Finite Group Databasebeta

← #28400082

Subgroups — #28400082

Order 14464.

494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16813647C211yesmaximal, characteristic
2C22×#14268634C211yesmaximal, characteristic, complemented
3#20299072C211yesmaximal, characteristic, complemented
4#20298810C214yesmaximal, complemented
5#20298800C214yesmaximal, complemented
6#20298625C211yesmaximal, characteristic, complemented
7#20298607C211yesmaximal, characteristic, complemented
8#20298594C211yesmaximal, characteristic, complemented
9#536×C113C211yesmaximal, characteristic, complemented
10C22×D452C2211yescharacteristic
11#16813647—24no—
12C2×#14268634—24no—
13C2×#14268634C2212yes—
14C2×#14268634C2214yes—
15C2×#14268632C2212yes—
16C2×#14268631C2211yescharacteristic
17C22×#11744751C2211yescharacteristic
18C4×D452C2214yes—
19#16813584—22no—
20#16813581C2211yescharacteristic
21C22⋊C4×D113—22no—
22C4⋊#11744751C2214yescomplemented
23#16813546C2212yescomplemented
24#16813546C2214yescomplemented
25#16813543C2212yescomplemented
26C2×#41×C113C2211yescharacteristic
27C22×Q8×C113C2211yescharacteristic
28C4⋊Q8×C113C2212yescomplemented
29#124×C113C2212yescomplemented
30#123×C113—22no—
31C22⋊Q8×C113—22no—
32#117×C113C2211yescharacteristic
33C23×D113—21no—
34C2×D452—21no—
35C2×D452—22no—
36C2×D452D414yes—
37C2×D452C2312yes—
38C2×C4×D113—24no—
39#14268634—28no—
40#14268634—24no—
41#14268632—24no—
42#14268631—22no—
43C2×#11744751—22no—
44C2×#11744751C2312yes—
45C2×#11744751C2312yes—
46C4⋊Dic113C2312yes—
47C22⋊Dic113—21no—
48#14268624—24no—
49C4×Dic113—21no—
50#41×C113—22no—
51#41×C113—22no—
52C2×Q8×C113—21no—
53C2×Q8×C113—22no—
54C2×Q8×C113—22no—
55C2×Q8×C113C2312yes—
56C2×Q8×C113C2311yescharacteristic
57C2×D4×C113—21no—
58C2×D4×C113C2311yescharacteristic
59C22×C4×C113—21no—
60C22×C4×C113—21no—
61C22×C4×C113C2311yescharacteristic
62C4⋊C4×C113—24no—
63C4⋊C4×C113D412yes—
64C22⋊C4×C113—24no—
65C22⋊C4×C113D412yes—
66C42×C113C2312yes—
67C23×C113—21no—
68C23×C113C2×D411yescharacteristic
69C22×D113—22no—
70C22×D113—24no—
71C22×D113—82no—
72Q8×C113—22no—
73Q8×C113—21no—
74Q8×C113—22no—
75Q8×C113—21no—
76Q8×C113—42no—
77D4×C113—21no—
78D4×C113—21no—
79D4×C113—42no—
80C2×C4×C113—22no—
81C2×C4×C113—21no—
82C2×C4×C113—42no—
83C2×C4×C113—42no—
84C2×C4×C113C2×D412yes—
85C2×C4×C113C2×D414yes—
86C2×C4×C113C2×D411yescharacteristic
87C2×C4×C113#4112yes—
88C2×C4×C113C2411yescharacteristic
89C2×Dic113—22no—
90D452—24no—
91D452—22no—
92D452C2×D414yes—
93C4×D113—84no—
94#11744751—22no—
95#11744751—22no—
96C22×C113—22no—
97C22×C113—41no—
98C22×C113—42no—
99C22×C113#12112yes—
100C22×C113C22×D411yescharacteristic
101C2×D113—24no—
102C2×D113—44no—
103C2×D113—84no—
104C4×C113—24no—
105C4×C113—41no—
106C4×C113—42no—
107C4×C113#12112yes—
108C4×C113C22×D411yescharacteristic
109C4×C113C2×#4111yescharacteristic
110Dic113—42no—
111C2×C113—22no—
112C2×C113—81no—
113C2×C113C2×#12111yescharacteristic
114C2×C113#57712yes—
115D113—44no—
116#3042—1131nomaximal, Sylow
117C113#304211yescharacteristic, complemented, Sylow
118C2×AGL(1,ℤ/8)—1131no—
