Finite Group Databasebeta

← #28391677

Subgroups — #28391677

Order 14464.

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

normal subgroups only

This group has 350 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#20299396C212yesmaximal, complemented
2#20298566C211yesmaximal, characteristic, complemented
3#20298565C212yesmaximal, complemented
4#20298356C211yesmaximal, characteristic, complemented
5#575×C113C211yesmaximal, characteristic, complemented
6C2×#14268647C2211yescharacteristic
7#16813653—22no—
8#16813652—22no—
9#16813648—22no—
10#16813647—22no—
11#16813642—24no—
12C2×#14268631C2212yes—
13C22×#11744751C2211yescharacteristic
14C22⋊#11744751—24no—
15#16813534—22no—
16C2×#41×C113C2212yes—
17#137×C113—22no—
18AGL(1,ℤ/8)×C113—22no—
19#135×C113—22no—
20C2×M16×C113C2211yescharacteristic
21#14268647—22no—
22#14268647—22no—
23C2×Dic226D411yescharacteristic
24C2×D452D411yescharacteristic
25C2×C22⋊D113—21no—
26C2×C4×D113—21no—
27#14268637—24no—
28#14268635—24no—
29#14268634—24no—
30#14268632—24no—
31#14268631—22no—
32#14268631—22no—
33C2×#11744751—21no—
34C2×#11744751—22no—
35C2×#11744751D414yes—
36#41×C113—22no—
37#41×C113—22no—
38#41×C113—22no—
39#41×C113—22no—
40C2×Q8×C113D412yes—
41C2×D4×C113—22no—
42C2×D4×C113D412yes—
43C22×C4×C113—22no—
44C22×C4×C113C2311yescharacteristic
45Q16×C113—22no—
46SD16×C113—24no—
47D8×C113—22no—
48M16×C113—22no—
49C2×C8×C113D412yes—
50C23×C113—22no—
51C23×C113#4111yescharacteristic
52C22×D113—21no—
53Q8×C113—22no—
54Q8×C113—22no—
55D4×C113—22no—
56D4×C113—22no—
57D4×C113—42no—
58D4×C113—42no—
59C2×C4×C113—22no—
60C2×C4×C113—42no—
61C2×C4×C113—42no—
62C2×C4×C113C2×D411yescharacteristic
63C2×C4×C113C2×D412yes—
64C2×C4×C113C2×D412yes—
65C2×C4×C113C2×D411yescharacteristic
66C22⋊D113—42no—
67C2×Dic113—21no—
68D452—22no—
69C4×D113—41no—
70C4×D113—41no—
71Dic226—22no—
72C8×C113—22no—
73#11744751—24no—
74#11744751—41no—
75C22×C113—41no—
76C22×C113—44no—
77C22×C113—42no—
78C22×C113#12111yescharacteristic
79C22×C113#12112yes—
80C2×D113—42no—
81C2×D113—41no—
82C4×C113—42no—
83C4×C113#12012yes—
84C4×C113#12011yescharacteristic
85C4×C113#12711yescharacteristic
86Dic113—41no—
87C2×C113—21no—
88C2×C113—22no—
89C2×C113—82no—
90C2×C113#39211yescharacteristic
91D113—81no—
92#2017—1131nomaximal, Sylow
93C113#201711yescharacteristic, complemented, Sylow
94#575—1132no—
95#575D11311yescharacteristic, complemented
96#408—1132no—
97#408—1131no—
98#338—1131no—
99C2×#41—1131no—
100C2×#41C2×D11312yes—
101#137—22no—
102#137—2262no—
103#137—2262no—
104AGL(1,ℤ/8)—22no—
105AGL(1,ℤ/8)—2262no—
106AGL(1,ℤ/8)—2262no—
107#135—22no—
108#135—2264no—
109C2×M16—1132no—
110C2×M16C2×D11311yescharacteristic
111C22×C8—1131no—
112C22⋊C8—2264no—
113C22⋊C8—2262no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118#41—2262no—
119#41—2262no—
120C2×Q8—1131no—
121C2×Q8C22⋊D11312yes—
122C2×D4—22no—
123C2×D4—1131no—
124C2×D4—2261no—
125C2×D4C22⋊D11312yes—
126C22×C4—22no—
127C22×C4—2261no—
128C22×C4C22×D11311yescharacteristic
129Q16—22no—
130Q16—2264no—
131SD16—24no—
132SD16—2264no—
133SD16—2264no—
134D8—22no—
135D8—2264no—
136M16—22no—
137M16—2262no—
138M16—2262no—
139C2×C8—1134no—
140C2×C8—2262no—
141C2×C8—2261no—
142C2×C8C22⋊D11312yes—
143C23—22no—
144C23—2261no—
145C23#1426864611yescharacteristic
146Q8—22no—
147Q8—22no—
148Q8—2262no—
149D4—22no—
150D4—22no—
151D4—42no—
152D4—42no—
153D4—4522no—
154D4—2262no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—4521no—
159C2×C4—4521no—
160C2×C4—2261no—
161C2×C4D4×D11311yescharacteristic
162C2×C4D4×D11312yes—
163C2×C4C2×C22⋊D11312yes—
164C2×C4C2×C22⋊D11311yescharacteristic
165C8—22no—
166C8—4521no—
167C8—2264no—
168C22—41no—
169C22—44no—
170C22—42no—
171C22—4522no—
172C22—4521no—
173C22#1681359311yescharacteristic
174C22#1681359412yes—
175C4—42no—
176C4—4521no—
177C4#1681359012yes—
178C4#1681359111yescharacteristic
179C4#1681361811yescharacteristic
180C2—22no—
181C2—21no—
182C2—82no—
183C2—9041no—
184C2#2029850611yescharacteristic
subgroupG/H
centerC4#16813618
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#575×C113C2
socleC2×C113#392
hypercenter#575D113
hypocenterC113#2017
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. #20299396C2semidirect
2. #20298566C2semidirect
3. #20298565C2semidirect
4. #20298356C2semidirect
5. #575×C113C2semidirect
93. C113#2017semidirect
95. #575D113semidirect

Maximal subgroups

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

subgroupindex
#202993962
#202985662
#202985652
#202983562
#575×C1132
#2017113