Finite Group Databasebeta

← #1983×C211 #41009603

Subgroups — #1983×C211 #41009603

Order 27008.

344 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 128 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
1C2×#124×C211C211yesmaximal, characteristic
2C2×C4⋊C8×C211C211yesmaximal, characteristic, complemented
3C2×#103×C211C212yesmaximal, complemented
4C2×#102×C211C212yesmaximal
5C4×C4⋊C4×C211C211yesmaximal, characteristic, complemented
6C22×Q8×C211C2211yescharacteristic
7C22×D4×C211C2211yescharacteristic
8C22×C8×C211C2212yes—
9#124×C211—22no—
10#124×C211C414yescomplemented
11C2×C4⋊C4×C211C2212yes—
12C2×C22⋊C4×C211—21no—
13C2×C22⋊C4×C211—21no—
14C2×C42×C211—21no—
15C2×C42×C211C2211yescharacteristic
16C4⋊C8×C211—22no—
17#103×C211—24no—
18#102×C211—24no—
19#95×C211—21no—
20C24×C211—21no—
21C2×Q8×C211—21no—
22C2×Q8×C211—22no—
23C2×Q8×C211—22no—
24C2×Q8×C211C2×C412yes—
25C2×D4×C211—22no—
26C2×D4×C211—21no—
27C2×D4×C211—22no—
28C2×D4×C211C2×C412yes—
29C22×C4×C211—22no—
30C22×C4×C211—21no—
31C22×C4×C211D411yescharacteristic
32C22×C4×C211D411yescharacteristic
33C22×C4×C211C2311yescharacteristic
34C2×C8×C211—22no—
35C2×C8×C211—22no—
36C2×C8×C211—22no—
37C4⋊C4×C211—22no—
38C4⋊C4×C211D414yes—
39C22⋊C4×C211—24no—
40C22⋊C4×C211—24no—
41C42×C211—42no—
42C42×C211C2×C412yes—
43C42×C211D412yes—
44C23×C211—22no—
45C23×C211—42no—
46C23×C211—42no—
47C23×C211—41no—
48C23×C211—41no—
49C23×C211C2×D411yescharacteristic
50Q8×C211—24no—
51Q8×C211—41no—
52Q8×C211—41no—
53D4×C211—24no—
54D4×C211—41no—
55D4×C211—41no—
56C2×C4×C211—22no—
57C2×C4×C211—21no—
58C2×C4×C211—21no—
59C2×C4×C211—22no—
60C2×C4×C211—24no—
61C2×C4×C211—42no—
62C2×C4×C211—42no—
63C2×C4×C211—42no—
64C2×C4×C211C22⋊C412yes—
65C2×C4×C211C22⋊C412yes—
66C2×C4×C211C22×C411yescharacteristic
67C2×C4×C211C2×D412yes—
68C2×C4×C211C2×D411yescharacteristic
69C2×C4×C211#4112yes—
70C8×C211—42no—
71C22×C211—42no—
72C22×C211—42no—
73C22×C211—42no—
74C22×C211—82no—
75C22×C211—82no—
76C22×C211C2×C22⋊C411yescharacteristic
77C22×C211#12112yes—
78C22×C211#13512yes—
79C22×C211AGL(1,ℤ/8)11yescharacteristic
80C22×C211#13711yescharacteristic
81C4×C211—22no—
82C4×C211—22no—
83C4×C211—42no—
84C4×C211—44no—
85C4×C211C4×D412yes—
86C4×C211#12411yescharacteristic
87C4×C211#12711yescharacteristic
88C2×C211—82no—
89C2×C211#39011yescharacteristic
90C2×C211#41611yescharacteristic
91C2×C211#41711yescharacteristic
92C2×C211#46312yes—
93C2×C211#46412yes—
94C211#198311yescharacteristic, direct product factor, Sylow
95#1983C21111yesmaximal, characteristic, direct product factor, Sylow
96C2×#124C2×C21111yescharacteristic
