Finite Group Databasebeta

← #44507232

Subgroups — #44507232

Order 30848.

412 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#21440602C211yesmaximal, characteristic
2C2×#21440556C212yesmaximal
3C22⋊C4×Dic241C212yesmaximal, complemented
4#29507484C211yesmaximal, characteristic, complemented
5#342×C241C211yesmaximal, characteristic, complemented
6C22×C22⋊D241C2211yescharacteristic
7C23×Dic241C2211yescharacteristic
8C22×C4×D241C411yescharacteristic, complemented
9#21440602—22no—
10#21440602—22no—
11C2×#16838749C411yescharacteristic, complemented
12C2×C22⋊Dic241C2212yes—
13C2×#16838747C411yescharacteristic, complemented
14C2×C4×Dic241—22no—
15C2×C4×Dic241C411yescharacteristic, complemented
16#21440556C418yescomplemented
17#21440549—22no—
18C2×C22⋊C4×C241C2211yescharacteristic
19C2×C22⋊C4×C241C2212yes—
20C23×D241C2×C411yescharacteristic
21C2×C22⋊D241—22no—
22C2×C22⋊D241—21no—
23C2×C22⋊D241—21no—
24C2×C22⋊D241C2×C414yes—
25C22×Dic241—22no—
26C22×Dic241—42no—
27C22×Dic241C2×C411yescharacteristic
28C22×Dic241C2×C411yescharacteristic
29C22×Dic241C2×C411yescharacteristic
30C22×Dic241D412yes—
31C22×Dic241D412yes—
32C2×C4×D241—21no—
33C2×C4×D241—21no—
34C2×C4×D241—42no—
35#16838749—22no—
36C22⋊Dic241—22no—
37C22⋊Dic241C2×C414yescomplemented
38#16838747—22no—
39C4×Dic241—21no—
40C4×Dic241—21no—
41C4×Dic241—44no—
42C24×C241C2311yescharacteristic
43C22×C4×C241—22no—
44C22×C4×C241C2×C411yescharacteristic
45C22×C4×C241C2×C411yescharacteristic
46C22⋊C4×C241—22no—
47C22⋊C4×C241—22no—
48C22⋊C4×C241C2×C414yescomplemented
49C22×D241—21no—
50C22×D241—21no—
51C22×D241—41no—
52C22×D241—41no—
53C22×D241C4212yescomplemented
54C22⋊D241—24no—
55C22⋊D241—24no—
56C2×Dic241—21no—
57C2×Dic241—21no—
58C2×Dic241—24no—
59C2×Dic241—22no—
60C2×Dic241—24no—
61C2×Dic241—41no—
62C2×Dic241—42no—
63C2×Dic241—42no—
64C2×Dic241—42no—
65C2×Dic241C4212yescomplemented
66C2×Dic241C22⋊C411yescharacteristic
67C2×Dic241C22⋊C412yes—
68C2×Dic241C22⋊C411yescharacteristic
69C4×D241—42no—
70C4×D241—42no—
71C23×C241—41no—
72C23×C241—41no—
73C23×C241C22×C411yescharacteristic
74C23×C241C22×C412yes—
75C23×C241C2×D412yes—
76C23×C241#4111yescharacteristic
77C23×C241#4111yescharacteristic
78C2×C4×C241—21no—
79C2×C4×C241—21no—
80C2×C4×C241—24no—
81C2×C4×C241—42no—
82C2×C4×C241—42no—
83C2×C4×C241—41no—
84C2×C4×C241—41no—
85C22×C241—21no—
86C22×C241—22no—
87C22×C241—21no—
88C22×C241—22no—
89C22×C241—42no—
90C22×C241—41no—
91C22×C241—41no—
92C22×C241C2×C4211yescharacteristic
93C22×C241C2×C22⋊C411yescharacteristic
94C22×C241#11711yescharacteristic
95C22×C241C4×D412yes—
96C22×C241C4×D412yes—
97C2×D241—22no—
98C2×D241—42no—
99C2×D241—41no—
100C2×D241—41no—
101C2×D241—42no—
102C4×C241—44no—
103C4×C241—41no—
104C4×C241—41no—
105Dic241—22no—
106Dic241—21no—
107Dic241—22no—
108Dic241—44no—
109Dic241#9912yescomplemented
110C2×C241—22no—
111C2×C241—22no—
112C2×C241—21no—
113C2×C241—21no—
114C2×C241C4×C22⋊C411yescharacteristic
115C2×C241C2×#9911yescharacteristic
116C2×C241#41011yescharacteristic
117D241—42no—
118C241C4×#9911yescharacteristic, complemented, Sylow
119C4×#99—2411nomaximal, Sylow
