Finite Group Databasebeta

← #26119381

Subgroups — #26119381

Order 12032.

400 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 99 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#20251751C211yesmaximal, characteristic
2#20241952C212yesmaximal
3#20241248C212yesmaximal
4#20241221C211yesmaximal, characteristic
5C47×#1994C211yesmaximal, characteristic
6C2×#13094016—21no—
7#15689176C2212yes—
8#15689021—24no—
9#15688993—21no—
10#15688989C2212yes—
11#15688860—24no—
12C47×#533C2211yescharacteristic
13C47×#423C2211yescharacteristic
14C43×C47C2211yescharacteristic
15C47×#339—21no—
16C47×#339—21no—
17#13094016—42no—
18#13094016—42no—
19C2×C4⋊Dic47—24no—
20C2×C4⋊Dic47—22no—
21C2×Dic47⋊C4—24no—
22C4⋊(C47⋊C8)—22no—
23C22⋊(C47⋊C8)—22no—
24C4×C47⋊C8—22no—
25C47⋊#95—22no—
26C47⋊#95D414yes—
27C2×M16×C47—21no—
28C4⋊Q8×C47Q812yes—
29#125×C47—21no—
30C22⋊Q8×C47—22no—
31C4×Q8×C47—22no—
32#117×C47—21no—
33C2×C42×C47—22no—
34C2×C42×C47D411yescharacteristic
35C2×C42×C47D411yescharacteristic
36C2×C42×C47C2311yescharacteristic
37C4⋊C8×C47—22no—
38C2×Q8×C47—22no—
39C22×C4×C47—21no—
40C22×C4×C47—21no—
41C22×C4×C47C2×D412yes—
42C22×C4×C47C2×D411yescharacteristic
43C22×Dic47—24no—
44M16×C47—41no—
45M16×C47—41no—
46C2×C8×C47—41no—
47C4⋊C4×C47—22no—
48C4⋊C4×C47—22no—
49C4⋊C4×C47—42no—
50C22⋊C4×C47—41no—
51C42×C47—21no—
52C42×C47—21no—
53C42×C47—44no—
54C42×C47—41no—
55C42×C47SD1612yes—
56C42×C47Q1612yes—
57C42×C47C2×Q811yescharacteristic
58C42×C47#4111yescharacteristic
59C42×C47#4112yes—
60C4⋊Dic47—48no—
61C4⋊Dic47—42no—
62C4⋊Dic47—42no—
63Dic47⋊C4—48no—
64C2×C47⋊C8—42no—
65C23×C47#12011yescharacteristic
66Q8×C47—82no—
67C2×C4×C47—24no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—42no—
71C2×C4×C47—42no—
72C2×C4×C47—42no—
73C2×C4×C47C22⋊Q812yes—
74C2×C4×C47C22⋊Q811yescharacteristic
75C2×C4×C47#12412yes—
76C2×C4×C47#12411yescharacteristic
77C2×C4×C47C2×SD1611yescharacteristic
78C2×C4×C47C2×Q1611yescharacteristic
79C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
80C2×C4×C47#13711yescharacteristic
81C2×Dic47—48no—
82C2×Dic47—44no—
83C8×C47—81no—
84C47⋊C8—82no—
85#10365—471nomaximal, Sylow
86C22×C47—22no—
87C22×C47#39311yescharacteristic
88C22×C47#45011yescharacteristic
89C22×C47#45111yescharacteristic
90C4×C47—24no—
91C4×C47—22no—
92C4×C47—22no—
93C4×C47—42no—
94C4×C47—82no—
95C4×C47#47511yescharacteristic
96C4×C47#47711yescharacteristic
97C4×C47#48711yescharacteristic
98C4×C47#48911yescharacteristic
99Dic47—84no—
100#2859—471no—
101#1994D4711yescharacteristic
102#1518—472no—
103#1286—472no—
104#1276—471no—
105C2×C47—21no—
106C2×C47—21no—
107C2×C47#202411yescharacteristic
108C2×C47#203112yes—
109#533C2×D4711yescharacteristic
110C2×#125—941no—
111#431—472no—
112#423C2×D4711yescharacteristic
113#389—944no—
114#384—941no—
115#382—472no—
116C43C2×D4711yescharacteristic
117#339—21no—
118#339—21no—
119#328—944no—
120C47#1036511yescharacteristic, complemented, Sylow
121C2×M16—21no—
122C4⋊Q8Dic9412yes—
123#125—21no—
124#125—1882no—
125#125—1882no—
126C22⋊Q8—22no—
127C4×Q8—22no—
128#117—21no—
129C2×C4⋊C4—944no—
130C2×C4⋊C4—944no—
131C2×C4⋊C4—942no—
132C2×C42—22no—
133C2×C42C22⋊D4711yescharacteristic
134C2×C42C22⋊D4711yescharacteristic
135C2×C42C22×D4711yescharacteristic
136C4⋊C8—22no—
137C4⋊C8—942no—
138C22⋊C8—942no—
139C4×C8—942no—
140#95—474no—
141#95—942no—
142C2×Q8—22no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—944no—
146C22×C4D4×D4712yes—
147C22×C4C2×C22⋊D4711yescharacteristic
148M16—41no—
149M16—41no—
150C2×C8—41no—
151C2×C8—1882no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—42no—
155C4⋊C4—1888no—
156C4⋊C4—1888no—
157C4⋊C4—1882no—
158C4⋊C4—1882no—
159C22⋊C4—41no—
160C42—21no—
161C42—21no—
162C42—44no—
163C42—41no—
164C42#1062533612yes—
165C42#1062533712yes—
166C42C2×Dic9411yescharacteristic
167C42#1062535011yescharacteristic
168C42#1062535212yes—
169C23#1309399211yescharacteristic
170Q8—82no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—1888no—
178C2×C4—1884no—
179C2×C4#1309400112yes—
180C2×C4#1309400311yescharacteristic
181C2×C4#1309401012yes—
182C2×C4#1309401111yescharacteristic
183C2×C4C2×#1062533611yescharacteristic
184C2×C4C2×#1062533711yescharacteristic
185C2×C4#1309404911yescharacteristic
186C2×C4#1309405411yescharacteristic
187C8—81no—
188C8—3762no—
189C22—22no—
190C22#1568903511yescharacteristic
191C22#1568927311yescharacteristic
192C22#1568927811yescharacteristic
193C4—24no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—82no—
198C4—3764no—
199C4#1568940811yescharacteristic
200C4#1568941811yescharacteristic
201C4#1568947311yescharacteristic
202C4#1568948211yescharacteristic
203C2—21no—
204C2—21no—
205C2#2024452911yescharacteristic
206C2#2024456012yes—
subgroupG/H
centerC22#15689035
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1994C2
socleC22×C47#393
prime radicalC23×C47#120
hypercenter#1994D47
hypocenterC47#10365
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
120. C47#10365semidirect

Maximal subgroups

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

subgroupindex
#202517512
#202419522
#202412482
#202412212
C47×#19942
#1036547