97C2×C4⋊C8C2×C21111yescharacteristic, complemented
98C2×#103C2×C21112yescomplemented
99C2×#102C2×C21112yes—
100C4×C4⋊C4C2×C21111yescharacteristic, complemented
101C22×Q8C22×C21111yescharacteristic
102C22×D4C22×C21111yescharacteristic
103C22×C8C22×C21112yes—
104#124—22no—
105#124C4×C21114yescomplemented
106C2×C4⋊C4C22×C21112yes—
107C2×C22⋊C4—21no—
108C2×C22⋊C4—21no—
109C2×C42—21no—
110C2×C42C22×C21111yescharacteristic
111C4⋊C8—22no—
112#103—24no—
113#102—24no—
114#95—21no—
115C24—21no—
116C2×Q8—21no—
117C2×Q8—22no—
118C2×Q8—22no—
119C2×Q8C2×C4×C21112yes—
120C2×D4—22no—
121C2×D4—21no—
122C2×D4—22no—
123C2×D4C2×C4×C21112yes—
124C22×C4—22no—
125C22×C4—21no—
126C22×C4D4×C21111yescharacteristic
127C22×C4D4×C21111yescharacteristic
128C22×C4C23×C21111yescharacteristic
129C2×C8—22no—
130C2×C8—22no—
131C2×C8—22no—
132C4⋊C4—22no—
133C4⋊C4D4×C21114yes—
134C22⋊C4—24no—
135C22⋊C4—24no—
136C42—42no—
137C42C2×C4×C21112yes—
138C42D4×C21112yes—
139C23—22no—
140C23—42no—
141C23—42no—
142C23—41no—
143C23—41no—
144C23C2×D4×C21111yescharacteristic
145Q8—24no—
146Q8—41no—
147Q8—41no—
148D4—24no—
149D4—41no—
150D4—41no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—24no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4C22⋊C4×C21112yes—
160C2×C4C22⋊C4×C21112yes—
161C2×C4C22×C4×C21111yescharacteristic
162C2×C4C2×D4×C21112yes—
163C2×C4C2×D4×C21111yescharacteristic
164C2×C4#41×C21112yes—
165C8—42no—
166C22—42no—
167C22—42no—
168C22—42no—
169C22—82no—
170C22—82no—
171C22C2×C22⋊C4×C21111yescharacteristic
172C22#121×C21112yes—
173C22#135×C21112yes—
174C22AGL(1,ℤ/8)×C21111yescharacteristic
175C22#137×C21111yescharacteristic
176C4—22no—
177C4—22no—
178C4—42no—
179C4—44no—
180C4C4×D4×C21112yes—
181C4#124×C21111yescharacteristic
182C4#127×C21111yescharacteristic
183C2—82no—
184C2#390×C21111yescharacteristic
185C2#416×C21111yescharacteristic
186C2#417×C21111yescharacteristic
187C2#463×C21112yes—
188C2#464×C21112yes—
subgroupG/H
center, socleC23×C211C2×D4
commutatorC2×C4C22×C4×C211
Frattini, cosocleC22×C4C23×C211
prime radicalC22×D4×C211C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C211 ◁ C2×C42×C211 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C8×C211C2semidirect
3. C2×#103×C211C2semidirect
5. C4×C4⋊C4×C211C2semidirect
10. #124×C211C4semidirect
94. C211#1983direct (N × H)
95. #1983C211direct (N × H)
97. C2×C4⋊C8C2×C211semidirect
98. C2×#103C2×C211semidirect
100. C4×C4⋊C4C2×C211semidirect
105. #124C4×C211semidirect

Maximal subgroups

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

subgroupindex
C2×#124×C2112
C2×C4⋊C8×C2112
C2×#103×C2112
C2×#102×C2112
C4×C4⋊C4×C2112
#1983211