Finite Group Databasebeta

← #31808388

Subgroups — #31808388

Order 17792.

354 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 45 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#22581139C212yesmaximal, complemented
2#22581120C211yesmaximal, characteristic, complemented
3#22580746C211yesmaximal, characteristic, complemented
4#22580740C212yesmaximal, complemented
5D42×C139C211yesmaximal, characteristic, complemented
6#17984887C2211yescharacteristic, complemented
7#17984868—21no—
8#17984811—22no—
9#17984770—21no—
10#17984759C2211yescharacteristic, complemented
11#17984757C2212yescomplemented
12#17984756—22no—
13C22×D4×C139—22no—
14#127×C139C2211yescharacteristic
15#121×C139—22no—
16#120×C139—21no—
17#120×C139C2212yes—
18C4×D4×C139—21no—
19#14555785—21no—
20#14555784—41no—
21C2×C22⋊D139—22no—
22C2×C22⋊D139—42no—
23D4×D139—41no—
24#14555773—41no—
25#14555770—41no—
26#14555769—21no—
27C22⋊Dic139—22no—
28C22⋊Dic139—42no—
29C24×C139—21no—
30C24×C139D412yescomplemented
31C2×D4×C139—21no—
32C2×D4×C139—22no—
33C2×D4×C139—22no—
34C2×D4×C139—22no—
35C2×D4×C139—48no—
36C2×D4×C139D411yescharacteristic, complemented
37C2×D4×C139C2311yescharacteristic
38C22×C4×C139—22no—
39C4⋊C4×C139—21no—
40C22⋊C4×C139—21no—
41C22⋊C4×C139—22no—
42C22⋊C4×C139D412yescomplemented
43C42×C139D411yescharacteristic, complemented
44C22×D139—22no—
45Dic278—21no—
46D556—21no—
47C22⋊D139—42no—
48C22⋊D139—41no—
49C22⋊D139—84no—
50C2×Dic139—22no—
51C2×Dic139—42no—
52C4×D139—41no—
53C139⋊C8—41no—
54C23×C139—22no—
55C23×C139—21no—
56C23×C139—44no—
57C23×C139—42no—
58C23×C139—44no—
59C23×C139—81no—
60C23×C139C2×D412yes—
61D4×C139—24no—
62D4×C139—41no—
63D4×C139—41no—
64D4×C139—44no—
65D4×C139—44no—
66D4×C139—44no—
67C2×C4×C139—21no—
68C2×C4×C139—22no—
69C2×C4×C139—44no—
70C2×C4×C139C2×D411yescharacteristic
71C22×C139—24no—
72C22×C139—22no—
73C22×C139—42no—
74C22×C139—42no—
75C22×C139—42no—
76C22×C139—44no—
77C22×C139—42no—
78C22×C139—41no—
79C22×C139—82no—
80C22×C139—84no—
81C22×C139#12011yescharacteristic
82C2×D139—41no—
83C2×D139—82no—
84C4×C139—22no—
85C4×C139—21no—
86C4×C139—42no—
87Dic139—41no—
88Dic139—82no—
89C2×C139—21no—
90C2×C139—42no—
91C2×C139—44no—
92C2×C139—81no—
93C2×C139B(4,𝔽2)11yescharacteristic
94D139—81no—
95C139#219611yescharacteristic, complemented, Sylow
96#2196—1391nomaximal, Sylow
97D42D13911yescharacteristic, complemented
98B(4,𝔽2)—1392no—
99#453—1391no—
100#353—1391no—
101AΣL(1,𝔽16)—1392no—
102H(5,𝔽2)—1391no—
103C22×D4—22no—
104AGL(1,ℤ/8)—2781no—
105#127C2×D13911yescharacteristic
106#121—22no—
107#120—21no—
108#120—2782no—
109#120C2×D13912yes—
110C4×D4—21no—
111#104—2781no—
112#100—1391no—
113#99—2782no—
114#99—1392no—
115C24—21no—
116C24C22⋊D13912yescomplemented
117#41—2781no—
118#41—5561no—
119C2×D4—21no—
120C2×D4—22no—
121C2×D4—22no—
122C2×D4—22no—
123C2×D4—48no—
124C2×D4—2782no—
125C2×D4—5561no—
126C2×D4—5562no—
127C2×D4C22⋊D13911yescharacteristic, complemented
128C2×D4C22×D13911yescharacteristic
129C22×C4—22no—
130SD16—5561no—
131D8—5561no—
132M16—2781no—
133C4⋊C4—21no—
134C22⋊C4—21no—
135C22⋊C4—22no—
136C22⋊C4—2782no—
137C22⋊C4—5562no—
138C22⋊C4C22⋊D13912yescomplemented
139C42C22⋊D13911yescharacteristic, complemented
140C23—22no—
141C23—21no—
142C23—42no—
143C23—44no—
144C23—44no—
145C23—81no—
146C23—2782no—
147C23C2×C22⋊D13912yes—
148Q8—2781no—
149D4—24no—
150D4—41no—
151D4—41no—
152D4—44no—
153D4—44no—
154D4—44no—
155D4—2781no—
156D4—5562no—
157D4—5561no—
158D4—11124no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—44no—
162C2×C4—2782no—
163C2×C4—5561no—
164C2×C4—5562no—
165C2×C4C2×C22⋊D13911yescharacteristic
166C8—5561no—
167C22—24no—
168C22—22no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—44no—
173C22—42no—
174C22—41no—
175C22—82no—
176C22—84no—
177C22—5561no—
178C22—11122no—
179C22#1798481111yescharacteristic
180C4—22no—
181C4—21no—
182C4—42no—
183C4—5561no—
184C4—11122no—
185C2—21no—
186C2—42no—
187C2—44no—
188C2—81no—
189C2—11121no—
190C2#2258114011yescharacteristic
subgroupG/H
centerC2#22581140
commutator, cosocleC2×D4×C139C23
FrattiniC2×D4C22×D139
FittingD42×C139C2
socleC2×C139B(4,𝔽2)
hypercenterD42D139
hypocenterC139#2196
LCSG ▷ C2×D4×C139 ▷ C22×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #22581139C2semidirect
2. #22581120C2semidirect
3. #22580746C2semidirect
4. #22580740C2semidirect
5. D42×C139C2semidirect
6. #17984887C22semidirect
10. #17984759C22semidirect
11. #17984757C22semidirect
30. C24×C139D4semidirect
36. C2×D4×C139D4semidirect
42. C22⋊C4×C139D4semidirect
43. C42×C139D4semidirect
95. C139#2196semidirect
97. D42D139semidirect
116. C24C22⋊D139semidirect
127. C2×D4C22⋊D139semidirect
138. C22⋊C4C22⋊D139semidirect
139. C42C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
#225811392
#225811202
#225807462
#225807402
D42×C1392
#2196139