Finite Group Databasebeta

← #44509476

Subgroups — #44509476

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#29507902C212yesmaximal
3#29507899C211yesmaximal, characteristic
4#29507515C212yesmaximal, complemented
5#356×C241C211yesmaximal, characteristic, complemented
6#21440690C2211yescharacteristic
7#21440675—22no—
8#21440673—21no—
9#21440641—22no—
10#21440640—21no—
11#21440640C2212yes—
12C4×Dic482—21no—
13#21440607—22no—
14#21440570—21no—
15#21440568—22no—
16#21440561C2211yescharacteristic
17C4⋊Q8×C241C2211yescharacteristic
18#101×C241C2212yes—
19#16838771—41no—
20#16838770—22no—
21#16838770—21no—
22C2×Dic482—21no—
23C2×Dic482—21no—
24C2×Dic482D412yes—
25Q8×D241—41no—
26Dic964—42no—
27#16838760—41no—
28#16838759—42no—
29#16838757—41no—
30#16838754—21no—
31C4⋊Dic241—21no—
32#16838749—22no—
33#16838749—22no—
34#16838749—22no—
35C4×Dic241—21no—
36C4×Dic241—22no—
37C4×Dic241D412yes—
38C2×Q8×C241D411yescharacteristic
39C2×Q8×C241C2311yescharacteristic
40M16×C241—22no—
41C4⋊C4×C241—22no—
42C42×C241D411yescharacteristic
43Dic482—24no—
44Dic482—21no—
45Dic482—22no—
46Dic482—42no—
47Dic482—81no—
48D964—21no—
49D964—22no—
50C22⋊D241—41no—
51C2×Dic241—22no—
52C2×Dic241—22no—
53C4×D241—42no—
54C4×D241—41no—
55#14515349—41no—
56Q8×C241—41no—
57Q8×C241—41no—
58C2×C4×C241—21no—
59C2×C4×C241—21no—
60C2×C4×C241C2×D412yes—
61C2×C4×C241C2×D411yescharacteristic
62C8×C241—42no—
63C22×C241#12011yescharacteristic
64C2×D241—41no—
65C4×C241—22no—
66C4×C241—22no—
67C4×C241—21no—
68C4×C241—41no—
69Dic241—24no—
70Dic241—41no—
71Dic241—42no—
72C2×C241—21no—
73C2×C241B(4,𝔽2)11yescharacteristic
74D241—81no—
75C241#220511yescharacteristic, complemented, Sylow
76#2205—2411nomaximal, Sylow
77Q82—2411no—
78#456—2411no—
79#456—2412no—
80#356—2412no—
81#356D24111yescharacteristic, complemented
822−1+4—2411no—
83#137—4822no—
84#137—4821no—
85C4⋊Q8—4822no—
86C4⋊Q8—4821no—
87C4⋊Q8—2412no—
88C4⋊Q8C2×D24111yescharacteristic
89C4×Q8—4822no—
90C4×Q8—4821no—
91#104—4822no—
92#104—4821no—
93#101—2411no—
94#101C2×D24112yes—
95#41—9641no—
96#41—4822no—
97#41—4821no—
98C2×Q8—9641no—
99C2×Q8—4821no—
100C2×Q8—4821no—
101C2×Q8—2412no—
102C2×Q8D96411yescharacteristic
103C2×Q8C22×D24111yescharacteristic
104Q16—9642no—
105Q16—9641no—
106SD16—9642no—
107SD16—9641no—
108M16—22no—
109M16—4821no—
110C4⋊C4—22no—
111C4⋊C4—4822no—
112C4⋊C4—4821no—
113C4⋊C4—4822no—
114C4⋊C4—4822no—
115C42—4822no—
116C42—4821no—
117C42—2412no—
118C42D96411yescharacteristic
119Q8—41no—
120Q8—41no—
121Q8—19281no—
122Q8—9642no—
123Q8—4822no—
124Q8—4821no—
125Q8—4824no—
126D4—9641no—
127D4—4822no—
128D4—4821no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—9642no—
132C2×C4—9641no—
133C2×C4—4822no—
134C2×C4—4822no—
135C2×C4D4×D24112yes—
136C2×C4C2×D96411yescharacteristic
137C8—42no—
138C8—9641no—
139C22—9641no—
140C22#2144061211yescharacteristic
141C4—22no—
142C4—22no—
143C4—21no—
144C4—41no—
145C4—9641no—
146C4—9642no—
147C4—4824no—
148C2—21no—
149C2—19281no—
150C2#2950790511yescharacteristic
subgroupG/H
centerC2#29507905
commutator, cosocleC2×Q8×C241C23
FrattiniC2×Q8C22×D241
Fitting#356×C241C2
socleC2×C241B(4,𝔽2)
prime radical#21440690C22
hypercenter#356D241
hypocenterC241#2205
LCSG ▷ C2×Q8×C241 ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
1. #29508447C2semidirect
4. #29507515C2semidirect
5. #356×C241C2semidirect
75. C241#2205semidirect
81. #356D241semidirect

Maximal subgroups

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

subgroupindex
#295084472
#295079022
#295078992
#295075152
#356×C2412
#2205241