Finite Group Databasebeta

← #26130694

Subgroups — #26130694

Order 12032.

240 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 63 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#20245611C211yesmaximal, characteristic, complemented
2#20245207C211yesmaximal, characteristic, complemented
3#20242778C211yesmaximal, characteristic, complemented
4#20242740C211yesmaximal, characteristic
5#20241459C211yesmaximal, characteristic, complemented
6#20241442C211yesmaximal, characteristic, complemented
7C47×#1361C211yesmaximal, characteristic, complemented
8C2×C16×D47—21no—
9#15689528C2211yescharacteristic
10#15689329—21no—
11#15689315—21no—
12C8×D188C2211yescharacteristic
13#15688924—21no—
14#15688924—21no—
15(C2×D47)⋊C16—21no—
16C4×C47⋊C16C2211yescharacteristic
17#15688876C2211yescharacteristic
18#15688870—21no—
19#15688867—21no—
20C47×#493C2211yescharacteristic
21C47×C4⋊C16C2211yescharacteristic
22C47×#335C2211yescharacteristic
23C2×#10625325—41no—
24C2×#10625334—41no—
25C2×C8×D47—21no—
26#13094024—21no—
27C4×D188D411yescharacteristic
28C2×C47⋊C16D411yescharacteristic
29C2×C47⋊C16D411yescharacteristic
30C16×D47—42no—
31#13093958—21no—
32#13093958—21no—
33C4⋊(C47⋊C8)—21no—
34C4⋊(C47⋊C8)D411yescharacteristic
35#13093949—41no—
36#13093945—41no—
37(C2×D47)⋊C8—21no—
38C2×D8×C47—21no—
39C2×D8×C47—21no—
40#127×C47—21no—
41C2×C16×C47—21no—
42C4⋊C8×C47—21no—
43C4×C8×C47C2311yescharacteristic
44C2×D4×C47—41no—
45C2×D4×C47—41no—
46C2×D4×C47—41no—
47C2×D188D811yescharacteristic
48C2×C4×D47—21no—
49C2×Dic94—41no—
50D8×C47—41no—
51D8×C47—41no—
52D8×C47—81no—
53C2×C8×C47—41no—
54C2×C8×C47C2×D411yescharacteristic
55C2×C8×C47#4111yescharacteristic
56C42×C47C2×D411yescharacteristic
57#10625334—82no—
58(C2×D47)⋊C4—21no—
59C4⋊Dic47—41no—
60C4⋊Dic47—41no—
61C4⋊Dic47D811yescharacteristic
62C2×C47⋊C8—21no—
63C2×C47⋊C8—41no—
64#10625325—82no—
65C8×D47—41no—
66C8×D47—41no—
67C16×C47—41no—
68C47⋊C16—21no—
69C47⋊C16—21no—
70C23×C47—81no—
71C22×D47—21no—
72D4×C47—81no—
73D4×C47—81no—
74D4×C47—81no—
75D4×C47—81no—
76D4×C47—161no—
77C2×C4×C47#12111yescharacteristic
78C2×C4×C47C2×D811yescharacteristic
79C2×C4×C47#13511yescharacteristic
80C2×Dic47—21no—
81C2×Dic47—81no—
82D188—21no—
83D188D1612yes—
84C4×D47—41no—
85C4×D47—41no—
86Dic94—81no—
87Dic94—81no—
88C8×C47—21no—
89C8×C47—81no—
90C8×C47#13511yescharacteristic
91C8×C47AGL(1,ℤ/8)11yescharacteristic
92C47⋊C8—41no—
93C47⋊C8—81no—
94#12467—471nomaximal, Sylow
95C22×C47—161no—
96C22×C47—161no—
97C22×C47—161no—
98C22×C47#46611yescharacteristic
99C2×D47—22no—
100C2×D47—41no—
101C2×D47—41no—
102C4×C47—21no—
103C4×C47#46311yescharacteristic
104C4×C47#47111yescharacteristic
105C4×C47C2×D1611yescharacteristic
106C4×C47#50811yescharacteristic
107Dic47—41no—
108Dic47—161no—
109#2240—471no—
110D4×C16—471no—
111#1673—471no—
112#1667—471no—
113#1371—471no—
114#1364—471no—
115#1361D4711yescharacteristic, complemented