119C22×SD16—1131no—
120#536D11311yescharacteristic, complemented
121#518—1131no—
122#463—1134no—
123#461—1134no—
124#424—1131no—
125#419—1131no—
126#416—1131no—
127C2×#41C2×D11311yescharacteristic
128C22×Q8C2×D11311yescharacteristic
129C22×D4—1131no—
130AGL(1,ℤ/8)—2264no—
131C2×SD16—1134no—
132C2×SD16—1132no—
133C2×SD16—2264no—
134C2×D8—1132no—
135C2×M16—1131no—
136C22×C8—1131no—
137C4⋊Q8C2×D11312yescomplemented
138#124C2×D11312yescomplemented
139#123—22no—
140C22⋊Q8—22no—
141C4×D4—1134no—
142C4×D4—2262no—
143#117—1131no—
144#117C2×D11311yescharacteristic
145C2×C22⋊C4—2262no—
146C4⋊C8—1134no—
147#103—1132no—
148#103—1134no—
149#102—1132no—
150C24—2261no—
151#41—22no—
152#41—22no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8C22×D11312yes—
157C2×Q8C22×D11311yescharacteristic
158C2×D4—21no—
159C2×D4—1134no—
160C2×D4—1132no—
161C2×D4—2261no—
162C2×D4—2262no—
163C2×D4C22×D11311yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—2264no—
167C22×C4C22×D11311yescharacteristic
168SD16—2268no—
169SD16—2264no—
170D8—2264no—
171M16—2262no—
172C2×C8—1132no—
173C2×C8—1132no—
174C2×C8—2262no—
175C4⋊C4—24no—
176C4⋊C4—1132no—
177C4⋊C4C22⋊D11312yes—
178C22⋊C4—24no—
179C22⋊C4—2261no—
180C22⋊C4—2264no—
181C22⋊C4C22⋊D11312yes—
182C42—2261no—
183C42C22×D11312yes—
184C23—21no—
185C23—9042no—
186C23—2264no—
187C23—2262no—
188C23C2×C22⋊D11311yescharacteristic
189Q8—22no—
190Q8—21no—
191Q8—22no—
192Q8—21no—
193Q8—42no—
194D4—21no—
195D4—21no—
196D4—42no—
197D4—1134no—
198D4—2264no—
199D4—2262no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—9044no—
205C2×C4—2262no—
206C2×C4D4×D11312yes—
207C2×C4C2×C22⋊D11314yes—
208C2×C4C2×C22⋊D11311yescharacteristic
209C2×C4#1426864612yes—
210C2×C4C23×D11311yescharacteristic
211C8—2262no—
212C8—2262no—
213C22—22no—
214C22—41no—
215C22—42no—
216C22—9044no—
217C22—4524no—
218C22—2264no—
219C22#1681359312yes—
220C22C22×C22⋊D11311yescharacteristic
221C4—24no—
222C4—41no—
223C4—42no—
224C4—4522no—
225C4#1681359312yes—
226C4C2×D4×D11311yescharacteristic
227C4C2×#1426864611yescharacteristic
228C2—22no—
229C2—81no—
230C2—4524no—
231C2C2×#1681359311yescharacteristic
232C2#2029940612yes—
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#536×C113C2
socleC22×C113C22×D4
prime radicalC2×#16813647C2
hypercenter#536D113
hypocenterC113#3042
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #536

Complements

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

NH ≅ G/Ntype
2. C22×#14268634C2semidirect
3. #20299072C2semidirect
4. #20298810C2semidirect
5. #20298800C2semidirect
6. #20298625C2semidirect
7. #20298607C2semidirect
8. #20298594C2semidirect
9. #536×C113C2semidirect
22. C4⋊#11744751C22semidirect
23. #16813546C22semidirect
24. #16813546C22semidirect
25. #16813543C22semidirect
28. C4⋊Q8×C113C22semidirect
29. #124×C113C22semidirect
117. C113#3042semidirect
120. #536D113semidirect
137. C4⋊Q8C2×D113semidirect
138. #124C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136472
C22×#142686342
#202990722
#202988102
#202988002
#202986252
#202986072
#202985942
#536×C1132
#3042113