Finite Group Databasebeta

← #44484534

Subgroups — #44484534

Order 30592.

380 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 95 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×D4×Dic239C211yesmaximal, characteristic
2C2×#21439875C211yesmaximal, characteristic
3#29504630C212yesmaximal, complemented
4#29504538C212yesmaximal, complemented
5C2×#99×C239C211yesmaximal, characteristic
6C23×Dic239C411yescharacteristic, complemented
7C23×Dic239C2211yescharacteristic
8D4×Dic239—22no—
9D4×Dic239—22no—
10C2×C4⋊Dic239C411yescharacteristic, complemented
11C2×Dic239⋊C4—22no—
12C2×C22⋊Dic239C411yescharacteristic, complemented
13C2×C22⋊Dic239C2212yes—
14C2×C22⋊Dic239C2211yescharacteristic
15C2×C4×Dic239C411yescharacteristic, complemented
16#21439875—22no—
17C239⋊#95—22no—
18C22×D4×C239C2211yescharacteristic
19C2×C22⋊C4×C239C2212yes—
20#99×C239—22no—
21C22×Dic239—21no—
22C22×Dic239—21no—
23C22×Dic239—22no—
24C22×Dic239—42no—
25C22×Dic239—42no—
26C22×Dic239C2×C411yescharacteristic
27C22×Dic239C2×C411yescharacteristic
28C22×Dic239C2×C411yescharacteristic
29C22×Dic239C2×C411yescharacteristic
30C22×Dic239D412yes—
31C22×Dic239D412yes—
32C4⋊Dic239—22no—
33Dic239⋊C4—44no—
34C22⋊Dic239—22no—
35C22⋊Dic239—22no—
36C22⋊Dic239—22no—
37C22⋊Dic239—22no—
38C4×Dic239—21no—
39C4×Dic239—21no—
40C24×C239C2×C411yescharacteristic
41C24×C239C2311yescharacteristic
42C2×D4×C239—22no—
43C2×D4×C239—22no—
44C2×D4×C239D412yes—
45C2×D4×C239Q812yes—
46C22×C4×C239—22no—
47C22×C4×C239C2×C411yescharacteristic
48C22⋊C4×C239—22no—
49C22⋊C4×C239—22no—
50C2×Dic239—24no—
51C2×Dic239—22no—
52C2×Dic239—21no—
53C2×Dic239—21no—
54C2×Dic239—41no—
55C2×Dic239—42no—
56C2×Dic239—42no—
57C2×Dic239—42no—
58C2×Dic239—41no—
59C2×Dic239—41no—
60C2×Dic239—42no—
61C2×Dic239—42no—
62C2×Dic239—42no—
63C2×Dic239C22⋊C411yescharacteristic
64C2×Dic239C22⋊C412yes—
65C2×Dic239C22⋊C411yescharacteristic
66C23×C239—21no—
67C23×C239—21no—
68C23×C239—41no—
69C23×C239—41no—
70C23×C239—41no—
71C23×C239—41no—
72C23×C239C4⋊C412yescomplemented
73C23×C239C22×C411yescharacteristic
74C23×C239C2×D412yes—
75C23×C239C2×D411yescharacteristic
76C23×C239C2×Q811yescharacteristic
77C23×C239#4112yes—
78D4×C239—24no—
79D4×C239—24no—
80C2×C4×C239—21no—
81C2×C4×C239—21no—
82C2×C4×C239—42no—
83C2×C4×C239—42no—
84C2×C4×C239—42no—
85C2×C4×C239C4⋊C412yescomplemented
86C22×C239—22no—
87C22×C239—21no—
88C22×C239—22no—
89C22×C239—21no—
90C22×C239—22no—
91C22×C239—41no—
92C22×C239—41no—
93C22×C239—42no—
94C22×C239—42no—
95C22×C239—42no—
96C22×C239—41no—
97C22×C239—41no—
98C22×C239C2×C22⋊C411yescharacteristic
99C22×C239C2×C4⋊C411yescharacteristic
100C22×C239#11711yescharacteristic
101C22×C239#12112yes—
102C22×C239C22⋊Q812yes—
103C4×C239—22no—
104C4×C239—82no—
105Dic239—21no—
106Dic239—22no—
107Dic239—41no—
108Dic239—41no—
109Dic239—82no—
110Dic239#9912yescomplemented
111C2×C239—22no—
112C2×C239—21no—
113C2×C239—21no—
114C2×C239—22no—
115C2×C239—42no—
116C2×C239#38011yescharacteristic
117C2×C239C2×#9911yescharacteristic
