Finite Group Databasebeta

← #26109679

Subgroups — #26109679

Order 12032.

554 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 111 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#382×D47C211yesmaximal, characteristic
2#20243151C212yesmaximal
3#20241270C212yesmaximal, complemented
4#20241269C211yesmaximal, characteristic, complemented
5C47×#1295C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D47C412yes—
7C2×C42×D47C2211yescharacteristic
8C2×(C2×D47)⋊C8—22no—
9C2×#13093935C2212yes—
10#15688989C2211yescharacteristic
11#15688988C412yes—
12#15688987—22no—
13#95×D47—22no—
14#15688877—22no—
15C2×#97×C47C2212yes—
16C47×#382C2211yescharacteristic
17C22×C4×D47—22no—
18C22×C4×D47C2×C411yescharacteristic
19C22×C4×D47D412yes—
20C22×C47⋊C8—22no—
21C2×C4⋊Dic47C2×C412yes—
22C2×Dic47⋊C4—22no—
23C4⋊C4×D47—44no—
24C2×C4×Dic47C2×C411yescharacteristic
25C2×C4×Dic47D412yes—
26C42×D47—22no—
27C42×D47—21no—
28C42×D47—21no—
29(C2×D47)⋊C8—28no—
30#13093935—22no—
31#13093935—22no—
32C47⋊#95—22no—
33C47⋊#95—24no—
34C22×C8×C47—22no—
35C2×C4⋊C4×C47C2×C412yes—
36C2×C42×C47C2311yescharacteristic
37#97×C47—22no—
38#97×C47—22no—
39#95×C47—22no—
40C23×D47C22⋊C411yescharacteristic
41C22×C4×C47—22no—
42C22×C4×C47C22×C411yescharacteristic
43C22×C4×C47C2×D412yes—
44C22×Dic47—22no—
45C22×Dic47C22⋊C412yes—
46C22×Dic47C22⋊C411yescharacteristic
47C2×C4×D47—22no—
48C2×C4×D47—21no—
49C2×C4×D47—21no—
50C2×C4×D47—22no—
51C2×C4×D47—24no—
52C2×C4×D47—22no—
53C2×C4×D47—22no—
54C2×C4×D47—42no—
55C2×C4×D47—44no—
56C2×C4×D47—44no—
57C2×C4×D47—44no—
58C2×C8×C47—24no—
59C2×C8×C47—42no—
60C2×C8×C47—42no—
61C4⋊C4×C47—42no—
62C42×C47#4112yes—
63C42×C47#4111yescharacteristic
64C42×C47#4111yescharacteristic
65C4⋊Dic47—42no—
66Dic47⋊C4—44no—
67C4×Dic47—21no—
68C4×Dic47—21no—
69C4×Dic47—22no—
70C4×Dic47—22no—
71C2×C47⋊C8—24no—
72C2×C47⋊C8—42no—
73C2×C47⋊C8—42no—
74C23×C47C2×C22⋊C411yescharacteristic
75C22×D47—21no—
76C22×D47—21no—
77C22×D47—22no—
78C22×D47#10112yes—
79C22×D47#10414yes—
80C2×C4×C47—21no—
81C2×C4×C47—21no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—42no—
85C2×C4×C47—42no—
86C2×C4×C47—42no—
87C2×C4×C47#11711yescharacteristic
88C2×C4×C47#11711yescharacteristic
89C2×C4×C47#12312yes—
90C2×C4×C47#12312yes—
91C2×Dic47—21no—
92C2×Dic47—21no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—42no—
97C2×Dic47—42no—
98C2×Dic47—42no—
99C2×Dic47#10012yes—
100C4×D47—24no—
101C4×D47—24no—
102C4×D47—44no—
103C4×D47—44no—
104C4×D47—88no—
105C8×C47—44no—
106C47⋊C8—44no—
107#8719—471nomaximal, Sylow
108C22×C47#38111yescharacteristic
109C22×C47C2×#10011yescharacteristic
110C22×C47C2×#10111yescharacteristic
111C22×C47C2×#10412yes—
112C22×C47#42112yes—
113C2×D47—22no—
114C2×D47—24no—
115C2×D47—24no—
116C2×D47—22no—
117C2×D47#33014yes—
118C4×C47—21no—
119C4×C47—21no—
120C4×C47—22no—
121C4×C47—22no—
122C4×C47—82no—
123Dic47—22no—
124Dic47—42no—
125Dic47—82no—
126C2×#382—471no—
127#1749—472no—
128#1295—472no—
129#1295—471no—
130#1295D4711yescharacteristic, complemented
