Finite Group Databasebeta

← #28406763

Subgroups — #28406763

Order 14464.

324 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 74 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#20299540C211yesmaximal, characteristic
2C4×C22⋊#90673C211yesmaximal, characteristic
3#20299476C214yesmaximal
4C2×#16813598C211yesmaximal, characteristic
5C2×C4⋊#90673—21no—
6C2×C22⋊#90673C2212yes—
7C2×C22⋊#90673C2212yes—
8C2×C4×#90673—21no—
9(C2×#90673)⋊C4—21no—
10(C2×#90673)⋊C4—21no—
11C22×C4×D113C2211yescharacteristic
12#16813598—21no—
13#16813598—21no—
14#16813598—21no—
15#16813598—21no—
16C2×C4⋊Dic113C411yescharacteristic, complemented
17C2×#14268626C412yescomplemented
18C2×#14268624C2212yes—
19C22×Q8×C113C411yescharacteristic, complemented
20C22×#90673—22no—
21C22×#90673—22no—
22C4⋊#90673—42no—
23C22⋊#90673—22no—
24C22⋊#90673—24no—
25C22⋊#90673Q814yescomplemented
26C4×#90673—42no—
27C23×D113C2311yescharacteristic
28C22×Dic113C2×C412yes—
29C22×Dic113C2×C411yescharacteristic
30C2×C4×D113—42no—
31C2×C4×D113D411yescharacteristic
32C2×C4×D113D411yescharacteristic
33C2×C4×D113D411yescharacteristic
34C2×C4×D113D411yescharacteristic
35C4⋊Dic113—21no—
36C4⋊Dic113—21no—
37#14268626—22no—
38#14268626—22no—
39#14268624—22no—
40#14268624—22no—
41C2×Q8×C113—21no—
42C2×Q8×C113—21no—
43C2×Q8×C113—42no—
44C22×C4×C113C2×C412yes—
45C22×C4×C113C2×C411yescharacteristic
46C23×C113C22×C411yescharacteristic
47C22×D113—41no—
48C22×D113—41no—
49C22×D113C2×D411yescharacteristic
50C22×D113C2×D411yescharacteristic
51C22×D113C2×Q812yes—
52C22×D113#4112yes—
53C2×#90673—24no—
54C2×#90673—42no—
55C2×#90673—42no—
56C2×#90673—42no—
57C2×#90673—42no—
58C2×#90673—42no—
59Q8×C113—42no—
60Q8×C113—42no—
61C2×C4×C113—22no—
62C2×C4×C113—22no—
63C2×C4×C113—42no—
64C2×C4×C113C22⋊C411yescharacteristic
65C2×C4×C113C22⋊C411yescharacteristic
66C2×Dic113—22no—
67C2×Dic113—41no—
68C2×Dic113—42no—
69C2×Dic113C22⋊C411yescharacteristic
70C2×Dic113C22⋊C411yescharacteristic
71C4×D113—22no—
72C4×D113—22no—
73C4×D113—41no—
74C4×D113—41no—
75C22×C113—21no—
76C22×C113—21no—
77C22×C113C2×C22⋊C411yescharacteristic
78C22×C113C4×Q812yes—
79C2×D113—21no—
80C2×D113—21no—
81C2×D113—21no—
82C2×D113—21no—
83C2×D113—42no—
84C2×D113—42no—
85C2×D113C22⋊Q812yes—
86C2×D113#12411yescharacteristic
87C2×D113C4⋊Q811yescharacteristic
88#90673—44no—
89#90673—82no—
90C4×C113—21no—
91C4×C113—42no—
92C4×C113#9912yes—
93Dic113—21no—
94Dic113—21no—
95Dic113—42no—
96C2×C113—22no—
97C2×C113#39111yescharacteristic
98C2×C113C2×#9911yescharacteristic
99C2×C113#41011yescharacteristic
100D113—22no—
101D113—21no—
102D113—21no—
103#1996—1131nomaximal, Sylow
104C113#199611yescharacteristic, complemented, Sylow
105C2×C22⋊Q8—1131no—
106#380—1131no—
107C4×C22⋊C4—1131no—
108#342—1134no—
109C22×Q8#9067311yescharacteristic, complemented
110C23×C4—1131no—
111C22⋊Q8—2261no—
112C22⋊Q8—2261no—
113C22⋊Q8—2261no—
114C22⋊Q8—2261no—
115C2×C4⋊C4—1132no—
116C2×C4⋊C4—1131no—
117C2×C4⋊C4—2261no—
118C2×C22⋊C4—1132no—
119C2×C22⋊C4—1132no—
120C2×C22⋊C4—1132no—
121C2×C42—2261no—
122#95—2261no—
123#95—2261no—
124C24—1131no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—42no—
128C22×C4—1131no—
129C22×C4—1131no—
130C22×C4—1131no—
131C22×C4—1131no—
132C22×C4—1131no—
133C22×C4—1132no—
134C22×C4—4522no—
135C22×C4—2262no—
136C22×C4—2262no—
137C22×C4C2×#9067312yes—
138C22×C4C2×#9067311yescharacteristic
139C4⋊C4—4522no—
140C4⋊C4—2262no—
141C4⋊C4—2262no—
142C4⋊C4—2261no—
143C4⋊C4—2261no—
144C22⋊C4—1134no—
145C22⋊C4—2262no—
146C22⋊C4—2262no—
147C22⋊C4—2264no—
148C22⋊C4—2262no—
149C42—4522no—
150C23—1132no—
151C23—1132no—
152C23—1131no—
153C23—1131no—
154C23—4521no—
155C23—4521no—
156C23C22×#9067311yescharacteristic
157Q8—42no—
158Q8—42no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—1131no—
163C2×C4—1131no—
164C2×C4—4521no—
165C2×C4—4521no—
166C2×C4—4522no—
167C2×C4—4522no—
168C2×C4—4522no—
169C2×C4—4522no—
170C2×C4—4522no—
171C2×C4—4522no—
172C2×C4—4521no—
173C2×C4—2264no—
174C2×C4—2262no—
175C2×C4—2262no—
176C2×C4—2262no—
177C2×C4C22⋊#9067311yescharacteristic
178C2×C4C22⋊#9067311yescharacteristic
179C22—21no—
180C22—21no—
181C22—1131no—
182C22—1132no—
183C22—1131no—
184C22—4522no—
185C22—4522no—
186C22—2261no—
187C22—2261no—
188C22—2261no—
189C22—2261no—
190C22C2×C22⋊#9067311yescharacteristic
191C22Q8×#9067312yes—
192C4—21no—
193C4—42no—
194C4—9042no—
195C4—4524no—
196C4—4522no—
197C4—2261no—
198C4—2261no—
199C4#1681368012yes—
200C2—22no—
201C2—2261no—
202C2—2262no—
203C2—2261no—
204C2(C2×#90673)⋊Q811yescharacteristic
205C2C2×#1681368011yescharacteristic
206C2#2029957911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC23×C113C22×C4
FrattiniC23C22×#90673
FittingC22×Q8×C113C4
socleC22×C113C2×C22⋊C4
prime radical, cosocleC23×D113C23
hypercenterC22×Q8#90673
hypocenterC113#1996
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
16. C2×C4⋊Dic113C4semidirect
17. C2×#14268626C4semidirect
19. C22×Q8×C113C4semidirect
25. C22⋊#90673Q8semidirect
104. C113#1996semidirect
109. C22×Q8#90673semidirect

Maximal subgroups

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

subgroupindex
#202995402
C4×C22⋊#906732
#202994762
C2×#168135982
#1996113