Finite Group Databasebeta

← C29×#11516 #20306416

Subgroups — C29×#11516 #20306416

Order 7424.

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

normal subgroups only

This group has 418 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×#2317C211yesmaximal, characteristic
2C29×#1464C212yesmaximal
3C29×#1325C214yesmaximal, complemented
4C2×C29×#117C411yescharacteristic
5C2×C29×#117C2211yescharacteristic
6C22×C4⋊C4×C29C411yescharacteristic
7C29×#432—22no—
8C29×#389—22no—
9C29×#385—22no—
10C29×#384C2212yes—
11C29×#382C412yes—
12C29×#324C2214yes—
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—21no—
20C2×C4⋊C4×C29—24no—
21C2×C4⋊C4×C29—42no—
22C2×C4⋊C4×C29C2×C412yes—
23C2×C4⋊C4×C29C2×C411yescharacteristic
24C2×C4⋊C4×C29C2311yescharacteristic
25C2×C22⋊C4×C29—21no—
26C2×C22⋊C4×C29D412yes—
27C2×C42×C29C2×C412yes—
28C2×C42×C29D412yes—
29C29×C4⋊C8—42no—
30C29×C22⋊C8—24no—
31C29×#97—42no—
32C29×#95—24no—
33C24×C29C22⋊C411yescharacteristic
34C22×C4×C29—22no—
35C22×C4×C29—22no—
36C22×C4×C29—22no—
37C22×C4×C29—22no—
38C22×C4×C29—22no—
39C22×C4×C29—42no—
40C22×C4×C29—82no—
41C22×C4×C29C22⋊C412yes—
42C22×C4×C29C22⋊C411yescharacteristic
43C22×C4×C29C22×C411yescharacteristic
44C22×C4×C29C2×D412yes—
45C2×C8×C29—44no—
46C4⋊C4×C29—24no—
47C4⋊C4×C29—41no—
48C4⋊C4×C29—41no—
49C4⋊C4×C29—42no—
50C4⋊C4×C29—42no—
51C4⋊C4×C29—84no—
52C22⋊C4×C29—24no—
53C22⋊C4×C29—42no—
54C42×C29—22no—
55C42×C29—22no—
56C42×C29—22no—
57C42×C29M1614yes—
58#11516C2911yesmaximal, characteristic, direct product factor, Sylow
59C23×C29—21no—
60C23×C29—21no—
61C23×C29—41no—
62C23×C29—41no—
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—22no—
73C2×C4×C29—42no—
74C2×C4×C29—42no—
75C2×C4×C29—42no—
76C2×C4×C29—42no—
77C2×C4×C29—44no—
78C2×C4×C29—42no—
79C2×C4×C29—84no—
80C2×C4×C29#9912yes—
81C2×C4×C29C2×M1612yes—
82C8×C29—84no—
83#2317C2×C2911yescharacteristic
84#1464C2×C2912yes—
85#1325C2×C2914yescomplemented
86C22×C29—21no—
87C22×C29—21no—
88C22×C29—22no—
89C22×C29—42no—
90C22×C29—42no—
91C22×C29—41no—
92C22×C29—41no—
93C22×C29#40711yescharacteristic
94C22×C29C2×#9911yescharacteristic
95C22×C29C2×#10111yescharacteristic
96C4×C29—22no—
97C4×C29—22no—
98C4×C29—44no—
99C4×C29—42no—
100C4×C29—42no—
101C4×C29—82no—
102C2×#117C4×C2911yescharacteristic
103C2×#117C22×C2911yescharacteristic
104C22×C4⋊C4C4×C2911yescharacteristic
105#432—22no—
106#389—22no—
107#385—22no—
108#384C22×C2912yes—
109#382C4×C2912yes—
110#324C22×C2914yes—
111#323—22no—
112C2×C29—21no—
113C2×C29—21no—
114C2×C29—42no—
115C2×C29#146311yescharacteristic
116C2×C29#212811yescharacteristic
117C2×C29#213511yescharacteristic
118C23×C4—21no—
119C23×C4C2×C4×C2911yescharacteristic
120#117—24no—
121#117—42no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—21no—
124C2×C4⋊C4—24no—
125C2×C4⋊C4—42no—
126C2×C4⋊C4C2×C4×C2912yes—
127C2×C4⋊C4C2×C4×C2911yescharacteristic
128C2×C4⋊C4C23×C2911yescharacteristic
129C2×C22⋊C4—21no—
130C2×C22⋊C4D4×C2912yes—
131C2×C42C2×C4×C2912yes—
132C2×C42D4×C2912yes—
133C4⋊C8—42no—
134C22⋊C8—24no—
135#97—42no—
136#95—24no—
137C29#1151611yescharacteristic, direct product factor, Sylow
138C24C22⋊C4×C2911yescharacteristic
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—42no—
145C22×C4—82no—
146C22×C4C22⋊C4×C2911yescharacteristic
147C22×C4C22⋊C4×C2912yes—
148C22×C4C22×C4×C2911yescharacteristic
149C22×C4C2×D4×C2912yes—
150C2×C8—44no—
151C4⋊C4—24no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—84no—
157C22⋊C4—24no—
158C22⋊C4—42no—
159C42—22no—
160C42—22no—
161C42—22no—
162C42M16×C2914yes—
163C23—21no—
164C23—21no—
165C23—41no—
166C23—41no—
167C23C29×#10112yes—
168C23C2×C22⋊C4×C2911yescharacteristic
169C2×C4—28no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—44no—
182C2×C4—42no—
183C2×C4—84no—
184C2×C4C29×#9912yes—
185C2×C4C2×M16×C2912yes—
186C8—84no—
187C22—21no—
188C22—21no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—41no—
193C22—41no—
194C22C29×#40711yescharacteristic
195C22C2×C29×#9911yescharacteristic
196C22C2×C29×#10111yescharacteristic
197C4—22no—
198C4—22no—
199C4—44no—
200C4—42no—
201C4—42no—
202C4—82no—
203C2—21no—
204C2—21no—
205C2—42no—
206C2C29×#146311yescharacteristic
207C2C29×#212811yescharacteristic
208C2C29×#213511yescharacteristic
subgroupG/H
center, socleC22×C29C2×#99
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C4⋊C4C23×C29
prime radicalC24×C29C22⋊C4
LCSG ▷ C22×C4 ▷ 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
3. C29×#1325C2semidirect
58. #11516C29direct (N × H)
85. #1325C2×C29semidirect
137. C29#11516direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#23172
C29×#14642
C29×#13252
#1151629