Finite Group Databasebeta

← #44506466

Subgroups — #44506466

Order 30848.

288 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 51 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#29508275C211yesmaximal, characteristic
2#29508036C211yesmaximal, characteristic, complemented
3#29508033C211yesmaximal, characteristic, complemented
4#29507654C211yesmaximal, characteristic, complemented
5#29507450C211yesmaximal, characteristic, complemented
6#29507440C211yesmaximal, characteristic, complemented
7#327×C241C211yesmaximal, characteristic, complemented
8C2×D4×D241—21no—
9#21440627—21no—
10#21440624—21no—
11#21440616C2211yescharacteristic
12#21440614—21no—
13#21440612—21no—
14#21440610—21no—
15C2×C4⋊Dic241—21no—
16C2×C4⋊Dic241C2211yescharacteristic, complemented
17C2×#16838747—21no—
18C2×#16838747C2211yescharacteristic
19#21440574—21no—
20#21440573—21no—
21#21440564—21no—
22#21440563—21no—
23C22⋊#14515349C2211yescharacteristic, complemented
24#121×C241C2211yescharacteristic
25C22⋊C8×C241C2211yescharacteristic, complemented
26#95×C241C2211yescharacteristic, complemented
27C23×D241—21no—
28C23×D241D411yescharacteristic
29C2×D964—21no—
30C2×D964D411yescharacteristic
31C2×C22⋊D241—21no—
32C2×C22⋊D241—21no—
33C2×C22⋊D241—21no—
34D4×D241—42no—
35D4×D241—42no—
36C22×Dic241—21no—
37C22×Dic241D411yescharacteristic
38C2×C4×D241—21no—
39C2×#14515349—21no—
40C4⋊Dic241—21no—
41C4⋊Dic241—21no—
42C4⋊Dic241—42no—
43C4⋊Dic241D411yescharacteristic
44#16838749—21no—
45C22⋊Dic241—21no—
46#16838747—21no—
47#16838747—21no—
48#16838747—21no—
49#16838747—21no—
50#16838747—42no—
51C2×D4×C241—21no—
52C2×D4×C241D411yescharacteristic
53C22×C4×C241—21no—
54C22×C4×C241C2311yescharacteristic
55C2×C8×C241—21no—
56C4⋊C4×C241D411yescharacteristic
57C22⋊C4×C241—21no—
58C22×D241—21no—
59C22×D241—21no—
60C22×D241—21no—
61C22×D241—42no—
62C22×D241—41no—
63C22×D241—41no—
64C22×D241—81no—
65C22×D241—81no—
66C22×D241SD1612yes—
67D964—41no—
68D964—42no—
69C22⋊D241—42no—
70C22⋊D241—41no—
71C22⋊D241—41no—
72C22⋊D241—81no—
73C2×Dic241—21no—
74C2×Dic241—21no—
75C2×Dic241—41no—
76C2×Dic241—41no—
77C2×Dic241—41no—
78C2×Dic241—41no—
79C4×D241—42no—
80#14515349—41no—
81C23×C241—21no—
82C23×C241C2×D411yescharacteristic
83D4×C241—41no—
84D4×C241—41no—
85D4×C241—41no—
86C2×C4×C241—22no—
87C2×C4×C241—21no—
88C2×C4×C241—41no—
89C2×C4×C241—41no—
90C2×C4×C241—41no—
91C2×C4×C241C2×D411yescharacteristic
92C2×C4×C241C2×D411yescharacteristic
93C8×C241—41no—
94C22×C241—21no—
95C22×C241—21no—
96C22×C241—41no—
97C22×C241—41no—
98C22×C241—41no—
99C22×C241#12011yescharacteristic
100C22×C241C2×SD1611yescharacteristic
101C22×C241AGL(1,ℤ/8)11yescharacteristic
102C2×D241—22no—
103C2×D241—41no—
104C2×D241—41no—
105C2×D241—42no—
106C2×D241—41no—
107C2×D241—41no—
108C2×D241—41no—
109C2×D241—81no—
110C2×D241—84no—
111C4×C241—21no—
112C4×C241—21no—
113C4×C241—42no—
114C4×C241—41no—
115Dic241—41no—
116Dic241—41no—
117Dic241—81no—
118C2×C241—21no—
119C2×C241—21no—
120C2×C241—81no—
121C2×C241#45011yescharacteristic
122C2×C241#45311yescharacteristic
123C2×C241#45811yescharacteristic
124D241—42no—
