Finite Group Databasebeta

← #26130418

Subgroups — #26130418

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#20245537C211yesmaximal, characteristic, complemented
2#20245429C211yesmaximal, characteristic
3#20242981C211yesmaximal, characteristic
4#20242194C211yesmaximal, characteristic, complemented
5#20241451C211yesmaximal, characteristic, complemented
6#20241433C211yesmaximal, characteristic
7C47×#1365C211yesmaximal, characteristic, complemented
8C2×#13093969—21no—
9#15689500C2211yescharacteristic
10#15689497—21no—
11#15689471—21no—
12#15689247—21no—
13C4×Dic188C2211yescharacteristic
14#15688948—21no—
15C4⋊(C47⋊C16)C2211yescharacteristic
16#15688926—21no—
17#15688925—21no—
18#15688853—21no—
19C8×C47⋊C8C2211yescharacteristic
20C47×#500C2211yescharacteristic
21C47×C4⋊C16C2211yescharacteristic
22C47×#335C2211yescharacteristic
23C2×Dic188D411yescharacteristic
24C2×#10625336—42no—
25C2×D376—21no—
26C2×D376—21no—
27#13094021—21no—
28C4×Dic94—21no—
29#13093969—42no—
30C2×C47⋊C16—21no—
31#13093958D411yescharacteristic
32Dic47⋊C8—41no—
33#13093949—21no—
34#13093944—41no—
35#13093944—41no—
36C4×C47⋊C8D411yescharacteristic
37C4×C47⋊C8D411yescharacteristic
38C8×Dic47—41no—
39C4⋊Q8×C47—21no—
40C2×C16×C47—21no—
41#107×C47—21no—
42#107×C47—21no—
43C4⋊C8×C47—21no—
44C4×C8×C47C2311yescharacteristic
45C2×Q8×C47—41no—
46C2×D188—41no—
47C2×D188—41no—
48C2×D188—41no—
49C2×Dic94—21no—
50C2×C8×C47—41no—
51C2×C8×C47C2×D411yescharacteristic
52C2×C8×C47#4111yescharacteristic
53C4⋊C4×C47—41no—
54C4⋊C4×C47—41no—
55C42×C47C2×D411yescharacteristic
56#10625336—84no—
57C4⋊Dic47—21no—
58Dic47⋊C4—41no—
59C4×Dic47—41no—
60C2×C47⋊C8—21no—
61C2×C47⋊C8D811yescharacteristic
62C2×C47⋊C8D811yescharacteristic
63Dic188—21no—
64Dic188SD1612yescomplemented
65D376—41no—
66D376—41no—
67D376—81no—
68C16×C47—41no—
69C47⋊C16—41no—
70C22×D47—81no—
71Q8×C47—82no—
72C2×C4×C47—81no—
73C2×C4×C47#12111yescharacteristic
74C2×C4×C47C2×D811yescharacteristic
75C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
76C2×Dic47—41no—
77C2×Dic47—41no—
78D188—82no—
79D188—81no—
80D188—81no—
81D188—81no—
82D188—81no—
83Dic94—22no—
84Dic94—41no—
85C8×C47—21no—
86C8×C47—81no—
87C8×C47C2×SD1611yescharacteristic
88C8×C47#13511yescharacteristic
89C47⋊C8—22no—
90C47⋊C8—21no—
91C47⋊C8—21no—
92#12419—471nomaximal, Sylow
93C22×C47#45911yescharacteristic
94C2×D47—161no—
95C2×D47—161no—
96C2×D47—161no—
97C4×C47—21no—
98C4×C47—161no—
99C4×C47#46511yescharacteristic
100C4×C47#47111yescharacteristic
101C4×C47#50811yescharacteristic
102C4×C47#51011yescharacteristic
103Dic47—42no—
104Dic47—81no—
105#2227—471no—
106#2207—471no—
107#1706—471no—
108C8×Q16—471no—
109#1367—471no—
110#1365D4711yescharacteristic, complemented
111#1361—471no—
112C2×C47#166511yescharacteristic
113C2×C47#221111yescharacteristic
114C2×C47#221311yescharacteristic
115D47—321no—
116C2×SD32—941no—
117#500C2×D4711yescharacteristic
118#493—471no—
119#492—941no—
120#486—941no—
121C8×Q8—941no—
122C4×Q16—471no—
123#366—941no—
124C4⋊C16—471no—
125C4⋊C16C2×D4711yescharacteristic
126#358—941no—
127#357—941no—
128#335C2×D4711yescharacteristic
129Q8⋊C8—941no—
130C82—471no—
131C47#1241911yescharacteristic, complemented, Sylow
132C2×Q16—471no—
133C2×SD16—1882no—
134C2×D8—941no—
135C2×D8—941no—
136C4⋊Q8—21no—
137#127—941no—
138C4×Q8—941no—
139SD32—1882no—
140C2×C16—21no—
141C2×C16—941no—
142#107—21no—
143#107—21no—
144#107—471no—
145C4⋊C8—21no—
146C4⋊C8—1881no—
147#103—941no—
148#102—1881no—
149#102—1881no—
150C4×C8—471no—
151C4×C8—471no—
152C4×C8—1881no—
153C4×C8C22×D4711yescharacteristic
154C2×Q8—41no—
155C2×Q8—941no—
156C2×D4—1881no—
157C2×D4—1881no—
158C2×D4—1881no—
159Q16—472no—
160Q16—941no—
161SD16—3764no—
162D8—3761no—
163D8—1881no—
164D8—1881no—
165C2×C8—41no—
166C2×C8—471no—
167C2×C8—471no—
168C2×C8—941no—
169C2×C8#1062535011yescharacteristic
170C2×C8D4×D4711yescharacteristic
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—941no—
174C4⋊C4—1881no—
175C42—1881no—
176C42D4×D4711yescharacteristic
177C16—41no—
178C16—1881no—
179C23—3761no—
180Q8—82no—
181Q8—942no—
182Q8—1881no—
183D4—3762no—
184D4—3761no—
185D4—3761no—
186D4—3761no—
187D4—3761no—
188C2×C4—81no—
189C2×C4—1881no—
190C2×C4—1881no—
191C2×C4#1309399711yescharacteristic
192C2×C4D8×D4711yescharacteristic
193C2×C4#1309405111yescharacteristic
194C8—21no—
195C8—81no—
196C8—942no—
197C8—941no—
198C8—941no—
199C8SD16×D4711yescharacteristic
200C8#1309404711yescharacteristic
201C22—7521no—
202C22—7521no—
203C22—7521no—
204C22#1568931711yescharacteristic
205C4—21no—
206C4—161no—
207C4—3761no—
208C4—1882no—
209C4#1568935511yescharacteristic
210C4#1568938911yescharacteristic
211C4#1568955411yescharacteristic
212C4#1568956511yescharacteristic
213C2—15041no—
214C2#2024273211yescharacteristic
215C2#2024545311yescharacteristic
216C2#2024546311yescharacteristic
subgroupG/H
centerC22#15689317
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#1365C2
socleC22×C47#459
prime radical#15689500C22
hypercenter#1365D47
hypocenterC47#12419
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1365

Complements

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

NH ≅ G/Ntype
1. #20245537C2semidirect
4. #20242194C2semidirect
5. #20241451C2semidirect
7. C47×#1365C2semidirect
64. Dic188SD16semidirect
110. #1365D47semidirect
131. C47#12419semidirect

Maximal subgroups

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

subgroupindex
#202455372
#202454292
#202429812
#202421942
#202414512
#202414332
C47×#13652
#1241947