Finite Group Databasebeta

← #26130516

Subgroups — #26130516

Order 12032.

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

normal subgroups only

This group has 234 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#20245637C211yesmaximal, characteristic, complemented
2#20245464C211yesmaximal, characteristic, complemented
3#20245225C211yesmaximal, characteristic, complemented
4#20241463C211yesmaximal, characteristic, complemented
5#20241425C211yesmaximal, characteristic, complemented
6#20241424C211yesmaximal, characteristic, complemented
7C47×#2213C211yesmaximal, characteristic, complemented
8#15689558—21no—
9C2×#13093965—21no—
10C2×#13093965—21no—
11#15689540—21no—
12#15689500C2211yescharacteristic
13#15688944C2211yescharacteristic
14#15688944C2211yescharacteristic
15#15688935—21no—
16#15688907—21no—
17C4×C47⋊C16C2211yescharacteristic
18C47×#509—21no—
19C47×#493C2211yescharacteristic
20C47×#443C2211yescharacteristic
21C47×#364C2211yescharacteristic
22C47×#361—21no—
23C2×D376—21no—
24C2×D376—21no—
25#13094021—21no—
26#13093967—41no—
27#13093965—42no—
28#13093965—41no—
29#13093965—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×D8×C47—21no—
39C2×D8×C47—21no—
40#131×C47—21no—
41#127×C47—21no—
42SD32×C47—41no—
43D16×C47—41no—
44M32×C47—21no—
45#108×C47D411yescharacteristic
46#104×C47—21no—
47C4×C8×C47C2311yescharacteristic
48#41×C47—21no—
49C2×D4×C47—41no—
50C2×D4×C47—81no—
51C2×D188—41no—
52C2×D188—81no—
53Q16×C47D811yescharacteristic
54SD16×C47—21no—
55D8×C47—41no—
56D8×C47—41no—
57D8×C47—41no—
58D8×C47—41no—
59D8×C47D811yescharacteristic
60M16×C47—21no—
61M16×C47—41no—
62C2×C8×C47—41no—
63C2×C8×C47C2×D411yescharacteristic
64C2×C8×C47C2×D411yescharacteristic
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
76C23×C47—81no—
77C22×D47—81no—
78Q8×C47—21no—
79D4×C47—21no—
80D4×C47—41no—
81D4×C47—81no—
82D4×C47—81no—
83D4×C47—162no—
84C2×C4×C47—21no—
85C2×C4×C47—41no—
86C2×C4×C47#12111yescharacteristic
87D188—81no—
88D188—81no—
89D188—162no—
90C8×C47—41no—
91C8×C47C2×D811yescharacteristic
92C8×C47C2×D811yescharacteristic
93C8×C47#13511yescharacteristic
94C8×C47AGL(1,ℤ/8)11yescharacteristic
95#12436—471nomaximal, Sylow
96C22×C47—41no—
97C22×C47—162no—
98C22×C47—161no—
99C22×C47#47211yescharacteristic
100C2×D47—162no—
101C2×D47—161no—
102C4×C47—22no—
103C4×C47—41no—
104C4×C47#45911yescharacteristic
105C4×C47#46611yescharacteristic
106#2246—471no—
107#2213—471no—
108#2213D4711yescharacteristic, complemented
109#2170—471no—
110#1373—471no—
111#1357—471no—
112#1357—471no—
113C2×C47—21no—
114C2×C47—81no—
115C2×C47—321no—
116C2×C47#166711yescharacteristic
117D47—321no—
118#509—21no—
119#509—941no—
120C2×D16—941no—
121C2×D16—941no—
122#504—941no—
123#493—471no—
124#493C2×D4711yescharacteristic
125#443C2×D4711yescharacteristic
126#364—471no—
127#364—471no—
128#364C2×D4711yescharacteristic
129#361—21no—
130#361—941no—
131#350—941no—
132C4×C16—471no—
133C47#1243611yescharacteristic, complemented, Sylow
134#135C22⋊D4711yescharacteristic
135C2×D8—21no—
136C2×D8—21no—
137C2×D8—941no—
138C2×D8—941no—
139#131—21no—
140#127—21no—
141#127—941no—
142SD32—41no—
143SD32—1881no—
144D16—41no—
145D16—1881no—
146D16—1881no—
147D16—1882no—
148D16—1881no—
149M32—21no—
150M32—941no—
151M32—941no—
152M32—1881no—
153C2×C16—471no—
154C2×C16—471no—
155C2×C16—1881no—
156#108C22⋊D4711yescharacteristic
157#104—21no—
158C4×C8C22×D4711yescharacteristic
159#41—21no—
160C2×D4—41no—
161C2×D4—81no—
162C2×D4—3761no—
163C2×D4—1881no—
164Q16#1062533411yescharacteristic
165SD16—21no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8—41no—
170D8—1881no—
171D8—1881no—
172D8—1881no—
173D8—1881no—
174D8#1062533411yescharacteristic
175M16—21no—
176M16—41no—
177C2×C8—41no—
178C2×C8D4×D4711yescharacteristic
179C2×C8C2×C22⋊D4711yescharacteristic
180C42#1062535211yescharacteristic
181C16—41no—
182C16—471no—
183C16—471no—
184C16—941no—
185C16—1881no—
186C16—1881no—
187C23—81no—
188C23—3761no—
189Q8—21no—
190D4—21no—
191D4—41no—
192D4—81no—
193D4—81no—
194D4—162no—
195D4—3761no—
196D4—3761no—
197D4—7522no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4#1309399611yescharacteristic
201C8—41no—
202C8D8×D4711yescharacteristic
203C8C2×#1062533411yescharacteristic
204C8#1309404411yescharacteristic
205C8#1309404811yescharacteristic
206C22—41no—
207C22—162no—
208C22—161no—
209C22—7522no—
210C22—7521no—
211C22#1568939111yescharacteristic
212C4—22no—
213C4—41no—
214C4#1568931611yescharacteristic
215C4#1568935711yescharacteristic
216C2—21no—
217C2—81no—
218C2—321no—
219C2—15041no—
220C2#2024274111yescharacteristic
subgroupG/H
centerC2#20242741
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#2213C2
socleC2×C47#1667
hypercenter#2213D47
hypocenterC47#12436
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2213

Complements

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

NH ≅ G/Ntype
1. #20245637C2semidirect
2. #20245464C2semidirect
3. #20245225C2semidirect
4. #20241463C2semidirect
5. #20241425C2semidirect
6. #20241424C2semidirect
7. C47×#2213C2semidirect
108. #2213D47semidirect
133. C47#12436semidirect

Maximal subgroups

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

subgroupindex
#202456372
#202454642
#202452252
#202414632
#202414252
#202414242
C47×#22132
#1243647