Finite Group Databasebeta

← C29×#8743 #20303643

Subgroups — C29×#8743 #20303643

Order 7424.

450 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C29×#2296C211yesmaximal, characteristic
2C29×#1464C212yesmaximal
3C29×#1285C214yesmaximal, complemented
4C2×C29×#117C411yescharacteristic
5C2×C29×#117C2211yescharacteristic
6C22×C42×C29C411yescharacteristic
7C29×#432C2214yes—
8C29×#389—22no—
9C29×#385—22no—
10C4×C4⋊C4×C29C412yes—
11C4×C4⋊C4×C29C2212yes—
12C29×#324—22no—
13C29×#323—22no—
14C23×C4×C29—21no—
15C23×C4×C29C2×C411yescharacteristic
16C29×#117—24no—
17C29×#117—42no—
18C2×C4⋊C4×C29—21no—
19C2×C4⋊C4×C29—22no—
20C2×C4⋊C4×C29—22no—
21C2×C4⋊C4×C29D412yes—
22C2×C22⋊C4×C29—21no—
23C2×C22⋊C4×C29D412yes—
24C2×C42×C29—21no—
25C2×C42×C29—42no—
26C2×C42×C29C2×C411yescharacteristic
27C2×C42×C29C2×C412yes—
28C2×C42×C29C2×C412yes—
29C2×C42×C29C2311yescharacteristic
30C29×C4⋊C8—24no—
31C29×C22⋊C8—24no—
32C29×#97—24no—
33C29×#95—22no—
34C29×#95—22no—
35C24×C29C22⋊C411yescharacteristic
36C22×C4×C29—22no—
37C22×C4×C29—22no—
38C22×C4×C29—22no—
39C22×C4×C29—22no—
40C22×C4×C29—22no—
41C22×C4×C29—44no—
42C22×C4×C29—42no—
43C22×C4×C29C22⋊C411yescharacteristic
44C22×C4×C29C22⋊C412yes—
45C22×C4×C29C22×C411yescharacteristic
46C22×C4×C29C2×D412yes—
47C2×C8×C29—44no—
48C4⋊C4×C29—24no—
49C4⋊C4×C29—44no—
50C4⋊C4×C29—44no—
51C4⋊C4×C29—42no—
52C22⋊C4×C29—24no—
53C22⋊C4×C29—42no—
54C42×C29—22no—
55C42×C29—42no—
56C42×C29—42no—
57C42×C29—42no—
58C42×C29#4114yes—
59#8743C2911yesmaximal, characteristic, direct product factor, Sylow
60C23×C29—21no—
61C23×C29—21no—
62C23×C29—42no—
63C23×C29#10112yes—
64C23×C29C2×C22⋊C411yescharacteristic
65C2×C4×C29—28no—
66C2×C4×C29—21no—
67C2×C4×C29—21no—
68C2×C4×C29—21no—
69C2×C4×C29—21no—
70C2×C4×C29—24no—
71C2×C4×C29—22no—
72C2×C4×C29—42no—
73C2×C4×C29—42no—
74C2×C4×C29—48no—
75C2×C4×C29—42no—
76C2×C4×C29—42no—
77C2×C4×C29—42no—
78C2×C4×C29—42no—
79C2×C4×C29—42no—
80C2×C4×C29#10012yes—
81C2×C4×C29#11712yes—
82C2×C4×C29#12314yes—
83C8×C29—84no—
84#2296C2×C2911yescharacteristic
85#1464C2×C2912yes—
86#1285C2×C2914yescomplemented
87C22×C29—22no—
88C22×C29—22no—
89C22×C29—42no—
90C22×C29—42no—
91C22×C29—42no—
92C22×C29#38111yescharacteristic
93C22×C29C2×#10011yescharacteristic
94C22×C29C2×#10111yescharacteristic
95C4×C29—22no—
96C4×C29—22no—
97C4×C29—24no—
98C4×C29—44no—
99C4×C29—42no—
100C4×C29—82no—
101C2×#117C4×C2911yescharacteristic
102C2×#117C22×C2911yescharacteristic
103C22×C42C4×C2911yescharacteristic
104#432C22×C2914yes—
105#389—22no—
106#385—22no—
107C4×C4⋊C4C4×C2912yes—
108C4×C4⋊C4C22×C2912yes—
109#324—22no—
110#323—22no—
111C2×C29—21no—
112C2×C29—21no—
113C2×C29—42no—
114C2×C29#182111yescharacteristic
115C2×C29#182712yes—
116C23×C4—21no—
117C23×C4C2×C4×C2911yescharacteristic
118#117—24no—
119#117—42no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—22no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4D4×C2912yes—
124C2×C22⋊C4—21no—
125C2×C22⋊C4D4×C2912yes—
126C2×C42—21no—
127C2×C42—42no—
128C2×C42C2×C4×C2911yescharacteristic
129C2×C42C2×C4×C2912yes—
130C2×C42C2×C4×C2912yes—
131C2×C42C23×C2911yescharacteristic
132C4⋊C8—24no—
133C22⋊C8—24no—
134#97—24no—
135#95—22no—
136#95—22no—
137C29#874311yescharacteristic, direct product factor, Sylow
138C24C22⋊C4×C2911yescharacteristic
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—44no—
145C22×C4—42no—
146C22×C4C22⋊C4×C2911yescharacteristic
147C22×C4C22⋊C4×C2912yes—
148C22×C4C22×C4×C2911yescharacteristic
149C22×C4C2×D4×C2912yes—
150C2×C8—44no—
151C4⋊C4—24no—
152C4⋊C4—44no—
153C4⋊C4—44no—
154C4⋊C4—42no—
155C22⋊C4—24no—
156C22⋊C4—42no—
157C42—22no—
158C42—42no—
159C42—42no—
160C42—42no—
161C42#41×C2914yes—
162C23—21no—
163C23—21no—
164C23—42no—
165C23C29×#10112yes—
166C23C2×C22⋊C4×C2911yescharacteristic
167C2×C4—28no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—24no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—48no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4C29×#10012yes—
183C2×C4C29×#11712yes—
184C2×C4C29×#12314yes—
185C8—84no—
186C22—22no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C29×#38111yescharacteristic
192C22C2×C29×#10011yescharacteristic
193C22C2×C29×#10111yescharacteristic
194C4—22no—
195C4—22no—
196C4—24no—
197C4—44no—
198C4—42no—
199C4—82no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2C29×#182111yescharacteristic
204C2C29×#182712yes—
subgroupG/H
center, socleC22×C29#381
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC24×C29C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1285C2semidirect
59. #8743C29direct (N × H)
86. #1285C2×C29semidirect
137. C29#8743direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#22962
C29×#14642
C29×#12852
#874329