Finite Group Databasebeta

← #31818197

Subgroups — #31818197

Order 17792.

460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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#22581759C214yesmaximal, complemented
2#22581213C214yesmaximal, complemented
3#22581135C212yesmaximal, complemented
4#22581120C212yesmaximal, complemented
5#22581071C212yesmaximal, complemented
6#492×C139C211yesmaximal, characteristic, complemented
7#17984890C2212yes—
8#17984887C2212yescomplemented
9#17984873C2214yescomplemented
10#17984871—24no—
11#17984869—24no—
12#17984868C2214yes—
13#17984864C2212yes—
14#17984863—24no—
15SD16×D139—24no—
16#17984848C2214yescomplemented
17#17984778C2212yescomplemented
18#17984770C2214yescomplemented
19#17984761C2212yescomplemented
20#17984759C2212yescomplemented
21C2×SD16×C139C2214yescomplemented
22C4⋊Q8×C139C2211yescharacteristic, complemented
23#127×C139C2211yescharacteristic
24C4×C8×C139C2211yescharacteristic, complemented
25#14555786—24no—
26#14555785—42no—
27#14555785C2314yes—
28#14555784—24no—
29Q8×D139—24no—
30C2×C22⋊D139—42no—
31D4×D139—24no—
32Dic556D412yescomplemented
33#14555775—24no—
34#14555774D414yescomplemented
35#14555773—24no—
36#14555772—24no—
37D1112D412yescomplemented
38#14555770—24no—
39#14555769C2314yes—
40#14555768—24no—
41C8×D139—24no—
42C2×Q8×C139C2312yes—
43C2×D4×C139—41no—
44C2×D4×C139C2312yes—
45SD16×C139—24no—
46SD16×C139—24no—
47C2×C8×C139C2312yes—
48C4⋊C4×C139—41no—
49C42×C139C2311yescharacteristic
50C22×D139—42no—
51Dic278—42no—
52Dic278C2×D414yes—
53D556—42no—
54D556C2×D414yes—
55C22⋊D139—24no—
56C22⋊D139—44no—
57C2×Dic139—42no—
58C4×D139—24no—
59C4×D139—44no—
60C139⋊C8—24no—
61C23×C139—22no—
62Q8×C139—24no—
63D4×C139—24no—
64D4×C139—82no—
65C2×C4×C139—21no—
66C2×C4×C139—22no—
67C2×C4×C139C2411yescharacteristic
68C8×C139C2×D412yes—
69C8×C139C2×D412yes—
70C22×C139—42no—
71C22×C139—82no—
72C22×C139H(5,𝔽2)11yescharacteristic
73C2×D139—24no—
74C2×D139—162no—
75C4×C139—22no—
76C4×C139—42no—
77C4×C139C22×D412yes—
78Dic139—24no—
79C2×C139—21no—
80C2×C139—82no—
81C2×C139D4211yescharacteristic
82D139—44no—
83C139#329111yescharacteristic, complemented, Sylow
84#3291—1391nomaximal, Sylow
85#577—1394no—
86#492D13911yescharacteristic, complemented
87#471—1394no—
88#456—1392no—
89#453—1392no—
90#443—1392no—
912−1+4—1392no—
92H(5,𝔽2)—1392no—
93#137—2784no—
94#137—1394no—
95AGL(1,ℤ/8)—2784no—
96AGL(1,ℤ/8)—1394no—
97#135—2784no—
98#135—1392no—
99C2×SD16—2784no—
100C2×SD16C2×D13914yescomplemented
101#131—1394no—
102C4⋊Q8C2×D13911yescharacteristic, complemented
103#127C2×D13911yescharacteristic
104#108—1392no—
105#104—1394no—
106#101—1392no—
107#100—1392no—
108C4×C8C2×D13911yescharacteristic, complemented
109#41—2784no—
110#41—2784no—
111#41—5562no—
112#41—1394no—
113C2×Q8—2784no—
114C2×Q8C22×D13912yes—
115C2×D4—41no—
116C2×D4—2784no—
117C2×D4—5562no—
118C2×D4C22×D13912yes—
119Q16—2784no—
120Q16—1392no—
121SD16—24no—
122SD16—24no—
123SD16—2784no—
124SD16—2784no—
125SD16—1394no—
126D8—2784no—
127D8—1392no—
128M16—2784no—
129M16—1394no—
130C2×C8—2784no—
131C2×C8C22×D13912yes—
132C4⋊C4—41no—
133C42C22×D13911yescharacteristic
134C23—22no—
135C23—5562no—
136Q8—24no—
137Q8—5562no—
138Q8—1394no—
139D4—24no—
140D4—82no—
141D4—2784no—
142D4—5562no—
143D4—5564no—
144D4—1394no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—2784no—
148C2×C4—5564no—
149C2×C4—5562no—
150C2×C4C23×D13911yescharacteristic
151C8—2784no—
152C8D4×D13912yes—
153C8D4×D13912yes—
154C22—42no—
155C22—82no—
156C22—2784no—
157C22—22242no—
158C22#1798488711yescharacteristic
159C4—22no—
160C4—42no—
161C4—2784no—
162C4C2×D4×D13912yes—
163C2—21no—
164C2—82no—
165C2—5564no—
166C2#2258158811yescharacteristic
subgroupG/H
centerC2#22581588
commutator, cosocleC2×C4×C139C24
FrattiniC2×C4C23×D139
Fitting#492×C139C2
socleC2×C139D42
hypercenter#492D139
hypocenterC139#3291
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #22581759C2semidirect
2. #22581213C2semidirect
3. #22581135C2semidirect
4. #22581120C2semidirect
5. #22581071C2semidirect
6. #492×C139C2semidirect
8. #17984887C22semidirect
9. #17984873C22semidirect
16. #17984848C22semidirect
17. #17984778C22semidirect
18. #17984770C22semidirect
19. #17984761C22semidirect
20. #17984759C22semidirect
21. C2×SD16×C139C22semidirect
22. C4⋊Q8×C139C22semidirect
24. C4×C8×C139C22semidirect
32. Dic556D4semidirect
34. #14555774D4semidirect
37. D1112D4semidirect
83. C139#3291semidirect
86. #492D139semidirect
100. C2×SD16C2×D139semidirect
102. C4⋊Q8C2×D139semidirect
108. C4×C8C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225817592
#225812132
#225811352
#225811202
#225810712
#492×C1392
#3291139