Finite Group Databasebeta

← #26111310

Subgroups — #26111310

Order 12032.

572 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 572 conjugacy classes of subgroups — too many to draw. Only its 127 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
1C2×#15689062C211yesmaximal, characteristic
2#20245991C211yesmaximal, characteristic
3#20243479C212yesmaximal
4#20241268C212yesmaximal
5C2×C47×#324C211yesmaximal, characteristic
6C22×C4⋊Dic47C2211yescharacteristic
7#15689062—22no—
8#15689062C414yescomplemented
9#15689009—24no—
10#15688986—21no—
11#15688983C2212yes—
12C4×C22⋊Dic47—21no—
13C2×C47⋊#95—21no—
14C2×C47⋊#95—21no—
15C2×C47⋊#95C2211yescharacteristic
16#15688886—24no—
17C22×C4⋊C4×C47C2211yescharacteristic
18C2×C22⋊C8×C47C2212yes—
19C47×#324—22no—
20C23×Dic47—21no—
21C23×Dic47—21no—
22C2×C4⋊Dic47—22no—
23C2×C4⋊Dic47—22no—
24C2×C4⋊Dic47—21no—
25C2×C4⋊Dic47C2×C412yes—
26C2×C4⋊Dic47D414yes—
27C2×C22⋊Dic47—22no—
28C2×C4×Dic47—22no—
29C47⋊#95—22no—
30C47⋊#95—24no—
31C47⋊#95—24no—
32C47⋊#95—24no—
33C47⋊#95—21no—
34C47⋊#95—22no—
35C47⋊#95C2×C412yes—
36C23×C4×C47D411yescharacteristic
37C23×C4×C47D411yescharacteristic
38C23×C4×C47C2311yescharacteristic
39C22×C8×C47—22no—
40C2×C4⋊C4×C47—22no—
41C2×C4⋊C4×C47—22no—
42C2×C4⋊C4×C47C2×C412yes—
43C2×C4⋊C4×C47D412yes—
44C22⋊C8×C47—22no—
45C22⋊C8×C47—22no—
46C24×C47C2×D411yescharacteristic
47C22×C4×C47—21no—
48C22×C4×C47—21no—
49C22×C4×C47—21no—
50C22×C4×C47—22no—
51C22×C4×C47—22no—
52C22×C4×C47—21no—
53C22×C4×C47—42no—
54C22×C4×C47—42no—
55C22×C4×C47C22⋊C412yes—
56C22×C4×C47C22⋊C412yes—
57C22×C4×C47C22×C411yescharacteristic
58C22×C4×C47C2×D412yes—
59C22×C4×C47C2×D411yescharacteristic
60C22×C4×C47#4112yes—
61C22×Dic47—22no—
62C22×Dic47—22no—
63C22×Dic47—24no—
64C22×Dic47—42no—
65C22×Dic47—42no—
66C22×Dic47—44no—
67C22×Dic47—41no—
68C22×Dic47—41no—
69C22×Dic47—42no—
70C2×C8×C47—44no—
71C2×C8×C47—42no—
72C4⋊C4×C47—24no—
73C4⋊C4×C47—24no—
74C22⋊Dic47—42no—
75C22⋊Dic47—42no—
76C4⋊Dic47—24no—
77C4⋊Dic47—42no—
78C4⋊Dic47—44no—
79C4×Dic47—82no—
80C23×C47—22no—
81C23×C47—22no—
82C23×C47C2×C22⋊C411yescharacteristic
83C23×C47#12011yescharacteristic
84C23×C47#12311yescharacteristic
85C23×C47#13512yes—
86C23×C47#13712yes—
87C2×C4×C47—24no—
88C2×C4×C47—22no—
89C2×C4×C47—22no—
90C2×C4×C47—22no—
91C2×C4×C47—22no—
92C2×C4×C47—41no—
93C2×C4×C47—41no—
94C2×C4×C47—42no—
95C2×C4×C47—42no—
96C2×C4×C47—42no—
97C2×C4×C47—42no—
98C2×C4×C47—42no—
99C2×C4×C47—81no—
100C2×C4×C47C4×D412yes—
101C2×C4×C47#12112yes—
102C2×Dic47—42no—
103C2×Dic47—42no—
104C2×Dic47—44no—
105C2×Dic47—42no—
106C2×Dic47—42no—
107C2×Dic47—44no—
108C2×Dic47—44no—
109C2×Dic47—44no—
110C2×Dic47—84no—
111C2×Dic47—82no—
112C2×Dic47—82no—
113C8×C47—82no—
114#9022—471nomaximal, Sylow
115C22×C47—24no—
116C22×C47—24no—
117C22×C47—21no—
118C22×C47—21no—
119C22×C47—21no—
120C22×C47—21no—
121C22×C47#38611yescharacteristic
122C22×C47#41611yescharacteristic
123C22×C47#41911yescharacteristic
124C22×C47#45212yes—
125C22×C47#45412yes—
126C22×C47#45812yes—
127C22×C47#48512yes—
128C4×C47—22no—
129C4×C47—22no—
130C4×C47—42no—
131C4×C47—42no—
132Dic47—82no—
133Dic47—84no—
134Dic47—82no—
135C2×#400—471no—
136#2313—471no—
