Finite Group Databasebeta

← #26120778

Subgroups — #26120778

Order 12032.

374 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 95 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#20251660C211yesmaximal, characteristic
2#20243523C212yesmaximal
3#20241270C212yesmaximal
4#20241269C211yesmaximal, characteristic
5C47×#1847C211yesmaximal, characteristic
6C2×#13093935C2212yes—
7#15689065—22no—
8#15689062—21no—
9#15689044—22no—
10#15689043—21no—
11#15688989C2212yes—
12#15688885—22no—
13#15688885—22no—
14C2×#107×C47—21no—
15C2×#106×C47—21no—
16C2×#97×C47C2211yescharacteristic
17C47×#384C2211yescharacteristic
18C47×#382C2211yescharacteristic
19C22×Dic94—21no—
20C22×C47⋊C8—22no—
21C2×C4⋊Dic47—21no—
22C2×C4⋊Dic47D412yes—
23C2×C4⋊Dic47D412yes—
24C2×Dic47⋊C4—22no—
25#13093935—22no—
26#13093935Q814yescomplemented
27C47⋊#95—21no—
28C47⋊#95—22no—
29C47⋊#95—21no—
30C47⋊#95—22no—
31C47⋊#95—22no—
32C22×C8×C47—21no—
33C2×C4⋊C4×C47—22no—
34C2×C4⋊C4×C47—21no—
35C2×C4⋊C4×C47D411yescharacteristic
36C2×C4⋊C4×C47D411yescharacteristic
37C2×C42×C47C2311yescharacteristic
38#107×C47—42no—
39#106×C47—42no—
40#97×C47—21no—
41#97×C47Q812yescomplemented
42#95×C47—22no—
43C22×C4×C47—21no—
44C22×C4×C47—21no—
45C22×C4×C47—41no—
46C22×C4×C47C2×D412yes—
47C22×C4×C47C2×D411yescharacteristic
48C22×Dic47—22no—
49C22×Dic47—22no—
50C2×Dic94—81no—
51C2×Dic94—82no—
52C2×C8×C47—22no—
53C2×C8×C47—22no—
54C2×C8×C47—22no—
55C4⋊C4×C47—41no—
56C4⋊C4×C47—41no—
57C4⋊C4×C47—41no—
58C4⋊C4×C47—41no—
59C4⋊C4×C47—44no—
60C42×C47C2×Q811yescharacteristic
61C42×C47C2×Q812yes—
62C42×C47#4111yescharacteristic
63C4⋊Dic47—42no—
64C4⋊Dic47—42no—
65C4⋊Dic47—81no—
66Dic47⋊C4—82no—
67C2×C47⋊C8—24no—
68C2×C47⋊C8—42no—
69C2×C47⋊C8—42no—
70C23×C47#12011yescharacteristic
71C2×C4×C47—21no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—21no—
75C2×C4×C47—41no—
76C2×C4×C47—41no—
77C2×C4×C47—42no—
78C2×C4×C47—42no—
79C2×C4×C47—81no—
80C2×C4×C47—82no—
81C2×C4×C47C22⋊Q812yes—
82C2×C4×C47C22⋊Q811yescharacteristic
83C2×C4×C47C4⋊Q811yescharacteristic
84C2×C4×C47C4⋊Q812yes—
85C2×Dic47—42no—
86C2×Dic47—42no—
87C2×Dic47—42no—
88C2×Dic47—42no—
89C2×Dic47—42no—
90C2×Dic47—42no—
91Dic94—84no—
92C8×C47—24no—
93C47⋊C8—44no—
94#10584—471nomaximal, Sylow
95C22×C47#39511yescharacteristic
96C22×C47#45311yescharacteristic
97C22×C47#45412yes—
98C22×C47#45512yes—
99C22×C47#45611yescharacteristic
100C4×C47—21no—
101C4×C47—21no—
102C4×C47—22no—
103C4×C47—22no—
104C4×C47—81no—
105C4×C47—81no—
106C4×C47—161no—
107Dic47—82no—
108Dic47—82no—
109#2844—471no—
110#1847D4711yescharacteristic
111#1836—472no—
112#1295—472no—
113#1295—471no—
114C2×C47#165711yescharacteristic
115C2×C47#165911yescharacteristic
116C2×C47#166412yes—
117C2×C47#206011yescharacteristic
118C2×C47#206112yes—
119C2×#107—21no—
120C2×#106—21no—
121C2×#97—472no—
122C2×#97C2×D4711yescharacteristic
123#400—942no—
124#400—941no—
125#395—942no—
126#395—941no—
127#384C2×D4711yescharacteristic
128#382—472no—
129#382C2×D4711yescharacteristic
130#340—942no—
131#340—942no—
132C47#1058411yescharacteristic, complemented, Sylow
133C22×Q8—941no—
134C22×C8—21no—
135C22×C8—942no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—472no—
139C2×C4⋊C4—472no—
140C2×C4⋊C4—942no—
141C2×C4⋊C4—941no—
142C2×C4⋊C4C22⋊D4711yescharacteristic
143C2×C4⋊C4C22⋊D4711yescharacteristic
144C2×C42C22×D4711yescharacteristic
145#107—42no—
146#106—42no—
147#97—21no—
148#97—474no—
149#97—942no—
150#97Dic9412yescomplemented
151#95—22no—
152#95—942no—
153#95—941no—
154#95—941no—
155#95—942no—
156#95—942no—
157C2×Q8—3761no—
158C2×Q8—3762no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—41no—
162C22×C4—942no—
163C22×C4—942no—
164C22×C4D4×D4712yes—
165C22×C4C2×C22⋊D4711yescharacteristic
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—944no—
170C2×C8—1882no—
171C2×C8—1882no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—44no—
177C4⋊C4—3762no—
178C4⋊C4—3761no—
179C4⋊C4—1882no—
180C4⋊C4—1882no—
181C42C2×Dic9411yescharacteristic
182C42#1062535011yescharacteristic
183C42Q8×D4712yes—
184C23#1309399211yescharacteristic
185Q8—3764no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—81no—
195C2×C4—82no—
196C2×C4—1882no—
197C2×C4—1882no—
198C2×C4—1882no—
199C2×C4—1882no—
200C2×C4—1882no—
201C2×C4—1882no—
202C2×C4#1309400212yes—
203C2×C4#1309400311yescharacteristic
204C2×C4#1309402211yescharacteristic
205C2×C4#1309402312yes—
206C8—24no—
207C8—1884no—
208C22#1568904311yescharacteristic
209C22#1568929011yescharacteristic
210C22#1568929412yes—
211C22#1568929912yes—
212C22#1568930511yescharacteristic
213C4—22no—
214C4—22no—
215C4—21no—
216C4—21no—
217C4—81no—
218C4—81no—
219C4—161no—
220C4—3762no—
221C4—3762no—
222C2#2024268411yescharacteristic
223C2#2024269211yescharacteristic
224C2#2024272012yes—
225C2#2024473311yescharacteristic
226C2#2024473612yes—
subgroupG/H
centerC23#13093992
commutator, cosocleC2×C42×C47C23
FrattiniC2×C42C22×D47
FittingC47×#1847C2
socle, prime radicalC23×C47#120
hypercenter#1847D47
hypocenterC47#10584
LCSG ▷ C2×C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
26. #13093935Q8semidirect
41. #97×C47Q8semidirect
132. C47#10584semidirect
150. #97Dic94semidirect

Maximal subgroups

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

subgroupindex
#202516602
#202435232
#202412702
#202412692
C47×#18472
#1058447