Finite Group Databasebeta

← #44506483

Subgroups — #44506483

Order 30848.

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

normal subgroups only

This group has 246 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#29508036C211yesmaximal, characteristic, complemented
3#29508033C211yesmaximal, characteristic, complemented
4#29507657C211yesmaximal, characteristic, complemented
5#29507450C211yesmaximal, characteristic, complemented
6#29507442C211yesmaximal, characteristic, complemented
7#327×C241C211yesmaximal, characteristic, complemented
8C2×#16838769—21no—
9#21440620—21no—
10#21440619—21no—
11#21440616C2211yescharacteristic
12#21440615—21no—
13#21440614—21no—
14#21440614—21no—
15C2×C4⋊Dic241C2211yescharacteristic
16C2×#16838749C2211yescharacteristic
17#21440574—21no—
18#21440573—21no—
19#21440564—21no—
20#21440563—21no—
21C22⋊#14515349C2211yescharacteristic
22#21440549—21no—
23#21440549—21no—
24#121×C241C2211yescharacteristic
25C22⋊C8×C241C2211yescharacteristic
26#95×C241C2211yescharacteristic
27#16838769—42no—
28#16838769—42no—
29C2×Dic482—21no—
30C2×D964D411yescharacteristic
31C2×C22⋊D241—21no—
32C2×C22⋊D241—21no—
33C2×C22⋊D241—21no—
34C22×Dic241—21no—
35C22×Dic241—21no—
36C22×Dic241D411yescharacteristic
37C22×Dic241D411yescharacteristic
38C2×C4×D241—21no—
39C2×#14515349—21no—
40C4⋊Dic241—21no—
41C4⋊Dic241—21no—
42C4⋊Dic241D411yescharacteristic
43#16838749—21no—
44#16838749—21no—
45#16838749—21no—
46C22⋊Dic241—21no—
47#16838747—21no—
48#16838747—21no—
49C2×D4×C241—21no—
50C2×D4×C241D411yescharacteristic
51C22×C4×C241—21no—
52C22×C4×C241C2311yescharacteristic
53C2×C8×C241—21no—
54C4⋊C4×C241D411yescharacteristic
55C22⋊C4×C241—21no—
56C22×D241—21no—
57Dic482—42no—
58D964—41no—
59C22⋊D241—42no—
60C22⋊D241—41no—
61C22⋊D241—41no—
62C22⋊D241—81no—
63C2×Dic241—21no—
64C2×Dic241—21no—
65C2×Dic241—21no—
66C2×Dic241—21no—
67C2×Dic241—42no—
68C2×Dic241—41no—
69C2×Dic241—42no—
70C2×Dic241—41no—
71C2×Dic241SD1612yes—
72C4×D241—42no—
73#14515349—41no—
74C23×C241—21no—
75C23×C241C2×D411yescharacteristic
76D4×C241—41no—
77D4×C241—41no—
78D4×C241—41no—
79C2×C4×C241—21no—
80C2×C4×C241—41no—
81C2×C4×C241—41no—
82C2×C4×C241—41no—
83C2×C4×C241—41no—
84C2×C4×C241C2×D411yescharacteristic
85C2×C4×C241C2×D411yescharacteristic
86C8×C241—41no—
87C22×C241—21no—
88C22×C241—21no—
89C22×C241—41no—
90C22×C241—41no—
91C22×C241—41no—
92C22×C241#12011yescharacteristic
93C22×C241C2×SD1611yescharacteristic
94C22×C241AGL(1,ℤ/8)11yescharacteristic
95C2×D241—41no—
96C2×D241—41no—
97C2×D241—41no—
98C4×C241—21no—
99C4×C241—21no—
100C4×C241—41no—
101C4×C241—81no—
102Dic241—22no—
103Dic241—41no—
104Dic241—41no—
105Dic241—81no—
106C2×C241—21no—
107C2×C241—21no—
108C2×C241—81no—
109C2×C241#45011yescharacteristic
110C2×C241#45411yescharacteristic
111C2×C241#45811yescharacteristic
112D241—81no—
113C241#161611yescharacteristic, complemented, Sylow
114#1616—2411nomaximal, Sylow
115#537—2411no—
116#481—2411no—
117#481—2411no—
118#400—2411no—
119#327—2411no—
120#327D24111yescharacteristic, complemented
121#324—2411no—
122C2×#41—4821no—
123C22⋊Q8—4821no—
124C22⋊Q8—4821no—
125#121—4821no—
126#121—4821no—
127#121—4821no—
128#121—2411no—
129#121C2×D24111yescharacteristic
130C2×C4⋊C4—2411no—
131C2×C4⋊C4—2411no—
132#106—4821no—
133#106—4821no—
134#102—4821no—
135#102—4821no—
136C22⋊C8—2411no—
137C22⋊C8C2×D24111yescharacteristic
138#95—4821no—
139#95—4821no—
140#95C2×D24111yescharacteristic
141#41—9642no—
142#41—9642no—
143C2×Q8—4821no—
144C2×D4—21no—
145C2×D4—4821no—
146C2×D4—4821no—
147C2×D4—4821no—
148C2×D4—2411no—
149C2×D4D96411yescharacteristic
150C22×C4—21no—
151C22×C4—4821no—
152C22×C4—4821no—
153C22×C4—4821no—
154C22×C4—2411no—
155C22×C4—2411no—
156C22×C4C22×D24111yescharacteristic
157C2×C8—21no—
158C2×C8—4821no—
159C4⋊C4—4821no—
160C4⋊C4—4821no—
161C4⋊C4—4821no—
162C4⋊C4—4821no—
163C4⋊C4—4821no—
164C4⋊C4—2411no—
165C4⋊C4D96411yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—4821no—
168C22⋊C4—4821no—
169C22⋊C4—4821no—
170C23—21no—
171C23—4821no—
172C23D4×D24111yescharacteristic
173Q8—9642no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—19281no—
178D4—9641no—
179D4—9641no—
180D4—9641no—
181D4—9642no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—9642no—
188C2×C4—9642no—
189C2×C4—9641no—
190C2×C4—9642no—
191C2×C4—9641no—
192C2×C4—4821no—
193C2×C4—4821no—
194C2×C4—4821no—
195C2×C4—4821no—
196C2×C4—2412no—
197C2×C4D4×D24111yescharacteristic
198C2×C4C2×D96411yescharacteristic
199C8—41no—
200C8—9641no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—9641no—
207C22—9641no—
208C22—9641no—
209C22#2144061211yescharacteristic
210C22SD16×D24111yescharacteristic
211C22#2144066611yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—19281no—
217C4—9641no—
218C4—9641no—
219C4—4822no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—19281no—
224C2#2950786911yescharacteristic
225C2#2950789111yescharacteristic
226C2#2950790811yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#327×C241C2
socleC22×C241#120
prime radical#29508294C2
hypercenter#327D241
hypocenterC241#1616
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. #29507657C2semidirect
5. #29507450C2semidirect
6. #29507442C2semidirect
7. #327×C241C2semidirect
113. C241#1616semidirect
120. #327D241semidirect

Maximal subgroups

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

subgroupindex
#295082942
#295080362
#295080332
#295076572
#295074502
#295074422
#327×C2412
#1616241