Finite Group Databasebeta

← #31816777

Subgroups — #31816777

Order 17792.

484 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 121 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#22581509C211yesmaximal, characteristic, complemented
2#127×D139C211yesmaximal, characteristic
3#22581319C211yesmaximal, characteristic, complemented
4#22581318C211yesmaximal, characteristic, complemented
5#22581317C211yesmaximal, characteristic, complemented
6#22581298C214yesmaximal, complemented
7#22580956C214yesmaximal, complemented
8#22580905C211yesmaximal, characteristic, complemented
9#490×C139C211yesmaximal, characteristic, complemented
10C2×D4×D139—22no—
11C2×D4×D139C2212yes—
12C2×#14555768C2212yes—
13#17984841C2212yescomplemented
14#17984839C2211yescharacteristic
15#17984838—22no—
16#17984838C2212yes—
17#17984834C2211yescharacteristic, complemented
18#17984820—22no—
19#17984807—22no—
20#17984800C2212yes—
21C42×D139C2211yescharacteristic
22#17984764C2214yescomplemented
23#17984763C2214yescomplemented
24#17984762C2214yescomplemented
25#17984753C2211yescharacteristic, complemented
26C8×Dic139C2212yescomplemented
27#127×C139C2211yescharacteristic
28#125×C139C2211yescharacteristic, complemented
29#102×C139C2214yescomplemented
30#97×C139C2211yescharacteristic, complemented
31C23×D139—22no—
32C2×Dic278—22no—
33C2×D556—22no—
34C2×D556C2312yes—
35C2×C22⋊D139—22no—
36C2×C22⋊D139—24no—
37D4×D139—28no—
38D4×D139—48no—
39C2×C4×D139D412yes—
40C2×C4×D139C2311yescharacteristic
41#14555768—24no—
42C2×C139⋊C8C2312yes—
43C4⋊Dic139C2312yes—
44Dic139⋊C4—22no—
45Dic139⋊C4—22no—
46(C2×D139)⋊C4—22no—
47C4×Dic139—22no—
48C4×Dic139D412yes—
49C4×Dic139C2311yescharacteristic
50C2×D4×C139—22no—
51C2×D4×C139C2312yes—
52C2×C8×C139C2312yes—
53C4⋊C4×C139—22no—
54C4⋊C4×C139C2312yes—
55C42×C139C2311yescharacteristic
56C22×D139—22no—
57C22×D139—48no—
58C22×D139—44no—
59C22×D139C2×D411yescharacteristic
60Dic278—44no—
61D556—24no—
62D556—44no—
63C22⋊D139—44no—
64C22⋊D139—48no—
65C2×Dic139—22no—
66C2×Dic139C2×D411yescharacteristic
67C2×Dic139C2×D412yes—
68C4×D139—24no—
69C4×D139#4114yes—
70C139⋊C8—22no—
71C23×C139—22no—
72D4×C139—24no—
73D4×C139—44no—
74C2×C4×C139—22no—
75C2×C4×C139C2×D412yes—
76C2×C4×C139C2411yescharacteristic
77C8×C139—22no—
78C22×C139—42no—
79C22×C139—44no—
80C22×C139C22×D411yescharacteristic
81C2×D139—22no—
82C2×D139—42no—
83C2×D139—44no—
84C2×D139—88no—
85C2×D139#12412yes—
86C4×C139—22no—
87C4×C139—42no—
88C4×C139C2×#4112yes—
89Dic139—42no—
90Dic139#12412yes—
91Dic139AGL(1,ℤ/8)14yes—
92C2×C139—82no—
93C2×C139C2×#12411yescharacteristic
94C2×C139C2×AGL(1,ℤ/8)12yes—
95D139—22no—
96D139—82no—
97C139#313811yescharacteristic, complemented, Sylow
98#3138—1391nomaximal, Sylow
99#533—1391no—
100C2×#127—1391no—
101#490—1391no—
102#490—1391no—
103#490—1391no—
104#490D13911yescharacteristic, complemented
105#486—1394no—
106#418—1394no—
107C4×M16—1391no—
108C22×D4—2782no—
109C22×D4—1392no—
110C2×M16—1392no—
111C4⋊Q8—1392no—
112#127—2782no—
113#127—1392no—
114#127—1391no—
115#127C2×D13911yescharacteristic
116#125—1391no—
117#125C2×D13911yescharacteristic, complemented
118C22⋊Q8—2782no—
119C4×Q8—2782no—
120#117—1392no—
121C2×C42—1391no—
122#102—1394no—
123#102—1394no—
124#102—1394no—
125#102C2×D13914yescomplemented
126#97—1391no—
127#97C2×D13911yescharacteristic, complemented
128C4×C8—1392no—
129C24—2782no—
130C2×Q8—2782no—
131C2×D4—22no—
132C2×D4—2788no—
133C2×D4—2782no—
134C2×D4—2784no—
135C2×D4—2782no—
136C2×D4—5568no—
137C2×D4—1392no—
138C2×D4C22×D13912yes—
139C22×C4—1392no—
140C22×C4—1391no—
141M16—2784no—
142C2×C8—1392no—
143C2×C8C22×D13912yes—
144C4⋊C4—22no—
145C4⋊C4—2782no—
146C4⋊C4—2782no—
147C4⋊C4—1392no—
148C4⋊C4C22×D13912yes—
149C22⋊C4—2782no—
150C42—2782no—
151C42—1392no—
152C42—1391no—
153C42C22×D13911yescharacteristic
154C23—22no—
155C23—2782no—
156C23—5568no—
157C23—5564no—
158C23—1391no—
159Q8—5564no—
160D4—24no—
161D4—44no—
162D4—2784no—
163D4—5564no—
164D4—5564no—
165D4—5568no—
166C2×C4—22no—
167C2×C4—2784no—
168C2×C4—2782no—
169C2×C4—1391no—
170C2×C4—1392no—
171C2×C4—1394no—
172C2×C4D4×D13912yes—
173C2×C4C23×D13911yescharacteristic
174C8—22no—
175C8—2782no—
176C22—42no—
177C22—44no—
178C22—2782no—
179C22—5562no—
180C22—5564no—
181C22—11128no—
182C22—1392no—
183C22C2×D4×D13911yescharacteristic
184C4—22no—
185C4—42no—
186C4—5562no—
187C4—1392no—
188C4—1394no—
189C4#41×D13912yes—
190C2—82no—
191C2—2782no—
192C2—11122no—
193C2#124×D13911yescharacteristic
194C2AGL(1,ℤ/8)×D13912yes—
subgroupG/H
centerC22C2×D4×D139
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#490×C139C2
socleC22×C139C22×D4
prime radical#127×D139C2
hypercenter#490D139
hypocenterC139#3138
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #22581509C2semidirect
3. #22581319C2semidirect
4. #22581318C2semidirect
5. #22581317C2semidirect
6. #22581298C2semidirect
7. #22580956C2semidirect
8. #22580905C2semidirect
9. #490×C139C2semidirect
13. #17984841C22semidirect
17. #17984834C22semidirect
22. #17984764C22semidirect
23. #17984763C22semidirect
24. #17984762C22semidirect
25. #17984753C22semidirect
26. C8×Dic139C22semidirect
28. #125×C139C22semidirect
29. #102×C139C22semidirect
30. #97×C139C22semidirect
97. C139#3138semidirect
104. #490D139semidirect
117. #125C2×D139semidirect
125. #102C2×D139semidirect
127. #97C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815092
#127×D1392
#225813192
#225813182
#225813172
#225812982
#225809562
#225809052
#490×C1392
#3138139