Finite Group Databasebeta

← #16834882

Subgroups — #16834882

Order 3712.

272 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 58 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#14272099C211yesmaximal, characteristic, complemented
3#14272015C212yesmaximal, complemented
4#14272014C212yesmaximal, complemented
5#14271710C211yesmaximal, characteristic
6C2×#90805—21no—
7C2×C4×#1181—21no—
8C4×D4×C29C411yescharacteristic, complemented
9#11745302C411yescharacteristic, complemented
10#11745300C2211yescharacteristic
11C4×C22⋊D29—21no—
12#11745257C2211yescharacteristic
13#11745250C411yescharacteristic, complemented
14#11745247—21no—
15#11745246—21no—
16C4×D116C411yescharacteristic, complemented
17C42×D29C2211yescharacteristic
18(C2×#1181)⋊C4—21no—
19(C2×#1181)⋊C4C2212yes—
20#11745220—21no—
21#11745219C2212yes—
22#11745218—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×#1181—24no—
39C4⋊C4×C29C2×C411yescharacteristic
40C22⋊C4×C29—21no—
41C42×C29C2×C411yescharacteristic
42C22⋊Dic29—21no—
43#90781—21no—
44#90781—21no—
45C4⋊Dic29C2×C411yescharacteristic
46#90779—21no—
47C4×Dic29C2×C411yescharacteristic
48C4×Dic29D411yescharacteristic
49C4×Dic29D411yescharacteristic
50C23×C29—21no—
51C22×D29—21no—
52C22×D29C2×D411yescharacteristic
53C2×#1181—24no—
54C2×#1181—42no—
55C2×#1181—42no—
56D4×C29—41no—
57C2×C4×C29—21no—
58C2×C4×C29—42no—
59C2×C4×C29C22⋊C411yescharacteristic
60C2×C4×C29C22⋊C411yescharacteristic
61C2×C4×C29C22×C411yescharacteristic
62C22⋊D29—42no—
63C22⋊D29—42no—
64C22⋊D29—42no—
65C2×Dic29—21no—
66C2×Dic29C22⋊C411yescharacteristic
67C2×Dic29C22⋊C411yescharacteristic
68C2×Dic29C2×D411yescharacteristic
69D116—41no—
70D116—42no—
71C4×D29—22no—
72C4×D29—22no—
73C4×D29—41no—
74C4×D29—42no—
75Dic58—42no—
76#6599—42no—
77#1505—291nomaximal, Sylow
78C22×C29—41no—
79C22×C29—41no—
80C22×C29—41no—
81C22×C29C2×C22⋊C411yescharacteristic
82C2×D29—21no—
83C2×D29—21no—
84C2×D29—41no—
85C2×D29—41no—
86C2×D29—41no—
87C2×D29AGL(1,ℤ/8)12yes—
88#1181—44no—
89C4×C29—21no—
90C4×C29—21no—
91C4×C29—21no—
92C4×C29—41no—
93Dic29—21no—
94Dic29—21no—
95Dic29—41no—
96Dic29#10412yes—
97#532—291no—
98#432—291no—
99#376—291no—
100#327—292no—
101#327—292no—
102C2×C29—81no—
103C2×C29#41011yescharacteristic
104C2×C29#41811yescharacteristic
105C2×C29C2×#10411yescharacteristic
106D29—22no—
107D29—81no—
108C2×#41—581no—
109C4⋊Q8—291no—
110#127—291no—
111#124—581no—
112#121—291no—
113#121—291no—
114#121—581no—
115C4×D4—291no—
116C4×D4—581no—
117C4×D4#118111yescharacteristic, complemented
118C2×C42—291no—
119C2×C42—581no—
120C4⋊C8—581no—
121C22⋊C8—292no—
122#97—581no—
123#95—292no—
124#95—581no—
125C29#150511yescharacteristic, complemented, Sylow
126#41—1164no—
127C2×Q8—581no—
128C2×D4—291no—
129C2×D4—581no—
130C2×D4—581no—
131C2×D4—581no—
132C2×D4—581no—
133C2×D4C2×#118111yescharacteristic
134C22×C4—21no—
135C22×C4—291no—
136C22×C4—291no—
137C22×C4—291no—
138C22×C4—582no—
139C22×C4—581no—
140C2×C8—582no—
141C4⋊C4—291no—
142C4⋊C4—581no—
143C4⋊C4C2×#118111yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—581no—
146C22⋊C4—581no—
147C22⋊C4—581no—
148C42—291no—
149C42—291no—
150C42—291no—
151C42—584no—
152C42C2×#118111yescharacteristic
153C23—21no—
154C23—291no—
155C23—581no—
156Q8—1162no—
157D4—41no—
158D4—1161no—
159D4—1162no—
160D4—1162no—
161D4—1162no—
162D4—1162no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—291no—
166C2×C4—291no—
167C2×C4—291no—
168C2×C4—582no—
169C2×C4—582no—
170C2×C4—584no—
171C2×C4—581no—
172C2×C4—1161no—
173C2×C4—1162no—
174C2×C4—1162no—
175C2×C4—1162no—
176C2×C4C22⋊#118111yescharacteristic
177C2×C4C22⋊#118111yescharacteristic
178C2×C4C22×#118111yescharacteristic
179C8—1162no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—292no—
184C22—581no—
185C22—581no—
186C22—1161no—
187C22—1161no—
188C22—1161no—
189C22C2×C22⋊#118111yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—41no—
194C4—292no—
195C4—581no—
196C4—581no—
197C4—1164no—
198C4—1161no—
199C2—81no—
200C2—582no—
201C2—2321no—
202C2#1427214211yescharacteristic
203C2#1427215511yescharacteristic
204C2D29⋊#10411yescharacteristic
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#1505
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. #14272186C2semidirect
2. #14272099C2semidirect
3. #14272015C2semidirect
4. #14272014C2semidirect
8. C4×D4×C29C4semidirect
9. #11745302C4semidirect
13. #11745250C4semidirect
16. C4×D116C4semidirect
117. C4×D4#1181semidirect
125. C29#1505semidirect

Maximal subgroups

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

subgroupindex
#142721862
#142720992
#142720152
#142720142
#142717102
#150529