Finite Group Databasebeta

← #16829811

Subgroups — #16829811

Order 3712.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#14271718C211yesmaximal, characteristic, complemented
2#14271711C211yesmaximal, characteristic
3#14271516C214yesmaximal, complemented
4#14271515C211yesmaximal, characteristic, complemented
5#14271514C211yesmaximal, characteristic, complemented
6#14271509C211yesmaximal, characteristic, complemented
7#14271156C214yesmaximal, complemented
8C4×C8×D29C211yesmaximal, characteristic, complemented
9C29×#486C211yesmaximal, characteristic, complemented
10C2×#90807C2212yes—
11C29×C4⋊Q8C2211yescharacteristic
12C29×#127C2211yescharacteristic
13#11745308—21no—
14Q8×Dic29—21no—
15#11745300—21no—
16#11745300—21no—
17#11745298C2212yes—
18D4×Dic29—21no—
19D4×Dic29—21no—
20C2×C8×D29C2212yes—
21#11745259—21no—
22#11745254C2212yes—
23#11745252C2212yes—
24#11745249—21no—
25C42×D29C2211yescharacteristic
26#11745231C2211yescharacteristic
27#11745231C2211yescharacteristic
28C29×#102C2214yes—
29C4×C8×C29C2211yescharacteristic
30#11745180C2214yes—
31#11745164C2214yes—
32C8×Dic29C2212yes—
33#11745158C2214yes—
34C4×#6597C2211yescharacteristic
35C2×Q8×C29—21no—
36C2×D4×C29—21no—
37C2×D4×C29—21no—
38C2×D4×C29C2312yes—
39C2×C22⋊D29—22no—
40C22×Dic29—22no—
41#90807—28no—
42C2×C4×D29D411yescharacteristic
43C2×C4×D29D411yescharacteristic
44C2×C4×D29C2311yescharacteristic
45C2×Dic58—21no—
46C2×Dic58C2312yes—
47C2×C8×C29C2312yes—
48C4⋊C4×C29—21no—
49C4⋊C4×C29C2312yes—
50C42×C29C2311yescharacteristic
51C22⋊Dic29—22no—
52C22⋊Dic29—22no—
53#90781—22no—
54C4⋊Dic29—21no—
55C4⋊Dic29—21no—
56C4⋊Dic29—21no—
57C4⋊Dic29—22no—
58C4⋊Dic29C2312yes—
59#90779—22no—
60C4×Dic29—22no—
61C4×Dic29D411yescharacteristic
62C4×Dic29D411yescharacteristic
63C4×Dic29C2311yescharacteristic
64C2×#6597C2312yes—
65C8×D29—24no—
66C23×C29—22no—
67C22×D29C2×D411yescharacteristic
68Q8×C29—42no—
69D4×C29—24no—
70D4×C29—42no—
71D4×C29—42no—
72C2×C4×C29—22no—
73C2×C4×C29C2×D411yescharacteristic
74C2×C4×C29C2×D411yescharacteristic
75C2×C4×C29C2411yescharacteristic
76C22⋊D29—44no—
77C2×Dic29—22no—
78C2×Dic29—22no—
79C2×Dic29—44no—
80C2×Dic29C2×D411yescharacteristic
81C2×Dic29C2×D411yescharacteristic
82C2×Dic29C2×D411yescharacteristic
83C4×D29—22no—
84C4×D29—22no—
85C4×D29#4114yes—
86Dic58—24no—
87Dic58—42no—
88C8×C29—22no—
89#6597—22no—
90#3131—291nomaximal, Sylow
91C22×C29—42no—
92C22×C29—42no—
93C22×C29—42no—
94C22×C29C22×D411yescharacteristic
95C2×D29—21no—
96C2×D29—21no—
97C2×D29#12412yes—
98C4×C29—42no—
99C4×C29#13512yes—
100C4×C29#13512yes—
101C4×C29C2×#4112yes—
102Dic29—21no—
103Dic29—21no—
104Dic29—42no—
105Dic29—42no—
106Dic29#12412yes—
107#533—291no—
108#532—291no—
109#488—294no—
110#487—291no—
