Finite Group Databasebeta

← #44506752

Subgroups — #44506752

Order 30848.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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#29508459C211yesmaximal, characteristic
2#29508112C211yesmaximal, characteristic, complemented
3#29508077C212yesmaximal, complemented
4#29507456C212yesmaximal, complemented
5#329×C241C211yesmaximal, characteristic, complemented
6C2×#16838760—21no—
7C2×#16838758—21no—
8#21440642C2211yescharacteristic, complemented
9#21440631—21no—
10#21440630C2212yes—
11#21440628—22no—
12#21440612—22no—
13#21440610—21no—
14#21440567—22no—
15#21440564—22no—
16#21440553C2211yescharacteristic, complemented
17#124×C241C2211yescharacteristic
18#97×C241C2212yescomplemented
19C23×D241—21no—
20C2×Dic482—21no—
21C2×Dic482D412yes—
22C2×D964—21no—
23C2×D964D412yes—
24C2×C22⋊D241—22no—
25#16838760—42no—
26#16838758—42no—
27C2×#14515349—21no—
28C4⋊Dic241—22no—
29C22⋊Dic241—21no—
30#16838747—22no—
31#16838747—22no—
32#16838747—22no—
33C4×Dic241—21no—
34C2×Q8×C241D411yescharacteristic
35C2×D4×C241D411yescharacteristic
36C2×C8×C241—22no—
37C22⋊C4×C241—22no—
38C42×C241C2311yescharacteristic
39C22×D241—22no—
40C22×D241—81no—
41C22×D241—82no—
42Dic482—42no—
43Dic482—41no—
44Dic482—41no—
45D964—42no—
46D964—81no—
47C22⋊D241—82no—
48C2×Dic241—22no—
49C2×Dic241—41no—
50#14515349—22no—
51C23×C241—21no—
52Q8×C241—41no—
53D4×C241—41no—
54C2×C4×C241—21no—
55C2×C4×C241C2×D412yes—
56C2×C4×C241C2×D411yescharacteristic
57C8×C241—42no—
58C22×C241—41no—
59C22×C241—42no—
60C22×C241#12011yescharacteristic
61C2×D241—42no—
62C2×D241—42no—
63C2×D241—42no—
64C2×D241—84no—
65C4×C241—21no—
66C4×C241—22no—
67C4×C241—41no—
68Dic241—42no—
69Dic241—81no—
70C2×C241—81no—
71C2×C241#45311yescharacteristic
72C2×C241#45512yes—
73D241—82no—
74C241#165911yescharacteristic, complemented, Sylow
75#1659—2411nomaximal, Sylow
76H(3,𝔽4)—2411no—
77#497—2411no—
78#489—2412no—
79#329—2412no—
80#329D24111yescharacteristic, complemented
81C2×Q16—4821no—
82C2×SD16—4821no—
83C4⋊Q8—2411no—
84#124—4822no—
85#124—4821no—
86#124—2412no—
87#124C2×D24111yescharacteristic
88#120—4822no—
89#120—4821no—
90#103—4822no—
91#102—4822no—
92#97—2411no—
93#97C2×D24112yescomplemented
94C24—4821no—
95C2×Q8—4821no—
96C2×Q8—2412no—
97C2×Q8D96411yescharacteristic
98C2×D4—4821no—
99C2×D4—4822no—
100C2×D4—2412no—
101C2×D4D96411yescharacteristic
102Q16—9642no—
103SD16—9642no—
104C2×C8—22no—
105C2×C8—4821no—
106C4⋊C4—4822no—
107C22⋊C4—22no—
108C22⋊C4—4822no—
109C22⋊C4—4821no—
110C22⋊C4—4822no—
111C22⋊C4—4822no—
112C42—4821no—
113C42C22×D24111yescharacteristic
114C23—21no—
115C23—19281no—
116C23—19282no—
117C23—4822no—
118Q8—41no—
119Q8—9641no—
120Q8—9641no—
121Q8—9642no—
122D4—41no—
123D4—19281no—
124D4—19282no—
125D4—9642no—
126C2×C4—21no—
127C2×C4—9641no—
128C2×C4—4822no—
129C2×C4D4×D24112yes—
130C2×C4C2×D96411yescharacteristic
131C8—42no—
132C8—4822no—
133C22—41no—
134C22—42no—
135C22—19284no—
136C22—9642no—
137C22—9642no—
138C22—9642no—
139C22#2144061211yescharacteristic
140C4—21no—
141C4—22no—
142C4—41no—
143C4—19281no—
144C4—9642no—
145C2—81no—
146C2—19282no—
147C2#2950788711yescharacteristic
148C2#2950789612yes—
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#329×C241C2
socleC22×C241#120
prime radical#29508459C2
hypercenter#329D241
hypocenterC241#1659
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #29508112C2semidirect
3. #29508077C2semidirect
4. #29507456C2semidirect
5. #329×C241C2semidirect
8. #21440642C22semidirect
16. #21440553C22semidirect
18. #97×C241C22semidirect
74. C241#1659semidirect
80. #329D241semidirect
93. #97C2×D241semidirect

Maximal subgroups

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

subgroupindex
#295084592
#295081122
#295080772
#295074562
#329×C2412
#1659241