Finite Group Databasebeta

← #26125573

Subgroups — #26125573

Order 12032.

392 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 87 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#20246106C211yesmaximal, characteristic
2#20241710C212yesmaximal
3#20241331C212yesmaximal
4#20241322C211yesmaximal, characteristic
5C47×#1319C211yesmaximal, characteristic
6C2×#13094022C411yescharacteristic
7C2×Q8×Dic47C411yescharacteristic
8C2×#13093989C2211yescharacteristic
9#15689173—22no—
10#15689029C411yescharacteristic
11#15689010—22no—
12#15689005—22no—
13#15688988C2211yescharacteristic
14#15688969C411yescharacteristic
15#15688849C2212yes—
16#15688848—22no—
17C47×#391C2211yescharacteristic
18C47×#324C2212yes—
19C22×Dic94C2×C411yescharacteristic
20#13094022—22no—
21#13094022C814yescomplemented
22Q8×Dic47—42no—
23#13093989—42no—
24C2×C4⋊Dic47—21no—
25C2×C4⋊Dic47C2×C411yescharacteristic
26C2×Dic47⋊C4—22no—
27C2×Dic47⋊C4D412yes—
28C2×C4×Dic47—21no—
29C2×C4×Dic47C2×C411yescharacteristic
30C2×C4×Dic47C2×C411yescharacteristic
31C2×C4×Dic47D412yes—
32Dic47⋊C8—42no—
33C22⋊(C47⋊C8)—22no—
34C8×Dic47—42no—
35C47⋊#95—22no—
36C47⋊#95—21no—
37C47⋊#95—21no—
38C47⋊#95—22no—
39C22×Q8×C47C2×C411yescharacteristic
40C2×C4⋊C4×C47C2311yescharacteristic
41C2×C42×C47C2×C411yescharacteristic
42C22⋊C8×C47—22no—
43#95×C47—22no—
44C2×Q8×C47—21no—
45C2×Q8×C47—41no—
46C2×Q8×C47—41no—
47C2×Q8×C47C2×C812yes—
48C22×C4×C47—21no—
49C22×C4×C47—21no—
50C22×C4×C47C22×C411yescharacteristic
51C22×C4×C47C2×D412yes—
52C22×Dic47—21no—
53C22×Dic47—21no—
54C22×Dic47C22⋊C412yes—
55C22×Dic47C22⋊C411yescharacteristic
56C22×Dic47C22⋊C411yescharacteristic
57C2×Dic94—41no—
58C2×Dic94—41no—
59C2×Dic94C2×C812yes—
60C2×Dic94M1612yes—
61C2×C8×C47—42no—
62C4⋊C4×C47—41no—
63C42×C47—41no—
64C4⋊Dic47—42no—
65C4⋊Dic47—41no—
66Dic47⋊C4—28no—
67Dic47⋊C4—42no—
68C4×Dic47—21no—
69C4×Dic47—22no—
70C4×Dic47—22no—
71C4×Dic47—22no—
72C4×Dic47—42no—
73C4×Dic47C2×C812yes—
74C2×C47⋊C8—42no—
75C23×C47C2×C22⋊C411yescharacteristic
76Q8×C47—42no—
77Q8×C47—42no—
78C2×C4×C47—21no—
79C2×C4×C47—21no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—41no—
83C2×C4×C47—41no—
84C2×C4×C47—42no—
85C2×C4×C47—41no—
86C2×C4×C47—41no—
87C2×C4×C47—41no—
88C2×C4×C47C22×C811yescharacteristic
89C2×C4×C47C2×M1611yescharacteristic
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—21no—
94C2×Dic47—41no—
95C2×Dic47—41no—
96C2×Dic47—41no—
97C2×Dic47—41no—
98C2×Dic47—42no—
99C2×Dic47—41no—
100C2×Dic47C22⋊C814yes—
101C2×Dic47#9912yes—
102Dic94—42no—
103Dic94—42no—
104C8×C47—82no—
105C47⋊C8—82no—
106#11482—471nomaximal, Sylow
107C22×C47—21no—
108C22×C47—21no—
109C22×C47C2×C22⋊C811yescharacteristic
110C22×C47C2×#9911yescharacteristic
111C22×C47#41311yescharacteristic
112C4×C47—21no—
113C4×C47—21no—
114C4×C47—42no—
115C4×C47—42no—
116C4×C47—81no—
117Dic47—22no—
118Dic47—24no—
119Dic47—42no—
