Finite Group Databasebeta

← #28406011

Subgroups — #28406011

Order 14464.

340 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 70 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#20299566C211yesmaximal, characteristic, complemented
2#20299540C211yesmaximal, characteristic, complemented
3#20299450C214yesmaximal, complemented
4C2×#16813597C211yesmaximal, characteristic
5C2×#14268655—21no—
6C2×C4⋊#90673—21no—
7C2×C22⋊#90673—21no—
8#16813679C2212yescomplemented
9C22⋊#11744753—21no—
10(C2×#90673)⋊C4C2212yescomplemented
11C22×D452—21no—
12C22×D452C411yescharacteristic, complemented
13C22×C4×D113C2211yescharacteristic
14#16813597—21no—
15#16813597—21no—
16#16813597C412yescomplemented
17#16813597C2212yes—
18C2×#14268624—21no—
19C2×C4⋊C4×C113C411yescharacteristic, complemented
20C22×#90673—22no—
21#14268655—42no—
22C2×#11744753—22no—
23C4⋊#90673—42no—
24C22⋊#90673—42no—
25C23×D113—21no—
26C23×D113D411yescharacteristic
27C2×D452—22no—
28C2×D452—22no—
29C2×D452—21no—
30C2×D452—42no—
31C2×D452—42no—
32C2×D452—42no—
33C2×D452C2×C412yes—
34C22×Dic113D411yescharacteristic
35C2×C4×D113—42no—
36C2×C4×D113C2×C411yescharacteristic
37C2×C4×D113D411yescharacteristic
38C2×C4×D113D411yescharacteristic
39C2×C4×D113C2311yescharacteristic
40#14268624—22no—
41#14268624—22no—
42C22×C4×C113—21no—
43C22×C4×C113C2×C411yescharacteristic
44C4⋊C4×C113—21no—
45C4⋊C4×C113C2×C412yes—
46C23×C113C22⋊C411yescharacteristic
47C22×D113—22no—
48C22×D113—41no—
49C22×D113—41no—
50C22×D113—42no—
51C22×D113—42no—
52C22×D113—42no—
53C22×D113C22⋊C411yescharacteristic
54C22×D113D812yes—
55C22×D113SD1612yes—
56C22×D113C2×D411yescharacteristic
57C2×#90673—42no—
58C2×#90673—42no—
59C2×#90673—42no—
60C2×C4×C113—22no—
61C2×C4×C113—22no—
62C2×C4×C113—42no—
63C2×C4×C113C22⋊C411yescharacteristic
64C2×C4×C113C22×C411yescharacteristic
65C2×Dic113—41no—
66C2×Dic113C22⋊C411yescharacteristic
67C2×Dic113C2×D411yescharacteristic
68D452—42no—
69D452—44no—
70D452—42no—
71D452—42no—
72D452—42no—
73C4×D113—22no—
74C4×D113—22no—
75C4×D113—41no—
76C4×D113—41no—
77#11744753—42no—
78C22×C113—21no—
79C22×C113—21no—
80C22×C113#10212yes—
81C22×C113C2×C22⋊C411yescharacteristic
82C2×D113—21no—
83C2×D113—21no—
84C2×D113—21no—
85C2×D113—21no—
86C2×D113—42no—
87C2×D113—42no—
88C2×D113—42no—
89C2×D113—42no—
90C2×D113—42no—
91C2×D113—84no—
92C2×D113#10212yes—
93C2×D113C2×D811yescharacteristic
94C2×D113C2×SD1611yescharacteristic
95#90673—82no—
96C4×C113—21no—
97C4×C113—42no—
98C4×C113#9912yes—
99Dic113—21no—
100Dic113—21no—
101C2×C113—22no—
102C2×C113C2×#9911yescharacteristic
103C2×C113C2×#10211yescharacteristic
104C2×C113#42111yescharacteristic
105D113—21no—
106D113—22no—
107D113—21no—
108D113—82no—
