Finite Group Databasebeta

← #44510021

Subgroups — #44510021

Order 30848.

1160 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C23×C22⋊D241C211yesmaximal, characteristic
2C2×C22⋊C4×D241C212yesmaximal, complemented
3#29507593C218yesmaximal, complemented
4#29507578C212yesmaximal, complemented
5#29507573C211yesmaximal, characteristic, complemented
6#379×C241C211yesmaximal, characteristic, complemented
7C24×D241C2211yescharacteristic
8C22×C22⋊D241—28no—
9C22×C22⋊D241C418yescomplemented
10C22×C22⋊D241C2214yes—
11C23×Dic241C2211yescharacteristic
12C22×C4×D241C2214yescomplemented
13C2×C22⋊Dic241C2212yes—
14C2×C22⋊Dic241C2214yescomplemented
15C2×#16838747C2214yescomplemented
16C22⋊C4×D241—28no—
17#21440549C2218yescomplemented
18C25×C241C2211yescharacteristic
19C2×C22⋊C4×C241C2212yes—
20C2×C22⋊C4×C241C2214yescomplemented
21C23×D241—44no—
22C23×D241C2×C414yes—
23C23×D241D418yes—
24C23×D241C2312yes—
25C2×C22⋊D241—232no—
26C2×C22⋊D241—28no—
27C2×C22⋊D241—28no—
28C2×C22⋊D241C2×C4116yescomplemented
29C22×Dic241—24no—
30C22×Dic241C2×C414yescomplemented
31C22×Dic241C2314yes—
32C22×Dic241C2312yes—
33C2×C4×D241—28no—
34C2×C4×D241—48no—
35C22⋊Dic241—24no—
36C22⋊Dic241—44no—
37#16838747—28no—
38C24×C241—24no—
39C24×C241—44no—
40C24×C241C2×C414yescomplemented
41C24×C241C2312yes—
42C24×C241C2311yescharacteristic
43C22×C4×C241C2314yes—
44C22⋊C4×C241—24no—
45C22⋊C4×C241—44no—
46C22×D241—28no—
47C22×D241—48no—
48C22×D241—416no—
49C22×D241C22⋊C4116yescomplemented
50C22×D241C22×C414yes—
51C22×D241C2×D414yes—
52C22×D241C2×D414yes—
53C22⋊D241—232no—
54C2×Dic241—28no—
55C2×Dic241—24no—
56C2×Dic241—24no—
57C2×Dic241—28no—
58C2×Dic241C22×C414yes—
59C4×D241—416no—
60C23×C241—24no—
61C23×C241—28no—
62C23×C241—24no—
63C23×C241—24no—
64C23×C241—24no—
65C23×C241—48no—
66C23×C241—416no—
67C23×C241C22×C414yes—
68C23×C241C22×C412yes—
69C23×C241C2×D414yes—
70C23×C241C2411yescharacteristic
71C2×C4×C241—24no—
72C2×C4×C241—28no—
73C22×C241—24no—
74C22×C241—28no—
75C22×C241—24no—
76C22×C241—24no—
77C22×C241—24no—
78C22×C241—416no—
79C22×C241—48no—
80C22×C241C2×C22⋊C414yes—
81C22×C241C23×C411yescharacteristic
82C22×C241C22×D412yes—
83C22×C241H(5,𝔽2)14yes—
84C2×D241—28no—
85C2×D241—28no—
86C2×D241—28no—
87C2×D241—416no—
88C2×D241C2×C22⋊C418yes—
89C4×C241—44no—
90Dic241—24no—
91Dic241—44no—
92C2×C241—24no—
93C2×C241—44no—
94C2×C241C22×C22⋊C411yescharacteristic
95C2×C241#51812yes—
96C2×C241#53414yes—
97D241—28no—
98C241#230811yescharacteristic, complemented, Sylow
99#2308—2411nomaximal, Sylow
100C23×D4—2411no—
101C22×C22⋊C4—2412no—
102#386—2418no—
103#381—2412no—
