Finite Group Databasebeta

← #16834906

Subgroups — #16834906

Order 3712.

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

normal subgroups only

This group has 222 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#14272185C211yesmaximal, characteristic, complemented
2#14272107C211yesmaximal, characteristic, complemented
3#14272016C212yesmaximal, complemented
4#14272015C212yesmaximal
5#14271698C211yesmaximal, characteristic
6C2×C4⋊#1181—21no—
7C29×#125C411yescharacteristic, complemented
8#11745260—21no—
9#11745259C2211yescharacteristic
10#11745257C2211yescharacteristic
11#11745256—21no—
12#11745255—21no—
13#11745255C411yescharacteristic, complemented
14#11745254—21no—
15#11745249C411yescharacteristic, complemented
16#11745237C411yescharacteristic, complemented
17C42×D29C2211yescharacteristic
18(C2×#1181)⋊C4—21no—
19(C2×#1181)⋊C4C2212yes—
20#11745219C2212yes—
21#11745218—21no—
22C4⋊#6599—21no—
23C22×#1181—22no—
24C2×D116—21no—
25C2×D116C2×C411yescharacteristic
26C2×C4×D29—21no—
27C2×C4×D29D411yescharacteristic
28C2×C4×D29D411yescharacteristic
29C2×C4×D29C2311yescharacteristic
30C2×Dic58C2×C411yescharacteristic
31C2×#6599—22no—
32C4⋊#1181—42no—
33C4⋊C4×C29—21no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29C2×C411yescharacteristic
36C4⋊C4×C29C2×C411yescharacteristic
37C42×C29C2×C411yescharacteristic
38#90781—21no—
39#90781—21no—
40#90781—21no—
41#90781—21no—
42#90781—21no—
43C4⋊Dic29—21no—
44#90779—21no—
45C4×Dic29—21no—
46C4×Dic29C2×C411yescharacteristic
47C4×Dic29D411yescharacteristic
48C4×Dic29D411yescharacteristic
49C22×D29—21no—
50C22×D29C2×D411yescharacteristic
51C2×#1181—42no—
52C2×#1181—42no—
53C2×#1181—42no—
54C2×C4×C29—21no—
55C2×C4×C29—21no—
56C2×C4×C29C22⋊C411yescharacteristic
57C2×C4×C29C22⋊C411yescharacteristic
58C2×C4×C29C22×C411yescharacteristic
59C2×Dic29—21no—
60C2×Dic29C22⋊C411yescharacteristic
61C2×Dic29C22⋊C411yescharacteristic
62C2×Dic29C2×D411yescharacteristic
63D116—41no—
64D116—41no—
65D116—41no—
66C4×D29—21no—
67C4×D29—21no—
68C4×D29—41no—
69C4×D29—41no—
70C4×D29—42no—
71Dic58—41no—
72#6599—42no—
73#1512—291nomaximal, Sylow
74C22×C29C2×C22⋊C411yescharacteristic
75C2×D29—21no—
76C2×D29—21no—
77C2×D29—41no—
78C2×D29—41no—
79C2×D29—41no—
80C2×D29AGL(1,ℤ/8)11yescharacteristic
81C2×D29#13711yescharacteristic
82#1181—82no—
83C4×C29—21no—
84C4×C29—21no—
85C4×C29—21no—
86C4×C29—41no—
87C4×C29—41no—
88Dic29—21no—
89Dic29—21no—
90Dic29—21no—
91Dic29—41no—
92#529—291no—
93#432—291no—
94#382—291no—
95#328—292no—
96#327—292no—
97C2×C29#41011yescharacteristic
98C2×C29#41711yescharacteristic
99C2×C29#42111yescharacteristic
100D29—21no—
101D29—21no—
102D29—81no—
103#126—581no—
104#125#118111yescharacteristic, complemented
105#124—291no—
106#123—581no—
107C22⋊Q8—291no—
108#121—291no—
109C4×Q8—291no—
110C4×D4—291no—
111C4×D4—581no—
112#117—581no—
113C2×C4⋊C4—581no—
114C2×C42—291no—
115C4⋊C8—581no—
116C22⋊C8—292no—
117#97—581no—
118#95—292no—
119#95—581no—
120C29#151211yescharacteristic, complemented, Sylow
121C2×Q8—291no—
122C2×D4—291no—
123C2×D4—581no—
124C22×C4—291no—
125C22×C4—291no—
126C22×C4—291no—
127C22×C4—581no—
128C22×C4—582no—
129C2×C8—582no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—581no—
133C4⋊C4—581no—
134C4⋊C4—1162no—
135C4⋊C4C2×#118111yescharacteristic
136C4⋊C4C2×#118111yescharacteristic
137C22⋊C4—581no—
138C22⋊C4—581no—
139C22⋊C4—581no—
140C22⋊C4—581no—
141C22⋊C4—581no—
142C42—291no—
143C42—291no—
144C42—291no—
145C42—581no—
146C42C2×#118111yescharacteristic
147C23—291no—
148C23—581no—
149Q8—1161no—
150D4—1161no—
151D4—1161no—
152D4—1161no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—291no—
156C2×C4—291no—
157C2×C4—291no—
158C2×C4—581no—
159C2×C4—581no—
160C2×C4—581no—
161C2×C4—1161no—
162C2×C4—1161no—
163C2×C4—1162no—
164C2×C4—1162no—
165C2×C4—1162no—
166C2×C4—1162no—
167C2×C4C22⋊#118111yescharacteristic
168C2×C4C22⋊#118111yescharacteristic
169C2×C4C22×#118111yescharacteristic
170C8—1162no—
171C22—291no—
172C22—291no—
173C22—581no—
174C22—581no—
175C22—1161no—
176C22—1161no—
177C22—1161no—
178C22C2×C22⋊#118111yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—41no—
183C4—41no—
184C4—581no—
185C4—581no—
186C4—581no—
187C4—1161no—
188C4—2322no—
189C2—581no—
190C2—581no—
191C2—2321no—
192C2#1427214411yescharacteristic
193C2#1427215411yescharacteristic
194C2#1427216011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#125C4
socleC22×C29C2×C22⋊C4
prime radical#11745257C22
cosocleC2×C4×D29C23
hypercenter#125#1181
hypocenterC29#1512
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #14272185C2semidirect
2. #14272107C2semidirect
3. #14272016C2semidirect
7. C29×#125C4semidirect
13. #11745255C4semidirect
15. #11745249C4semidirect
16. #11745237C4semidirect
104. #125#1181semidirect
120. C29#1512semidirect

Maximal subgroups

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

subgroupindex
#142721852
#142721072
#142720162
#142720152
#142716982
#151229