131C2×C47C2×#33011yescharacteristic
132C2×C47#152712yes—
133C2×C47#153411yescharacteristic
134C2×C47#182111yescharacteristic
135C2×C47#182612yes—
136D47—24no—
137C22×C4⋊C4—472no—
138C22×C42—471no—
139C2×C22⋊C8—942no—
140C2×#97—472no—
141C2×#97C2×D4712yes—
142#382—472no—
143#382—471no—
144#382—942no—
145#382C2×D4711yescharacteristic
146C2×#95—942no—
147#336—942no—
148C47#871911yescharacteristic, complemented, Sylow
149C23×C4—471no—
150C23×C4—472no—
151C23×C4—942no—
152C22×C8—22no—
153C22×C8—942no—
154C2×C4⋊C4—472no—
155C2×C4⋊C4—942no—
156C2×C4⋊C4—1884no—
157C2×C4⋊C4C4×D4712yes—
158C2×C42—471no—
159C2×C42—472no—
160C2×C42—942no—
161C2×C42—941no—
162C2×C42—941no—
163C2×C42C22×D4711yescharacteristic
164C22⋊C8—948no—
165#97—22no—
166#97—22no—
167#97—942no—
168#97—942no—
169#95—22no—
170#95—944no—
171#95—942no—
172C24—471no—
173C22×C4—22no—
174C22×C4—471no—
175C22×C4—472no—
176C22×C4—942no—
177C22×C4—942no—
178C22×C4—944no—
179C22×C4—941no—
180C22×C4—941no—
181C22×C4—942no—
182C22×C4—942no—
183C22×C4—942no—
184C22×C4—1882no—
185C22×C4—1884no—
186C22×C4—1884no—
187C22×C4—1884no—
188C22×C4C2×C4×D4711yescharacteristic
189C22×C4D4×D4712yes—
190C2×C8—24no—
191C2×C8—42no—
192C2×C8—42no—
193C2×C8—944no—
194C2×C8—1882no—
195C2×C8—1882no—
196C4⋊C4—42no—
197C4⋊C4—1882no—
198C4⋊C4—1884no—
199C42—941no—
200C42—941no—
201C42—942no—
202C42—942no—
203C42#1062535012yes—
204C42#1062535211yescharacteristic
205C42#1062535411yescharacteristic
206C23—472no—
207C23—474no—
208C23—941no—
209C23—941no—
210C23—942no—
211C23C22⋊C4×D4711yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—42no—
219C2×C4—472no—
220C2×C4—944no—
221C2×C4—944no—
222C2×C4—941no—
223C2×C4—941no—
224C2×C4—942no—
225C2×C4—942no—
226C2×C4—942no—
227C2×C4—3768no—
228C2×C4—1884no—
229C2×C4—1884no—
230C2×C4—1882no—
231C2×C4—1882no—
232C2×C4—1882no—
233C2×C4#1309398111yescharacteristic
234C2×C4#1309398211yescharacteristic
235C2×C4#1309400612yes—
236C2×C4#1309400912yes—
237C8—44no—
238C8—1884no—
239C22—474no—
240C22—942no—
241C22—944no—
242C22—944no—
243C22—942no—
244C22#1568898511yescharacteristic
245C22#100×D4711yescharacteristic
246C22#101×D4711yescharacteristic
247C22#104×D4712yes—
248C22#1568913812yes—
249C4—21no—
250C4—21no—
251C4—22no—
252C4—22no—
253C4—82no—
254C4—942no—
255C4—3762no—
256C4—1882no—
257C2—944no—
258C2#330×D4711yescharacteristic
259C2#2024198412yes—
260C2#2024201311yescharacteristic
261C2#2024346711yescharacteristic
262C2#2024348612yes—
subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C4×C47C22×C4
FrattiniC2×C42C22×D47
FittingC47×#1295C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC2×C42×C47C23
hypercenter#1295D47
hypocenterC47#8719
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
3. #20241270C2semidirect
4. #20241269C2semidirect
5. C47×#1295C2semidirect
130. #1295D47semidirect
148. C47#8719semidirect

Maximal subgroups

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

subgroupindex
#382×D472
#202431512
#202412702
#202412692
C47×#12952
#871947