Finite Group Databasebeta

← #26127793

Subgroups — #26127793

Order 12032.

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

normal subgroups only

This group has 292 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#20254038C211yesmaximal, characteristic
2#20245204C211yesmaximal, characteristic, complemented
3#20241450C212yesmaximal, complemented
4#20241424C212yesmaximal, complemented
5C47×#2153C211yesmaximal, characteristic, complemented
6#15689728C412yes—
7#15689525C2211yescharacteristic
8#15689500C2211yescharacteristic
9#15689488C412yes—
10#15689376—21no—
11#15689359—21no—
12#15689236—21no—
13C4×D376—21no—
14#15688944C2212yes—
15#15688905—21no—
16#15688901—21no—
17C2×M32×C47—21no—
18C47×#405C2211yescharacteristic
19C47×#364—21no—
20C47×#364C2212yes—
21C2×D376—21no—
22C2×D376—21no—
23#13094021C2×C412yes—
24#13094016C2×C412yes—
25#13094009—42no—
26#13093998—22no—
27#13093997—42no—
28C4×D188—22no—
29#13093964—22no—
30#13093958—21no—
31#13093956—21no—
32#13093946—22no—
33#13093946—22no—
34C2×M16×C47D411yescharacteristic
35C22×C8×C47D411yescharacteristic
36#117×C47C2×C411yescharacteristic
37M32×C47—22no—
38M32×C47—41no—
39C2×C16×C47—41no—
40#97×C47C2×C411yescharacteristic
41#97×C47D411yescharacteristic
42C4×C8×C47D411yescharacteristic
43C4×C8×C47C2311yescharacteristic
44C22×C4×C47C22⋊C411yescharacteristic
45C2×C22⋊D47—42no—
46C2×D188—22no—
47C2×D188—42no—
48C2×C4×D47—42no—
49M16×C47—22no—
50C2×C8×C47—21no—
51C2×C8×C47—21no—
52C2×C8×C47C22⋊C411yescharacteristic
53C2×C8×C47C22⋊C411yescharacteristic
54C2×C8×C47C2×D411yescharacteristic
55C2×C8×C47C2×D411yescharacteristic
56C4⋊C4×C47—21no—
57C22⋊C4×C47—21no—
58C42×C47C22⋊C411yescharacteristic
59C42×C47C22×C411yescharacteristic
60(C2×D47)⋊C4—42no—
61(C2×D47)⋊C4—42no—
62C4⋊Dic47—22no—
63Dic47⋊C4—42no—
64D376—42no—
65D376—41no—
66D376—41no—
67C16×C47—42no—
68C47⋊C16—42no—
69C23×C47#10011yescharacteristic
70C22×D47—42no—
71C2×C4×C47—21no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47#10011yescharacteristic
76C2×C4×C47C2×C22⋊C411yescharacteristic
77C22⋊D47—162no—
78C2×Dic47—42no—
79D188—42no—
80D188—42no—
81D188—162no—
82C4×D47—162no—
83C8×C47—21no—
84C8×C47—21no—
85C8×C47#13512yes—
86C8×C47AGL(1,ℤ/8)11yescharacteristic
87C8×C47#13711yescharacteristic
88#11989—471nomaximal, Sylow
89C22×C47—21no—
90C22×C47—41no—
91C22×C47C2×#10011yescharacteristic
92C2×D47—82no—
93C2×D47—82no—
94C2×D47—82no—
95C4×C47—21no—
96C4×C47—41no—
97C4×C47—41no—
98C4×C47#41611yescharacteristic
99C4×C47#41711yescharacteristic
100Dic47—82no—
101#3176—471no—
102#2166—471no—
103#2153D4711yescharacteristic, complemented
104#1366—472no—
105#1357—472no—
106C2×C47—21no—
107C2×C47—41no—
108C2×C47#155111yescharacteristic
109D47—162no—
110#540—472no—
111C2×M32—21no—
112#499—471no—
113#493—471no—
114#490—472no—
115#469—941no—
116#466—941no—
117#442—941no—
118C4×D8—941no—
119#405C2×D4711yescharacteristic
120#364—21no—
121#364—472no—
122#364C2×D4712yes—
123#349—941no—
124#347—941no—
125C47#1198911yescharacteristic, complemented, Sylow
126C2×D8—941no—
127C2×D8—941no—
128C2×M16D18811yescharacteristic
129C22×C8C22⋊D4711yescharacteristic
130#127—472no—
131#125—472no—
132#123—1882no—
133#121—942no—
134#121—1882no—
135C4×D4—942no—
136#117C4×D4711yescharacteristic
137M32—22no—
138M32—41no—
139M32—942no—
140C2×C16—41no—
141#107—941no—
142#106—941no—
143#102—942no—
144#102—942no—
145#97C4×D4711yescharacteristic
146#97D18811yescharacteristic
147C4×C8C22⋊D4711yescharacteristic
148C4×C8C22×D4711yescharacteristic
149C2×D4—942no—
150C2×D4—1882no—
151C2×D4—1882no—
152C22×C4—1882no—
153C22×C4(C2×D47)⋊C411yescharacteristic
154D8—1882no—
155D8—1881no—
156D8—1881no—
157M16—22no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8(C2×D47)⋊C411yescharacteristic
161C2×C8(C2×D47)⋊C411yescharacteristic
162C2×C8C2×D18811yescharacteristic
163C2×C8C2×C22⋊D4711yescharacteristic
164C4⋊C4—21no—
165C4⋊C4—942no—
166C4⋊C4—1882no—
167C22⋊C4—21no—
168C22⋊C4—1882no—
169C22⋊C4—1882no—
170C42(C2×D47)⋊C411yescharacteristic
171C42C2×C4×D4711yescharacteristic
172C16—42no—
173C16—1882no—
174C23—1882no—
175C23#1309394011yescharacteristic
176D4—1882no—
177D4—1882no—
178D4—7522no—
179D4—7522no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—1882no—
185C2×C4—7522no—
186C2×C4#1309394011yescharacteristic
187C2×C4C2×(C2×D47)⋊C411yescharacteristic
188C8—21no—
189C8—21no—
190C8#1309404612yes—
191C8#1309405011yescharacteristic
192C8#1309405511yescharacteristic
193C22—21no—
194C22—41no—
195C22—3762no—
196C22—3762no—
197C22—3762no—
198C22C2×#1309394011yescharacteristic
199C4—21no—
200C4—41no—
201C4—41no—
202C4—3762no—
203C4#1568912011yescharacteristic
204C4#1568912211yescharacteristic
205C2—21no—
206C2—41no—
207C2—7522no—
208C2#2024208111yescharacteristic
subgroupG/H
centerC2#20242081
commutatorC42×C47C22×C4
FrattiniC4×C8C22×D47
FittingC47×#2153C2
socleC2×C47#1551
prime radical#20254038C2
cosocleC4×C8×C47C23
hypercenter#2153D47
hypocenterC47#11989
LCSG ▷ C42×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2153

Complements

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

NH ≅ G/Ntype
2. #20245204C2semidirect
3. #20241450C2semidirect
4. #20241424C2semidirect
5. C47×#2153C2semidirect
103. #2153D47semidirect
125. C47#11989semidirect

Maximal subgroups

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

subgroupindex
#202540382
#202452042
#202414502
#202414242
C47×#21532
#1198947