Finite Group Databasebeta

← #16834889

Subgroups — #16834889

Order 3712.

346 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 64 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#14272134C211yesmaximal, characteristic, complemented
2C4×C22⋊#1181C211yesmaximal, characteristic, complemented
3#14272015C214yesmaximal, complemented
4C2×#11745257C211yesmaximal, characteristic
5C22×D116—21no—
6C22×D116C411yescharacteristic, complemented
7C22×C4×D29C2211yescharacteristic
8C2×C22⋊#1181—21no—
9C2×C4×#1181—21no—
10C2×#90796—21no—
11C2×C4⋊C4×C29C411yescharacteristic, complemented
12C2×#90781—21no—
13#11745257—21no—
14#11745257—21no—
15#11745257C412yescomplemented
16#11745257C2212yes—
17C22⋊#6599—21no—
18(C2×#1181)⋊C4C2212yescomplemented
19#11745219C2212yescomplemented
20C23×D29—21no—
21C23×D29D411yescharacteristic
22C22×#1181—22no—
23C22×C4×C29—21no—
24C22×C4×C29C2×C411yescharacteristic
25C22×Dic29D411yescharacteristic
26C2×D116—22no—
27C2×D116—22no—
28C2×D116—21no—
29C2×D116—44no—
30C2×D116—42no—
31C2×D116C2×C412yes—
32C2×C4×D29—42no—
33C2×C4×D29C2×C411yescharacteristic
34C2×C4×D29D411yescharacteristic
35C2×C4×D29D411yescharacteristic
36C2×C4×D29C2311yescharacteristic
37C22⋊#1181—24no—
38C2×#6599—22no—
39C4×#1181—42no—
40#90796—42no—
41C4⋊C4×C29—21no—
42C4⋊C4×C29C2×C412yes—
43#90781—22no—
44#90781—22no—
45C23×C29C22⋊C411yescharacteristic
46C22×D29—22no—
47C22×D29—22no—
48C22×D29—22no—
49C22×D29—41no—
50C22×D29—42no—
51C22×D29—42no—
52C22×D29—42no—
53C22×D29C22⋊C411yescharacteristic
54C22×D29C2×D411yescharacteristic
55C2×#1181—24no—
56C2×#1181—42no—
57C2×#1181—42no—
58C2×C4×C29—22no—
59C2×C4×C29—22no—
60C2×C4×C29—42no—
61C2×C4×C29C22⋊C411yescharacteristic
62C2×C4×C29C22×C411yescharacteristic
63C2×Dic29—41no—
64C2×Dic29C22⋊C411yescharacteristic
65C2×Dic29C2×D411yescharacteristic
66D116—42no—
67D116—44no—
68D116—44no—
69D116—42no—
70C4×D29—22no—
71C4×D29—22no—
72C4×D29—41no—
73C4×D29—41no—
74#6599—42no—
75#1507—291nomaximal, Sylow
76C22×C29—21no—
77C22×C29—21no—
78C22×C29#10412yes—
79C22×C29C2×C22⋊C411yescharacteristic
80C2×D29—21no—
81C2×D29—21no—
82C2×D29—21no—
83C2×D29—21no—
84C2×D29—21no—
85C2×D29—44no—
86C2×D29—42no—
87C2×D29—42no—
88C2×D29—42no—
89C2×D29—84no—
90C2×D29AGL(1,ℤ/8)12yes—
91#1181—44no—
92C4×C29—21no—
93C4×C29—42no—
94C4×C29#9912yes—
95Dic29—21no—
96Dic29—21no—
97C2×#121—291no—
98#407—291no—
99C4×C22⋊C4—291no—
100#327—294no—
101C2×C29—22no—
102C2×C29C2×#9911yescharacteristic
103C2×C29#41811yescharacteristic
104C2×C29C2×#10411yescharacteristic
105D29—22no—
106D29—41no—
107D29—82no—
108C22×D4—291no—
109C22×D4—581no—
110C23×C4—291no—
111C2×M16—581no—
112#121—292no—
113#121—292no—
114#121—581no—
115#121—581no—
116C2×C4⋊C4#118111yescharacteristic, complemented
117C2×C22⋊C4—581no—
118C2×C22⋊C4—581no—
119C2×C42—581no—
120C22⋊C8—292no—
121C22⋊C8—581no—
122#95—292no—
123C29#150711yescharacteristic, complemented, Sylow
124C24—291no—
125C24—581no—
126C2×D4—292no—
127C2×D4—582no—
128C2×D4—582no—
129C2×D4—581no—
130C2×D4—1162no—
131C2×D4—1164no—
132C22×C4—21no—
133C22×C4—291no—
134C22×C4—291no—
135C22×C4—291no—
136C22×C4—291no—
137C22×C4—291no—
138C22×C4—582no—
139C22×C4—1162no—
140C22×C4C2×#118111yescharacteristic
141M16—1162no—
142C2×C8—582no—
143C4⋊C4—21no—
144C4⋊C4C2×#118112yes—
145C22⋊C4—582no—
146C22⋊C4—582no—
147C22⋊C4—584no—
148C42—1162no—
149C23—291no—
150C23—291no—
151C23—582no—
152C23—582no—
153C23—582no—
154C23—1161no—
155C23—1162no—
156C23—1162no—
157C23—1162no—
158C23C22⋊#118111yescharacteristic
159D4—1162no—
160D4—1164no—
161D4—1164no—
162D4—1162no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—42no—
166C2×C4—291no—
167C2×C4—291no—
168C2×C4—582no—
169C2×C4—582no—
170C2×C4—584no—
171C2×C4—1161no—
172C2×C4—1161no—
173C2×C4—1161no—
174C2×C4—1162no—
175C2×C4—1162no—
176C2×C4C22⋊#118111yescharacteristic
177C2×C4C22×#118111yescharacteristic
178C8—1162no—
179C22—21no—
180C22—21no—
181C22—292no—
182C22—581no—
183C22—581no—
184C22—581no—
185C22—581no—
186C22—581no—
187C22—1164no—
188C22—1162no—
189C22—1162no—
190C22—1162no—
191C22—2324no—
192C22#1174522612yes—
193C22C2×C22⋊#118111yescharacteristic
194C4—21no—
195C4—42no—
196C4—581no—
197C4—581no—
198C4—1164no—
199C4#1174521512yes—
200C2—22no—
201C2—582no—
202C2—1161no—
203C2—2322no—
204C2C2×#1174521511yescharacteristic
205C2#1427215511yescharacteristic
206C2C2×#1174522611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC2×C4⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC2×#11745257C2
cosocleC2×C4×D29C23
hypercenterC2×C4⋊C4#1181
hypocenterC29#1507
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #14272134C2semidirect
2. C4×C22⋊#1181C2semidirect
3. #14272015C2semidirect
6. C22×D116C4semidirect
11. C2×C4⋊C4×C29C4semidirect
15. #11745257C4semidirect
18. (C2×#1181)⋊C4C22semidirect
19. #11745219C22semidirect
116. C2×C4⋊C4#1181semidirect
123. C29#1507semidirect

Maximal subgroups

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

subgroupindex
#142721342
C4×C22⋊#11812
#142720152
C2×#117452572
#150729