116C2×C47—321no—
117C2×C47#168111yescharacteristic
118C2×C47#221511yescharacteristic
119C2×C47#222311yescharacteristic
120D47—42no—
121C22×C16—941no—
122#500—471no—
123#493C2×D4711yescharacteristic
124#461—941no—
125#459—941no—
126C8×D4—471no—
127C4⋊C16C2×D4711yescharacteristic
128#357—941no—
129#357—941no—
130C22⋊C16—941no—
131C4×C16—471no—
132#335—471no—
133#335C2×D4711yescharacteristic
134#332—941no—
135#331—941no—
136C47#1246711yescharacteristic, complemented, Sylow
137C2×SD16—1881no—
138C2×D8—21no—
139C2×D8—21no—
140C2×D8—1881no—
141C22×C8—941no—
142C4⋊Q8—941no—
143#127—21no—
144C4×D4—471no—
145C2×C16—21no—
146C2×C16—471no—
147C2×C16—471no—
148C2×C16—1882no—
149#107—941no—
150#107—941no—
151C4⋊C8—21no—
152C4⋊C8—471no—
153C4⋊C8—941no—
154#103—1881no—
155#102—1881no—
156C22⋊C8—941no—
157C4×C8C22×D4711yescharacteristic
158C2×Q8—1881no—
159C2×D4—41no—
160C2×D4—41no—
161C2×D4—41no—
162C2×D4—471no—
163C22×C4—941no—
164SD16—3762no—
165D8—41no—
166D8—41no—
167D8—81no—
168D8—3762no—
169C2×C8—41no—
170C2×C8—941no—
171C2×C8—1881no—
172C2×C8—1881no—
173C2×C8—1881no—
174C2×C8#1062535011yescharacteristic
175C2×C8D4×D4711yescharacteristic
176C4⋊C4—471no—
177C4⋊C4—1881no—
178C4⋊C4—1881no—
179C22⋊C4—941no—
180C42D4×D4711yescharacteristic
181C16—41no—
182C16—941no—
183C16—941no—
184C23—81no—
185C23—941no—
186Q8—3761no—
187Q8—3761no—
188D4—81no—
189D4—81no—
190D4—81no—
191D4—81no—
192D4—161no—
193D4—472no—
194D4—941no—
195C2×C4—941no—
196C2×C4—3761no—
197C2×C4—1881no—
198C2×C4—1881no—
199C2×C4#1309399711yescharacteristic
200C2×C4D8×D4711yescharacteristic
201C2×C4#1309404511yescharacteristic
202C8—21no—
203C8—81no—
204C8—3761no—
205C8—1881no—
206C8#1309404511yescharacteristic
207C8#1309404811yescharacteristic
208C22—161no—
209C22—161no—
210C22—161no—
211C22—942no—
212C22—1881no—
213C22—1881no—
214C22#1568935811yescharacteristic
215C4—21no—
216C4—1881no—
217C4—7521no—
218C4#1568933711yescharacteristic
219C4#1568938511yescharacteristic
220C4D16×D4711yescharacteristic
221C4#1568955411yescharacteristic
222C2—321no—
223C2—1882no—
224C2#2024282411yescharacteristic
225C2#2024547311yescharacteristic
226C2#2024551711yescharacteristic
subgroupG/H
centerC22#15689358
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#1361C2
socleC22×C47#466
prime radical#20242740C2
hypercenter#1361D47
hypocenterC47#12467
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1361

Complements

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

NH ≅ G/Ntype
1. #20245611C2semidirect
2. #20245207C2semidirect
3. #20242778C2semidirect
5. #20241459C2semidirect
6. #20241442C2semidirect
7. C47×#1361C2semidirect
115. #1361D47semidirect
136. C47#12467semidirect

Maximal subgroups

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

subgroupindex
#202456112
#202452072
#202427782
#202427402
#202414592
#202414422
C47×#13612
#1246747