Finite Group Databasebeta

← #28399934

Subgroups — #28399934

Order 14464.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 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×#16813667C211yesmaximal, characteristic, complemented
2#20299398C212yesmaximal, complemented
3#20299165C211yesmaximal, characteristic, complemented
4#20298778C214yesmaximal, complemented
5#20298768C214yesmaximal, complemented
6#20298614C212yesmaximal, complemented
7C2×#100×C113C211yesmaximal, characteristic, complemented
8#16813667—24no—
9#16813667—22no—
10#16813667C2214yes—
11C2×#14268647C2212yes—
12C2×#14268647C2211yescharacteristic, complemented
13C2×#14268646—22no—
14C22×C22⋊D113—22no—
15C2×D4×D113—22no—
16#16813655—22no—
17#16813655C2214yescomplemented
18#16813650—22no—
19#16813650C2214yescomplemented
20#16813644—24no—
21#16813618C2212yescomplemented
22#16813609C2212yescomplemented
23#16813593—22no—
24#16813591—22no—
25#16813581C2211yescharacteristic, complemented
26#16813548C2218yescomplemented
27C22×D4×C113C2211yescharacteristic
28C2×M16×C113C2212yescomplemented
29#100×C113C2214yescomplemented
30C23×D113—22no—
31#14268647—22no—
32#14268647—22no—
33#14268647—22no—
34#14268647—22no—
35#14268647D414yescomplemented
36#14268647C2314yes—
37#14268646—28no—
38#14268646—28no—
39C2×Dic226D412yescomplemented
40C2×Dic226C2311yescharacteristic, complemented
41C2×D452D412yescomplemented
42C2×D452C2311yescharacteristic, complemented
43C2×C22⋊D113—24no—
44C2×C22⋊D113—28no—
45C2×C22⋊D113—22no—
46C2×C22⋊D113—28no—
47C2×C22⋊D113—21no—
48C2×C22⋊D113—24no—
49D4×D113—28no—
50D4×D113—28no—
51C22×Dic113—22no—
52C2×C4×D113—22no—
53C2×C4×D113—21no—
54Dic452—24no—
55#14268636—24no—
56#14268636—24no—
57D904—24no—
58C4⋊Dic113—21no—
59C22⋊Dic113—21no—
60C22⋊Dic113—24no—
61C4×Dic113C2312yescomplemented
62C24×C113D412yes—
63C2×D4×C113—22no—
64C2×D4×C113—22no—
65C2×D4×C113D412yes—
66C2×D4×C113C2312yes—
67C22×C4×C113C2311yescharacteristic
68M16×C113—22no—
69M16×C113C2314yescomplemented
70C2×C8×C113—22no—
71C23×C113—22no—
72C23×C113—22no—
73C23×C113—82no—
74C23×C113C2×D414yes—
75C23×C113C2×D411yescharacteristic
76C22×D113—22no—
77C22×D113—28no—
78C22×D113—21no—
79C22×D113—84no—
80D4×C113—24no—
81D4×C113—24no—
82C2×C4×C113C2×D412yes—
83C2×C4×C113C2×D412yes—
84C2×C4×C113C2×D411yescharacteristic
85C2×C4×C113C2411yescharacteristic
86C22⋊D113—216no—
87C22⋊D113—24no—
88C22⋊D113—24no—
89C22⋊D113—41no—
90C22⋊D113—41no—
91C22⋊D113—84no—
92C2×Dic113—28no—
93C2×Dic113—22no—
94C2×Dic113—22no—
95C2×Dic113—21no—
96D452—22no—
97D452—22no—
98D452C2×D414yes—
99C4×D113—24no—
100C4×D113—24no—
101C4×D113—42no—
102Dic226—22no—
103Dic226—22no—
104Dic226C2×D414yes—
105C8×C113—24no—
106C22×C113—24no—
107C22×C113—41no—
108C22×C113—44no—
109C22×C113—44no—
110C22×C113—82no—
111C22×C113#12011yescharacteristic
112C22×C113#12011yescharacteristic
113C22×C113C22×D411yescharacteristic
114C2×D113—24no—
115C2×D113—44no—
116C2×D113—42no—
117C2×D113—41no—
118C2×D113—88no—
119C4×C113#12012yes—
120C4×C113C22×D412yes—
121Dic113—24no—
122Dic113—42no—
123Dic113—41no—
124C2×C113—21no—
125C2×C113—21no—
126C2×C113—21no—
127C2×C113—44no—
128C2×C113C2×#12011yescharacteristic
129D113—44no—
130D113—81no—
131#3019—1131nomaximal, Sylow
132C113#301911yescharacteristic, complemented, Sylow
133C2×H(5,𝔽2)—1131no—
134#575—1132no—
135#535—1131no—
136#455—1134no—
