Finite Group Databasebeta

← #26127444

Subgroups — #26127444

Order 12032.

388 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 99 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#20248593C211yesmaximal, characteristic
2#20241712C211yesmaximal, characteristic
3#20241417C214yesmaximal
4C47×#1801C211yesmaximal, characteristic
5C2×#13094024C411yescharacteristic
6#15689176—21no—
7#15689043C412yes—
8#15689043C2212yes—
9#15689030—21no—
10#15689021—21no—
11#15689021—21no—
12#15688992—21no—
13C4×C4⋊Dic47C411yescharacteristic
14#15688849—21no—
15#15688849C2212yes—
16C2×C4×Q8×C47C2211yescharacteristic
17C47×#423—21no—
18C2×#101×C47—21no—
19C47×#343C2212yes—
20C22×Dic94C2×C412yes—
21#13094024—41no—
22#13094024—41no—
23C2×C4⋊Dic47—21no—
24C2×C4⋊Dic47—21no—
25C2×C4⋊Dic47—21no—
26C2×Dic47⋊C4—22no—
27C2×Dic47⋊C4—22no—
28C2×C4×Dic47—21no—
29C4⋊(C47⋊C8)—41no—
30C22⋊(C47⋊C8)—22no—
31C4×C47⋊C8—41no—
32C47⋊#95—22no—
33C47⋊#95—22no—
34C47⋊#95C2×C412yes—
35C22×Q8×C47D411yescharacteristic
36C2×M16×C47—22no—
37C4×Q8×C47—41no—
38C4×Q8×C47—41no—
39C2×C4⋊C4×C47C2×C411yescharacteristic
40C2×C4⋊C4×C47D411yescharacteristic
41C2×C4⋊C4×C47C2311yescharacteristic
42C2×C42×C47C2×C411yescharacteristic
43C2×C42×C47D411yescharacteristic
44C2×C42×C47D411yescharacteristic
45C4⋊C8×C47—41no—
46C4⋊C8×C47—41no—
47#101×C47—42no—
48C2×Q8×C47—41no—
49C2×Q8×C47—41no—
50C2×Q8×C47SD1612yes—
51C2×Q8×C47Q1612yes—
52C22×C4×C47C22⋊C411yescharacteristic
53C22×C4×C47C22⋊C411yescharacteristic
54C22×C4×C47C22⋊C411yescharacteristic
55C22×C4×C47C22⋊C411yescharacteristic
56C22×C4×C47C22×C411yescharacteristic
57C22×C4×C47C2×D411yescharacteristic
58C22×C4×C47C2×D411yescharacteristic
59C22×Dic47—22no—
60C22×Dic47—22no—
61C2×Dic94—42no—
62C2×Dic94—82no—
63M16×C47—42no—
64M16×C47—42no—
65C2×C8×C47—42no—
66C4⋊C4×C47—41no—
67C4⋊C4×C47—41no—
68C4⋊C4×C47—41no—
69C42×C47—21no—
70C42×C47—21no—
71C42×C47—21no—
72C42×C47—21no—
73C42×C47—21no—
74C42×C47—21no—
75C4⋊Dic47—24no—
76C4⋊Dic47—42no—
77C4⋊Dic47—41no—
78C4⋊Dic47—41no—
79Dic47⋊C4—82no—
80Dic47⋊C4—82no—
81C4×Dic47—42no—
82C2×C47⋊C8—42no—
83C23×C47C2×C22⋊C411yescharacteristic
84Q8×C47—42no—
85Q8×C47—42no—
86C2×C4×C47—21no—
87C2×C4×C47—21no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47—21no—
91C2×C4×C47—21no—
92C2×C4×C47—22no—
93C2×C4×C47—21no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—41no—
97C2×C4×C47—41no—
98C2×C4×C47—41no—
99C2×C4×C47#9911yescharacteristic
100C2×C4×C47#9911yescharacteristic
101C2×C4×C47#10312yes—
102C2×C4×C47#10312yes—
103C2×C4×C47C2×SD1611yescharacteristic
104C2×C4×C47C2×Q1611yescharacteristic
105C2×Dic47—24no—
106C2×Dic47—42no—
107C2×Dic47—42no—
108C2×Dic47—42no—
109C2×Dic47—42no—
110C2×Dic47—42no—
111Dic94—84no—
112C8×C47—82no—
113C47⋊C8—82no—
114#11908—471nomaximal, Sylow
115C22×C47—21no—
116C22×C47—21no—
117C22×C47C2×#9911yescharacteristic
118C22×C47C2×#10311yescharacteristic
119C22×C47#42111yescharacteristic
120C4×C47—21no—
121C4×C47—21no—
122C4×C47—22no—
123C4×C47—22no—
124C4×C47—21no—
125C4×C47—41no—
126C4×C47—41no—
127C4×C47—41no—
128C4×C47#35612yes—
129Dic47—44no—
130Dic47—82no—
131#2567—471no—
132#1801D4711yescharacteristic
133#1461—471no—
134#1354—474no—
