Finite Group Databasebeta

← #28406480

Subgroups — #28406480

Order 14464.

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

normal subgroups only

This group has 306 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#20299569C211yesmaximal, characteristic
2C4×C22⋊#90673C211yesmaximal, characteristic
3#20299468C214yesmaximal, complemented
4C2×#16813580C211yesmaximal, characteristic
5C2×#14268657C2212yes—
6C2×C22⋊#90673—21no—
7C2×C4×#90673C2212yes—
8#16813679—21no—
9C22⋊#11744753—21no—
10(C2×#90673)⋊C4—21no—
11C22×C4×D113C2211yescharacteristic
12#16813580—21no—
13#16813580—21no—
14#16813580C412yescomplemented
15#16813580C2212yes—
16C2×C4⋊Dic113C411yescharacteristic, complemented
17C2×#14268624—21no—
18C2×C4×Dic113—21no—
19C2×C4⋊C4×C113C411yescharacteristic, complemented
20C22×#90673—22no—
21#14268657—24no—
22C2×#11744753—22no—
23C22⋊#90673—24no—
24C4×#90673—24no—
25C23×D113D411yescharacteristic
26C22×Dic113—21no—
27C22×Dic113D411yescharacteristic
28C2×C4×D113—24no—
29C2×C4×D113C2×C411yescharacteristic
30C2×C4×D113D411yescharacteristic
31C2×C4×D113D411yescharacteristic
32C2×C4×D113C2311yescharacteristic
33C4⋊Dic113—21no—
34C4⋊Dic113C2×C412yes—
35#14268624—22no—
36#14268624—22no—
37C4×Dic113—22no—
38C4×Dic113—22no—
39C22×C4×C113—21no—
40C22×C4×C113C2×C411yescharacteristic
41C4⋊C4×C113—21no—
42C4⋊C4×C113C2×C412yes—
43C23×C113C22⋊C411yescharacteristic
44C22×D113—22no—
45C22×D113—22no—
46C22×D113—41no—
47C22×D113C22⋊C411yescharacteristic
48C22×D113C2×D411yescharacteristic
49C2×#90673—24no—
50C2×#90673—42no—
51C2×#90673—42no—
52C2×C4×C113—22no—
53C2×C4×C113—22no—
54C2×C4×C113—42no—
55C2×C4×C113C22⋊C411yescharacteristic
56C2×C4×C113C22×C411yescharacteristic
57C2×Dic113—22no—
58C2×Dic113—22no—
59C2×Dic113—42no—
60C2×Dic113C22⋊C411yescharacteristic
61C2×Dic113C2×D411yescharacteristic
62C4×D113—22no—
63C4×D113—22no—
64C4×D113—22no—
65C4×D113#4114yes—
66#11744753—42no—
67C22×C113—21no—
68C22×C113—21no—
69C22×C113#10412yes—
70C22×C113C2×C22⋊C411yescharacteristic
71C2×D113—21no—
72C2×D113—21no—
73C2×D113—21no—
74C2×D113—21no—
75C2×D113—21no—
76C2×D113—44no—
77C2×D113#12312yes—
78#90673—44no—
79C4×C113—21no—
80C4×C113—42no—
81C4×C113#11712yes—
82Dic113—21no—
83Dic113—42no—
84Dic113#12312yes—
85C2×C113—22no—
86C2×C113#38111yescharacteristic
87C2×C113C2×#10411yescharacteristic
88C2×C113#42111yescharacteristic
89D113—22no—
90D113—41no—
91#1826—1131nomaximal, Sylow
92C113#182611yescharacteristic, complemented, Sylow
93C2×#117—1131no—
94#407—1131no—
95C4×C22⋊C4—1131no—
96#339—1134no—
97C23×C4—1131no—
98C2×M16—1132no—
99#117—1132no—
100#117—1132no—
101#117—2261no—
102#117—2261no—
103C2×C4⋊C4—1131no—
104C2×C4⋊C4#9067311yescharacteristic, complemented
105C2×C22⋊C4—2261no—
106C2×C22⋊C4—2261no—
107C2×C42—1132no—
108C2×C42—2261no—
109C22⋊C8—2261no—
110C22⋊C8—2261no—
111#95—2261no—
112C24—1131no—
113C22×C4—21no—
114C22×C4—1131no—
115C22×C4—1131no—
116C22×C4—1131no—
117C22×C4—1131no—
118C22×C4—1131no—
119C22×C4—2264no—
120C22×C4—2262no—
121C22×C4—2261no—
122C22×C4C2×#9067311yescharacteristic
123M16—2264no—
124C2×C8—2262no—
125C4⋊C4—21no—
126C4⋊C4—1132no—
127C4⋊C4—2261no—
128C4⋊C4C2×#9067312yes—
129C22⋊C4—2262no—
130C22⋊C4—2262no—
131C22⋊C4—2264no—
132C42—2262no—
133C42—2262no—
134C42—2264no—
135C23—1131no—
136C23—1131no—
137C23—4521no—
138C23—2262no—
139C23—2262no—
140C23C22⋊#9067311yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—1131no—
145C2×C4—1134no—
146C2×C4—1131no—
147C2×C4—4522no—
148C2×C4—4522no—
149C2×C4—4522no—
150C2×C4—2262no—
151C2×C4—2262no—
152C2×C4—2262no—
153C2×C4—2264no—
154C2×C4—2262no—
155C2×C4—2262no—
156C2×C4C22⋊#9067311yescharacteristic
157C2×C4C22×#9067311yescharacteristic
158C8—4522no—
159C22—21no—
160C22—21no—
161C22—1132no—
162C22—4524no—
163C22—2261no—
164C22—2261no—
165C22—2261no—
166C22—2261no—
167C22—2261no—
168C22#1681368612yes—
169C22C2×C22⋊#9067311yescharacteristic
170C4—21no—
171C4—42no—
172C4—1132no—
173C4—4524no—
174C4—4522no—
175C4—2261no—
176C4#1681370112yes—
177C2—22no—
178C2—4521no—
179C2—2262no—
180C2#2029954111yescharacteristic
181C2C2×#1681368611yescharacteristic
182C2#2029959711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC2×C4⋊C4×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC23×D113D4
cosocleC2×C4×D113C23
hypercenterC2×C4⋊C4#90673
hypocenterC113#1826
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #20299468C2semidirect
14. #16813580C4semidirect
16. C2×C4⋊Dic113C4semidirect
19. C2×C4⋊C4×C113C4semidirect
92. C113#1826semidirect
104. C2×C4⋊C4#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
C2×#168135802
#1826113