Finite Group Databasebeta

← #28401592

Subgroups — #28401592

Order 14464.

490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#20299132C211yesmaximal, characteristic, complemented
2#20298985C212yesmaximal, complemented
3#20298962C212yesmaximal, complemented
4#20298795C212yesmaximal, complemented
5#20298790C212yesmaximal, complemented
6#20298749C212yesmaximal, complemented
7#20298732C212yesmaximal, complemented
8#20298655C211yesmaximal, characteristic, complemented
9C2×#127×C113C211yesmaximal, characteristic, complemented
10C2×#14268635C2214yescomplemented
11C2×#14268632C2214yescomplemented
12#16813616—21no—
13#16813614C2211yescharacteristic, complemented
14#16813610C2211yescharacteristic, complemented
15#16813605—21no—
16#16813601C2211yescharacteristic
17#16813596C2211yescharacteristic
18C4×Dic226C2211yescharacteristic, complemented
19C4×D452C2211yescharacteristic, complemented
20C4×C22⋊D113—21no—
21#16813579—21no—
22C4⋊#11744751C2212yescomplemented
23#16813543C2214yescomplemented
24#16813543C2214yescomplemented
25C22⋊#11744751C2212yes—
26#16813533C2212yescomplemented
27C22×D4×C113—21no—
28C22×D4×C113—21no—
29C22×D4×C113C2212yes—
30#127×C113—21no—
31#127×C113—21no—
32#127×C113C2212yes—
33#127×C113C2212yes—
34C2×C42×C113C2211yescharacteristic
35C2×Dic226C2311yescharacteristic
36C2×D452C2311yescharacteristic
37C2×C22⋊D113—21no—
38C2×C4×D113—21no—
39#14268635—44no—
40#14268632—44no—
41C2×#11744751C2314yes—
42C4⋊Dic113C2311yescharacteristic
43C4⋊Dic113C2311yescharacteristic
44#14268626—21no—
45#14268626—21no—
46#14268626—21no—
47#14268626—21no—
48C22⋊Dic113—21no—
49#14268624—21no—
50#14268624—21no—
51#14268624—21no—
52#14268624—21no—
53C4×Dic113—21no—
54C24×C113—22no—
55C2×D4×C113—22no—
56C2×D4×C113—22no—
57C2×D4×C113—22no—
58C2×D4×C113—22no—
59C2×D4×C113—22no—
60C2×D4×C113—44no—
61C2×D4×C113—44no—
62C2×D4×C113—44no—
63C2×D4×C113C2314yes—
64C22×C4×C113D411yescharacteristic
65C22×C4×C113D411yescharacteristic
66C22×C4×C113C2311yescharacteristic
67C42×C113D411yescharacteristic
68C42×C113D411yescharacteristic
69C42×C113C2311yescharacteristic
70C42×C113C2311yescharacteristic
71C23×C113—24no—
72C23×C113—44no—
73C23×C113—44no—
74C23×C113—44no—
75C23×C113C2×D411yescharacteristic
76C22×D113—21no—
77D4×C113—24no—
78D4×C113—24no—
79D4×C113—44no—
80D4×C113—44no—
81D4×C113—44no—
82D4×C113—44no—
83D4×C113—44no—
84C2×C4×C113—22no—
85C2×C4×C113—22no—
86C2×C4×C113—22no—
87C2×C4×C113C2×D411yescharacteristic
88C2×C4×C113C2×D411yescharacteristic
89C2×C4×C113C2×D411yescharacteristic
90C2×C4×C113C2×D411yescharacteristic
91C2×C4×C113C2×D411yescharacteristic
92C2×C4×C113C2411yescharacteristic
93C22⋊D113—42no—
94C2×Dic113—21no—
95C2×Dic113—21no—
96C2×Dic113—21no—
97D452—22no—
98C4×D113—42no—
99Dic226—22no—
100#11744751—24no—
101C22×C113—21no—
102C22×C113—21no—
103C22×C113—44no—
104C22×C113—44no—
105C22×C113—44no—
106C22×C113—88no—
107C22×C113AGL(1,ℤ/8)12yes—
108C22×C113C22×D411yescharacteristic
109C2×D113—41no—
110C2×D113—41no—
111C2×D113—41no—
112C4×C113—21no—
113C4×C113—21no—
114C4×C113—21no—
115C4×C113—21no—
116C4×C113AGL(1,ℤ/8)12yes—
117C4×C113H(5,𝔽2)12yes—
118Dic113—41no—
119Dic113—41no—
120Dic113—41no—
121C2×C113—22no—
122C2×C113—84no—
123C2×C113#53511yescharacteristic
124C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
125C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
126D113—81no—
127#3217—1131nomaximal, Sylow
