Finite Group Databasebeta

← #28406477

Subgroups — #28406477

Order 14464.

344 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 84 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
2#20299540C211yesmaximal, characteristic
3#20299471C214yesmaximal, complemented
4C2×C4⋊C4×D113C211yesmaximal, characteristic
5C2×#14268655C2212yes—
6C2×C4⋊#90673C2212yes—
7C2×C22⋊#90673—21no—
8#16813679—21no—
9C22⋊#11744753—21no—
10(C2×#90673)⋊C4—21no—
11C22×C4×D113—21no—
12C22×C4×D113C2211yescharacteristic
13C2×C4⋊Dic113C411yescharacteristic, complemented
14C2×#14268626—21no—
15C4⋊C4×D113—21no—
16C4⋊C4×D113—21no—
17C4⋊C4×D113C412yescomplemented
18C4⋊C4×D113C2212yes—
19C2×C4⋊C4×C113C411yescharacteristic, complemented
20C22×#90673—22no—
21#14268655—24no—
22C2×#11744753—22no—
23C4⋊#90673—24no—
24C22⋊#90673—42no—
25C23×D113D411yescharacteristic
26C22×Dic113—21no—
27C22×Dic113D411yescharacteristic
28C2×C4×D113—24no—
29C2×C4×D113—22no—
30C2×C4×D113—22no—
31C2×C4×D113—42no—
32C2×C4×D113—42no—
33C2×C4×D113C2×C411yescharacteristic
34C2×C4×D113D411yescharacteristic
35C2×C4×D113D411yescharacteristic
36C2×C4×D113C2311yescharacteristic
37C4⋊Dic113—21no—
38C4⋊Dic113C2×C412yes—
39#14268626—22no—
40#14268626—22no—
41C22×C4×C113—21no—
42C22×C4×C113C2×C411yescharacteristic
43C4⋊C4×C113—21no—
44C4⋊C4×C113C2×C412yes—
45C23×C113C22⋊C411yescharacteristic
46C22×D113—22no—
47C22×D113—22no—
48C22×D113C22⋊C411yescharacteristic
49C22×D113D812yes—
50C22×D113SD1612yes—
51C22×D113C2×D411yescharacteristic
52C2×#90673—42no—
53C2×#90673—42no—
54C2×#90673—42no—
55C2×C4×C113—22no—
56C2×C4×C113—22no—
57C2×C4×C113—42no—
58C2×C4×C113C22⋊C411yescharacteristic
59C2×C4×C113C22×C411yescharacteristic
60C2×Dic113—22no—
61C2×Dic113—22no—
62C2×Dic113—42no—
63C2×Dic113C22⋊C411yescharacteristic
64C2×Dic113C2×D411yescharacteristic
65C4×D113—22no—
66C4×D113—22no—
67C4×D113—22no—
68C4×D113—44no—
69C4×D113—42no—
70C4×D113—42no—
71C4×D113#4114yes—
72#11744753—42no—
73C22×C113—21no—
74C22×C113—21no—
75C22×C113#10212yes—
76C22×C113C2×C22⋊C411yescharacteristic
77C2×D113—21no—
78C2×D113—21no—
79C2×D113—24no—
80C2×D113—24no—
81C2×D113#10212yes—
82C2×D113#12312yes—
83C2×D113C2×D811yescharacteristic
84C2×D113C2×SD1611yescharacteristic
85C2×D113#13712yes—
86#90673—82no—
87C4×C113—21no—
88C4×C113—42no—
89C4×C113#11712yes—
90Dic113—21no—
91Dic113—42no—
92Dic113#12312yes—
93C2×C113—22no—
94C2×C113#38111yescharacteristic
95C2×C113C2×#10211yescharacteristic
96C2×C113#41911yescharacteristic
97D113—22no—
98D113#48012yes—
99D113#48312yes—
100#1823—1131nomaximal, Sylow
101C113#182311yescharacteristic, complemented, Sylow
102C22×C4⋊C4—1131no—
103C2×C22⋊C8—1131no—
104#380—1131no—
105#340—1134no—
106C23×C4—1131no—
107C23×C4—2261no—
108C22×C8—1132no—
109C2×C4⋊C4—1131no—
110C2×C4⋊C4—1132no—
111C2×C4⋊C4—1132no—
112C2×C4⋊C4—1132no—
113C2×C4⋊C4—2261no—
114C2×C4⋊C4—2261no—
115C2×C4⋊C4—2261no—
116C2×C4⋊C4#9067311yescharacteristic, complemented
117C2×C22⋊C4—2261no—
118C22⋊C8—2261no—
119C22⋊C8—2261no—
120#95—2261no—
121C24—1131no—
122C22×C4—21no—
123C22×C4—1131no—
124C22×C4—1131no—
125C22×C4—1131no—
126C22×C4—1131no—
127C22×C4—1131no—
128C22×C4—4522no—
129C22×C4—4522no—
130C22×C4—2264no—
131C22×C4—2262no—
132C22×C4—2262no—
133C22×C4—2262no—
134C22×C4—2261no—
135C22×C4C2×#9067311yescharacteristic
136C2×C8—2262no—
137C2×C8—2264no—
138C4⋊C4—21no—
139C4⋊C4—1132no—
140C4⋊C4—2262no—
141C4⋊C4—2262no—
142C4⋊C4—2264no—
143C4⋊C4—2261no—
144C4⋊C4C2×#9067312yes—
145C22⋊C4—4522no—
146C23—1131no—
147C23—1132no—
148C23—1132no—
149C23—1131no—
150C23—2262no—
151C23—2262no—
152C23C22⋊#9067311yescharacteristic
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—42no—
156C2×C4—1131no—
157C2×C4—1134no—
158C2×C4—1131no—
159C2×C4—4522no—
160C2×C4—4522no—
161C2×C4—4524no—
162C2×C4—4522no—
163C2×C4—4522no—
164C2×C4—4522no—
165C2×C4—4522no—
166C2×C4—2262no—
167C2×C4—2262no—
168C2×C4—2262no—
169C2×C4—2262no—
170C2×C4—2262no—
171C2×C4C22⋊#9067311yescharacteristic
172C2×C4C22×#9067311yescharacteristic
173C8—4522no—
174C22—21no—
175C22—21no—
176C22—1132no—
177C22—1131no—
178C22—1131no—
179C22—1132no—
180C22—1132no—
181C22—2264no—
182C22—2264no—
183C22—2261no—
184C22—2261no—
185C22#1681368412yes—
186C22C2×C22⋊#9067311yescharacteristic
187C4—21no—
188C4—42no—
189C4—1132no—
190C4—9042no—
191C4—4522no—
192C4—2261no—
193C4#1681370112yes—
194C2—22no—
195C2—1132no—
196C2—1132no—
197C2—2262no—
198C2#2029954111yescharacteristic
199C2C2×#1681368411yescharacteristic
200C2#2029959111yescharacteristic
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#1823
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. #20299471C2semidirect
13. C2×C4⋊Dic113C4semidirect
17. C4⋊C4×D113C4semidirect
19. C2×C4⋊C4×C113C4semidirect
101. C113#1823semidirect
116. 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
#202994712
C2×C4⋊C4×D1132
#1823113