Finite Group Databasebeta

← #28400510

Subgroups — #28400510

Order 14464.

462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16813581C211yesmaximal, characteristic, complemented
2#20298919C214yesmaximal, complemented
3#20298914C212yesmaximal, complemented
4#20298909C212yesmaximal, complemented
5#20298638C212yesmaximal, complemented
6#20298603C212yesmaximal, complemented
7#20298562C211yesmaximal, characteristic, complemented
8C2×#121×C113C211yesmaximal, characteristic
9C2×#14268631C2212yes—
10#16813581—21no—
11#16813581—21no—
12#16813581C2212yes—
13#16813581C2212yescomplemented
14C2×C4⋊Dic113C2211yescharacteristic, complemented
15C2×C4⋊Dic113C2211yescharacteristic, complemented
16C2×C22⋊Dic113—21no—
17C2×C4×Dic113—21no—
18#16813555C2214yescomplemented
19#16813553C2214yescomplemented
20#16813543C2214yescomplemented
21#16813543C2214yescomplemented
22C22⋊#11744751C2212yescomplemented
23C22⋊#11744751C2212yescomplemented
24C22×D4×C113—21no—
25C22×D4×C113C2211yescharacteristic
26C23×C4×C113C2211yescharacteristic
27#121×C113—21no—
28#121×C113—21no—
29#121×C113C2212yes—
30#121×C113C2212yes—
31C2×C4⋊C4×C113C2211yescharacteristic
32C2×C22⋊C4×C113—21no—
33C22×Dic113—21no—
34C22×Dic113—21no—
35#14268631—24no—
36C2×#11744751C2314yes—
37C4⋊Dic113—21no—
38C4⋊Dic113—21no—
39C4⋊Dic113C2312yes—
40C4⋊Dic113C2312yes—
41C22⋊Dic113—22no—
42C22⋊Dic113—22no—
43C4×Dic113—22no—
44C4×Dic113—22no—
45C24×C113—21no—
46C24×C113D411yescharacteristic
47C2×D4×C113—22no—
48C2×D4×C113—22no—
49C2×D4×C113—21no—
50C2×D4×C113—24no—
51C2×D4×C113—44no—
52C2×D4×C113C2312yes—
53C22×C4×C113—24no—
54C22×C4×C113—21no—
55C22×C4×C113D411yescharacteristic
56C22×C4×C113D411yescharacteristic
57C22×C4×C113D411yescharacteristic
58C22×C4×C113C2311yescharacteristic
59C22×C4×C113C2311yescharacteristic
60C22×C4×C113C2311yescharacteristic
61C4⋊C4×C113—21no—
62C4⋊C4×C113C2312yes—
63C22⋊C4×C113—22no—
64C22⋊C4×C113—22no—
65C23×C113—22no—
66C23×C113—22no—
67C23×C113—22no—
68C23×C113—41no—
69C23×C113—42no—
70C23×C113—42no—
71C23×C113—42no—
72C23×C113C2×D411yescharacteristic
73C23×C113C2×D411yescharacteristic
74C23×C113C2×D411yescharacteristic
75D4×C113—24no—
76D4×C113—44no—
77D4×C113—44no—
78D4×C113—42no—
79C2×C4×C113—22no—
80C2×C4×C113—22no—
81C2×C4×C113—22no—
82C2×C4×C113—22no—
83C2×C4×C113—22no—
84C2×C4×C113—22no—
85C2×C4×C113—42no—
86C2×C4×C113C2×D411yescharacteristic
87C2×C4×C113C2×D411yescharacteristic
88C2×C4×C113C2×D411yescharacteristic
89C2×C4×C113#4114yes—
90C2×C4×C113C2411yescharacteristic
91C2×Dic113—22no—
92C2×Dic113—22no—
93C2×Dic113—42no—
94C2×Dic113—42no—
95#11744751—24no—
96C22×C113—21no—
97C22×C113—21no—
98C22×C113—21no—
99C22×C113—21no—
100C22×C113—21no—
101C22×C113—21no—
102C22×C113—21no—
103C22×C113—44no—
104C22×C113—42no—
105C22×C113—42no—
106C22×C113—42no—
107C22×C113—84no—
108C22×C113#12312yes—
109C22×C113AGL(1,ℤ/8)12yes—
110C22×C113C22×D411yescharacteristic
111C4×C113—21no—
112C4×C113—21no—
113C4×C113—42no—
114C4×C113#12312yes—
115C4×C113C2×#4112yes—
116Dic113—42no—
117Dic113—42no—
118C2×C113—22no—
119C2×C113—22no—
120C2×C113—41no—
121C2×C113—82no—
122C2×C113C2×#12311yescharacteristic
123C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
124C2×C113#57511yescharacteristic
125#3094—1131nomaximal, Sylow
