Finite Group Databasebeta

← #16818461

Subgroups — #16818461

Order 3712.

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

normal subgroups only

This group has 282 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#14271301C212yesmaximal, complemented
2#14271083C211yesmaximal, characteristic, complemented
3#14270897C212yesmaximal, complemented
4#14270889C211yesmaximal, characteristic, complemented
5C29×#537C211yesmaximal, characteristic
6C2×#41×C29—21no—
7C22×Dic58C2211yescharacteristic
8C29×C22⋊Q8—22no—
9C29×#121—22no—
10C29×#121—21no—
11C29×#121C2212yes—
12C2×C4⋊C4×C29C2211yescharacteristic
13C2×#90783—22no—
14C2×#90779—21no—
15#11745179—21no—
16#11745179C2211yescharacteristic
17C22⋊#6597C2212yes—
18#11745158—22no—
19#41×C29—42no—
20#41×C29—42no—
21C2×Q8×C29—21no—
22C2×D4×C29—21no—
23C2×D4×C29—22no—
24C2×D4×C29—21no—
25C2×D4×C29D412yes—
26C22×C4×C29—22no—
27C22×C4×C29D411yescharacteristic
28C22×C4×C29D411yescharacteristic
29C22×C4×C29C2311yescharacteristic
30C22×Dic29—21no—
31C22×Dic29—21no—
32C2×Dic58—22no—
33C2×Dic58—42no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29—22no—
36C4⋊C4×C29D412yes—
37C22⋊C4×C29—22no—
38C22⋊C4×C29—22no—
39#90783—44no—
40#90779—42no—
41C2×#6597—22no—
42C23×C29—22no—
43C23×C29C2×D411yescharacteristic
44Q8×C29—42no—
45D4×C29—42no—
46D4×C29—42no—
47D4×C29—42no—
48D4×C29—42no—
49D4×C29—81no—
50C2×C4×C29—21no—
51C2×C4×C29—21no—
52C2×C4×C29—21no—
53C2×C4×C29—22no—
54C2×C4×C29—41no—
55C2×C4×C29—44no—
56C2×C4×C29—41no—
57C2×C4×C29SD1612yescomplemented
58C2×C4×C29C2×D412yes—
59C2×Dic29—22no—
60C2×Dic29—22no—
61C2×Dic29—41no—
62C2×Dic29—41no—
63C2×Dic29—41no—
64C2×Dic29—41no—
65Dic58—24no—
66Dic58—42no—
67#6597—42no—
68#1604—291nomaximal, Sylow
69C22×C29—21no—
70C22×C29—21no—
71C22×C29—42no—
72C22×C29—42no—
73C22×C29—42no—
74C22×C29#12011yescharacteristic
75C22×C29C2×SD1611yescharacteristic
76C22×C29AGL(1,ℤ/8)11yescharacteristic
77C4×C29—22no—
78C4×C29—22no—
79C4×C29—42no—
80C4×C29—41no—
81Dic29—42no—
82Dic29—42no—
83#537D2911yescharacteristic
84#448—292no—
85#395—291no—
86#327—292no—
87#324—291no—
88C2×C29—21no—
89C2×C29—21no—
90C2×C29—82no—
91C2×C29#45011yescharacteristic
92C2×C29#45611yescharacteristic
93C2×C29B(4,𝔽2)11yescharacteristic
94C2×#41—21no—
95C22×Q8—291no—
96C2×SD16—582no—
97C22⋊Q8—22no—
98#121—22no—
99#121—21no—
100#121C2×D2912yes—
101C2×C4⋊C4—581no—
102C2×C4⋊C4C2×D2911yescharacteristic
103#103—582no—
104C22⋊C8—292no—
105#95—291no—
106#95—581no—
107C29#160411yescharacteristic, complemented, Sylow
108#41—42no—
109#41—42no—
110C2×Q8—21no—
111C2×Q8—582no—
112C2×Q8—1162no—
113C2×D4—21no—
114C2×D4—22no—
115C2×D4—21no—
116C2×D4C22⋊D2912yes—
117C22×C4—22no—
118C22×C4—581no—
119C22×C4—581no—
120C22×C4C22⋊D2911yescharacteristic
121C22×C4C22⋊D2911yescharacteristic
122C22×C4C22×D2911yescharacteristic
123SD16—1164no—
124C2×C8—582no—
125C4⋊C4—21no—
126C4⋊C4—22no—
127C4⋊C4—1162no—
128C4⋊C4C22⋊D2912yes—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C23—22no—
132C23C2×C22⋊D2911yescharacteristic
133Q8—42no—
134Q8—584no—
135Q8—1162no—
136D4—42no—
137D4—42no—
138D4—42no—
139D4—42no—
140D4—81no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—44no—
147C2×C4—41no—
148C2×C4—582no—
149C2×C4—582no—
150C2×C4—1161no—
151C2×C4—1161no—
152C2×C4—1161no—
153C2×C4—1161no—
154C2×C4#9078312yescomplemented
155C2×C4C2×C22⋊D2912yes—
156C8—1162no—
157C22—21no—
158C22—21no—
159C22—42no—
160C22—42no—
161C22—42no—
162C22#1174529411yescharacteristic
163C22C2×#9078311yescharacteristic
164C22#1174531511yescharacteristic
165C4—22no—
166C4—22no—
167C4—42no—
168C4—41no—
169C4—1162no—
170C4—1162no—
171C2—21no—
172C2—21no—
173C2—82no—
174C2#1427131411yescharacteristic
175C2#1427134611yescharacteristic
176C2#1427135011yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
Fitting, prime radicalC29×#537C2
socleC22×C29#120
hypercenter#537D29
hypocenterC29#1604
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #14271301C2semidirect
2. #14271083C2semidirect
3. #14270897C2semidirect
4. #14270889C2semidirect
57. C2×C4×C29SD16semidirect
107. C29#1604semidirect
154. C2×C4#90783semidirect

Maximal subgroups

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

subgroupindex
#142713012
#142710832
#142708972
#142708892
C29×#5372
#160429