Finite Group Databasebeta

← #44509474

Subgroups — #44509474

Order 30848.

224 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 41 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#29508447C211yesmaximal, characteristic, complemented
2#29507900C212yesmaximal
3#29507516C211yesmaximal, characteristic, complemented
4#29507515C212yesmaximal, complemented
5#456×C241C211yesmaximal, characteristic
6#21440672—22no—
7#21440641—22no—
8#21440640—21no—
9#21440640C2212yes—
10C4×Dic482—21no—
11#21440607—22no—
12#21440569—22no—
13#21440561C2212yes—
142−1+4×C241C2211yescharacteristic
15#137×C241—21no—
16C4⋊Q8×C241C2211yescharacteristic
17#104×C241—21no—
18#101×C241C2211yescharacteristic
19C2×Dic482—21no—
20C2×Dic482—21no—
21C2×Dic482D412yes—
22#16838760—42no—
23#16838758—42no—
24#16838754—22no—
25C4⋊Dic241—21no—
26#16838749—22no—
27#16838749—22no—
28#16838749—22no—
29C4×Dic241—21no—
30C4×Dic241—22no—
31C4×Dic241D412yes—
32#41×C241—21no—
33#41×C241—22no—
34#41×C241—41no—
35C2×Q8×C241—41no—
36C2×Q8×C241D411yescharacteristic
37C2×Q8×C241C2311yescharacteristic
38Q16×C241—41no—
39SD16×C241—41no—
40M16×C241—21no—
41C4⋊C4×C241—22no—
42C42×C241D411yescharacteristic
43Dic482—24no—
44Dic482—42no—
45Dic482—81no—
46C2×Dic241—22no—
47C2×Dic241—22no—
48#14515349—42no—
49Q8×C241—21no—
50Q8×C241—22no—
51Q8×C241—41no—
52Q8×C241—41no—
53D4×C241—21no—
54D4×C241—22no—
55D4×C241—41no—
56C2×C4×C241—21no—
57C2×C4×C241—21no—
58C2×C4×C241—41no—
59C2×C4×C241—42no—
60C2×C4×C241C2×D412yes—
61C2×C4×C241C2×D411yescharacteristic
62C8×C241—41no—
63C22×C241—41no—
64C22×C241#12011yescharacteristic
65C4×C241—22no—
66C4×C241—21no—
67C4×C241—22no—
68C4×C241—41no—
69C4×C241—41no—
70Dic241—24no—
71Dic241—42no—
72C2×C241—21no—
73C2×C241—81no—
74C2×C241B(4,𝔽2)11yescharacteristic
75C241#220511yescharacteristic, complemented, Sylow
76#2205—2411nomaximal, Sylow
77Q82—2411no—
78#456—2412no—
79#456D24111yescharacteristic
80#356—2411no—
81#356—2412no—
822−1+4C2×D24111yescharacteristic
83#137—21no—
84#137—4822no—
85C4⋊Q8—4822no—
86C4⋊Q8—4821no—
87C4⋊Q8—2412no—
88C4⋊Q8C2×D24111yescharacteristic
89C4×Q8—4822no—
90C4×Q8—4821no—
91#104—21no—
92#104—4822no—
93#101—2412no—
94#101C2×D24111yescharacteristic
95#41—22no—
96#41—21no—
97#41—41no—
98C2×Q8—41no—
99C2×Q8—4821no—
100C2×Q8—4821no—
101C2×Q8—2412no—
102C2×Q8C22⋊D24111yescharacteristic
103C2×Q8C22×D24111yescharacteristic
104Q16—41no—
105Q16—9642no—
106SD16—41no—
107SD16—9642no—
108M16—21no—
109M16—4822no—
110C4⋊C4—22no—
111C4⋊C4—4822no—
112C4⋊C4—4821no—
113C4⋊C4—4822no—
114C4⋊C4—4822no—
115C42—4822no—
116C42—4821no—
117C42—2412no—
118C42C22⋊D24111yescharacteristic
119Q8—21no—
120Q8—22no—
121Q8—41no—
122Q8—41no—
123Q8—19281no—
124Q8—9642no—
125Q8—4824no—
126D4—21no—
127D4—22no—
128D4—41no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—42no—
133C2×C4—4822no—
134C2×C4—4822no—
135C2×C4D4×D24112yes—
136C2×C4C2×C22⋊D24111yescharacteristic
137C8—41no—
138C8—9642no—
139C22—41no—
140C22#2144061011yescharacteristic
141C4—22no—
142C4—21no—
143C4—22no—
144C4—41no—
145C4—41no—
146C4—9642no—
147C4—4824no—
148C2—21no—
149C2—81no—
150C2#2950790311yescharacteristic
subgroupG/H
centerC2#29507903
commutator, cosocleC2×Q8×C241C23
FrattiniC2×Q8C22×D241
Fitting#456×C241C2
socleC2×C241B(4,𝔽2)
prime radical2−1+4×C241C22
hypercenter#456D241
hypocenterC241#2205
LCSG ▷ C2×Q8×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #29508447C2semidirect
3. #29507516C2semidirect
4. #29507515C2semidirect
75. C241#2205semidirect

Maximal subgroups

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

subgroupindex
#295084472
#295079002
#295075162
#295075152
#456×C2412
#2205241