Finite Group Databasebeta

← #26129361

Subgroups — #26129361

Order 12032.

330 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 59 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#20242430C212yesmaximal
3#20241414C212yesmaximal
4#20241332C211yesmaximal, characteristic
5C47×#2061C211yesmaximal, characteristic
6#15689456—22no—
7#15689065—22no—
8#15689062C2212yes—
9#15689044—22no—
10#15689043—21no—
11#15688989—21no—
12#15688860—22no—
13#15688849C2212yes—
14C47×#544C2211yescharacteristic
15C47×#428—21no—
16C47×#382C2211yescharacteristic
17C47×#343C2211yescharacteristic
18C47×#339—21no—
19C22×Dic94—21no—
20C2×C4⋊Dic47—21no—
21C2×C4⋊Dic47—21no—
22C2×C4⋊Dic47D412yes—
23C2×Dic47⋊C4—22no—
24#13093957—42no—
25#13093948—42no—
26C22⋊(C47⋊C8)—22no—
27C47⋊#95—22no—
28C47⋊#95—21no—
29C47⋊#95—22no—
30C47⋊#95—22no—
31C47⋊#95D412yes—
32C2×M16×C47—21no—
33C4⋊Q8×C47—41no—
34#125×C47—41no—
35C22⋊Q8×C47—22no—
36#117×C47—21no—
37C2×C4⋊C4×C47D411yescharacteristic
38C2×C4⋊C4×C47C2311yescharacteristic
39C2×C42×C47D411yescharacteristic
40#107×C47—41no—
41#106×C47—41no—
42#95×C47—22no—
43C2×Q8×C47—22no—
44C22×C4×C47—21no—
45C22×C4×C47—21no—
46C22×C4×C47C2×D411yescharacteristic
47C22×C4×C47C2×D412yes—
48C22×Dic47—22no—
49C22×Dic47—22no—
50C2×Dic94—82no—
51C2×Dic94—81no—
52M16×C47—22no—
53M16×C47—41no—
54C2×C8×C47—41no—
55C4⋊C4×C47—21no—
56C4⋊C4×C47—21no—
57C4⋊C4×C47—22no—
58C4⋊C4×C47—41no—
59C4⋊C4×C47—42no—
60C4⋊C4×C47—41no—
61C22⋊C4×C47—41no—
62C42×C47—21no—
63C42×C47—41no—
64C42×C47Q1612yes—
65C4⋊Dic47—42no—
66C4⋊Dic47—81no—
67C4⋊Dic47—81no—
68Dic47⋊C4—82no—
69C2×C47⋊C8—42no—
70C23×C47#12011yescharacteristic
71Q8×C47—82no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—41no—
77C2×C4×C47—41no—
78C2×C4×C47—42no—
79C2×C4×C47—42no—
80C2×C4×C47—41no—
81C2×C4×C47—41no—
82C2×C4×C47—41no—
83C2×C4×C47C2×Q1611yescharacteristic
84C2×C4×C47#13711yescharacteristic
85C2×Dic47—42no—
86C2×Dic47—42no—
87C2×Dic47—42no—
88C2×Dic47—42no—
89C2×Dic47—42no—
90C2×Dic47—42no—
91Dic94—84no—
92C8×C47—42no—
93C47⋊C8—82no—
94#12261—471nomaximal, Sylow
95C22×C47—21no—
96C22×C47—21no—
97C22×C47#45111yescharacteristic
98C22×C47#45611yescharacteristic
99C22×C47B(4,𝔽2)11yescharacteristic
100C4×C47—21no—
101C4×C47—21no—
102C4×C47—42no—
103C4×C47—42no—
104C4×C47—81no—
105C4×C47—81no—
106C4×C47—81no—
107Dic47—82no—
108Dic47—82no—
109#2844—471no—
110#2061D4711yescharacteristic
111#1617—472no—
112#1353—472no—
113#1324—471no—
114C2×C47—21no—
115C2×C47—21no—
116C2×C47#160511yescharacteristic
117C2×C47#220111yescharacteristic
118C2×C47#220211yescharacteristic
119#544C2×D4711yescharacteristic
120#484—942no—
121#428—21no—
122#400—472no—
123#400—942no—
124#395—942no—
125#395—941no—
126#382—941no—
127#382C2×D4711yescharacteristic
128#343C2×D4711yescharacteristic
129#339—21no—
130#328—942no—
131#324—472no—
132C47#1226111yescharacteristic, complemented, Sylow
133C22×Q8—941no—
134C2×M16—21no—
135C4⋊Q8—41no—
136#125—41no—
137C22⋊Q8—22no—
138#117—21no—
139C2×C4⋊C4—472no—
140C2×C4⋊C4—942no—
141C2×C4⋊C4—941no—
142C2×C4⋊C4—941no—
143C2×C4⋊C4C22⋊D4711yescharacteristic
144C2×C4⋊C4C22×D4711yescharacteristic
145C2×C42C22⋊D4711yescharacteristic
146#107—41no—
147#107—1882no—
148#106—41no—
149#103—1882no—
150C22⋊C8—942no—
151#95—22no—
152#95—472no—
153#95—942no—
154#95—941no—
155#95—942no—
156#95—942no—
157C2×Q8—22no—
158C2×Q8—3762no—
159C2×Q8—3761no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—942no—
163C22×C4—942no—
164C22×C4D4×D4712yes—
165C22×C4C2×C22⋊D4711yescharacteristic
166M16—22no—
167M16—41no—
168C2×C8—41no—
169C2×C8—1882no—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—22no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—42no—
176C4⋊C4—3762no—
177C4⋊C4—3761no—
178C4⋊C4—3761no—
179C4⋊C4—1882no—
180C22⋊C4—41no—
181C42—21no—
182C42—41no—
183C42#1062533712yes—
184C23#1309399211yescharacteristic
185Q8—82no—
186Q8—3764no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—1882no—
199C2×C4—1882no—
200C2×C4—1882no—
201C2×C4—1882no—
202C2×C4—1882no—
203C2×C4—1882no—
204C2×C4C2×#1062533711yescharacteristic
205C2×C4#1309405411yescharacteristic
206C8—42no—
207C8—3762no—
208C22—21no—
209C22—21no—
210C22#1568927811yescharacteristic
211C22#1568930511yescharacteristic
212C22#1568930911yescharacteristic
213C4—21no—
214C4—21no—
215C4—42no—
216C4—42no—
217C4—81no—
218C4—81no—
219C4—81no—
220C4—3762no—
221C4—3762no—
222C2—21no—
223C2—21no—
224C2#2024236111yescharacteristic
225C2#2024540011yescharacteristic
226C2#2024540411yescharacteristic
subgroupG/H
centerC22#15689309
commutator, cosocleC2×C4⋊C4×C47C23
FrattiniC2×C4⋊C4C22×D47
FittingC47×#2061C2
socleC22×C47B(4,𝔽2)
prime radicalC23×C47#120
hypercenter#2061D47
hypocenterC47#12261
LCSG ▷ C2×C4⋊C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2061

Complements

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

NH ≅ G/Ntype
132. C47#12261semidirect

Maximal subgroups

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

subgroupindex
#202516602
#202424302
#202414142
#202413322
C47×#20612
#1226147