Finite Group Databasebeta

← C29×#11518 #20306418

Subgroups — C29×#11518 #20306418

Order 7424.

446 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 110 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×#1326C214yesmaximal
4C2×C29×#117C411yescharacteristic
5C2×C29×#117C2211yescharacteristic
6C22×C42×C29C411yescharacteristic
7C29×#432—22no—
8C29×#389—22no—
9C29×#385C412yes—
10C29×#385C2212yes—
11C4×C4⋊C4×C29—22no—
12C29×#324—22no—
13C29×#323C2214yes—
14C23×C4×C29C2×C411yescharacteristic
15C23×C4×C29C2×C412yes—
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×C29C2×C412yes—
23C2×C22⋊C4×C29C2×C411yescharacteristic
24C2×C22⋊C4×C29C2311yescharacteristic
25C2×C42×C29—21no—
26C2×C42×C29—21no—
27C2×C42×C29—21no—
28C2×C42×C29—42no—
29C2×C42×C29D412yes—
30C29×C4⋊C8—42no—
31C29×C22⋊C8—24no—
32C29×#97—42no—
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—42no—
50C4⋊C4×C29—44no—
51C4⋊C4×C29—44no—
52C22⋊C4×C29—22no—
53C22⋊C4×C29—41no—
54C22⋊C4×C29—41no—
55C22⋊C4×C29M1614yes—
56C42×C29—24no—
57C42×C29—22no—
58C42×C29—22no—
59C42×C29—42no—
60C42×C29—42no—
61#11518C2911yesmaximal, characteristic, direct product factor, Sylow
62C23×C29—21no—
63C23×C29—21no—
64C23×C29—42no—
65C23×C29C2×C22⋊C411yescharacteristic
66C23×C29C2×M1612yes—
67C2×C4×C29—28no—
68C2×C4×C29—21no—
69C2×C4×C29—21no—
70C2×C4×C29—21no—
71C2×C4×C29—21no—
72C2×C4×C29—24no—
73C2×C4×C29—24no—
74C2×C4×C29—22no—
75C2×C4×C29—22no—
76C2×C4×C29—42no—
77C2×C4×C29—42no—
78C2×C4×C29—42no—
79C2×C4×C29—44no—
80C2×C4×C29—42no—
81C2×C4×C29—42no—
82C2×C4×C29—42no—
83C2×C4×C29—44no—
84C2×C4×C29#9912yes—
85C2×C4×C29#10112yes—
86C8×C29—84no—
87#2296C2×C2911yescharacteristic
88#1464C2×C2912yes—
89#1326C2×C2914yes—
90C22×C29—22no—
91C22×C29—22no—
92C22×C29—42no—
93C22×C29—42no—
94C22×C29—42no—
95C22×C29#40711yescharacteristic
96C22×C29C2×#9911yescharacteristic
97C22×C29C2×#10111yescharacteristic
98C4×C29—22no—
99C4×C29—22no—
100C4×C29—44no—
101C4×C29—42no—
102C4×C29—42no—
103C4×C29—44no—
104C2×#117C4×C2911yescharacteristic
105C2×#117C22×C2911yescharacteristic
106C22×C42C4×C2911yescharacteristic
107#432—22no—
108#389—22no—
109#385C4×C2912yes—
110#385C22×C2912yes—
111C4×C4⋊C4—22no—
112#324—22no—
113#323C22×C2914yes—
114C2×C29—21no—
115C2×C29—21no—
116C2×C29—42no—
117C2×C29#146311yescharacteristic
118C2×C29#212012yes—
119C23×C4C2×C4×C2911yescharacteristic
120C23×C4C2×C4×C2912yes—
121#117—24no—
122#117—42no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—22no—
126C2×C4⋊C4D4×C2912yes—
127C2×C22⋊C4C2×C4×C2912yes—
128C2×C22⋊C4C2×C4×C2911yescharacteristic
129C2×C22⋊C4C23×C2911yescharacteristic
130C2×C42—21no—
131C2×C42—21no—
132C2×C42—21no—
133C2×C42—42no—
134C2×C42D4×C2912yes—
135C4⋊C8—42no—
136C22⋊C8—24no—
137#97—42no—
138#95—22no—
139#95—22no—
140C29#1151811yescharacteristic, direct product factor, Sylow
141C24C22×C4×C2911yescharacteristic
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—44no—
148C22×C4—42no—
149C22×C4C22⋊C4×C2911yescharacteristic
150C22×C4C22⋊C4×C2911yescharacteristic
151C22×C4C22⋊C4×C2912yes—
152C22×C4C2×D4×C2912yes—
153C2×C8—44no—
154C4⋊C4—24no—
155C4⋊C4—42no—
156C4⋊C4—44no—
157C4⋊C4—44no—
158C22⋊C4—22no—
159C22⋊C4—41no—
160C22⋊C4—41no—
161C22⋊C4M16×C2914yes—
162C42—24no—
163C42—22no—
164C42—22no—
165C42—42no—
166C42—42no—
167C23—21no—
168C23—21no—
169C23—42no—
170C23C2×C22⋊C4×C2911yescharacteristic
171C23C2×M16×C2912yes—
172C2×C4—28no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—24no—
178C2×C4—24no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—44no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—44no—
189C2×C4C29×#9912yes—
190C2×C4C29×#10112yes—
191C8—84no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22C29×#40711yescharacteristic
198C22C2×C29×#9911yescharacteristic
199C22C2×C29×#10111yescharacteristic
200C4—22no—
201C4—22no—
202C4—44no—
203C4—42no—
204C4—44no—
205C4—42no—
206C2—21no—
207C2—21no—
208C2—42no—
209C2C29×#146311yescharacteristic
210C2C29×#212012yes—
subgroupG/H
center, socleC22×C29C2×#99
commutatorC24C22×C4×C29
Frattini, cosocleC2×C22⋊C4C23×C29
prime radicalC24×C29C22×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C2×C29×#117 ◁ G

Complements

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

NH ≅ G/Ntype
61. #11518C29direct (N × H)
140. C29#11518direct (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×#13262
#1151829