Finite Group Databasebeta

← #26136937

Subgroups — #26136937

Order 12032.

284 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C2×Q32×D47C211yesmaximal, characteristic
2C2×#15688963C211yesmaximal, characteristic, complemented
3#20245476C211yesmaximal, characteristic
4#20241570C211yesmaximal, characteristic, complemented
5#20241569C211yesmaximal, characteristic, complemented
6(C2×D47)⋊C32C211yesmaximal, characteristic
7C2×C47×Q64C211yesmaximal, characteristic, complemented
8C2×Q16×D47—21no—
9C2×Dic376C2211yescharacteristic
10C2×#13093970—21no—
11Q32×D47—22no—
12Q32×D47—22no—
13C2×C16×D47C2211yescharacteristic
14#15689361—21no—
15#15688963—22no—
16C2×C47⋊C32C2211yescharacteristic
17#15688949C2211yescharacteristic
18#15688927—21no—
19C2×Q32×C47C2211yescharacteristic
20C2×Q32×C47C2211yescharacteristic
21C47×Q64—22no—
22C2×C32×C47C2211yescharacteristic
23C2×Q8×D47—41no—
24C2×Dic188—21no—
25C2×#10625337—41no—
26Q16×D47—24no—
27Q16×D47—42no—
28C2×C8×D47D411yescharacteristic
29#13094000—41no—
30Dic376—21no—
31Dic376D412yes—
32#13093970—24no—
33C2×C47⋊C16D411yescharacteristic
34C16×D47—21no—
35C16×D47—21no—
36#13093958—21no—
37#13093948—41no—
38C47⋊C32—21no—
39C2×Q16×C47—21no—
40C2×Q16×C47—21no—
41Q32×C47—21no—
42Q32×C47—21no—
43Q32×C47—21no—
44Q32×C47D412yes—
45C2×C16×C47C2311yescharacteristic
46C32×C47—21no—
47C2×Q8×C47—41no—
48C2×Q8×C47—41no—
49Q8×D47—44no—
50Q8×D47—82no—
51C2×C4×D47—81no—
52C2×C4×D47D811yescharacteristic
53C2×Dic94—41no—
54C2×Dic94—81no—
55Q16×C47—22no—
56Q16×C47—41no—
57Q16×C47—41no—
58Q16×C47—41no—
59C2×C8×C47C2×D411yescharacteristic
60#10625337—44no—
61(C2×D47)⋊C4—81no—
62C4⋊Dic47—41no—
63Dic47⋊C4—81no—
64C2×C47⋊C8D811yescharacteristic
65Dic188—22no—
66Dic188—41no—
67C8×D47—21no—
68C8×D47—21no—
69C16×C47C2×D411yescharacteristic
70C16×C47C2×D411yescharacteristic
71C47⋊C16—21no—
72C22×D47D1611yescharacteristic
73Q8×C47—42no—
74Q8×C47—81no—
75Q8×C47—81no—
76Q8×C47—81no—
77C2×C4×C47—81no—
78C2×C4×C47—81no—
79C2×C4×C47C2×D811yescharacteristic
80C2×Dic47—81no—
81C2×Dic47—81no—
82C2×Dic47D1611yescharacteristic
83C4×D47—21no—
84C4×D47—21no—
85C4×D47—84no—
86Dic94—42no—
87Dic94—84no—
88Dic94—81no—
89C8×C47#12011yescharacteristic
90C8×C47AGL(1,ℤ/8)11yescharacteristic
91C47⋊C8—21no—
92#13665—471nomaximal, Sylow
93C22×C47C2×D1611yescharacteristic
94C2×D47—21no—
95C2×D47—21no—
96C2×D47Q6412yescomplemented
97C4×C47—82no—
98C4×C47—161no—
99C4×C47#44711yescharacteristic
100C4×C47#50911yescharacteristic
101Dic47—21no—
102Dic47—82no—
103Dic47—161no—
104C22×Q32—471no—
105C2×Q64—471no—
106C2×Q64D4711yescharacteristic, complemented
107#2216—471no—
108#1416—471no—
109#1416—471no—
110C22⋊C32—471no—
111C2×C47#218411yescharacteristic
