Finite Group Databasebeta

← #26130539

Subgroups — #26130539

Order 12032.

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

normal subgroups only

This group has 216 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#20245640C211yesmaximal, characteristic
2#20245290C211yesmaximal, characteristic
3#20242759C211yesmaximal, characteristic
4#20242755C211yesmaximal, characteristic
5#20241459C211yesmaximal, characteristic
6#20241438C211yesmaximal, characteristic
7C47×#1362C211yesmaximal, characteristic
8C2×#13093970—21no—
9C2×#13093970—21no—
10#15689503C2211yescharacteristic
11#15689409—21no—
12#15689405—21no—
13C8×Dic94C2211yescharacteristic
14Dic47⋊C16—21no—
15C4×C47⋊C16C2211yescharacteristic
16C16×Dic47—21no—
17#15688876C2211yescharacteristic
18#15688869—21no—
19#15688868—21no—
20C47×#494C2211yescharacteristic
21C47×C4⋊C16C2211yescharacteristic
22C47×#335C2211yescharacteristic
23C2×Dic188—21no—
24C2×Dic188—21no—
25#13094024—21no—
26C4×Dic94D411yescharacteristic
27#13093970—42no—
28#13093970—42no—
29C2×C47⋊C16D411yescharacteristic
30C2×C47⋊C16D411yescharacteristic
31#13093956—41no—
32#13093955—41no—
33C4⋊(C47⋊C8)—21no—
34C4⋊(C47⋊C8)D411yescharacteristic
35Dic47⋊C8—21no—
36#13093949—41no—
37#13093947—41no—
38C8×Dic47—21no—
39C2×Q16×C47—21no—
40C2×Q16×C47—21no—
41C4⋊Q8×C47—21no—
42C2×C16×C47—21no—
43C4⋊C8×C47—21no—
44C4×C8×C47C2311yescharacteristic
45C2×Q8×C47—41no—
46C2×Dic94—41no—
47C2×Dic94D811yescharacteristic
48Q16×C47—41no—
49Q16×C47—41no—
50Q16×C47—81no—
51C2×C8×C47—41no—
52C2×C8×C47C2×D411yescharacteristic
53C2×C8×C47#4111yescharacteristic
54C4⋊C4×C47—41no—
55C4⋊C4×C47—41no—
56C42×C47C2×D411yescharacteristic
57C4⋊Dic47—41no—
58C4⋊Dic47—41no—
59C4⋊Dic47D811yescharacteristic
60Dic47⋊C4—21no—
61C4×Dic47—21no—
62C2×C47⋊C8—21no—
63C2×C47⋊C8—41no—
64Dic188—41no—
65Dic188—41no—
66Dic188—81no—
67C16×C47—41no—
68C47⋊C16—21no—
69C47⋊C16SD1612yes—
70Q8×C47—81no—
71Q8×C47—81no—
72C2×C4×C47—81no—
73C2×C4×C47#12111yescharacteristic
74C2×C4×C47C2×D811yescharacteristic
75C2×C4×C47#13511yescharacteristic
76C2×Dic47—21no—
77C2×Dic47—21no—
78C2×Dic47—81no—
79Dic94—21no—
80Dic94—81no—
81Dic94—81no—
82Dic94Q3212yescomplemented
83C8×C47—21no—
84C8×C47—81no—
85C8×C47C2×SD1611yescharacteristic
86C8×C47AGL(1,ℤ/8)11yescharacteristic
87C47⋊C8—41no—
88C47⋊C8—81no—
89#12440—471nomaximal, Sylow
90C22×C47#46611yescharacteristic
91C4×C47—21no—
92C4×C47—161no—
93C4×C47#46011yescharacteristic
94C4×C47#47211yescharacteristic
95C4×C47C2×Q3211yescharacteristic
96C4×C47#50811yescharacteristic
97Dic47—22no—
98Dic47—41no—
99Dic47—161no—
100#2247—471no—
101Q8×C16—471no—
102#1670—471no—
103#1670—471no—
104#1371—471no—
105#1362—471no—
106#1362D4711yescharacteristic
107C2×C47#166811yescharacteristic
108C2×C47#221611yescharacteristic
109C2×C47#222211yescharacteristic
110C2×Q32—941no—
111C2×Q32—941no—
112#494—471no—
113#494C2×D4711yescharacteristic
114#475—941no—
115#475—941no—
116C8×Q8—471no—
117C4⋊C16—941no—
118C4⋊C16C2×D4711yescharacteristic
119C4×C16—471no—
120C4×C16—941no—
121#335—471no—
122#335C2×D4711yescharacteristic
123#332—941no—
124#332—941no—
125C47#1244011yescharacteristic, complemented, Sylow
126C2×Q16—21no—
127C2×Q16—21no—
128C2×Q16—941no—
129C2×Q16—941no—
130C4⋊Q8—21no—
131C4⋊Q8—941no—
132C4×Q8—471no—
133Q32—1882no—
134Q32—1882no—
135C2×C16—21no—
136C2×C16—471no—
137C2×C16—471no—
138#106—1881no—
139#106—1881no—
140C4⋊C8—21no—
141C4⋊C8—471no—
142C4⋊C8—941no—
143C4⋊C8—941no—
144#103—1881no—
145#103—1881no—
146C4×C8—941no—
147C4×C8C22×D4711yescharacteristic
148C2×Q8—41no—
149C2×Q8—471no—
150C2×Q8—1881no—
151Q16—41no—
152Q16—41no—
153Q16—81no—
154Q16—3761no—
155Q16—1881no—
156Q16—1881no—
157C2×C8—41no—
158C2×C8—941no—
159C2×C8—1881no—
160C2×C8#1062535011yescharacteristic
161C2×C8D4×D4711yescharacteristic
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—471no—
165C4⋊C4—941no—
166C4⋊C4—1881no—
167C4⋊C4—1881no—
168C42—941no—
169C42D4×D4711yescharacteristic
170C16—41no—
171C16—472no—
172C16—941no—
173Q8—81no—
174Q8—81no—
175Q8—472no—
176Q8—941no—
177Q8—3761no—
178Q8—3761no—
179C2×C4—81no—
180C2×C4—941no—
181C2×C4—941no—
182C2×C4—3761no—
183C2×C4#1309399711yescharacteristic
184C2×C4D8×D4711yescharacteristic
185C2×C4#1309404511yescharacteristic
186C8—21no—
187C8—81no—
188C8—3761no—
189C8—1881no—
190C8SD16×D4711yescharacteristic
191C8#1309404811yescharacteristic
192C22#1568935811yescharacteristic
193C4—21no—
194C4—161no—
195C4—942no—
196C4—1881no—
197C4—7521no—
198C4#1568932211yescharacteristic
199C4#1568939211yescharacteristic
200C4Q32×D4711yescharacteristic
201C4#1568955411yescharacteristic
202C2#2024274711yescharacteristic
203C2#2024547811yescharacteristic
204C2#2024551211yescharacteristic
subgroupG/H
centerC22#15689358
commutator, cosocleC4×C8×C47C23
FrattiniC4×C8C22×D47
FittingC47×#1362C2
socle, prime radicalC22×C47#466
hypercenter#1362D47
hypocenterC47#12440
LCSG ▷ C4×C8×C47 ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1362

Complements

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

NH ≅ G/Ntype
82. Dic94Q32semidirect
125. C47#12440semidirect

Maximal subgroups

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

subgroupindex
#202456402
#202452902
#202427592
#202427552
#202414592
#202414382
C47×#13622
#1244047