Finite Group Databasebeta

← #26130446

Subgroups — #26130446

Order 12032.

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

normal subgroups only

This group has 218 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#20245527C211yesmaximal, characteristic
2#20245439C211yesmaximal, characteristic
3#20242986C211yesmaximal, characteristic
4#20242194C211yesmaximal, characteristic
5#20241451C211yesmaximal, characteristic
6#20241436C211yesmaximal, characteristic
7C47×#1364C211yesmaximal, characteristic
8C2×Dic376—21no—
9#15689519—21no—
10#15689503C2211yescharacteristic
11#15689473—21no—
12#15689247—21no—
13C4×Dic188C2211yescharacteristic
14#15688950—21no—
15C4⋊(C47⋊C16)C2211yescharacteristic
16#15688928—21no—
17#15688926—21no—
18#15688853—21no—
19C8×C47⋊C8C2211yescharacteristic
20C47×#500C2211yescharacteristic
21C47×C4⋊C16C2211yescharacteristic
22C47×#335C2211yescharacteristic
23C2×Dic188—21no—
24C2×Dic188—21no—
25C2×Dic188D411yescharacteristic
26#13094024—21no—
27C4×Dic94—21no—
28Dic376—42no—
29C2×C47⋊C16—21no—
30#13093958D411yescharacteristic
31#13093955—42no—
32Dic47⋊C8—41no—
33#13093949—21no—
34#13093948—41no—
35#13093948—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×Dic94—21no—
47C2×Dic94—41no—
48C2×C8×C47—41no—
49C2×C8×C47C2×D411yescharacteristic
50C2×C8×C47#4111yescharacteristic
51C4⋊C4×C47—41no—
52C4⋊C4×C47—41no—
53C42×C47C2×D411yescharacteristic
54C4⋊Dic47—21no—
55C4⋊Dic47—41no—
56C4⋊Dic47—41no—
57Dic47⋊C4—41no—
58C4×Dic47—41no—
59C2×C47⋊C8—21no—
60C2×C47⋊C8D811yescharacteristic
61C2×C47⋊C8D811yescharacteristic
62Dic188—21no—
63Dic188—41no—
64Dic188—41no—
65Dic188—81no—
66Dic188SD1612yes—
67C16×C47—41no—
68C47⋊C16—41no—
69Q8×C47—81no—
70Q8×C47—81no—
71C2×C4×C47—81no—
72C2×C4×C47#12111yescharacteristic
73C2×C4×C47C2×D811yescharacteristic
74C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
75C2×Dic47—41no—
76C2×Dic47—41no—
77C2×Dic47—81no—
78Dic94—22no—
79Dic94—41no—
80Dic94—81no—
81Dic94—81no—
82C8×C47—21no—
83C8×C47—81no—
84C8×C47C2×SD1611yescharacteristic
85C8×C47#13511yescharacteristic
86C47⋊C8—22no—
87C47⋊C8—21no—
88C47⋊C8—21no—
89#12423—471nomaximal, Sylow
90C22×C47#45911yescharacteristic
91C4×C47—21no—
92C4×C47—161no—
93C4×C47#46511yescharacteristic
94C4×C47#47111yescharacteristic
95C4×C47#50811yescharacteristic
96C4×C47#51011yescharacteristic
97Dic47—42no—
98Dic47—81no—
99Dic47—161no—
100#2225—471no—
101#2209—471no—
102#1707—471no—
103C8×Q16—471no—
104#1367—471no—
105#1364D4711yescharacteristic
106#1362—471no—
107C2×C47#166511yescharacteristic
108C2×C47#221111yescharacteristic
109C2×C47#221411yescharacteristic
110C2×Q32—941no—
111#500C2×D4711yescharacteristic
112#498—941no—
113#494—471no—
114#487—941no—
115C8×Q8—941no—
116C4×Q16—471no—
117#367—941no—
118C4⋊C16—471no—
119C4⋊C16C2×D4711yescharacteristic
120#358—941no—
121#358—941no—
122#335C2×D4711yescharacteristic
123Q8⋊C8—941no—
124C82—471no—
125C47#1242311yescharacteristic, complemented, Sylow
126C2×Q16—471no—
127C2×Q16—941no—
128C2×Q16—941no—
129C4⋊Q8—21no—
130C4⋊Q8—941no—
131C4×Q8—941no—
132Q32—1882no—
133C2×C16—21no—
134C2×C16—941no—
135#107—21no—
136#107—21no—
137#107—471no—
138#106—1882no—
139C4⋊C8—21no—
140C4⋊C8—1881no—
141#103—941no—
142#103—1881no—
143#103—1881no—
144C4×C8—471no—
145C4×C8—471no—
146C4×C8—1881no—
147C4×C8C22×D4711yescharacteristic
148C2×Q8—41no—
149C2×Q8—941no—
150C2×Q8—1881no—
151Q16—472no—
152Q16—941no—
153Q16—3761no—
154Q16—1881no—
155Q16—1881no—
156C2×C8—41no—
157C2×C8—471no—
158C2×C8—471no—
159C2×C8—941no—
160C2×C8#1062535011yescharacteristic
161C2×C8D4×D4711yescharacteristic
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—941no—
165C4⋊C4—1881no—
166C4⋊C4—1881no—
167C4⋊C4—1881no—
168C42—1881no—
169C42D4×D4711yescharacteristic
170C16—41no—
171C16—1881no—
172Q8—81no—
173Q8—81no—
174Q8—942no—
175Q8—3761no—
176Q8—3761no—
177Q8—1881no—
178C2×C4—81no—
179C2×C4—3761no—
180C2×C4—1881no—
181C2×C4—1881no—
182C2×C4#1309399711yescharacteristic
183C2×C4D8×D4711yescharacteristic
184C2×C4#1309405111yescharacteristic
185C8—21no—
186C8—81no—
187C8—942no—
188C8—941no—
189C8—941no—
190C8SD16×D4711yescharacteristic
191C8#1309404711yescharacteristic
192C22#1568931711yescharacteristic
193C4—21no—
194C4—161no—
195C4—3761no—
196C4—1882no—
197C4—7521no—
198C4#1568935511yescharacteristic
199C4#1568938911yescharacteristic
200C4#1568955211yescharacteristic
201C4#1568956211yescharacteristic
202C2#2024273211yescharacteristic
203C2#2024544911yescharacteristic
204C2#2024546811yescharacteristic
subgroupG/H
centerC22#15689317
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#1364C2
socle, prime radicalC22×C47#459
hypercenter#1364D47
hypocenterC47#12423
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
125. C47#12423semidirect

Maximal subgroups

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

subgroupindex
#202455272
#202454392
#202429862
#202421942
#202414512
#202414362
C47×#13642
#1242347