Finite Group Databasebeta

← #31804729

Subgroups — #31804729

Order 17792.

440 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 71 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⋊C4×D139C211yesmaximal, characteristic
2#22580915C212yesmaximal, complemented
3#22580677C211yesmaximal, characteristic, complemented
4#22580676C212yesmaximal, complemented
5#323×C139C211yesmaximal, characteristic, complemented
6C24×D139C411yescharacteristic
7C22×C4×D139C411yescharacteristic
8C22×C4×D139C2211yescharacteristic
9C2×#14555768—22no—
10C2×C22⋊Dic139C411yescharacteristic
11C2×(C2×D139)⋊C4C411yescharacteristic
12C2×(C2×D139)⋊C4C2211yescharacteristic
13C22⋊C4×D139—22no—
14C22⋊C4×D139—22no—
15C22⋊(C139⋊C8)C2212yescomplemented
16(C2×D139)⋊C8—22no—
17C2×C22⋊C4×C139C2211yescharacteristic
18C22⋊C8×C139C2212yescomplemented
19C23×D139—21no—
20C23×D139—21no—
21C23×D139—22no—
22C23×D139—22no—
23C23×D139—42no—
24C23×D139—42no—
25C23×D139C2×C411yescharacteristic
26C23×D139C2×C411yescharacteristic
27C22×Dic139C2×C411yescharacteristic
28C22×Dic139C2×C411yescharacteristic
29C2×C4×D139—21no—
30C2×C4×D139—21no—
31C2×C4×D139—42no—
32C2×C4×D139—42no—
33C2×C4×D139D412yes—
34C2×C4×D139D412yes—
35#14555768—44no—
36C2×C139⋊C8—22no—
37C22⋊Dic139—22no—
38(C2×D139)⋊C4—22no—
39(C2×D139)⋊C4—22no—
40C24×C139C2×C411yescharacteristic
41C22×C4×C139C2×C411yescharacteristic
42C22×C4×C139C2311yescharacteristic
43C2×C8×C139—22no—
44C22⋊C4×C139—22no—
45C22×D139—21no—
46C22×D139—21no—
47C22×D139—22no—
48C22×D139—22no—
49C22×D139—24no—
50C22×D139—24no—
51C22×D139—21no—
52C22×D139—21no—
53C22×D139—48no—
54C22×D139—48no—
55C22×D139—42no—
56C22×D139—42no—
57C22×D139—42no—
58C22×D139—42no—
59C22×D139—41no—
60C22×D139—41no—
61C22×D139C22⋊C411yescharacteristic
62C22×D139C22⋊C411yescharacteristic
63C22×D139M1612yescomplemented
64C2×Dic139—21no—
65C2×Dic139—41no—
66C2×Dic139—41no—
67C2×Dic139C22⋊C412yes—
68C4×D139—24no—
69C4×D139—42no—
70C4×D139—42no—
71C4×D139—42no—
72C139⋊C8—42no—
73C23×C139—21no—
74C23×C139—21no—
75C23×C139—41no—
76C23×C139—41no—
77C23×C139M1612yescomplemented
78C23×C139C22×C411yescharacteristic
79C2×C4×C139—21no—
80C2×C4×C139—41no—
81C2×C4×C139—41no—
82C2×C4×C139C2×D412yes—
83C8×C139—42no—
84C22×C139—21no—
85C22×C139—21no—
86C22×C139—22no—
87C22×C139—42no—
88C22×C139—42no—
89C22×C139—41no—
90C22×C139—41no—
91C22×C139C2×C22⋊C411yescharacteristic
92C22×C139C2×M1611yescharacteristic
93C22×C139C2×M1611yescharacteristic
94C2×D139—24no—
95C2×D139—24no—
96C2×D139—21no—
97C2×D139—21no—
98C2×D139—21no—
99C2×D139—21no—
100C2×D139—22no—
101C2×D139—48no—
102C2×D139—48no—
103C2×D139—42no—
104C2×D139—41no—
105C2×D139—41no—
106C2×D139—42no—
107C2×D139#9912yes—
108C2×D139#10012yes—
109C4×C139—22no—
110C4×C139—41no—
111Dic139—22no—
112Dic139—41no—
113C2×C139—21no—
114C2×C139—21no—
115C2×C139—42no—
116C2×C139#40711yescharacteristic
117C2×C139C2×#9911yescharacteristic
118C2×C139C2×#10011yescharacteristic
119D139—22no—
120D139—22no—
121D139—42no—
