Finite Group Databasebeta

← #26130483

Subgroups — #26130483

Order 12032.

268 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 65 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#20245207C211yesmaximal, characteristic, complemented
3#20242744C211yesmaximal, characteristic, complemented
4#20242740C211yesmaximal, characteristic, complemented
5#20241459C211yesmaximal, characteristic, complemented
6#20241435C211yesmaximal, characteristic, complemented
7C47×#1361C211yesmaximal, characteristic, complemented
8C2×#13093965—21no—
9C2×#13093965—21no—
10C2×C16×D47—21no—
11#15689500C2211yescharacteristic
12#15689319—21no—
13#15689315—21no—
14C8×D188C2211yescharacteristic
15(C2×D47)⋊C16—21no—
16C4×C47⋊C16C2211yescharacteristic
17#15688876C2211yescharacteristic
18#15688867—21no—
19#15688866—21no—
20C47×#493C2211yescharacteristic
21C47×C4⋊C16C2211yescharacteristic
22C47×#335C2211yescharacteristic
23C2×D376—21no—
24C2×D376—21no—
25C2×D376—41no—
26C2×#10625334—41no—
27C2×C8×D47—21no—
28#13094021—21no—
29C4×D188D411yescharacteristic
30#13093965—42no—
31#13093965—42no—
32C2×C47⋊C16D411yescharacteristic
33C2×C47⋊C16D411yescharacteristic
34C16×D47—42no—
35C4⋊(C47⋊C8)—21no—
36C4⋊(C47⋊C8)D411yescharacteristic
37#13093946—41no—
38#13093945—41no—
39(C2×D47)⋊C8—21no—
40C2×D8×C47—21no—
41C2×D8×C47—21no—
42#127×C47—21no—
43C2×C16×C47—21no—
44C4⋊C8×C47—21no—
45C4×C8×C47C2311yescharacteristic
46C2×D4×C47—41no—
47C2×D4×C47—41no—
48C2×D4×C47—41no—
49C2×D188—41no—
50C2×D188—41no—
51C2×D188—41no—
52C2×D188D811yescharacteristic
53C2×C4×D47—21no—
54D8×C47—41no—
55D8×C47—41no—
56D8×C47—81no—
57C2×C8×C47—41no—
58C2×C8×C47C2×D411yescharacteristic
59C2×C8×C47#4111yescharacteristic
60C42×C47C2×D411yescharacteristic
61#10625334—82no—
62(C2×D47)⋊C4—21no—
63C4⋊Dic47D811yescharacteristic
64C2×C47⋊C8—21no—
65C2×C47⋊C8—41no—
66D376—41no—
67D376—41no—
68D376—81no—
69D376—82no—
70C8×D47—41no—
71C8×D47—41no—
72C16×C47—41no—
73C47⋊C16—21no—
74C47⋊C16D812yescomplemented
75C23×C47—81no—
76C22×D47—21no—
77C22×D47—81no—
78D4×C47—81no—
79D4×C47—81no—
80D4×C47—81no—
81D4×C47—81no—
82D4×C47—161no—
83C2×C4×C47#12111yescharacteristic
84C2×C4×C47C2×D811yescharacteristic
85C2×C4×C47#13511yescharacteristic
86C2×Dic47—21no—
87D188—21no—
88D188—81no—
89D188—81no—
90D188—81no—
91D188—81no—
92D188—161no—
93D188D1612yescomplemented
94C4×D47—41no—
95C4×D47—41no—
96C8×C47—21no—
97C8×C47—81no—
98C8×C47C2×D811yescharacteristic
99C8×C47AGL(1,ℤ/8)11yescharacteristic
100C47⋊C8—41no—
101C47⋊C8—81no—
102#12430—471nomaximal, Sylow
103C22×C47—161no—
104C22×C47—161no—
105C22×C47—161no—
106C22×C47#46611yescharacteristic
107C2×D47—22no—
108C2×D47—41no—
109C2×D47—41no—
110C2×D47—161no—
111C2×D47—161no—
112C2×D47—161no—
113C4×C47—21no—
114C4×C47#45911yescharacteristic
115C4×C47#47211yescharacteristic
116C4×C47C2×D1611yescharacteristic
117C4×C47#50811yescharacteristic
118Dic47—41no—
119#2246—471no—
120D4×C16—471no—
121#1667—471no—
122#1667—471no—
123#1371—471no—
124#1361—471no—
125#1361D4711yescharacteristic, complemented
