Finite Group Databasebeta

← #16834769

Subgroups — #16834769

Order 3712.

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

normal subgroups only

This group has 322 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
2D29⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
3#14272007C214yesmaximal, complemented
4C2×#11745257C211yesmaximal, characteristic
5C22×D116C412yes—
6C22×D116C411yescharacteristic
7C22×C4×D29C2211yescharacteristic
8C2×#90796—21no—
9C2×D29⋊C8—21no—
10C2×C4⋊C4×C29C411yescharacteristic
11C2×#90781C2212yes—
12#11745257—21no—
13#11745257—21no—
14#11745257—21no—
15#11745257—21no—
16C22⋊#6599C2212yes—
17C22⋊#6599C2212yes—
18#11745219—21no—
19#11745219—21no—
20C23×D29C2×C411yescharacteristic
21C23×D29C2×C412yes—
22C22×C4×C29C2×C412yes—
23C22×C4×C29C2×C411yescharacteristic
24C22×Dic29C2311yescharacteristic
25C2×D116—22no—
26C2×D116—22no—
27C2×D116—21no—
28C2×D116—21no—
29C2×D116—42no—
30C2×D116—44no—
31C2×C4×D29—42no—
32C2×C4×D29D411yescharacteristic
33C2×C4×D29D411yescharacteristic
34C2×C4×D29D411yescharacteristic
35C2×C4×D29D411yescharacteristic
36C2×#6599—22no—
37C2×#6599—22no—
38#90796—42no—
39D29⋊C8—42no—
40C4⋊C4×C29—21no—
41C4⋊C4×C29—21no—
42#90781—22no—
43#90781—22no—
44C23×C29C22×C411yescharacteristic
45C22×D29—22no—
46C22×D29—22no—
47C22×D29—22no—
48C22×D29—24no—
49C22×D29—41no—
50C22×D29—42no—
51C22×D29—42no—
52C22×D29C22⋊C411yescharacteristic
53C22×D29C22⋊C411yescharacteristic
54C2×C4×C29—22no—
55C2×C4×C29—22no—
56C2×C4×C29—42no—
57C2×C4×C29C22⋊C411yescharacteristic
58C2×C4×C29C22⋊C411yescharacteristic
59C2×Dic29—41no—
60C2×Dic29C2×D411yescharacteristic
61C2×Dic29C2×D411yescharacteristic
62D116—42no—
63D116—44no—
64D116—44no—
65D116—42no—
66C4×D29—22no—
67C4×D29—22no—
68C4×D29—41no—
69C4×D29—41no—
70#6599—42no—
71#6599—42no—
72#1471—291nomaximal, Sylow
73C22×C29—21no—
74C22×C29—21no—
75C22×C29C2×C22⋊C411yescharacteristic
76C22×C29#13112yes—
77C2×D29—21no—
78C2×D29—21no—
79C2×D29—21no—
80C2×D29—21no—
81C2×D29—21no—
82C2×D29—44no—
83C2×D29—42no—
84C2×D29—42no—
85C2×D29—42no—
86C2×D29—84no—
87C2×D29#10012yes—
88C4×C29—21no—
89C4×C29—42no—
90C4×C29#9912yes—
91Dic29—21no—
92Dic29—21no—
93C2×#121—291no—
94#407—291no—
95C2×C22⋊C8—291no—
96#323—294no—
97C2×C29—22no—
98C2×C29#40811yescharacteristic
99C2×C29C2×#9911yescharacteristic
100C2×C29C2×#10011yescharacteristic
101D29—22no—
102D29—41no—
103D29—82no—
104C22×D4—292no—
105C22×D4—291no—
106C23×C4—291no—
107C2×M16—581no—
108C22×C8—581no—
109#121—581no—
110#121—581no—
111#121—581no—
112#121—581no—
113C2×C4⋊C4#118111yescharacteristic
114C2×C22⋊C4—292no—
115C22⋊C8—292no—
116C22⋊C8—292no—
117C22⋊C8—581no—
118C22⋊C8—581no—
119C29#147111yescharacteristic, complemented, Sylow
120C24—291no—
121C24—292no—
122C2×D4—582no—
123C2×D4—582no—
124C2×D4—581no—
125C2×D4—581no—
126C2×D4—1162no—
127C2×D4—1164no—
128C22×C4—291no—
129C22×C4—291no—
130C22×C4—291no—
131C22×C4—291no—
132C22×C4—291no—
133C22×C4—1162no—
134C22×C4C2×#118112yes—
135C22×C4C2×#118111yescharacteristic
136M16—1162no—
137C2×C8—582no—
138C2×C8—582no—
139C2×C8—1162no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C22⋊C4—582no—
143C22⋊C4—582no—
144C23—291no—
145C23—291no—
146C23—582no—
147C23—582no—
148C23—582no—
149C23—584no—
150C23—1161no—
151C23—1162no—
152C23—1162no—
153C23C22×#118111yescharacteristic
154D4—1162no—
155D4—1164no—
156D4—1164no—
157D4—1162no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—42no—
161C2×C4—291no—
162C2×C4—291no—
163C2×C4—582no—
164C2×C4—582no—
165C2×C4—1161no—
166C2×C4—1161no—
167C2×C4—1161no—
168C2×C4C22⋊#118111yescharacteristic
169C2×C4C22⋊#118111yescharacteristic
170C8—1162no—
171C8—1162no—
172C22—21no—
173C22—21no—
174C22—292no—
175C22—581no—
176C22—581no—
177C22—581no—
178C22—581no—
179C22—581no—
180C22—1164no—
181C22—1162no—
182C22—1162no—
183C22—1162no—
184C22—2324no—
185C22#1174534812yes—
186C22C2×C22⋊#118111yescharacteristic
187C4—21no—
188C4—42no—
189C4—581no—
190C4—581no—
191C4#1174521512yes—
192C2—22no—
193C2—582no—
194C2—1161no—
195C2—2322no—
196C2#1427213811yescharacteristic
197C2C2×#1174521511yescharacteristic
198C2D29⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC2×C4⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC2×#11745257C2
cosocleC22×Dic29C23
hypercenterC2×C4⋊C4#1181
hypocenterC29#1471
LCSG ▷ C23×C29 ▷ C2×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. D29⋊(C22⋊C8)C2semidirect
3. #14272007C2semidirect
119. C29#1471semidirect

Maximal subgroups

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

subgroupindex
#142721342
D29⋊(C22⋊C8)2
#142720072
C2×#117452572
#147129