111#487—291no—
112#486—291no—
113#486D2911yescharacteristic, complemented
114#416—294no—
115C2×C4×C8—291no—
116C2×C29—82no—
117C2×C29C2×#12411yescharacteristic
118C2×C29C2×#13511yescharacteristic
119C2×C29C2×#13511yescharacteristic
120D29—22no—
121C2×#41—292no—
122C22×C8—292no—
123C4⋊Q8—291no—
124C4⋊Q8—291no—
125C4⋊Q8C2×D2911yescharacteristic
126#127C2×D2911yescharacteristic
127#125—292no—
128#124—292no—
129C22⋊Q8—581no—
130C22⋊Q8—581no—
131#121—581no—
132#121—581no—
133C4×Q8—581no—
134C4×Q8—581no—
135C4×D4—581no—
136C4×D4—581no—
137#117—292no—
138C2×C42—291no—
139#103—294no—
140#103—294no—
141#102—294no—
142#102C2×D2914yes—
143C4×C8—292no—
144C4×C8—291no—
145C4×C8C2×D2911yescharacteristic
146C29#313111yescharacteristic, complemented, Sylow
147#41—588no—
148C2×Q8—21no—
149C2×Q8—292no—
150C2×Q8—581no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—582no—
154C2×D4C22×D2912yes—
155C22×C4—291no—
156C22×C4—291no—
157C22×C4—291no—
158C22×C4—582no—
159C2×C8—292no—
160C2×C8—584no—
161C2×C8C22×D2912yes—
162C4⋊C4—21no—
163C4⋊C4—292no—
164C4⋊C4—582no—
165C4⋊C4—582no—
166C4⋊C4—581no—
167C4⋊C4—581no—
168C4⋊C4—581no—
169C4⋊C4C22×D2912yes—
170C22⋊C4—582no—
171C22⋊C4—582no—
172C22⋊C4—582no—
173C42—291no—
174C42—291no—
175C42—291no—
176C42—582no—
177C42C22×D2911yescharacteristic
178C23—22no—
179C23—291no—
180Q8—42no—
181Q8—584no—
182Q8—1162no—
183D4—24no—
184D4—42no—
185D4—42no—
186D4—1164no—
187C2×C4—22no—
188C2×C4—291no—
189C2×C4—294no—
190C2×C4—291no—
191C2×C4—291no—
192C2×C4—582no—
193C2×C4—582no—
194C2×C4—582no—
195C2×C4—582no—
196C2×C4—1164no—
197C2×C4D4×D2911yescharacteristic
198C2×C4D4×D2911yescharacteristic
199C2×C4C23×D2911yescharacteristic
200C8—22no—
201C8—582no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—292no—
206C22—581no—
207C22—581no—
208C22C2×D4×D2911yescharacteristic
209C4—42no—
210C4—292no—
211C4—581no—
212C4—581no—
213C4—1162no—
214C4—1162no—
215C4#1174527412yes—
216C4#1174527812yes—
217C4#41×D2912yes—
218C2—82no—
219C2—582no—
220C2#124×D2911yescharacteristic
221C2C2×#1174527411yescharacteristic
222C2C2×#1174527811yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#486C2
socleC22×C29C22×D4
prime radical#14271711C2
hypercenter#486D29
hypocenterC29#3131
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #14271718C2semidirect
3. #14271516C2semidirect
4. #14271515C2semidirect
5. #14271514C2semidirect
6. #14271509C2semidirect
7. #14271156C2semidirect
8. C4×C8×D29C2semidirect
9. C29×#486C2semidirect
113. #486D29semidirect
146. C29#3131semidirect

Maximal subgroups

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

subgroupindex
#142717182
#142717112
#142715162
#142715152
#142715142
#142715092
#142711562
C4×C8×D292
C29×#4862
#313129