Finite Group Databasebeta

← #28401055

Subgroups — #28401055

Order 14464.

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×#16813648C212yesmaximal, complemented
2C2×#16813644C211yesmaximal, characteristic, complemented
3#20299165C212yesmaximal, complemented
4#20298986C214yesmaximal, complemented
5#20298981C212yesmaximal, complemented
6#20298973C212yesmaximal, complemented
7#20298553C211yesmaximal, characteristic, complemented
8C22×D8×C113C211yesmaximal, characteristic, complemented
9C2×#14268647C2212yes—
10#16813648—28no—
11#16813644—24no—
12C2×Dic452C2211yescharacteristic, complemented
13C2×#14268636C2212yescomplemented
14C2×#14268635C2214yescomplemented
15C2×D904C2211yescharacteristic, complemented
16C2×#14268632C2214yescomplemented
17C2×#14268631C2211yescharacteristic
18#16813618C2214yescomplemented
19#16813609C2214yescomplemented
20#16813593—24no—
21#16813591—24no—
22#16813581C2211yescharacteristic
23#16813532C2212yescomplemented
24C8×Dic113C2212yescomplemented
25C22×D4×C113C2212yes—
26C2×D8×C113—24no—
27C2×D8×C113C2212yes—
28C2×D8×C113C2212yes—
29C22×C8×C113C2211yescharacteristic
30#14268647—24no—
31#14268647—24no—
32C2×Dic226C2312yes—
33C2×D452C2312yes—
34C2×C22⋊D113—22no—
35C2×C22⋊D113—28no—
36C2×C4×D113—22no—
37Dic452—22no—
38#14268636—24no—
39#14268635—28no—
40D904—22no—
41#14268632—28no—
42#14268631D414yescomplemented
43C2×#11744751C2312yes—
44C4⋊Dic113D412yes—
45C22⋊Dic113—28no—
46C22⋊Dic113D412yes—
47C4×Dic113C2312yes—
48C24×C113—22no—
49C2×D4×C113—24no—
50C2×D4×C113—24no—
51C2×D4×C113—22no—
52C2×D4×C113C2314yes—
53C22×C4×C113C2311yescharacteristic
54D8×C113—24no—
55D8×C113—24no—
56C2×C8×C113D414yescomplemented
57C2×C8×C113C2311yescharacteristic
58C2×C8×C113C2311yescharacteristic
59C23×C113—24no—
60C23×C113—44no—
61C23×C113—84no—
62C23×C113C2×D411yescharacteristic
63C22×D113—22no—
64D4×C113—24no—
65D4×C113—24no—
66D4×C113—44no—
67C2×C4×C113C2×D411yescharacteristic
68C2×C4×C113C2×D412yes—
69C2×C4×C113C2×D412yes—
70C2×C4×C113C2411yescharacteristic
71C22⋊D113—44no—
72C22⋊D113—88no—
73C2×Dic113—22no—
74C2×Dic113C2×D414yes—
75D452—22no—
76D452—22no—
77C4×D113—44no—
78Dic226—22no—
79Dic226—22no—
80C8×C113C2×D412yes—
81C8×C113C2×D412yes—
82#11744751C2×D414yes—
83C22×C113—22no—
84C22×C113—44no—
85C22×C113—48no—
86C22×C113—88no—
87C22×C113#12712yes—
88C22×C113C22×D411yescharacteristic
89C2×D113—42no—
90C2×D113—44no—
91C4×C113#12712yes—
92C4×C113C22×D411yescharacteristic
93C4×C113C22×D411yescharacteristic
94Dic113—24no—
95Dic113—42no—
96C2×C113—22no—
97C2×C113—84no—
98C2×C113C2×#12711yescharacteristic
99C2×C113#57612yes—
100D113—82no—
101#3155—1131nomaximal, Sylow
102C113#315511yescharacteristic, complemented, Sylow
103C2×AGL(1,ℤ/8)—1132no—
104C2×#135—1131no—