135C2×C47—21no—
136C2×C47—21no—
137C2×C47#152011yescharacteristic
138C2×C47#212211yescharacteristic
139C2×C47C2×#35611yescharacteristic
140C2×C4⋊Q8—471no—
141C2×C4×Q8C2×D4711yescharacteristic
142#431—941no—
143#423—21no—
144C2×#101—21no—
145#395—472no—
146#395—472no—
147#391—941no—
148#389—941no—
149#389—941no—
150#384—941no—
151C4×C4⋊C4—471no—
152#343C2×D4712yes—
153#324—472no—
154#324—941no—
155C47#1190811yescharacteristic, complemented, Sylow
156C22×Q8—472no—
157C22×Q8C22⋊D4711yescharacteristic
158C2×M16—22no—
159C4⋊Q8—1881no—
160C4⋊Q8—1881no—
161C4×Q8—41no—
162C4×Q8—41no—
163C2×C4⋊C4—941no—
164C2×C4⋊C4—942no—
165C2×C4⋊C4—942no—
166C2×C4⋊C4—941no—
167C2×C4⋊C4—941no—
168C2×C4⋊C4C4×D4711yescharacteristic
169C2×C4⋊C4D18811yescharacteristic
170C2×C4⋊C4C22×D4711yescharacteristic
171C2×C42—941no—
172C2×C42C4×D4711yescharacteristic
173C2×C42D18811yescharacteristic
174C2×C42C22⋊D4711yescharacteristic
175C4⋊C8—41no—
176C4⋊C8—41no—
177C4⋊C8—1881no—
178#101—42no—
179C22⋊C8—942no—
180C4×C8—1881no—
181#95—472no—
182#95—942no—
183#95—942no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—3762no—
187C2×Q8—1882no—
188C2×Q8#1062533512yes—
189C2×Q8#1062533712yes—
190C22×C4—942no—
191C22×C4—942no—
192C22×C4(C2×D47)⋊C411yescharacteristic
193C22×C4(C2×D47)⋊C411yescharacteristic
194C22×C4(C2×D47)⋊C411yescharacteristic
195C22×C4(C2×D47)⋊C411yescharacteristic
196C22×C4C2×C4×D4711yescharacteristic
197C22×C4C2×D18811yescharacteristic
198C22×C4C2×C22⋊D4711yescharacteristic
199M16—42no—
200M16—42no—
201C2×C8—42no—
202C2×C8—1882no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—944no—
207C4⋊C4—3762no—
208C4⋊C4—3762no—
209C4⋊C4—1882no—
210C4⋊C4—1881no—
211C4⋊C4—1881no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—1882no—
219C23C2×(C2×D47)⋊C411yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—3764no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—944no—
237C2×C4—1882no—
238C2×C4—1882no—
239C2×C4—1882no—
240C2×C4—1882no—
241C2×C4—1882no—
242C2×C4#1309393811yescharacteristic
243C2×C4#1309393811yescharacteristic
244C2×C4#1309394712yes—
245C2×C4#1309394712yes—
246C2×C4C2×#1062533511yescharacteristic
247C2×C4C2×#1062533711yescharacteristic
248C8—82no—
249C8—3762no—
250C22—21no—
251C22—21no—
252C22C2×#1309393811yescharacteristic
253C22C2×#1309394711yescharacteristic
254C22#1568914111yescharacteristic
255C4—21no—
256C4—22no—
257C4—22no—
258C4—21no—
259C4—21no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—3762no—
264C4—1884no—
265C4#1568892112yes—
266C2—21no—
267C2—21no—
268C2#2024195911yescharacteristic
269C2#2024503911yescharacteristic
270C2C2×#1568892111yescharacteristic
subgroupG/H
centerC22C2×#13093938
commutatorC22×C4×C47C22×C4
FrattiniC2×C4⋊C4C22×D47
FittingC47×#1801C2
socleC22×C47C2×#99
prime radicalC23×C47C2×C22⋊C4
cosocleC2×C4⋊C4×C47C23
hypercenter#1801D47
hypocenterC47#11908
LCSG ▷ C22×C4×C47 ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1801

Complements

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

NH ≅ G/Ntype
155. C47#11908semidirect

Maximal subgroups

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

subgroupindex
#202485932
#202417122
#202414172
C47×#18012
#1190847