Finite Group Databasebeta

← #44509397

Subgroups — #44509397

Order 30848.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#29508514C211yesmaximal, characteristic
2#29508160C211yesmaximal, characteristic, complemented
3#29508157C211yesmaximal, characteristic, complemented
4#29507976C211yesmaximal, characteristic, complemented
5#29507526C211yesmaximal, characteristic, complemented
6#29507498C211yesmaximal, characteristic, complemented
7#360×C241C211yesmaximal, characteristic, complemented
8#41×D241—21no—
9#21440674—21no—
10#21440671—21no—
11#21440669—21no—
12#21440666—21no—
13#21440664C2211yescharacteristic
14#21440662—21no—
15C2×Dic964C2211yescharacteristic, complemented
16C2×#16838753C2211yescharacteristic
17#21440622—21no—
18Dic1928—21no—
19#21440588—21no—
20#21440587—21no—
21#21440586—21no—
22#21440582C2211yescharacteristic, complemented
23#21440565—21no—
24#135×C241C2211yescharacteristic
25M32×C241C2211yescharacteristic, complemented
26#106×C241C2211yescharacteristic, complemented
27#16838771—21no—
28#16838770—21no—
29#16838770—41no—
30#16838769—21no—
31#16838769—41no—
32C2×Dic482—21no—
33Q8×D241—21no—
34D4×D241—21no—
35D4×D241—41no—
36C2×C4×D241—41no—
37C2×C4×D241D411yescharacteristic
38Dic964—21no—
39Dic964—21no—
40Dic964D411yescharacteristic
41#16838760—21no—
42#16838759—21no—
43#16838758—21no—
44#16838757—21no—
45D1928D411yescharacteristic
46#16838755—21no—
47#16838753—21no—
48#16838753—21no—
49C2×#14515349D411yescharacteristic
50C4⋊Dic241—41no—
51#16838747—41no—
52#16838745—21no—
53#41×C241—21no—
54Q16×C241D411yescharacteristic
55SD16×C241—21no—
56D8×C241D411yescharacteristic
57C2×C8×C241C2311yescharacteristic
58C4⋊C4×C241—21no—
59C16×C241—21no—
60C22×D241—41no—
61C22×D241D811yescharacteristic
62Dic482—21no—
63Dic482—41no—
64Dic482—41no—
65Dic482—41no—
66D964—21no—
67D964—41no—
68C22⋊D241—41no—
69C22⋊D241—41no—
70C22⋊D241—41no—
71C2×Dic241—41no—
72C2×Dic241—41no—
73C2×Dic241D811yescharacteristic
74C4×D241—21no—
75C4×D241—21no—
76C4×D241—41no—
77C4×D241—41no—
78C4×D241—41no—
79#14515349—21no—
80Q8×C241—21no—
81D4×C241—21no—
82D4×C241—41no—
83C2×C4×C241—41no—
84C2×C4×C241—41no—
85C2×C4×C241C2×D411yescharacteristic
86C8×C241C2×D411yescharacteristic
87C8×C241C2×D411yescharacteristic
88C22×C241—41no—
89C22×C241C2×D811yescharacteristic
90C2×D241—21no—
91C2×D241—41no—
92C2×D241—41no—
93C2×D241—82no—
94C4×C241—41no—
95C4×C241—81no—
96C4×C241#12011yescharacteristic
97C4×C241AGL(1,ℤ/8)11yescharacteristic
98Dic241—21no—
99Dic241—41no—
100Dic241—81no—
101C2×C241—21no—
102C2×C241—81no—
103C2×C241#44711yescharacteristic
104D241—41no—
105D241—81no—
106C241#219111yescharacteristic, complemented, Sylow
107#2191—2411nomaximal, Sylow
108#575—2411no—
109#510—2411no—
110#510—2411no—
111#470—2411no—
112#360—2411no—
113#360D24111yescharacteristic, complemented
114#349—2411no—
115C2×#41—4821no—
116#137—4821no—
117#137—4821no—
118AGL(1,ℤ/8)—4821no—
119AGL(1,ℤ/8)—4821no—
120#135—4821no—
121#135—2411no—
122#135C2×D24111yescharacteristic
123C2×Q16—2411no—
124C2×M16—2411no—
125C22⋊Q8—4821no—
126Q32—4821no—
127Q32—4821no—
128SD32—4821no—
129SD32—4821no—
130M32—2411no—
131M32C2×D24111yescharacteristic, complemented
132#106C2×D24111yescharacteristic, complemented
133#103—4821no—
134#41—21no—
135#41—9641no—
136#41—9641no—
137#41—4821no—
138#41—4821no—
139#41—4821no—
140C2×Q8—4821no—
141C2×Q8—4821no—
142C2×D4—9641no—
143C2×D4—4821no—
144C22×C4—9641no—
145C22×C4—2411no—
146Q16—4821no—
147Q16—4821no—
148Q16—4821no—
149Q16—2411no—
150Q16D96411yescharacteristic
151SD16—21no—
152SD16—4821no—
153SD16—4821no—
154SD16—4821no—
155D8—4821no—
156D8—2411no—
157D8D96411yescharacteristic
158M16—4821no—
159M16—4821no—
160C2×C8—2411no—
161C2×C8C22×D24111yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—9641no—
164C22⋊C4—9641no—
165C16—21no—
166C16—4821no—
167C23—9641no—
168C23—2411no—
169Q8—21no—
170Q8—9641no—
171Q8—9641no—
172Q8—9641no—
173Q8—4821no—
174D4—21no—
175D4—41no—
176D4—9641no—
177D4—9641no—
178D4—9641no—
179D4—9641no—
180D4—4821no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—9641no—
184C2×C4—9641no—
185C2×C4—9641no—
186C2×C4—9641no—
187C2×C4—9641no—
188C2×C4—4821no—
189C2×C4—4821no—
190C2×C4—2411no—
191C2×C4D4×D24111yescharacteristic
192C8—4821no—
193C8D4×D24111yescharacteristic
194C8C2×D96411yescharacteristic
195C22—41no—
196C22—19282no—
197C22—9641no—
198C22—9641no—
199C22—4821no—
200C22D8×D24111yescharacteristic
201C4—41no—
202C4—81no—
203C4—19281no—
204C4—9641no—
205C4—4821no—
206C4#2144061211yescharacteristic
207C4#2144066911yescharacteristic
208C2—21no—
209C2—81no—
210C2—19281no—
211C2—9641no—
212C2#2950785211yescharacteristic
subgroupG/H
centerC2#29507852
commutator, cosocleC2×C8×C241C23
FrattiniC2×C8C22×D241
Fitting#360×C241C2
socleC2×C241#447
prime radical#29508514C2
hypercenter#360D241
hypocenterC241#2191
LCSG ▷ C2×C8×C241 ▷ C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. #29508160C2semidirect
3. #29508157C2semidirect
4. #29507976C2semidirect
5. #29507526C2semidirect
6. #29507498C2semidirect
7. #360×C241C2semidirect
15. C2×Dic964C22semidirect
22. #21440582C22semidirect
25. M32×C241C22semidirect
26. #106×C241C22semidirect
106. C241#2191semidirect
113. #360D241semidirect
131. M32C2×D241semidirect
132. #106C2×D241semidirect

Maximal subgroups

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

subgroupindex
#295085142
#295081602
#295081572
#295079762
#295075262
#295074982
#360×C2412
#2191241