Finite Group Databasebeta

← #44507883

Subgroups — #44507883

Order 30848.

412 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C2×#21440616C211yesmaximal, characteristic
2C2×#21440564C212yesmaximal, complemented
3#29507577C211yesmaximal, characteristic, complemented
4#29507480C212yesmaximal, complemented
5C22×M16×C241C211yesmaximal, characteristic, complemented
6C22×D964C2211yescharacteristic
7C22×C22⋊D241—21no—
8#21440616—22no—
9#21440616C414yescomplemented
10C2×C4⋊Dic241C2212yes—
11C2×C4⋊Dic241C2211yescharacteristic
12C2×C22⋊Dic241—21no—
13C2×#16838747—21no—
14#21440564—24no—
15#21440549—21no—
16C23×C4×C241C2211yescharacteristic
17C2×M16×C241—22no—
18C2×M16×C241—24no—
19C22×C8×C241C2212yes—
20C23×D241—21no—
21C2×D964—22no—
22C2×D964—21no—
23C2×D964—22no—
24C2×D964C2×C412yes—
25C2×C22⋊D241—24no—
26C2×C22⋊D241—44no—
27C22×Dic241—21no—
28C22×Dic241—22no—
29C4⋊Dic241—21no—
30C4⋊Dic241—22no—
31C4⋊Dic241—22no—
32C4⋊Dic241C2×C412yes—
33C22⋊Dic241—42no—
34#16838747—24no—
35C24×C241D411yescharacteristic
36C22×C4×C241—22no—
37C22×C4×C241—22no—
38C22×C4×C241C2×C412yes—
39C22×C4×C241D412yes—
40C22×C4×C241D411yescharacteristic
41C22×C4×C241C2311yescharacteristic
42M16×C241—28no—
43C2×C8×C241—22no—
44C2×C8×C241—22no—
45C2×C8×C241D414yescomplemented
46C22×D241—22no—
47C22×D241—42no—
48C22×D241—42no—
49C22×D241—41no—
50C22×D241—41no—
51D964—24no—
52D964—41no—
53D964—41no—
54C22⋊D241—48no—
55C2×Dic241—22no—
56C2×Dic241—42no—
57C2×Dic241—42no—
58C2×Dic241—42no—
59C2×Dic241—42no—
60C23×C241—22no—
61C23×C241—21no—
62C23×C241—22no—
63C23×C241—21no—
64C23×C241C22⋊C412yes—
65C23×C241C2×D411yescharacteristic
66C2×C4×C241—22no—
67C2×C4×C241—24no—
68C2×C4×C241—22no—
69C2×C4×C241—22no—
70C2×C4×C241C22⋊C412yes—
71C2×C4×C241C22×C411yescharacteristic
72C2×C4×C241C2×D412yes—
73C2×C4×C241C2×D411yescharacteristic
74C2×C4×C241#4112yes—
75C8×C241—24no—
76C22×C241—22no—
77C22×C241—22no—
78C22×C241—22no—
79C22×C241—42no—
80C22×C241—42no—
81C22×C241C2×C22⋊C411yescharacteristic
82C22×C241#12112yes—
83C22×C241AGL(1,ℤ/8)11yescharacteristic
84C22×C241AGL(1,ℤ/8)12yes—
85C22×C241#13711yescharacteristic
86C2×D241—42no—
87C2×D241—42no—
88C2×D241—42no—
89C2×D241—82no—
90C2×D241—82no—
91C4×C241—22no—
92C4×C241C4×D412yes—
93C4×C241#12011yescharacteristic
94C4×C241#12311yescharacteristic
95Dic241—42no—
96Dic241—82no—
97C2×C241—42no—
98C2×C241#38611yescharacteristic
99C2×C241#41711yescharacteristic
100C2×C241#41811yescharacteristic
101C2×C241#46812yes—
102C2×C241#46912yes—
103D241—82no—
104C241#189511yescharacteristic, complemented, Sylow
105#1895—2411nomaximal, Sylow
106C22×M16D24111yescharacteristic, complemented
107C2×#121—2411no—
