Finite Group Databasebeta

← #44506458

Subgroups — #44506458

Order 30848.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#29508307C211yesmaximal, characteristic
2#29508030C211yesmaximal, characteristic, complemented
3#29507643C211yesmaximal, characteristic, complemented
4#29507454C211yesmaximal, characteristic, complemented
5#29507452C211yesmaximal, characteristic, complemented
6#29507440C211yesmaximal, characteristic, complemented
7#483×C241C211yesmaximal, characteristic, complemented
8#21440637—21no—
9#21440631—21no—
10#21440627—21no—
11#21440617—21no—
12#21440616C2211yescharacteristic
13#21440612—21no—
14#21440602—21no—
15C2×#16838747—21no—
16C2×#16838747C2211yescharacteristic
17#21440575—21no—
18#21440562—21no—
19C22⋊#14515349C2211yescharacteristic
20#21440549—21no—
21#21440549C2211yescharacteristic
22C22⋊Q8×C241C2211yescharacteristic
23C2×C4⋊C4×C241C2211yescharacteristic
24#106×C241—21no—
25#103×C241—21no—
26C22⋊C8×C241C2211yescharacteristic
27C23×D241D411yescharacteristic
28C2×D964—21no—
29C2×D964—21no—
30C2×D964D411yescharacteristic
31C2×C22⋊D241—21no—
32C22×Dic241—21no—
33C22×Dic241D411yescharacteristic
34C2×C4×D241—21no—
35C2×#14515349—21no—
36C4⋊Dic241D411yescharacteristic
37#16838749—21no—
38#16838747—21no—
39#16838747—21no—
40#16838747—21no—
41#16838747—21no—
42#16838747—21no—
43#16838747—21no—
44#16838747—42no—
45C4×Dic241—21no—
46C2×Q8×C241D411yescharacteristic
47C22×C4×C241—21no—
48C22×C4×C241C2311yescharacteristic
49C2×C8×C241—21no—
50C4⋊C4×C241—21no—
51C4⋊C4×C241—21no—
52C4⋊C4×C241—21no—
53C4⋊C4×C241D411yescharacteristic
54C22⋊C4×C241—21no—
55C22×D241—21no—
56C22×D241—21no—
57C22×D241—21no—
58C22×D241—21no—
59C22×D241—41no—
60C22×D241—41no—
61D964—41no—
62D964—81no—
63D964—81no—
64C22⋊D241—41no—
65C22⋊D241—41no—
66C2×Dic241—21no—
67C2×Dic241—21no—
68C2×Dic241—41no—
69C2×Dic241—41no—
70C2×Dic241—41no—
71C2×Dic241—41no—
72C4×D241—81no—
73#14515349—41no—
74C23×C241C2×D411yescharacteristic
75Q8×C241—41no—
76C2×C4×C241—21no—
77C2×C4×C241—21no—
78C2×C4×C241—41no—
79C2×C4×C241—41no—
80C2×C4×C241—41no—
81C2×C4×C241—41no—
82C2×C4×C241C2×D411yescharacteristic
83C2×C4×C241C2×D411yescharacteristic
84C8×C241—41no—
85C22×C241—21no—
86C22×C241—21no—
87C22×C241#12011yescharacteristic
88C22×C241#13511yescharacteristic
89C22×C241AGL(1,ℤ/8)11yescharacteristic
90C2×D241—42no—
91C2×D241—41no—
92C2×D241—41no—
93C2×D241—41no—
94C2×D241—41no—
95C2×D241—41no—
96C2×D241—41no—
97C2×D241—81no—
98C4×C241—21no—
99C4×C241—21no—
100C4×C241—41no—
101C4×C241—41no—
102C4×C241—81no—
103Dic241—41no—
104Dic241—41no—
105Dic241—81no—
106C2×C241—21no—
107C2×C241—21no—
108C2×C241#44911yescharacteristic
109C2×C241#45511yescharacteristic
110C2×C241#45811yescharacteristic
111D241—81no—
112D241—81no—
113C241#161211yescharacteristic, complemented, Sylow
114#1612—2411nomaximal, Sylow
115#538—2411no—
116#483D24111yescharacteristic, complemented
117#480—2411no—
118#397—2411no—
119#328—2411no—
120#327—2411no—
121#323—2411no—
122#126—4821no—
123#124—4821no—
124#123—4821no—
125C22⋊Q8C2×D24111yescharacteristic
126#121—4821no—
127#121—2411no—
128#120—4821no—
129C4×D4—4821no—
130C2×C4⋊C4C2×D24111yescharacteristic
131C2×C22⋊C4—4821no—
132C2×C22⋊C4—2411no—
133#107—4821no—
134#106—21no—
135#103—21no—
136#102—4821no—
137C22⋊C8—2411no—
138C22⋊C8C2×D24111yescharacteristic
139#95—4821no—
140#95—2411no—
141C24—2411no—
142C2×Q8C22⋊D24111yescharacteristic
143C2×D4—4821no—
144C2×D4—4821no—
145C2×D4—4821no—
146C2×D4—2411no—
147C22×C4—21no—
148C22×C4—4821no—
149C22×C4—4821no—
150C22×C4—2411no—
151C22×C4C22×D24111yescharacteristic
152C2×C8—21no—
153C2×C8—4821no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—4821no—
158C4⋊C4—2411no—
159C4⋊C4C22⋊D24111yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—9642no—
162C22⋊C4—4821no—
163C22⋊C4—4821no—
164C22⋊C4—4821no—
165C22⋊C4—4821no—
166C22⋊C4—4821no—
167C22⋊C4—4821no—
168C42—4821no—
169C23—9641no—
170C23—9641no—
171C23—4821no—
172C23—4821no—
173C23—4821no—
174C23—4821no—
175C23D4×D24111yescharacteristic
176Q8—41no—
177D4—19281no—
178D4—19281no—
179D4—9641no—
180D4—9641no—
181D4—9641no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—19281no—
189C2×C4—9641no—
190C2×C4—9641no—
191C2×C4—9641no—
192C2×C4—9641no—
193C2×C4—4821no—
194C2×C4—4821no—
195C2×C4D4×D24111yescharacteristic
196C2×C4C2×C22⋊D24111yescharacteristic
197C8—41no—
198C8—9641no—
199C22—21no—
200C22—21no—
201C22—19281no—
202C22—9642no—
203C22—9641no—
204C22—9641no—
205C22—9641no—
206C22—9641no—
207C22—9641no—
208C22—9641no—
209C22#2144061011yescharacteristic
210C22#2144066311yescharacteristic
211C22#2144066911yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—81no—
217C4—19281no—
218C4—9641no—
219C4—9641no—
220C2—21no—
221C2—21no—
222C2—19281no—
223C2—19281no—
224C2#2950786111yescharacteristic
225C2#2950789311yescharacteristic
226C2#2950790611yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#483×C241C2
socleC22×C241#120
prime radical#29508307C2
hypercenter#483D241
hypocenterC241#1612
LCSG ▷ C22×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #29508030C2semidirect
3. #29507643C2semidirect
4. #29507454C2semidirect
5. #29507452C2semidirect
6. #29507440C2semidirect
7. #483×C241C2semidirect
113. C241#1612semidirect
116. #483D241semidirect

Maximal subgroups

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

subgroupindex
#295083072
#295080302
#295076432
#295074542
#295074522
#295074402
#483×C2412
#1612241