Finite Group Databasebeta

← #31806944

Subgroups — #31806944

Order 17792.

380 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 85 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#22581512C211yesmaximal, characteristic
2#22581428C211yesmaximal, characteristic, complemented
3C2×#17984756C212yesmaximal, complemented
4#22580720C212yesmaximal, complemented
5C2×#99×C139C211yesmaximal, characteristic, complemented
6C22×C22⋊D139C2211yescharacteristic
7#17984825—21no—
8#17984823C412yescomplemented
9#17984814—22no—
10#17984811—21no—
11#17984810C412yescomplemented
12D4×Dic139—24no—
13#17984801—21no—
14C2×C22⋊Dic139—21no—
15C2×C22⋊Dic139C2211yescharacteristic
16C2×C22⋊Dic139C2212yes—
17#17984756—24no—
18C22×D4×C139C2211yescharacteristic
19C2×C22⋊C4×C139C2212yes—
20#99×C139—22no—
21C23×D139C2×C411yescharacteristic, complemented
22C2×C22⋊D139—22no—
23C2×C22⋊D139—21no—
24C2×C22⋊D139—21no—
25C2×C22⋊D139—22no—
26C2×C22⋊D139—22no—
27C22×Dic139—22no—
28C22×Dic139—22no—
29C22×Dic139—21no—
30C22×Dic139C2×C411yescharacteristic, complemented
31C4⋊Dic139—22no—
32Dic139⋊C4—22no—
33C22⋊Dic139—22no—
34C22⋊Dic139—22no—
35C22⋊Dic139—22no—
36C22⋊Dic139—21no—
37C22⋊Dic139C2×C412yescomplemented
38C22⋊Dic139D414yescomplemented
39(C2×D139)⋊C4—22no—
40C4×Dic139—22no—
41C24×C139D411yescharacteristic
42C24×C139C2311yescharacteristic
43C2×D4×C139—22no—
44C2×D4×C139—22no—
45C2×D4×C139C2×C412yes—
46C2×D4×C139D412yes—
47C22×C4×C139—22no—
48C22×C4×C139D411yescharacteristic
49C22⋊C4×C139—22no—
50C22⋊C4×C139—22no—
51C22×D139—21no—
52C22×D139—22no—
53C22×D139—81no—
54C22⋊D139—41no—
55C22⋊D139—42no—
56C22⋊D139—41no—
57C22⋊D139—82no—
58C2×Dic139—22no—
59C2×Dic139—21no—
60C2×Dic139—22no—
61C2×Dic139—24no—
62C2×Dic139—82no—
63C2×Dic139—82no—
64C2×Dic139—81no—
65C23×C139—21no—
66C23×C139—21no—
67C23×C139—81no—
68C23×C139—81no—
69C23×C139C22⋊C412yes—
70C23×C139C22×C411yescharacteristic
71C23×C139C2×D412yes—
72C23×C139C2×D411yescharacteristic
73C23×C139C2×D411yescharacteristic
74C23×C139#4112yes—
75D4×C139—24no—
76D4×C139—24no—
77C2×C4×C139—21no—
78C2×C4×C139—21no—
79C2×C4×C139—42no—
80C2×C4×C139—82no—
81C2×C4×C139C22⋊C412yes—
82C22×C139—22no—
83C22×C139—42no—
84C22×C139—41no—
85C22×C139—41no—
86C22×C139—42no—
87C22×C139—41no—
88C22×C139—42no—
89C22×C139—42no—
90C22×C139—81no—
91C22×C139C2×C22⋊C411yescharacteristic
92C22×C139C4×D412yes—
93C22×C139#12011yescharacteristic
94C22×C139#12112yes—
95C22×C139#12311yescharacteristic
96C2×D139—42no—
97C2×D139—41no—
98C2×D139—82no—
99C4×C139—22no—
100C4×C139—82no—
101Dic139—44no—
102Dic139—42no—
103Dic139—41no—
104C2×C139—21no—
105C2×C139—21no—
106C2×C139—22no—
107C2×C139—22no—
108C2×C139—21no—
109C2×C139—42no—
110C2×C139#38611yescharacteristic
111D139—81no—
112C139#191311yescharacteristic, complemented, Sylow
