Finite Group Databasebeta

← #44487813

Subgroups — #44487813

Order 30592.

560 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 147 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×(C22⋊D239)⋊C4C211yesmaximal, characteristic
2C2×#21439918C211yesmaximal, characteristic, complemented
3#29504710C211yesmaximal, characteristic, complemented
4#29504704C211yesmaximal, characteristic, complemented
5#29504698C212yesmaximal, complemented
6#29504697C211yesmaximal, characteristic, complemented
7#29504688C212yesmaximal
8C4⋊C4×Dic239C212yesmaximal, complemented
9C22⋊C4×Dic239C212yesmaximal, complemented
10#29504619C211yesmaximal, characteristic, complemented
11#399×C239C211yesmaximal, characteristic, complemented
12C22×C22⋊D239C2211yescharacteristic
13C23×Dic239C2211yescharacteristic
14C22×C4×D239C2211yescharacteristic
15(C22⋊D239)⋊C4—24no—
16#21439918—24no—
17C2×C4⋊Dic239C2212yes—
18C2×C4⋊Dic239C2211yescharacteristic
19C2×Dic239⋊C4C2211yescharacteristic
20C2×C22⋊Dic239C2212yes—
21C2×(C2×D239)⋊C4C2212yes—
22C2×(C2×D239)⋊C4C2212yes—
23C2×(C2×D239)⋊C4C2211yescharacteristic
24C2×C4×Dic239C2212yes—
25C2×C4×Dic239C2212yes—
26C2×C4×Dic239C2211yescharacteristic
27C239⋊#95C2211yescharacteristic
28C239⋊#95C2212yes—
29C239⋊#95C2212yes—
30C239⋊#95C2212yes—
31C239⋊#95C2212yes—
32C2×C4⋊C4×C239C2212yes—
33C2×C4⋊C4×C239C2211yescharacteristic
34C2×C22⋊C4×C239C2212yes—
35C2×C22⋊C4×C239C2211yescharacteristic
36#95×C239C2211yescharacteristic
37C23×D239C2311yescharacteristic
38C2×C22⋊D239—22no—
39C2×C22⋊D239—22no—
40C2×C22⋊D239—22no—
41C22×Dic239—22no—
42C22×Dic239—24no—
43C22×Dic239C2312yes—
44C22×Dic239C2311yescharacteristic
45C22×Dic239C2312yes—
46C22×Dic239C2311yescharacteristic
47C22×Dic239C2311yescharacteristic
48C2×C4×D239—24no—
49C2×C4×D239D414yes—
50C4⋊Dic239—24no—
51C4⋊Dic239—22no—
52Dic239⋊C4—22no—
53C22⋊Dic239—24no—
54(C2×D239)⋊C4—24no—
55(C2×D239)⋊C4—22no—
56(C2×D239)⋊C4—24no—
57C4×Dic239—24no—
58C4×Dic239—22no—
59C4×Dic239—24no—
60C24×C239C2311yescharacteristic
61C22×C4×C239C2311yescharacteristic
62C22×C4×C239C2312yes—
63C22×C4×C239C2311yescharacteristic
64C22×C4×C239C2312yes—
65C4⋊C4×C239—22no—
66C4⋊C4×C239—24no—
67C22⋊C4×C239—22no—
68C22⋊C4×C239—24no—
69C22×D239—22no—
70C22×D239—22no—
71C22×D239—21no—
72C22×D239—21no—
73C22×D239C2×D412yes—
74C22⋊D239—28no—
75C2×Dic239—21no—
76C2×Dic239—21no—
77C2×Dic239—22no—
78C2×Dic239—21no—
79C2×Dic239—22no—
80C2×Dic239—22no—
81C2×Dic239—22no—
82C2×Dic239—22no—
83C2×Dic239—22no—
84C2×Dic239—22no—
85C2×Dic239—44no—
86C2×Dic239C2×D412yes—
87C2×Dic239#4112yes—
88C2×Dic239#4114yes—
89C4×D239—28no—
90C23×C239—21no—
91C23×C239—22no—
92C23×C239—22no—
93C23×C239—21no—
94C23×C239#4112yes—
95C23×C239C2411yescharacteristic
96C2×C4×C239—22no—
97C2×C4×C239—22no—
98C2×C4×C239—22no—
99C2×C4×C239—21no—
100C2×C4×C239—22no—
101C2×C4×C239—22no—
102C2×C4×C239—22no—
103C2×C4×C239—22no—
104C2×C4×C239C2×D412yes—
105C2×C4×C239#4114yes—
106C22×C239—22no—
107C22×C239—24no—
108C22×C239—41no—
109C22×C239—42no—
110C22×C239—41no—
111C22×C239C22×D411yescharacteristic
112C22×C239C2×#4112yes—
113C22×C239C2×#4111yescharacteristic
114C22×C239C2×#4112yes—
115C22×C239C2×#4111yescharacteristic
116C2×D239—22no—
117C2×D239—22no—
118C2×D239—22no—
119C2×D239—42no—
120C2×D239—42no—
121C4×C239—22no—
122C4×C239—24no—
123C4×C239—41no—
124C4×C239—42no—
125Dic239—22no—
126Dic239—41no—
127Dic239—42no—
128Dic239—42no—
129Dic239#12314yes—
130C2×C239—42no—
131C2×C239C2×#12311yescharacteristic
