Finite Group Databasebeta

← #16817805

Subgroups — #16817805

Order 3712.

264 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C2×#11745254C211yesmaximal, characteristic
2#14271213C212yesmaximal, complemented
3#14270889C211yesmaximal, characteristic, complemented
4#14270886C212yesmaximal
5C29×#324C211yesmaximal, characteristic, complemented
6C22×C4×D29C411yescharacteristic
7C2×C4⋊C4×C29C2211yescharacteristic
8C2×#90781C411yescharacteristic
9C2×#90781C2211yescharacteristic
10C2×C4⋊Dic29C411yescharacteristic
11C2×C4×Dic29C411yescharacteristic
12C2×C4×Dic29C2211yescharacteristic
13#11745254—22no—
14#11745254—22no—
15C29×C22⋊C8C2212yes—
16C22⋊#6597C2212yes—
17#11745162—22no—
18C8×Dic29—22no—
19C23×D29C2×C411yescharacteristic
20C22×C4×C29C2×C411yescharacteristic
21C22×C4×C29C2×C411yescharacteristic
22C22×C4×C29C2311yescharacteristic
23C22×Dic29C2×C411yescharacteristic
24C22×Dic29C2×C411yescharacteristic
25C22×Dic29C2×C411yescharacteristic
26C2×C4×D29—21no—
27C2×C4×D29—21no—
28C2×C4×D29—22no—
29C2×C4×D29C814yescomplemented
30C2×C8×C29—22no—
31C4⋊C4×C29—22no—
32#90781—22no—
33#90781—22no—
34C4⋊Dic29—22no—
35C4×Dic29—21no—
36C4×Dic29—21no—
37C4×Dic29D412yes—
38C4×Dic29D412yes—
39C2×#6597—22no—
40C23×C29C22×C411yescharacteristic
41C22×D29—21no—
42C22×D29—21no—
43C22×D29—41no—
44C22×D29—41no—
45C22×D29C2×C812yes—
46C2×C4×C29—21no—
47C2×C4×C29—21no—
48C2×C4×C29—21no—
49C2×C4×C29—41no—
50C2×C4×C29—41no—
51C2×C4×C29C2×C812yes—
52C2×C4×C29C2×D412yes—
53C2×Dic29—21no—
54C2×Dic29—41no—
55C2×Dic29—41no—
56C2×Dic29C22⋊C412yes—
57C2×Dic29C22⋊C411yescharacteristic
58C2×Dic29C22⋊C411yescharacteristic
59C2×Dic29C2×C812yes—
60C2×Dic29M1612yes—
61C4×D29—24no—
62C4×D29—24no—
63C8×C29—42no—
64#6597—42no—
65#1458—291nomaximal, Sylow
66C22×C29—21no—
67C22×C29—21no—
68C22×C29C2×C22⋊C411yescharacteristic
69C22×C29C22×C811yescharacteristic
70C22×C29C2×M1611yescharacteristic
71C2×D29—22no—
72C2×D29—42no—
73C2×D29—41no—
74C2×D29—41no—
75C2×D29—42no—
76C4×C29—22no—
77C4×C29—22no—
78C4×C29—41no—
79Dic29—22no—
80Dic29—41no—
81Dic29C22⋊C812yes—
82Dic29C22⋊C812yes—
83C2×#117—291no—
84#431—292no—
85#324—291no—
86#324D2911yescharacteristic, complemented
87#323—292no—
88C2×C29—21no—
89C2×C29—21no—
90C2×C29C2×C22⋊C811yescharacteristic
91C2×C29#41011yescharacteristic
92C2×C29#41311yescharacteristic
93D29—42no—
94C23×C4—291no—
95#117—582no—
96#117—582no—
97C2×C4⋊C4—291no—
98C2×C4⋊C4C2×D2911yescharacteristic
99C2×C22⋊C4—291no—
100C2×C22⋊C4—291no—
101C2×C42—291no—
102C2×C42—291no—
103C4⋊C8—582no—
104C22⋊C8—292no—
105C22⋊C8C2×D2912yes—
106C4×C8—582no—
107C29#145811yescharacteristic, complemented, Sylow
108C24—291no—
109C22×C4—291no—
110C22×C4—291no—
111C22×C4—294no—
112C22×C4—291no—
113C22×C4—581no—
114C22×C4—581no—
115C22×C4—582no—
116C22×C4C4×D2911yescharacteristic
117C22×C4C4×D2911yescharacteristic
118C22×C4C22×D2911yescharacteristic
119C2×C8—22no—
120C2×C8—582no—
121C4⋊C4—22no—
122C4⋊C4—582no—
123C22⋊C4—582no—
124C22⋊C4—582no—
125C42—292no—
126C42—292no—
127C42—581no—
128C42—581no—
129C23—292no—
130C23—581no—
131C23—581no—
132C23—1161no—
133C23—1161no—
134C23C2×C4×D2911yescharacteristic
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—291no—
141C2×C4—291no—
142C2×C4—292no—
143C2×C4—292no—
144C2×C4—292no—
145C2×C4—584no—
146C2×C4—584no—
147C2×C4—581no—
148C2×C4—1161no—
149C2×C4—1161no—
150C2×C4C8×D2912yes—
151C2×C4D4×D2912yes—
152C8—42no—
153C8—1162no—
154C22—21no—
155C22—21no—
156C22—582no—
157C22—1162no—
158C22—1162no—
159C22—1161no—
160C22—1161no—
161C22C22⋊C4×D2911yescharacteristic
162C22C2×C8×D2911yescharacteristic
163C22M16×D2911yescharacteristic
164C4—22no—
165C4—22no—
166C4—41no—
167C4—292no—
168C4—292no—
169C4—582no—
170C4—1161no—
171C2—21no—
172C2—21no—
173C2—1162no—
174C2C22⋊C8×D2911yescharacteristic
175C2#1427113511yescharacteristic
176C2#1427114611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D29
commutatorC22×C29C22×C8
FrattiniC22×C4C22×D29
FittingC29×#324C2
socleC22×C29C2×C22⋊C4
prime radicalC23×D29C2×C4
cosocleC22×C4×C29C23
hypercenter#324D29
hypocenterC29#1458
LCSG ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #14271213C2semidirect
3. #14270889C2semidirect
5. C29×#324C2semidirect
29. C2×C4×D29C8semidirect
86. #324D29semidirect
107. C29#1458semidirect

Maximal subgroups

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

subgroupindex
C2×#117452542
#142712132
#142708892
#142708862
C29×#3242
#145829