Finite Group Databasebeta

← #44506629

Subgroups — #44506629

Order 30848.

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

normal subgroups only

This group has 212 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#29508452C211yesmaximal, characteristic
2#29508065C211yesmaximal, characteristic
3#29507999C211yesmaximal, characteristic, complemented
4#29507460C211yesmaximal, characteristic
5Q8⋊#14515349C211yesmaximal, characteristic, complemented
6#29507447C211yesmaximal, characteristic, complemented
7#462×C241C211yesmaximal, characteristic, complemented
8#21440639C2211yescharacteristic
9#21440631—21no—
10#21440630—21no—
11#21440627—22no—
12C4×Dic482C2211yescharacteristic
13C4×D964—21no—
14#21440604—21no—
15#21440573—21no—
16C4⋊#14515349C2211yescharacteristic
17#21440565—21no—
18#21440562—22no—
19C4×#14515349C2211yescharacteristic
20C2×Q16×C241—21no—
21C4⋊Q8×C241C2211yescharacteristic
22C4×Q8×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24#103×C241—21no—
25C2×Dic482D411yescharacteristic
26C2×D964—21no—
27C2×D964—21no—
28C2×D964D412yes—
29C2×C4×D241—22no—
30C2×#14515349—21no—
31C2×#14515349—21no—
32C4⋊Dic241D411yescharacteristic
33#16838749—21no—
34#16838747—22no—
35#16838747—22no—
36#16838747—22no—
37C4×Dic241—21no—
38C2×Q8×C241—21no—
39C2×Q8×C241D411yescharacteristic
40Q16×C241—42no—
41C2×C8×C241—21no—
42C4⋊C4×C241—21no—
43C4⋊C4×C241—21no—
44C4⋊C4×C241—21no—
45C4⋊C4×C241D411yescharacteristic
46C42×C241—21no—
47C42×C241C2311yescharacteristic
48C22×D241—22no—
49Dic482—21no—
50Dic482—21no—
51D964—42no—
52D964—41no—
53D964—41no—
54D964—41no—
55D964—41no—
56C2×Dic241—21no—
57C2×Dic241—21no—
58C4×D241—82no—
59#14515349—41no—
60#14515349—41no—
61Q8×C241—21no—
62Q8×C241—21no—
63Q8×C241—41no—
64Q8×C241—41no—
65C2×C4×C241—21no—
66C2×C4×C241—21no—
67C2×C4×C241—41no—
68C2×C4×C241C2×D411yescharacteristic
69C2×C4×C241C2×D411yescharacteristic
70C2×C4×C241C2×D411yescharacteristic
71C8×C241—41no—
72C22×C241#12011yescharacteristic
73C2×D241—42no—
74C2×D241—42no—
75C2×D241—42no—
76C4×C241—21no—
77C4×C241—41no—
78C4×C241—41no—
79C4×C241—81no—
80C4×C241#13511yescharacteristic
81C4×C241#13511yescharacteristic
82C4×C241AGL(1,ℤ/8)11yescharacteristic
83C4×C241#13711yescharacteristic
84Dic241—41no—
85Dic241—41no—
86C2×C241#44911yescharacteristic
87C2×C241#45211yescharacteristic
88C2×C241#45511yescharacteristic
89D241—82no—
90C241#164011yescharacteristic, complemented, Sylow
91#1640—2411nomaximal, Sylow
92#559—2411no—
93#486—2411no—
94#475—2411no—
95#462D24111yescharacteristic, complemented
96#331—2411no—
97Q8⋊C8—2411no—
98Q8⋊C8—2411no—
99C2×Q16—21no—
100C4⋊Q8C2×D24111yescharacteristic
101#127—2411no—
102#124—4821no—
103#124—4821no—
104#123—4822no—
105C4×Q8—2411no—
106C4×Q8C2×D24111yescharacteristic
107C4×D4—4821no—
108C4×D4—4821no—
109#106—4821no—
110C4⋊C8—2411no—
111C4⋊C8C2×D24111yescharacteristic
112#103—21no—
113#103—4821no—
114#102—4822no—
115C4×C8—2411no—
116C2×Q8—21no—
117C2×Q8—2411no—
118C2×Q8C22⋊D24111yescharacteristic
119C2×D4—4821no—
120C2×D4—4821no—
121C2×D4—2412no—
122C22×C4—4822no—
123Q16—42no—
124C2×C8—21no—
125C2×C8—4821no—
126C2×C8—4821no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—4821no—
131C4⋊C4—2411no—
132C4⋊C4C22⋊D24111yescharacteristic
133C22⋊C4—4822no—
134C22⋊C4—4822no—
135C22⋊C4—4822no—
136C42—21no—
137C42—4821no—
138C42C22×D24111yescharacteristic
139C23—4822no—
140Q8—21no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—4821no—
145Q8—4821no—
146D4—9642no—
147D4—9641no—
148D4—9641no—
149D4—9641no—
150D4—9641no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—19282no—
155C2×C4—4821no—
156C2×C4—4821no—
157C2×C4D4×D24111yescharacteristic
158C2×C4D4×D24111yescharacteristic
159C2×C4C2×C22⋊D24111yescharacteristic
160C8—41no—
161C8—9641no—
162C8—9641no—
163C22—9642no—
164C22—9642no—
165C22—9642no—
166C22#2144061011yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—81no—
171C4—9641no—
172C4—9641no—
173C4#2144066211yescharacteristic
174C4#2144066511yescharacteristic
175C4#2144066811yescharacteristic
176C4#2144067411yescharacteristic
177C2—19282no—
178C2#2950786011yescharacteristic
179C2#2950787811yescharacteristic
180C2#2950789311yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#462×C241C2
socleC22×C241#120
prime radical#21440639C22
hypercenter#462D241
hypocenterC241#1640
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #29507999C2semidirect
5. Q8⋊#14515349C2semidirect
6. #29507447C2semidirect
7. #462×C241C2semidirect
90. C241#1640semidirect
95. #462D241semidirect

Maximal subgroups

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

subgroupindex
#295084522
#295080652
#295079992
#295074602
Q8⋊#145153492
#295074472
#462×C2412
#1640241