Finite Group Databasebeta

← D29×#392 #16822686

Subgroups — D29×#392 #16822686

Order 3712.

1812 conjugacy classes of subgroups; only the 223 normal subgroups are shown.

normal subgroups only

This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 223 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×D4×D29C213yesmaximal, complemented
2C2×C22⋊C4×D29C213yesmaximal, complemented
3#14271073C211yesmaximal, characteristic, complemented
4#14271072C213yesmaximal, complemented
5#14271071C213yesmaximal, complemented
6#95×D29C211yesmaximal, characteristic, complemented
7C29×#392C211yesmaximal, characteristic, complemented
8C24×D29C2213yes—
9C22×D4×C29C2213yescomplemented
10C22×C22⋊D29C2216yescomplemented
11C2×D4×D29—224no—
12C2×D4×D29—212no—
13C22×D116C2213yescomplemented
14C22×C4×D29C2211yescharacteristic
15C22×C4×D29C2213yes—
16C2×C22⋊C4×C29C2213yescomplemented
17C2×C22⋊Dic29C2213yescomplemented
18C2×#90781C2213yescomplemented
19C2×#90781C2213yescomplemented
20C22⋊C4×D29—212no—
21C29×#95C2211yescharacteristic, complemented
22#11745179C2213yescomplemented
23C24×C29C2313yes—
24C23×D29—212no—
25C23×D29—212no—
26C23×D29—26no—
27C23×D29—26no—
28C23×D29D4112yescomplemented
29C23×D29C2313yes—
30C23×D29C2311yescharacteristic
31C2×D4×C29—212no—
32C2×D4×C29—26no—
33C22×C4×C29C2311yescharacteristic
34C22×C4×C29C2313yes—
35C2×C22⋊D29—212no—
36C2×C22⋊D29—212no—
37C2×C22⋊D29—212no—
38C22×Dic29C2311yescharacteristic
39C22×Dic29C2313yes—
40D4×D29—296no—
41C2×D116—212no—
42C2×D116—26no—
43C2×C4×D29—212no—
44C2×C4×D29—26no—
45C2×C4×D29D4112yescomplemented
46C22⋊C4×C29—26no—
47C22⋊Dic29—26no—
48#90781—26no—
49#90781—26no—
50C23×C29—23no—
51C23×C29—26no—
52C23×C29—26no—
53C23×C29—23no—
54C23×C29C2×D416yescomplemented
55C23×C29C2411yescharacteristic
56C22×D29—23no—
57C22×D29—26no—
58C22×D29—26no—
59C22×D29—23no—
60C22×D29—248no—
61C22×D29—224no—
62C22×D29—412no—
63C22×D29—424no—
64C22×D29—412no—
65C22×D29C2×D416yes—
66C22×D29C2×D416yes—
67C22×D29C2×D416yescomplemented
68C22×D29#4112yes—
69D4×C29—224no—
70C2×C4×C29—26no—
71C2×C4×C29—23no—
72C2×C4×C29C2×D416yescomplemented
73C22⋊D29—248no—
74C2×Dic29—26no—
75C2×Dic29—23no—
76C2×Dic29C2×D416yescomplemented
77D116—224no—
78C4×D29—224no—
79C4×D29—44no—
80C2×#392—291nomaximal, Sylow
81C22×C29—212no—
82C22×C29—26no—
83C22×C29—43no—
84C22×C29—46no—
85C22×C29—43no—
86C22×C29C22×D413yes—
87C22×C29C22×D413yes—
88C22×C29C2×#4111yescharacteristic
89C2×D29—212no—
90C2×D29—26no—
91C2×D29—43no—
92C2×D29—46no—
93C2×D29—43no—
94C2×D29—448no—
95C2×D29#120112yes—
96C2×D29#121112yes—
97C2×D29#12714yes—
98C4×C29—26no—
99C4×C29—41no—
100Dic29—26no—
101Dic29—41no—
102C23×D4—293no—
103C22×C22⋊C4—293no—
104#392—293no—
105#392—293no—
106#392—291no—
107#392D2911yescharacteristic, direct product factor
108C2×#95—291no—
109C2×C29—46no—
110C2×C29C2×#12013yes—
111C2×C29C2×#12113yes—
112C2×C29C2×#12711yescharacteristic
113D29—46no—
114D29#39218yesdirect product factor