126C113#309411yescharacteristic, complemented, Sylow
127C2×#121D11311yescharacteristic
128C2×#117—1131no—
129#482—1134no—
130#481—1132no—
131#480—1132no—
132#428—1132no—
133#418—1132no—
134#407—1131no—
135C22×D4—21no—
136C22×D4C2×D11311yescharacteristic
137C23×C4C2×D11311yescharacteristic
138C2×M16—1132no—
139#121—21no—
140#121—21no—
141#121C2×D11312yes—
142#121C2×D11312yes—
143#117—1132no—
144#117—1132no—
145#117—2261no—
146#117—2261no—
147C2×C4⋊C4—1131no—
148C2×C4⋊C4—1131no—
149C2×C4⋊C4C2×D11311yescharacteristic
150C2×C22⋊C4—21no—
151C2×C22⋊C4—2261no—
152C2×C42—2261no—
153#107—1134no—
154#106—1134no—
155#102—1134no—
156#102—1134no—
157C22⋊C8—1132no—
158C22⋊C8—1132no—
159C24—21no—
160C24C22⋊D11311yescharacteristic
161C2×D4—22no—
162C2×D4—22no—
163C2×D4—21no—
164C2×D4—24no—
165C2×D4—44no—
166C2×D4C22×D11312yes—
167C22×C4—24no—
168C22×C4—21no—
169C22×C4—2261no—
170C22×C4—2261no—
171C22×C4C22⋊D11311yescharacteristic
172C22×C4C22⋊D11311yescharacteristic
173C22×C4C22⋊D11311yescharacteristic
174C22×C4C22×D11311yescharacteristic
175C22×C4C22×D11311yescharacteristic
176C22×C4C22×D11311yescharacteristic
177M16—2264no—
178C2×C8—1134no—
179C4⋊C4—21no—
180C4⋊C4—1132no—
181C4⋊C4—1132no—
182C4⋊C4—2261no—
183C4⋊C4—2261no—
184C4⋊C4C22×D11312yes—
185C22⋊C4—22no—
186C22⋊C4—22no—
187C22⋊C4—2262no—
188C22⋊C4—2262no—
189C42—2262no—
190C42—2262no—
191C23—22no—
192C23—22no—
193C23—22no—
194C23—41no—
195C23—42no—
196C23—42no—
197C23—42no—
198C23C2×C22⋊D11311yescharacteristic
199C23C2×C22⋊D11311yescharacteristic
200C23C2×C22⋊D11311yescharacteristic
201D4—24no—
202D4—44no—
203D4—44no—
204D4—42no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—42no—
212C2×C4—4522no—
213C2×C4—4522no—
214C2×C4—2262no—
215C2×C4—2262no—
216C2×C4C2×C22⋊D11311yescharacteristic
217C2×C4C2×C22⋊D11311yescharacteristic
218C2×C4C2×C22⋊D11311yescharacteristic
219C2×C4#1426864614yes—
220C2×C4C23×D11311yescharacteristic
221C8—2264no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—44no—
230C22—42no—
231C22—42no—
232C22—42no—
233C22—84no—
234C22#1681360312yes—
235C22#1681364812yes—
236C22C22×C22⋊D11311yescharacteristic
237C4—21no—
238C4—21no—
239C4—42no—
240C4—4522no—
241C4—4522no—
242C4#1681360312yes—
243C4C2×#1426864612yes—
244C2—22no—
245C2—22no—
246C2—41no—
247C2—82no—
248C2C2×#1681360311yescharacteristic
249C2C2×#1681364811yescharacteristic
250C2#2029939611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting, prime radicalC2×#121×C113C2
socleC22×C113C22×D4
hypercenterC2×#121D113
hypocenterC113#3094
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#16813581C2semidirect
2. #20298919C2semidirect
3. #20298914C2semidirect
4. #20298909C2semidirect
5. #20298638C2semidirect
6. #20298603C2semidirect
7. #20298562C2semidirect
13. #16813581C22semidirect
14. C2×C4⋊Dic113C22semidirect
15. C2×C4⋊Dic113C22semidirect
18. #16813555C22semidirect
19. #16813553C22semidirect
20. #16813543C22semidirect
21. #16813543C22semidirect
22. C22⋊#11744751C22semidirect
23. C22⋊#11744751C22semidirect
126. C113#3094semidirect

Maximal subgroups

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

subgroupindex
C2×#168135812
#202989192
#202989142
#202989092
#202986382
#202986032
#202985622
C2×#121×C1132
#3094113