Finite Group Databasebeta

← #28406403

Subgroups — #28406403

Order 14464.

612 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 86 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×#16813681C212yesmaximal, complemented
2C2×#16813680C212yesmaximal, complemented
3#20299541C212yesmaximal, complemented
4C22×#14268647C211yesmaximal, characteristic
5C2×C22⋊#90673C2214yes—
6#16813681—24no—
7#16813680—24no—
8(C2×#90673)⋊C4—24no—
9C2×#14268647—24no—
10C2×#14268647—24no—
11C2×#14268647—24no—
12C22×Dic226C411yescharacteristic, complemented
13C22×D452C2211yescharacteristic
14C22×C22⋊D113C411yescharacteristic, complemented
15C22×C22⋊D113C2211yescharacteristic
16C22×C4×D113C411yescharacteristic, complemented
17C22×C4×D113C2211yescharacteristic
18C23×C4×C113C411yescharacteristic, complemented
19C22×#90673—24no—
20C22⋊#90673—24no—
21C22⋊#90673—24no—
22C23×D113C2×C411yescharacteristic
23C23×D113C2311yescharacteristic
24#14268647—232no—
25C2×Dic226—22no—
26C2×Dic226—22no—
27C2×Dic226—22no—
28C2×D452—22no—
29C2×D452—22no—
30C2×D452D414yes—
31C2×C22⋊D113—22no—
32C2×C22⋊D113—22no—
33C2×C22⋊D113—22no—
34C2×C22⋊D113—22no—
35C2×C22⋊D113—22no—
36C2×C22⋊D113D414yes—
37C22×Dic113C2×C411yescharacteristic
38C22×Dic113C2×C411yescharacteristic
39C2×C4×D113—22no—
40C2×C4×D113—22no—
41C2×C4×D113—22no—
42C2×C4×D113—22no—
43C2×C4×D113—22no—
44C2×C4×D113D414yes—
45C24×C113C2×C411yescharacteristic
46C22×C4×C113—22no—
47C22×C4×C113—22no—
48C22×C4×C113—22no—
49C22×C4×C113C2×C411yescharacteristic
50C22×C4×C113C2×C411yescharacteristic
51C23×C113—21no—
52C23×C113—21no—
53C23×C113—42no—
54C23×C113C22⋊C412yes—
55C23×C113C22×C411yescharacteristic
56C22×D113—21no—
57C22×D113—21no—
58C22×D113—42no—
59C22×D113—42no—
60C22×D113C22⋊C412yes—
61C22×D113C2×D412yes—
62C22×D113C2×D412yes—
63C22×D113C2×D412yes—
64C2×#90673—48no—
65C2×#90673—44no—
66C2×C4×C113—28no—
67C2×C4×C113—21no—
68C2×C4×C113—21no—
69C2×C4×C113—21no—
70C2×C4×C113—21no—
71C2×C4×C113C22⋊C412yes—
72C2×C4×C113C22⋊C412yes—
73C22⋊D113—28no—
74C22⋊D113—28no—
75C2×Dic113—21no—
76C2×Dic113—21no—
77C2×Dic113—21no—
78C2×Dic113—21no—
79C2×Dic113C22⋊C412yes—
80C2×Dic113C22⋊C412yes—
81D452—28no—
82C4×D113—28no—
83C4×D113—28no—
84Dic226—28no—
85C22×C113—22no—
86C22×C113—22no—
87C22×C113—42no—
88C22×C113—42no—
89C22×C113—42no—
90C22×C113C2×C22⋊C411yescharacteristic
91C22×C113C2×C22⋊C411yescharacteristic
92C22×C113C2×C22⋊C411yescharacteristic
93C2×D113—24no—
94C2×D113—22no—
95C2×D113—42no—
96C2×D113—42no—
97C2×D113—42no—
98C2×D113—42no—
99C2×D113—42no—
100C2×D113#12014yes—
101#90673—84no—
102C4×C113—22no—
103C4×C113—22no—
104Dic113—22no—
105Dic113—22no—
106C2×C113—21no—
107C2×C113—21no—
108C2×C113—42no—
109C2×C113#37911yescharacteristic
110C2×C113#41012yes—
111D113—24no—
112D113—42no—
