Finite Group Databasebeta

← #16829097

Subgroups — #16829097

Order 3712.

500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#90772C211yesmaximal, characteristic, complemented
2#14271670C212yesmaximal, complemented
3#14271418C212yesmaximal, complemented
4#14271413C212yesmaximal, complemented
5#14271406C214yesmaximal, complemented
6#14271201C211yesmaximal, characteristic, complemented
7#14271159C212yesmaximal, complemented
8C2×C29×#135C211yesmaximal, characteristic, complemented
9C2×#41×C29C2212yes—
10C22×C4×D29C2211yescharacteristic
11C29×#135—24no—
12C2×Q16×C29C2211yescharacteristic, complemented
13C2×SD16×C29C2212yescomplemented
14C2×D8×C29C2211yescharacteristic, complemented
15C22×C8×C29C2211yescharacteristic
16#11745308C2214yes—
17#11745300C2214yes—
18#11745299—22no—
19#11745297—22no—
20C4×C22⋊D29—24no—
21#11745288C2212yes—
22C22×#6597C2211yescharacteristic
23C2×#90772—24no—
24C2×#90772C2212yes—
25C2×#90772C2212yes—
26#11745183C2214yescomplemented
27#11745180C2214yescomplemented
28#11745166C2212yescomplemented
29#11745165C2212yescomplemented
30C23×D29D411yescharacteristic
31#41×C29—24no—
32#41×C29—24no—
33C2×Q8×C29C2312yes—
34C2×D4×C29—22no—
35C2×D4×C29C2312yes—
36C22×C4×C29—22no—
37C22×C4×C29C2311yescharacteristic
38C2×C22⋊D29—24no—
39C22×Dic29D411yescharacteristic
40C2×C4×D29—22no—
41C2×C4×D29—22no—
42C2×C4×D29D412yes—
43C2×C4×D29C2312yes—
44Q16×C29—22no—
45SD16×C29—24no—
46D8×C29—22no—
47C2×C8×C29D414yescomplemented
48C2×C8×C29C2311yescharacteristic
49C2×C8×C29C2311yescharacteristic
50C22⋊Dic29—22no—
51C22⋊Dic29—24no—
52#90781—24no—
53C4⋊Dic29C2314yes—
54#90779—24no—
55C4×Dic29—22no—
56C2×#6597—22no—
57C2×#6597C2312yes—
58#90772—24no—
59#90772—24no—
60C23×C29—22no—
61C23×C29C2×D411yescharacteristic
62C22×D29—22no—
63C22×D29—42no—
64C22×D29C2×D412yes—
65Q8×C29—22no—
66Q8×C29—22no—
67D4×C29—22no—
68D4×C29—22no—
69D4×C29—44no—
70C2×C4×C29—22no—
71C2×C4×C29—44no—
72C2×C4×C29C2×D411yescharacteristic
73C2×C4×C29C2×D412yes—
74C2×C4×C29#4112yes—
75C2×C4×C29C2411yescharacteristic
76C22⋊D29—48no—
77C2×Dic29—22no—
78C2×Dic29—24no—
79C2×Dic29C2×D412yes—
80C4×D29—24no—
81C4×D29—22no—
82C4×D29—22no—
83C8×C29C2×D412yes—
84C8×C29C2×D412yes—
85#6597—22no—
86#3054—291nomaximal, Sylow
87C22×C29—22no—
88C22×C29—42no—
89C22×C29—44no—
90C22×C29#12112yes—
91C22×C29C22×D411yescharacteristic
92C2×D29—22no—
93C2×D29—24no—
94C2×D29—44no—
95C4×C29—42no—
96C4×C29#12112yes—
97C4×C29C22×D411yescharacteristic
98C4×C29C2×#4111yescharacteristic
99Dic29—22no—
100Dic29—44no—
101C2×#135D2911yescharacteristic, complemented
102C22×M16—291no—
103#525—292no—
104#470—292no—
105#469—292no—
106#468—294no—
107#427—291no—
108#416—292no—
109C2×C29—22no—
110C2×C29—82no—
111C2×C29C2×#12111yescharacteristic
112C2×C29#57512yes—
113D29—42no—
114C2×#41C2×D2912yes—
