Finite Group Databasebeta

← #16829074

Subgroups — #16829074

Order 3712.

520 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 145 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×C8×D29C211yesmaximal, characteristic, complemented
3#14271675C212yesmaximal, complemented
4#14271405C212yesmaximal, complemented
5#14271400C212yesmaximal, complemented
6#14271393C214yesmaximal, 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×C8×D29—24no—
19C2×C8×D29C2212yes—
20C2×C8×D29C2212yes—
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—
58C8×D29—24no—
59C8×D29—24no—
60C23×C29C2×D411yescharacteristic
61C22×D29—22no—
62C22×D29—24no—
63C22×D29—22no—
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#3050—291nomaximal, Sylow
87C22×C29—22no—
88C22×C29#12112yes—
89C22×C29C22×D411yescharacteristic
90C2×D29—28no—
91C2×D29—22no—
92C2×D29—22no—
93C2×D29—42no—
94C2×D29—44no—
95C2×D29#13514yescomplemented
96C4×C29—44no—
97C4×C29#12112yes—
98C4×C29C22×D411yescharacteristic
99C4×C29C2×#4111yescharacteristic
100Dic29—22no—
101Dic29—42no—
102C2×#135—291no—
103C23×C8—291no—
104#525—292no—
105#467—292no—
106#466—292no—
107#465—294no—
108#427D2911yescharacteristic, complemented
109#416—292no—
110C2×C29—22no—
111C2×C29C2×#12111yescharacteristic
112C2×C29C2×#13512yes—
113D29—24no—
114D29—82no—
115C2×#41—292no—
116C23×C4—291no—
117#135—584no—
118C2×Q16—291no—
119C2×SD16—292no—
120C2×D8—291no—
121C22×C8—291no—
122C22×C8—292no—
123C22×C8—292no—
124C22×C8—584no—
125C22×C8C2×D2911yescharacteristic
126#123—582no—
127C22⋊Q8—294no—
128#121—294no—
129#120—582no—
130C4×D4—584no—
131#117C2×D2912yes—
132#107C2×D2912yescomplemented
133#106C2×D2912yescomplemented
134#103—294no—
135#102—294no—
136C29#305011yescharacteristic, complemented, Sylow
137C24—291no—
138#41—584no—
139#41—584no—
140C2×Q8—292no—
141C2×D4—292no—
142C2×D4—584no—
143C2×D4—582no—
144C22×C4—291no—
145C22×C4—292no—
146C22×C4—292no—
147C22×C4—582no—
148C22×C4—582no—
149C22×C4—582no—
150C22×C4C22×D2911yescharacteristic
151Q16—582no—
152SD16—584no—
153D8—582no—
154C2×C8—292no—
155C2×C8—582no—
156C2×C8—584no—
157C2×C8—584no—
158C2×C8D11614yescomplemented
159C2×C8C22×D2911yescharacteristic
160C2×C8C22×D2911yescharacteristic
161C4⋊C4—584no—
162C4⋊C4C22×D2914yes—
163C22⋊C4—22no—
164C22⋊C4—584no—
165C22⋊C4—584no—
166C42—22no—
167C23—292no—
168C23—584no—
169C23—582no—
170C23—582no—
171C23D4×D2911yescharacteristic
172Q8—582no—
173Q8—582no—
174D4—582no—
175D4—582no—
176D4—1168no—
177D4—1164no—
178C2×C4—24no—
179C2×C4—292no—
180C2×C4—582no—
181C2×C4—582no—
182C2×C4—582no—
183C2×C4—584no—
184C2×C4—582no—
185C2×C4—1164no—
186C2×C4C2×D11612yes—
187C2×C4D4×D2911yescharacteristic
188C2×C4#9080912yes—
189C2×C4C23×D2911yescharacteristic
190C8—582no—
191C8C2×D11612yes—
192C8C2×D11612yes—
193C22—22no—
194C22—294no—
195C22—588no—
196C22—582no—
197C22—582no—
198C22—1162no—
199C22—1164no—
200C22#1174525712yes—
201C22C2×D4×D2911yescharacteristic
202C4—44no—
203C4—582no—
204C4—1162no—
205C4#1174525712yes—
206C4C22×D11611yescharacteristic
207C4C2×#9080911yescharacteristic
208C2—22no—
209C2—584no—
210C2—2322no—
211C2C2×#1174525711yescharacteristic
212C2#135×D2912yes—
subgroupG/H
centerC2×C4D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#427C2
socleC22×C29C22×D4
hypercenter#427D29
hypocenterC29#3050
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×C8×D29C2semidirect
3. #14271675C2semidirect
4. #14271405C2semidirect
5. #14271400C2semidirect
6. #14271393C2semidirect
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
95. C2×D29#135semidirect
108. #427D29semidirect
132. #107C2×D29semidirect
133. #106C2×D29semidirect
136. C29#3050semidirect
158. 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×C8×D292
#142716752
#142714052
#142714002
#142713932
#142711572
C29×#4272
#305029