Finite Group Databasebeta

← #44506778

Subgroups — #44506778

Order 30848.

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

normal subgroups only

This group has 184 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#29508467C211yesmaximal, characteristic
2#29508123C211yesmaximal, characteristic, complemented
3#29508085C211yesmaximal, characteristic, complemented
4#29507458C211yesmaximal, characteristic, complemented
5#29507458C211yesmaximal, characteristic, complemented
6#29507457C211yesmaximal, characteristic
7#489×C241C211yesmaximal, characteristic
8#21440640—21no—
9#21440635—21no—
10#21440635—21no—
11#21440634C2211yescharacteristic
12#21440634C2211yescharacteristic
13#21440623—21no—
14#21440619—21no—
15#21440619—21no—
16#21440575—21no—
17#21440573—21no—
18#21440566—21no—
19#21440566—21no—
20#21440553C2211yescharacteristic
21#21440553C2211yescharacteristic
22C4⋊Q8×C241C2211yescharacteristic
23#124×C241C2211yescharacteristic
24#103×C241—21no—
25#102×C241—21no—
26#97×C241C2211yescharacteristic
27C2×Dic482—21no—
28C22×Dic241—21no—
29C2×#14515349—21no—
30C2×#14515349—21no—
31C4⋊Dic241D411yescharacteristic
32C4⋊Dic241D411yescharacteristic
33C4⋊Dic241D411yescharacteristic
34C4⋊Dic241D411yescharacteristic
35#16838749—21no—
36#16838749—21no—
37#16838749—21no—
38#16838749—21no—
39#16838749—21no—
40#16838749—21no—
41C22⋊Dic241—21no—
42C22⋊Dic241—21no—
43C22⋊Dic241—21no—
44C4×Dic241—21no—
45C2×Q8×C241—21no—
46C2×Q8×C241D411yescharacteristic
47C2×D4×C241D411yescharacteristic
48C2×C8×C241—21no—
49C4⋊C4×C241—21no—
50C4⋊C4×C241—21no—
51C22⋊C4×C241—21no—
52C22⋊C4×C241—21no—
53C42×C241C2311yescharacteristic
54Dic482—81no—
55C2×Dic241—21no—
56C2×Dic241—21no—
57C2×Dic241—21no—
58C2×Dic241—21no—
59C2×Dic241—81no—
60#14515349—22no—
61#14515349—41no—
62C23×C241—21no—
63Q8×C241—41no—
64Q8×C241—42no—
65D4×C241—41no—
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—41no—
73C22×C241—41no—
74C22×C241—41no—
75C22×C241#12011yescharacteristic
76C4×C241—21no—
77C4×C241—21no—
78C4×C241—21no—
79C4×C241—41no—
80C4×C241—81no—
81Dic241—41no—
82Dic241—41no—
83Dic241—41no—
84Dic241—41no—
85C2×C241—81no—
86C2×C241#45411yescharacteristic
87C2×C241#45511yescharacteristic
88C2×C241#45611yescharacteristic
89C241#166411yescharacteristic, complemented, Sylow
90#1664—2411nomaximal, Sylow
91#563—2411no—
92#501—2411no—
93#491—2411no—
94#489D24111yescharacteristic
95#330—2411no—
96#330—2411no—
97#329—2411no—
98C4⋊Q8—4821no—
99C4⋊Q8C2×D24111yescharacteristic
100#126—4821no—
101#126—4821no—
102#125—2411no—
103#125—2411no—
104#124C2×D24111yescharacteristic
105#123—4821no—
106C22⋊Q8—4821no—
107C22⋊Q8—4821no—
108#107—4821no—
109#106—4821no—
110#103—21no—
111#103—4821no—
112#103—4821no—
113#102—21no—
114#97—2411no—
115#97—2411no—
116#97C2×D24111yescharacteristic
117C2×Q8—21no—
118C2×Q8—4821no—
119C2×Q8C22⋊D24111yescharacteristic
120C2×D4C22⋊D24111yescharacteristic
121C22×C4—4821no—
122C2×C8—21no—
123C2×C8—4821no—
124C2×C8—4821no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—4821no—
128C4⋊C4—4821no—
129C4⋊C4—4821no—
130C4⋊C4—4821no—
131C4⋊C4—4821no—
132C4⋊C4—4821no—
133C4⋊C4—2411no—
134C4⋊C4—2411no—
135C4⋊C4—2411no—
136C4⋊C4—2411no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—4821no—
140C22⋊C4—4821no—
141C22⋊C4—4821no—
142C42—4821no—
143C42C22×D24111yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—42no—
147Q8—19281no—
148D4—41no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—19281no—
152C2×C4—4821no—
153C2×C4—4821no—
154C2×C4—4821no—
155C2×C4—4821no—
156C2×C4D4×D24111yescharacteristic
157C2×C4D4×D24111yescharacteristic
158C2×C4C2×C22⋊D24111yescharacteristic
159C8—41no—
160C8—9641no—
161C8—4822no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#2144061011yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—81no—
171C4—9641no—
172C4—9641no—
173C4—9641no—
174C4—9641no—
175C2—81no—
176C2#2950788811yescharacteristic
177C2#2950789411yescharacteristic
178C2#2950789811yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#489×C241C2
socleC22×C241#120
prime radicalC2×D4×C241D4
hypercenter#489D241
hypocenterC241#1664
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #29508123C2semidirect
3. #29508085C2semidirect
4. #29507458C2semidirect
5. #29507458C2semidirect
89. C241#1664semidirect

Maximal subgroups

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

subgroupindex
#295084672
#295081232
#295080852
#295074582
#295074572
#489×C2412
#1664241