Finite Group Databasebeta

← #16834912

Subgroups — #16834912

Order 3712.

252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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#14272186C211yesmaximal, characteristic, complemented
2#14272108C211yesmaximal, characteristic, complemented
3#14272014C214yesmaximal, complemented
4#14271711C211yesmaximal, characteristic
5C2×#90807—21no—
6C29×#127C411yescharacteristic, complemented
7#11745300—21no—
8#11745300C2212yes—
9#11745298—21no—
10D4×Dic29—21no—
11D4×Dic29C412yescomplemented
12C42×D29C2211yescharacteristic
13#11745231C411yescharacteristic, complemented
14(C2×#1181)⋊C4—21no—
15(C2×#1181)⋊C4—21no—
16(C2×#1181)⋊C4C2212yes—
17#11745220—21no—
18#11745219C2212yes—
19#11745218—21no—
20C22×#1181—22no—
21C2×D4×C29—21no—
22C2×D4×C29—21no—
23C2×D4×C29C2×C412yes—
24C2×C22⋊D29—22no—
25C22×Dic29—22no—
26#90807—44no—
27C2×C4×D29D411yescharacteristic
28C2×C4×D29D411yescharacteristic
29C2×C4×D29C2311yescharacteristic
30C2×Dic58—21no—
31C2×#6599—22no—
32C42×C29C2×C411yescharacteristic
33C22⋊Dic29—22no—
34C22⋊Dic29—22no—
35C4⋊Dic29—21no—
36C4⋊Dic29C2×C412yes—
37C4×Dic29C2×C411yescharacteristic
38C4×Dic29D411yescharacteristic
39C4×Dic29D411yescharacteristic
40C23×C29—22no—
41C22×D29C2×D411yescharacteristic
42C2×#1181—42no—
43C2×#1181—42no—
44C2×#1181—42no—
45D4×C29—42no—
46D4×C29—42no—
47D4×C29—42no—
48C2×C4×C29C22⋊C411yescharacteristic
49C2×C4×C29C22⋊C411yescharacteristic
50C2×C4×C29C22×C411yescharacteristic
51C22⋊D29—44no—
52C2×Dic29—22no—
53C2×Dic29—44no—
54C2×Dic29C22⋊C411yescharacteristic
55C2×Dic29C22⋊C411yescharacteristic
56C2×Dic29C2×D411yescharacteristic
57C4×D29—22no—
58C4×D29—41no—
59C4×D29—41no—
60Dic58—42no—
61#6599—42no—
62#1514—291nomaximal, Sylow
63C22×C29—42no—
64C22×C29—42no—
65C22×C29—42no—
66C22×C29C2×C22⋊C411yescharacteristic
67C2×D29—21no—
68C2×D29—21no—
69C2×D29AGL(1,ℤ/8)12yes—
70#1181—82no—
71C4×C29—21no—
72C4×C29—21no—
73C4×C29—21no—
74Dic29—21no—
75Dic29—21no—
76Dic29—21no—
77Dic29—42no—
78#532—291no—
79#432—291no—
80#383—291no—
81#327—294no—
82C2×C29—82no—
83C2×C29#41011yescharacteristic
84C2×C29#41811yescharacteristic
85C2×C29#42111yescharacteristic
86D29—22no—
87C2×#41—581no—
88C4⋊Q8—291no—
89#127#118111yescharacteristic, complemented
90#124—581no—
91#121—292no—
92#121—581no—
93C4×D4—292no—
94C4×D4—581no—
95C2×C42—291no—
96C4⋊C8—581no—
97C22⋊C8—292no—
98#97—581no—
99#95—292no—
100#95—581no—
101#95—581no—
102C29#151411yescharacteristic, complemented, Sylow
103#41—1164no—
104C2×Q8—581no—
105C2×D4—21no—
106C2×D4—21no—
107C2×D4—582no—
108C2×D4C2×#118112yes—
109C22×C4—291no—
110C22×C4—291no—
111C22×C4—291no—
112C22×C4—582no—
113C22×C4—582no—
114C2×C8—582no—
115C4⋊C4—292no—
116C4⋊C4—581no—
117C22⋊C4—582no—
118C22⋊C4—582no—
119C42—291no—
120C42—291no—
121C42—291no—
122C42C2×#118111yescharacteristic
123C23—22no—
124C23—291no—
125Q8—1162no—
126D4—42no—
127D4—42no—
128D4—42no—
129D4—1164no—
130C2×C4—291no—
131C2×C4—291no—
132C2×C4—291no—
133C2×C4—582no—
134C2×C4—582no—
135C2×C4—1161no—
136C2×C4—1161no—
137C2×C4—1164no—
138C2×C4—1162no—
139C2×C4—1162no—
140C2×C4—1162no—
141C2×C4C22⋊#118111yescharacteristic
142C2×C4C22⋊#118111yescharacteristic
143C2×C4C22×#118111yescharacteristic
144C8—1162no—
145C22—42no—
146C22—42no—
147C22—42no—
148C22—292no—
149C22—581no—
150C22—581no—
151C22C2×C22⋊#118111yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—581no—
156C4—581no—
157C4—581no—
158C4—1162no—
159C4—2322no—
160C2—82no—
161C2—582no—
162C2#1427214311yescharacteristic
163C2#1427215511yescharacteristic
164C2#1427216111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#127C4
socleC22×C29C2×C22⋊C4
prime radical#14271711C2
cosocleC2×C4×D29C23
hypercenter#127#1181
hypocenterC29#1514
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #14272186C2semidirect
2. #14272108C2semidirect
3. #14272014C2semidirect
6. C29×#127C4semidirect
11. D4×Dic29C4semidirect
13. #11745231C4semidirect
89. #127#1181semidirect
102. C29#1514semidirect

Maximal subgroups

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

subgroupindex
#142721862
#142721082
#142720142
#142717112
#151429