115C23×C4—291no—
116#135—24no—
117C2×Q16C2×D2911yescharacteristic, complemented
118C2×SD16C2×D2912yescomplemented
119C2×D8C2×D2911yescharacteristic, complemented
120C2×M16—292no—
121C2×M16—292no—
122C2×M16—584no—
123C22×C8—291no—
124C22×C8C2×D2911yescharacteristic
125#123—582no—
126C22⋊Q8—294no—
127#121—294no—
128#120—582no—
129C4×D4—584no—
130#117—292no—
131#107—292no—
132#106—292no—
133#103—294no—
134#102—294no—
135C29#305411yescharacteristic, complemented, Sylow
136C24—291no—
137#41—24no—
138#41—24no—
139C2×Q8C22×D2912yes—
140C2×D4—22no—
141C2×D4—584no—
142C2×D4C22×D2912yes—
143C22×C4—22no—
144C22×C4—291no—
145C22×C4—292no—
146C22×C4—292no—
147C22×C4—582no—
148C22×C4—582no—
149C22×C4C22×D2911yescharacteristic
150Q16—22no—
151SD16—24no—
152D8—22no—
153M16—584no—
154M16—584no—
155C2×C8—292no—
156C2×C8—582no—
157C2×C8C22⋊D2914yescomplemented
158C2×C8C22×D2911yescharacteristic
159C2×C8C22×D2911yescharacteristic
160C4⋊C4—294no—
161C4⋊C4—584no—
162C22⋊C4—584no—
163C22⋊C4—584no—
164C22⋊C4—582no—
165C42—582no—
166C23—22no—
167C23—292no—
168C23—582no—
169C23—1162no—
170C23D4×D2911yescharacteristic
171Q8—22no—
172Q8—22no—
173D4—22no—
174D4—22no—
175D4—44no—
176D4—1168no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—292no—
180C2×C4—582no—
181C2×C4—584no—
182C2×C4—582no—
183C2×C4—582no—
184C2×C4—584no—
185C2×C4D4×D2911yescharacteristic
186C2×C4#9080712yes—
187C2×C4C2×C22⋊D2912yes—
188C2×C4C23×D2911yescharacteristic
189C8—582no—
190C8C2×C22⋊D2912yes—
191C8C2×C22⋊D2912yes—
192C22—22no—
193C22—42no—
194C22—44no—
195C22—582no—
196C22—584no—
197C22—1164no—
198C22#1174530012yes—
199C22C2×D4×D2911yescharacteristic
200C4—42no—
201C4—582no—
202C4—1164no—
203C4#1174530012yes—
204C4C2×#9080711yescharacteristic
205C4C22×C22⋊D2911yescharacteristic
206C2—22no—
207C2—82no—
208C2—1162no—
209C2C2×#1174530011yescharacteristic
210C2#1427196012yes—
subgroupG/H
centerC2×C4D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#135C2
socleC22×C29C22×D4
hypercenterC2×#135D29
hypocenterC29#3054
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C22×#90772C2semidirect
2. #14271670C2semidirect
3. #14271418C2semidirect
4. #14271413C2semidirect
5. #14271406C2semidirect
6. #14271201C2semidirect
7. #14271159C2semidirect
8. C2×C29×#135C2semidirect
12. C2×Q16×C29C22semidirect
13. C2×SD16×C29C22semidirect
14. C2×D8×C29C22semidirect
26. #11745183C22semidirect
27. #11745180C22semidirect
28. #11745166C22semidirect
29. #11745165C22semidirect
47. C2×C8×C29D4semidirect
101. C2×#135D29semidirect
117. C2×Q16C2×D29semidirect
118. C2×SD16C2×D29semidirect
119. C2×D8C2×D29semidirect
135. C29#3054semidirect
157. C2×C8C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
C22×#907722
#142716702
#142714182
#142714132
#142714062
#142712012
#142711592
C2×C29×#1352
#305429