104#379—2411no—
105#379D24111yescharacteristic, complemented
106C25—2411no—
107C25C2×D24111yescharacteristic
108C22×D4—4828no—
109C22×D4—2418no—
110C22×D4—2414no—
111C23×C4—2414no—
112C23×C4—2411no—
113C2×C22⋊C4—4828no—
114C2×C22⋊C4—2414no—
115C2×C22⋊C4—2412no—
116C2×C22⋊C4—2414no—
117C2×C22⋊C4C2×D24112yes—
118C2×C22⋊C4C2×D24114yescomplemented
119#95—2418no—
120C24—24no—
121C24—44no—
122C24—9644no—
123C24—2414no—
124C24—2418no—
125C24—2412no—
126C24C4×D24114yescomplemented
127C24C22×D24112yes—
128C24C22×D24111yescharacteristic
129C2×D4—48232no—
130C2×D4—4828no—
131C2×D4—4828no—
132C2×D4—24116no—
133C22×C4—9648no—
134C22×C4—4828no—
135C22×C4—4824no—
136C22×C4—2414no—
137C22×C4—2414no—
138C22×C4—2412no—
139C22×C4C22×D24114yes—
140C22⋊C4—24no—
141C22⋊C4—44no—
142C22⋊C4—9644no—
143C22⋊C4—4828no—
144C22⋊C4—4824no—
145C23—24no—
146C23—28no—
147C23—24no—
148C23—24no—
149C23—24no—
150C23—48no—
151C23—416no—
152C23—9648no—
153C23—96416no—
154C23—4828no—
155C23—24116no—
156C23—2414no—
157C23—2414no—
158C23—2414no—
159C23C2×C4×D24114yes—
160C23C2×C4×D24112yes—
161C23D4×D24114yes—
162C23C23×D24111yescharacteristic
163D4—48232no—
164C2×C4—24no—
165C2×C4—28no—
166C2×C4—96416no—
167C2×C4—4824no—
168C2×C4—4828no—
169C2×C4—4828no—
170C2×C4—4824no—
171C2×C4—2414no—
172C22—24no—
173C22—28no—
174C22—24no—
175C22—24no—
176C22—24no—
177C22—416no—
178C22—48no—
179C22—96416no—
180C22—4828no—
181C22—4828no—
182C22—4828no—
183C22—2418no—
184C22C22⋊C4×D24114yes—
185C22C22×C4×D24111yescharacteristic
186C22C2×D4×D24112yes—
187C22#2144068714yes—
188C4—44no—
189C4—9644no—
190C4—4824no—
191C2—24no—
192C2—44no—
193C2—4828no—
194C2C2×C22⋊C4×D24111yescharacteristic
195C2#2950819012yes—
196C2#2950827714yes—
subgroupG/H
center, FrattiniC23C23×D241
commutatorC22×C241C23×C4
Fitting#379×C241C2
socle, cosocleC23×C241C24
prime radicalC23×C22⋊D241C2
hypercenter#379D241
hypocenterC241#2308
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D241C2semidirect
3. #29507593C2semidirect
4. #29507578C2semidirect
5. #29507573C2semidirect
6. #379×C241C2semidirect
9. C22×C22⋊D241C4semidirect
12. C22×C4×D241C22semidirect
14. C2×C22⋊Dic241C22semidirect
15. C2×#16838747C22semidirect
17. #21440549C22semidirect
20. C2×C22⋊C4×C241C22semidirect
28. C2×C22⋊D241C2×C4semidirect
30. C22×Dic241C2×C4semidirect
40. C24×C241C2×C4semidirect
49. C22×D241C22⋊C4semidirect
98. C241#2308semidirect
105. #379D241semidirect
118. C2×C22⋊C4C2×D241semidirect
126. C24C4×D241semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊D2412
C2×C22⋊C4×D2412
#295075932
#295075782
#295075732
#379×C2412
#2308241