Finite Group Databasebeta

← #44487840

Subgroups — #44487840

Order 30592.

504 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 163 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×#21439925C211yesmaximal, characteristic
2C2×#21439925C211yesmaximal, characteristic
3#29504706C212yesmaximal
4#29504703C211yesmaximal, characteristic
5#29504693C211yesmaximal, characteristic
6#29504692C212yesmaximal
7#29504692C211yesmaximal, characteristic
8C4⋊C4×Dic239C212yesmaximal
9#29504623C212yesmaximal
10#29504617C211yesmaximal, characteristic
11#398×C239C211yesmaximal, characteristic
12C22×Dic478C2211yescharacteristic
13C22×Dic478C2211yescharacteristic
14#21439925—24no—
15#21439925—24no—
16C2×C4⋊Dic239C2212yes—
17C2×Dic239⋊C4C2212yes—
18C2×Dic239⋊C4C2212yes—
19C2×Dic239⋊C4C2212yes—
20C2×Dic239⋊C4C2211yescharacteristic
21C2×Dic239⋊C4C2211yescharacteristic
22C2×C4×Dic239C2211yescharacteristic
23C2×C4×Dic239C2212yes—
24C2×C4×Dic239C2211yescharacteristic
25C2×C4×Dic239C2211yescharacteristic
26C2×C4×Dic239C2212yes—
27C239⋊#95C2211yescharacteristic
28C239⋊#95C2212yes—
29C239⋊#95C2212yes—
30C239⋊#95C2212yes—
31C239⋊#95C2212yes—
32C2×C4⋊C4×C239C2212yes—
33C2×C4⋊C4×C239C2211yescharacteristic
34C2×C4⋊C4×C239C2211yescharacteristic
35#95×C239C2211yescharacteristic
36#95×C239C2212yes—
37C2×Dic478—22no—
38C2×Dic478—22no—
39C2×Dic478—24no—
40C2×Dic478—22no—
41C2×Dic478—22no—
42C22×Dic239C2311yescharacteristic
43C22×Dic239C2311yescharacteristic
44C22×Dic239C2312yes—
45C22×Dic239C2311yescharacteristic
46C22×Dic239C2312yes—
47C22×Dic239C2311yescharacteristic
48C4⋊Dic239—24no—
49Dic239⋊C4—24no—
50Dic239⋊C4—22no—
51Dic239⋊C4—24no—
52Dic239⋊C4—24no—
53Dic239⋊C4—22no—
54C4×Dic239—22no—
55C4×Dic239—22no—
56C4×Dic239—24no—
57C4×Dic239D414yes—
58C4×Dic239Q818yescomplemented
59C22×C4×C239C2311yescharacteristic
60C22×C4×C239C2312yes—
61C22×C4×C239C2311yescharacteristic
62C22×C4×C239C2312yes—
63C22×C4×C239C2311yescharacteristic
64C4⋊C4×C239—22no—
65C4⋊C4×C239—22no—
66C4⋊C4×C239—24no—
67Dic478—28no—
68Dic478—28no—
69C2×Dic239—22no—
70C2×Dic239—21no—
71C2×Dic239—22no—
72C2×Dic239—22no—
73C2×Dic239—21no—
74C2×Dic239—21no—
75C2×Dic239—22no—
76C2×Dic239—21no—
77C2×Dic239—21no—
78C2×Dic239—22no—
79C2×Dic239C2×D412yes—
80C2×Dic239C2×D412yes—
81C2×Dic239C2×Q814yes—
82C2×Dic239C2×Q814yes—
83C2×Dic239#4112yes—
84C2×Dic239#4114yes—
85C23×C239C2411yescharacteristic
86C2×C4×C239—21no—
87C2×C4×C239—22no—
88C2×C4×C239—22no—
89C2×C4×C239—22no—
90C2×C4×C239—21no—
91C2×C4×C239—21no—
92C2×C4×C239—22no—
93C2×C4×C239—22no—
94C2×C4×C239—22no—
95C2×C4×C239—22no—
96C2×C4×C239C2×D412yes—
97C2×C4×C239C2×Q814yes—
98C2×C4×C239#4112yes—
99C22×C239C22×D411yescharacteristic
100C22×C239C22×Q812yes—
101C22×C239C2×#4112yes—
102C22×C239C2×#4111yescharacteristic
103C22×C239C2×#4111yescharacteristic
104C4×C239—22no—
105C4×C239—22no—
106C4×C239—24no—
107C4×C239—41no—
108C4×C239—42no—
109Dic239—22no—
110Dic239—24no—
111Dic239—22no—
112Dic239—24no—
