Finite Group Databasebeta

← #44509460

Subgroups — #44509460

Order 30848.

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

normal subgroups only

This group has 226 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#29508467C211yesmaximal, characteristic, complemented
2#29507908C212yesmaximal
3#29507894C211yesmaximal, characteristic
4#29507506C212yesmaximal, complemented
5#354×C241C211yesmaximal, characteristic, complemented
6#21440687C2211yescharacteristic
7#21440673—21no—
8#21440640—21no—
9#21440635—22no—
10#21440634—21no—
11#21440626—22no—
12#21440623C2212yes—
13#21440619—22no—
14#21440570—21no—
15#21440559C2211yescharacteristic
16#21440556—22no—
17#124×C241C2211yescharacteristic
18#99×C241C2212yes—
19#16838770—21no—
20#16838769—41no—
21C2×Dic482—21no—
22C2×C22⋊D241—22no—
23D4×D241—41no—
24C22×Dic241D412yes—
25#16838760—41no—
26#16838757—41no—
27#16838754—21no—
28C4⋊Dic241—21no—
29C4⋊Dic241—21no—
30C4⋊Dic241—42no—
31#16838749—22no—
32#16838749—22no—
33#16838749—22no—
34C22⋊Dic241—22no—
35C22⋊Dic241D412yes—
36#16838747—42no—
37C4×Dic241—21no—
38C2×Q8×C241D411yescharacteristic
39C2×D4×C241C2311yescharacteristic
40C22⋊C4×C241—22no—
41C22⋊C4×C241—22no—
42C42×C241D411yescharacteristic
43C22×D241—22no—
44Dic482—21no—
45Dic482—81no—
46D964—21no—
47C22⋊D241—42no—
48C22⋊D241—41no—
49C2×Dic241—22no—
50C2×Dic241—22no—
51C2×Dic241—22no—
52C2×Dic241—42no—
53C4×D241—41no—
54#14515349—41no—
55C23×C241C2×D412yes—
56Q8×C241—41no—
57D4×C241—41no—
58C2×C4×C241—21no—
59C2×C4×C241—21no—
60C2×C4×C241—42no—
61C2×C4×C241C2×D411yescharacteristic
62C22×C241—22no—
63C22×C241—42no—
64C22×C241#12011yescharacteristic
65C2×D241—41no—
66C2×D241—82no—
67C4×C241—21no—
68C4×C241—41no—
69C4×C241—41no—
70C4×C241—82no—
71Dic241—42no—
72Dic241—41no—
73Dic241—42no—
74C2×C241—21no—
75C2×C241—42no—
76C2×C241B(4,𝔽2)11yescharacteristic
77D241—81no—
78C241#220111yescharacteristic, complemented, Sylow
79#2201—2411nomaximal, Sylow
80#563—2411no—
81#458—2412no—
82#455—2411no—
83#354D24111yescharacteristic, complemented
84#352—2412no—
85H(5,𝔽2)—2411no—
86#137—4821no—
87C4⋊Q8—4821no—
88#126—4822no—
89#125—4821no—
90#124C2×D24111yescharacteristic
91#123—4822no—
92#123—2412no—
93C22⋊Q8—4822no—
94#104—4821no—
95#100—2411no—
96#99—4822no—
97#99C2×D24112yes—
98#41—9641no—
99#41—4821no—
100C2×Q8—4821no—
101C2×Q8D96411yescharacteristic
102C2×D4—9641no—
103C2×D4—4822no—
104C2×D4C22×D24111yescharacteristic
105C22×C4—2412no—
106Q16—9641no—
107SD16—9641no—
108M16—4821no—
109C4⋊C4—9642no—
110C4⋊C4—4822no—
111C4⋊C4—4822no—
112C4⋊C4—4821no—
113C4⋊C4—4821no—
114C4⋊C4—4822no—
115C22⋊C4—22no—
116C22⋊C4—22no—
117C22⋊C4—9642no—
118C22⋊C4—4822no—
119C22⋊C4—2412no—
120C42—4821no—
121C42D96411yescharacteristic
122C23—4822no—
123C23D4×D24112yes—
124Q8—41no—
125Q8—19281no—
126Q8—4821no—
127D4—41no—
128D4—9642no—
129D4—9641no—
130D4—4821no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—42no—
134C2×C4—9641no—
135C2×C4—9642no—
136C2×C4—4822no—
137C2×C4—4822no—
138C2×C4—4822no—
139C2×C4C2×D96411yescharacteristic
140C8—9641no—
141C22—22no—
142C22—42no—
143C22—19282no—
144C22—9641no—
145C22#2144061211yescharacteristic
146C4—21no—
147C4—41no—
148C4—41no—
149C4—82no—
150C4—9642no—
151C4—9641no—
152C4—9642no—
153C2—21no—
154C2—42no—
155C2—19281no—
156C2#2950790511yescharacteristic
subgroupG/H
centerC2#29507905
commutator, cosocleC2×D4×C241C23
FrattiniC2×D4C22×D241
Fitting#354×C241C2
socleC2×C241B(4,𝔽2)
prime radical#21440687C22
hypercenter#354D241
hypocenterC241#2201
LCSG ▷ C2×D4×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
1. #29508467C2semidirect
4. #29507506C2semidirect
5. #354×C241C2semidirect
78. C241#2201semidirect
83. #354D241semidirect

Maximal subgroups

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

subgroupindex
#295084672
#295079082
#295078942
#295075062
#354×C2412
#2201241