108C2×#102—2412no—
109#380—2411no—
110#340—2412no—
111C22×D4—4821no—
112C22×D4—2411no—
113C23×C4C2×D24111yescharacteristic
114C2×M16—22no—
115C2×M16—24no—
116C22×C8C2×D24112yes—
117#121—4822no—
118#121—2414no—
119C2×C4⋊C4—2412no—
120C2×C4⋊C4—2411no—
121C2×C22⋊C4—4821no—
122C2×C22⋊C4—4821no—
123#102—4824no—
124#95—4821no—
125C24—4821no—
126C24D96411yescharacteristic
127C2×D4—9644no—
128C2×D4—4824no—
129C2×D4—4821no—
130C2×D4—4822no—
131C2×D4—4822no—
132C2×D4—2412no—
133C22×C4—22no—
134C22×C4—22no—
135C22×C4—4822no—
136C22×C4—4821no—
137C22×C4C4×D24112yes—
138C22×C4C22⋊D24112yes—
139C22×C4D96411yescharacteristic
140C22×C4C22×D24111yescharacteristic
141M16—28no—
142C2×C8—22no—
143C2×C8—22no—
144C2×C8C22⋊D24114yescomplemented
145C4⋊C4—4822no—
146C4⋊C4—4822no—
147C4⋊C4—4821no—
148C4⋊C4—2412no—
149C22⋊C4—9642no—
150C22⋊C4—4824no—
151C23—22no—
152C23—21no—
153C23—22no—
154C23—21no—
155C23—9642no—
156C23—9642no—
157C23—9641no—
158C23—9641no—
159C23—4822no—
160C23#1683874712yes—
161C23C2×D96411yescharacteristic
162D4—9648no—
163D4—9641no—
164D4—9641no—
165D4—4824no—
166C2×C4—22no—
167C2×C4—24no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—9642no—
171C2×C4—9642no—
172C2×C4—9642no—
173C2×C4—9642no—
174C2×C4—4822no—
175C2×C4#1683874712yes—
176C2×C4C2×C4×D24111yescharacteristic
177C2×C4C2×C22⋊D24112yes—
178C2×C4C2×C22⋊D24111yescharacteristic
179C2×C4#1683877012yes—
180C8—24no—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—19282no—
187C22—19282no—
188C22—9642no—
189C22—9642no—
190C22—9642no—
191C22C2×#1683874711yescharacteristic
192C22#2144061612yes—
193C22#2144067012yes—
194C22#2144067011yescharacteristic
195C22#2144067511yescharacteristic
196C4—22no—
197C4—19282no—
198C4—9642no—
199C4C4×C22⋊D24112yes—
200C4#2144061111yescharacteristic
201C4#2144062511yescharacteristic
202C2—42no—
203C2—19282no—
204C2#2950759611yescharacteristic
205C2#2950771911yescharacteristic
206C2#2950772311yescharacteristic
207C2#2950796312yes—
208C2#2950797012yes—
subgroupG/H
centerC23C2×D964
commutatorC2×C4×C241C22×C4
FrattiniC22×C4C22×D241
FittingC22×M16×C241C2
socleC23×C241C2×D4
prime radicalC2×#21440616C2
cosocleC22×C4×C241C23
hypercenterC22×M16D241
hypocenterC241#1895
LCSG ▷ C2×C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#21440564C2semidirect
3. #29507577C2semidirect
4. #29507480C2semidirect
5. C22×M16×C241C2semidirect
9. #21440616C4semidirect
45. C2×C8×C241D4semidirect
104. C241#1895semidirect
106. C22×M16D241semidirect
144. C2×C8C22⋊D241semidirect

Maximal subgroups

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

subgroupindex
C2×#214406162
C2×#214405642
#295075772
#295074802
C22×M16×C2412
#1895241