Finite Group Databasebeta

← #31806951

Subgroups — #31806951

Order 17792.

340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 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#22581517C211yesmaximal, characteristic
2#22580937C211yesmaximal, characteristic, complemented
3C2×#17984758C212yesmaximal, complemented
4#22580725C212yesmaximal, complemented
5#568×C139C211yesmaximal, characteristic, complemented
6C22×D556C2211yescharacteristic
7C2×#14555769C2212yes—
8#17984838—21no—
9#17984831—21no—
10#17984816—22no—
11#17984810C414yes—
12#17984801C2211yescharacteristic
13#17984761—21no—
14#17984759—21no—
15#17984758—24no—
16C2×#41×C139C2211yescharacteristic
17#131×C139—24no—
18C2×M16×C139—22no—
19C2×M16×C139C2212yes—
20C23×D139C2×C412yes—
21C2×D556—21no—
22C2×D556—21no—
23C2×D556—22no—
24C2×D556—22no—
25C2×C22⋊D139—24no—
26#14555769—22no—
27#14555769—22no—
28C2×C139⋊C8—22no—
29C4⋊Dic139—21no—
30C22⋊Dic139C2×C412yes—
31(C2×D139)⋊C4—24no—
32C4×Dic139—21no—
33#41×C139—22no—
34#41×C139—22no—
35C2×Q8×C139D411yescharacteristic
36C2×D4×C139C2×C412yes—
37C2×D4×C139D411yescharacteristic
38C22×C4×C139D412yes—
39C22×C4×C139C2311yescharacteristic
40M16×C139—24no—
41M16×C139—22no—
42M16×C139D414yescomplemented
43C2×C8×C139—24no—
44C2×C8×C139—22no—
45C22×D139—22no—
46C22×D139—24no—
47C22×D139—82no—
48D556—41no—
49D556—42no—
50D556—41no—
51C22⋊D139—84no—
52C2×Dic139—22no—
53C139⋊C8—42no—
54C23×C139C22⋊C412yes—
55C23×C139C22×C411yescharacteristic
56Q8×C139—22no—
57D4×C139—24no—
58D4×C139—22no—
59C2×C4×C139—22no—
60C2×C4×C139—22no—
61C2×C4×C139C22⋊C412yes—
62C2×C4×C139C2×D412yes—
63C2×C4×C139C2×D411yescharacteristic
64C2×C4×C139C2×D411yescharacteristic
65C2×C4×C139#4112yes—
66C8×C139—24no—
67C22×C139—22no—
68C22×C139—41no—
69C22×C139—42no—
70C22×C139C2×C22⋊C411yescharacteristic
71C22×C139C4×D412yes—
72C2×D139—44no—
73C2×D139—42no—
74C2×D139—84no—
75C4×C139—22no—
76C4×C139#12011yescharacteristic
77C4×C139#12112yes—
78C4×C139#12311yescharacteristic
79Dic139—42no—
80C2×C139—21no—
81C2×C139—22no—
82C2×C139—42no—
83C2×C139#38611yescharacteristic
84D139—82no—
85C139#191411yescharacteristic, complemented, Sylow
86#1914—1391nomaximal, Sylow
87#568D13911yescharacteristic, complemented
88#535—1391no—
89#413—1391no—
90C2×#100—1392no—
91#344—1392no—
92C2×#41C2×D13911yescharacteristic
93C22×D4—1391no—
94#131—24no—
95C2×M16—22no—
96C2×M16—1392no—
97C2×M16C2×D13912yes—
98#127—2781no—
99#124—2781no—
100#121—2782no—
101#120—1394no—
102#117—1391no—
103#101—2781no—
104#100—2781no—
105#100—2784no—
106C24—1392no—
107#41—22no—
108#41—22no—
109C2×Q8D55611yescharacteristic
110C2×D4—2784no—
111C2×D4—2782no—
112C2×D4—2781no—
113C2×D4—2781no—
114C2×D4—2782no—
115C2×D4C4×D13912yes—
116C2×D4D55611yescharacteristic
117C22×C4C22⋊D13912yes—
118C22×C4C22×D13911yescharacteristic
119M16—24no—
120M16—22no—
121M16—2782no—
122M16—2782no—
123M16C22⋊D13914yescomplemented
124C2×C8—24no—
125C2×C8—22no—
126C2×C8—2782no—
127C4⋊C4—2781no—
128C22⋊C4—2784no—
129C22⋊C4—1392no—
130C42—2781no—
131C23—2782no—
132C23—2784no—
133C23—11122no—
134C23(C2×D139)⋊C412yes—
135C23C2×C4×D13911yescharacteristic
136Q8—22no—
137D4—24no—
138D4—22no—
139D4—5561no—
140D4—5562no—
141D4—5561no—
142D4—11124no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—2782no—
146C2×C4(C2×D139)⋊C412yes—
147C2×C4C2×C22⋊D13912yes—
148C2×C4C2×C22⋊D13911yescharacteristic
149C2×C4C2×D55611yescharacteristic
150C2×C4#1455578512yes—
151C8—24no—
152C8—5562no—
153C22—22no—
154C22—41no—
155C22—42no—
156C22—5564no—
157C22—5562no—
158C22—11124no—
159C22C2×(C2×D139)⋊C411yescharacteristic
160C22C4×C22⋊D13912yes—
161C4—22no—
162C4—5562no—
163C4#1798481111yescharacteristic
164C4#1798481612yes—
165C4#1798482511yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—11122no—
170C2#2258083211yescharacteristic
subgroupG/H
centerC2#22580832
commutatorC23×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#568×C139C2
socleC2×C139#386
prime radical#22581517C2
cosocleC22×C4×C139C23
hypercenter#568D139
hypocenterC139#1914
LCSG ▷ C23×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #22580937C2semidirect
3. C2×#17984758C2semidirect
4. #22580725C2semidirect
5. #568×C139C2semidirect
42. M16×C139D4semidirect
85. C139#1914semidirect
87. #568D139semidirect
123. M16C22⋊D139semidirect

Maximal subgroups

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

subgroupindex
#225815172
#225809372
C2×#179847582
#225807252
#568×C1392
#1914139