Finite Group Databasebeta

← #28400971

Subgroups — #28400971

Order 14464.

392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299147C211yesmaximal, characteristic
2#125×D113C211yesmaximal, characteristic, complemented
3#20298965C212yesmaximal, complemented
4#20298961C212yesmaximal, complemented
5#20298955C211yesmaximal, characteristic, complemented
6#20298953C211yesmaximal, characteristic, complemented
7#20298952C211yesmaximal, characteristic, complemented
8#20298598C212yesmaximal, complemented
9#20298596C212yesmaximal, complemented
10C4×#14268630C211yesmaximal, characteristic, complemented
11#488×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2211yescharacteristic
13C2×#14268646C2211yescharacteristic
14C2×#14268630C2212yes—
15#16813620C2211yescharacteristic
16#16813618C2211yescharacteristic
17#16813614C2211yescharacteristic
18#16813613C2212yes—
19#16813612—22no—
20#16813610C2211yescharacteristic
21#16813595—22no—
22#16813582—22no—
23C4⋊C4×D113—22no—
24C4⋊C4×D113C2212yes—
25C42×D113C2211yescharacteristic
26#16813547C2212yes—
27#16813546C2212yes—
28#16813545C2212yes—
29#16813544C2212yes—
30#16813543C2212yes—
31#16813542C2212yes—
32#16813532C2212yes—
33C4×#11744751C2211yescharacteristic
34#125×C113C2211yescharacteristic
35#124×C113C2211yescharacteristic
36#103×C113C2212yes—
37#102×C113C2212yes—
38C4×C8×C113C2211yescharacteristic
39#14268648—24no—
40#14268646—24no—
41C2×Dic226C2311yescharacteristic
42C2×D452—21no—
43C2×D452C2311yescharacteristic
44C2×C22⋊D113—21no—
45C2×C22⋊D113—22no—
46C22×Dic113—21no—
47C2×C4×D113—22no—
48C2×C4×D113—21no—
49C2×C4×D113D412yes—
50C2×C4×D113C2311yescharacteristic
51#14268630—24no—
52C2×#11744751C2312yes—
53C4⋊Dic113—22no—
54C4⋊Dic113C2312yes—
55#14268626—22no—
56#14268626—22no—
57#14268626—22no—
58#14268626—22no—
59#14268624—22no—
60C4×Dic113D412yes—
61C4×Dic113C2311yescharacteristic
62C2×Q8×C113C2311yescharacteristic
63C2×D4×C113C2311yescharacteristic
64C2×C8×C113C2312yes—
65C4⋊C4×C113—22no—
66C4⋊C4×C113C2312yes—
67C22⋊C4×C113—22no—
68C42×C113C2311yescharacteristic
69C23×C113—21no—
70C22×D113—21no—
71C22×D113C2×D411yescharacteristic
72Q8×C113—22no—
73D4×C113—22no—
74C2×C4×C113—21no—
75C2×C4×C113—22no—
76C2×C4×C113C2×D412yes—
77C2×C4×C113C2411yescharacteristic
78C22⋊D113—44no—
79C22⋊D113—42no—
80C2×Dic113—21no—
81C2×Dic113—22no—
82C2×Dic113—42no—
83C2×Dic113C2×D412yes—
84C2×Dic113C2×D411yescharacteristic
85D452—22no—
86D452—42no—
87C4×D113—42no—
88C4×D113—44no—
89C4×D113—42no—
90C4×D113#4114yes—
91Dic226—22no—
92C8×C113—22no—
93#11744751—22no—
94C22×C113—41no—
95C22×C113—42no—
96C22×C113C22×D411yescharacteristic
97C2×D113—22no—
98C2×D113—41no—
99C2×D113—42no—
100C2×D113#12412yes—
101C4×C113—22no—
102C4×C113—41no—
103C4×C113—42no—
104C4×C113C2×#4112yes—
105Dic113—22no—
106Dic113—41no—
107Dic113—42no—
108Dic113#12412yes—
109C2×C113—81no—
110C2×C113C2×#12411yescharacteristic
111C2×C113#57512yes—
