Finite Group Databasebeta

← #37580980

Subgroups — #37580980

Order 24448.

800 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 249 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×#20259367C211yesmaximal, characteristic
2#27133138C211yesmaximal, characteristic, complemented
3#27132636C214yesmaximal, complemented
4C2×#20259236C218yesmaximal, complemented
5#518×C191C211yesmaximal, characteristic, complemented
6#20259367—24no—
7#20259367—24no—
8C2×#15690287C2212yes—
9C2×#15690286C414yescomplemented
10C22×C22⋊D191C2214yes—
11C2×D4×D191C414yescomplemented
12D4×Dic191—24no—
13#20259281C2212yescomplemented
14C2×C22⋊Dic191C2214yescomplemented
15#20259236C22116yescomplemented
16C22×D4×C191C2211yescharacteristic
17C4×D4×C191—24no—
18#117×C191C2212yescomplemented
19C2×C22⋊C4×C191C2214yescomplemented
20C23×D191C2×C414yescomplemented
21#15690287—24no—
22#15690287—24no—
23#15690286—216no—
24C2×Dic382C2×C412yescomplemented
25C2×D764C2×C412yescomplemented
26C2×C22⋊D191—28no—
27C2×C22⋊D191—28no—
28C2×C22⋊D191C2×C418yescomplemented
29C2×C22⋊D191C2314yes—
30D4×D191—216no—
31C22×Dic191—24no—
32C22×Dic191C2×C414yescomplemented
33C2×C4×D191C2×C414yescomplemented
34C4⋊Dic191—22no—
35C22⋊Dic191—24no—
36C22⋊Dic191C2314yes—
37C4×Dic191—22no—
38C24×C191C2312yes—
39C2×D4×C191C2×C414yes—
40C2×D4×C191D414yes—
41C2×D4×C191D414yes—
42C22×C4×C191—24no—
43C22×C4×C191C2311yescharacteristic
44C4⋊C4×C191—22no—
45C22⋊C4×C191—24no—
46C22⋊C4×C191C2314yes—
47C42×C191—22no—
48C22×D191—28no—
49C22×D191—84no—
50C22×D191C22×C414yes—
51Dic382—24no—
52D764—24no—
53C22⋊D191—216no—
54C22⋊D191—24no—
55C22⋊D191—24no—
56C2×Dic191—28no—
57C2×Dic191—24no—
58C2×Dic191—84no—
59C2×Dic191C22×C414yes—
60C4×D191—28no—
61C23×C191—82no—
62C23×C191C22×C414yes—
63C23×C191C2×D414yes—
64C23×C191C2×D414yes—
65C23×C191C2411yescharacteristic
66D4×C191C22⋊C4116yes—
67C2×C4×C191—24no—
68C2×C4×C191—84no—
69C2×C4×C191C22×C412yes—
70C2×C4×C191C2×D412yes—
71C2×C4×C191C2×D412yes—
72C22×C191—44no—
73C22×C191—41no—
74C22×C191—44no—
75C22×C191—44no—
76C22×C191C2×C22⋊C418yes—
77C22×C191C23×C411yescharacteristic
78C22×C191C22×D411yescharacteristic
79C22×C191C22×D411yescharacteristic
80C2×D191—24no—
81C2×D191—44no—
82C2×D191—88no—
83C4×C191—44no—
84C4×C191C2×C22⋊C414yes—
85Dic191—24no—
86Dic191—44no—
87C2×C191—21no—
88C2×C191—21no—
89C2×C191—21no—
90C2×C191—28no—
91C2×C191C22×C22⋊C411yescharacteristic
92D191—44no—
93C191#288311yescharacteristic, complemented, Sylow
94#2883—1911nomaximal, Sylow
95C2×H(5,𝔽2)—1911no—
96#518—1911no—
97#518D19111yescharacteristic, complemented
98#410—1914no—
99C2×#99—1918no—
100H(5,𝔽2)—3824no—
101H(5,𝔽2)—3824no—
