Finite Group Databasebeta

← #1478×C241 #44503145

Subgroups — #1478×C241 #44503145

Order 30848.

312 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 124 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×C4×D4×C241C211yesmaximal, characteristic
2#431×C241C211yesmaximal, characteristic, complemented
3#431×C241C211yesmaximal, characteristic, complemented
4D4⋊C8×C241C214yesmaximal, complemented
5C22×D4×C241C411yescharacteristic
6C23×C4×C241—21no—
7C4×D4×C241—21no—
8C4×D4×C241—21no—
9C4×D4×C241C412yes—
10C4×D4×C241C2212yes—
11C2×C4⋊C4×C241C411yescharacteristic
12C2×C22⋊C4×C241—21no—
13C2×C42×C241C2211yescharacteristic
14C4⋊C8×C241—21no—
15C4⋊C8×C241C2212yescomplemented
16C22⋊C8×C241—21no—
17C22⋊C8×C241—21no—
18C4×C8×C241—21no—
19C4×C8×C241C2212yescomplemented
20C24×C241—21no—
21C2×D4×C241—21no—
22C2×D4×C241—22no—
23C2×D4×C241C814yescomplemented
24C2×D4×C241C2×C412yes—
25C22×C4×C241—21no—
26C22×C4×C241—22no—
27C22×C4×C241—22no—
28C22×C4×C241—44no—
29C22×C4×C241C2×C411yescharacteristic
30C22×C4×C241D411yescharacteristic
31C22×C4×C241D411yescharacteristic
32C2×C8×C241—22no—
33C2×C8×C241—22no—
34C4⋊C4×C241—21no—
35C4⋊C4×C241C2×C412yes—
36C22⋊C4×C241—22no—
37C22⋊C4×C241—22no—
38C42×C241C2×C411yescharacteristic
39C42×C241D411yescharacteristic
40C42×C241D411yescharacteristic
41C42×C241C2311yescharacteristic
42C23×C241—24no—
43C23×C241—22no—
44C23×C241—42no—
45C23×C241—42no—
46C23×C241C22⋊C411yescharacteristic
47D4×C241—24no—
48D4×C241—22no—
49D4×C241C2×C814yes—
50C2×C4×C241—22no—
51C2×C4×C241—22no—
52C2×C4×C241—41no—
53C2×C4×C241—44no—
54C2×C4×C241—42no—
55C2×C4×C241—44no—
56C2×C4×C241C22⋊C411yescharacteristic
57C2×C4×C241C22⋊C411yescharacteristic
58C2×C4×C241C22⋊C411yescharacteristic
59C2×C4×C241C2×C812yes—
60C2×C4×C241M1612yes—
61C2×C4×C241C22×C411yescharacteristic
62C2×C4×C241C2×D411yescharacteristic
63C2×C4×C241C2×D411yescharacteristic
64C8×C241—42no—
65C8×C241—42no—
66C22×C241—21no—
67C22×C241—21no—
68C22×C241—24no—
69C22×C241—48no—
70C22×C241—42no—
71C22×C241—42no—
72C22×C241C22⋊C812yes—
73C22×C241C2×C22⋊C411yescharacteristic
74C4×C241—21no—
75C4×C241—21no—
76C4×C241—21no—
77C4×C241—42no—
78C4×C241C22⋊C812yes—
79C4×C241C22×C811yescharacteristic
80C4×C241C2×M1611yescharacteristic
81C4×C241AGL(1,ℤ/8)12yes—
82C2×C241—22no—
83C2×C241—44no—
84C2×C241C2×C22⋊C811yescharacteristic
85C2×C241#41811yescharacteristic
86C2×C241#42111yescharacteristic
87C241#147811yescharacteristic, direct product factor, Sylow
88#1478C24111yesmaximal, characteristic, direct product factor, Sylow
89C2×C4×D4C2×C24111yescharacteristic
90#431C2×C24111yescharacteristic, complemented
91#431C2×C24111yescharacteristic, complemented