125D241—81no—
126C241#161311yescharacteristic, complemented, Sylow
127#1613—2411nomaximal, Sylow
128#534—2411no—
129#481—2411no—
130#481—2411no—
131#399—2411no—
132#327—2411no—
133#327D24111yescharacteristic, complemented
134#323—2411no—
135C22×D4—4821no—
136#123—4821no—
137#123—4821no—
138#121—4821no—
139#121—2411no—
140#121C2×D24111yescharacteristic
141#120—4821no—
142#120—4821no—
143C2×C4⋊C4—4821no—
144C2×C4⋊C4—2411no—
145C2×C22⋊C4—4821no—
146C2×C22⋊C4—2411no—
147#106—4821no—
148#106—4821no—
149#102—4821no—
150#102—4821no—
151C22⋊C8—2411no—
152C22⋊C8C2×D24111yescharacteristic, complemented
153#95C2×D24111yescharacteristic, complemented
154C24—4821no—
155C24—2411no—
156C2×D4—21no—
157C2×D4—9642no—
158C2×D4—9642no—
159C2×D4—4821no—
160C2×D4—4821no—
161C2×D4—4821no—
162C2×D4—4821no—
163C2×D4—2411no—
164C2×D4D96411yescharacteristic
165C22×C4—21no—
166C22×C4—4821no—
167C22×C4—4821no—
168C22×C4—2411no—
169C22×C4C22×D24111yescharacteristic
170C2×C8—21no—
171C2×C8—4821no—
172C4⋊C4—9642no—
173C4⋊C4—4821no—
174C4⋊C4—4821no—
175C4⋊C4—4821no—
176C4⋊C4—2411no—
177C4⋊C4D96411yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—9642no—
180C22⋊C4—4821no—
181C22⋊C4—4821no—
182C22⋊C4—4821no—
183C22⋊C4—4821no—
184C22⋊C4—4821no—
185C23—21no—
186C23—19281no—
187C23—19281no—
188C23—9641no—
189C23—9641no—
190C23—9642no—
191C23—4821no—
192C23—4821no—
193C23—4821no—
194C23—2412no—
195C23D4×D24111yescharacteristic
196D4—41no—
197D4—41no—
198D4—41no—
199D4—19281no—
200D4—9641no—
201D4—9642no—
202D4—9642no—
203D4—9641no—
204D4—9641no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—9642no—
211C2×C4—9641no—
212C2×C4—9641no—
213C2×C4—9641no—
214C2×C4—9641no—
215C2×C4—4821no—
216C2×C4—4821no—
217C2×C4D4×D24111yescharacteristic
218C2×C4C2×D96411yescharacteristic
219C8—41no—
220C8—9641no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—19281no—
227C22—19284no—
228C22—9642no—
229C22—9641no—
230C22—9641no—
231C22—9641no—
232C22—9641no—
233C22—9641no—
234C22—4822no—
235C22#2144061211yescharacteristic
236C22SD16×D24111yescharacteristic
237C22#2144066611yescharacteristic
238C4—21no—
239C4—21no—
240C4—42no—
241C4—41no—
242C4—19281no—
243C4—9641no—
244C4—9641no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—19281no—
249C2—9642no—
250C2#2950786911yescharacteristic
251C2#2950788611yescharacteristic
252C2#2950790811yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#327×C241C2
socleC22×C241#120
prime radical#29508275C2
hypercenter#327D241
hypocenterC241#1613
LCSG ▷ C22×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #29508036C2semidirect
3. #29508033C2semidirect
4. #29507654C2semidirect
5. #29507450C2semidirect
6. #29507440C2semidirect
7. #327×C241C2semidirect
16. C2×C4⋊Dic241C22semidirect
23. C22⋊#14515349C22semidirect
25. C22⋊C8×C241C22semidirect
26. #95×C241C22semidirect
126. C241#1613semidirect
133. #327D241semidirect
152. C22⋊C8C2×D241semidirect
153. #95C2×D241semidirect

Maximal subgroups

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

subgroupindex
#295082752
#295080362
#295080332
#295076542
#295074502
#295074402
#327×C2412
#1613241