Finite Group Databasebeta

← #26131039

Subgroups — #26131039

Order 12032.

306 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 75 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#20245616C211yesmaximal, characteristic, complemented
3#20245611C211yesmaximal, characteristic, complemented
4#20242993C211yesmaximal, characteristic, complemented
5#20242977C211yesmaximal, characteristic, complemented
6#20241307C211yesmaximal, characteristic, complemented
7C47×#2246C211yesmaximal, characteristic
8C2×#13093968—22no—
9#15689528C2211yescharacteristic
10#15689503C2211yescharacteristic
11#15689495—21no—
12#15689469—21no—
13#15689469—21no—
14#15689469—21no—
15#15688928—22no—
16#15688924—22no—
17C4×C47⋊C16C2211yescharacteristic
18C8×C47⋊C8C2211yescharacteristic
19C2×D16×C47—22no—
20C47×#493C2211yescharacteristic
21C47×#493C2211yescharacteristic
22C4×C16×C47C2211yescharacteristic
23C2×Dic188—21no—
24C2×Dic188—21no—
25C2×#10625335—42no—
26#13094024—21no—
27#13094024—21no—
28#13093968—44no—
29C2×C47⋊C16D412yes—
30#13093958—21no—
31#13093958—21no—
32#13093945—42no—
33#13093945—42no—
34#13093945—42no—
35C4×C47⋊C8D411yescharacteristic
36C4×C47⋊C8D411yescharacteristic
37C2×D8×C47—21no—
38C2×D8×C47—21no—
39C2×D8×C47—21no—
40C2×D8×C47—21no—
41#127×C47—21no—
42#127×C47—21no—
43D16×C47—44no—
44C2×C16×C47D412yes—
45C4×C8×C47C2311yescharacteristic
46C2×D4×C47—41no—
47C2×D4×C47—41no—
48C2×D4×C47—41no—
49C2×D4×C47—41no—
50C2×D4×C47—41no—
51C2×D4×C47—41no—
52C2×Dic94—41no—
53C2×Dic94—41no—
54D8×C47—42no—
55D8×C47—42no—
56D8×C47—42no—
57D8×C47—42no—
58C2×C8×C47C2×D411yescharacteristic
59C2×C8×C47C2×D411yescharacteristic
60C42×C47C2×D411yescharacteristic
61#10625335—84no—
62C4⋊Dic47—41no—
63C4⋊Dic47—41no—
64C4⋊Dic47—41no—
65C4⋊Dic47—41no—
66C2×C47⋊C8D812yes—
67C2×C47⋊C8D812yes—
68Dic188—42no—
69Dic188—42no—
70C16×C47—22no—
71C47⋊C16—22no—
72C23×C47—81no—
73C23×C47—81no—
74D4×C47—81no—
75D4×C47—81no—
76D4×C47—81no—
77D4×C47—81no—
78D4×C47—82no—
79D4×C47—82no—
80D4×C47—82no—
81D4×C47—82no—
82C2×C4×C47#12711yescharacteristic
83C2×C4×C47C2×D811yescharacteristic
84C2×C4×C47C2×D811yescharacteristic
85C2×Dic47—81no—
86C2×Dic47—81no—
87Dic94—81no—
88Dic94—81no—
89Dic94—82no—
90C8×C47AGL(1,ℤ/8)12yes—
91C8×C47AGL(1,ℤ/8)12yes—
92C47⋊C8—22no—
93C47⋊C8—22no—
94#12527—471nomaximal, Sylow
95C22×C47—161no—
96C22×C47—161no—
97C22×C47—161no—
98C22×C47—161no—
99C22×C47—161no—
100C22×C47—161no—
101C22×C47#49311yescharacteristic
102C4×C47#49611yescharacteristic
103C4×C47#49611yescharacteristic
104C4×C47#50812yes—
105C4×C47#50912yes—
106Dic47—161no—
107Dic47—161no—
108#2248—471no—
109#2246D4711yescharacteristic
110#2241—471no—
111#2240—471no—
112#1709—471no—
113#1706—471no—
114#1312—471no—
115C2×C47—321no—