137#1824—472no—
138C2×#324D4711yescharacteristic
139#1294—472no—
140C2×C47—21no—
141C2×C47—21no—
142C2×C47—22no—
143C2×C47#161514yes—
144C2×C47#187311yescharacteristic
145C2×C47#188811yescharacteristic
146C2×C47#189011yescharacteristic
147C22×C4⋊C4—471no—
148C22×C4⋊C4C2×D4711yescharacteristic
149C2×C22⋊C8C2×D4712yes—
150#400—474no—
151#400—942no—
152#387—944no—
153#381—941no—
154#380—472no—
155C4×C22⋊C4—941no—
156C2×#95—471no—
157C2×#95—941no—
158C2×#95—941no—
159#340—944no—
160#324—22no—
161C47#902211yescharacteristic, complemented, Sylow
162C23×C4—941no—
163C23×C4—941no—
164C23×C4D18811yescharacteristic
165C23×C4D18811yescharacteristic
166C23×C4C22×D4711yescharacteristic
167C22×C8—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—472no—
171C2×C4⋊C4—474no—
172C2×C4⋊C4—942no—
173C2×C4⋊C4—942no—
174C2×C4⋊C4—941no—
175C2×C4⋊C4C4×D4712yes—
176C2×C4⋊C4C22⋊D4712yes—
177C2×C22⋊C4—942no—
178C2×C42—942no—
179C22⋊C8—22no—
180C22⋊C8—22no—
181#95—472no—
182#95—942no—
183#95—944no—
184#95—944no—
185#95—944no—
186#95—942no—
187#95—941no—
188C24C2×D18811yescharacteristic
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—21no—
195C22×C4—42no—
196C22×C4—42no—
197C22×C4—942no—
198C22×C4—942no—
199C22×C4—944no—
200C22×C4—1882no—
201C22×C4—1882no—
202C22×C4—1884no—
203C22×C4—1881no—
204C22×C4—1881no—
205C22×C4—1882no—
206C22×C4(C2×D47)⋊C412yes—
207C22×C4(C2×D47)⋊C412yes—
208C22×C4C2×C4×D4711yescharacteristic
209C22×C4D4×D4712yes—
210C22×C4#1062535212yes—
211C22×C4C2×C22⋊D4711yescharacteristic
212C2×C8—44no—
213C2×C8—42no—
214C4⋊C4—24no—
215C4⋊C4—24no—
216C4⋊C4—944no—
217C4⋊C4—1884no—
218C4⋊C4—1882no—
219C22⋊C4—1882no—
220C22⋊C4—1882no—
221C42—3762no—
222C23—22no—
223C23—22no—
224C23C2×(C2×D47)⋊C411yescharacteristic
225C23#1309399411yescharacteristic
226C23#1309400811yescharacteristic
227C23#1309404612yes—
228C23#1309405712yes—
229C2×C4—24no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—81no—
242C2×C4—3764no—
243C2×C4—3762no—
244C2×C4—3762no—
245C2×C4—1882no—
246C2×C4—1882no—
247C2×C4—1884no—
248C2×C4—1882no—
249C2×C4—1884no—
250C2×C4—1884no—
251C2×C4—1884no—
252C2×C4—1882no—
253C2×C4(C22⋊D47)⋊C412yes—
254C2×C4#1309399612yes—
255C8—82no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—24no—
261C22—24no—
262C22#1568900011yescharacteristic
263C22#1568912011yescharacteristic
264C22#1568913311yescharacteristic
265C22#1568928712yes—
266C22#1568929812yes—
267C22#1568931412yes—
268C22#1568946512yes—
269C4—22no—
270C4—22no—
271C4—42no—
272C4—42no—
273C4—3762no—
274C4—3762no—
275C4—3764no—
276C2—21no—
277C2—21no—
278C2—22no—
279C2#2024242114yes—
280C2#2024369811yescharacteristic
281C2#2024378911yescharacteristic
282C2#2024379911yescharacteristic
subgroupG/H
centerC23#13093994
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC2×C47×#324C2
socleC23×C47#120
prime radicalC24×C47C2×D4
cosocleC23×C4×C47C23
hypercenterC2×#324D47
hypocenterC47#9022
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
8. #15689062C4semidirect
161. C47#9022semidirect

Maximal subgroups

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

subgroupindex
C2×#156890622
#202459912
#202434792
#202412682
C2×C47×#3242
#902247