Finite Group Databasebeta

← #26130530

Subgroups — #26130530

Order 12032.

224 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 59 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#20245645C211yesmaximal, characteristic, complemented
2#20245464C211yesmaximal, characteristic
3#20245225C211yesmaximal, characteristic, complemented
4#20241463C211yesmaximal, characteristic, complemented
5#20241427C211yesmaximal, characteristic, complemented
6#20241424C211yesmaximal, characteristic, complemented
7C47×#2214C211yesmaximal, characteristic, complemented
8#15689558—21no—
9C2×#13093967—21no—
10C2×#13093967—21no—
11#15689540—21no—
12#15689500C2211yescharacteristic
13#15688944C2211yescharacteristic
14#15688944C2211yescharacteristic
15#15688935—21no—
16#15688907—21no—
17C4×C47⋊C16C2211yescharacteristic
18C47×#510—21no—
19C47×#494C2211yescharacteristic
20C47×#443C2211yescharacteristic
21C47×#364C2211yescharacteristic
22C47×#362—21no—
23C2×D376—21no—
24C2×D376—21no—
25#13094021—21no—
26#13093967—42no—
27#13093967—41no—
28#13093967—41no—
29#13093967—41no—
30#13093965—41no—
31#13093964—21no—
32#13093964—21no—
33#13093964—41no—
34C2×C47⋊C16—41no—
35C2×C47⋊C16D411yescharacteristic
36C2×C47⋊C16D411yescharacteristic
37#135×C47D411yescharacteristic
38C2×Q16×C47—21no—
39C2×Q16×C47—21no—
40#131×C47—21no—
41C4⋊Q8×C47—21no—
42Q32×C47—41no—
43SD32×C47—41no—
44M32×C47—21no—
45#108×C47D411yescharacteristic
46#104×C47—21no—
47C4×C8×C47C2311yescharacteristic
48#41×C47—21no—
49C2×Q8×C47—41no—
50C2×D188—41no—
51C2×D188—81no—
52Q16×C47—41no—
53Q16×C47—41no—
54Q16×C47—41no—
55Q16×C47—41no—
56Q16×C47D811yescharacteristic
57SD16×C47—21no—
58D8×C47D811yescharacteristic
59M16×C47—21no—
60M16×C47—41no—
61C2×C8×C47—41no—
62C2×C8×C47C2×D411yescharacteristic
63C2×C8×C47C2×D411yescharacteristic
64C4⋊C4×C47—81no—
65C42×C47#4111yescharacteristic
66D376—41no—
67D376—41no—
68D376—41no—
69D376—41no—
70C16×C47—41no—
71C47⋊C16—21no—
72C47⋊C16—41no—
73C47⋊C16—41no—
74C47⋊C16D811yescharacteristic
75C47⋊C16D811yescharacteristic
76C22×D47—81no—
77Q8×C47—21no—
78Q8×C47—81no—
79Q8×C47—81no—
80D4×C47—21no—
81D4×C47—41no—
82C2×C4×C47—21no—
83C2×C4×C47—41no—
84C2×C4×C47—81no—
85C2×C4×C47#12111yescharacteristic
86D188—81no—
87D188—81no—
88D188—162no—
89C8×C47—41no—
90C8×C47C2×D811yescharacteristic
91C8×C47C2×D811yescharacteristic
92C8×C47#13511yescharacteristic
93C8×C47AGL(1,ℤ/8)11yescharacteristic
94#12438—471nomaximal, Sylow
95C22×C47—41no—
96C22×C47#47211yescharacteristic
97C2×D47—162no—
98C2×D47—161no—
99C4×C47—22no—
100C4×C47—41no—
101C4×C47—161no—
102C4×C47#45911yescharacteristic
103C4×C47#46611yescharacteristic
104#2248—471no—
105#2214D4711yescharacteristic, complemented
106#2213—471no—
107#2170—471no—
108#1373—471no—
109#1358—471no—
110#1357—471no—
111C2×C47—21no—
112C2×C47—81no—
113C2×C47#166711yescharacteristic
114D47—321no—
115#510—21no—
116#509—941no—
117C2×SD32—941no—
118C2×SD32—941no—
119#504—941no—
120#494C2×D4711yescharacteristic
121#493—471no—
122#443C2×D4711yescharacteristic
123#364—471no—
124#364—471no—
125#364C2×D4711yescharacteristic
126#362—21no—
127#361—941no—
128#350—941no—
129C4×C16—471no—
130C47#1243811yescharacteristic, complemented, Sylow
131#135C22⋊D4711yescharacteristic
132C2×Q16—21no—
133C2×Q16—21no—
134C2×D8—941no—
135C2×D8—941no—
136#131—21no—
137C4⋊Q8—21no—
138#127—941no—
139Q32—41no—
140SD32—41no—
141SD32—1881no—
142SD32—1881no—
143SD32—1882no—
144SD32—1881no—
145D16—1881no—
146M32—21no—
147M32—941no—
148M32—941no—
149M32—1881no—
150C2×C16—471no—
151C2×C16—471no—
152C2×C16—1881no—
153#108C22⋊D4711yescharacteristic
154#104—21no—
155C4×C8C22×D4711yescharacteristic
156#41—21no—
157C2×Q8—41no—
158C2×D4—3761no—
159C2×D4—1881no—
160Q16—41no—
161Q16—41no—
162Q16—41no—
163Q16—41no—
164Q16#1062533411yescharacteristic
165SD16—21no—
166D8—1881no—
167D8—1881no—
168D8—1881no—
169D8—1881no—
170D8#1062533411yescharacteristic
171M16—21no—
172M16—41no—
173C2×C8—41no—
174C2×C8D4×D4711yescharacteristic
175C2×C8C2×C22⋊D4711yescharacteristic
176C4⋊C4—81no—
177C42#1062535211yescharacteristic
178C16—41no—
179C16—471no—
180C16—471no—
181C16—941no—
182C16—1881no—
183C16—1881no—
184C23—3761no—
185Q8—21no—
186Q8—81no—
187Q8—81no—
188D4—21no—
189D4—41no—
190D4—3761no—
191D4—3761no—
192D4—7522no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—81no—
196C2×C4#1309399611yescharacteristic
197C8—41no—
198C8D8×D4711yescharacteristic
199C8C2×#1062533411yescharacteristic
200C8#1309404411yescharacteristic
201C8#1309404811yescharacteristic
202C22—41no—
203C22—7522no—
204C22—7521no—
205C22#1568939111yescharacteristic
206C4—22no—
207C4—41no—
208C4—161no—
209C4#1568931611yescharacteristic
210C4#1568935711yescharacteristic
211C2—21no—
212C2—81no—
213C2—15041no—
214C2#2024274111yescharacteristic
subgroupG/H
centerC2#20242741
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#2214C2
socleC2×C47#1667
prime radical#20245464C2
hypercenter#2214D47
hypocenterC47#12438
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2214

Complements

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

NH ≅ G/Ntype
1. #20245645C2semidirect
3. #20245225C2semidirect
4. #20241463C2semidirect
5. #20241427C2semidirect
6. #20241424C2semidirect
7. C47×#2214C2semidirect
105. #2214D47semidirect
130. C47#12438semidirect

Maximal subgroups

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

subgroupindex
#202456452
#202454642
#202452252
#202414632
#202414272
#202414242
C47×#22142
#1243847