118C2×C239#41011yescharacteristic
119C239#179911yescharacteristic, complemented, Sylow
120#1799—2391nomaximal, Sylow
121C2×C4×D4—2391no—
122C2×#99—2391no—
123C2×#99D23911yescharacteristic
124#380—2392no—
125#342—2392no—
126C22×D4C2×D23911yescharacteristic
127C23×C4—2391no—
128C23×C4—2391no—
129C4×D4—4782no—
130C4×D4—4782no—
131C2×C4⋊C4—4782no—
132C2×C4⋊C4—2391no—
133C2×C22⋊C4—2392no—
134C2×C22⋊C4—2391no—
135C2×C22⋊C4—2391no—
136C2×C22⋊C4C2×D23912yes—
137C2×C42—2391no—
138#99—22no—
139#99—4782no—
140#95—4782no—
141C24C4×D23911yescharacteristic
142C24C22×D23911yescharacteristic
143C2×D4—22no—
144C2×D4—22no—
145C2×D4C22⋊D23912yes—
146C2×D4Dic47812yes—
147C22×C4—22no—
148C22×C4—9562no—
149C22×C4—9562no—
150C22×C4—4782no—
151C22×C4—4781no—
152C22×C4—4781no—
153C22×C4—2391no—
154C22×C4—2391no—
155C22×C4—2391no—
156C22×C4—2392no—
157C22×C4—2391no—
158C22×C4—2392no—
159C22×C4C4×D23911yescharacteristic
160C4⋊C4—9564no—
161C4⋊C4—4782no—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C22⋊C4—4782no—
165C22⋊C4—4782no—
166C22⋊C4—4782no—
167C22⋊C4—4782no—
168C42—4781no—
169C42—4781no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23Dic239⋊C412yescomplemented
177C23C2×C4×D23911yescharacteristic
178C23D4×D23912yes—
179C23C2×C22⋊D23911yescharacteristic
180C23C2×Dic47811yescharacteristic
181C23#1683854712yes—
182D4—24no—
183D4—24no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—9562no—
190C2×C4—9562no—
191C2×C4—9562no—
192C2×C4—9562no—
193C2×C4—9562no—
194C2×C4—9561no—
195C2×C4—9561no—
196C2×C4—9562no—
197C2×C4—9561no—
198C2×C4—4781no—
199C2×C4—4781no—
200C2×C4—4784no—
201C2×C4—4782no—
202C2×C4—2391no—
203C2×C4—2392no—
204C2×C4—2391no—
205C2×C4Dic239⋊C412yescomplemented
206C22—22no—
207C22—21no—
208C22—22no—
209C22—21no—
210C22—22no—
211C22—41no—
212C22—41no—
213C22—42no—
214C22—42no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22C22⋊C4×D23911yescharacteristic
219C22C2×Dic239⋊C411yescharacteristic
220C22#2143991611yescharacteristic
221C22#2143993212yes—
222C22#2143993712yes—
223C4—22no—
224C4—82no—
225C4—19122no—
226C4—9561no—
227C4—9561no—
228C4—4781no—
229C4—4782no—
230C4—2392no—
231C2—22no—
232C2—21no—
233C2—21no—
234C2—22no—
235C2—42no—
236C2#2950463011yescharacteristic
237C2#99×D23911yescharacteristic
238C2#2950474411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D239
commutatorC23×C239C22×C4
FrattiniC24C22×D239
FittingC2×#99×C239C2
socleC22×C239C2×C22⋊C4
prime radicalC22×D4×C239C22
cosocleC24×C239C23
hypercenterC2×#99D239
hypocenterC239#1799
LCSG ▷ C23×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #29504630C2semidirect
4. #29504538C2semidirect
6. C23×Dic239C4semidirect
10. C2×C4⋊Dic239C4semidirect
12. C2×C22⋊Dic239C4semidirect
15. C2×C4×Dic239C4semidirect
72. C23×C239C4⋊C4semidirect
85. C2×C4×C239C4⋊C4semidirect
110. Dic239#99semidirect
119. C239#1799semidirect
176. C23Dic239⋊C4semidirect
205. C2×C4Dic239⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic2392
C2×#214398752
#295046302
#295045382
C2×#99×C2392
#1799239