Finite Group Databasebeta

← #26130526

Subgroups — #26130526

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#20245643C211yesmaximal, characteristic, complemented
2#20245469C211yesmaximal, characteristic, complemented
3#20245225C211yesmaximal, characteristic, complemented
4#20241463C211yesmaximal, characteristic, complemented
5#20241426C211yesmaximal, characteristic, complemented
6#20241425C211yesmaximal, characteristic, complemented
7C47×#2213C211yesmaximal, characteristic
8#15689563—21no—
9C2×#13093968—21no—
10C2×#13093968—21no—
11#15689540—21no—
12#15689503C2211yescharacteristic
13#15688944C2211yescharacteristic
14#15688944C2211yescharacteristic
15#15688938—21no—
16#15688907—21no—
17C4×C47⋊C16C2211yescharacteristic
18C47×#509—21no—
19C47×#493C2211yescharacteristic
20C47×#443C2211yescharacteristic
21C47×#364C2211yescharacteristic
22C47×#361—21no—
23C2×Dic188—21no—
24C2×Dic188—21no—
25#13094024—21no—
26#13093970—41no—
27#13093968—42no—
28#13093968—41no—
29#13093968—41no—
30#13093968—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×Dic94—41no—
52Q16×C47D811yescharacteristic
53SD16×C47—21no—
54D8×C47—41no—
55D8×C47—41no—
56D8×C47—41no—
57D8×C47—41no—
58D8×C47D811yescharacteristic
59M16×C47—21no—
60M16×C47—41no—
61C2×C8×C47—41no—
62C2×C8×C47C2×D411yescharacteristic
63C2×C8×C47C2×D411yescharacteristic
64C42×C47#4111yescharacteristic
65C4⋊Dic47—81no—
66Dic188—41no—
67Dic188—41no—
68Dic188—41no—
69Dic188—41no—
70C16×C47—41no—
71C47⋊C16—21no—
72C47⋊C16—41no—
73C47⋊C16—41no—
74C47⋊C16D811yescharacteristic
75C47⋊C16D811yescharacteristic
76C23×C47—81no—
77Q8×C47—21no—
78D4×C47—21no—
79D4×C47—41no—
80D4×C47—81no—
81D4×C47—81no—
82D4×C47—162no—
83C2×C4×C47—21no—
84C2×C4×C47—41no—
85C2×C4×C47#12111yescharacteristic
86C2×Dic47—81no—
87Dic94—81no—
88Dic94—81no—
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—162no—
97C22×C47—161no—
98C22×C47#47211yescharacteristic
99C4×C47—22no—
100C4×C47—41no—
101C4×C47#45911yescharacteristic
102C4×C47#46611yescharacteristic
103Dic47—161no—
104#2248—471no—
105#2214—471no—
106#2213D4711yescharacteristic
107#2170—471no—
108#1373—471no—
109#1358—471no—
110#1357—471no—
111C2×C47—21no—
112C2×C47—81no—
113C2×C47—321no—
114C2×C47#166711yescharacteristic
115#510—941no—
116#509—21no—
117C2×SD32—941no—
118C2×SD32—941no—
119#504—941no—
120#494—471no—
121#493C2×D4711yescharacteristic
122#443C2×D4711yescharacteristic
123#364—471no—
124#364—471no—
125#364C2×D4711yescharacteristic
126#362—941no—
127#361—21no—
128#350—941no—
129C4×C16—471no—
130C47#1243811yescharacteristic, complemented, Sylow
131#135C22⋊D4711yescharacteristic
132C2×Q16—941no—
133C2×Q16—941no—
134C2×D8—21no—
135C2×D8—21no—
136#131—21no—
137C4⋊Q8—941no—
138#127—21no—
139Q32—1881no—
140SD32—41no—
141SD32—1881no—
142SD32—1881no—
143SD32—1882no—
144SD32—1881no—
145D16—41no—
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—1881no—
158C2×D4—41no—
159C2×D4—81no—
160Q16—1881no—
161Q16—1881no—
162Q16—1881no—
163Q16—1881no—
164Q16#1062533411yescharacteristic
165SD16—21no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8—41no—
170D8#1062533411yescharacteristic
171M16—21no—
172M16—41no—
173C2×C8—41no—
174C2×C8D4×D4711yescharacteristic
175C2×C8C2×C22⋊D4711yescharacteristic
176C4⋊C4—3761no—
177C42#1062535211yescharacteristic
178C16—41no—
179C16—471no—
180C16—471no—
181C16—941no—
182C16—1881no—
183C16—1881no—
184C23—81no—
185Q8—21no—
186Q8—3761no—
187Q8—3761no—
188D4—21no—
189D4—41no—
190D4—81no—
191D4—81no—
192D4—162no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—3761no—
196C2×C4#1309399611yescharacteristic
197C8—41no—
198C8D8×D4711yescharacteristic
199C8C2×#1062533411yescharacteristic
200C8#1309404411yescharacteristic
201C8#1309404811yescharacteristic
202C22—41no—
203C22—162no—
204C22—161no—
205C22#1568939111yescharacteristic
206C4—22no—
207C4—41no—
208C4—7521no—
209C4#1568931611yescharacteristic
210C4#1568935711yescharacteristic
211C2—21no—
212C2—81no—
213C2—321no—
214C2#2024274111yescharacteristic
subgroupG/H
centerC2#20242741
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
Fitting, prime radicalC47×#2213C2
socleC2×C47#1667
hypercenter#2213D47
hypocenterC47#12438
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. #20245643C2semidirect
2. #20245469C2semidirect
3. #20245225C2semidirect
4. #20241463C2semidirect
5. #20241426C2semidirect
6. #20241425C2semidirect
130. C47#12438semidirect

Maximal subgroups

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

subgroupindex
#202456432
#202454692
#202452252
#202414632
#202414262
#202414252
C47×#22132
#1243847