Finite Group Databasebeta

← #44506398

Subgroups — #44506398

Order 30848.

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

normal subgroups only

This group has 308 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#29507858C211yesmaximal, characteristic, complemented
3#29507855C211yesmaximal, characteristic, complemented
4#29507630C211yesmaximal, characteristic, complemented
5#29507450C211yesmaximal, characteristic, complemented
6#29507440C211yesmaximal, characteristic, complemented
7#327×C241C211yesmaximal, characteristic, complemented
8C22×Dic482C2211yescharacteristic, complemented
9C2×D4×D241—21no—
10C2×#16838759—21no—
11C2×#16838758—21no—
12#21440627—21no—
13#21440624—21no—
14#21440616C2211yescharacteristic
15#21440614—21no—
16#21440612—21no—
17#21440610—21no—
18C2×#16838747—21no—
19C2×#16838747C2211yescharacteristic
20#21440567—21no—
21#21440565—21no—
22C22⋊#14515349C2211yescharacteristic, complemented
23#21440549—21no—
24#121×C241C2211yescharacteristic
25C22⋊C8×C241C2211yescharacteristic, complemented
26#95×C241C2211yescharacteristic, complemented
27C23×D241—21no—
28C23×D241D411yescharacteristic
29C2×Dic482—21no—
30C2×Dic482—21no—
31C2×Dic482—42no—
32C2×D964—21no—
33C2×D964D411yescharacteristic
34C2×C22⋊D241—21no—
35C2×C22⋊D241—21no—
36C2×C22⋊D241—21no—
37D4×D241—42no—
38D4×D241—42no—
39C22×Dic241—21no—
40C22×Dic241D411yescharacteristic
41C2×C4×D241—21no—
42#16838759—42no—
43#16838758—42no—
44C2×#14515349—21no—
45C4⋊Dic241D411yescharacteristic
46#16838749—21no—
47C22⋊Dic241—21no—
48#16838747—21no—
49#16838747—21no—
50#16838747—21no—
51#16838747—21no—
52#16838747—42no—
53C2×D4×C241—21no—
54C2×D4×C241D411yescharacteristic
55C22×C4×C241—21no—
56C22×C4×C241C2311yescharacteristic
57C2×C8×C241—21no—
58C4⋊C4×C241D411yescharacteristic
59C22⋊C4×C241—21no—
60C22×D241—21no—
61C22×D241—21no—
62C22×D241—21no—
63C22×D241—42no—
64C22×D241—41no—
65C22×D241—41no—
66C22×D241—81no—
67C22×D241—81no—
68C22×D241SD1612yescomplemented
69Dic482—22no—
70Dic482—22no—
71Dic482—41no—
72Dic482—41no—
73D964—41no—
74D964—42no—
75C22⋊D241—42no—
76C22⋊D241—41no—
77C22⋊D241—41no—
78C22⋊D241—81no—
79C2×Dic241—22no—
80C2×Dic241—21no—
81C2×Dic241—21no—
82C2×Dic241—41no—
83C2×Dic241—41no—
84C2×Dic241—41no—
85C4×D241—42no—
86#14515349—41no—
87C23×C241—21no—
88C23×C241C2×D411yescharacteristic
89D4×C241—41no—
90D4×C241—41no—
91D4×C241—41no—
92C2×C4×C241—21no—
93C2×C4×C241—41no—
94C2×C4×C241—41no—
95C2×C4×C241—41no—
96C2×C4×C241—41no—
97C2×C4×C241C2×D411yescharacteristic
98C2×C4×C241C2×D411yescharacteristic
99C8×C241—41no—
100C22×C241—21no—
101C22×C241—21no—
102C22×C241—41no—
103C22×C241—41no—
104C22×C241—41no—
105C22×C241#12011yescharacteristic
106C22×C241C2×SD1611yescharacteristic
107C22×C241AGL(1,ℤ/8)11yescharacteristic
108C2×D241—22no—
109C2×D241—41no—
110C2×D241—41no—
111C2×D241—42no—
112C2×D241—41no—
113C2×D241—41no—
114C2×D241—41no—
115C2×D241—81no—
116C2×D241—84no—
117C4×C241—21no—
118C4×C241—21no—
119C4×C241—41no—
120C4×C241—81no—
121Dic241—41no—
122Dic241—41no—
123Dic241—42no—
124C2×C241—21no—
125C2×C241—21no—
126C2×C241—81no—
127C2×C241#45011yescharacteristic
128C2×C241#45511yescharacteristic
129C2×C241B(4,𝔽2)11yescharacteristic
130D241—42no—
