Finite Group Databasebeta

← #44508512

Subgroups — #44508512

Order 30848.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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#29508517C211yesmaximal, characteristic, complemented
2#29508228C212yesmaximal, complemented
3#29507733C212yesmaximal, complemented
4#29507474C211yesmaximal, characteristic, complemented
5#407×C241C211yesmaximal, characteristic, complemented
6C2×#16838770C2212yes—
7#21440675—22no—
8#21440670—22no—
9#21440664—22no—
10#21440625—22no—
11#21440621—22no—
12#21440616—22no—
13#21440611—22no—
14C4×C22⋊D241—24no—
15#21440601C2212yes—
16#21440568—24no—
17C23×C4×C241C2211yescharacteristic
18C2×M16×C241C2211yescharacteristic
19C2×M16×C241C2211yescharacteristic
20C22⋊C8×C241—22no—
21#16838770—22no—
22#16838770—22no—
23#16838770—22no—
24#16838770—22no—
25C2×Dic482D412yescomplemented
26C2×D964D412yescomplemented
27C2×C22⋊D241—24no—
28C2×C22⋊D241—22no—
29C2×C4×D241—22no—
30Dic964—22no—
31#16838759—24no—
32D1928—22no—
33C4⋊Dic241—22no—
34#16838749—24no—
35C22⋊Dic241—24no—
36C22⋊Dic241—22no—
37#16838747—24no—
38C4×Dic241D414yescomplemented
39C24×C241D411yescharacteristic
40C22×C4×C241—22no—
41C22×C4×C241—22no—
42C22×C4×C241—21no—
43C22×C4×C241—21no—
44C22×C4×C241D411yescharacteristic
45C22×C4×C241C2311yescharacteristic
46M16×C241—22no—
47M16×C241—22no—
48C2×C8×C241—21no—
49C2×C8×C241D412yescomplemented
50C22×D241—22no—
51Dic482—22no—
52Dic482—22no—
53D964—22no—
54D964—22no—
55C22⋊D241—48no—
56C22⋊D241—42no—
57C22⋊D241—42no—
58C2×Dic241—24no—
59C2×Dic241—22no—
60C4×D241—42no—
61C4×D241—42no—
62C23×C241—22no—
63C23×C241—21no—
64C23×C241—42no—
65C23×C241C2×D411yescharacteristic
66C2×C4×C241—22no—
67C2×C4×C241—21no—
68C2×C4×C241—41no—
69C2×C4×C241—42no—
70C2×C4×C241—41no—
71C2×C4×C241C2×D412yes—
72C2×C4×C241C2×D412yes—
73C2×C4×C241C2×D411yescharacteristic
74C2×C4×C241#4111yescharacteristic
75C8×C241—22no—
76C8×C241—41no—
77C22×C241—22no—
78C22×C241—24no—
79C22×C241—41no—
80C22×C241—42no—
81C22×C241—41no—
82C22×C241—41no—
83C22×C241#12012yes—
84C22×C241#12111yescharacteristic
85C2×D241—44no—
86C2×D241—42no—
87C4×C241—41no—
88C4×C241#12011yescharacteristic
89C4×C241#12112yes—
90C4×C241#12711yescharacteristic
91Dic241—44no—
92Dic241—42no—
93C2×C241—22no—
94C2×C241—21no—
95C2×C241—42no—
96C2×C241#39211yescharacteristic
97D241—82no—
98C241#201011yescharacteristic, complemented, Sylow
99#2010—2411nomaximal, Sylow
100#575—2411no—
101#525—2412no—
102#421—2412no—
103#407D24111yescharacteristic, complemented
104H(3,ℤ/4)—2411no—
105C2×#41—2412no—
106C23×C4C2×D24111yescharacteristic
107#137—4822no—
108AGL(1,ℤ/8)—4822no—
109#135—4822no—
110C2×M16C2×D24111yescharacteristic
111C2×M16C2×D24111yescharacteristic
112#123—4822no—
113C22⋊Q8—4822no—
114#121—4822no—
115#120—4822no—
116C4×D4—4824no—
117#117—2412no—
118#104—4824no—
119C22⋊C8—22no—
120C24D96411yescharacteristic
121#41—4822no—
122#41—4822no—
123#41—4822no—
124#41—4822no—
125C2×Q8—2412no—
126C2×D4—4824no—
127C2×D4—4822no—
128C2×D4—2412no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—4822no—
134C22×C4D96411yescharacteristic
135C22×C4C22×D24111yescharacteristic
136Q16—4822no—
137SD16—4824no—
138D8—4822no—
139M16—22no—
140M16—22no—
141C2×C8—21no—
142C2×C8C22⋊D24112yescomplemented
143C4⋊C4—4824no—
144C4⋊C4—4822no—
145C22⋊C4—4824no—
146C22⋊C4—4824no—
147C22⋊C4—4822no—
148C42—2414no—
149C23—22no—
150C23—21no—
151C23—42no—
152C23—4822no—
153C23C2×D96411yescharacteristic
154Q8—4822no—
155Q8—4822no—
156D4—9648no—
157D4—9642no—
158D4—9642no—
159D4—4822no—
160D4—4822no—
161C2×C4—22no—
162C2×C4—21no—
163C2×C4—41no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—9642no—
167C2×C4—9642no—
168C2×C4—4824no—
169C2×C4—4822no—
170C2×C4D4×D24112yes—
171C2×C4D4×D24112yes—
172C2×C4C2×C22⋊D24111yescharacteristic
173C2×C4#1683877011yescharacteristic
174C8—22no—
175C8—41no—
176C22—24no—
177C22—22no—
178C22—41no—
179C22—42no—
180C22—41no—
181C22—41no—
182C22—9644no—
183C22—9642no—
184C22#2144061212yes—
185C22#2144061611yescharacteristic
186C4—41no—
187C4—9644no—
188C4—9642no—
189C4#2144061011yescharacteristic
190C4#2144061512yes—
191C4#2144063811yescharacteristic
192C2—22no—
193C2—21no—
194C2—42no—
195C2—19282no—
196C2#2950762611yescharacteristic
subgroupG/H
centerC4#21440638
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#407×C241C2
socleC2×C241#392
hypercenter#407D241
hypocenterC241#2010
LCSG ▷ C22×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C4 ◁ C22×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #29508517C2semidirect
2. #29508228C2semidirect
3. #29507733C2semidirect
4. #29507474C2semidirect
5. #407×C241C2semidirect
25. C2×Dic482D4semidirect
26. C2×D964D4semidirect
38. C4×Dic241D4semidirect
49. C2×C8×C241D4semidirect
98. C241#2010semidirect
103. #407D241semidirect
142. C2×C8C22⋊D241semidirect

Maximal subgroups

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

subgroupindex
#295085172
#295082282
#295077332
#295074742
#407×C2412
#2010241