Finite Group Databasebeta

← #44509825

Subgroups — #44509825

Order 30848.

1088 conjugacy classes of subgroups; only the 245 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 245 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×C4×D241C211yesmaximal, characteristic
2C2×#21440598C212yesmaximal, complemented
3#29507580C211yesmaximal, characteristic, complemented
4#29507576C214yesmaximal, complemented
5#29507572C212yesmaximal
6#29507564C214yesmaximal, complemented
7#381×C241C211yesmaximal, characteristic, complemented
8C24×D241C2211yescharacteristic
9C23×Dic241C2211yescharacteristic
10C22×C4×D241—28no—
11C22×C4×D241C418yescomplemented
12C22×C4×D241C2212yes—
13C22×C4×D241C2212yes—
14#21440598—28no—
15C2×#16838749C2214yescomplemented
16C2×C22⋊Dic241C2212yes—
17C2×#16838747C2218yes—
18C2×C4×Dic241C2214yescomplemented
19#21440549C2214yescomplemented
20C23×C4×C241C2211yescharacteristic
21C2×C22⋊C4×C241C2212yes—
22#95×C241C2214yescomplemented
23C23×D241—28no—
24C23×D241—24no—
25C23×D241C2×C414yes—
26C23×D241C2312yes—
27C22×Dic241C2×C414yes—
28C22×Dic241D418yes—
29C22×Dic241C2314yes—
30C22×Dic241C2311yescharacteristic
31C22×Dic241C2311yescharacteristic
32C2×C4×D241—232no—
33C2×C4×D241—28no—
34C2×C4×D241—28no—
35C2×C4×D241C2×C418yes—
36C2×C4×D241C2×C418yes—
37#16838749—28no—
38C22⋊Dic241—24no—
39#16838747—216no—
40C4×Dic241—28no—
41C24×C241C2311yescharacteristic
42C22×C4×C241—24no—
43C22×C4×C241C2×C414yes—
44C22×C4×C241C2314yes—
45C22×C4×C241C2312yes—
46C22⋊C4×C241—24no—
47C22×D241—232no—
48C22×D241—28no—
49C22×D241—24no—
50C22×D241—24no—
51C22×D241—216no—
52C22×D241C22×C414yes—
53C22×D241#4118yes—
54C2×Dic241—24no—
55C2×Dic241—28no—
56C2×Dic241C22⋊C4116yescomplemented
57C2×Dic241C22×C412yes—
58C2×Dic241C22×C412yes—
59C2×Dic241C2×D414yes—
60C2×Dic241C2×D414yes—
61C4×D241—216no—
62C4×D241—216no—
63C23×C241—24no—
64C23×C241C22×C412yes—
65C23×C241C2×D414yes—
66C23×C241C2411yescharacteristic
67C2×C4×C241—28no—
68C2×C4×C241—24no—
69C2×C4×C241—24no—
70C2×C4×C241—28no—
71C2×C4×C241C22×C414yes—
72C22×C241—24no—
73C22×C241—28no—
74C22×C241C2×C22⋊C414yes—
75C22×C241C23×C411yescharacteristic
76C22×C241C22×D412yes—
77C22×C241C2×#4114yes—
78C2×D241—232no—
79C2×D241—24no—
80C2×D241—24no—
81C2×D241—216no—
82C2×D241#11718yescomplemented
83C4×C241—24no—
84C4×C241—44no—
85Dic241—44no—
86Dic241C2×C22⋊C414yes—
87Dic241C2×C22⋊C414yes—
88C2×C241—24no—
89C2×C241C22×C22⋊C411yescharacteristic
90C2×C241C2×#11712yes—
91C2×C241#52514yes—
92D241—28no—
93C241#228011yescharacteristic, complemented, Sylow
94#2280—2411nomaximal, Sylow
95C24×C4—2411no—
96C2×#117—2412no—
97#381—2411no—
98#381D24111yescharacteristic, complemented
99#380—2414no—
100#379—2412no—
101C4×C22⋊C4—2414no—
102C25—2411no—
103C23×C4—4828no—
104C23×C4—2418no—
105C23×C4—2412no—
106C23×C4—2412no—
107C23×C4—2411no—
108C23×C4C2×D24111yescharacteristic
109#117—4828no—
110C2×C4⋊C4—2414no—
111C2×C22⋊C4—2412no—
112C2×C22⋊C4—2418no—
113C2×C22⋊C4C2×D24112yes—
114C2×C42—2414no—
115#95—2414no—
116#95C2×D24114yescomplemented
117C24—4828no—
118C24—4824no—
119C24—2414no—
120C24—2412no—
121C24C22×D24111yescharacteristic
122C22×C4—24no—
123C22×C4—48232no—
124C22×C4—4828no—
125C22×C4—4828no—
126C22×C4—2414no—
127C22×C4—2418no—
128C22×C4—2418no—
129C22×C4—2414no—
130C22×C4—2418no—
131C22×C4—2411no—
132C22×C4—2411no—
133C22×C4C4×D24114yes—
134C22×C4C22×D24114yes—
135C22×C4C22×D24112yes—
136C4⋊C4—4828no—
137C22⋊C4—24no—
138C22⋊C4—48216no—
139C22⋊C4—4824no—
140C42—4828no—
141C23—24no—
142C23—48232no—
143C23—48216no—
144C23—4828no—
145C23—4824no—
146C23—4824no—
147C23—2414no—
148C23—2418no—
149C23C2×C4×D24112yes—
150C23D4×D24114yes—
151C23C23×D24111yescharacteristic
152C2×C4—28no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—28no—
156C2×C4—48216no—
157C2×C4—48216no—
158C2×C4—4824no—
159C2×C4—4828no—
160C2×C4—24116no—
161C2×C4—2412no—
162C2×C4—2412no—
163C2×C4—2414no—
164C2×C4—2414no—
165C2×C4C2×C4×D24114yes—
166C22—24no—
167C22—28no—
168C22—48232no—
169C22—4824no—
170C22—4824no—
171C22—48216no—
172C22—2418no—
173C22C22⋊C4×D24114yes—
174C22C22×C4×D24111yescharacteristic
175C22C2×D4×D24112yes—
176C22#41×D24114yes—
177C4—24no—
178C4—44no—
179C4—9644no—
180C4—2414no—
181C4—2414no—
182C2—24no—
183C2—4828no—
184C2C2×C22⋊C4×D24111yescharacteristic
185C2#117×D24112yes—
186C2#2950822514yes—
subgroupG/H
center, FrattiniC23C23×D241
commutatorC22×C241C23×C4
Fitting#381×C241C2
socle, cosocleC23×C241C24
prime radicalC24×D241C22
hypercenter#381D241
hypocenterC241#2280
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#21440598C2semidirect
3. #29507580C2semidirect
4. #29507576C2semidirect
6. #29507564C2semidirect
7. #381×C241C2semidirect
11. C22×C4×D241C4semidirect
15. C2×#16838749C22semidirect
18. C2×C4×Dic241C22semidirect
19. #21440549C22semidirect
22. #95×C241C22semidirect
56. C2×Dic241C22⋊C4semidirect
82. C2×D241#117semidirect
93. C241#2280semidirect
98. #381D241semidirect
116. #95C2×D241semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D2412
C2×#214405982
#295075802
#295075762
#295075722
#295075642
#381×C2412
#2280241