211yescharacteristic
11C4×D376C2211yescharacteristic
12#15689200—21no—
13#15688949C411yescharacteristic
14#15688928C411yescharacteristic
15#15688925C411yescharacteristic
16#15688899C2211yescharacteristic
17#15688853—21no—
18#15688850—21no—
19#15688844C2211yescharacteristic
20C47×#346C2211yescharacteristic
21C47×#334C2211yescharacteristic
22C47×#334C2211yescharacteristic
23C2×Dic188C2×C411yescharacteristic
24C2×D376C2×C411yescharacteristic
25C2×#10625324—41no—
26C4×Dic94—21no—
27C4×D188—21no—
28#13093969—22no—
29C2×C47⋊C16—21no—
30#13093958C2×C411yescharacteristic
31#13093958C2×C411yescharacteristic
32Dic47⋊C8—41no—
33#13093949—21no—
34#13093946—21no—
35(C2×D47)⋊C8—41no—
36#13093934—41no—
37C4×C47⋊C8D411yescharacteristic
38C4×C47⋊C8D411yescharacteristic
39C2×C16×C47C2×C411yescharacteristic
40C2×C16×C47C2×C411yescharacteristic
41C4⋊C8×C47—21no—
42C4⋊C8×C47—21no—
43C4×C8×C47C2311yescharacteristic
44C2×D188—21no—
45C2×C4×D47—41no—
46C2×Dic94—21no—
47C2×C8×C47—41no—
48C2×C8×C47—41no—
49C2×C8×C47C22×C411yescharacteristic
50C2×C8×C47#4111yescharacteristic
51C42×C47C2×D411yescharacteristic
52(C2×D47)⋊C4—41no—
53C4⋊Dic47—21no—
54C4⋊Dic47—21no—
55Dic47⋊C4—41no—
56C4×Dic47—41no—
57C2×C47⋊C8—21no—
58C2×C47⋊C8—21no—
59Dic188—21no—
60Dic188—21no—
61D376—21no—
62D376—21no—
63#10625324—82no—
64C16×C47—21no—
65C16×C47M1612yescomplemented
66C47⋊C16—41no—
67C22×D47—41no—
68C2×C4×C47C4×D411yescharacteristic
69C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
70C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
71C2×Dic47—41no—
72C2×Dic47—41no—
73C2×Dic47—41no—
74D188—41no—
75D188—41no—
76C4×D47—81no—
77C4×D47—81no—
78Dic94—41no—
79Dic94—41no—
80C8×C47—21no—
81C8×C47—81no—
82C8×C47—81no—
83C8×C47C2×M1611yescharacteristic
84C8×C47#13111yescharacteristic
85C47⋊C8—41no—
86C47⋊C8—41no—
87#12087—471nomaximal, Sylow
88C22×C47#44211yescharacteristic
89C2×D47—81no—
90C2×D47—81no—
91C2×D47—81no—
92C4×C47—21no—
93C4×C47—21no—
94C4×C47#43611yescharacteristic
95C4×C47#44411yescharacteristic
96Dic47—81no—
97Dic47—81no—
98Dic47—81no—
99#2175—471no—
100#1594—471no—
101#1593—471no—
102#1368D4711yescharacteristic, complemented
103#1334—471no—
104#1333—471no—
105#1313—471no—
106C2×C47#159411yescharacteristic
107C2×C47#218011yescharacteristic
108C2×C47AGL(1,ℤ/16)11yescharacteristic
109D47—161no—
110C2×SD32—471no—
111#446—941no—
112C4×Q16—471no—
113C4×D8—471no—
114#436—941no—
115#366—471no—
116#358—471no—
117#357—471no—
118#346—471no—
119#346C2×D4711yescharacteristic
120#334C2×D4711yescharacteristic
121#334C2×D4711yescharacteristic
122Q8⋊C8—941no—
123D4⋊C8—941no—
124#322—471no—
125C47#1208711yescharacteristic, complemented, Sylow
126C2×Q16—471no—
127C2×D8—471no—
128C2×M16—1881no—
129C4×Q8—941no—
130C4×D4—941no—
131SD32—942no—
132C2×C16—941no—
133C2×C16C4×D4711yescharacteristic
134C2×C16C4×D4711yescharacteristic
135#107—471no—
136#107—471no—
137C4⋊C8—21no—
138C4⋊C8—21no—
139C4⋊C8—1881no—
140#103—941no—
141#102—941no—
142C22⋊C8—1881no—
143#97—1881no—
144C4×C8—471no—
145C4×C8—471no—
146C4×C8C22×D4711yescharacteristic
147C2×Q8—941no—
148C2×D4—941no—
149C22×C4—1881no—
150Q16—941no—
151Q16—941no—
152D8—941no—
153D8—941no—
154M16—3762no—
155C2×C8—41no—
156C2×C8—41no—
157C2×C8—941no—
158C2×C8—941no—
159C2×C8C2×C4×D4711yescharacteristic
160C2×C8#1062535411yescharacteristic
161C4⋊C4—941no—
162C4⋊C4—941no—
163C4⋊C4—1881no—
164C22⋊C4—1881no—
165C42—1881no—
166C42D4×D4711yescharacteristic
167C16—21no—
168C16—1881no—
169C16#1062532412yescomplemented
170C23—1881no—
171Q8—1881no—
172Q8—1881no—
173D4—1881no—
174D4—1881no—
175C2×C4—3761no—
176C2×C4—3761no—
177C2×C4—1881no—
178C2×C4—1881no—
179C2×C4—1881no—
180C2×C4#1309398611yescharacteristic
181C2×C4#1309405111yescharacteristic
182C2×C4#1309405111yescharacteristic
183C8—21no—
184C8—81no—
185C8—81no—
186C8—1881no—
187C8—1881no—
188C8C2×#1062532411yescharacteristic
189C8#1309403211yescharacteristic
190C22—3761no—
191C22—3761no—
192C22—3761no—
193C22#1568923411yescharacteristic
194C4—21no—
195C4—21no—
196C4—3761no—
197C4—3761no—
198C4—3761no—
199C4#1568920011yescharacteristic
200C4#1568924411yescharacteristic
201C2—7521no—
202C2#2024230111yescharacteristic
203C2#2024527811yescharacteristic
204C2#2024528511yescharacteristic
subgroupG/H
centerC22#15689234
commutatorC2×C8×C47C22×C4
FrattiniC4×C8C22×D47
FittingC47×#1368C2
socleC22×C47#442
prime radicalC2×D376C2×C4
cosocleC4×C8×C47C23
hypercenter#1368D47
hypocenterC47#12087
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1368

Complements

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

NH ≅ G/Ntype
3. #20242296C2semidirect
4. #20241357C2semidirect
6. #20241308C2semidirect
7. C47×#1368C2semidirect
65. C16×C47M16semidirect
102. #1368D47semidirect
125. C47#12087semidirect
169. C16#10625324semidirect

Maximal subgroups

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

subgroupindex
#202452542
#202423012
#202422962
#202413572
#202413542
#202413082
C47×#13682
#1208747