Finite Group Databasebeta

← #26129636

Subgroups — #26129636

Order 12032.

286 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 55 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#20254827C211yesmaximal, characteristic
2#20245602C212yesmaximal, complemented
3#20241378C212yesmaximal, complemented
4#20241341C211yesmaximal, characteristic, complemented
5C47×#2103C211yesmaximal, characteristic, complemented
6#15689728—21no—
7#15689424—22no—
8#15689376C2212yes—
9#15689359—21no—
10#15689319—22no—
11#15688947—22no—
12#15688935—22no—
13#15688905C2212yes—
14C47×#430C2211yescharacteristic
15C47×#424C2211yescharacteristic
16C47×#344—21no—
17C47×#341—21no—
18C47×#338C2211yescharacteristic
19C2×D376—21no—
20C2×D376D412yes—
21#13094021—21no—
22#13094016—21no—
23#13094009—42no—
24#13093998—22no—
25#13093997—42no—
26C4×D188—22no—
27#13093964—22no—
28#13093958—21no—
29#13093956D412yes—
30#13093946—22no—
31#13093946—22no—
32C2×M16×C47—21no—
33C2×M16×C47—21no—
34C2×M16×C47C2311yescharacteristic
35C22×C8×C47D411yescharacteristic
36#117×C47D411yescharacteristic
37#108×C47—22no—
38C4⋊C8×C47—22no—
39C22×C4×C47C2×D411yescharacteristic
40C2×C22⋊D47—42no—
41C2×D188—22no—
42C2×D188—42no—
43C2×C4×D47—42no—
44M16×C47—41no—
45M16×C47—41no—
46M16×C47—41no—
47M16×C47—41no—
48M16×C47—41no—
49C2×C8×C47—21no—
50C2×C8×C47—41no—
51C2×C8×C47—41no—
52C2×C8×C47—41no—
53C2×C8×C47C2×D412yes—
54C4⋊C4×C47—21no—
55C22⋊C4×C47SD1612yes—
56C42×C47—21no—
57(C2×D47)⋊C4—42no—
58(C2×D47)⋊C4—42no—
59C4⋊Dic47—22no—
60Dic47⋊C4—42no—
61D376—42no—
62D376—81no—
63C47⋊C16—42no—
64C23×C47C2×SD1611yescharacteristic
65C22×D47—42no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—22no—
69C2×C4×C47#12011yescharacteristic
70C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
71C22⋊D47—162no—
72C2×Dic47—42no—
73D188—42no—
74D188—42no—
75D188—162no—
76C4×D47—162no—
77C8×C47—22no—
78C8×C47—41no—
79C8×C47—81no—
80C8×C47—81no—
81#12304—471nomaximal, Sylow
82C22×C47—21no—
83C22×C47—41no—
84C22×C47#45011yescharacteristic
85C2×D47—82no—
86C2×D47—82no—
87C2×D47—82no—
88C4×C47—21no—
89C4×C47—42no—
90C4×C47#45411yescharacteristic
91C4×C47#45811yescharacteristic
92Dic47—82no—
93#3259—471no—
94#2238—472no—
95#2103D4711yescharacteristic, complemented
96#1341—472no—
97#1328—471no—
98C2×C47—21no—
99C2×C47—41no—
100C2×C47#161611yescharacteristic
101D47—162no—
102#540—941no—
103#478—942no—
104#469—472no—
105#466—941no—
106#459—942no—
107#430C2×D4711yescharacteristic
108#424C2×D4711yescharacteristic
109#365—942no—
110#361—942no—
111#349—472no—
112#344—21no—
113#341—21no—
114#338C2×D4711yescharacteristic
115C47#1230411yescharacteristic, complemented, Sylow
116C2×D8—472no—
117C2×D8—941no—
118C2×M16—21no—
119C2×M16—21no—
120C2×M16C22×D4711yescharacteristic
121C22×C8C22⋊D4711yescharacteristic
122#127—941no—
123#125—941no—
124#123—1882no—
125#121—942no—
126#121—1882no—
127C4×D4—942no—
128#117C22⋊D4711yescharacteristic
129M32—942no—
130#108—22no—
131#107—941no—
132#106—472no—
133C4⋊C8—22no—
134#102—942no—
135#102—942no—
136C2×D4—942no—
137C2×D4—1882no—
138C2×D4—1882no—
139C22×C4—1882no—
140C22×C4C2×C22⋊D4711yescharacteristic
141D8—3761no—
142D8—1882no—
143M16—41no—
144M16—41no—
145M16—41no—
146M16—41no—
147M16—41no—
148C2×C8—21no—
149C2×C8—41no—
150C2×C8—41no—
151C2×C8—41no—
152C2×C8D4×D4712yes—
153C4⋊C4—21no—
154C4⋊C4—942no—
155C4⋊C4—1882no—
156C22⋊C4—1882no—
157C22⋊C4—1882no—
158C22⋊C4#1062533612yes—
159C42—21no—
160C16—1882no—
161C23—1882no—
162C23C2×#1062533611yescharacteristic
163D4—1882no—
164D4—1882no—
165D4—7522no—
166D4—7522no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—1882no—
171C2×C4—7522no—
172C2×C4#1309399211yescharacteristic
173C2×C4#1309404911yescharacteristic
174C8—22no—
175C8—41no—
176C8—81no—
177C8—81no—
178C22—21no—
179C22—41no—
180C22—3762no—
181C22—3762no—
182C22—3762no—
183C22#1568927311yescharacteristic
184C4—21no—
185C4—42no—
186C4—3762no—
187C4#1568929511yescharacteristic
188C4#1568931211yescharacteristic
189C2—21no—
190C2—41no—
191C2—7522no—
192C2#2024242411yescharacteristic
subgroupG/H
centerC2#20242424
commutator, cosocleC2×M16×C47C23
FrattiniC2×M16C22×D47
FittingC47×#2103C2
socleC2×C47#1616
prime radical#20254827C2
hypercenter#2103D47
hypocenterC47#12304
LCSG ▷ C2×M16×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2103

Complements

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

NH ≅ G/Ntype
2. #20245602C2semidirect
3. #20241378C2semidirect
4. #20241341C2semidirect
5. C47×#2103C2semidirect
95. #2103D47semidirect
115. C47#12304semidirect

Maximal subgroups

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

subgroupindex
#202548272
#202456022
#202413782
#202413412
C47×#21032
#1230447