115C25—293no—
116C22×D4—296no—
117C22×D4—293no—
118C22×D4—5812no—
119C22×D4—5824no—
120C22×D4C2×D2913yescomplemented
121C23×C4—293no—
122C23×C4—291no—
123C2×C22⋊C4—293no—
124C2×C22⋊C4—293no—
125C2×C22⋊C4—293no—
126C2×C22⋊C4—5812no—
127C2×C22⋊C4C2×D2913yescomplemented
128#95—293no—
129#95C2×D2911yescharacteristic, complemented
130C29C2×#39211yescharacteristic, complemented, Sylow
131C24—291no—
132C24—2912no—
133C24—293no—
134C24—586no—
135C24—5812no—
136C24—5812no—
137C24—586no—
138C24C22×D2913yes—
139C2×D4—212no—
140C2×D4—26no—
141C2×D4—5812no—
142C2×D4—5812no—
143C2×D4—5896no—
144C2×D4—5812no—
145C2×D4—5812no—
146C2×D4—586no—
147C22×C4—293no—
148C22×C4—2912no—
149C22×C4—291no—
150C22×C4—5812no—
151C22×C4—586no—
152C22×C4C22×D2911yescharacteristic
153C22×C4C22×D2913yes—
154C22⋊C4—26no—
155C22⋊C4—586no—
156C22⋊C4—586no—
157C22⋊C4—586no—
158C23—23no—
159C23—26no—
160C23—26no—
161C23—23no—
162C23—296no—
163C23—296no—
164C23—292no—
165C23—296no—
166C23—5848no—
167C23—5824no—
168C23—583no—
169C23—586no—
170C23—586no—
171C23—583no—
172C23—11612no—
173C23—11624no—
174C23—11612no—
175C23D4×D2916yescomplemented
176C23C23×D2911yescharacteristic
177D4—224no—
178D4—5824no—
179D4—5848no—
180C2×C4—26no—
181C2×C4—23no—
182C2×C4—296no—
183C2×C4—5824no—
184C2×C4—586no—
185C2×C4—583no—
186C2×C4—1164no—
187C2×C4D4×D2916yescomplemented
188C22—212no—
189C22—26no—
190C22—43no—
191C22—46no—
192C22—43no—
193C22—2912no—
194C22—2912no—
195C22—294no—
196C22—5812no—
197C22—586no—
198C22—11648no—
199C22—1163no—
200C22—1166no—
201C22—1163no—
202C22C2×D4×D2913yes—
203C22C2×D4×D2913yes—
204C22#41×D2911yescharacteristic
205C4—26no—
206C4—41no—
207C4—586no—
208C4—1161no—
209C2—46no—
210C2—298no—
211C2—1166no—
212C2#120×D2913yes—
213C2#121×D2913yes—
214C2#127×D2911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D29
commutator, socle, cosocleC23×C29C24
FittingC29×#392C2
hypercenter#392D29
hypocenterC29C2×#392
LCSG ▷ C23×C29 ▷ C29
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×D29C2semidirect
2. C2×C22⋊C4×D29C2semidirect
3. #14271073C2semidirect
4. #14271072C2semidirect
5. #14271071C2semidirect
6. #95×D29C2semidirect
7. C29×#392C2semidirect
9. C22×D4×C29C22semidirect
10. C22×C22⋊D29C22semidirect
13. C22×D116C22semidirect
16. C2×C22⋊C4×C29C22semidirect
17. C2×C22⋊Dic29C22semidirect
18. C2×#90781C22semidirect
19. C2×#90781C22semidirect
21. C29×#95C22semidirect
22. #11745179C22semidirect
28. C23×D29D4semidirect
45. C2×C4×D29D4semidirect
54. C23×C29C2×D4semidirect
67. C22×D29C2×D4semidirect
72. C2×C4×C29C2×D4semidirect
76. C2×Dic29C2×D4semidirect
107. #392D29direct (N × H)
114. D29#392direct (N × H)
120. C22×D4C2×D29semidirect
127. C2×C22⋊C4C2×D29semidirect
129. #95C2×D29semidirect
130. C29C2×#392semidirect
175. C23D4×D29semidirect
187. C2×C4D4×D29semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D292
C2×C22⋊C4×D292
#142710732
#142710722
#142710712
#95×D292
C29×#3922
C2×#39229