126C2×C47—321no—
127C2×C47#166711yescharacteristic
128C2×C47#221511yescharacteristic
129C2×C47#222111yescharacteristic
130D47—42no—
131D47—321no—
132C2×D16—941no—
133C2×D16—941no—
134C22×C16—941no—
135#493—471no—
136#493C2×D4711yescharacteristic
137#459—941no—
138#459—941no—
139C8×D4—471no—
140C4⋊C16C2×D4711yescharacteristic
141C22⋊C16—941no—
142C4×C16—471no—
143#335—471no—
144#335C2×D4711yescharacteristic
145#331—941no—
146#331—941no—
147C47#1243011yescharacteristic, complemented, Sylow
148C2×D8—21no—
149C2×D8—21no—
150C2×D8—941no—
151C2×D8—941no—
152C2×D8—1881no—
153C2×D8—1881no—
154C22×C8—941no—
155#127—21no—
156#127—941no—
157C4×D4—471no—
158D16—1882no—
159D16—1882no—
160C2×C16—21no—
161C2×C16—471no—
162C2×C16—471no—
163C2×C16—1882no—
164C4⋊C8—21no—
165C4⋊C8—471no—
166C4⋊C8—941no—
167#102—1881no—
168#102—1881no—
169C22⋊C8—941no—
170C4×C8C22×D4711yescharacteristic
171C2×D4—41no—
172C2×D4—41no—
173C2×D4—41no—
174C2×D4—471no—
175C2×D4—1881no—
176C2×D4—1881no—
177C2×D4—1881no—
178C22×C4—941no—
179D8—41no—
180D8—41no—
181D8—81no—
182D8—3761no—
183D8—3762no—
184D8—3762no—
185D8—1881no—
186D8—1881no—
187C2×C8—41no—
188C2×C8—941no—
189C2×C8—1881no—
190C2×C8—1881no—
191C2×C8—1881no—
192C2×C8#1062535011yescharacteristic
193C2×C8D4×D4711yescharacteristic
194C4⋊C4—471no—
195C22⋊C4—941no—
196C42D4×D4711yescharacteristic
197C16—41no—
198C16—472no—
199C16—941no—
200C23—81no—
201C23—941no—
202C23—3761no—
203D4—81no—
204D4—81no—
205D4—81no—
206D4—81no—
207D4—161no—
208D4—472no—
209D4—941no—
210D4—3761no—
211D4—3761no—
212D4—3761no—
213D4—3761no—
214D4—7521no—
215C2×C4—941no—
216C2×C4—1881no—
217C2×C4—1881no—
218C2×C4#1309399711yescharacteristic
219C2×C4D8×D4711yescharacteristic
220C2×C4#1309404511yescharacteristic
221C8—21no—
222C8—81no—
223C8—3761no—
224C8—1881no—
225C8D8×D4711yescharacteristic
226C8#1309405111yescharacteristic
227C22—161no—
228C22—161no—
229C22—161no—
230C22—942no—
231C22—1881no—
232C22—1881no—
233C22—7521no—
234C22—7521no—
235C22—7521no—
236C22#1568935811yescharacteristic
237C4—21no—
238C4—1881no—
239C4#1568931711yescharacteristic
240C4#1568939211yescharacteristic
241C4D16×D4711yescharacteristic
242C4#1568955411yescharacteristic
243C2—321no—
244C2—1882no—
245C2—15041no—
246C2#2024274211yescharacteristic
247C2#2024547311yescharacteristic
248C2#2024550711yescharacteristic
subgroupG/H
centerC22#15689358
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#1361C2
socleC22×C47#466
hypercenter#1361D47
hypocenterC47#12430
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. #20245637C2semidirect
2. #20245207C2semidirect
3. #20242744C2semidirect
4. #20242740C2semidirect
5. #20241459C2semidirect
6. #20241435C2semidirect
7. C47×#1361C2semidirect
74. C47⋊C16D8semidirect
93. D188D16semidirect
125. #1361D47semidirect
147. C47#12430semidirect

Maximal subgroups

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

subgroupindex
#202456372
#202452072
#202427442
#202427402
#202414592
#202414352
C47×#13612
#1243047