120C2×C4×D4—2411no—
121C2×#99—2412no—
122C4×C22⋊C4—2412no—
123#342—2411no—
124#342D24111yescharacteristic, complemented
125C22×D4—2411no—
126C23×C4—2411no—
127C23×C4—2411no—
128C4×D4—4822no—
129C4×D4—4822no—
130C2×C4⋊C4—2411no—
131C2×C22⋊C4—2411no—
132C2×C22⋊C4—2412no—
133C2×C22⋊C4C2×D24111yescharacteristic
134C2×C22⋊C4C2×D24112yes—
135C2×C42—4822no—
136C2×C42—2411no—
137#99—2418no—
138#95—4822no—
139C24—2411no—
140C24C22×D24111yescharacteristic
141C2×D4—4822no—
142C2×D4—4821no—
143C2×D4—4821no—
144C2×D4—2414no—
145C22×C4—22no—
146C22×C4—9642no—
147C22×C4—9642no—
148C22×C4—4821no—
149C22×C4—4821no—
150C22×C4—4822no—
151C22×C4—2411no—
152C22×C4—2412no—
153C22×C4—2411no—
154C22×C4—2411no—
155C22×C4—2412no—
156C22×C4C4×D24111yescharacteristic
157C22×C4C4×D24111yescharacteristic
158C4⋊C4—4822no—
159C22⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—4822no—
162C22⋊C4—4822no—
163C22⋊C4—2414no—
164C22⋊C4C4×D24114yescomplemented
165C42—9644no—
166C42—4821no—
167C42—4821no—
168C23—41no—
169C23—41no—
170C23—9641no—
171C23—9641no—
172C23—4821no—
173C23—4821no—
174C23—2412no—
175C23C2×C4×D24111yescharacteristic
176C23C2×C4×D24112yes—
177C23D4×D24112yes—
178C23#1683876911yescharacteristic
179C23#1683877111yescharacteristic
180D4—4824no—
181D4—4824no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—24no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—9642no—
190C2×C4—9642no—
191C2×C4—9642no—
192C2×C4—9642no—
193C2×C4—9642no—
194C2×C4—9641no—
195C2×C4—4824no—
196C2×C4—4821no—
197C2×C4—4821no—
198C2×C4—4824no—
199C2×C4—4822no—
200C2×C4—2412no—
201C2×C4—2411no—
202C2×C4—2412no—
203C2×C4—2411no—
204C22—22no—
205C22—21no—
206C22—22no—
207C22—21no—
208C22—42no—
209C22—41no—
210C22—41no—
211C22—9642no—
212C22—9642no—
213C22—9641no—
214C22—9641no—
215C22—4822no—
216C22C42×D24111yescharacteristic
217C22C22⋊C4×D24111yescharacteristic
218C22#2144060011yescharacteristic
219C22#2144060212yes—
220C22#2144060412yes—
221C4—44no—
222C4—41no—
223C4—41no—
224C4—9644no—
225C4—4821no—
226C4—4822no—
227C4—4822no—
228C4—2412no—
229C2—22no—
230C2—22no—
231C2—21no—
232C2—21no—
233C2—9642no—
234C2#2950756411yescharacteristic
235C2#99×D24111yescharacteristic
236C2#2950768911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D241
commutatorC22×C241C2×C42
FrattiniC24C22×D241
Fitting#342×C241C2
socleC22×C241C2×C22⋊C4
prime radicalC22×C22⋊D241C22
cosocleC24×C241C23
hypercenter#342D241
hypocenterC241C4×#99
LCSG ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. C22⋊C4×Dic241C2semidirect
4. #29507484C2semidirect
5. #342×C241C2semidirect
8. C22×C4×D241C4semidirect
11. C2×#16838749C4semidirect
13. C2×#16838747C4semidirect
15. C2×C4×Dic241C4semidirect
16. #21440556C4semidirect
37. C22⋊Dic241C2×C4semidirect
48. C22⋊C4×C241C2×C4semidirect
53. C22×D241C42semidirect
65. C2×Dic241C42semidirect
109. Dic241#99semidirect
118. C241C4×#99semidirect
124. #342D241semidirect
164. C22⋊C4C4×D241semidirect

Maximal subgroups

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

subgroupindex
C2×#214406022
C2×#214405562
C22⋊C4×Dic2412
#295074842
#342×C2412
C4×#99241