Finite Group Databasebeta

← #26129676

Subgroups — #26129676

Order 12032.

366 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 67 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#20245464C212yesmaximal, complemented
2#20242995C211yesmaximal, characteristic, complemented
3#20241427C211yesmaximal, characteristic, complemented
4#20241361C212yesmaximal, complemented
5C47×#3293C211yesmaximal, characteristic, complemented
6#15689558—22no—
7#15689500C2211yescharacteristic
8#15689471—22no—
9#15688944C2212yes—
10#15688935—22no—
11C8×C47⋊C8C2211yescharacteristic
12C47×#578—22no—
13C47×#494C2211yescharacteristic
14C47×#473—22no—
15C47×#456—22no—
16C47×#443C2212yes—
17C2×D376—22no—
18#13094021—21no—
19#13093967—42no—
20#13093965—42no—
21#13093964—22no—
22#13093944—44no—
23C4×C47⋊C8—21no—
242−1+4×C47—22no—
25#137×C47—24no—
26#137×C47—44no—
27#135×C47—42no—
28#135×C47D412yes—
29C2×Q16×C47—22no—
30C2×Q16×C47—42no—
31#131×C47—22no—
32C4⋊Q8×C47D412yes—
33#108×C47D412yes—
34#104×C47—22no—
35#101×C47—22no—
36C4×C8×C47C2311yescharacteristic
37#41×C47—22no—
38#41×C47—44no—
39#41×C47—82no—
40C2×Q8×C47—22no—
41C2×Q8×C47—44no—
42C2×D188—42no—
43C2×D188—41no—
44Q16×C47—44no—
45Q16×C47—42no—
46Q16×C47—42no—
47Q16×C47D812yes—
48SD16×C47—22no—
49SD16×C47—44no—
50D8×C47D812yes—
51M16×C47—22no—
52M16×C47—42no—
53C2×C8×C47—42no—
54C2×C8×C47C2×D412yes—
55C4⋊C4×C47—42no—
56C42×C47C2×D411yescharacteristic
57C2×C47⋊C8—22no—
58D376—42no—
59D376—42no—
60C47⋊C16—42no—
61C22×D47—81no—
62Q8×C47—22no—
63Q8×C47—44no—
64Q8×C47—82no—
65D4×C47—22no—
66D4×C47—42no—
67D4×C47—82no—
68C2×C4×C47—21no—
69C2×C4×C47—42no—
70C2×C4×C47—42no—
71C2×C4×C47—84no—
72C2×C4×C47#12011yescharacteristic
73D188—84no—
74D188—82no—
75C8×C47—42no—
76C8×C47C2×D812yes—
77C8×C47AGL(1,ℤ/8)12yes—
78C47⋊C8—42no—
79#12311—471nomaximal, Sylow
80C22×C47—42no—
81C22×C47#45311yescharacteristic
82C2×D47—162no—
83C2×D47—161no—
84C4×C47—22no—
85C4×C47—42no—
86C4×C47—82no—
87C4×C47#44712yes—
88#3293D4711yescharacteristic, complemented
89#2213—472no—
90#1709—471no—
91#1358—471no—
92#1335—472no—
93C2×C47—21no—
94C2×C47—82no—
95C2×C47#161911yescharacteristic
96D47—321no—
97#578—22no—
98#509—942no—
99#494C2×D4711yescharacteristic
100#493—471no—
101#486—942no—
102#473—22no—
103#456—22no—
104#443C2×D4712yes—
105#364—472no—
106#361—942no—
107C82—471no—
108C47#1231111yescharacteristic, complemented, Sylow
1092−1+4—22no—
110#137—24no—
111#137—44no—
112#135—42no—
113#135C22⋊D4712yes—
114C2×Q16—22no—
115C2×Q16—42no—
116C2×D8—942no—
117#131—22no—
118C4⋊Q8C22⋊D4712yes—
119#127—941no—
120SD32—1882no—
121D16—1882no—
122M32—942no—
123#108C22⋊D4712yes—
124#104—22no—
125#102—1884no—
126#101—22no—
127C4×C8—941no—
128C4×C8C22×D4711yescharacteristic
129#41—22no—
130#41—44no—
131#41—82no—
132C2×Q8—22no—
133C2×Q8—44no—
134C2×D4—1882no—
135C2×D4—1881no—
136Q16—44no—
137Q16—42no—
138Q16—42no—
139Q16#1062533412yes—
140SD16—22no—
141SD16—44no—
142D8—1882no—
143D8—1882no—
144D8#1062533412yes—
145M16—22no—
146M16—42no—
147C2×C8—42no—
148C2×C8—942no—
149C2×C8C2×C22⋊D4712yes—
150C4⋊C4—42no—
151C42C2×C22⋊D4711yescharacteristic
152C16—1882no—
153C23—3761no—
154Q8—22no—
155Q8—44no—
156Q8—82no—
157D4—22no—
158D4—42no—
159D4—82no—
160D4—3764no—
161D4—3762no—
162C2×C4—21no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—84no—
166C2×C4#1309399311yescharacteristic
167C8—42no—
168C8—1882no—
169C8C2×#1062533412yes—
170C8#1309405012yes—
171C22—42no—
172C22—7522no—
173C22—7521no—
174C22#1568929111yescharacteristic
175C4—22no—
176C4—42no—
177C4—82no—
178C4#1568925712yes—
179C2—21no—
180C2—82no—
181C2—15041no—
182C2#2024244211yescharacteristic
subgroupG/H
centerC2#20242442
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#3293C2
socleC2×C47#1619
hypercenter#3293D47
hypocenterC47#12311
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #3293

Complements

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

NH ≅ G/Ntype
1. #20245464C2semidirect
2. #20242995C2semidirect
3. #20241427C2semidirect
4. #20241361C2semidirect
5. C47×#3293C2semidirect
88. #3293D47semidirect
108. C47#12311semidirect

Maximal subgroups

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

subgroupindex
#202454642
#202429952
#202414272
#202413612
C47×#32932
#1231147