131D241—81no—
132C241#160111yescharacteristic, complemented, Sylow
133#1601—2411nomaximal, Sylow
134#534—2411no—
135#448—2411no—
136#448—2411no—
137#393—2411no—
138#327—2411no—
139#327D24111yescharacteristic, complemented
140#323—2411no—
141C22×Q8—2411no—
142C22×D4—4821no—
143C2×SD16—4821no—
144C2×SD16—4821no—
145#123—4821no—
146#123—4821no—
147#121—4821no—
148#121—2411no—
149#121C2×D24111yescharacteristic
150#120—4821no—
151#120—4821no—
152C2×C22⋊C4—4821no—
153C2×C22⋊C4—2411no—
154#103—4821no—
155#103—4821no—
156C22⋊C8—2411no—
157C22⋊C8C2×D24111yescharacteristic, complemented
158#95—4821no—
159#95C2×D24111yescharacteristic, complemented
160C24—4821no—
161C24—2411no—
162C2×Q8—9642no—
163C2×Q8—4821no—
164C2×Q8—4821no—
165C2×D4—21no—
166C2×D4—9642no—
167C2×D4—9642no—
168C2×D4—4821no—
169C2×D4—4821no—
170C2×D4—4821no—
171C2×D4—4821no—
172C2×D4—2411no—
173C2×D4D96411yescharacteristic
174C22×C4—21no—
175C22×C4—4821no—
176C22×C4—4821no—
177C22×C4—2411no—
178C22×C4C22×D24111yescharacteristic
179SD16—9642no—
180SD16—9642no—
181C2×C8—21no—
182C2×C8—4821no—
183C4⋊C4—4821no—
184C4⋊C4—2411no—
185C4⋊C4D96411yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—9642no—
188C22⋊C4—4821no—
189C22⋊C4—4821no—
190C22⋊C4—4821no—
191C22⋊C4—4821no—
192C22⋊C4—4821no—
193C23—21no—
194C23—19281no—
195C23—19281no—
196C23—9641no—
197C23—9641no—
198C23—9642no—
199C23—4821no—
200C23—4821no—
201C23—4821no—
202C23—2412no—
203C23D4×D24111yescharacteristic
204Q8—9641no—
205Q8—9641no—
206Q8—4822no—
207Q8—4822no—
208D4—41no—
209D4—41no—
210D4—41no—
211D4—19281no—
212D4—9641no—
213D4—9642no—
214D4—9642no—
215D4—9641no—
216D4—9641no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—9642no—
223C2×C4—9641no—
224C2×C4—9641no—
225C2×C4—9641no—
226C2×C4—4822no—
227C2×C4—4821no—
228C2×C4—4821no—
229C2×C4D4×D24111yescharacteristic
230C2×C4C2×D96411yescharacteristic
231C8—41no—
232C8—9641no—
233C22—21no—
234C22—21no—
235C22—41no—
236C22—41no—
237C22—41no—
238C22—19281no—
239C22—19284no—
240C22—9642no—
241C22—9641no—
242C22—9641no—
243C22—9641no—
244C22—9641no—
245C22—9641no—
246C22—4822no—
247C22#2144061211yescharacteristic
248C22SD16×D24111yescharacteristic
249C22#2144066611yescharacteristic
250C4—21no—
251C4—21no—
252C4—41no—
253C4—81no—
254C4—9641no—
255C4—9641no—
256C4—9642no—
257C2—21no—
258C2—21no—
259C2—81no—
260C2—19281no—
261C2—9642no—
262C2#2950786911yescharacteristic
263C2#2950789611yescharacteristic
264C2#2950790511yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#327×C241C2
socleC22×C241#120
prime radical#29508275C2
hypercenter#327D241
hypocenterC241#1601
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. #29507858C2semidirect
3. #29507855C2semidirect
4. #29507630C2semidirect
5. #29507450C2semidirect
6. #29507440C2semidirect
7. #327×C241C2semidirect
8. C22×Dic482C22semidirect
22. C22⋊#14515349C22semidirect
25. C22⋊C8×C241C22semidirect
26. #95×C241C22semidirect
68. C22×D241SD16semidirect
132. C241#1601semidirect
139. #327D241semidirect
157. C22⋊C8C2×D241semidirect
159. #95C2×D241semidirect

Maximal subgroups

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

subgroupindex
#295082752
#295078582
#295078552
#295076302
#295074502
#295074402
#327×C2412
#1601241