Finite Group Databasebeta

← #44506702

Subgroups — #44506702

Order 30848.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#29508441C211yesmaximal, characteristic
2#29508120C211yesmaximal, characteristic, complemented
3#29508003C211yesmaximal, characteristic, complemented
4#29507923C211yesmaximal, characteristic
5#29507447C211yesmaximal, characteristic, complemented
6#29507444C211yesmaximal, characteristic
7#332×C241C211yesmaximal, characteristic, complemented
8C2×#16838759—21no—
9#21440642C2211yescharacteristic
10#21440637—22no—
11#21440631—21no—
12#21440622—21no—
13Q8×Dic241—21no—
14C4×Dic482C2211yescharacteristic
15C4×D964C2211yescharacteristic
16#21440600—21no—
17#21440575—22no—
18#21440574—21no—
19#21440567—21no—
20#21440567—21no—
21C4×#14515349C2211yescharacteristic
22C4⋊Q8×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4⋊C8×C241C2211yescharacteristic
25C2×Dic482—21no—
26C2×Dic482D411yescharacteristic
27C2×D964D411yescharacteristic
28C2×C4×D241—21no—
29#16838759—42no—
30C2×#14515349—21no—
31C4⋊Dic241—22no—
32C4⋊Dic241—21no—
33C4⋊Dic241—21no—
34C4⋊Dic241D411yescharacteristic
35C4⋊Dic241D411yescharacteristic
36#16838749—21no—
37#16838747—22no—
38#16838747—22no—
39#16838747—21no—
40C4×Dic241—22no—
41C4×Dic241—21no—
42C2×Q8×C241—21no—
43C2×C8×C241—21no—
44C2×C8×C241—21no—
45C4⋊C4×C241—21no—
46C4⋊C4×C241D412yes—
47C42×C241C2311yescharacteristic
48C22×D241—21no—
49Dic482—21no—
50Dic482—21no—
51Dic482—41no—
52Dic482—41no—
53D964—21no—
54D964—21no—
55C2×Dic241—21no—
56C2×Dic241—21no—
57C2×Dic241—21no—
58C2×Dic241—41no—
59C4×D241—41no—
60C4×D241—41no—
61#14515349—22no—
62Q8×C241—41no—
63Q8×C241—41no—
64C2×C4×C241—22no—
65C2×C4×C241C2×D411yescharacteristic
66C2×C4×C241C2×D411yescharacteristic
67C2×C4×C241C2×D411yescharacteristic
68C8×C241—41no—
69C8×C241—41no—
70C22×C241#12011yescharacteristic
71C2×D241—41no—
72C2×D241—41no—
73C2×D241—41no—
74C4×C241—21no—
75C4×C241—42no—
76C4×C241#13511yescharacteristic
77C4×C241#13511yescharacteristic
78C4×C241AGL(1,ℤ/8)11yescharacteristic
79C4×C241#13711yescharacteristic
80Dic241—41no—
81Dic241—41no—
82Dic241—41no—
83Dic241—81no—
84C2×C241#44911yescharacteristic
85C2×C241#45211yescharacteristic
86C2×C241#45611yescharacteristic
87D241—81no—
88C241#165011yescharacteristic, complemented, Sylow
89#1650—2411nomaximal, Sylow
90#556—2411no—
91#500—2411no—
92#475—2411no—
93#461—2411no—
94#332D24111yescharacteristic, complemented
95Q8⋊C8—2411no—
96D4⋊C8—2411no—
97C2×SD16—4821no—
98C4⋊Q8—2411no—
99C4⋊Q8C2×D24111yescharacteristic
100#126—4822no—
101#124—4821no—
102C22⋊Q8—4821no—
103C4×Q8—4821no—
104C4×Q8—2411no—
105C4×D4—2411no—
106#117—4821no—
107#107—4822no—
108#106—4821no—
109C4⋊C8C2×D24111yescharacteristic
110C4⋊C8C2×D24111yescharacteristic
111#103—4821no—
112#103—4821no—
113C4×C8—2411no—
114C2×Q8—21no—
115C2×Q8—4821no—
116C2×Q8—2411no—
117C2×D4—2411no—
118C22×C4—4821no—
119SD16—9642no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—4821no—
123C4⋊C4—21no—
124C4⋊C4—4822no—
125C4⋊C4—4821no—
126C4⋊C4—4821no—
127C4⋊C4—4821no—
128C4⋊C4—2411no—
129C4⋊C4—2411no—
130C4⋊C4D96412yes—
131C22⋊C4—4822no—
132C22⋊C4—4822no—
133C22⋊C4—4821no—
134C42—4822no—
135C42—4821no—
136C42C22×D24111yescharacteristic
137C23—4821no—
138Q8—41no—
139Q8—41no—
140Q8—9641no—
141Q8—9641no—
142Q8—4821no—
143Q8—4821no—
144D4—4821no—
145D4—4821no—
146C2×C4—22no—
147C2×C4—9641no—
148C2×C4—9641no—
149C2×C4—9641no—
150C2×C4—4821no—
151C2×C4—4821no—
152C2×C4—4821no—
153C2×C4D4×D24111yescharacteristic
154C2×C4D4×D24111yescharacteristic
155C2×C4C2×D96411yescharacteristic
156C8—41no—
157C8—41no—
158C8—4822no—
159C22—9641no—
160C22—9641no—
161C22—9641no—
162C22#2144061211yescharacteristic
163C4—21no—
164C4—42no—
165C4—19281no—
166C4—9641no—
167C4—9641no—
168C4—9641no—
169C4#2144066311yescharacteristic
170C4#2144066311yescharacteristic
171C4#2144066611yescharacteristic
172C4#2144067411yescharacteristic
173C2—19281no—
174C2#2950786311yescharacteristic
175C2#2950788211yescharacteristic
176C2#2950790211yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#332×C241C2
socleC22×C241#120
prime radicalC2×D964D4
hypercenter#332D241
hypocenterC241#1650
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #29508120C2semidirect
3. #29508003C2semidirect
5. #29507447C2semidirect
7. #332×C241C2semidirect
88. C241#1650semidirect
94. #332D241semidirect

Maximal subgroups

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

subgroupindex
#295084412
#295081202
#295080032
#295079232
#295074472
#295074442
#332×C2412
#1650241