112C2×C47C2×Q6411yescharacteristic
113C2×C47#226411yescharacteristic
114D47—22no—
115C22×Q16—941no—
116C2×Q32—471no—
117C2×Q32—941no—
118C2×Q32—942no—
119C2×Q32—942no—
120C2×Q32C2×D4711yescharacteristic
121C2×Q32C2×D4711yescharacteristic
122C22×C16—471no—
123#467—941no—
124Q64—22no—
125Q64—942no—
126C2×C32—471no—
127C2×C32C2×D4711yescharacteristic
128#366—471no—
129#358—941no—
130C47#1366511yescharacteristic, complemented, Sylow
131C22×Q8—1881no—
132C2×Q16—21no—
133C2×Q16—21no—
134C2×Q16—944no—
135C2×Q16—941no—
136C2×Q16—1881no—
137C2×Q16—1882no—
138C22×C8—471no—
139C22⋊Q8—1881no—
140Q32—21no—
141Q32—21no—
142Q32—21no—
143Q32—472no—
144Q32—944no—
145Q32—941no—
146Q32C22⋊D4712yes—
147C2×C16—471no—
148C2×C16—941no—
149C2×C16—941no—
150C2×C16C22×D4711yescharacteristic
151#107—941no—
152#103—1881no—
153C32—21no—
154C32—941no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—3761no—
158C2×Q8—3762no—
159C2×Q8—1884no—
160C2×Q8—1881no—
161C22×C4—471no—
162C22×C4—3761no—
163Q16—22no—
164Q16—41no—
165Q16—41no—
166Q16—41no—
167Q16—942no—
168Q16—1884no—
169Q16—1881no—
170C2×C8—471no—
171C2×C8—941no—
172C2×C8—941no—
173C2×C8D4×D4711yescharacteristic
174C4⋊C4—3761no—
175C4⋊C4—1881no—
176C22⋊C4—3761no—
177C16—941no—
178C16D4×D4711yescharacteristic
179C16C2×C22⋊D4711yescharacteristic
180C23—471no—
181Q8—42no—
182Q8—81no—
183Q8—81no—
184Q8—81no—
185Q8—3764no—
186Q8—3761no—
187Q8—1882no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—471no—
191C2×C4—941no—
192C2×C4—941no—
193C2×C4—3764no—
194C2×C4—3761no—
195C2×C4—3761no—
196C2×C4D8×D4711yescharacteristic
197C8—941no—
198C8#1309399211yescharacteristic
199C8#1309404811yescharacteristic
200C22—472no—
201C22—941no—
202C22—941no—
203C22D16×D4711yescharacteristic
204C4—82no—
205C4—161no—
206C4—941no—
207C4—3762no—
208C4—7521no—
209C4#1568925511yescharacteristic
210C4#1568955711yescharacteristic
211C2—942no—
212C2#2024529811yescharacteristic
213C2Q64×D4711yescharacteristic
214C2#2024570711yescharacteristic
subgroupG/H
centerC22D16×D47
commutator, cosocleC2×C16×C47C23
FrattiniC2×C16C22×D47
FittingC2×C47×Q64C2
socleC22×C47C2×D16
prime radicalC22×D47D16
hypercenterC2×Q64D47
hypocenterC47#13665
LCSG ▷ C2×C16×C47 ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×Q64

Complements

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

NH ≅ G/Ntype
2. C2×#15688963C2semidirect
4. #20241570C2semidirect
5. #20241569C2semidirect
7. C2×C47×Q64C2semidirect
96. C2×D47Q64semidirect
106. C2×Q64D47semidirect
130. C47#13665semidirect

Maximal subgroups

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

subgroupindex
C2×Q32×D472
C2×#156889632
#202454762
#202415702
#202415692
(C2×D47)⋊C322
C2×C47×Q642
#1366547