105C22×D8D11311yescharacteristic, complemented
106#535—1132no—
107#496—1134no—
108#495—1132no—
109#493—1132no—
110#405—1131no—
111C2×#41—1132no—
112C22×D4C2×D11312yes—
113AGL(1,ℤ/8)—2268no—
114#135—2264no—
115C2×Q16—1131no—
116C2×SD16—1134no—
117C2×SD16—1132no—
118C2×D8—24no—
119C2×D8—1134no—
120C2×D8—1131no—
121C2×D8C2×D11312yes—
122C2×D8C2×D11312yes—
123C2×M16—1131no—
124C22×C8C2×D11311yescharacteristic
125#127—1134no—
126#124—1134no—
127#121—2264no—
128#120—2264no—
129#117—1131no—
130#97—1132no—
131C4×C8—1132no—
132C24—22no—
133#41—2264no—
134#41—2264no—
135C2×Q8—1132no—
136C2×D4—24no—
137C2×D4—22no—
138C2×D4—24no—
139C2×D4—1132no—
140C2×D4—2268no—
141C2×D4—2262no—
142C2×D4C22×D11314yes—
143C22×C4—2262no—
144C22×C4C22×D11311yescharacteristic
145Q16—2262no—
146SD16—2268no—
147SD16—2264no—
148D8—24no—
149D8—24no—
150D8—2268no—
151D8—2262no—
152M16—1134no—
153C2×C8—1132no—
154C2×C8C22⋊D11314yescomplemented
155C2×C8C22×D11311yescharacteristic
156C2×C8C22×D11311yescharacteristic
157C4⋊C4—1132no—
158C22⋊C4—1132no—
159C22⋊C4—2268no—
160C42—1132no—
161C23—24no—
162C23—44no—
163C23—84no—
164C23—2262no—
165C23D4×D11311yescharacteristic
166Q8—2262no—
167Q8—2262no—
168D4—24no—
169D4—24no—
170D4—44no—
171D4—9048no—
172D4—4524no—
173D4—2262no—
174D4—2262no—
175C2×C4—1134no—
176C2×C4—4524no—
177C2×C4—2262no—
178C2×C4D4×D11311yescharacteristic
179C2×C4D4×D11312yes—
180C2×C4C2×C22⋊D11312yes—
181C2×C4C23×D11311yescharacteristic
182C8—1134no—
183C8C2×C22⋊D11312yes—
184C8C2×C22⋊D11312yes—
185C22—22no—
186C22—44no—
187C22—48no—
188C22—88no—
189C22—4522no—
190C22—4524no—
191C22#1681361812yes—
192C22C2×D4×D11311yescharacteristic
193C4—4522no—
194C4—2264no—
195C4#1681361812yes—
196C4C2×D4×D11311yescharacteristic
197C4C22×C22⋊D11311yescharacteristic
198C2—22no—
199C2—84no—
200C2—9042no—
201C2C2×#1681361811yescharacteristic
202C2#2029939912yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC22×D8×C113C2
socleC22×C113C22×D4
hypercenterC22×D8D113
hypocenterC113#3155
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C2×#16813648C2semidirect
2. C2×#16813644C2semidirect
3. #20299165C2semidirect
4. #20298986C2semidirect
5. #20298981C2semidirect
6. #20298973C2semidirect
7. #20298553C2semidirect
8. C22×D8×C113C2semidirect
12. C2×Dic452C22semidirect
13. C2×#14268636C22semidirect
14. C2×#14268635C22semidirect
15. C2×D904C22semidirect
16. C2×#14268632C22semidirect
18. #16813618C22semidirect
19. #16813609C22semidirect
23. #16813532C22semidirect
24. C8×Dic113C22semidirect
42. #14268631D4semidirect
56. C2×C8×C113D4semidirect
102. C113#3155semidirect
105. C22×D8D113semidirect
154. C2×C8C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
C2×#168136442
#202991652
#202989862
#202989812
#202989732
#202985532
C22×D8×C1132
#3155113