Finite Group Databasebeta

← #31806929

Subgroups — #31806929

Order 17792.

344 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 85 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#22581720C211yesmaximal, characteristic, complemented
2#22581517C211yesmaximal, characteristic
3#22580957C212yesmaximal, complemented
4#22580709C212yesmaximal, complemented
5#410×C139C211yesmaximal, characteristic, complemented
6C22×D556C2211yescharacteristic
7#17984849—24no—
8C2×#14555769—22no—
9C2×#14555769C2212yes—
10#17984838C412yescomplemented
11#17984831C412yescomplemented
12#17984816—22no—
13#17984810—22no—
14#17984801C2211yescharacteristic
15#17984762—24no—
16C2×#41×C139C2211yescharacteristic
17#117×C139C2212yes—
18#99×C139—22no—
19C23×D139—21no—
20C2×D556—22no—
21C2×D556—21no—
22C2×D556—22no—
23C2×D556C2×C412yes—
24C2×C22⋊D139—24no—
25#14555769—24no—
26#14555769—22no—
27#14555769—22no—
28C2×C139⋊C8—24no—
29C2×C139⋊C8D414yescomplemented
30C4⋊Dic139—21no—
31C22⋊Dic139—21no—
32(C2×D139)⋊C4—24no—
33C4×Dic139C2×C412yes—
34#41×C139—22no—
35#41×C139—22no—
36C2×Q8×C139C2×C411yescharacteristic
37C2×D4×C139C2×C411yescharacteristic
38C2×D4×C139D412yes—
39C22×C4×C139D412yes—
40C22×C4×C139C2311yescharacteristic
41C4⋊C4×C139—22no—
42C22⋊C4×C139—22no—
43C42×C139—22no—
44C22×D139—22no—
45C22×D139—42no—
46C22×D139—82no—
47D556—24no—
48D556—41no—
49D556—41no—
50C22⋊D139—84no—
51C2×Dic139—22no—
52C139⋊C8—24no—
53C23×C139C22⋊C412yes—
54C23×C139C2×D411yescharacteristic
55Q8×C139—22no—
56D4×C139—24no—
57D4×C139—22no—
58C2×C4×C139—22no—
59C2×C4×C139—22no—
60C2×C4×C139—42no—
61C2×C4×C139C22⋊C412yes—
62C2×C4×C139C22×C411yescharacteristic
63C2×C4×C139C2×D412yes—
64C2×C4×C139C2×D411yescharacteristic
65C2×C4×C139#4112yes—
66C22×C139—22no—
67C22×C139—41no—
68C22×C139—42no—
69C22×C139C2×C22⋊C411yescharacteristic
70C22×C139#12112yes—
71C2×D139—44no—
72C2×D139—42no—
73C2×D139—84no—
74C4×C139—22no—
75C4×C139—82no—
76C4×C139C4×D412yes—
77C4×C139#12011yescharacteristic
78C4×C139#12311yescharacteristic
79Dic139—42no—
80C2×C139—21no—
81C2×C139—22no—
82C2×C139—42no—
83C2×C139#38611yescharacteristic
84D139—82no—
85C139#191011yescharacteristic, complemented, Sylow
86#1910—1391nomaximal, Sylow
87#568—1391no—
88#535—1391no—
89#418—1392no—
90#410D13911yescharacteristic, complemented
91H(3,ℤ/4)—1392no—
92C2×#41C2×D13911yescharacteristic
93C22×D4—1391no—
94#131—2784no—
95C2×M16—2782no—
96C2×M16—1392no—
97#127—1392no—
98#124—1392no—
99#121—2782no—
100#120—2782no—
101#117—1391no—
102#117C2×D13912yes—
103#102—2784no—
104#99—22no—
105C24—2781no—
106#41—22no—
107#41—22no—
108C2×Q8C4×D13911yescharacteristic
109C2×D4—2784no—
110C2×D4—2782no—
111C2×D4—2781no—
112C2×D4—2782no—
113C2×D4—1392no—
114C2×D4C4×D13911yescharacteristic
115C2×D4C22⋊D13912yes—
116C22×C4D55612yes—
117C22×C4C22×D13911yescharacteristic
118M16—2784no—
119M16—2782no—
120M16—2782no—
121C2×C8—2784no—
122C2×C8—1394no—
123C4⋊C4—22no—
124C4⋊C4—2781no—
125C22⋊C4—22no—
126C22⋊C4—2781no—
127C22⋊C4—2784no—
128C42—22no—
129C42—1392no—
130C23—2782no—
131C23—5562no—
132C23—11122no—
133C23(C2×D139)⋊C412yes—
134C23C2×C22⋊D13911yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—2784no—
139D4—5561no—
140D4—5561no—
141D4—11124no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—42no—
145C2×C4—2782no—
146C2×C4(C2×D139)⋊C412yes—
147C2×C4C2×C4×D13911yescharacteristic
148C2×C4D4×D13912yes—
149C2×C4C2×D55611yescharacteristic
150C2×C4#1455578412yes—
151C8—2784no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—5564no—
156C22—5562no—
157C22—11124no—
158C22C2×(C2×D139)⋊C411yescharacteristic
159C22#1798481412yes—
160C4—22no—
161C4—82no—
162C4—5562no—
163C4(C22⋊D139)⋊C412yes—
164C4#1798481211yescharacteristic
165C4#1798482611yescharacteristic
166C2—22no—
167C2—21no—
168C2—42no—
169C2—11122no—
170C2#2258083011yescharacteristic
subgroupG/H
centerC2#22580830
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#410×C139C2
socleC2×C139#386
prime radical#22581517C2
cosocleC22×C4×C139C23
hypercenter#410D139
hypocenterC139#1910
LCSG ▷ C2×C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #22581720C2semidirect
3. #22580957C2semidirect
4. #22580709C2semidirect
5. #410×C139C2semidirect
10. #17984838C4semidirect
11. #17984831C4semidirect
29. C2×C139⋊C8D4semidirect
85. C139#1910semidirect
90. #410D139semidirect

Maximal subgroups

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

subgroupindex
#225817202
#225815172
#225809572
#225807092
#410×C1392
#1910139