Finite Group Databasebeta

← #37583001

Subgroups — #37583001

Order 24448.

596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#20259348C212yesmaximal, complemented
2C2×#20259344C211yesmaximal, characteristic, complemented
3#27133230C212yesmaximal, complemented
4#27133051C214yesmaximal, complemented
5#27133046C212yesmaximal, complemented
6#27133038C212yesmaximal, complemented
7#27132618C211yesmaximal, characteristic, complemented
8C22×D8×C191C211yesmaximal, characteristic, complemented
9C2×#15690287C2212yes—
10#20259348—28no—
11#20259344—24no—
12C2×Dic764C2211yescharacteristic, complemented
13C2×#15690276C2212yescomplemented
14C2×#15690275C2214yescomplemented
15C2×D1528C2211yescharacteristic, complemented
16C2×#15690272C2214yescomplemented
17C2×#15690271C2211yescharacteristic
18#20259318C2214yescomplemented
19#20259309C2214yescomplemented
20#20259293—24no—
21#20259291—24no—
22#20259281C2211yescharacteristic
23#20259232C2212yescomplemented
24C8×Dic191C2212yescomplemented
25C22×D4×C191C2212yes—
26C2×D8×C191—24no—
27C2×D8×C191C2212yes—
28C2×D8×C191C2212yes—
29C22×C8×C191C2211yescharacteristic
30#15690287—24no—
31#15690287—24no—
32C2×Dic382C2312yes—
33C2×D764C2312yes—
34C2×C22⋊D191—28no—
35C2×C22⋊D191—22no—
36C2×C4×D191—22no—
37Dic764—22no—
38#15690276—24no—
39#15690275—28no—
40D1528—22no—
41#15690272—28no—
42#15690271D414yescomplemented
43C2×C191⋊C8C2312yes—
44C4⋊Dic191D412yes—
45C22⋊Dic191—28no—
46C22⋊Dic191D412yes—
47C4×Dic191C2312yes—
48C24×C191—22no—
49C2×D4×C191—24no—
50C2×D4×C191—24no—
51C2×D4×C191—22no—
52C2×D4×C191C2314yes—
53C22×C4×C191C2311yescharacteristic
54D8×C191—24no—
55D8×C191—24no—
56C2×C8×C191D414yescomplemented
57C2×C8×C191C2311yescharacteristic
58C2×C8×C191C2311yescharacteristic
59C22×D191—22no—
60Dic382—22no—
61Dic382—22no—
62D764—22no—
63D764—22no—
64C22⋊D191—44no—
65C22⋊D191—88no—
66C2×Dic191—22no—
67C2×Dic191C2×D414yes—
68C4×D191—44no—
69C191⋊C8C2×D414yes—
70C23×C191—24no—
71C23×C191—44no—
72C23×C191—84no—
73C23×C191C2×D411yescharacteristic
74D4×C191—24no—
75D4×C191—24no—
76D4×C191—44no—
77C2×C4×C191C2×D411yescharacteristic
78C2×C4×C191C2×D412yes—
79C2×C4×C191C2×D412yes—
80C2×C4×C191C2411yescharacteristic
81C8×C191C2×D412yes—
82C8×C191C2×D412yes—
83C22×C191—22no—
84C22×C191—44no—
85C22×C191—48no—
86C22×C191—88no—
87C22×C191#12712yes—
88C22×C191C22×D411yescharacteristic
89C2×D191—42no—
90C2×D191—44no—
91C4×C191#12712yes—
92C4×C191C22×D411yescharacteristic
93C4×C191C22×D411yescharacteristic
94Dic191—24no—
95Dic191—42no—
96C2×C191—22no—
97C2×C191—84no—
98C2×C191C2×#12711yescharacteristic
99C2×C191#57612yes—
100D191—82no—
101C191#315511yescharacteristic, complemented, Sylow
102#3155—1911nomaximal, Sylow
103C2×AGL(1,ℤ/8)—1912no—
104C2×#135—1911no—
105C22×D8D19111yescharacteristic, complemented
