Finite Group Databasebeta

← #26129337

Subgroups — #26129337

Order 12032.

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

normal subgroups only

This group has 342 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#20248630C211yesmaximal, characteristic
2#20242430C212yesmaximal
3#20241414C212yesmaximal
4#20241334C211yesmaximal, characteristic
5C47×#2060C211yesmaximal, characteristic
6#15689456—22no—
7#15689062—21no—
8#15689062C2212yes—
9#15689022—22no—
10#15688988—22no—
11C4×C4⋊Dic47—21no—
12#15688860—22no—
13#15688849C2212yes—
14C47×#544C2211yescharacteristic
15C47×#428—21no—
16C47×#384C2211yescharacteristic
17C47×#343C2211yescharacteristic
18C47×#339—21no—
19C2×C4⋊Dic47—21no—
20C2×C4⋊Dic47—21no—
21C2×C4⋊Dic47—21no—
22C2×C4⋊Dic47D412yes—
23C2×C4×Dic47—22no—
24#13093957—42no—
25#13093948—42no—
26C22⋊(C47⋊C8)—22no—
27C47⋊#95—21no—
28C47⋊#95—22no—
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×C47—22no—
38C2×C4⋊C4×C47D411yescharacteristic
39C2×C4⋊C4×C47C2311yescharacteristic
40C2×C42×C47D411yescharacteristic
41#107×C47—41no—
42#106×C47—41no—
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—
50M16×C47—22no—
51M16×C47—41no—
52C2×C8×C47—41no—
53C4⋊C4×C47—21no—
54C4⋊C4×C47—21no—
55C4⋊C4×C47—22no—
56C4⋊C4×C47—41no—
57C4⋊C4×C47—44no—
58C4⋊C4×C47—42no—
59C4⋊C4×C47—41no—
60C22⋊C4×C47—41no—
61C42×C47—21no—
62C42×C47—41no—
63C42×C47Q1612yes—
64C4⋊Dic47—42no—
65C4⋊Dic47—42no—
66C4⋊Dic47—42no—
67C4⋊Dic47—81no—
68C4×Dic47—44no—
69C2×C47⋊C8—42no—
70C23×C47#12011yescharacteristic
71Q8×C47—82no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—22no—
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—
91C8×C47—42no—
92C47⋊C8—82no—
93#12257—471nomaximal, Sylow
94C22×C47—21no—
95C22×C47—21no—
96C22×C47#45111yescharacteristic
97C22×C47#45611yescharacteristic
98C22×C47B(4,𝔽2)11yescharacteristic
99C4×C47—24no—
100C4×C47—21no—
101C4×C47—21no—
102C4×C47—42no—
103C4×C47—81no—
104C4×C47—81no—
105C4×C47—81no—
106Dic47—82no—
107Dic47—82no—
108#2571—471no—
109#2060D4711yescharacteristic
110#1617—472no—
111#1353—472no—
112#1325—471no—
113C2×C47—21no—
114C2×C47—21no—
115C2×C47#160511yescharacteristic
116C2×C47#219811yescharacteristic
117C2×C47#220411yescharacteristic
118#544C2×D4711yescharacteristic
119#484—942no—
120#428—21no—
121#400—472no—
122#400—941no—
123#389—942no—
124#384C2×D4711yescharacteristic
125#382—942no—
126C4×C4⋊C4—941no—
127#343C2×D4711yescharacteristic
128#339—21no—
129#328—942no—
130#324—472no—
131C47#1225711yescharacteristic, complemented, Sylow
132C2×M16—21no—
133C4⋊Q8—41no—
134#125—41no—
135C22⋊Q8—22no—
136#117—21no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—472no—
139C2×C4⋊C4—941no—
140C2×C4⋊C4—941no—
141C2×C4⋊C4—941no—
142C2×C4⋊C4C22⋊D4711yescharacteristic
143C2×C4⋊C4C22×D4711yescharacteristic
144C2×C42—942no—
145C2×C42C22⋊D4711yescharacteristic
146#107—41no—
147#107—1882no—
148#106—41no—
149#103—1882no—
150C22⋊C8—942no—
151#95—472no—
152#95—941no—
153#95—942no—
154#95—942no—
155#95—942no—
156C2×Q8—22no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—942no—
160C22×C4—942no—
161C22×C4D4×D4712yes—
162C22×C4C2×C22⋊D4711yescharacteristic
163M16—22no—
164M16—41no—
165C2×C8—41no—
166C2×C8—1882no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—22no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—44no—
173C4⋊C4—42no—
174C4⋊C4—3761no—
175C4⋊C4—1882no—
176C4⋊C4—1882no—
177C4⋊C4—1882no—
178C22⋊C4—41no—
179C42—21no—
180C42—41no—
181C42—1884no—
182C42#1062533712yes—
183C23#1309399211yescharacteristic
184Q8—82no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—1882no—
197C2×C4—1882no—
198C2×C4—1882no—
199C2×C4—1882no—
200C2×C4—1882no—
201C2×C4—1882no—
202C2×C4C2×#1062533711yescharacteristic
203C2×C4#1309405411yescharacteristic
204C8—42no—
205C8—3762no—
206C22—21no—
207C22—21no—
208C22#1568927811yescharacteristic
209C22#1568930511yescharacteristic
210C22#1568930911yescharacteristic
211C4—24no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—81no—
216C4—81no—
217C4—81no—
218C4—3762no—
219C4—3762no—
220C2—21no—
221C2—21no—
222C2#2024236111yescharacteristic
223C2#2024538311yescharacteristic
224C2#2024541311yescharacteristic
subgroupG/H
centerC22#15689309
commutator, cosocleC2×C4⋊C4×C47C23
FrattiniC2×C4⋊C4C22×D47
FittingC47×#2060C2
socleC22×C47B(4,𝔽2)
prime radicalC23×C47#120
hypercenter#2060D47
hypocenterC47#12257
LCSG ▷ C2×C4⋊C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2060

Complements

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

NH ≅ G/Ntype
131. C47#12257semidirect

Maximal subgroups

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

subgroupindex
#202486302
#202424302
#202414142
#202413342
C47×#20602
#1225747