Finite Group Databasebeta

← #26110320

Subgroups — #26110320

Order 12032.

348 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 107 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#20244329C211yesmaximal, characteristic
2#20242174C212yesmaximal
3#20241712C211yesmaximal, characteristic
4#20241286C212yesmaximal
5C47×#2983C211yesmaximal, characteristic
6#15689176C2212yes—
7C2×C4⋊(C47⋊C8)C2211yescharacteristic
8C2×#13093935C2211yescharacteristic
9#15688878—21no—
10#15688878—21no—
11#15688875—22no—
12#15688873—22no—
13#15688849C412yes—
14#15688849C412yes—
15C2×C4×Q8×C47C2211yescharacteristic
16C47×#446—22no—
17C47×#446—22no—
18C47×#432—21no—
19C47×#432C2212yes—
20C47×#431—21no—
21C22×C47⋊C8—21no—
22C22×C47⋊C8—21no—
23C4⋊(C47⋊C8)—22no—
24C4⋊(C47⋊C8)—22no—
25C22⋊(C47⋊C8)C2×C414yes—
26#13093935—22no—
27C4×C47⋊C8—22no—
28C22×Q8×C47Q811yescharacteristic
29C4×Q8×C47—22no—
30C4×Q8×C47—22no—
31C2×C4⋊C4×C47C2×C411yescharacteristic
32C2×C4⋊C4×C47C2×C411yescharacteristic
33C2×C4⋊C4×C47Q811yescharacteristic
34C2×C42×C47D411yescharacteristic
35C2×C42×C47D411yescharacteristic
36C2×C42×C47C2311yescharacteristic
37C4⋊C8×C47—21no—
38C4⋊C8×C47—21no—
39C4⋊C8×C47—21no—
40C4⋊C8×C47—21no—
41C4⋊C8×C47D412yes—
42C4⋊C8×C47D412yes—
43C22⋊C8×C47—22no—
44#97×C47—22no—
45#97×C47—22no—
46C4×C8×C47—22no—
47C2×Q8×C47—22no—
48C2×Q8×C47—22no—
49C2×Q8×C47—41no—
50C22×C4×C47C4⋊C411yescharacteristic
51C22×C4×C47C4⋊C411yescharacteristic
52C22×C4×C47C4⋊C411yescharacteristic
53C22×C4×C47C4⋊C411yescharacteristic
54C22×C4×C47C22×C411yescharacteristic
55C22×C4×C47C2×D411yescharacteristic
56C22×C4×C47C2×Q811yescharacteristic
57C2×C8×C47—22no—
58C2×C8×C47—22no—
59C4⋊C4×C47—22no—
60C4⋊C4×C47—22no—
61C4⋊C4×C47—22no—
62C42×C47—21no—
63C42×C47—21no—
64C42×C47—21no—
65C42×C47—21no—
66C42×C47C2×D412yes—
67C42×C47#4112yes—
68C2×C47⋊C8—22no—
69C2×C47⋊C8—24no—
70C2×C47⋊C8—41no—
71C2×C47⋊C8—41no—
72C2×C47⋊C8—42no—
73C2×C47⋊C8—41no—
74C23×C47C2×C4⋊C411yescharacteristic
75Q8×C47—44no—
76C2×C4×C47—21no—
77C2×C4×C47—21no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—21no—
85C2×C4×C47—21no—
86C2×C4×C47—21no—
87C2×C4×C47—41no—
88C2×C4×C47—41no—
89C2×C4×C47—41no—
90C2×C4×C47#10812yes—
91C2×C4×C47C4×D412yes—
92C2×C4×C47#12011yescharacteristic
93C2×C4×C47C22⋊Q812yes—
94C2×C4×C47#12311yescharacteristic
95C8×C47—42no—
96C8×C47—42no—
97C47⋊C8—44no—
98C47⋊C8—42no—
99C47⋊C8—81no—
100#8865—471nomaximal, Sylow
101C22×C47—21no—
102C22×C47—21no—
103C22×C47#38511yescharacteristic
104C22×C47C2×#10811yescharacteristic
105C22×C47#43011yescharacteristic
106C4×C47—22no—
107C4×C47—22no—
108C4×C47—21no—
109C4×C47—22no—
110C4×C47—41no—
111C4×C47—41no—
112C4×C47—41no—
113C4×C47#45411yescharacteristic
114C4×C47#45611yescharacteristic
115#2983D4711yescharacteristic
116#1985—471no—
117#1573—472no—
