Finite Group Databasebeta

← C29×#13586 #20308486

Subgroups — C29×#13586 #20308486

Order 7424.

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

normal subgroups only

This group has 406 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×#3152C211yesmaximal, characteristic
2C29×#2126C212yesmaximal
3C29×#1409C214yesmaximal, complemented
4C2×C29×#137—22no—
5C29×#532C2211yescharacteristic
6C2×C29×C4⋊Q8C411yescharacteristic, complemented
7C29×#497—22no—
8C29×#494C412yescomplemented
9C29×#492C2212yes—
10C29×#410—22no—
11C4×M16×C29C411yescharacteristic, complemented
12C29×#354—22no—
13C29×#353C2214yes—
14C2×#41×C29D412yes—
15C22×Q8×C29—21no—
16C29×#137—44no—
17C29×#137—44no—
18C2×Q16×C29—24no—
19C2×SD16×C29—24no—
20C2×M16×C29—21no—
21C29×C4⋊Q8—21no—
22C29×C4⋊Q8—41no—
23C29×C4⋊Q8C2×C412yes—
24C29×C4⋊Q8C2×C411yescharacteristic
25C29×#127C2311yescharacteristic
26C29×#124D412yes—
27C29×#121—41no—
28C4×D4×C29—41no—
29C29×#117—42no—
30C2×C4⋊C4×C29—41no—
31C2×C42×C29C2×C411yescharacteristic
32C29×#99—24no—
33C29×#99—42no—
34C29×#97—21no—
35C4×C8×C29C2×C412yes—
36#41×C29—42no—
37#41×C29—42no—
38C2×Q8×C29—22no—
39C2×Q8×C29—42no—
40C2×Q8×C29—42no—
41C2×Q8×C29—41no—
42C2×Q8×C29C22⋊C412yes—
43C2×D4×C29—22no—
44C2×D4×C29—41no—
45C2×D4×C29C2×D412yes—
46C22×C4×C29—21no—
47C22×C4×C29—22no—
48C22×C4×C29—41no—
49C22×C4×C29C22⋊C411yescharacteristic
50Q16×C29—48no—
51SD16×C29—48no—
52M16×C29—24no—
53C2×C8×C29—22no—
54C4⋊C4×C29—41no—
55C4⋊C4×C29—42no—
56C4⋊C4×C29—42no—
57C4⋊C4×C29—82no—
58C22⋊C4×C29—42no—
59C22⋊C4×C29—44no—
60C42×C29—21no—
61C42×C29—82no—
62C42×C29C22⋊C411yescharacteristic
63C42×C29C22×C411yescharacteristic
64#13586C2911yesmaximal, characteristic, direct product factor, Sylow
65C23×C29—22no—
66C23×C29#9911yescharacteristic
67Q8×C29—42no—
68Q8×C29—44no—
69Q8×C29—82no—
70D4×C29—42no—
71D4×C29—82no—
72D4×C29—82no—
73C2×C4×C29—21no—
74C2×C4×C29—22no—
75C2×C4×C29—21no—
76C2×C4×C29—22no—
77C2×C4×C29—42no—
78C2×C4×C29—42no—
79C2×C4×C29—42no—
80C2×C4×C29—42no—
81C2×C4×C29—81no—
82C2×C4×C29—81no—
83C2×C4×C29—84no—
84C2×C4×C29#9911yescharacteristic
85C2×C4×C29C2×C22⋊C411yescharacteristic
86C8×C29—24no—
87#3152C2×C2911yescharacteristic
88#2126C2×C2912yes—
89#1409C2×C2914yescomplemented
90C22×C29—21no—
91C22×C29—41no—
92C22×C29—42no—
93C22×C29—82no—
94C22×C29C2×#9911yescharacteristic
95C4×C29—22no—
96C4×C29—21no—
97C4×C29—41no—
98C4×C29—42no—
99C4×C29—82no—
100C4×C29—164no—
101C4×C29#35312yes—
102C2×#137—22no—
103#532C22×C2911yescharacteristic
104C2×C4⋊Q8C4×C2911yescharacteristic, complemented
105#497—22no—
106#494C4×C2912yescomplemented
107#492C22×C2912yes—
108#410—22no—
109C4×M16C4×C2911yescharacteristic, complemented
110#354—22no—
111#353C22×C2914yes—
112C2×C29—21no—
113C2×C29—41no—
114C2×C29—82no—
115C2×C29C2×#35311yescharacteristic
116C2×#41D4×C2912yes—
117C22×Q8—21no—
118#137—44no—
119#137—44no—
120C2×Q16—24no—
121C2×SD16—24no—
122C2×M16—21no—
123C4⋊Q8—21no—
124C4⋊Q8—41no—
125C4⋊Q8C2×C4×C2912yes—
126C4⋊Q8C2×C4×C2911yescharacteristic
127#127C23×C2911yescharacteristic
128#124D4×C2912yes—
129#121—41no—
130C4×D4—41no—
131#117—42no—
132C2×C4⋊C4—41no—
133C2×C42C2×C4×C2911yescharacteristic
134#99—24no—
135#99—42no—
136#97—21no—
137C4×C8C2×C4×C2912yes—
138C29#1358611yescharacteristic, direct product factor, Sylow
139#41—42no—
140#41—42no—
141C2×Q8—22no—
142C2×Q8—42no—
143C2×Q8—42no—
144C2×Q8—41no—
145C2×Q8C22⋊C4×C2912yes—
146C2×D4—22no—
147C2×D4—41no—
148C2×D4C2×D4×C2912yes—
149C22×C4—21no—
150C22×C4—22no—
151C22×C4—41no—
152C22×C4C22⋊C4×C2911yescharacteristic
153Q16—48no—
154SD16—48no—
155M16—24no—
156C2×C8—22no—
157C4⋊C4—41no—
158C4⋊C4—42no—
159C4⋊C4—42no—
160C4⋊C4—82no—
161C22⋊C4—42no—
162C22⋊C4—44no—
163C42—21no—
164C42—82no—
165C42C22⋊C4×C2911yescharacteristic
166C42C22×C4×C2911yescharacteristic
167C23—22no—
168C23C29×#9911yescharacteristic
169Q8—42no—
170Q8—44no—
171Q8—82no—
172D4—42no—
173D4—82no—
174D4—82no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—81no—
184C2×C4—81no—
185C2×C4—84no—
186C2×C4C29×#9911yescharacteristic
187C2×C4C2×C22⋊C4×C2911yescharacteristic
188C8—24no—
189C22—21no—
190C22—41no—
191C22—42no—
192C22—82no—
193C22C2×C29×#9911yescharacteristic
194C4—22no—
195C4—21no—
196C4—41no—
197C4—42no—
198C4—82no—
199C4—164no—
200C4C29×#35312yes—
201C2—21no—
202C2—41no—
203C2—82no—
204C2C2×C29×#35311yescharacteristic
subgroupG/H
center, socleC2×C29C2×#353
commutatorC42C22×C4×C29
Frattini, cosocle#127C23×C29
prime radicalC29×#532C22
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C22×C4×C29 ◁ C29×#532 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1409C2semidirect
6. C2×C29×C4⋊Q8C4semidirect
8. C29×#494C4semidirect
11. C4×M16×C29C4semidirect
64. #13586C29direct (N × H)
89. #1409C2×C29semidirect
104. C2×C4⋊Q8C4×C29semidirect
106. #494C4×C29semidirect
109. C4×M16C4×C29semidirect
138. C29#13586direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31522
C29×#21262
C29×#14092
#1358629