Finite Group Databasebeta

← #1509×C241 #44503176

Subgroups — #1509×C241 #44503176

Order 30848.

242 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 92 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#529×C241C211yesmaximal, characteristic
2#432×C241C211yesmaximal, characteristic, complemented
3C4×C4⋊C4×C241C211yesmaximal, characteristic, complemented
4#328×C241C212yesmaximal, complemented
5#327×C241C212yesmaximal
6#126×C241—21no—
7#125×C241C411yescharacteristic, complemented
8#124×C241C411yescharacteristic, complemented
9#123×C241—21no—
10C22⋊Q8×C241C2211yescharacteristic
11#121×C241C2211yescharacteristic
12C4×Q8×C241C411yescharacteristic, complemented
13C4×D4×C241—21no—
14C4×D4×C241C411yescharacteristic, complemented
15#117×C241—21no—
16C2×C4⋊C4×C241—21no—
17C2×C42×C241—21no—
18C2×C42×C241C2211yescharacteristic
19C4⋊C8×C241—21no—
20C22⋊C8×C241C2212yes—
21#97×C241—21no—
22#95×C241C2212yes—
23C2×Q8×C241C2×C411yescharacteristic
24C2×D4×C241—21no—
25C2×D4×C241C2×C411yescharacteristic
26C22×C4×C241—22no—
27C22×C4×C241—21no—
28C22×C4×C241D411yescharacteristic
29C22×C4×C241D411yescharacteristic
30C22×C4×C241C2311yescharacteristic
31C2×C8×C241—22no—
32C4⋊C4×C241—24no—
33C4⋊C4×C241—21no—
34C4⋊C4×C241—21no—
35C4⋊C4×C241—21no—
36C4⋊C4×C241—21no—
37C4⋊C4×C241C2×C411yescharacteristic
38C4⋊C4×C241C2×C411yescharacteristic
39C22⋊C4×C241—21no—
40C22⋊C4×C241—21no—
41C22⋊C4×C241—21no—
42C22⋊C4×C241—21no—
43C22⋊C4×C241—21no—
44C42×C241—21no—
45C42×C241—42no—
46C42×C241C2×C411yescharacteristic
47C42×C241C2×C411yescharacteristic
48C42×C241D411yescharacteristic
49C42×C241D411yescharacteristic
50C23×C241—21no—
51C23×C241C2×D411yescharacteristic
52Q8×C241—41no—
53D4×C241—41no—
54D4×C241—41no—
55D4×C241—41no—
56C2×C4×C241—21no—
57C2×C4×C241—21no—
58C2×C4×C241—22no—
59C2×C4×C241—24no—
60C2×C4×C241—21no—
61C2×C4×C241—21no—
62C2×C4×C241—21no—
63C2×C4×C241—41no—
64C2×C4×C241—42no—
65C2×C4×C241—42no—
66C2×C4×C241—42no—
67C2×C4×C241C22⋊C411yescharacteristic
68C2×C4×C241C22⋊C411yescharacteristic
69C2×C4×C241C22⋊C411yescharacteristic
70C2×C4×C241C22⋊C411yescharacteristic
71C2×C4×C241C22×C411yescharacteristic
72C2×C4×C241C2×D411yescharacteristic
73C8×C241—42no—
74C22×C241—21no—
75C22×C241—21no—
76C22×C241—41no—
77C22×C241—41no—
78C22×C241—41no—
79C22×C241C2×C22⋊C411yescharacteristic
80C22×C241AGL(1,ℤ/8)11yescharacteristic
81C22×C241#13711yescharacteristic
82C4×C241—21no—
83C4×C241—21no—
84C4×C241—21no—
85C4×C241—21no—
86C4×C241—21no—
87C4×C241—44no—
88C4×C241—41no—
89C4×C241—41no—
90C4×C241—41no—
91C4×C241#10412yes—
92C2×C241—21no—
93C2×C241—21no—
94C2×C241—81no—
95C2×C241#41011yescharacteristic
96C2×C241#41711yescharacteristic
97C2×C241C2×#10411yescharacteristic
98C241#150911yescharacteristic, direct product factor, Sylow
99#1509C24111yesmaximal, characteristic, direct product factor, Sylow
100#529C2×C24111yescharacteristic
101#432C2×C24111yescharacteristic, complemented
