Finite Group Databasebeta

← #44506527

Subgroups — #44506527

Order 30848.

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

normal subgroups only

This group has 240 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#29508432C211yesmaximal, characteristic, complemented
2#29508089C211yesmaximal, characteristic, complemented
3#29507909C211yesmaximal, characteristic, complemented
4#29507465C211yesmaximal, characteristic, complemented
5D4⋊#14515349C211yesmaximal, characteristic, complemented
6#29507444C211yesmaximal, characteristic, complemented
7#459×C241C211yesmaximal, characteristic, complemented
8C2×#16838758—22no—
9C2×#16838755—21no—
10#21440642C2211yescharacteristic
11#21440628—22no—
12#21440616—21no—
13#21440613—21no—
14C4×D964C2211yescharacteristic
15#21440601—21no—
16#21440600—21no—
17C4⋊#14515349C2211yescharacteristic
18#21440563—21no—
19C4×#14515349C2211yescharacteristic
20C2×D8×C241—21no—
21#127×C241C2211yescharacteristic
22C4×D4×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24#102×C241—21no—
25C2×Dic482D412yes—
26C2×D964D411yescharacteristic
27C2×C22⋊D241—22no—
28C2×C4×D241—21no—
29#16838758—44no—
30#16838755—42no—
31C2×#14515349—21no—
32C2×#14515349—21no—
33C4⋊Dic241—21no—
34C4⋊Dic241—21no—
35C4⋊Dic241D411yescharacteristic
36C22⋊Dic241—22no—
37#16838747—22no—
38#16838747—21no—
39C4×Dic241—22no—
40C2×D4×C241—21no—
41C2×D4×C241—21no—
42C2×D4×C241—21no—
43C2×D4×C241D411yescharacteristic
44C22×C4×C241—21no—
45D8×C241—42no—
46C2×C8×C241—21no—
47C4⋊C4×C241D411yescharacteristic
48C22⋊C4×C241—21no—
49C42×C241C2311yescharacteristic
50C22×D241—21no—
51Dic482—42no—
52D964—21no—
53D964—21no—
54C22⋊D241—82no—
55C2×Dic241—21no—
56C2×Dic241—22no—
57C4×D241—41no—
58C4×D241—41no—
59#14515349—22no—
60#14515349—41no—
61C23×C241—21no—
62C23×C241—41no—
63D4×C241—21no—
64D4×C241—21no—
65D4×C241—42no—
66D4×C241—41no—
67D4×C241—41no—
68D4×C241—41no—
69D4×C241—41no—
70C2×C4×C241—21no—
71C2×C4×C241—41no—
72C2×C4×C241—41no—
73C2×C4×C241C2×D411yescharacteristic
74C2×C4×C241C2×D411yescharacteristic
75C2×C4×C241C2×D411yescharacteristic
76C8×C241—41no—
77C22×C241—41no—
78C22×C241—41no—
79C22×C241—41no—
80C22×C241—81no—
81C22×C241—81no—
82C22×C241—81no—
83C22×C241#12011yescharacteristic
84C2×D241—41no—
85C2×D241—41no—
86C2×D241—41no—
87C4×C241—21no—
88C4×C241—41no—
89C4×C241#13511yescharacteristic
90C4×C241#13511yescharacteristic
91C4×C241AGL(1,ℤ/8)11yescharacteristic
92C4×C241AGL(1,ℤ/8)11yescharacteristic
93Dic241—41no—
94Dic241—42no—
95C2×C241—81no—
96C2×C241—161no—
97C2×C241#44911yescharacteristic
98C2×C241#44911yescharacteristic
99C2×C241#45311yescharacteristic
100D241—81no—
101C241#162411yescharacteristic, complemented, Sylow
102#1624—2411nomaximal, Sylow
103#555—2411no—
104#492—2411no—
105#459—2411no—
106#459D24111yescharacteristic, complemented
107#333—2411no—
108D4⋊C8—2411no—
109D4⋊C8—2411no—
110C2×SD16—4822no—
111C2×D8—21no—
112C2×D8—4821no—
113C4⋊Q8—2411no—
114#127C2×D24111yescharacteristic
115#124—4822no—
116#121—4821no—
117#121—4821no—
118C4×D4—2411no—
119C4×D4C2×D24111yescharacteristic
120#117—4821no—
121#117—4821no—
122C4⋊C8—2411no—
123C4⋊C8C2×D24111yescharacteristic
124#102—21no—
125#102—4821no—
126C4×C8—2411no—
127C2×Q8—2412no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—21no—
131C2×D4—4822no—
132C2×D4—2411no—
133C2×D4C22⋊D24111yescharacteristic
134C22×C4—21no—
135C22×C4—4821no—
136SD16—9644no—
137D8—42no—
138D8—9642no—
139C2×C8—21no—
140C2×C8—4821no—
141C2×C8—4821no—
142C4⋊C4—4821no—
143C4⋊C4—4821no—
144C4⋊C4—2411no—
145C4⋊C4C22⋊D24111yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—4822no—
148C22⋊C4—4822no—
149C22⋊C4—4821no—
150C42—4822no—
151C42C22×D24111yescharacteristic
152C23—21no—
153C23—41no—
154C23—4821no—
155Q8—9642no—
156D4—21no—
157D4—21no—
158D4—42no—
159D4—41no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—19282no—
164D4—4821no—
165D4—4821no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—9641no—
170C2×C4—9641no—
171C2×C4—4821no—
172C2×C4—4822no—
173C2×C4D4×D24111yescharacteristic
174C2×C4D4×D24111yescharacteristic
175C2×C4C2×C22⋊D24111yescharacteristic
176C8—41no—
177C8—9641no—
178C8—4822no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—9641no—
186C22—9641no—
187C22—9641no—
188C22#2144061011yescharacteristic
189C4—21no—
190C4—41no—
191C4—9641no—
192C4—9642no—
193C4#2144066111yescharacteristic
194C4#2144066211yescharacteristic
195C4#2144066611yescharacteristic
196C4#2144066811yescharacteristic
197C2—81no—
198C2—161no—
199C2—19281no—
200C2#2950785911yescharacteristic
201C2#2950786011yescharacteristic
202C2#2950788311yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#459×C241C2
socleC22×C241#120
hypercenter#459D241
hypocenterC241#1624
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #29508432C2semidirect
2. #29508089C2semidirect
3. #29507909C2semidirect
4. #29507465C2semidirect
5. D4⋊#14515349C2semidirect
6. #29507444C2semidirect
7. #459×C241C2semidirect
101. C241#1624semidirect
106. #459D241semidirect

Maximal subgroups

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

subgroupindex
#295084322
#295080892
#295079092
#295074652
D4⋊#145153492
#295074442
#459×C2412
#1624241