113#1913—1391nomaximal, Sylow
114#534—1391no—
115#518—1391no—
116C2×#99—1392no—
117C2×#99D13911yescharacteristic, complemented
118#342—1392no—
119C22×D4—1391no—
120C22×D4C2×D13911yescharacteristic
121#123—2781no—
122#123—1392no—
123#121—2782no—
124#120—2781no—
125#120—1392no—
126C4×D4—2784no—
127#117—2781no—
128C2×C22⋊C4—2781no—
129C2×C22⋊C4—1392no—
130C2×C22⋊C4—1391no—
131C2×C22⋊C4C2×D13912yes—
132#99—22no—
133#99—2784no—
134C24—1391no—
135C24D55611yescharacteristic
136C24C22×D13911yescharacteristic
137C2×D4—22no—
138C2×D4—22no—
139C2×D4—2782no—
140C2×D4—2781no—
141C2×D4—2781no—
142C2×D4—2782no—
143C2×D4—2782no—
144C2×D4C4×D13912yes—
145C2×D4C22⋊D13912yes—
146C22×C4—22no—
147C22×C4—2782no—
148C22×C4—2782no—
149C22×C4—2781no—
150C22×C4—1391no—
151C22×C4D55611yescharacteristic
152C4⋊C4—2782no—
153C4⋊C4—2782no—
154C22⋊C4—22no—
155C22⋊C4—22no—
156C22⋊C4—2782no—
157C22⋊C4—2782no—
158C22⋊C4—2782no—
159C22⋊C4—2781no—
160C22⋊C4—2782no—
161C22⋊C4—1392no—
162C22⋊C4—1394no—
163C42—2782no—
164C23—21no—
165C23—21no—
166C23—81no—
167C23—81no—
168C23—2781no—
169C23—2782no—
170C23—11121no—
171C23(C2×D139)⋊C412yes—
172C23C2×C4×D13911yescharacteristic
173C23D4×D13912yes—
174C23C2×C22⋊D13911yescharacteristic
175C23C2×D55611yescharacteristic
176C23#1455578412yes—
177D4—24no—
178D4—24no—
179D4—5561no—
180D4—5562no—
181D4—5561no—
182D4—11122no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—42no—
186C2×C4—82no—
187C2×C4—2782no—
188C2×C4—2781no—
189C2×C4—2782no—
190C2×C4—2784no—
191C2×C4—11122no—
192C2×C4—11122no—
193C2×C4—11121no—
194C2×C4(C2×D139)⋊C412yes—
195C22—22no—
196C22—42no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22—81no—
204C22—5562no—
205C22—5561no—
206C22—11122no—
207C22C2×(C2×D139)⋊C411yescharacteristic
208C22(C22⋊D139)⋊C412yes—
209C22#1798481211yescharacteristic
210C22#1798481412yes—
211C22#1798482611yescharacteristic
212C4—22no—
213C4—82no—
214C4—5564no—
215C4—5562no—
216C4—5561no—
217C2—22no—
218C2—21no—
219C2—21no—
220C2—21no—
221C2—22no—
222C2—42no—
223C2—11121no—
224C2#2258083011yescharacteristic
subgroupG/H
centerC2#22580830
commutatorC23×C139C22×C4
FrattiniC24C22×D139
FittingC2×#99×C139C2
socleC2×C139#386
prime radical#22581512C2
cosocleC24×C139C23
hypercenterC2×#99D139
hypocenterC139#1913
LCSG ▷ C23×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. #22581428C2semidirect
3. C2×#17984756C2semidirect
4. #22580720C2semidirect
5. C2×#99×C139C2semidirect
8. #17984823C4semidirect
11. #17984810C4semidirect
21. C23×D139C2×C4semidirect
30. C22×Dic139C2×C4semidirect
37. C22⋊Dic139C2×C4semidirect
38. C22⋊Dic139D4semidirect
112. C139#1913semidirect
117. C2×#99D139semidirect

Maximal subgroups

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

subgroupindex
#225815122
#225814282
C2×#179847562
#225807202
C2×#99×C1392
#1913139