106#535—1912no—
107#496—1914no—
108#495—1912no—
109#493—1912no—
110#405—1911no—
111C2×#41—1912no—
112C22×D4C2×D19112yes—
113AGL(1,ℤ/8)—3828no—
114#135—3824no—
115C2×Q16—1911no—
116C2×SD16—1914no—
117C2×SD16—1912no—
118C2×D8—24no—
119C2×D8—1914no—
120C2×D8—1911no—
121C2×D8C2×D19112yes—
122C2×D8C2×D19112yes—
123C2×M16—1911no—
124C22×C8C2×D19111yescharacteristic
125#127—1914no—
126#124—1914no—
127#121—3824no—
128#120—3824no—
129#117—1911no—
130#97—1912no—
131C4×C8—1912no—
132C24—22no—
133#41—3824no—
134#41—3824no—
135C2×Q8—1912no—
136C2×D4—24no—
137C2×D4—22no—
138C2×D4—24no—
139C2×D4—3822no—
140C2×D4—3828no—
141C2×D4—1912no—
142C2×D4C22×D19114yes—
143C22×C4—3822no—
144C22×C4C22×D19111yescharacteristic
145Q16—3822no—
146SD16—3828no—
147SD16—3824no—
148D8—24no—
149D8—24no—
150D8—3828no—
151D8—3822no—
152M16—1914no—
153C2×C8—1912no—
154C2×C8C22⋊D19114yescomplemented
155C2×C8C22×D19111yescharacteristic
156C2×C8C22×D19111yescharacteristic
157C4⋊C4—1912no—
158C22⋊C4—3828no—
159C22⋊C4—1912no—
160C42—1912no—
161C23—24no—
162C23—44no—
163C23—84no—
164C23—3822no—
165C23D4×D19111yescharacteristic
166Q8—3822no—
167Q8—3822no—
168D4—24no—
169D4—24no—
170D4—44no—
171D4—3822no—
172D4—3822no—
173D4—15288no—
174D4—7644no—
175C2×C4—3822no—
176C2×C4—1914no—
177C2×C4—7644no—
178C2×C4D4×D19112yes—
179C2×C4D4×D19111yescharacteristic
180C2×C4C2×C22⋊D19112yes—
181C2×C4C23×D19111yescharacteristic
182C8—1914no—
183C8C2×C22⋊D19112yes—
184C8C2×C22⋊D19112yes—
185C22—22no—
186C22—44no—
187C22—48no—
188C22—88no—
189C22—7642no—
190C22—7644no—
191C22#2025931812yes—
192C22C2×D4×D19111yescharacteristic
193C4—3824no—
194C4—7642no—
195C4#2025931812yes—
196C4C2×D4×D19111yescharacteristic
197C4C22×C22⋊D19111yescharacteristic
198C2—22no—
199C2—84no—
200C2—15282no—
201C2C2×#2025931811yescharacteristic
202C2#2713346412yes—
subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
FittingC22×D8×C191C2
socleC22×C191C22×D4
hypercenterC22×D8D191
hypocenterC191#3155
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#20259348C2semidirect
2. C2×#20259344C2semidirect
3. #27133230C2semidirect
4. #27133051C2semidirect
5. #27133046C2semidirect
6. #27133038C2semidirect
7. #27132618C2semidirect
8. C22×D8×C191C2semidirect
12. C2×Dic764C22semidirect
13. C2×#15690276C22semidirect
14. C2×#15690275C22semidirect
15. C2×D1528C22semidirect
16. C2×#15690272C22semidirect
18. #20259318C22semidirect
19. #20259309C22semidirect
23. #20259232C22semidirect
24. C8×Dic191C22semidirect
42. #15690271D4semidirect
56. C2×C8×C191D4semidirect
101. C191#3155semidirect
105. C22×D8D191semidirect
154. C2×C8C22⋊D191semidirect

Maximal subgroups

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

subgroupindex
C2×#202593482
C2×#202593442
#271332302
#271330512
#271330462
#271330382
#271326182
C22×D8×C1912
#3155191