102C2×#41—1914no—
103C2×#41—1912no—
104C22×D4—1914no—
105C22×D4—1914no—
106C22×D4C2×D19111yescharacteristic
107C4×D4—24no—
108C4×D4—3824no—
109#117—1912no—
110#117C2×D19112yescomplemented
111C2×C22⋊C4—1914no—
112C2×C22⋊C4C2×D19114yescomplemented
113#99—19116no—
114C24—1914no—
115C24C22×D19112yes—
116#41—38216no—
117#41—3824no—
118#41—3824no—
119C2×Q8—1912no—
120C2×D4—3828no—
121C2×D4—3828no—
122C2×D4—38216no—
123C2×D4—1918no—
124C2×D4—1914no—
125C2×D4—1912no—
126C2×D4C4×D19114yes—
127C2×D4C22⋊D19114yes—
128C2×D4D76414yes—
129C22×C4—24no—
130C22×C4—3824no—
131C22×C4—1914no—
132C22×C4—1914no—
133C22×C4C22×D19111yescharacteristic
134C4⋊C4—22no—
135C4⋊C4—3822no—
136C22⋊C4—24no—
137C22⋊C4—3824no—
138C22⋊C4—1914no—
139C22⋊C4C22×D19114yes—
140C42—22no—
141C42—3822no—
142C23—82no—
143C23—3828no—
144C23—1914no—
145C23—15284no—
146C23C2×C4×D19114yes—
147C23C2×C22⋊D19114yes—
148C23C2×D76414yes—
149C23C23×D19111yescharacteristic
150Q8—3824no—
151D4—3824no—
152D4—3824no—
153D4—38216no—
154D4—3824no—
155D4(C2×D191)⋊C4116yes—
156C2×C4—24no—
157C2×C4—84no—
158C2×C4—3828no—
159C2×C4—3828no—
160C2×C4—3824no—
161C2×C4—1914no—
162C2×C4—15284no—
163C2×C4C2×C4×D19112yes—
164C2×C4C2×C22⋊D19112yes—
165C2×C4C2×D76412yes—
166C22—44no—
167C22—44no—
168C22—41no—
169C22—44no—
170C22—3824no—
171C22—15288no—
172C22—7644no—
173C22C2×(C2×D191)⋊C418yes—
174C22C22×C4×D19111yescharacteristic
175C22C22×C22⋊D19111yescharacteristic
176C22C22×D76411yescharacteristic
177C4—44no—
178C4—3824no—
179C4—7644no—
180C4C2×(C2×D191)⋊C414yes—
181C2—21no—
182C2—21no—
183C2—21no—
184C2—28no—
185C2—7644no—
186C2C22×(C2×D191)⋊C411yescharacteristic
subgroupG/H
centerC2C22×(C2×D191)⋊C4
commutatorC22×C191C23×C4
FrattiniC23C23×D191
Fitting#518×C191C2
socleC2×C191C22×C22⋊C4
prime radicalC2×#20259367C2
cosocleC23×C191C24
hypercenter#518D191
hypocenterC191#2883
LCSG ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C22×D4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #27133138C2semidirect
3. #27132636C2semidirect
4. C2×#20259236C2semidirect
5. #518×C191C2semidirect
9. C2×#15690286C4semidirect
11. C2×D4×D191C4semidirect
13. #20259281C22semidirect
14. C2×C22⋊Dic191C22semidirect
15. #20259236C22semidirect
18. #117×C191C22semidirect
19. C2×C22⋊C4×C191C22semidirect
20. C23×D191C2×C4semidirect
24. C2×Dic382C2×C4semidirect
25. C2×D764C2×C4semidirect
28. C2×C22⋊D191C2×C4semidirect
32. C22×Dic191C2×C4semidirect
33. C2×C4×D191C2×C4semidirect
93. C191#2883semidirect
97. #518D191semidirect
110. #117C2×D191semidirect
112. C2×C22⋊C4C2×D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593672
#271331382
#271326362
C2×#202592362
#518×C1912
#2883191