137#453—1134no—
138#421—1132no—
139C2×#100D11311yescharacteristic, complemented
140H(5,𝔽2)—1134no—
141H(5,𝔽2)—2264no—
142H(5,𝔽2)—2262no—
143C2×#41—1132no—
144C2×#41—1131no—
145C2×#41—2262no—
146C22×D4—2262no—
147C22×D4—2262no—
148C22×D4C2×D11311yescharacteristic
149#137—1134no—
150#137—2262no—
151AGL(1,ℤ/8)—1134no—
152AGL(1,ℤ/8)—2262no—
153#135—2264no—
154C2×M16C2×D11312yescomplemented
155#127—1132no—
156#124—1132no—
157#121—2262no—
158#120—2262no—
159#117—1131no—
160#104—1138no—
161#100C2×D11314yescomplemented
162C24—2262no—
163C24D45212yes—
164#41—1134no—
165#41—1134no—
166#41—2262no—
167#41—2262no—
168#41—2268no—
169#41—2268no—
170#41—2262no—
171#41—2262no—
172C2×Q8—1132no—
173C2×Q8—1131no—
174C2×D4—22no—
175C2×D4—22no—
176C2×D4—1132no—
177C2×D4—1131no—
178C2×D4—2268no—
179C2×D4—2268no—
180C2×D4—2264no—
181C2×D4—2261no—
182C2×D4—2264no—
183C2×D4—2268no—
184C2×D4—2262no—
185C2×D4—2268no—
186C2×D4D45212yes—
187C2×D4C22×D11312yes—
188C22×C4—2261no—
189C22×C4—2262no—
190C22×C4—2262no—
191C22×C4C22×D11311yescharacteristic
192Q16—2264no—
193SD16—2264no—
194SD16—2264no—
195D8—2264no—
196M16—22no—
197M16C22×D11314yescomplemented
198C2×C8—22no—
199C4⋊C4—2261no—
200C22⋊C4—2261no—
201C22⋊C4—2264no—
202C42—1132no—
203C23—22no—
204C23—22no—
205C23—82no—
206C23—9044no—
207C23—2268no—
208C23—2261no—
209C23—2262no—
210C23C2×D45214yes—
211C23C2×D45211yescharacteristic
212Q8—1134no—
213Q8—2262no—
214Q8—2262no—
215D4—24no—
216D4—24no—
217D4—1134no—
218D4—9044no—
219D4—4521no—
220D4—4521no—
221D4—22616no—
222D4—2264no—
223D4—2264no—
224D4—2262no—
225D4—2262no—
226C2×C4—4522no—
227C2×C4—2262no—
228C2×C4—2261no—
229C2×C4—2268no—
230C2×C4—2262no—
231C2×C4—2264no—
232C2×C4—2264no—
233C2×C4D4×D11312yes—
234C2×C4D4×D11312yes—
235C2×C4C2×D45211yescharacteristic
236C2×C4C23×D11311yescharacteristic
237C8—24no—
238C22—24no—
239C22—41no—
240C22—44no—
241C22—44no—
242C22—82no—
243C22—9048no—
244C22—4522no—
245C22—4524no—
246C22—4521no—
247C22—2264no—
248C22#1681359211yescharacteristic
249C22#1681359211yescharacteristic
250C22C22×D45211yescharacteristic
251C4—4522no—
252C4—4521no—
253C4—2264no—
254C4#1681359212yes—
255C4C2×D4×D11312yes—
256C2—21no—
257C2—21no—
258C2—21no—
259C2—44no—
260C2—9041no—
261C2—4524no—
262C2C2×#1681359211yescharacteristic
subgroupG/H
centerC2C2×#16813592
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#100×C113C2
socleC2×C113C2×#120
hypercenterC2×#100D113
hypocenterC113#3019
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#16813667C2semidirect
2. #20299398C2semidirect
3. #20299165C2semidirect
4. #20298778C2semidirect
5. #20298768C2semidirect
6. #20298614C2semidirect
7. C2×#100×C113C2semidirect
12. C2×#14268647C22semidirect
17. #16813655C22semidirect
19. #16813650C22semidirect
21. #16813618C22semidirect
22. #16813609C22semidirect
25. #16813581C22semidirect
26. #16813548C22semidirect
28. C2×M16×C113C22semidirect
29. #100×C113C22semidirect
35. #14268647D4semidirect
39. C2×Dic226D4semidirect
40. C2×Dic226C23semidirect
41. C2×D452D4semidirect
42. C2×D452C23semidirect
61. C4×Dic113C23semidirect
69. M16×C113C23semidirect
132. C113#3019semidirect
139. C2×#100D113semidirect
154. C2×M16C2×D113semidirect
161. #100C2×D113semidirect
197. M16C22×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136672
#202993982
#202991652
#202987782
#202987682
#202986142
C2×#100×C1132
#3019113