102C4×C4⋊C4C2×C24111yescharacteristic, complemented
103#328C2×C24112yescomplemented
104#327C2×C24112yes—
105#126—21no—
106#125C4×C24111yescharacteristic, complemented
107#124C4×C24111yescharacteristic, complemented
108#123—21no—
109C22⋊Q8C22×C24111yescharacteristic
110#121C22×C24111yescharacteristic
111C4×Q8C4×C24111yescharacteristic, complemented
112C4×D4—21no—
113C4×D4C4×C24111yescharacteristic, complemented
114#117—21no—
115C2×C4⋊C4—21no—
116C2×C42—21no—
117C2×C42C22×C24111yescharacteristic
118C4⋊C8—21no—
119C22⋊C8C22×C24112yes—
120#97—21no—
121#95C22×C24112yes—
122C2×Q8C2×C4×C24111yescharacteristic
123C2×D4—21no—
124C2×D4C2×C4×C24111yescharacteristic
125C22×C4—22no—
126C22×C4—21no—
127C22×C4D4×C24111yescharacteristic
128C22×C4D4×C24111yescharacteristic
129C22×C4C23×C24111yescharacteristic
130C2×C8—22no—
131C4⋊C4—24no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4C2×C4×C24111yescharacteristic
137C4⋊C4C2×C4×C24111yescharacteristic
138C22⋊C4—21no—
139C22⋊C4—21no—
140C22⋊C4—21no—
141C22⋊C4—21no—
142C22⋊C4—21no—
143C42—21no—
144C42—42no—
145C42C2×C4×C24111yescharacteristic
146C42C2×C4×C24111yescharacteristic
147C42D4×C24111yescharacteristic
148C42D4×C24111yescharacteristic
149C23—21no—
150C23C2×D4×C24111yescharacteristic
151Q8—41no—
152D4—41no—
153D4—41no—
154D4—41no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—24no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4C22⋊C4×C24111yescharacteristic
167C2×C4C22⋊C4×C24111yescharacteristic
168C2×C4C22⋊C4×C24111yescharacteristic
169C2×C4C22⋊C4×C24111yescharacteristic
170C2×C4C22×C4×C24111yescharacteristic
171C2×C4C2×D4×C24111yescharacteristic
172C8—42no—
173C22—21no—
174C22—21no—
175C22—41no—
176C22—41no—
177C22—41no—
178C22C2×C22⋊C4×C24111yescharacteristic
179C22AGL(1,ℤ/8)×C24111yescharacteristic
180C22#137×C24111yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—44no—
187C4—41no—
188C4—41no—
189C4—41no—
190C4#104×C24112yes—
191C2—21no—
192C2—21no—
193C2—81no—
194C2#410×C24111yescharacteristic
195C2#417×C24111yescharacteristic
196C2C2×#104×C24111yescharacteristic
subgroupG/H
center, socleC22×C241C2×C22⋊C4
commutatorC2×C4C22×C4×C241
Frattini, cosocleC22×C4C23×C241
prime radical#121×C241C22
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C241 ◁ C2×C42×C241 ◁ G

Complements

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

NH ≅ G/Ntype
2. #432×C241C2semidirect
3. C4×C4⋊C4×C241C2semidirect
4. #328×C241C2semidirect
7. #125×C241C4semidirect
8. #124×C241C4semidirect
12. C4×Q8×C241C4semidirect
14. C4×D4×C241C4semidirect
98. C241#1509direct (N × H)
99. #1509C241direct (N × H)
101. #432C2×C241semidirect
102. C4×C4⋊C4C2×C241semidirect
103. #328C2×C241semidirect
106. #125C4×C241semidirect
107. #124C4×C241semidirect
111. C4×Q8C4×C241semidirect
113. C4×D4C4×C241semidirect

Maximal subgroups

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

subgroupindex
#529×C2412
#432×C2412
C4×C4⋊C4×C2412
#328×C2412
#327×C2412
#1509241