Finite Group Databasebeta

← #2039×C239 #44480809

Subgroups — #2039×C239 #44480809

Order 30592.

306 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 84 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#537×C239C211yesmaximal, characteristic
2C2×#104×C239C212yesmaximal, complemented
3#417×C239C212yesmaximal, complemented
4#384×C239C211yesmaximal, characteristic, complemented
5#343×C239C211yesmaximal, characteristic, complemented
6C2×#41×C239C2212yes—
7C2×M16×C239C2212yes—
8C22⋊Q8×C239—22no—
9#121×C239—22no—
10#121×C239—22no—
11C2×C4⋊C4×C239—22no—
12C2×C4⋊C4×C239C2211yescharacteristic
13C2×C4⋊C4×C239C2211yescharacteristic
14C2×C42×C239C2211yescharacteristic
15#104×C239—24no—
16#103×C239—22no—
17#102×C239—22no—
18#41×C239—22no—
19#41×C239—22no—
20#41×C239—22no—
21#41×C239—22no—
22C2×Q8×C239D412yes—
23C2×D4×C239—22no—
24C2×D4×C239—22no—
25C2×D4×C239D412yes—
26C22×C4×C239—21no—
27C22×C4×C239—22no—
28C22×C4×C239—21no—
29C22×C4×C239D412yes—
30C22×C4×C239C2311yescharacteristic
31M16×C239—22no—
32M16×C239—22no—
33C2×C8×C239—22no—
34C4⋊C4×C239—22no—
35C4⋊C4×C239—22no—
36C4⋊C4×C239—22no—
37C4⋊C4×C239—44no—
38C22⋊C4×C239—24no—
39C42×C239—21no—
40C42×C239D412yescomplemented
41C23×C239—22no—
42C23×C239C2×D411yescharacteristic
43Q8×C239—22no—
44Q8×C239—22no—
45D4×C239—22no—
46D4×C239—22no—
47D4×C239—42no—
48D4×C239—42no—
49D4×C239—82no—
50C2×C4×C239—22no—
51C2×C4×C239—22no—
52C2×C4×C239—22no—
53C2×C4×C239—22no—
54C2×C4×C239—22no—
55C2×C4×C239—42no—
56C2×C4×C239—42no—
57C2×C4×C239—42no—
58C2×C4×C239—42no—
59C2×C4×C239—41no—
60C2×C4×C239C2×D411yescharacteristic
61C2×C4×C239C2×D412yes—
62C2×C4×C239#4112yes—
63C2×C4×C239#4111yescharacteristic
64C8×C239—42no—
65C22×C239—21no—
66C22×C239—21no—
67C22×C239—42no—
68C22×C239—42no—
69C22×C239—42no—
70C22×C239#12011yescharacteristic
71C22×C239#12111yescharacteristic
72C22×C239#12411yescharacteristic
73C4×C239—24no—
74C4×C239—42no—
75C4×C239—42no—
76C4×C239—81no—
77C4×C239#12112yes—
78C4×C239#12312yes—
79C2×C239—21no—
80C2×C239—21no—
81C2×C239—82no—
82C2×C239#39411yescharacteristic
83C2×C239#45311yescharacteristic
84C2×C239#45611yescharacteristic
85C239#203911yescharacteristic, direct product factor, Sylow
86#2039C23911yesmaximal, characteristic, direct product factor, Sylow
87#537C2×C23911yescharacteristic
88C2×#104C2×C23912yescomplemented
89#417C2×C23912yescomplemented
90#384C2×C23911yescharacteristic, complemented
91#343C2×C23911yescharacteristic, complemented
92C2×#41C22×C23912yes—
93C2×M16C22×C23912yes—
94C22⋊Q8—22no—
95#121—22no—
96#121—22no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4C22×C23911yescharacteristic
99C2×C4⋊C4C22×C23911yescharacteristic
100C2×C42C22×C23911yescharacteristic
101#104—24no—
102#103—22no—
103#102—22no—
104#41—22no—
105#41—22no—
106#41—22no—
107#41—22no—
108C2×Q8D4×C23912yes—
109C2×D4—22no—
110C2×D4—22no—
111C2×D4D4×C23912yes—
112C22×C4—21no—
113C22×C4—22no—
114C22×C4—21no—
115C22×C4D4×C23912yes—
116C22×C4C23×C23911yescharacteristic
117M16—22no—
118M16—22no—
119C2×C8—22no—
120C4⋊C4—22no—
121C4⋊C4—22no—
122C4⋊C4—22no—
123C4⋊C4—44no—
124C22⋊C4—24no—
125C42—21no—
126C42D4×C23912yescomplemented
127C23—22no—
128C23C2×D4×C23911yescharacteristic
129Q8—22no—
130Q8—22no—
131D4—22no—
132D4—22no—
133D4—42no—
134D4—42no—
135D4—82no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—42no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—42no—
145C2×C4—41no—
146C2×C4C2×D4×C23911yescharacteristic
147C2×C4C2×D4×C23912yes—
148C2×C4#41×C23912yes—
149C2×C4#41×C23911yescharacteristic
150C8—42no—
151C22—21no—
152C22—21no—
153C22—42no—
154C22—42no—
155C22—42no—
156C22#120×C23911yescharacteristic
157C22#121×C23911yescharacteristic
158C22#124×C23911yescharacteristic
159C4—24no—
160C4—42no—
161C4—42no—
162C4—81no—
163C4#121×C23912yes—
164C4#123×C23912yes—
165C2—21no—
166C2—21no—
167C2—82no—
168C2#394×C23911yescharacteristic
169C2#453×C23911yescharacteristic
170C2#456×C23911yescharacteristic
subgroupG/H
center, socleC22×C239#120
commutator, Frattini, cosocleC22×C4C23×C239
prime radical#537×C239C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C239 ◁ C22×C4×C239 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#104×C239C2semidirect
3. #417×C239C2semidirect
4. #384×C239C2semidirect
5. #343×C239C2semidirect
40. C42×C239D4semidirect
85. C239#2039direct (N × H)
86. #2039C239direct (N × H)
88. C2×#104C2×C239semidirect
89. #417C2×C239semidirect
90. #384C2×C239semidirect
91. #343C2×C239semidirect
126. C42D4×C239semidirect

Maximal subgroups

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

subgroupindex
#537×C2392
C2×#104×C2392
#417×C2392
#384×C2392
#343×C2392
#2039239