Finite Group Databasebeta

← #28389089

Subgroups — #28389089

Order 14464.

346 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 77 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×#16813596C211yesmaximal, characteristic
2#20298562C211yesmaximal, characteristic, complemented
3#20298331C214yesmaximal, complemented
4C4×C22⋊C4×C113C211yesmaximal, characteristic, complemented
5C22×D452C411yescharacteristic, complemented
6C22×C22⋊D113—21no—
7C2×#14268631—21no—
8#16813596—21no—
9#16813596—21no—
10#16813596C412yescomplemented
11#16813596C2212yes—
12C2×C4⋊Dic113C411yescharacteristic, complemented
13C2×#14268624—21no—
14C22⋊#11744751—21no—
15C22⋊#11744751C2212yescomplemented
16C23×C4×C113C2211yescharacteristic
17C2×C22⋊C4×C113—21no—
18C2×C42×C113—21no—
19#95×C113C2212yescomplemented
20C23×D113—21no—
21C2×D452—21no—
22C2×D452—42no—
23C2×D452C2×C412yes—
24C2×C22⋊D113—22no—
25C2×C22⋊D113—22no—
26C2×C22⋊D113—44no—
27C22×Dic113—21no—
28#14268631—42no—
29C2×#11744751—22no—
30C4⋊Dic113—21no—
31C4⋊Dic113C2×C412yes—
32#14268624—22no—
33#14268624—22no—
34C24×C113D411yescharacteristic
35C22×C4×C113—22no—
36C22×C4×C113—42no—
37C22×C4×C113C2×C411yescharacteristic
38C22×C4×C113C2×C411yescharacteristic
39C22×C4×C113D411yescharacteristic
40C22×C4×C113D411yescharacteristic
41C22×C4×C113D411yescharacteristic
42C22×C4×C113C2311yescharacteristic
43C22⋊C4×C113—24no—
44C42×C113—42no—
45C23×C113—22no—
46C23×C113—22no—
47C23×C113—41no—
48C23×C113C22⋊C411yescharacteristic
49C23×C113C22⋊C411yescharacteristic
50C23×C113C2×D411yescharacteristic
51C22×D113—22no—
52C22×D113—42no—
53C22×D113—42no—
54C22×D113—42no—
55C2×C4×C113—22no—
56C2×C4×C113—22no—
57C2×C4×C113—22no—
58C2×C4×C113—24no—
59C2×C4×C113—41no—
60C2×C4×C113—41no—
61C2×C4×C113—41no—
62C2×C4×C113—42no—
63C2×C4×C113—42no—
64C2×C4×C113C22⋊C411yescharacteristic
65C2×C4×C113C22⋊C411yescharacteristic
66C2×C4×C113C22×C411yescharacteristic
67C2×C4×C113C2×D411yescharacteristic
68C22⋊D113—44no—
69C22⋊D113—44no—
70C2×Dic113—22no—
71C2×Dic113—42no—
72D452—42no—
73D452—42no—
74#11744751—42no—
75C22×C113—21no—
76C22×C113—21no—
77C22×C113—21no—
78C22×C113—21no—
79C22×C113—21no—
80C22×C113—21no—
81C22×C113—21no—
82C22×C113—44no—
83C22×C113#10412yes—
84C22×C113C2×C22⋊C411yescharacteristic
85C22×C113AGL(1,ℤ/8)12yes—
86C2×D113—42no—
87C2×D113—42no—
88C2×D113—42no—
89C2×D113—84no—
90C4×C113—21no—
91C4×C113—21no—
92C4×C113—21no—
93C4×C113—44no—
94C4×C113#9912yes—
95Dic113—42no—
96C2×C113—22no—
97C2×C113—22no—
98C2×C113—41no—
99C2×C113C2×#9911yescharacteristic
100C2×C113#41811yescharacteristic
101C2×C113C2×#10411yescharacteristic
102D113—82no—
103#1507—1131nomaximal, Sylow
104C113#150711yescharacteristic, complemented, Sylow
105C2×#121—1131no—
106#407—1131no—
107C4×C22⋊C4D11311yescharacteristic, complemented
108#327—1134no—
109C22×D4—1131no—
110C22×D4—2261no—
111C23×C4C2×D11311yescharacteristic
112C2×M16—2261no—
113#121—1132no—
114#121—1132no—
115#121—2261no—
116#121—2261no—
117C2×C4⋊C4—1131no—
118C2×C22⋊C4—21no—
119C2×C22⋊C4—2261no—
120C2×C42—21no—
121C22⋊C8—1132no—
122C22⋊C8—2261no—
123#95C2×D11312yescomplemented
124C24—2261no—
125C24C22⋊D11311yescharacteristic
126C2×D4—1132no—
127C2×D4—4522no—
128C2×D4—4524no—
129C2×D4—2262no—
130C2×D4—2262no—
131C2×D4—2261no—
132C22×C4—22no—
133C22×C4—42no—
134C22×C4—2261no—
135C22×C4C4×D11311yescharacteristic
136C22×C4C4×D11311yescharacteristic
137C22×C4D45211yescharacteristic
138C22×C4D45211yescharacteristic
139C22×C4C22⋊D11311yescharacteristic
140C22×C4C22×D11311yescharacteristic
141M16—4522no—
142C2×C8—2262no—
143C4⋊C4—1132no—
144C4⋊C4—2261no—
145C22⋊C4—24no—
146C22⋊C4—2262no—
147C22⋊C4—2262no—
148C42—42no—
149C23—22no—
150C23—22no—
151C23—41no—
152C23—4522no—
153C23—4522no—
154C23—4522no—
155C23—2262no—
156C23#1426862411yescharacteristic
157C23#1426862411yescharacteristic
158C23C2×C22⋊D11311yescharacteristic
159D4—4522no—
160D4—4524no—
161D4—4524no—
162D4—4522no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—24no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—4522no—
173C2×C4—2262no—
174C2×C4#1426862411yescharacteristic
175C2×C4#1426862411yescharacteristic
176C2×C4C2×C4×D11311yescharacteristic
177C2×C4C2×D45211yescharacteristic
178C8—4522no—
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—44no—
187C22—9044no—
188C22—4522no—
189C22—4522no—
190C22—4522no—
191C22#1681355012yes—
192C22C2×#1426862411yescharacteristic
193C22#1681364712yes—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—44no—
198C4—4522no—
199C4#1681353612yes—
200C2—22no—
201C2—22no—
202C2—41no—
203C2—9042no—
204C2C2×#1681353611yescharacteristic
205C2#2029860211yescharacteristic
206C2C2×#1681355011yescharacteristic
subgroupG/H
centerC22C2×#14268624
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC4×C22⋊C4×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC2×#16813596C2
cosocleC22×C4×C113C23
hypercenterC4×C22⋊C4D113
hypocenterC113#1507
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #20298562C2semidirect
3. #20298331C2semidirect
4. C4×C22⋊C4×C113C2semidirect
5. C22×D452C4semidirect
10. #16813596C4semidirect
12. C2×C4⋊Dic113C4semidirect
15. C22⋊#11744751C22semidirect
19. #95×C113C22semidirect
104. C113#1507semidirect
107. C4×C22⋊C4D113semidirect
123. #95C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168135962
#202985622
#202983312
C4×C22⋊C4×C1132
#1507113