Finite Group Databasebeta

← #16829735

Subgroups — #16829735

Order 3712.

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

normal subgroups only

This group has 418 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#14271768C211yesmaximal, characteristic, complemented
2#14271487C212yesmaximal, complemented
3#14271463C212yesmaximal, complemented
4#14271358C212yesmaximal, complemented
5#14271297C212yesmaximal, complemented
6#14271273C212yesmaximal, complemented
7C4×#90782C212yesmaximal, complemented
8#14271224C211yesmaximal, characteristic, complemented
9C29×#518C211yesmaximal, characteristic, complemented
10C22×D4×C29C2211yescharacteristic
11C4×D4×C29—22no—
12C4×D4×C29C2212yes—
13C4×D4×C29C2212yes—
14C29×#117C2211yescharacteristic
15C29×#117C2211yescharacteristic
16C2×C22⋊C4×C29—22no—
17C2×#90782C2212yes—
18C2×#90782C2212yes—
19#11745292C2212yes—
20#11745256—22no—
21#11745246—22no—
22#11745236C2211yescharacteristic, complemented
23C4×D116C2212yescomplemented
24#11745232C2211yescharacteristic, complemented
25#11745180C2212yes—
26#11745180C2212yes—
27C22⋊#6597C2212yes—
28#11745157C2212yescomplemented
29#11745157C2212yescomplemented
30#11745156C2212yescomplemented
31#11745155C2212yescomplemented
32C4⋊#6597C2212yescomplemented
33#11745151C2211yescharacteristic, complemented
34C4×#6597C2211yescharacteristic, complemented
35C24×C29—21no—
36C2×D4×C29—24no—
37C2×D4×C29—21no—
38C2×D4×C29C2312yes—
39C22×C4×C29—22no—
40C22×C4×C29—22no—
41C22×C4×C29C2311yescharacteristic
42C2×C22⋊D29—22no—
43C2×D116—22no—
44C2×D116C2312yes—
45C2×C4×D29—22no—
46C4⋊C4×C29D412yes—
47C4⋊C4×C29C2312yes—
48C22⋊C4×C29—21no—
49C22⋊C4×C29—22no—
50C22⋊C4×C29—22no—
51C22⋊C4×C29D412yes—
52C42×C29—21no—
53C42×C29C2311yescharacteristic
54C42×C29C2311yescharacteristic
55#90782—24no—
56#90782—24no—
57#90781—22no—
58#90781—22no—
59C4⋊Dic29C2312yes—
60#90779—22no—
61C2×#6597C2312yes—
62C2×#6597C2312yes—
63C23×C29—24no—
64C23×C29—22no—
65C23×C29—82no—
66C23×C29C2×D411yescharacteristic
67C22×D29—22no—
68D4×C29—24no—
69D4×C29—22no—
70D4×C29#4114yes—
71C2×C4×C29—22no—
72C2×C4×C29—22no—
73C2×C4×C29—82no—
74C2×C4×C29—82no—
75C2×C4×C29C2×D412yes—
76C2×C4×C29C2×D411yescharacteristic
77C2×C4×C29C2×D412yes—
78C2×C4×C29C2411yescharacteristic
79C22⋊D29—82no—
80C2×Dic29—22no—
81D116—22no—
82D116—22no—
83D116—82no—
84C4×D29—82no—
85#6597—22no—
86#6597—22no—
87#3122—291nomaximal, Sylow
88C22×C29—21no—
89C22×C29—24no—
90C22×C29—22no—
91C22×C29—42no—
92C22×C29—42no—
93C22×C29—84no—
94C22×C29C22×D411yescharacteristic
95C2×D29—42no—
96C2×D29—42no—
97C2×D29—42no—
98C4×C29—21no—
99C4×C29—22no—
100C4×C29—22no—
101C4×C29—42no—
102C4×C29C2×#4112yes—
103Dic29—42no—
104#540—291no—
105#518D2911yescharacteristic, complemented
106#482—292no—
107#478—292no—
108#459—292no—
109#447—292no—
110#442—292no—
111C4×D8—292no—
112#433—291no—
113C2×C29—41no—
114C2×C29—44no—
115C2×C29#52511yescharacteristic
116C2×C29#57612yes—
117D29—82no—
118C22×D4C2×D2911yescharacteristic
119C2×D8—292no—
120C2×D8—292no—
121#127—291no—
122#125—291no—
123#123—582no—
124#121—292no—
125#121—582no—
126C4×D4—22no—
127C4×D4—292no—
128C4×D4C2×D2912yes—
129C4×D4C2×D2912yes—
130#117C2×D2911yescharacteristic
131#117C2×D2911yescharacteristic
132C2×C22⋊C4—22no—
133#107—292no—
134#106—292no—
135C4⋊C8—292no—
136#102—292no—
137#102—292no—
138#102—292no—
139#102—292no—
140C22⋊C8—292no—
141#97—291no—
142C4×C8—291no—
143C29#312211yescharacteristic, complemented, Sylow
144C24—21no—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—292no—
148C2×D4—582no—
149C2×D4—582no—
150C2×D4C22×D2912yes—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—582no—
154C22×C4C22×D2911yescharacteristic
155D8—584no—
156D8—584no—
157C2×C8—292no—
158C2×C8—292no—
159C4⋊C4—292no—
160C4⋊C4—582no—
161C4⋊C4C22⋊D2912yes—
162C4⋊C4C22×D2912yes—
163C22⋊C4—21no—
164C22⋊C4—22no—
165C22⋊C4—22no—
166C22⋊C4—582no—
167C22⋊C4—582no—
168C22⋊C4C22⋊D2912yes—
169C42—21no—
170C42C22×D2911yescharacteristic
171C42C22×D2911yescharacteristic
172C23—24no—
173C23—22no—
174C23—82no—
175C23—582no—
176C23C2×C22⋊D2911yescharacteristic
177D4—24no—
178D4—22no—
179D4—582no—
180D4—582no—
181D4—2322no—
182D4—2322no—
183D4#9080514yes—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—582no—
189C2×C4—2322no—
190C2×C4C2×C22⋊D2911yescharacteristic
191C2×C4C2×C22⋊D2912yes—
192C2×C4C2×C22⋊D2912yes—
193C2×C4C23×D2911yescharacteristic
194C8—582no—
195C8—582no—
196C22—21no—
197C22—24no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—84no—
202C22—1162no—
203C22—1162no—
204C22—1162no—
205C22C22×C22⋊D2911yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—1162no—
211C4C2×#9080512yes—
212C2—41no—
213C2—44no—
214C2—2322no—
215C2#1427167411yescharacteristic
216C2#1427196612yes—
subgroupG/H
centerC22C22×C22⋊D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#518C2
socleC22×C29C22×D4
hypercenter#518D29
hypocenterC29#3122
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #14271768C2semidirect
2. #14271487C2semidirect
3. #14271463C2semidirect
4. #14271358C2semidirect
5. #14271297C2semidirect
6. #14271273C2semidirect
7. C4×#90782C2semidirect
8. #14271224C2semidirect
9. C29×#518C2semidirect
22. #11745236C22semidirect
23. C4×D116C22semidirect
24. #11745232C22semidirect
28. #11745157C22semidirect
29. #11745157C22semidirect
30. #11745156C22semidirect
31. #11745155C22semidirect
32. C4⋊#6597C22semidirect
33. #11745151C22semidirect
34. C4×#6597C22semidirect
105. #518D29semidirect
143. C29#3122semidirect

Maximal subgroups

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

subgroupindex
#142717682
#142714872
#142714632
#142713582
#142712972
#142712732
C4×#907822
#142712242
C29×#5182
#312229