Finite Group Databasebeta

← #44506457

Subgroups — #44506457

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#29508305C211yesmaximal, characteristic
2#29508047C211yesmaximal, characteristic, complemented
3#29508030C211yesmaximal, characteristic, complemented
4#29507453C211yesmaximal, characteristic, complemented
5#29507450C211yesmaximal, characteristic, complemented
6#29507441C211yesmaximal, characteristic, complemented
7#397×C241C211yesmaximal, characteristic, complemented
8#21440635—21no—
9#21440628—21no—
10#21440624—21no—
11#21440621C2211yescharacteristic
12#21440616C2211yescharacteristic
13#21440615—21no—
14#21440611—21no—
15C4×C22⋊D241—21no—
16#21440575—21no—
17#21440573—21no—
18#21440565—21no—
19#21440562—21no—
20C22⋊#14515349C2211yescharacteristic
21C22⋊#14515349C2211yescharacteristic
22C2×C4⋊C4×C241C2211yescharacteristic
23C2×C22⋊C4×C241—21no—
24C2×C22⋊C4×C241C2211yescharacteristic
25#95×C241—21no—
26#95×C241C2211yescharacteristic
27C2×Dic482D411yescharacteristic
28C2×D964D411yescharacteristic
29C2×C22⋊D241—21no—
30C2×C22⋊D241—21no—
31C2×C22⋊D241—21no—
32C2×C4×D241—21no—
33C2×#14515349—21no—
34C2×#14515349—21no—
35C4⋊Dic241D411yescharacteristic
36C4⋊Dic241D411yescharacteristic
37#16838749—21no—
38#16838749—21no—
39C22⋊Dic241—21no—
40C22⋊Dic241—21no—
41C22⋊Dic241—21no—
42#16838747—21no—
43#16838747—21no—
44C4×Dic241—21no—
45C24×C241D411yescharacteristic
46C22×C4×C241—21no—
47C22×C4×C241—21no—
48C22×C4×C241D411yescharacteristic
49C22×C4×C241C2311yescharacteristic
50C4⋊C4×C241—21no—
51C4⋊C4×C241—21no—
52C22⋊C4×C241—21no—
53C22⋊C4×C241—21no—
54C22⋊C4×C241—42no—
55C22×D241—21no—
56Dic482—41no—
57D964—41no—
58C22⋊D241—41no—
59C22⋊D241—41no—
60C22⋊D241—81no—
61C22⋊D241—81no—
62C2×Dic241—21no—
63C2×Dic241—21no—
64C2×Dic241—21no—
65C4×D241—81no—
66#14515349—41no—
67#14515349—41no—
68C23×C241—21no—
69C23×C241—21no—
70C23×C241—21no—
71C23×C241—41no—
72C23×C241—41no—
73C23×C241C2×D411yescharacteristic
74C2×C4×C241—21no—
75C2×C4×C241—41no—
76C2×C4×C241—41no—
77C2×C4×C241—41no—
78C2×C4×C241—41no—
79C2×C4×C241—41no—
80C2×C4×C241—41no—
81C2×C4×C241—41no—
82C2×C4×C241—41no—
83C2×C4×C241C2×D411yescharacteristic
84C2×C4×C241C2×D411yescharacteristic
85C22×C241—21no—
86C22×C241—21no—
87C22×C241—42no—
88C22×C241—41no—
89C22×C241—41no—
90C22×C241—41no—
91C22×C241—81no—
92C22×C241#12011yescharacteristic
93C22×C241#13511yescharacteristic
94C22×C241AGL(1,ℤ/8)11yescharacteristic
95C2×D241—41no—
96C2×D241—41no—
97C2×D241—41no—
98C4×C241—21no—
99C4×C241—21no—
100C4×C241—41no—
101C4×C241—81no—
102C4×C241—81no—
103Dic241—41no—
104Dic241—41no—
105Dic241—41no—
106C2×C241—21no—
107C2×C241—21no—
108C2×C241—81no—
109C2×C241#44911yescharacteristic
110C2×C241#45511yescharacteristic
111C2×C241#45811yescharacteristic
112D241—81no—
113C241#161211yescharacteristic, complemented, Sylow
114#1612—2411nomaximal, Sylow
115#538—2411no—
116#483—2411no—
117#480—2411no—
118#397D24111yescharacteristic, complemented
119#328—2411no—
120#327—2411no—
121#323—2411no—
122#126—4821no—
123#124—4821no—
124#123—4821no—
125C22⋊Q8—2411no—
126#121—4821no—
127#121—2411no—
128#120—4821no—
129C4×D4—4821no—
130C2×C4⋊C4C2×D24111yescharacteristic
131C2×C22⋊C4—21no—
132C2×C22⋊C4C2×D24111yescharacteristic
133#107—4821no—
134#106—4821no—
135#103—4821no—
136#102—4821no—
137C22⋊C8—2411no—
138C22⋊C8—2411no—
139#95—21no—
140#95C2×D24111yescharacteristic
141C24C22⋊D24111yescharacteristic
142C2×Q8—2411no—
143C2×D4—4821no—
144C2×D4—4821no—
145C2×D4—4821no—
146C2×D4—2411no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—4821no—
150C22×C4C22⋊D24111yescharacteristic
151C22×C4C22×D24111yescharacteristic
152C2×C8—4821no—
153C2×C8—4821no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—4821no—
157C4⋊C4—4821no—
158C4⋊C4—2411no—
159C4⋊C4—2411no—
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—42no—
163C22⋊C4—4821no—
164C22⋊C4—4821no—
165C22⋊C4—4821no—
166C22⋊C4—4821no—
167C22⋊C4—4821no—
168C42—4821no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—41no—
173C23—41no—
174C23—4821no—
175C23C2×C22⋊D24111yescharacteristic
176Q8—9641no—
177D4—19281no—
178D4—19281no—
179D4—9641no—
180D4—9641no—
181D4—9641no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—19281no—
192C2×C4—4821no—
193C2×C4—4821no—
194C2×C4—4821no—
195C2×C4D4×D24111yescharacteristic
196C2×C4D4×D24111yescharacteristic
197C8—9641no—
198C8—9641no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22—9641no—
207C22—9641no—
208C22—9641no—
209C22#2144061011yescharacteristic
210C22#2144066211yescharacteristic
211C22#2144066811yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—81no—
217C4—9641no—
218C4—9641no—
219C4—9641no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—19281no—
224C2#2950786011yescharacteristic
225C2#2950789411yescharacteristic
226C2#2950790611yescharacteristic
subgroupG/H
centerC22#21440610
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#397×C241C2
socleC22×C241#120
prime radical#29508305C2
hypercenter#397D241
hypocenterC241#1612
LCSG ▷ C22×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #397

Complements

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

NH ≅ G/Ntype
2. #29508047C2semidirect
3. #29508030C2semidirect
4. #29507453C2semidirect
5. #29507450C2semidirect
6. #29507441C2semidirect
7. #397×C241C2semidirect
113. C241#1612semidirect
118. #397D241semidirect

Maximal subgroups

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

subgroupindex
#295083052
#295080472
#295080302
#295074532
#295074502
#295074412
#397×C2412
#1612241