Finite Group Databasebeta

← #28406411

Subgroups — #28406411

Order 14464.

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

normal subgroups only

This group has 584 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×#16813683C212yesmaximal, complemented
2C2×#16813682C212yesmaximal, complemented
3#20299568C212yesmaximal, complemented
4C22×#14268646C211yesmaximal, characteristic
5C2×#14268656C2214yes—
6#16813683—24no—
7#16813682—24no—
8C22⋊#11744753—24no—
9C2×#14268646—24no—
10C2×#14268646—24no—
11C2×#14268646—24no—
12C22×Dic226C2211yescharacteristic
13C22×C22⋊D113C411yescharacteristic
14C22×C22⋊D113C2211yescharacteristic
15C23×Dic113C411yescharacteristic
16C23×Dic113C2211yescharacteristic
17C22×C4×D113C411yescharacteristic
18C22×D4×C113C411yescharacteristic
19#14268656—24no—
20#14268656—24no—
21C2×#11744753—24no—
22C23×D113C2×C411yescharacteristic
23#14268646—232no—
24C2×Dic226—22no—
25C2×Dic226—22no—
26C2×Dic226D414yes—
27C2×C22⋊D113—22no—
28C2×C22⋊D113—22no—
29C2×C22⋊D113—22no—
30C2×C22⋊D113—22no—
31C2×C22⋊D113—22no—
32C2×C22⋊D113D414yes—
33C22×Dic113—22no—
34C22×Dic113—22no—
35C22×Dic113—22no—
36C22×Dic113—22no—
37C22×Dic113—22no—
38C22×Dic113C2×C411yescharacteristic
39C22×Dic113C2×C411yescharacteristic
40C22×Dic113D414yes—
41C22×Dic113C2311yescharacteristic
42C2×C4×D113—22no—
43C2×C4×D113—22no—
44C2×C4×D113—22no—
45C24×C113C2×C411yescharacteristic
46C24×C113C2×C411yescharacteristic
47C2×D4×C113—22no—
48C2×D4×C113—22no—
49C2×D4×C113—22no—
50C22×C4×C113C2×C411yescharacteristic
51C23×C113—21no—
52C23×C113—21no—
53C23×C113—21no—
54C23×C113—21no—
55C23×C113—42no—
56C23×C113—42no—
57C23×C113C22⋊C412yes—
58C23×C113C22⋊C412yes—
59C23×C113C22×C411yescharacteristic
60C22×D113—21no—
61C22×D113—21no—
62C22×D113—42no—
63C22×D113C22⋊C412yes—
64D4×C113—28no—
65C2×C4×C113—21no—
66C2×C4×C113—21no—
67C2×C4×C113C22⋊C412yes—
68C22⋊D113—28no—
69C22⋊D113—28no—
70C2×Dic113—28no—
71C2×Dic113—21no—
72C2×Dic113—21no—
73C2×Dic113—21no—
74C2×Dic113—21no—
75C2×Dic113—28no—
76C2×Dic113C22⋊C412yes—
77C2×Dic113C22⋊C412yes—
78C2×Dic113C2×D412yes—
79C2×Dic113C2×D412yes—
80C2×Dic113C2×D412yes—
81C4×D113—28no—
82Dic226—28no—
83#11744753—44no—
84C22×C113—22no—
85C22×C113—22no—
86C22×C113—22no—
87C22×C113—24no—
88C22×C113—42no—
89C22×C113—42no—
90C22×C113—42no—
91C22×C113—42no—
92C22×C113—42no—
93C22×C113C2×C22⋊C411yescharacteristic
94C22×C113C2×C22⋊C411yescharacteristic
95C22×C113C2×C22⋊C411yescharacteristic
96C2×D113—22no—
97C2×D113—42no—
98C2×D113—42no—
99C2×D113—42no—
100C4×C113—22no—
101Dic113—22no—
102Dic113—22no—
103Dic113#12014yes—
104C2×C113—21no—
105C2×C113—21no—
106C2×C113—42no—
107C2×C113—42no—
108C2×C113#37911yescharacteristic
109C2×C113#41312yes—
110D113—42no—
111#1785—1131nomaximal, Sylow
112C113#178511yescharacteristic, complemented, Sylow
113C22×#41—1131no—
114C2×#101—1132no—
115C2×#100—1132no—
116#407—1132no—
117C2×#41—2264no—
118C2×#41—2264no—
119C2×#41—2264no—
120C22×Q8—1131no—
121C22×D4—1131no—
122C22×D4—1131no—
123C22×D4#9067311yescharacteristic
124C23×C4—1131no—
125C23×C4—1131no—
126C23×C4—1131no—
127C2×M16—1134no—
128#101—2264no—
129#100—2264no—
130C22⋊C8—2264no—
131C24—1131no—
132C24C2×#9067311yescharacteristic
133C24C2×#9067311yescharacteristic
134#41—22632no—
135C2×Q8—1134no—
136C2×Q8—2262no—
137C2×Q8—2262no—
138C2×D4—22no—
139C2×D4—22no—
140C2×D4—22no—
141C2×D4—1134no—
142C2×D4—2262no—
143C2×D4—2262no—
144C2×D4—2262no—
145C2×D4—2262no—
146C2×D4—2262no—
147C22×C4—1131no—
148C22×C4—1134no—
149C22×C4—1131no—
150C22×C4—1131no—
151C22×C4—2262no—
152C22×C4—2262no—
153C22×C4—2262no—
154C22×C4—2262no—
155C22×C4—2262no—
156C22×C4—2262no—
157C22×C4—2262no—
158C22×C4—2262no—
159C22×C4C2×#9067311yescharacteristic
160M16—2264no—
161M16—2264no—
162C2×C8—2264no—
163C23—21no—
164C23—21no—
165C23—21no—
166C23—21no—
167C23—42no—
168C23—42no—
169C23—1132no—
170C23—4522no—
171C23—2261no—
172C23—2261no—
173C23C22⋊#9067312yes—
174C23C22⋊#9067312yes—
175C23C22×#9067311yescharacteristic
176Q8—2268no—
177D4—28no—
178D4—2268no—
179D4—2268no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—1132no—
183C2×C4—1132no—
184C2×C4—1132no—
185C2×C4—1132no—
186C2×C4—1132no—
187C2×C4—2268no—
188C2×C4—2268no—
189C2×C4—2268no—
190C2×C4—2261no—
191C2×C4—2261no—
192C2×C4—2261no—
193C2×C4—2261no—
194C2×C4C22⋊#9067312yes—
195C8—4524no—
196C22—22no—
197C22—22no—
198C22—22no—
199C22—24no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—4522no—
206C22—4522no—
207C22—4522no—
208C22—2262no—
209C22C2×C22⋊#9067311yescharacteristic
210C22C2×C22⋊#9067311yescharacteristic
211C22C2×C22⋊#9067311yescharacteristic
212C4—22no—
213C4—1134no—
214C4—2262no—
215C4—2262no—
216C2—21no—
217C2—21no—
218C2—42no—
219C2—42no—
220C2—4522no—
221C2#2029953911yescharacteristic
222C2#2029958512yes—
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC23×C113C22×C4
FrattiniC23C22×#90673
FittingC22×D4×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC22×#14268646C2
cosocleC22×Dic113C23
hypercenterC22×D4#90673
hypocenterC113#1785
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16813683C2semidirect
2. C2×#16813682C2semidirect
3. #20299568C2semidirect
112. C113#1785semidirect

Maximal subgroups

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

subgroupindex
C2×#168136832
C2×#168136822
#202995682
C22×#142686462
#1785113