Finite Group Databasebeta

← #31808074

Subgroups — #31808074

Order 17792.

270 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 55 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#22581516C211yesmaximal, characteristic
2#22580925C212yesmaximal, complemented
3#22580746C211yesmaximal, characteristic, complemented
4#22580745C212yesmaximal, complemented
5#353×C139C211yesmaximal, characteristic, complemented
6C2×#14555784C2211yescharacteristic
7C2×D4×D139C411yescharacteristic, complemented
8#17984838C2211yescharacteristic
9#17984830C411yescharacteristic, complemented
10#17984829C411yescharacteristic, complemented
11#17984814—22no—
12#17984810—22no—
13#17984799C411yescharacteristic, complemented
14#17984798—22no—
15#17984757C2212yescomplemented
16#17984756—22no—
17#127×C139C2211yescharacteristic
18#99×C139C2212yescomplemented
19C23×D139—21no—
20#14555784—42no—
21C2×Dic278C2×C411yescharacteristic
22C2×D556C2×C411yescharacteristic
23C2×C22⋊D139—21no—
24C2×C22⋊D139—22no—
25C2×C22⋊D139D412yes—
26D4×D139—42no—
27C22×Dic139D412yes—
28C2×C4×D139C2×C411yescharacteristic
29Dic139⋊C4—21no—
30Dic139⋊C4—42no—
31C22⋊Dic139—22no—
32C22⋊Dic139—22no—
33(C2×D139)⋊C4—21no—
34(C2×D139)⋊C4—22no—
35C4×Dic139—42no—
36C4×Dic139C2×C411yescharacteristic
37C2×D4×C139—22no—
38C2×D4×C139C2×C411yescharacteristic
39C2×D4×C139C2311yescharacteristic
40C22⋊C4×C139—22no—
41C42×C139C2×C411yescharacteristic
42C22×D139—21no—
43C22×D139—42no—
44C22×D139—82no—
45C22×D139C22⋊C411yescharacteristic
46Dic278—41no—
47D556—41no—
48C22⋊D139—42no—
49C22⋊D139—42no—
50C22⋊D139—82no—
51C2×Dic139—22no—
52C2×Dic139—22no—
53C2×Dic139—21no—
54C2×Dic139—42no—
55C2×Dic139C22⋊C412yes—
56C2×Dic139C22⋊C411yescharacteristic
57C4×D139—22no—
58C23×C139—21no—
59C23×C139C2×D412yes—
60D4×C139—41no—
61D4×C139—41no—
62D4×C139—82no—
63C2×C4×C139—21no—
64C2×C4×C139—42no—
65C2×C4×C139C22×C411yescharacteristic
66C22×C139—22no—
67C22×C139—42no—
68C22×C139—42no—
69C22×C139—41no—
70C22×C139C2×C22⋊C411yescharacteristic
71C2×D139—21no—
72C2×D139—41no—
73C2×D139—42no—
74C2×D139—41no—
75C2×D139—84no—
76C4×C139—21no—
77C4×C139—41no—
78C4×C139—82no—
79Dic139—22no—
80Dic139—41no—
81Dic139—82no—
82Dic139#9912yes—
83C2×C139—21no—
84C2×C139—42no—
85C2×C139—81no—
86C2×C139C2×#9911yescharacteristic
87D139—41no—
88D139—81no—
89C139#212811yescharacteristic, complemented, Sylow
90#2128—1391nomaximal, Sylow
91#535—1391no—
92#410—1392no—
93#353—1391no—
94#353—1392no—
95#353D13911yescharacteristic, complemented
96C2×#41—1391no—
97C22×D4—1391no—
98#127—1391no—
99#127C2×D13911yescharacteristic
100#124—1391no—
101#124—1391no—
102#121—2782no—
103#120—2782no—
104#117—2782no—
105#117—1391no—
106#99—2782no—
107#99—1392no—
108#99C2×D13912yescomplemented
109C24—2781no—
110#41—5562no—
111C2×Q8—1391no—
112C2×D4—22no—
113C2×D4—2782no—
114C2×D4—2781no—
115C2×D4—5562no—
116C2×D4—1392no—
117C2×D4—1391no—
118C2×D4C4×D13911yescharacteristic
119C2×D4C22×D13911yescharacteristic
120C22×C4—1392no—
121C22×C4—1391no—
122C4⋊C4—2781no—
123C4⋊C4—5562no—
124C22⋊C4—22no—
125C22⋊C4—2781no—
126C22⋊C4—2782no—
127C22⋊C4—2782no—
128C22⋊C4—2782no—
129C42—5562no—
130C42—1391no—
131C42C4×D13911yescharacteristic
132C23—21no—
133C23—2781no—
134C23—5562no—
135C23—11122no—
136C23—1391no—
137C23D4×D13912yes—
138Q8—5561no—
139D4—41no—
140D4—41no—
141D4—82no—
142D4—5561no—
143D4—5562no—
144D4—5562no—
145D4—11122no—
146C2×C4—21no—
147C2×C4—42no—
148C2×C4—2782no—
149C2×C4—2782no—
150C2×C4—2782no—
151C2×C4—2781no—
152C2×C4—5562no—
153C2×C4—1392no—
154C2×C4—1391no—
155C2×C4C2×C4×D13911yescharacteristic
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—2781no—
161C22—5561no—
162C22—5562no—
163C22—5561no—
164C22—11124no—
165C22C22⋊C4×D13911yescharacteristic
166C4—21no—
167C4—41no—
168C4—82no—
169C4—2782no—
170C4—5561no—
171C4—11122no—
172C4—1392no—
173C2—21no—
174C2—42no—
175C2—81no—
176C2—5561no—
177C2—11121no—
178C2#99×D13911yescharacteristic
subgroupG/H
centerC2#99×D139
commutatorC2×C4×C139C22×C4
FrattiniC2×D4C22×D139
Fitting#353×C139C2
socleC2×C139C2×#99
prime radical#22581516C2
cosocleC2×D4×C139C23
hypercenter#353D139
hypocenterC139#2128
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #22580925C2semidirect
3. #22580746C2semidirect
4. #22580745C2semidirect
5. #353×C139C2semidirect
7. C2×D4×D139C4semidirect
9. #17984830C4semidirect
10. #17984829C4semidirect
13. #17984799C4semidirect
15. #17984757C22semidirect
18. #99×C139C22semidirect
89. C139#2128semidirect
95. #353D139semidirect
108. #99C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815162
#225809252
#225807462
#225807452
#353×C1392
#2128139