92D4⋊C8C2×C24114yescomplemented
93C22×D4C4×C24111yescharacteristic
94C23×C4—21no—
95C4×D4—21no—
96C4×D4—21no—
97C4×D4C4×C24112yes—
98C4×D4C22×C24112yes—
99C2×C4⋊C4C4×C24111yescharacteristic
100C2×C22⋊C4—21no—
101C2×C42C22×C24111yescharacteristic
102C4⋊C8—21no—
103C4⋊C8C22×C24112yescomplemented
104C22⋊C8—21no—
105C22⋊C8—21no—
106C4×C8—21no—
107C4×C8C22×C24112yescomplemented
108C24—21no—
109C2×D4—21no—
110C2×D4—22no—
111C2×D4C8×C24114yescomplemented
112C2×D4C2×C4×C24112yes—
113C22×C4—21no—
114C22×C4—22no—
115C22×C4—22no—
116C22×C4—44no—
117C22×C4C2×C4×C24111yescharacteristic
118C22×C4D4×C24111yescharacteristic
119C22×C4D4×C24111yescharacteristic
120C2×C8—22no—
121C2×C8—22no—
122C4⋊C4—21no—
123C4⋊C4C2×C4×C24112yes—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C42C2×C4×C24111yescharacteristic
127C42D4×C24111yescharacteristic
128C42D4×C24111yescharacteristic
129C42C23×C24111yescharacteristic
130C23—22no—
131C23—24no—
132C23—42no—
133C23—42no—
134C23C22⋊C4×C24111yescharacteristic
135D4—22no—
136D4—24no—
137D4C2×C8×C24114yes—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—41no—
141C2×C4—44no—
142C2×C4—42no—
143C2×C4—44no—
144C2×C4C22⋊C4×C24111yescharacteristic
145C2×C4C22⋊C4×C24111yescharacteristic
146C2×C4C22⋊C4×C24111yescharacteristic
147C2×C4C2×C8×C24112yes—
148C2×C4M16×C24112yes—
149C2×C4C22×C4×C24111yescharacteristic
150C2×C4C2×D4×C24111yescharacteristic
151C2×C4C2×D4×C24111yescharacteristic
152C8—42no—
153C8—42no—
154C22—21no—
155C22—21no—
156C22—24no—
157C22—48no—
158C22—42no—
159C22—42no—
160C22C22⋊C8×C24112yes—
161C22C2×C22⋊C4×C24111yescharacteristic
162C4—21no—
163C4—21no—
164C4—21no—
165C4—42no—
166C4C22⋊C8×C24112yes—
167C4C22×C8×C24111yescharacteristic
168C4C2×M16×C24111yescharacteristic
169C4AGL(1,ℤ/8)×C24112yes—
170C2—22no—
171C2—44no—
172C2C2×C22⋊C8×C24111yescharacteristic
173C2#418×C24111yescharacteristic
174C2#421×C24111yescharacteristic
subgroupG/H
centerC2×C4×C241C2×D4
commutatorC4C22×C8×C241
Frattini, cosocleC42C23×C241
socleC22×C241C2×C22⋊C4
prime radicalC22×D4×C241C4
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C241 ◁ C2×C42×C241 ◁ G

Complements

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

NH ≅ G/Ntype
2. #431×C241C2semidirect
3. #431×C241C2semidirect
4. D4⋊C8×C241C2semidirect
15. C4⋊C8×C241C22semidirect
19. C4×C8×C241C22semidirect
23. C2×D4×C241C8semidirect
87. C241#1478direct (N × H)
88. #1478C241direct (N × H)
90. #431C2×C241semidirect
91. #431C2×C241semidirect
92. D4⋊C8C2×C241semidirect
103. C4⋊C8C22×C241semidirect
107. C4×C8C22×C241semidirect
111. C2×D4C8×C241semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C2412
#431×C2412
D4⋊C8×C2412
#1478241