112D113—22no—
113D113—81no—
114#3142—1131nomaximal, Sylow
115C113#314211yescharacteristic, complemented, Sylow
116#532—1131no—
117C2×#125—1131no—
118#491—1132no—
119#490—1132no—
120#488—1131no—
121#488—1131no—
122#488—1131no—
123#488D11311yescharacteristic, complemented
124#417—1132no—
125#417—1132no—
126C4×M16—1131no—
127C2×#41—1131no—
128C2×#41—1131no—
129C2×M16—1132no—
130C4⋊Q8—1131no—
131#127—1131no—
132#125—1132no—
133#125—1131no—
134#125—2262no—
135#125C2×D11311yescharacteristic
136#124—1131no—
137#124C2×D11311yescharacteristic
138#121—2262no—
139C4×D4—2262no—
140C2×C4⋊C4—1132no—
141C2×C4⋊C4—2262no—
142C2×C42—1131no—
143#103—1132no—
144#103—1132no—
145#103—1132no—
146#103C2×D11312yes—
147#102—1132no—
148#102—1132no—
149#102—1132no—
150#102C2×D11312yes—
151#97—1132no—
152C4×C8—1131no—
153C4×C8C2×D11311yescharacteristic
154#41—2264no—
155#41—2264no—
156C2×Q8—1131no—
157C2×Q8C22×D11311yescharacteristic
158C2×D4—1131no—
159C2×D4—2261no—
160C2×D4—2262no—
161C2×D4—2261no—
162C2×D4C22×D11311yescharacteristic
163C22×C4—1131no—
164C22×C4—1132no—
165C22×C4—2261no—
166C22×C4—2262no—
167C22×C4—2261no—
168M16—2264no—
169C2×C8—1132no—
170C2×C8C22×D11312yes—
171C4⋊C4—22no—
172C4⋊C4—1132no—
173C4⋊C4—2262no—
174C4⋊C4—2262no—
175C4⋊C4—2262no—
176C4⋊C4—2262no—
177C4⋊C4—2262no—
178C4⋊C4C22×D11312yes—
179C22⋊C4—22no—
180C22⋊C4—2262no—
181C42—1132no—
182C42—1131no—
183C42C22×D11311yescharacteristic
184C23—21no—
185C23—1131no—
186C23—2261no—
187Q8—22no—
188Q8—2262no—
189D4—22no—
190D4—4522no—
191D4—4522no—
192D4—4524no—
193D4—2262no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—1131no—
197C2×C4—1134no—
198C2×C4—1132no—
199C2×C4—4522no—
200C2×C4—4522no—
201C2×C4—4524no—
202C2×C4—4522no—
203C2×C4—2261no—
204C2×C4—2262no—
205C2×C4D4×D11312yes—
206C2×C4C23×D11311yescharacteristic
207C8—22no—
208C8—2262no—
209C22—41no—
210C22—42no—
211C22—1132no—
212C22—4521no—
213C22—4522no—
214C22—2262no—
215C22C2×D4×D11311yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—1132no—
220C4—4521no—
221C4—4522no—
222C4—2262no—
223C4#41×D11312yes—
224C2—81no—
225C2—9041no—
226C2—2262no—
227C2#124×D11311yescharacteristic
228C2#2029939512yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#488×C113C2
socleC22×C113C22×D4
prime radical#20299147C2
hypercenter#488D113
hypocenterC113#3142
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
2. #125×D113C2semidirect
3. #20298965C2semidirect
4. #20298961C2semidirect
5. #20298955C2semidirect
6. #20298953C2semidirect
7. #20298952C2semidirect
8. #20298598C2semidirect
9. #20298596C2semidirect
10. C4×#14268630C2semidirect
11. #488×C113C2semidirect
115. C113#3142semidirect
123. #488D113semidirect

Maximal subgroups

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

subgroupindex
#202991472
#125×D1132
#202989652
#202989612
#202989552
#202989532
#202989522
#202985982
#202985962
C4×#142686302
#488×C1132
#3142113