Finite Group Databasebeta

← #44506427

Subgroups — #44506427

Order 30848.

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

normal subgroups only

This group has 260 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#29507875C211yesmaximal, characteristic, complemented
3#29507858C211yesmaximal, characteristic, complemented
4#29507629C211yesmaximal, characteristic, complemented
5#29507455C211yesmaximal, characteristic, complemented
6#29507452C211yesmaximal, characteristic, complemented
7#323×C241C211yesmaximal, characteristic, complemented
8C22×Dic482C2211yescharacteristic
9C2×Dic964—21no—
10C2×#16838759—21no—
11#21440635—21no—
12#21440628—21no—
13#21440624—21no—
14#21440621C2211yescharacteristic
15#21440616C2211yescharacteristic
16#21440615—21no—
17#21440611—21no—
18C4×C22⋊D241—21no—
19C2×C22⋊Dic241—21no—
20#21440567—21no—
21#21440567—21no—
22#21440549—21no—
23#21440549C2211yescharacteristic
24C2×C22⋊C4×C241C2211yescharacteristic
25C22⋊C8×C241C2211yescharacteristic
26C22⋊C8×C241C2211yescharacteristic
27C2×Dic482—21no—
28C2×Dic482—21no—
29C2×Dic482—42no—
30C2×Dic482D411yescharacteristic
31C2×D964D411yescharacteristic
32C2×C22⋊D241—21no—
33C2×C22⋊D241—21no—
34C2×C22⋊D241—21no—
35C22×Dic241—21no—
36C22×Dic241—21no—
37C2×C4×D241—21no—
38Dic964—42no—
39#16838759—42no—
40C4⋊Dic241D411yescharacteristic
41C4⋊Dic241D411yescharacteristic
42#16838749—21no—
43#16838749—21no—
44C22⋊Dic241—21no—
45C22⋊Dic241—21no—
46C22⋊Dic241—21no—
47C22⋊Dic241—42no—
48#16838747—21no—
49#16838747—21no—
50C4×Dic241—21no—
51C24×C241D411yescharacteristic
52C22×C4×C241D411yescharacteristic
53C22×C4×C241C2311yescharacteristic
54C2×C8×C241—21no—
55C2×C8×C241—21no—
56C22⋊C4×C241—21no—
57C22⋊C4×C241—21no—
58C22×D241—21no—
59Dic482—22no—
60Dic482—22no—
61Dic482—41no—
62Dic482—41no—
63Dic482—41no—
64D964—41no—
65C22⋊D241—41no—
66C22⋊D241—41no—
67C22⋊D241—81no—
68C22⋊D241—81no—
69C2×Dic241—22no—
70C2×Dic241—21no—
71C2×Dic241—21no—
72C2×Dic241—21no—
73C2×Dic241—41no—
74C2×Dic241—41no—
75C2×Dic241—41no—
76C2×Dic241—41no—
77C2×Dic241—41no—
78C4×D241—81no—
79C23×C241—21no—
80C23×C241—21no—
81C23×C241—21no—
82C23×C241—41no—
83C23×C241—41no—
84C23×C241C2×D411yescharacteristic
85C2×C4×C241—21no—
86C2×C4×C241—41no—
87C2×C4×C241—41no—
88C2×C4×C241C2×D411yescharacteristic
89C2×C4×C241C2×D411yescharacteristic
90C8×C241—41no—
91C8×C241—41no—
92C22×C241—21no—
93C22×C241—21no—
94C22×C241—42no—
95C22×C241—41no—
96C22×C241—41no—
97C22×C241—41no—
98C22×C241—81no—
99C22×C241#12011yescharacteristic
100C22×C241#13511yescharacteristic
101C22×C241#13711yescharacteristic
102C2×D241—41no—
103C2×D241—41no—
104C2×D241—41no—
105C4×C241—21no—
106C4×C241—21no—
107C4×C241—41no—
108Dic241—41no—
109Dic241—41no—
110Dic241—42no—
111Dic241—41no—
112Dic241—81no—
113C2×C241—21no—
114C2×C241—21no—
115C2×C241—81no—
116C2×C241#45211yescharacteristic
117C2×C241#45511yescharacteristic