132C2×C239#52511yescharacteristic
133C2×C239#52912yes—
134C2×C239#52912yes—
135C2×C239#53211yescharacteristic
136D239—42no—
137C239#239511yescharacteristic, complemented, Sylow
138#2395—2391nomaximal, Sylow
139C2×C4×D4—2391no—
140C2×#117—2391no—
141#400—2391no—
142#399D23911yescharacteristic, complemented
143#398—2391no—
144#397—2392no—
145#397—2391no—
146#394—2392no—
147C4×C4⋊C4—2392no—
148C4×C22⋊C4—2392no—
149C4×C22⋊C4—2391no—
150C22×D4—2391no—
151C23×C4—2391no—
152C23×C4—2391no—
153C4×D4—4784no—
154#117—4784no—
155C2×C4⋊C4—2391no—
156C2×C4⋊C4—2391no—
157C2×C4⋊C4—2392no—
158C2×C4⋊C4C2×D23911yescharacteristic
159C2×C4⋊C4C2×D23912yes—
160C2×C22⋊C4—2392no—
161C2×C22⋊C4—2392no—
162C2×C22⋊C4—2391no—
163C2×C22⋊C4—2392no—
164C2×C22⋊C4C2×D23911yescharacteristic
165C2×C22⋊C4C2×D23912yes—
166C2×C42—2392no—
167C2×C42—2391no—
168C2×C42—2392no—
169#95—2392no—
170#95—2391no—
171#95—2392no—
172#95—2392no—
173#95—2392no—
174#95C2×D23911yescharacteristic
175C24—2391no—
176C24C22×D23911yescharacteristic
177C2×D4—4782no—
178C2×D4—4782no—
179C2×D4—4782no—
180C22×C4—4784no—
181C22×C4—4782no—
182C22×C4—4784no—
183C22×C4—2392no—
184C22×C4—2391no—
185C22×C4—2392no—
186C22×C4—2391no—
187C22×C4—2394no—
188C22×C4—2391no—
189C22×C4C22×D23912yes—
190C22×C4C22×D23911yescharacteristic
191C22×C4C22×D23911yescharacteristic
192C22×C4C22×D23912yes—
193C4⋊C4—22no—
194C4⋊C4—24no—
195C4⋊C4—4784no—
196C4⋊C4—4782no—
197C4⋊C4—4782no—
198C22⋊C4—22no—
199C22⋊C4—24no—
200C22⋊C4—4784no—
201C22⋊C4—4782no—
202C22⋊C4—4784no—
203C22⋊C4—4784no—
204C42—4784no—
205C42—4782no—
206C42—4784no—
207C23—22no—
208C23—21no—
209C23—22no—
210C23—21no—
211C23—4782no—
212C23—4781no—
213C23—4782no—
214C23—4781no—
215C23—2392no—
216C23#1683854912yes—
217C23C23×D23911yescharacteristic
218D4—4788no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—9564no—
228C2×C4—4788no—
229C2×C4—4782no—
230C2×C4—4782no—
231C2×C4—4782no—
232C2×C4—4782no—
233C2×C4—4782no—
234C2×C4—4782no—
235C2×C4—4782no—
236C2×C4—4781no—
237C2×C4—4781no—
238C2×C4—4781no—
239C2×C4—2392no—
240C2×C4—2394no—
241C2×C4—2392no—
242C2×C4D4×D23912yes—
243C2×C4#1683854714yes—
244C22—22no—
245C22—24no—
246C22—42no—
247C22—41no—
248C22—41no—
249C22—9562no—
250C22—9562no—
251C22—4782no—
252C22—4782no—
253C22—4782no—
254C22C2×D4×D23911yescharacteristic
255C22#41×D23911yescharacteristic
256C22#41×D23912yes—
257C22C2×#1683854712yes—
258C22C2×#1683854911yescharacteristic
259C4—24no—
260C4—22no—
261C4—42no—
262C4—41no—
263C4—9562no—
264C4—9562no—
265C4—9561no—
266C4—4782no—
267C4—2394no—
268C2—42no—
269C2—9562no—
270C2#123×D23911yescharacteristic
271C2#2950528511yescharacteristic
272C2#2950529912yes—
273C2#2950530812yes—
274C2#2950532011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D239
commutator, socle, cosocleC23×C239C24
Fitting#399×C239C2
prime radicalC22×C22⋊D239C22
hypercenter#399D239
hypocenterC239#2395
LCSG ▷ C23×C239 ▷ C239
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. C2×#21439918C2semidirect
3. #29504710C2semidirect
4. #29504704C2semidirect
5. #29504698C2semidirect
6. #29504697C2semidirect
8. C4⋊C4×Dic239C2semidirect
9. C22⋊C4×Dic239C2semidirect
10. #29504619C2semidirect
11. #399×C239C2semidirect
137. C239#2395semidirect
142. #399D239semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D239)⋊C42
C2×#214399182
#295047102
#295047042
#295046982
#295046972
#295046882
C4⋊C4×Dic2392
C22⋊C4×Dic2392
#295046192
#399×C2392
#2395239