Finite Group Databasebeta

← #44506415

Subgroups — #44506415

Order 30848.

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

normal subgroups only

This group has 282 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#29508294C211yesmaximal, characteristic
2#29507858C211yesmaximal, characteristic, complemented
3#29507855C211yesmaximal, characteristic, complemented
4#29507638C211yesmaximal, characteristic, complemented
5#29507450C211yesmaximal, characteristic, complemented
6#29507442C211yesmaximal, characteristic, complemented
7#327×C241C211yesmaximal, characteristic, complemented
8C2×#16838769—21no—
9C22×Dic482C2211yescharacteristic
10C2×#16838759—21no—
11C2×#16838758—21no—
12#21440620—21no—
13#21440619—21no—
14#21440616C2211yescharacteristic
15#21440615—21no—
16#21440614—21no—
17#21440614—21no—
18C2×C4⋊Dic241—21no—
19C2×#16838749C2211yescharacteristic
20#21440567—21no—
21#21440565—21no—
22C22⋊#14515349C2211yescharacteristic
23#21440549—21no—
24#121×C241C2211yescharacteristic
25C22⋊C8×C241C2211yescharacteristic
26#95×C241C2211yescharacteristic
27#16838769—42no—
28#16838769—42no—
29C2×Dic482—21no—
30C2×Dic482—21no—
31C2×Dic482—21no—
32C2×Dic482—42no—
33C2×D964D411yescharacteristic
34C2×C22⋊D241—21no—
35C2×C22⋊D241—21no—
36C2×C22⋊D241—21no—
37C22×Dic241—21no—
38C22×Dic241—21no—
39C22×Dic241D411yescharacteristic
40C22×Dic241D411yescharacteristic
41C2×C4×D241—21no—
42#16838759—42no—
43#16838758—42no—
44C2×#14515349—21no—
45C4⋊Dic241—42no—
46C4⋊Dic241D411yescharacteristic
47#16838749—21no—
48#16838749—21no—
49#16838749—21no—
50C22⋊Dic241—21no—
51#16838747—21no—
52#16838747—21no—
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—
61Dic482—22no—
62Dic482—22no—
63Dic482—42no—
64Dic482—41no—
65Dic482—41no—
66D964—41no—
67C22⋊D241—42no—
68C22⋊D241—41no—
69C22⋊D241—41no—
70C22⋊D241—81no—
71C2×Dic241—21no—
72C2×Dic241—21no—
73C2×Dic241—22no—
74C2×Dic241—21no—
75C2×Dic241—21no—
76C2×Dic241—42no—
77C2×Dic241—41no—
78C2×Dic241—41no—
79C2×Dic241—41no—
80C2×Dic241SD1612yescomplemented
81C4×D241—42no—
82#14515349—41no—
83C23×C241—21no—
84C23×C241C2×D411yescharacteristic
85D4×C241—41no—
86D4×C241—41no—
87D4×C241—41no—
88C2×C4×C241—22no—
89C2×C4×C241—21no—
90C2×C4×C241—41no—
91C2×C4×C241—41no—
92C2×C4×C241—41no—
93C2×C4×C241C2×D411yescharacteristic
94C2×C4×C241C2×D411yescharacteristic
95C8×C241—41no—
96C22×C241—21no—
97C22×C241—21no—
98C22×C241—41no—
99C22×C241—41no—
100C22×C241—41no—
101C22×C241#12011yescharacteristic
102C22×C241C2×SD1611yescharacteristic
103C22×C241AGL(1,ℤ/8)11yescharacteristic
104C2×D241—41no—
105C2×D241—41no—
106C2×D241—41no—
107C4×C241—21no—
108C4×C241—21no—
109C4×C241—42no—
110C4×C241—41no—
111Dic241—22no—
112Dic241—41no—
113Dic241—42no—
114Dic241—41no—
115C2×C241—21no—
116C2×C241—21no—
117C2×C241—81no—
118C2×C241#45011yescharacteristic
119C2×C241#45611yescharacteristic