113#1782—1131nomaximal, Sylow
114C113#178211yescharacteristic, complemented, Sylow
115C22×#41—1131no—
116C2×#99—1132no—
117C2×#99—1132no—
118#381—1132no—
119C2×#41—2264no—
120C2×#41—2264no—
121C2×#41—2264no—
122C22×Q8—1131no—
123C22×D4—1131no—
124C22×D4—1131no—
125C22×D4—1131no—
126C23×C4—1131no—
127C23×C4—1131no—
128C23×C4#9067311yescharacteristic, complemented
129C2×C22⋊C4—1134no—
130#99—2264no—
131#99—2264no—
132#95—2264no—
133C24—1131no—
134C24—1131no—
135C24C2×#9067311yescharacteristic
136#41—22632no—
137C2×Q8—2262no—
138C2×Q8—2262no—
139C2×Q8—2262no—
140C2×D4—1134no—
141C2×D4—1134no—
142C2×D4—2262no—
143C2×D4—2262no—
144C2×D4—2262no—
145C2×D4—2262no—
146C2×D4—2262no—
147C2×D4—2262no—
148C2×D4—2262no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—1131no—
153C22×C4—1131no—
154C22×C4—1134no—
155C22×C4—2262no—
156C22×C4—2262no—
157C22×C4—2262no—
158C22×C4—2262no—
159C22×C4—2264no—
160C22×C4—2262no—
161C22×C4C2×#9067311yescharacteristic
162C22×C4C2×#9067311yescharacteristic
163C22⋊C4—2264no—
164C22⋊C4—2264no—
165C23—21no—
166C23—21no—
167C23—42no—
168C23—1132no—
169C23—1132no—
170C23—1132no—
171C23—1132no—
172C23—4522no—
173C23—4522no—
174C23—2261no—
175C23—2261no—
176C23C22⋊#9067312yes—
177C23C22×#9067311yescharacteristic
178Q8—2268no—
179D4—2268no—
180D4—2268no—
181D4—2268no—
182C2×C4—28no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—1132no—
188C2×C4—1132no—
189C2×C4—4524no—
190C2×C4—4528no—
191C2×C4—2268no—
192C2×C4—2268no—
193C2×C4—2261no—
194C2×C4—2261no—
195C2×C4—2261no—
196C2×C4—2261no—
197C2×C4C22⋊#9067312yes—
198C2×C4C22⋊#9067312yes—
199C22—22no—
200C22—22no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—1134no—
205C22—4522no—
206C22—4522no—
207C22—4522no—
208C22—4522no—
209C22—4522no—
210C22—2262no—
211C22—2264no—
212C22C2×C22⋊#9067311yescharacteristic
213C22C2×C22⋊#9067311yescharacteristic
214C22C2×C22⋊#9067311yescharacteristic
215C4—22no—
216C4—22no—
217C4—9044no—
218C4—2262no—
219C4—2262no—
220C2—21no—
221C2—21no—
222C2—42no—
223C2—4522no—
224C2—2264no—
225C2#2029953911yescharacteristic
226C2#2029957712yes—
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC23×C113C22×C4
FrattiniC23C22×#90673
FittingC23×C4×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC22×#14268647C2
cosocleC23×D113C23
hypercenterC23×C4#90673
hypocenterC113#1782
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#16813681C2semidirect
2. C2×#16813680C2semidirect
3. #20299541C2semidirect
12. C22×Dic226C4semidirect
14. C22×C22⋊D113C4semidirect
16. C22×C4×D113C4semidirect
18. C23×C4×C113C4semidirect
114. C113#1782semidirect
128. C23×C4#90673semidirect

Maximal subgroups

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

subgroupindex
C2×#168136812
C2×#168136802
#202995412
C22×#142686472
#1782113