118C2×C241B(4,𝔽2)11yescharacteristic
119D241—81no—
120C241#160611yescharacteristic, complemented, Sylow
121#1606—2411nomaximal, Sylow
122#538—2411no—
123#451—2411no—
124#448—2411no—
125#393—2411no—
126#328—2411no—
127#327—2411no—
128#323D24111yescharacteristic, complemented
129C22×Q8—2411no—
130C2×Q16—4821no—
131C2×SD16—4821no—
132#126—4821no—
133#124—4821no—
134#123—4821no—
135C22⋊Q8—2411no—
136#121—4821no—
137#121—2411no—
138#120—4821no—
139C4×D4—4821no—
140C2×C22⋊C4—4821no—
141C2×C22⋊C4C2×D24111yescharacteristic
142#103—4821no—
143#103—4821no—
144C22⋊C8C2×D24111yescharacteristic
145C22⋊C8C2×D24111yescharacteristic
146#95—4821no—
147#95—2411no—
148C24D96411yescharacteristic
149C2×Q8—9642no—
150C2×Q8—4821no—
151C2×Q8—4821no—
152C2×Q8—2411no—
153C2×D4—4821no—
154C2×D4—4821no—
155C2×D4—4821no—
156C2×D4—2411no—
157C22×C4—4821no—
158C22×C4—4821no—
159C22×C4—4821no—
160C22×C4D96411yescharacteristic
161C22×C4C22×D24111yescharacteristic
162Q16—9642no—
163SD16—9642no—
164C2×C8—21no—
165C2×C8—21no—
166C4⋊C4—4821no—
167C4⋊C4—4821no—
168C4⋊C4—2411no—
169C4⋊C4—2411no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—9642no—
173C22⋊C4—4821no—
174C22⋊C4—4821no—
175C22⋊C4—4821no—
176C22⋊C4—4821no—
177C22⋊C4—4821no—
178C42—4821no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23—41no—
183C23—41no—
184C23—4821no—
185C23C2×D96411yescharacteristic
186Q8—9641no—
187Q8—9641no—
188Q8—9641no—
189Q8—4822no—
190Q8—4822no—
191D4—19281no—
192D4—19281no—
193D4—9641no—
194D4—9641no—
195D4—9641no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—19281no—
200C2×C4—9641no—
201C2×C4—9641no—
202C2×C4—9641no—
203C2×C4—9641no—
204C2×C4—9641no—
205C2×C4—4822no—
206C2×C4—4821no—
207C2×C4—4821no—
208C2×C4—4821no—
209C2×C4D4×D24111yescharacteristic
210C2×C4D4×D24111yescharacteristic
211C8—41no—
212C8—41no—
213C22—21no—
214C22—21no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—9641no—
221C22—9641no—
222C22—9641no—
223C22#2144061211yescharacteristic
224C22#2144066411yescharacteristic
225C22#2144067511yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—19281no—
230C4—9641no—
231C4—9641no—
232C4—9642no—
233C4—9641no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—19281no—
238C2#2950788111yescharacteristic
239C2#2950789711yescharacteristic
240C2#2950790511yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#323×C241C2
socleC22×C241#120
prime radical#29508305C2
hypercenter#323D241
hypocenterC241#1606
LCSG ▷ C22×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #29507875C2semidirect
3. #29507858C2semidirect
4. #29507629C2semidirect
5. #29507455C2semidirect
6. #29507452C2semidirect
7. #323×C241C2semidirect
120. C241#1606semidirect
128. #323D241semidirect

Maximal subgroups

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

subgroupindex
#295083052
#295078752
#295078582
#295076292
#295074552
#295074522
#323×C2412
#1606241