Finite Group Databasebeta

← C29×#13595 #20308495

Subgroups — C29×#13595 #20308495

Order 7424.

388 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3138C211yesmaximal, characteristic
2C2×C29×#353C212yesmaximal
3C29×#1412C214yesmaximal, complemented
4C29×#533C411yescharacteristic, complemented
5C2×C29×#127C2211yescharacteristic
6C29×#490C412yescomplemented
7C29×#490C2212yes—
8C29×#486—22no—
9C29×#418—22no—
10C2×C29×#99—22no—
11C4×M16×C29C411yescharacteristic, complemented
12C29×#353—22no—
13C29×#353C2214yes—
14C22×D4×C29—41no—
15C22×D4×C29D412yes—
16C2×M16×C29—21no—
17C29×C4⋊Q8—21no—
18C29×#127—41no—
19C29×#127C2×C411yescharacteristic
20C29×#127D412yes—
21C29×#127C2311yescharacteristic
22C29×#125C2×C412yescomplemented
23C29×C22⋊Q8—41no—
24C4×Q8×C29—41no—
25C29×#117—21no—
26C2×C22⋊C4×C29—42no—
27C2×C42×C29C2×C411yescharacteristic
28C29×#102—24no—
29C29×#102—24no—
30C29×#99—24no—
31C29×#99—42no—
32C29×#97C2×C412yescomplemented
33C4×C8×C29—21no—
34C24×C29—22no—
35C2×Q8×C29—41no—
36C2×D4×C29—22no—
37C2×D4×C29—42no—
38C2×D4×C29—42no—
39C2×D4×C29—41no—
40C2×D4×C29—42no—
41C2×D4×C29—41no—
42C2×D4×C29—84no—
43C2×D4×C29C22⋊C412yes—
44C2×D4×C29C2×D412yes—
45C22×C4×C29—21no—
46C22×C4×C29—82no—
47C22×C4×C29C22⋊C411yescharacteristic
48M16×C29—42no—
49C2×C8×C29—22no—
50C4⋊C4×C29—22no—
51C4⋊C4×C29—42no—
52C4⋊C4×C29—41no—
53C22⋊C4×C29—41no—
54C22⋊C4×C29—44no—
55C22⋊C4×C29—82no—
56C42×C29—21no—
57C42×C29—41no—
58C42×C29C22⋊C411yescharacteristic
59C42×C29C22×C411yescharacteristic
60#13595C2911yesmaximal, characteristic, direct product factor, Sylow
61C23×C29—22no—
62C23×C29—22no—
63C23×C29—42no—
64C23×C29—42no—
65C23×C29—84no—
66C23×C29#9911yescharacteristic
67Q8×C29—82no—
68D4×C29—42no—
69D4×C29—42no—
70D4×C29—82no—
71D4×C29—84no—
72D4×C29—82no—
73D4×C29—82no—
74C2×C4×C29—22no—
75C2×C4×C29—21no—
76C2×C4×C29—21no—
77C2×C4×C29—42no—
78C2×C4×C29—42no—
79C2×C4×C29—84no—
80C2×C4×C29—164no—
81C2×C4×C29#9911yescharacteristic
82C2×C4×C29C2×C22⋊C411yescharacteristic
83C8×C29—42no—
84#3138C2×C2911yescharacteristic
85C2×#353C2×C2912yes—
86#1412C2×C2914yescomplemented
87C22×C29—41no—
88C22×C29—42no—
89C22×C29—42no—
90C22×C29—82no—
91C22×C29—82no—
92C22×C29—84no—
93C22×C29—162no—
94C22×C29#35412yes—
95C22×C29C2×#9911yescharacteristic
96C4×C29—22no—
97C4×C29—21no—
98C4×C29—21no—
99C4×C29—41no—
100C4×C29—82no—
101C4×C29—164no—
102#533C4×C2911yescharacteristic, complemented
103C2×#127C22×C2911yescharacteristic
104#490C4×C2912yescomplemented
105#490C22×C2912yes—
106#486—22no—
107#418—22no—
108C2×#99—22no—
109C4×M16C4×C2911yescharacteristic, complemented
110#353—22no—
111#353C22×C2914yes—
112C2×C29—21no—
113C2×C29—22no—
114C2×C29—82no—
115C2×C29—82no—
116C2×C29C2×#35411yescharacteristic
117C22×D4—41no—
118C22×D4D4×C2912yes—
119C2×M16—21no—
120C4⋊Q8—21no—
121#127—41no—
122#127C2×C4×C2911yescharacteristic
123#127D4×C2912yes—
124#127C23×C2911yescharacteristic
125#125C2×C4×C2912yescomplemented
126C22⋊Q8—41no—
127C4×Q8—41no—
128#117—21no—
129C2×C22⋊C4—42no—
130C2×C42C2×C4×C2911yescharacteristic
131#102—24no—
132#102—24no—
133#99—24no—
134#99—42no—
135#97C2×C4×C2912yescomplemented
136C4×C8—21no—
137C29#1359511yescharacteristic, direct product factor, Sylow
138C24—22no—
139C2×Q8—41no—
140C2×D4—22no—
141C2×D4—42no—
142C2×D4—42no—
143C2×D4—41no—
144C2×D4—42no—
145C2×D4—41no—
146C2×D4—84no—
147C2×D4C22⋊C4×C2912yes—
148C2×D4C2×D4×C2912yes—
149C22×C4—21no—
150C22×C4—82no—
151C22×C4C22⋊C4×C2911yescharacteristic
152M16—42no—
153C2×C8—22no—
154C4⋊C4—22no—
155C4⋊C4—42no—
156C4⋊C4—41no—
157C22⋊C4—41no—
158C22⋊C4—44no—
159C22⋊C4—82no—
160C42—21no—
161C42—41no—
162C42C22⋊C4×C2911yescharacteristic
163C42C22×C4×C2911yescharacteristic
164C23—22no—
165C23—22no—
166C23—42no—
167C23—42no—
168C23—84no—
169C23C29×#9911yescharacteristic
170Q8—82no—
171D4—42no—
172D4—42no—
173D4—82no—
174D4—84no—
175D4—82no—
176D4—82no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—84no—
183C2×C4—164no—
184C2×C4C29×#9911yescharacteristic
185C2×C4C2×C22⋊C4×C2911yescharacteristic
186C8—42no—
187C22—41no—
188C22—42no—
189C22—42no—
190C22—82no—
191C22—82no—
192C22—84no—
193C22—162no—
194C22C29×#35412yes—
195C22C2×C29×#9911yescharacteristic
196C4—22no—
197C4—21no—
198C4—21no—
199C4—41no—
200C4—82no—
201C4—164no—
202C2—21no—
203C2—22no—
204C2—82no—
205C2—82no—
206C2C2×C29×#35411yescharacteristic
subgroupG/H
center, socleC2×C29C2×#354
commutatorC42C22×C4×C29
Frattini, cosocle#127C23×C29
prime radicalC2×C29×#127C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C23×C29 ◁ C22×C4×C29 ◁ C2×C29×#127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1412C2semidirect
4. C29×#533C4semidirect
6. C29×#490C4semidirect
11. C4×M16×C29C4semidirect
22. C29×#125C2×C4semidirect
32. C29×#97C2×C4semidirect
60. #13595C29direct (N × H)
86. #1412C2×C29semidirect
102. #533C4×C29semidirect
104. #490C4×C29semidirect
109. C4×M16C4×C29semidirect
125. #125C2×C4×C29semidirect
135. #97C2×C4×C29semidirect
137. C29#13595direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31382
C2×C29×#3532
C29×#14122
#1359529