Finite Group Databasebeta

← #16818511

Subgroups — #16818511

Order 3712.

288 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 53 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#14271725C211yesmaximal, characteristic
2#14271481C212yesmaximal, complemented
3#14270896C212yesmaximal, complemented
4#14270887C211yesmaximal, characteristic, complemented
5C29×#399C211yesmaximal, characteristic, complemented
6C22×C22⋊D29—21no—
7C2×C4⋊C4×C29—21no—
8C2×C4⋊C4×C29C2211yescharacteristic, complemented
9C2×C22⋊C4×C29—21no—
10C2×C22⋊C4×C29C2211yescharacteristic
11#11745292—21no—
12#11745292C2212yes—
13#11745248—22no—
14#11745244—22no—
15C29×#95C2211yescharacteristic, complemented
16C22⋊#6597C2212yescomplemented
17#11745157—22no—
18#11745156—22no—
19C24×C29D411yescharacteristic
20C23×D29—21no—
21C22×C4×C29—21no—
22C22×C4×C29—21no—
23C22×C4×C29D411yescharacteristic
24C22×C4×C29C2311yescharacteristic
25C2×C22⋊D29—22no—
26C2×C22⋊D29—22no—
27C2×C22⋊D29—42no—
28C2×C22⋊D29—42no—
29C22×Dic29—21no—
30C2×D116—21no—
31C2×D116D412yes—
32C4⋊C4×C29—22no—
33C4⋊C4×C29—42no—
34C22⋊C4×C29—22no—
35C22⋊C4×C29—42no—
36#90781—22no—
37#90781—22no—
38C4⋊Dic29—21no—
39C4⋊Dic29D412yes—
40C2×#6597—22no—
41C23×C29—21no—
42C23×C29—21no—
43C23×C29—41no—
44C23×C29—41no—
45C23×C29SD1612yes—
46C23×C29C2×D411yescharacteristic
47C22×D29—22no—
48C22×D29—42no—
49C22×D29—81no—
50C22×D29—81no—
51C2×C4×C29—22no—
52C2×C4×C29—21no—
53C2×C4×C29—41no—
54C2×C4×C29—41no—
55C2×C4×C29—41no—
56C2×C4×C29—41no—
57C2×C4×C29—41no—
58C2×C4×C29—41no—
59C2×C4×C29—41no—
60C2×C4×C29C2×D412yes—
61C22⋊D29—44no—
62C22⋊D29—42no—
63C22⋊D29—42no—
64C2×Dic29—22no—
65C2×Dic29—42no—
66D116—42no—
67D116—81no—
68#6597—42no—
69#1613—291nomaximal, Sylow
70C22×C29—21no—
71C22×C29—21no—
72C22×C29—22no—
73C22×C29—42no—
74C22×C29—41no—
75C22×C29—41no—
76C22×C29—81no—
77C22×C29#12011yescharacteristic
78C22×C29C2×SD1611yescharacteristic
79C22×C29AGL(1,ℤ/8)11yescharacteristic
80C2×D29—42no—
81C2×D29—42no—
82C2×D29—42no—
83C2×D29—84no—
84C4×C29—22no—
85C4×C29—42no—
86C4×C29—41no—
87C4×C29—81no—
88Dic29—42no—
89#534—291no—
90#481—292no—
91#399D2911yescharacteristic, complemented
92#327—292no—
93#323—291no—
94C2×C29—21no—
95C2×C29—21no—
96C2×C29—42no—
97C2×C29#45011yescharacteristic
98C2×C29#45311yescharacteristic
99C2×C29#45811yescharacteristic
100D29—82no—
101C22×D4—581no—
102#123—582no—
103#121—292no—
104#121—581no—
105#120—582no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4C2×D2911yescharacteristic, complemented
108C2×C22⋊C4—21no—
109C2×C22⋊C4C2×D2911yescharacteristic
110#106—582no—
111#102—582no—
112C22⋊C8—292no—
113#95C2×D2911yescharacteristic, complemented
114C29#161311yescharacteristic, complemented, Sylow
115C24—581no—
116C24C22⋊D2911yescharacteristic
117C2×D4—292no—
118C2×D4—581no—
119C2×D4—582no—
120C2×D4—582no—
121C2×D4—1162no—
122C2×D4—1162no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—581no—
126C22×C4C22⋊D2911yescharacteristic
127C22×C4C22×D2911yescharacteristic
128C2×C8—582no—
129C4⋊C4—22no—
130C4⋊C4—42no—
131C4⋊C4—292no—
132C4⋊C4—581no—
133C22⋊C4—22no—
134C22⋊C4—42no—
135C22⋊C4—582no—
136C22⋊C4—582no—
137C23—21no—
138C23—21no—
139C23—41no—
140C23—41no—
141C23—582no—
142C23—1162no—
143C23—2321no—
144C23—2321no—
145C23#9078412yes—
146C23C2×C22⋊D2911yescharacteristic
147D4—1162no—
148D4—1164no—
149D4—1162no—
150D4—1162no—
151D4—2321no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—582no—
162C2×C4—1162no—
163C2×C4D4×D2912yes—
164C8—1162no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—81no—
172C22—1162no—
173C22—1162no—
174C22—1162no—
175C22—2324no—
176C22#1174529911yescharacteristic
177C22C2×#9078411yescharacteristic
178C22#1174531111yescharacteristic
179C4—22no—
180C4—42no—
181C4—41no—
182C4—81no—
183C4—1162no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—2322no—
188C2#1427131311yescharacteristic
189C2#1427133011yescharacteristic
190C2#1427135211yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#399C2
socleC22×C29#120
prime radical#14271725C2
hypercenter#399D29
hypocenterC29#1613
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #14271481C2semidirect
3. #14270896C2semidirect
4. #14270887C2semidirect
5. C29×#399C2semidirect
8. C2×C4⋊C4×C29C22semidirect
15. C29×#95C22semidirect
16. C22⋊#6597C22semidirect
91. #399D29semidirect
107. C2×C4⋊C4C2×D29semidirect
113. #95C2×D29semidirect
114. C29#1613semidirect

Maximal subgroups

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

subgroupindex
#142717252
#142714812
#142708962
#142708872
C29×#3992
#161329