Finite Group Databasebeta

← #31808072

Subgroups — #31808072

Order 17792.

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

normal subgroups only

This group has 286 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#22581521C211yesmaximal, characteristic
2#99×D139C212yesmaximal, complemented
3#22580748C211yesmaximal, characteristic, complemented
4#22580745C212yesmaximal, complemented
5#354×C139C211yesmaximal, characteristic, complemented
6C2×#14555786C411yescharacteristic, complemented
7C2×D4×D139C2211yescharacteristic
8#17984839C411yescharacteristic, complemented
9#17984838C2211yescharacteristic
10#17984831C411yescharacteristic, complemented
11#17984815—22no—
12#17984812—22no—
13#17984799C411yescharacteristic, complemented
14C22⋊C4×D139—22no—
15#17984757C2212yes—
16#17984756—22no—
17#124×C139C2211yescharacteristic
18#99×C139C2212yes—
19C23×D139D412yes—
20#14555786—42no—
21C2×D556—21no—
22C2×D556—22no—
23C2×D556C2×C411yescharacteristic
24C2×D556C2×C411yescharacteristic, complemented
25C2×C22⋊D139—22no—
26C2×C22⋊D139D412yes—
27D4×D139—42no—
28C2×C4×D139—21no—
29C2×C4×D139—42no—
30C2×C4×D139C2×C411yescharacteristic
31Dic139⋊C4—21no—
32C22⋊Dic139—22no—
33(C2×D139)⋊C4—21no—
34(C2×D139)⋊C4—22no—
35(C2×D139)⋊C4—42no—
36C4×Dic139C2×C411yescharacteristic, complemented
37C2×Q8×C139C2×C411yescharacteristic, complemented
38C2×D4×C139C2311yescharacteristic
39C22⋊C4×C139—22no—
40C22⋊C4×C139—22no—
41C42×C139C2×C411yescharacteristic, complemented
42C22×D139—22no—
43C22×D139—22no—
44C22×D139—21no—
45C22×D139—82no—
46C22×D139C22⋊C412yes—
47C22×D139C22⋊C411yescharacteristic
48D556—41no—
49D556—41no—
50D556—42no—
51D556—82no—
52C22⋊D139—42no—
53C22⋊D139—82no—
54C2×Dic139—21no—
55C2×Dic139—42no—
56C2×Dic139C22⋊C411yescharacteristic
57C4×D139—22no—
58C4×D139—42no—
59C4×D139—84no—
60C23×C139C2×D412yes—
61Q8×C139—41no—
62D4×C139—41no—
63C2×C4×C139—21no—
64C2×C4×C139—21no—
65C2×C4×C139—42no—
66C2×C4×C139C22×C411yescharacteristic
67C22×C139—22no—
68C22×C139—42no—
69C22×C139C2×C22⋊C411yescharacteristic
70C2×D139—22no—
71C2×D139—41no—
72C2×D139—44no—
73C2×D139—42no—
74C2×D139—42no—
75C2×D139—41no—
76C2×D139—82no—
77C2×D139#9912yes—
78C4×C139—21no—
79C4×C139—41no—
80C4×C139—41no—
81C4×C139—82no—
82Dic139—21no—
83Dic139—41no—
84Dic139—82no—
85C2×C139—21no—
86C2×C139—42no—
87C2×C139C2×#9911yescharacteristic
88D139—22no—
89D139—42no—
90D139—81no—
91C139#212711yescharacteristic, complemented, Sylow
92#2127—1391nomaximal, Sylow
93#535—1391no—
94C2×#99—1392no—
95#354—1391no—
96#354D13911yescharacteristic, complemented
97#353—1392no—
98C2×#41—1391no—
99C22×D4—1391no—
100#127—1391no—
101#127—1391no—
102#124—1391no—
103#124C2×D13911yescharacteristic
104#121—2782no—
105#120—2782no—
106#117—1391no—
107C2×C22⋊C4—2782no—
108#99—2782no—
109#99—1392no—
110#99C2×D13912yes—
111C24—1392no—
112#41—5562no—
113C2×Q8C4×D13911yescharacteristic, complemented
114C2×D4—2781no—
115C2×D4—2782no—
116C2×D4—2782no—
117C2×D4—5562no—
118C2×D4—1392no—
119C2×D4—1391no—
120C2×D4—1391no—
121C2×D4C22×D13911yescharacteristic
122C22×C4—2781no—
123C22×C4—5562no—
124C22×C4—1391no—
125C4⋊C4—2781no—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C22⋊C4—2781no—
129C22⋊C4—2782no—
130C22⋊C4—2782no—
131C22⋊C4—5562no—
132C42—1391no—
133C42C4×D13911yescharacteristic, complemented
134C23—2782no—
135C23—2782no—
136C23—2781no—
137C23—11122no—
138C23—1392no—
139C23—1391no—
140C23D4×D13912yes—
141Q8—41no—
142D4—41no—
143D4—5561no—
144D4—5561no—
145D4—5562no—
146D4—5562no—
147D4—11122no—
148D4—11122no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—2782no—
153C2×C4—2781no—
154C2×C4—5562no—
155C2×C4—5562no—
156C2×C4—11124no—
157C2×C4—1391no—
158C2×C4C2×C4×D13911yescharacteristic
159C22—22no—
160C22—42no—
161C22—2782no—
162C22—5561no—
163C22—5562no—
164C22—5562no—
165C22—5564no—
166C22—5561no—
167C22—11122no—
168C22—1392no—
169C22C22⋊C4×D13911yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—2781no—
175C4—5561no—
176C4—11122no—
177C2—21no—
178C2—42no—
179C2—2782no—
180C2—5562no—
181C2—11121no—
182C2#99×D13911yescharacteristic
subgroupG/H
centerC2#99×D139
commutatorC2×C4×C139C22×C4
FrattiniC2×D4C22×D139
Fitting#354×C139C2
socleC2×C139C2×#99
prime radical#22581521C2
cosocleC2×D4×C139C23
hypercenter#354D139
hypocenterC139#2127
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
2. #99×D139C2semidirect
3. #22580748C2semidirect
4. #22580745C2semidirect
5. #354×C139C2semidirect
6. C2×#14555786C4semidirect
8. #17984839C4semidirect
10. #17984831C4semidirect
13. #17984799C4semidirect
24. C2×D556C2×C4semidirect
36. C4×Dic139C2×C4semidirect
37. C2×Q8×C139C2×C4semidirect
41. C42×C139C2×C4semidirect
91. C139#2127semidirect
96. #354D139semidirect
113. C2×Q8C4×D139semidirect
133. C42C4×D139semidirect

Maximal subgroups

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

subgroupindex
#225815212
#99×D1392
#225807482
#225807452
#354×C1392
#2127139