Finite Group Databasebeta

← #28406482

Subgroups — #28406482

Order 14464.

306 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 68 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#20299569C211yesmaximal, characteristic
2C4×C22⋊#90673C211yesmaximal, characteristic
3#20299468C212yesmaximal, complemented
4#20299468C212yesmaximal, complemented
5#117×D113C211yesmaximal, characteristic
6C2×#14268657C2212yes—
7C2×C22⋊#90673—21no—
8C2×C4×#90673C2212yes—
9#16813679—21no—
10C22⋊#11744753—21no—
11(C2×#90673)⋊C4—21no—
12C22×C4×D113C2211yescharacteristic
13#16813581C411yescharacteristic, complemented
14#16813580C2211yescharacteristic
15#16813580C2211yescharacteristic
16#16813579—21no—
17#16813578—21no—
18C4⋊C4×D113C411yescharacteristic, complemented
19C4⋊C4×D113C411yescharacteristic, complemented
20C22⋊C4×D113—21no—
21C42×D113—21no—
22#117×C113C411yescharacteristic, complemented
23C22×#90673—22no—
24#14268657—24no—
25C2×#11744753—22no—
26C22⋊#90673—24no—
27C4×#90673—24no—
28C23×D113D411yescharacteristic
29C22×Dic113D411yescharacteristic
30C2×C4×D113—24no—
31C2×C4×D113—21no—
32C2×C4×D113—21no—
33C2×C4×D113C2×C411yescharacteristic
34C2×C4×D113D411yescharacteristic
35C2×C4×D113D411yescharacteristic
36C2×C4×D113C2311yescharacteristic
37C4⋊Dic113C2×C411yescharacteristic
38C4⋊Dic113C2×C411yescharacteristic
39#14268626—21no—
40#14268626—21no—
41C22⋊Dic113—21no—
42#14268624—21no—
43#14268624—21no—
44C4×Dic113—21no—
45C4×Dic113—21no—
46C4×Dic113—21no—
47C22×C4×C113C2×C411yescharacteristic
48C4⋊C4×C113C2×C411yescharacteristic
49C4⋊C4×C113C2×C411yescharacteristic
50C22⋊C4×C113—21no—
51C42×C113—21no—
52C23×C113C22⋊C411yescharacteristic
53C22×D113—22no—
54C22×D113—22no—
55C22×D113—41no—
56C22×D113C22⋊C411yescharacteristic
57C22×D113C2×D411yescharacteristic
58C2×#90673—24no—
59C2×#90673—42no—
60C2×#90673—42no—
61C2×C4×C113—22no—
62C2×C4×C113—21no—
63C2×C4×C113—21no—
64C2×C4×C113C22⋊C411yescharacteristic
65C2×C4×C113C22×C411yescharacteristic
66C2×Dic113—22no—
67C2×Dic113—21no—
68C2×Dic113—21no—
69C2×Dic113C22⋊C411yescharacteristic
70C2×Dic113C2×D411yescharacteristic
71C4×D113—22no—
72C4×D113—22no—
73C4×D113—22no—
74C4×D113—42no—
75C4×D113—42no—
76C4×D113#4114yes—
77#11744753—42no—
78C22×C113—21no—
79C22×C113—21no—
80C22×C113—21no—
81C22×C113C2×C22⋊C411yescharacteristic
82C2×D113—21no—
83C2×D113—21no—
84C2×D113—21no—
85C2×D113—21no—
86C2×D113—44no—
87C2×D113#10412yes—
88C2×D113#12312yes—
89#90673—44no—
90C4×C113—21no—
91C4×C113—41no—
92C4×C113—41no—
93C4×C113#11712yes—
94Dic113—21no—
95Dic113—41no—
96Dic113—41no—
97Dic113#12312yes—
98C2×C113—41no—
99C2×C113#38111yescharacteristic
100C2×C113C2×#10411yescharacteristic
101C2×C113#42111yescharacteristic
102D113—22no—
103D113—22no—
104#1826—1131nomaximal, Sylow
105C113#182611yescharacteristic, complemented, Sylow
106C2×#117—1131no—
107#407—1131no—
108C4×C22⋊C4—1131no—
109#339—1132no—
110#339—1132no—
111C23×C4—1131no—
112C2×M16—1132no—
113#117—1131no—
114#117—1131no—
115#117—1131no—
116#117—2261no—
117#117—2261no—
118#117#9067311yescharacteristic, complemented
119C2×C4⋊C4—1131no—
120C2×C4⋊C4—1131no—
121C2×C22⋊C4—2261no—
122C2×C22⋊C4—2261no—
123C2×C42—1132no—
124C2×C42—2261no—
125C22⋊C8—2261no—
126C22⋊C8—2261no—
127#95—2261no—
128C24—1131no—
129C22×C4—1131no—
130C22×C4—1131no—
131C22×C4—1131no—
132C22×C4—1131no—
133C22×C4—1131no—
134C22×C4—2264no—
135C22×C4—2261no—
136C22×C4—2261no—
137C22×C4—2262no—
138C22×C4C2×#9067311yescharacteristic
139M16—2264no—
140C2×C8—2262no—
141C4⋊C4—1131no—
142C4⋊C4—1131no—
143C4⋊C4—2261no—
144C4⋊C4—2261no—
145C4⋊C4C2×#9067311yescharacteristic
146C4⋊C4C2×#9067311yescharacteristic
147C22⋊C4—21no—
148C22⋊C4—2261no—
149C22⋊C4—2261no—
150C22⋊C4—2264no—
151C22⋊C4—2261no—
152C42—21no—
153C42—2261no—
154C42—2261no—
155C42—2264no—
156C42—2261no—
157C23—1131no—
158C23—1131no—
159C23—4521no—
160C23—2262no—
161C23—2262no—
162C23C22⋊#9067311yescharacteristic
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—1131no—
167C2×C4—1134no—
168C2×C4—1131no—
169C2×C4—4522no—
170C2×C4—4522no—
171C2×C4—4522no—
172C2×C4—4522no—
173C2×C4—2262no—
174C2×C4—2262no—
175C2×C4—2262no—
176C2×C4—2264no—
177C2×C4—2261no—
178C2×C4—2261no—
179C2×C4—2262no—
180C2×C4C22⋊#9067311yescharacteristic
181C2×C4C22×#9067311yescharacteristic
182C8—4522no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—1132no—
187C22—1132no—
188C22—4524no—
189C22—2261no—
190C22—2261no—
191C22—2261no—
192C22—2261no—
193C22C2×C22⋊#9067311yescharacteristic
194C4—21no—
195C4—41no—
196C4—41no—
197C4—1132no—
198C4—4524no—
199C4—4521no—
200C4—4521no—
201C4—2261no—
202C4#1681370112yes—
203C2—41no—
204C2—2262no—
205C2—2262no—
206C2#2029954111yescharacteristic
207C2D113⋊#10411yescharacteristic
208C2#2029959511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#117×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC23×D113D4
cosocleC2×C4×D113C23
hypercenter#117#90673
hypocenterC113#1826
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #20299468C2semidirect
4. #20299468C2semidirect
13. #16813581C4semidirect
18. C4⋊C4×D113C4semidirect
19. C4⋊C4×D113C4semidirect
22. #117×C113C4semidirect
105. C113#1826semidirect
118. #117#90673semidirect

Maximal subgroups

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

subgroupindex
#202995692
C4×C22⋊#906732
#202994682
#117×D1132
#1826113