120Dic47—41no—
121Dic47—81no—
122#2327—471no—
123#1461—472no—
124#1324—472no—
125#1319—471no—
126#1319D4711yescharacteristic
127C2×C47—21no—
128C2×C47—21no—
129C2×C47#145911yescharacteristic
130C2×C47#212911yescharacteristic
131C2×C47#213311yescharacteristic
132C2×C4⋊Q8—471no—
133C2×C4×Q8—471no—
134C2×C4×Q8—471no—
135#431—942no—
136#391—471no—
137#391C2×D4711yescharacteristic
138#387—942no—
139#387—942no—
140#382—471no—
141#376—471no—
142#324—472no—
143#324—942no—
144#324C2×D4712yes—
145C47#1148211yescharacteristic, complemented, Sylow
146C22×Q8—471no—
147C22×Q8C4×D4711yescharacteristic
148C4⋊Q8—474no—
149C4⋊Q8—942no—
150C4×Q8—1882no—
151C4×Q8—1882no—
152C2×C4⋊C4—472no—
153C2×C4⋊C4—471no—
154C2×C4⋊C4—942no—
155C2×C4⋊C4—941no—
156C2×C4⋊C4C22×D4711yescharacteristic
157C2×C42—471no—
158C2×C42—471no—
159C2×C42—472no—
160C2×C42—941no—
161C2×C42C4×D4711yescharacteristic
162C4⋊C8—1882no—
163C22⋊C8—22no—
164C22⋊C8—942no—
165C4×C8—1882no—
166#95—22no—
167#95—941no—
168#95—941no—
169#95—942no—
170#95—942no—
171C2×Q8—21no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—472no—
175C2×Q8—472no—
176C2×Q8—1881no—
177C2×Q8—1881no—
178C2×Q8C8×D4712yes—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—472no—
182C22×C4—471no—
183C22×C4—471no—
184C22×C4—941no—
185C22×C4—941no—
186C22×C4C2×C4×D4711yescharacteristic
187C22×C4D4×D4712yes—
188C2×C8—42no—
189C2×C8—1882no—
190C4⋊C4—41no—
191C4⋊C4—948no—
192C4⋊C4—1882no—
193C4⋊C4—1881no—
194C4⋊C4—1882no—
195C42—41no—
196C42—472no—
197C42—942no—
198C42—942no—
199C42—942no—
200C42—941no—
201C42—1882no—
202C23C22⋊C4×D4711yescharacteristic
203Q8—42no—
204Q8—42no—
205Q8—1882no—
206Q8—1882no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—474no—
218C2×C4—472no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—941no—
223C2×C4—1881no—
224C2×C4—1882no—
225C2×C4—1881no—
226C2×C4—1881no—
227C2×C4—1881no—
228C2×C4—1881no—
229C2×C4C2×C8×D4711yescharacteristic
230C2×C4M16×D4711yescharacteristic
231C8—82no—
232C8—3762no—
233C22—21no—
234C22—21no—
235C22C22⋊C8×D4711yescharacteristic
236C22#99×D4711yescharacteristic
237C22#1568910411yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—42no—
242C4—81no—
243C4—944no—
244C4—942no—
245C4—3761no—
246C4—1882no—
247C4—1881no—
248C2—21no—
249C2—21no—
250C2#2024170311yescharacteristic
251C2#2024506111yescharacteristic
252C2#2024507611yescharacteristic
subgroupG/H
centerC22#99×D47
commutatorC2×C4×C47C22×C8
FrattiniC2×C4⋊C4C22×D47
FittingC47×#1319C2
socleC22×C47C2×#99
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C4⋊C4×C47C23
hypercenter#1319D47
hypocenterC47#11482
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
21. #13094022C8semidirect
145. C47#11482semidirect

Maximal subgroups

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

subgroupindex
#202461062
#202417102
#202413312
#202413222
C47×#13192
#1148247