113Dic239—41no—
114Dic239C4⋊Q814yes—
115C2×C239#52511yescharacteristic
116C2×C239#52511yescharacteristic
117C2×C239C2×C4⋊Q811yescharacteristic
118C2×C239#53312yes—
119C2×C239#53312yes—
120C239#239911yescharacteristic, complemented, Sylow
121#2399—2391nomaximal, Sylow
122C2×C4×Q8—2391no—
123C2×C4×Q8—2391no—
124#398—2391no—
125#398—2392no—
126#398D23911yescharacteristic
127#395—2392no—
128#395—2391no—
129#395—2391no—
130C4×C4⋊C4—2392no—
131C4×C4⋊C4—2392no—
132#376—2391no—
133C22×Q8—2391no—
134C22×Q8—2391no—
135C4×Q8—4784no—
136C4×Q8—4784no—
137C2×C4⋊C4—2392no—
138C2×C4⋊C4—2391no—
139C2×C4⋊C4—2391no—
140C2×C4⋊C4—2392no—
141C2×C4⋊C4—2392no—
142C2×C4⋊C4—2392no—
143C2×C4⋊C4C2×D23911yescharacteristic
144C2×C4⋊C4C2×D23911yescharacteristic
145C2×C4⋊C4C2×D23912yes—
146C2×C42—2391no—
147C2×C42—2392no—
148C2×C42—2391no—
149C2×C42—2391no—
150C2×C42—2392no—
151#95—2391no—
152#95—2392no—
153#95—2392no—
154#95—2392no—
155#95—2392no—
156#95C2×D23911yescharacteristic
157#95C2×D23912yes—
158C2×Q8—4782no—
159C2×Q8—4784no—
160C2×Q8—4782no—
161C2×Q8—4782no—
162C2×Q8—4782no—
163C22×C4—2391no—
164C22×C4—2392no—
165C22×C4—2391no—
166C22×C4—2392no—
167C22×C4—2391no—
168C22×C4—2391no—
169C22×C4C22×D23912yes—
170C22×C4C22×D23911yescharacteristic
171C22×C4C22×D23911yescharacteristic
172C22×C4C22×D23912yes—
173C22×C4C22×D23911yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—24no—
177C4⋊C4—4782no—
178C4⋊C4—4784no—
179C4⋊C4—4784no—
180C4⋊C4—4784no—
181C4⋊C4—4784no—
182C4⋊C4—4782no—
183C42—4782no—
184C42—4782no—
185C42—4784no—
186C42—2394no—
187C42—2398no—
188C23C23×D23911yescharacteristic
189Q8—4788no—
190Q8—4788no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—4782no—
202C2×C4—4781no—
203C2×C4—4782no—
204C2×C4—4782no—
205C2×C4—4782no—
206C2×C4—4781no—
207C2×C4—4781no—
208C2×C4—4781no—
209C2×C4—4782no—
210C2×C4—4781no—
211C2×C4—2394no—
212C2×C4—2392no—
213C2×C4—2392no—
214C2×C4—2394no—
215C2×C4—2392no—
216C2×C4—2394no—
217C2×C4D4×D23912yes—
218C2×C4Q8×D23914yes—
219C2×C4#1683854712yes—
220C22C2×D4×D23911yescharacteristic
221C22C2×Q8×D23912yes—
222C22#41×D23912yes—
223C22#41×D23911yescharacteristic
224C22C2×#1683854711yescharacteristic
225C4—22no—
226C4—22no—
227C4—24no—
228C4—41no—
229C4—42no—
230C4—9561no—
231C4—4784no—
232C4—4782no—
233C4—4782no—
234C4—4784no—
235C4—2394no—
236C2#2950528011yescharacteristic
237C2#2950528211yescharacteristic
238C2C4⋊Q8×D23911yescharacteristic
239C2#2950532412yes—
240C2#2950532812yes—
subgroupG/H
center, FrattiniC23C23×D239
commutator, socle, prime radical, cosocleC23×C239C24
Fitting#398×C239C2
hypercenter#398D239
hypocenterC239#2399
LCSG ▷ C23×C239 ▷ C239
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
58. C4×Dic239Q8semidirect
120. C239#2399semidirect

Maximal subgroups

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

subgroupindex
C2×#214399252
#295047062
#295047032
#295046932
#295046922
C4⋊C4×Dic2392
#295046232
#295046172
#398×C2392
#2399239