109#1519—1131nomaximal, Sylow
110C113#151911yescharacteristic, complemented, Sylow
111C2×#121—1131no—
112C2×C22⋊C8—1131no—
113#380—1131no—
114#327—1134no—
115C22×D4—1131no—
116C22×D4—2261no—
117C23×C4—1131no—
118C22×C8—2261no—
119#121—1132no—
120#121—1132no—
121#121—2261no—
122#121—2261no—
123C2×C4⋊C4—2261no—
124C2×C4⋊C4#9067311yescharacteristic, complemented
125C2×C22⋊C4—2261no—
126C2×C22⋊C4—2261no—
127C22⋊C8—1132no—
128C22⋊C8—2261no—
129#95—1132no—
130C24—1131no—
131C24—2261no—
132C2×D4—1132no—
133C2×D4—4522no—
134C2×D4—4522no—
135C2×D4—4522no—
136C2×D4—2262no—
137C2×D4—2262no—
138C2×D4—2261no—
139C22×C4—21no—
140C22×C4—1131no—
141C22×C4—1131no—
142C22×C4—1131no—
143C22×C4—1131no—
144C22×C4—1131no—
145C22×C4—4522no—
146C22×C4—2262no—
147C22×C4C2×#9067311yescharacteristic
148C2×C8—4522no—
149C2×C8—2262no—
150C4⋊C4—21no—
151C4⋊C4—4522no—
152C4⋊C4C2×#9067312yes—
153C22⋊C4—4522no—
154C22⋊C4—2262no—
155C22⋊C4—2262no—
156C23—1132no—
157C23—1132no—
158C23—1131no—
159C23—1131no—
160C23—4522no—
161C23—4522no—
162C23—4521no—
163C23—4521no—
164C23—4522no—
165C23—2262no—
166C23C22⋊#9067311yescharacteristic
167D4—4522no—
168D4—4522no—
169D4—4524no—
170D4—4522no—
171D4—4522no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—1131no—
176C2×C4—1131no—
177C2×C4—4521no—
178C2×C4—4521no—
179C2×C4—4522no—
180C2×C4—4522no—
181C2×C4—4522no—
182C2×C4—4521no—
183C2×C4—2262no—
184C2×C4—2262no—
185C2×C4C22⋊#9067311yescharacteristic
186C2×C4C22×#9067311yescharacteristic
187C8—4522no—
188C22—21no—
189C22—21no—
190C22—1131no—
191C22—1132no—
192C22—1131no—
193C22—9044no—
194C22—4522no—
195C22—4522no—
196C22—4522no—
197C22—4522no—
198C22—4522no—
199C22—2261no—
200C22—2261no—
201C22—2261no—
202C22—2261no—
203C22#1681368412yes—
204C22C2×C22⋊#9067311yescharacteristic
205C4—21no—
206C4—42no—
207C4—9042no—
208C4—2261no—
209C4—2261no—
210C4#1681368112yes—
211C2—22no—
212C2—9042no—
213C2—2261no—
214C2—2262no—
215C2—2261no—
216C2C2×#1681368111yescharacteristic
217C2C2×#1681368411yescharacteristic
218C2#2029959711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC2×C4⋊C4×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC2×#16813597C2
cosocleC2×C4×D113C23
hypercenterC2×C4⋊C4#90673
hypocenterC113#1519
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #20299566C2semidirect
2. #20299540C2semidirect
3. #20299450C2semidirect
8. #16813679C22semidirect
10. (C2×#90673)⋊C4C22semidirect
12. C22×D452C4semidirect
16. #16813597C4semidirect
19. C2×C4⋊C4×C113C4semidirect
110. C113#1519semidirect
124. C2×C4⋊C4#90673semidirect

Maximal subgroups

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

subgroupindex
#202995662
#202995402
#202994502
C2×#168135972
#1519113