116C2×C47—321no—
117C2×C47#172111yescharacteristic
118C2×C47#224911yescharacteristic
119C2×C47#225011yescharacteristic
120C2×SD32—942no—
121C2×D16—22no—
122#500—471no—
123#494—471no—
124#493C2×D4711yescharacteristic
125#493C2×D4711yescharacteristic
126#492—941no—
127#486—941no—
128#486—941no—
129#486—941no—
130#358—942no—
131#357—942no—
132C4×C16—471no—
133C4×C16C2×D4711yescharacteristic
134C82—471no—
135C47#1252711yescharacteristic, complemented, Sylow
136C2×Q16—941no—
137C2×Q16—941no—
138C2×SD16—1882no—
139C2×D8—21no—
140C2×D8—21no—
141C2×D8—21no—
142C2×D8—21no—
143C4⋊Q8—941no—
144C4⋊Q8—941no—
145#127—21no—
146#127—21no—
147SD32—1884no—
148D16—44no—
149C2×C16—472no—
150C2×C16C22⋊D4712yes—
151#107—941no—
152#107—941no—
153#102—1882no—
154#102—1882no—
155#102—1882no—
156C4×C8—471no—
157C4×C8—471no—
158C4×C8C22×D4711yescharacteristic
159C2×Q8—1881no—
160C2×Q8—1881no—
161C2×D4—41no—
162C2×D4—41no—
163C2×D4—41no—
164C2×D4—41no—
165C2×D4—41no—
166C2×D4—41no—
167Q16—1882no—
168Q16—1882no—
169SD16—3764no—
170D8—42no—
171D8—42no—
172D8—42no—
173D8—42no—
174C2×C8—472no—
175C2×C8—472no—
176C2×C8D4×D4711yescharacteristic
177C2×C8C2×C22⋊D4711yescharacteristic
178C4⋊C4—1881no—
179C4⋊C4—1881no—
180C4⋊C4—1881no—
181C4⋊C4—1881no—
182C42D4×D4711yescharacteristic
183C16—22no—
184C16—942no—
185C23—81no—
186C23—81no—
187Q8—3761no—
188Q8—3761no—
189Q8—3762no—
190D4—81no—
191D4—81no—
192D4—81no—
193D4—81no—
194D4—82no—
195D4—82no—
196D4—82no—
197D4—82no—
198C2×C4—3761no—
199C2×C4—3761no—
200C2×C4#1309402011yescharacteristic
201C2×C4D8×D4711yescharacteristic
202C2×C4D8×D4711yescharacteristic
203C8—942no—
204C8—942no—
205C8#1309404812yes—
206C8#1309405012yes—
207C22—161no—
208C22—161no—
209C22—161no—
210C22—161no—
211C22—161no—
212C22—161no—
213C22#1568949811yescharacteristic
214C4—7521no—
215C4—7521no—
216C4#1568951011yescharacteristic
217C4#1568951111yescharacteristic
218C4#1568955212yes—
219C4#1568955712yes—
220C2—321no—
221C2—321no—
222C2#2024305311yescharacteristic
223C2#2024564611yescharacteristic
224C2#2024565111yescharacteristic
subgroupG/H
centerC22#15689498
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
Fitting, prime radicalC47×#2246C2
socleC22×C47#493
hypercenter#2246D47
hypocenterC47#12527
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2246

Complements

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

NH ≅ G/Ntype
1. #20245643C2semidirect
2. #20245616C2semidirect
3. #20245611C2semidirect
4. #20242993C2semidirect
5. #20242977C2semidirect
6. #20241307C2semidirect
135. C47#12527semidirect

Maximal subgroups

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

subgroupindex
#202456432
#202456162
#202456112
#202429932
#202429772
#202413072
C47×#22462
#1252747