Finite Group Databasebeta

← #16834911

Subgroups — #16834911

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#14272185C211yesmaximal, characteristic, complemented
2#14272108C211yesmaximal, characteristic, complemented
3#14272015C212yesmaximal, complemented
4#14272014C212yesmaximal, complemented
5#14271710C211yesmaximal, characteristic
6C2×#90805—21no—
7C4×D4×C29C411yescharacteristic, complemented
8#11745302C411yescharacteristic, complemented
9#11745300C2211yescharacteristic
10C4×C22⋊D29—21no—
11#11745257C2211yescharacteristic
12#11745250C411yescharacteristic, complemented
13#11745247—21no—
14#11745246—21no—
15C4×D116C411yescharacteristic, complemented
16C42×D29C2211yescharacteristic
17(C2×#1181)⋊C4—21no—
18(C2×#1181)⋊C4—21no—
19(C2×#1181)⋊C4C2212yes—
20#11745219C2212yes—
21#11745218—21no—
22C4⋊#6599—21no—
23C22×#1181—22no—
24C2×D4×C29C2×C411yescharacteristic
25C22×C4×C29—21no—
26C2×C22⋊D29—21no—
27C2×C22⋊D29—21no—
28C2×C22⋊D29—21no—
29#90805—44no—
30C2×D116—21no—
31C2×D116C2×C411yescharacteristic
32C2×C4×D29—21no—
33C2×C4×D29D411yescharacteristic
34C2×C4×D29D411yescharacteristic
35C2×C4×D29C2311yescharacteristic
36C2×Dic58—21no—
37C2×#6599—22no—
38C4⋊C4×C29C2×C411yescharacteristic
39C22⋊C4×C29—21no—
40C42×C29C2×C411yescharacteristic
41C22⋊Dic29—21no—
42#90781—21no—
43#90781—21no—
44C4⋊Dic29C2×C411yescharacteristic
45#90779—21no—
46C4×Dic29C2×C411yescharacteristic
47C4×Dic29D411yescharacteristic
48C4×Dic29D411yescharacteristic
49C23×C29—21no—
50C22×D29—21no—
51C22×D29C2×D411yescharacteristic
52C2×#1181—42no—
53C2×#1181—42no—
54C2×#1181—42no—
55D4×C29—41no—
56C2×C4×C29—21no—
57C2×C4×C29—42no—
58C2×C4×C29C22⋊C411yescharacteristic
59C2×C4×C29C22⋊C411yescharacteristic
60C2×C4×C29C22×C411yescharacteristic
61C22⋊D29—42no—
62C22⋊D29—42no—
63C22⋊D29—42no—
64C2×Dic29—21no—
65C2×Dic29C22⋊C411yescharacteristic
66C2×Dic29C22⋊C411yescharacteristic
67C2×Dic29C2×D411yescharacteristic
68D116—41no—
69D116—42no—
70C4×D29—22no—
71C4×D29—41no—
72C4×D29—41no—
73C4×D29—42no—
74Dic58—42no—
75#6599—42no—
76#1514—291nomaximal, Sylow
77C22×C29—41no—
78C22×C29—41no—
79C22×C29—41no—
80C22×C29C2×C22⋊C411yescharacteristic
81C2×D29—21no—
82C2×D29—21no—
83C2×D29—41no—
84C2×D29—41no—
85C2×D29—41no—
86C2×D29AGL(1,ℤ/8)12yes—
87#1181—82no—
88C4×C29—21no—
89C4×C29—21no—
90C4×C29—21no—
91C4×C29—41no—
92Dic29—21no—
93Dic29—21no—
94Dic29—21no—
95Dic29—41no—
96#532—291no—
97#432—291no—
98#383—291no—
99#327—292no—
100#327—292no—
101C2×C29—81no—
102C2×C29#41011yescharacteristic
103C2×C29#41811yescharacteristic
104C2×C29#42111yescharacteristic
105D29—22no—
106D29—81no—
107C2×#41—581no—
108C4⋊Q8—291no—
109#127—291no—
110#124—581no—
111#121—291no—
112#121—291no—
113#121—581no—
114C4×D4—291no—
115C4×D4—581no—
116C4×D4#118111yescharacteristic, complemented
117C2×C42—291no—
118C4⋊C8—581no—
119C22⋊C8—292no—
120#97—581no—
121#95—292no—
122#95—581no—
123#95—581no—
124C29#151411yescharacteristic, complemented, Sylow
125#41—1164no—
126C2×Q8—581no—
127C2×D4—291no—
128C2×D4—581no—
129C2×D4—581no—
130C2×D4—581no—
131C2×D4—581no—
132C2×D4C2×#118111yescharacteristic
133C22×C4—21no—
134C22×C4—291no—
135C22×C4—291no—
136C22×C4—291no—
137C22×C4—581no—
138C22×C4—582no—
139C2×C8—582no—
140C4⋊C4—291no—
141C4⋊C4—581no—
142C4⋊C4C2×#118111yescharacteristic
143C22⋊C4—21no—
144C22⋊C4—581no—
145C22⋊C4—581no—
146C22⋊C4—581no—
147C42—291no—
148C42—291no—
149C42—291no—
150C42C2×#118111yescharacteristic
151C23—21no—
152C23—291no—
153C23—581no—
154Q8—1162no—
155D4—41no—
156D4—1161no—
157D4—1162no—
158D4—1162no—
159D4—1162no—
160D4—1162no—
161C2×C4—21no—
162C2×C4—42no—
163C2×C4—291no—
164C2×C4—291no—
165C2×C4—291no—
166C2×C4—582no—
167C2×C4—581no—
168C2×C4—1161no—
169C2×C4—1161no—
170C2×C4—1162no—
171C2×C4—1162no—
172C2×C4—1162no—
173C2×C4—1162no—
174C2×C4C22⋊#118111yescharacteristic
175C2×C4C22⋊#118111yescharacteristic
176C2×C4C22×#118111yescharacteristic
177C8—1162no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—292no—
182C22—581no—
183C22—581no—
184C22—1161no—
185C22—1161no—
186C22—1161no—
187C22C2×C22⋊#118111yescharacteristic
188C4—21no—
189C4—21no—
190C4—21no—
191C4—41no—
192C4—581no—
193C4—581no—
194C4—581no—
195C4—1161no—
196C4—2322no—
197C2—81no—
198C2—582no—
199C2—2321no—
200C2#1427214211yescharacteristic
201C2#1427215511yescharacteristic
202C2#1427216011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC4×D4×C29C4
socleC22×C29C2×C22⋊C4
prime radical#14271710C2
cosocleC2×C4×D29C23
hypercenterC4×D4#1181
hypocenterC29#1514
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #14272185C2semidirect
2. #14272108C2semidirect
3. #14272015C2semidirect
4. #14272014C2semidirect
7. C4×D4×C29C4semidirect
8. #11745302C4semidirect
12. #11745250C4semidirect
15. C4×D116C4semidirect
116. C4×D4#1181semidirect
124. C29#1514semidirect

Maximal subgroups

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

subgroupindex
#142721852
#142721082
#142720152
#142720142
#142717102
#151429