128C113#321711yescharacteristic, complemented, Sylow
129C2×#127D11311yescharacteristic, complemented
130#529—1131no—
131#496—1132no—
132#490—1132no—
133#460—1132no—
134#459—1132no—
135#450—1132no—
136#447—1132no—
137#432—1131no—
138C22×D4—21no—
139C22×D4—21no—
140C22×D4C2×D11312yes—
141C2×SD16—1134no—
142C2×D8—1134no—
143#127—21no—
144#127—21no—
145#127C2×D11312yes—
146#127C2×D11312yes—
147#126—2261no—
148#125—1131no—
149#124—1131no—
150#123—2261no—
151C22⋊Q8—1131no—
152#121—1131no—
153C4×Q8—1131no—
154C4×D4—1131no—
155C4×D4—2261no—
156#117—2261no—
157C2×C42C2×D11311yescharacteristic
158C4⋊C8—1132no—
159#102—1134no—
160#102—1134no—
161C22⋊C8—1132no—
162#97—1132no—
163C24—22no—
164C2×Q8—1131no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4—22no—
168C2×D4—22no—
169C2×D4—22no—
170C2×D4—44no—
171C2×D4—44no—
172C2×D4—44no—
173C2×D4—1131no—
174C2×D4—2261no—
175C2×D4C22×D11314yes—
176C22×C4—2261no—
177C22×C4C22⋊D11311yescharacteristic
178C22×C4C22⋊D11311yescharacteristic
179C22×C4C22×D11311yescharacteristic
180SD16—4524no—
181D8—4524no—
182C2×C8—1134no—
183C4⋊C4—1131no—
184C4⋊C4—1131no—
185C4⋊C4—2261no—
186C4⋊C4—2261no—
187C4⋊C4—2261no—
188C4⋊C4—2261no—
189C22⋊C4—2261no—
190C22⋊C4—2261no—
191C22⋊C4—2261no—
192C22⋊C4—2261no—
193C22⋊C4—2261no—
194C42—2261no—
195C42C22⋊D11311yescharacteristic
196C42C22⋊D11311yescharacteristic
197C42C22×D11311yescharacteristic
198C42C22×D11311yescharacteristic
199C23—24no—
200C23—44no—
201C23—44no—
202C23—44no—
203C23—2261no—
204C23C2×C22⋊D11311yescharacteristic
205Q8—2262no—
206D4—24no—
207D4—24no—
208D4—44no—
209D4—44no—
210D4—44no—
211D4—44no—
212D4—44no—
213D4—4522no—
214D4—2262no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—4522no—
219C2×C4—2261no—
220C2×C4—2261no—
221C2×C4—2261no—
222C2×C4C2×C22⋊D11311yescharacteristic
223C2×C4C2×C22⋊D11311yescharacteristic
224C2×C4C2×C22⋊D11311yescharacteristic
225C2×C4C2×C22⋊D11311yescharacteristic
226C2×C4C2×C22⋊D11311yescharacteristic
227C2×C4C23×D11311yescharacteristic
228C8—2264no—
229C22—21no—
230C22—21no—
231C22—44no—
232C22—44no—
233C22—44no—
234C22—88no—
235C22—4521no—
236C22—4521no—
237C22—4521no—
238C22#1681364812yes—
239C22C22×C22⋊D11311yescharacteristic
240C4—21no—
241C4—21no—
242C4—21no—
243C4—21no—
244C4—4521no—
245C4—4521no—
246C4—4521no—
247C4#1681364812yes—
248C4#1681366712yes—
249C2—22no—
250C2—84no—
251C2—9041no—
252C2#2029916511yescharacteristic
253C2C2×#1681364811yescharacteristic
254C2C2×#1681364811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#127×C113C2
socleC22×C113C22×D4
hypercenterC2×#127D113
hypocenterC113#3217
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. #20299132C2semidirect
2. #20298985C2semidirect
3. #20298962C2semidirect
4. #20298795C2semidirect
5. #20298790C2semidirect
6. #20298749C2semidirect
7. #20298732C2semidirect
8. #20298655C2semidirect
9. C2×#127×C113C2semidirect
10. C2×#14268635C22semidirect
11. C2×#14268632C22semidirect
13. #16813614C22semidirect
14. #16813610C22semidirect
18. C4×Dic226C22semidirect
19. C4×D452C22semidirect
22. C4⋊#11744751C22semidirect
23. #16813543C22semidirect
24. #16813543C22semidirect
26. #16813533C22semidirect
128. C113#3217semidirect
129. C2×#127D113semidirect

Maximal subgroups

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

subgroupindex
#202991322
#202989852
#202989622
#202987952
#202987902
#202987492
#202987322
#202986552
C2×#127×C1132
#3217113