Finite Group Databasebeta

← #16829102

Subgroups — #16829102

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
1C2×#11745266C211yesmaximal, characteristic, complemented
2C22×#90772C211yesmaximal, characteristic, complemented
3#14271675C212yesmaximal, complemented
4#14271422C212yesmaximal, complemented
5#14271417C212yesmaximal, complemented
6#14271410C214yesmaximal, complemented
7#14271157C212yesmaximal, complemented
8C29×#427C211yesmaximal, characteristic, complemented
9C2×#90805C2212yes—
10C22×C4×D29C2211yescharacteristic
11C22×C8×C29C2211yescharacteristic
12C29×#117C2212yes—
13C22×#6597C2211yescharacteristic
14C2×Dic116C2211yescharacteristic, complemented
15#11745266—24no—
16C2×D232C2211yescharacteristic, complemented
17C2×#90773C2212yescomplemented
18C2×#90772—24no—
19C2×#90772C2212yes—
20C2×#90772C2212yes—
21#11745259C2214yes—
22#11745257C2214yes—
23#11745248—22no—
24#11745244—22no—
25C4×D116—24no—
26C29×#107C2212yescomplemented
27C29×#106C2212yescomplemented
28#11745158C2214yescomplemented
29#11745157C2214yescomplemented
30C23×D29D411yescharacteristic
31C22×C4×C29C2311yescharacteristic
32C2×C22⋊D29—22no—
33C22×Dic29D411yescharacteristic
34#90805—24no—
35#90805—24no—
36C2×D116—24no—
37C2×D116C2312yes—
38C2×C4×D29—22no—
39C2×C4×D29—22no—
40C2×C4×D29—22no—
41C2×C4×D29D412yes—
42C2×C4×D29C2312yes—
43C2×Dic58C2312yes—
44C2×C8×C29D414yescomplemented
45C2×C8×C29C2311yescharacteristic
46C2×C8×C29C2311yescharacteristic
47C4⋊C4×C29C2314yes—
48C22⋊C4×C29—22no—
49C42×C29—22no—
50#90781—24no—
51#90781—24no—
52C4⋊Dic29—24no—
53C2×#6597—22no—
54C2×#6597C2312yes—
55Dic116—22no—
56D232—22no—
57#90773—24no—
58#90772—24no—
59#90772—24no—
60C23×C29C2×D411yescharacteristic
61C22×D29—22no—
62C22×D29—22no—
63C22×D29—42no—
64C22×D29C2×D412yes—
65C2×C4×C29—24no—
66C2×C4×C29C2×D412yes—
67C2×C4×C29C2×D411yescharacteristic
68C2×C4×C29#4112yes—
69C2×C4×C29C2411yescharacteristic
70C22⋊D29—44no—
71C2×Dic29—22no—
72C2×Dic29—22no—
73C2×Dic29C2×D412yes—
74D116—22no—
75D116—22no—
76D116—48no—
77C4×D29—24no—
78C4×D29—22no—
79C4×D29—22no—
80C4×D29—44no—
81Dic58—22no—
82Dic58—22no—
83C8×C29C2×D412yes—
84C8×C29C2×D412yes—
85#6597—22no—
86#3054—291nomaximal, Sylow
87C22×C29—22no—
88C22×C29#12112yes—
89C22×C29C22×D411yescharacteristic
90C2×D29—22no—
91C2×D29—24no—
92C2×D29—44no—
93C2×D29—42no—
94C2×D29—44no—
95C4×C29—44no—
96C4×C29#12112yes—
97C4×C29C22×D411yescharacteristic
98C4×C29C2×#4111yescharacteristic
99Dic29—22no—
100Dic29—42no—
101C2×#135—291no—
102C22×M16—291no—
103#525—292no—
104#470—292no—
105#469—292no—
106#468—294no—
107#427D2911yescharacteristic, complemented
108#416—292no—
109C2×C29—22no—
110C2×C29C2×#12111yescharacteristic
111C2×C29#57512yes—
112D29—42no—
113D29—82no—
114C2×#41—292no—
115C23×C4—291no—
116#135—584no—
117C2×Q16—291no—
118C2×SD16—292no—
119C2×D8—291no—
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#117C2×D2912yes—
131#107C2×D2912yescomplemented
132#106C2×D2912yescomplemented
133#103—294no—
134#102—294no—
135C29#305411yescharacteristic, complemented, Sylow
136C24—291no—
137#41—584no—
138#41—584no—
139C2×Q8—292no—
140C2×D4—292no—
141C2×D4—584no—
142C2×D4—582no—
143C22×C4—291no—
144C22×C4—292no—
145C22×C4—292no—
146C22×C4—582no—
147C22×C4—582no—
148C22×C4—582no—
149C22×C4C22×D2911yescharacteristic
150Q16—582no—
151SD16—584no—
152D8—582no—
153M16—584no—
154M16—584no—
155C2×C8—292no—
156C2×C8—582no—
157C2×C8D11614yescomplemented
158C2×C8C22×D2911yescharacteristic
159C2×C8C22×D2911yescharacteristic
160C4⋊C4—584no—
161C4⋊C4C22×D2914yes—
162C22⋊C4—22no—
163C22⋊C4—584no—
164C22⋊C4—584no—
165C42—22no—
166C23—292no—
167C23—582no—
168C23—582no—
169C23—1162no—
170C23D4×D2911yescharacteristic
171Q8—582no—
172Q8—582no—
173D4—582no—
174D4—582no—
175D4—1168no—
176D4—1164no—
177C2×C4—24no—
178C2×C4—292no—
179C2×C4—582no—
180C2×C4—582no—
181C2×C4—582no—
182C2×C4—584no—
183C2×C4—582no—
184C2×C4—1164no—
185C2×C4C2×D11612yes—
186C2×C4D4×D2911yescharacteristic
187C2×C4#9080912yes—
188C2×C4C23×D2911yescharacteristic
189C8—582no—
190C8C2×D11612yes—
191C8C2×D11612yes—
192C22—22no—
193C22—582no—
194C22—584no—
195C22—1164no—
196C22—1162no—
197C22—1164no—
198C22#1174525712yes—
199C22C2×D4×D2911yescharacteristic
200C4—44no—
201C4—582no—
202C4—1162no—
203C4#1174525712yes—
204C4C22×D11611yescharacteristic
205C4C2×#9080911yescharacteristic
206C2—22no—
207C2—1162no—
208C2—2322no—
209C2C2×#1174525711yescharacteristic
210C2#1427196012yes—
subgroupG/H
centerC2×C4D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#427C2
socleC22×C29C22×D4
hypercenter#427D29
hypocenterC29#3054
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #427

Complements

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

NH ≅ G/Ntype
1. C2×#11745266C2semidirect
2. C22×#90772C2semidirect
3. #14271675C2semidirect
4. #14271422C2semidirect
5. #14271417C2semidirect
6. #14271410C2semidirect
7. #14271157C2semidirect
8. C29×#427C2semidirect
14. C2×Dic116C22semidirect
16. C2×D232C22semidirect
17. C2×#90773C22semidirect
26. C29×#107C22semidirect
27. C29×#106C22semidirect
28. #11745158C22semidirect
29. #11745157C22semidirect
44. C2×C8×C29D4semidirect
107. #427D29semidirect
131. #107C2×D29semidirect
132. #106C2×D29semidirect
135. C29#3054semidirect
157. C2×C8D116semidirect

Maximal subgroups

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

subgroupindex
C2×#117452662
C22×#907722
#142716752
#142714222
#142714172
#142714102
#142711572
C29×#4272
#305429