120C2×C241B(4,𝔽2)11yescharacteristic
121D241—81no—
122C241#160411yescharacteristic, complemented, Sylow
123#1604—2411nomaximal, Sylow
124#537—2411no—
125#448—2411no—
126#448—2411no—
127#395—2411no—
128#327—2411no—
129#327D24111yescharacteristic, complemented
130#324—2411no—
131C2×#41—4821no—
132C22×Q8—2411no—
133C2×SD16—4821no—
134C2×SD16—4821no—
135C22⋊Q8—4821no—
136C22⋊Q8—4821no—
137#121—4821no—
138#121—4821no—
139#121—4821no—
140#121—2411no—
141#121C2×D24111yescharacteristic
142C2×C4⋊C4—4821no—
143C2×C4⋊C4—2411no—
144#103—4821no—
145#103—4821no—
146C22⋊C8—2411no—
147C22⋊C8C2×D24111yescharacteristic
148#95—4821no—
149#95C2×D24111yescharacteristic
150#41—9642no—
151#41—9642no—
152C2×Q8—9642no—
153C2×Q8—4821no—
154C2×Q8—4821no—
155C2×Q8—4821no—
156C2×D4—21no—
157C2×D4—4821no—
158C2×D4—4821no—
159C2×D4—4821no—
160C2×D4—2411no—
161C2×D4D96411yescharacteristic
162C22×C4—21no—
163C22×C4—4821no—
164C22×C4—4821no—
165C22×C4—4821no—
166C22×C4—2411no—
167C22×C4—2411no—
168C22×C4C22×D24111yescharacteristic
169SD16—9642no—
170SD16—9642no—
171C2×C8—21no—
172C2×C8—4821no—
173C4⋊C4—9642no—
174C4⋊C4—4821no—
175C4⋊C4—4821no—
176C4⋊C4—4821no—
177C4⋊C4—2411no—
178C4⋊C4D96411yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—4821no—
181C22⋊C4—4821no—
182C22⋊C4—4821no—
183C23—21no—
184C23—4821no—
185C23D4×D24111yescharacteristic
186Q8—9641no—
187Q8—9641no—
188Q8—9642no—
189Q8—4822no—
190Q8—4822no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—19281no—
195D4—9641no—
196D4—9641no—
197D4—9641no—
198D4—9642no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—9642no—
205C2×C4—9641no—
206C2×C4—9641no—
207C2×C4—9642no—
208C2×C4—9641no—
209C2×C4—4822no—
210C2×C4—4821no—
211C2×C4—4821no—
212C2×C4—4821no—
213C2×C4—4821no—
214C2×C4—2412no—
215C2×C4D4×D24111yescharacteristic
216C2×C4C2×D96411yescharacteristic
217C8—41no—
218C8—9641no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—9641no—
225C22—9641no—
226C22—9641no—
227C22#2144061211yescharacteristic
228C22SD16×D24111yescharacteristic
229C22#2144066611yescharacteristic
230C4—21no—
231C4—21no—
232C4—42no—
233C4—41no—
234C4—9641no—
235C4—9642no—
236C4—9641no—
237C4—4822no—
238C2—21no—
239C2—21no—
240C2—81no—
241C2—19281no—
242C2#2950786911yescharacteristic
243C2#2950790111yescharacteristic
244C2#2950790511yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#327×C241C2
socleC22×C241#120
prime radical#29508294C2
hypercenter#327D241
hypocenterC241#1604
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. #29507638C2semidirect
5. #29507450C2semidirect
6. #29507442C2semidirect
7. #327×C241C2semidirect
80. C2×Dic241SD16semidirect
122. C241#1604semidirect
129. #327D241semidirect

Maximal subgroups

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

subgroupindex
#295082942
#295078582
#295078552
#295076382
#295074502
#295074422
#327×C2412
#1604241