Finite Group Databasebeta

← #31808400

Subgroups — #31808400

Order 17792.

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

normal subgroups only

This group has 246 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#22581142C212yesmaximal, complemented
2#22581120C211yesmaximal, characteristic
3#22580746C211yesmaximal, characteristic, complemented
4#22580743C212yesmaximal, complemented
5#559×C139C211yesmaximal, characteristic, complemented
6#17984887C2211yescharacteristic
7#17984868—21no—
8#17984825—22no—
9#17984770—21no—
10#17984759C2211yescharacteristic
11#17984757C2212yes—
12#17984756—22no—
13#127×C139C2211yescharacteristic
14#124×C139—22no—
15#123×C139—21no—
16#123×C139C2212yes—
17C4×Q8×C139—21no—
18C4×D4×C139—22no—
19#14555785—21no—
20#14555784—41no—
21C2×C22⋊D139—22no—
22D4×D139—41no—
23#14555773—41no—
24#14555770—41no—
25#14555769—21no—
26Dic139⋊C4—42no—
27C22⋊Dic139—22no—
28(C2×D139)⋊C4—42no—
29C2×Q8×C139—21no—
30C2×D4×C139—22no—
31C2×D4×C139D411yescharacteristic
32C2×D4×C139C2311yescharacteristic
33C22×C4×C139—21no—
34C22×C4×C139D412yes—
35C4⋊C4×C139—21no—
36C4⋊C4×C139—22no—
37C22⋊C4×C139—22no—
38C22⋊C4×C139—21no—
39C22⋊C4×C139—22no—
40C22⋊C4×C139D412yes—
41C42×C139—22no—
42C42×C139D411yescharacteristic
43C22×D139—22no—
44Dic278—21no—
45D556—21no—
46C22⋊D139—42no—
47C22⋊D139—41no—
48C2×Dic139—22no—
49C2×Dic139—42no—
50C4×D139—41no—
51C139⋊C8—41no—
52C23×C139—21no—
53C23×C139C2×D412yes—
54Q8×C139—42no—
55D4×C139—41no—
56D4×C139—41no—
57D4×C139—44no—
58C2×C4×C139—21no—
59C2×C4×C139—22no—
60C2×C4×C139—22no—
61C2×C4×C139—42no—
62C2×C4×C139—81no—
63C2×C4×C139C2×D411yescharacteristic
64C22×C139—22no—
65C22×C139—42no—
66C22×C139—42no—
67C22×C139—41no—
68C22×C139#12011yescharacteristic
69C2×D139—41no—
70C2×D139—82no—
71C4×C139—22no—
72C4×C139—21no—
73C4×C139—42no—
74C4×C139—42no—
75Dic139—41no—
76Dic139—82no—
77C2×C139—21no—
78C2×C139—42no—
79C2×C139—81no—
80C2×C139B(4,𝔽2)11yescharacteristic
81D139—81no—
82C139#219811yescharacteristic, complemented, Sylow
83#2198—1391nomaximal, Sylow
84#559D13911yescharacteristic, complemented
85#458—1392no—
86#453—1391no—
87#353—1391no—
88#352—1392no—
89H(5,𝔽2)—1391no—
90AGL(1,ℤ/8)—2781no—
91#127C2×D13911yescharacteristic
92#124—22no—
93#123—21no—
94#123—2782no—
95#123C2×D13912yes—
96C4×Q8—21no—
97C4×D4—22no—
98#104—2781no—
99#100—1391no—
100#99—2782no—
101#99—1392no—
102#41—2781no—
103#41—5561no—
104C2×Q8—21no—
105C2×D4—22no—
106C2×D4—2782no—
107C2×D4—5561no—
108C2×D4C22⋊D13911yescharacteristic
109C2×D4C22×D13911yescharacteristic
110C22×C4—21no—
111C22×C4C22⋊D13912yes—
112SD16—5561no—
113D8—5561no—
114M16—2781no—
115C4⋊C4—21no—
116C4⋊C4—22no—
117C4⋊C4—5562no—
118C22⋊C4—22no—
119C22⋊C4—21no—
120C22⋊C4—22no—
121C22⋊C4—2782no—
122C22⋊C4—5562no—
123C22⋊C4C22⋊D13912yes—
124C42—22no—
125C42C22⋊D13911yescharacteristic
126C23—21no—
127C23—2782no—
128C23C2×C22⋊D13912yes—
129Q8—42no—
130Q8—2781no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—2781no—
135D4—5562no—
136D4—5561no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—81no—
142C2×C4—2782no—
143C2×C4—5561no—
144C2×C4—5562no—
145C2×C4C2×C22⋊D13911yescharacteristic
146C8—5561no—
147C22—22no—
148C22—42no—
149C22—42no—
150C22—41no—
151C22—5561no—
152C22—11122no—
153C22#1798481111yescharacteristic
154C4—22no—
155C4—21no—
156C4—42no—
157C4—42no—
158C4—5561no—
159C4—11122no—
160C2—21no—
161C2—42no—
162C2—81no—
163C2—11121no—
164C2#2258114011yescharacteristic
subgroupG/H
centerC2#22581140
commutator, cosocleC2×D4×C139C23
FrattiniC2×D4C22×D139
Fitting#559×C139C2
socleC2×C139B(4,𝔽2)
prime radical#22581120C2
hypercenter#559D139
hypocenterC139#2198
LCSG ▷ C2×D4×C139 ▷ C22×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #22581142C2semidirect
3. #22580746C2semidirect
4. #22580743C2semidirect
5. #559×C139C2semidirect
82. C139#2198semidirect
84. #559D139semidirect

Maximal subgroups

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

subgroupindex
#225811422
#225811202
#225807462
#225807432
#559×C1392
#2198139