Finite Group Databasebeta

← #16818512

Subgroups — #16818512

Order 3712.

288 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 57 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#14271479C212yesmaximal, complemented
2#14271099C211yesmaximal, characteristic, complemented
3#14270897C212yesmaximal, complemented
4#14270887C211yesmaximal, characteristic, complemented
5C29×#534C211yesmaximal, characteristic
6C22×D4×C29—21no—
7C29×#123—22no—
8C29×#121—21no—
9C29×#121C2212yes—
10C29×#120—22no—
11C2×C22⋊C4×C29C2211yescharacteristic
12C2×C22⋊Dic29—21no—
13C2×C4⋊Dic29C2211yescharacteristic, complemented
14C2×#90779—21no—
15#11745180—22no—
16#11745179C2211yescharacteristic, complemented
17C22⋊#6597C2212yescomplemented
18#11745156—22no—
19C24×C29—21no—
20C24×C29D411yescharacteristic
21C2×D4×C29—22no—
22C2×D4×C29—22no—
23C2×D4×C29—21no—
24C2×D4×C29—42no—
25C2×D4×C29—42no—
26C2×D4×C29D412yes—
27C22×C4×C29—21no—
28C22×C4×C29D411yescharacteristic
29C22×C4×C29C2311yescharacteristic
30C22×Dic29—21no—
31C22×Dic29—21no—
32C4⋊C4×C29—21no—
33C4⋊C4×C29D412yes—
34C22⋊C4×C29—22no—
35C22⋊C4×C29—22no—
36C22⋊C4×C29—22no—
37C22⋊Dic29—42no—
38C4⋊Dic29—22no—
39#90779—42no—
40C2×#6597—22no—
41C23×C29—21no—
42C23×C29—21no—
43C23×C29—22no—
44C23×C29—41no—
45C23×C29—41no—
46C23×C29—42no—
47C23×C29—81no—
48C23×C29—81no—
49C23×C29SD1612yes—
50C23×C29C2×D411yescharacteristic
51D4×C29—42no—
52D4×C29—44no—
53D4×C29—42no—
54D4×C29—42no—
55D4×C29—81no—
56C2×C4×C29—21no—
57C2×C4×C29—22no—
58C2×C4×C29—41no—
59C2×C4×C29—42no—
60C2×C4×C29—41no—
61C2×C4×C29C2×D412yes—
62C2×Dic29—22no—
63C2×Dic29—41no—
64C2×Dic29—41no—
65C2×Dic29—41no—
66C2×Dic29—41no—
67C2×Dic29—41no—
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—42no—
77C22×C29—42no—
78C22×C29—42no—
79C22×C29—81no—
80C22×C29—84no—
81C22×C29#12011yescharacteristic
82C22×C29C2×SD1611yescharacteristic
83C22×C29AGL(1,ℤ/8)11yescharacteristic
84C4×C29—22no—
85C4×C29—42no—
86C4×C29—41no—
87Dic29—42no—
88Dic29—81no—
89#534D2911yescharacteristic
90#481—292no—
91#399—291no—
92#327—292no—
93#323—291no—
94C2×C29—21no—
95C2×C29—21no—
96C2×C29—42no—
97C2×C29—82no—
98C2×C29#45011yescharacteristic
99C2×C29#45311yescharacteristic
100C2×C29#45811yescharacteristic
101C22×D4—21no—
102#123—22no—
103#121—21no—
104#121C2×D2912yes—
105#120—22no—
106C2×C4⋊C4—291no—
107C2×C4⋊C4—581no—
108C2×C22⋊C4—581no—
109C2×C22⋊C4C2×D2911yescharacteristic
110#106—582no—
111#102—582no—
112C22⋊C8—292no—
113#95—291no—
114C29#161311yescharacteristic, complemented, Sylow
115C24—21no—
116C24C22⋊D2911yescharacteristic
117C2×D4—22no—
118C2×D4—22no—
119C2×D4—21no—
120C2×D4—42no—
121C2×D4—42no—
122C2×D4C22⋊D2912yes—
123C22×C4—21no—
124C22×C4—581no—
125C22×C4—581no—
126C22×C4C22⋊D2911yescharacteristic
127C22×C4C22×D2911yescharacteristic
128C2×C8—582no—
129C4⋊C4—21no—
130C4⋊C4—582no—
131C4⋊C4—1162no—
132C4⋊C4C22⋊D2912yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—1162no—
137C23—21no—
138C23—21no—
139C23—22no—
140C23—41no—
141C23—41no—
142C23—42no—
143C23—81no—
144C23—81no—
145C23#9078312yes—
146C23C2×C22⋊D2911yescharacteristic
147D4—42no—
148D4—44no—
149D4—42no—
150D4—42no—
151D4—81no—
152C2×C4—21no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—42no—
156C2×C4—41no—
157C2×C4—582no—
158C2×C4—1161no—
159C2×C4—1161no—
160C2×C4—1161no—
161C2×C4—1161no—
162C2×C4—1161no—
163C2×C4C2×C22⋊D2912yes—
164C8—1162no—
165C22—21no—
166C22—21no—
167C22—22no—
168C22—42no—
169C22—41no—
170C22—41no—
171C22—42no—
172C22—42no—
173C22—42no—
174C22—81no—
175C22—84no—
176C22#1174529411yescharacteristic
177C22C2×#9078311yescharacteristic
178C22#1174531511yescharacteristic
179C4—22no—
180C4—42no—
181C4—41no—
182C4—1162no—
183C4—2321no—
184C2—21no—
185C2—21no—
186C2—42no—
187C2—82no—
188C2#1427131411yescharacteristic
189C2#1427133111yescharacteristic
190C2#1427135311yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
Fitting, prime radicalC29×#534C2
socleC22×C29#120
hypercenter#534D29
hypocenterC29#1613
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #14271479C2semidirect
2. #14271099C2semidirect
3. #14270897C2semidirect
4. #14270887C2semidirect
13. C2×C4⋊Dic29C22semidirect
16. #11745179C22semidirect
17. C22⋊#6597C22semidirect
114. C29#1613semidirect

Maximal subgroups

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

subgroupindex
#142714792
#142710992
#142708972
#142708872
C29×#5342
#161329