Finite Group Databasebeta

← #16818432

Subgroups — #16818432

Order 3712.

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

normal subgroups only

This group has 266 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#14271313C212yesmaximal
2#14271080C211yesmaximal, characteristic
3#14270900C212yesmaximal, complemented
4#14270889C211yesmaximal, characteristic, complemented
5C29×#544C211yesmaximal, characteristic, complemented
6C22×D116C2211yescharacteristic
7C29×C4⋊Q8—22no—
8C29×#125—22no—
9C29×C22⋊Q8—21no—
10C29×C22⋊Q8C2212yes—
11C29×#117—21no—
12C2×C4⋊C4×C29C2211yescharacteristic
13C2×#90784—22no—
14C2×#90781—21no—
15C2×#90781—21no—
16#11745179C2211yescharacteristic
17C22⋊#6597C2212yes—
18#11745157—22no—
19C23×D29—21no—
20C2×Q8×C29—21no—
21C2×Q8×C29D412yes—
22C22×C4×C29D411yescharacteristic
23C22×C4×C29D411yescharacteristic
24C22×C4×C29C2311yescharacteristic
25C22×Dic29—21no—
26C2×D116—22no—
27C2×D116—42no—
28C4⋊C4×C29—21no—
29C4⋊C4×C29—21no—
30C4⋊C4×C29—21no—
31C4⋊C4×C29—22no—
32C4⋊C4×C29—22no—
33C4⋊C4×C29—22no—
34C4⋊C4×C29D412yes—
35C22⋊C4×C29—22no—
36C42×C29—22no—
37#90784—44no—
38#90781—42no—
39#90781—42no—
40C2×#6597—22no—
41C23×C29C2×D411yescharacteristic
42C22×D29—22no—
43C22×D29—41no—
44C22×D29—41no—
45C22×D29—41no—
46C22×D29—41no—
47C22×D29—41no—
48C22×D29—41no—
49Q8×C29—42no—
50Q8×C29—81no—
51C2×C4×C29—21no—
52C2×C4×C29—21no—
53C2×C4×C29—22no—
54C2×C4×C29—22no—
55C2×C4×C29—21no—
56C2×C4×C29—41no—
57C2×C4×C29—41no—
58C2×C4×C29SD1612yescomplemented
59C2×C4×C29C2×D412yes—
60C2×Dic29—41no—
61C2×Dic29—41no—
62C2×Dic29—41no—
63D116—24no—
64D116—42no—
65#6597—42no—
66#1599—291nomaximal, Sylow
67C22×C29—21no—
68C22×C29—21no—
69C22×C29#12011yescharacteristic
70C22×C29C2×SD1611yescharacteristic
71C22×C29#13711yescharacteristic
72C2×D29—42no—
73C2×D29—42no—
74C2×D29—42no—
75C2×D29—81no—
76C2×D29—81no—
77C2×D29—81no—
78C2×D29—81no—
79C4×C29—22no—
80C4×C29—22no—
81C4×C29—42no—
82C4×C29—41no—
83C4×C29—42no—
84Dic29—81no—
85#544D2911yescharacteristic, complemented
86#450—292no—
87#394—291no—
88#328—292no—
89#324—291no—
90C2×C29—21no—
91C2×C29—21no—
92C2×C29#44811yescharacteristic
93C2×C29#45411yescharacteristic
94C2×C29B(4,𝔽2)11yescharacteristic
95D29—82no—
96C22×D4—291no—
97C2×SD16—582no—
98C4⋊Q8—22no—
99#125—22no—
100C22⋊Q8—21no—
101C22⋊Q8C2×D2912yes—
102#117—21no—
103C2×C4⋊C4C2×D2911yescharacteristic
104C2×C22⋊C4—581no—
105C2×C22⋊C4—581no—
106#102—582no—
107C22⋊C8—292no—
108#95—291no—
109C29#159911yescharacteristic, complemented, Sylow
110C24—581no—
111C2×Q8—21no—
112C2×Q8C22⋊D2912yes—
113C2×D4—582no—
114C2×D4—1162no—
115C22×C4—581no—
116C22×C4C22⋊D2911yescharacteristic
117C22×C4C22⋊D2911yescharacteristic
118C22×C4C22×D2911yescharacteristic
119SD16—1164no—
120C2×C8—582no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—22no—
125C4⋊C4—22no—
126C4⋊C4—22no—
127C4⋊C4C22⋊D2912yes—
128C22⋊C4—22no—
129C22⋊C4—1162no—
130C22⋊C4—1162no—
131C42—22no—
132C23—582no—
133C23—1161no—
134C23—1161no—
135C23—1161no—
136C23—1161no—
137C23—1161no—
138C23—1161no—
139C23C2×C22⋊D2911yescharacteristic
140Q8—42no—
141Q8—81no—
142D4—584no—
143D4—1162no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—1161no—
152C2×C4—1161no—
153C2×C4—1161no—
154C2×C4#9078412yescomplemented
155C2×C4C2×C22⋊D2912yes—
156C8—1162no—
157C22—21no—
158C22—21no—
159C22—1162no—
160C22—1162no—
161C22—1162no—
162C22—2321no—
163C22—2321no—
164C22—2321no—
165C22—2321no—
166C22C2×#9078411yescharacteristic
167C22#1174530411yescharacteristic
168C22#1174531511yescharacteristic
169C4—22no—
170C4—22no—
171C4—42no—
172C4—41no—
173C4—42no—
174C4—2321no—
175C2—21no—
176C2—21no—
177C2—2322no—
178C2#1427130211yescharacteristic
179C2#1427133611yescharacteristic
180C2#1427135011yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#544C2
socleC22×C29#120
prime radicalC22×D116C22
hypercenter#544D29
hypocenterC29#1599
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #14270900C2semidirect
4. #14270889C2semidirect
5. C29×#544C2semidirect
58. C2×C4×C29SD16semidirect
85. #544D29semidirect
109. C29#1599semidirect
154. C2×C4#90784semidirect

Maximal subgroups

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

subgroupindex
#142713132
#142710802
#142709002
#142708892
C29×#5442
#159929