Finite Group Databasebeta

← #28391638

Subgroups — #28391638

Order 14464.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#20299105C212yesmaximal, complemented
2#20298615C212yesmaximal, complemented
3#20298561C211yesmaximal, characteristic, complemented
4#20298355C211yesmaximal, characteristic, complemented
5#575×C113C211yesmaximal, characteristic, complemented
6C22×C4×D113C2211yescharacteristic
7C2×#14268631C2211yescharacteristic
8#16813603—22no—
9#16813598—22no—
10#16813593—22no—
11#16813590—22no—
12C4×C22⋊D113—24no—
13#16813581C2212yes—
14#16813549—24no—
15#16813534—22no—
16C2×#41×C113C2212yes—
17#137×C113—22no—
18AGL(1,ℤ/8)×C113—22no—
19#135×C113—22no—
20C2×M16×C113C2211yescharacteristic
21C23×D113D411yescharacteristic
22C2×C22⋊D113—24no—
23C22×Dic113D411yescharacteristic
24C2×C4×D113—22no—
25C2×C4×D113—22no—
26C2×C4×D113—21no—
27C2×C4×D113—21no—
28#14268631—22no—
29C2×#11744751—21no—
30C4⋊Dic113—22no—
31#14268626—24no—
32C22⋊Dic113—24no—
33C22⋊Dic113—22no—
34#14268624—24no—
35C4×Dic113D414yescomplemented
36#41×C113—22no—
37#41×C113—22no—
38#41×C113—22no—
39#41×C113—22no—
40C2×Q8×C113D412yescomplemented
41C2×D4×C113—22no—
42C2×D4×C113D412yescomplemented
43C22×C4×C113—22no—
44C22×C4×C113C2311yescharacteristic
45Q16×C113—22no—
46SD16×C113—24no—
47D8×C113—22no—
48M16×C113—22no—
49C2×C8×C113D412yescomplemented
50C23×C113—22no—
51C23×C113C2×D411yescharacteristic
52C22×D113—22no—
53C22×D113—21no—
54C22×D113—42no—
55Q8×C113—22no—
56Q8×C113—22no—
57D4×C113—22no—
58D4×C113—22no—
59D4×C113—42no—
60D4×C113—42no—
61C2×C4×C113—22no—
62C2×C4×C113—42no—
63C2×C4×C113—42no—
64C2×C4×C113C2×D412yes—
65C2×C4×C113C2×D412yes—
66C2×C4×C113C2×D411yescharacteristic
67C2×C4×C113#4111yescharacteristic
68C22⋊D113—48no—
69C2×Dic113—24no—
70C2×Dic113—22no—
71C2×Dic113—21no—
72C4×D113—41no—
73C4×D113—42no—
74C4×D113—41no—
75C8×C113—22no—
76#11744751—41no—
77C22×C113—41no—
78C22×C113—44no—
79C22×C113—42no—
80C22×C113#12012yes—
81C22×C113#12111yescharacteristic
82C2×D113—24no—
83C2×D113—22no—
84C2×D113—42no—
85C2×D113—41no—
86C2×D113—41no—
87C4×C113—42no—
88C4×C113#12011yescharacteristic
89C4×C113#12112yes—
90C4×C113#12711yescharacteristic
91Dic113—44no—
92Dic113—41no—
93C2×C113—22no—
94C2×C113—21no—
95C2×C113—82no—
96C2×C113#39211yescharacteristic
97D113—42no—
98#2010—1131nomaximal, Sylow
99C113#201011yescharacteristic, complemented, Sylow
100#575D11311yescharacteristic, complemented
101#525—1132no—
102#421—1132no—
103#407—1131no—
104H(3,ℤ/4)—1131no—
105C2×#41C2×D11312yes—
106C23×C4—1131no—
107#137—22no—
108AGL(1,ℤ/8)—22no—
109#135—22no—
110C2×M16—1131no—
111C2×M16C2×D11311yescharacteristic
112#123—2262no—
113C22⋊Q8—2262no—
114#121—2262no—
115#120—2262no—
116C4×D4—2264no—
117#117—1132no—
118#104—2264no—
119C22⋊C8—2262no—
120C24—1131no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D11312yescomplemented
126C2×D4—22no—
127C2×D4—2264no—
128C2×D4C22⋊D11312yescomplemented
129C22×C4—22no—
130C22×C4—1131no—
131C22×C4—2262no—
132C22×C4—2261no—
133C22×C4—2262no—
134C22×C4—2261no—
135C22×C4C22×D11311yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—2262no—
141C2×C8—2261no—
142C2×C8C22⋊D11312yescomplemented
143C4⋊C4—2264no—
144C4⋊C4—2262no—
145C22⋊C4—2264no—
146C22⋊C4—2264no—
147C22⋊C4—2262no—
148C42—1134no—
149C23—22no—
150C23—4522no—
151C23—2262no—
152C23—2261no—
153C23D4×D11311yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—4528no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—4521no—
165C2×C4—4522no—
166C2×C4—4521no—
167C2×C4—2264no—
168C2×C4—2262no—
169C2×C4—2261no—
170C2×C4D4×D11312yes—
171C2×C4C2×C22⋊D11312yes—
172C2×C4C2×C22⋊D11311yescharacteristic
173C2×C4#1426864611yescharacteristic
174C8—22no—
175C8—4521no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—4522no—
180C22—4521no—
181C22—4521no—
182C22—2264no—
183C22—2262no—
184C22#1681359012yes—
185C22#1681359311yescharacteristic
186C4—42no—
187C4—4524no—
188C4—4521no—
189C4#1681359111yescharacteristic
190C4#1681359412yes—
191C4#1681361811yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—4522no—
196C2#2029850611yescharacteristic
subgroupG/H
centerC4#16813618
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#575×C113C2
socleC2×C113#392
hypercenter#575D113
hypocenterC113#2010
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #20299105C2semidirect
2. #20298615C2semidirect
3. #20298561C2semidirect
4. #20298355C2semidirect
5. #575×C113C2semidirect
35. C4×Dic113D4semidirect
40. C2×Q8×C113D4semidirect
42. C2×D4×C113D4semidirect
49. C2×C8×C113D4semidirect
99. C113#2010semidirect
100. #575D113semidirect
125. C2×Q8C22⋊D113semidirect
128. C2×D4C22⋊D113semidirect
142. C2×C8C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
#202991052
#202986152
#202985612
#202983552
#575×C1132
#2010113