122C139#146211yescharacteristic, complemented, Sylow
123#1462—1391nomaximal, Sylow
124C22×C22⋊C4—1391no—
125#407—1392no—
126#323—1391no—
127#323—1392no—
128#323D13911yescharacteristic, complemented
129C25—1391no—
130C23×C4—1391no—
131C23×C4—1391no—
132C2×M16—2782no—
133C2×C22⋊C4—2782no—
134C2×C22⋊C4—2782no—
135C2×C22⋊C4—1391no—
136C2×C22⋊C4—1391no—
137C2×C22⋊C4—1391no—
138C2×C22⋊C4C2×D13911yescharacteristic
139C22⋊C8—2782no—
140C22⋊C8—1392no—
141C22⋊C8C2×D13912yescomplemented
142C24—2781no—
143C24—2781no—
144C24—2782no—
145C24—2782no—
146C24—5562no—
147C24—5562no—
148C24—1391no—
149C24—1391no—
150C24C4×D13911yescharacteristic
151C22×C4—2781no—
152C22×C4—2781no—
153C22×C4—5562no—
154C22×C4—5562no—
155C22×C4—1392no—
156C22×C4—1391no—
157C22×C4—1391no—
158C22×C4—1392no—
159C22×C4C4×D13911yescharacteristic
160C22×C4C22×D13911yescharacteristic
161M16—5564no—
162C2×C8—22no—
163C2×C8—2782no—
164C22⋊C4—22no—
165C22⋊C4—2782no—
166C22⋊C4—2782no—
167C22⋊C4—2782no—
168C23—21no—
169C23—21no—
170C23—41no—
171C23—41no—
172C23—2782no—
173C23—2782no—
174C23—2784no—
175C23—2784no—
176C23—2781no—
177C23—2781no—
178C23—2781no—
179C23—2781no—
180C23—5561no—
181C23—5561no—
182C23—5568no—
183C23—5568no—
184C23—5562no—
185C23—5562no—
186C23—5562no—
187C23—5562no—
188C23—1391no—
189C23—1391no—
190C23—1392no—
191C23#1455576812yescomplemented
192C23C2×C4×D13911yescharacteristic
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—2784no—
197C2×C4—2781no—
198C2×C4—5562no—
199C2×C4—5562no—
200C2×C4—5562no—
201C2×C4—5561no—
202C2×C4—5561no—
203C2×C4—1392no—
204C2×C4D4×D13912yes—
205C8—42no—
206C8—5562no—
207C22—21no—
208C22—21no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22—41no—
213C22—41no—
214C22—2784no—
215C22—2784no—
216C22—2781no—
217C22—2781no—
218C22—2781no—
219C22—2781no—
220C22—2782no—
221C22—5562no—
222C22—5562no—
223C22—5568no—
224C22—5568no—
225C22—5561no—
226C22—5561no—
227C22—1392no—
228C22—1392no—
229C22C22⋊C4×D13911yescharacteristic
230C22M16×D13911yescharacteristic
231C22C2×#1455576811yescharacteristic
232C4—22no—
233C4—41no—
234C4—2782no—
235C4—5561no—
236C2—21no—
237C2—21no—
238C2—42no—
239C2—2782no—
240C2—2782no—
241C2—5562no—
242C2#2258091511yescharacteristic
243C2#99×D13911yescharacteristic
244C2#100×D13911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D139
commutatorC23×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#323×C139C2
socleC22×C139C2×C22⋊C4
prime radicalC24×D139C4
cosocleC22×C4×C139C23
hypercenter#323D139
hypocenterC139#1462
LCSG ▷ C23×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #22580915C2semidirect
3. #22580677C2semidirect
4. #22580676C2semidirect
5. #323×C139C2semidirect
15. C22⋊(C139⋊C8)C22semidirect
18. C22⋊C8×C139C22semidirect
63. C22×D139M16semidirect
77. C23×C139M16semidirect
122. C139#1462semidirect
128. #323D139semidirect
141. C22⋊C8C2×D139semidirect
191. C23#14555768semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D1392
#225809152
#225806772
#225806762
#323×C1392
#1462139