118#1461—471no—
119#1302—472no—
120C2×C47—21no—
121C2×C47—21no—
122C2×C47#185511yescharacteristic
123C2×C47#185711yescharacteristic
124C2×C47#186811yescharacteristic
125C2×C4×Q8C2×D4711yescharacteristic
126#446—22no—
127#446—22no—
128#432—21no—
129#432C2×D4712yes—
130#431—21no—
131#431—472no—
132C2×C4⋊C8—471no—
133C2×#97—471no—
134#336—941no—
135#336—941no—
136#335—942no—
137#334—942no—
138#324—472no—
139#324—472no—
140C47#886511yescharacteristic, complemented, Sylow
141C22×Q8Dic9411yescharacteristic
142C22×C8—941no—
143C22×C8—941no—
144C4×Q8—22no—
145C4×Q8—22no—
146C2×C4⋊C4Dic9411yescharacteristic
147C2×C4⋊C4C4×D4711yescharacteristic
148C2×C4⋊C4C4×D4711yescharacteristic
149C2×C42C22⋊D4711yescharacteristic
150C2×C42C22⋊D4711yescharacteristic
151C2×C42C22×D4711yescharacteristic
152C4⋊C8—21no—
153C4⋊C8—21no—
154C4⋊C8—21no—
155C4⋊C8—21no—
156C4⋊C8—942no—
157C4⋊C8—942no—
158C4⋊C8C22⋊D4712yes—
159C4⋊C8C22⋊D4712yes—
160C22⋊C8—22no—
161C22⋊C8—474no—
162#97—22no—
163#97—22no—
164#97—942no—
165C4×C8—22no—
166C4×C8—942no—
167C2×Q8—22no—
168C2×Q8—22no—
169C2×Q8—41no—
170C22×C4Dic47⋊C411yescharacteristic
171C22×C4Dic47⋊C411yescharacteristic
172C22×C4Dic47⋊C411yescharacteristic
173C22×C4Dic47⋊C411yescharacteristic
174C22×C4C2×Dic9411yescharacteristic
175C22×C4C2×C4×D4711yescharacteristic
176C22×C4C2×C22⋊D4711yescharacteristic
177C2×C8—22no—
178C2×C8—22no—
179C2×C8—942no—
180C2×C8—944no—
181C2×C8—1882no—
182C2×C8—1881no—
183C2×C8—1881no—
184C2×C8—1881no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—22no—
188C42—21no—
189C42—21no—
190C42—21no—
191C42—21no—
192C42#1062535012yes—
193C42C2×C22⋊D4712yes—
194C23C2×Dic47⋊C411yescharacteristic
195Q8—44no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4#1309395912yes—
211C2×C4C4×C22⋊D4712yes—
212C2×C4#1309399311yescharacteristic
213C2×C4#1309400312yes—
214C2×C4#1309400711yescharacteristic
215C8—42no—
216C8—42no—
217C8—3761no—
218C8—1884no—
219C8—1882no—
220C22—21no—
221C22—21no—
222C22#1568899611yescharacteristic
223C22C2×#1309395911yescharacteristic
224C22#1568917111yescharacteristic
225C4—22no—
226C4—22no—
227C4—21no—
228C4—22no—
229C4—41no—
230C4—41no—
231C4—41no—
232C4#1568929611yescharacteristic
233C4#1568930611yescharacteristic
234C2—21no—
235C2—21no—
236C2#2024359311yescharacteristic
237C2#2024360311yescharacteristic
238C2#2024367411yescharacteristic
subgroupG/H
centerC2×C4#13093993
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#2983C2
socleC22×C47#385
prime radicalC23×C47C2×C4⋊C4
cosocleC2×C42×C47C23
hypercenter#2983D47
hypocenterC47#8865
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
140. C47#8865semidirect

Maximal subgroups

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

subgroupindex
#202443292
#202421742
#202417122
#202412862
C47×#29832
#886547