Finite Group Databasebeta

← C29×#9429 #20304329

Subgroups — C29×#9429 #20304329

Order 7424.

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

normal subgroups only

This group has 508 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×#3152C211yesmaximal, characteristic
2C29×#2381C211yesmaximal, characteristic, complemented
3C29×#1558C211yesmaximal, characteristic, complemented
4C29×#1514C212yesmaximal
5C29×#1288C212yesmaximal, complemented
6C2×C29×#137—22no—
7C29×#532C2211yescharacteristic
8C2×C29×C4⋊Q8C2211yescharacteristic
9C29×#497—22no—
10C29×#494C412yescomplemented
11C29×#492C412yescomplemented
12C29×#432C2212yes—
13C4×M16×C29C2211yescharacteristic
14C29×#391—22no—
15C29×#387—24no—
16C29×#383C2212yes—
17C29×#333—22no—
18C29×#327—24no—
19C2×#41×C29—21no—
20C22×Q8×C29D412yes—
21C29×#137—44no—
22C29×#137—44no—
23C2×Q16×C29—24no—
24C2×SD16×C29—24no—
25C2×M16×C29—21no—
26C29×C4⋊Q8—22no—
27C29×C4⋊Q8C2×C411yescharacteristic
28C29×C4⋊Q8C2×C412yes—
29C29×C4⋊Q8D412yes—
30C29×#127C2×C411yescharacteristic
31C29×#124—21no—
32C29×#121—22no—
33C4×D4×C29—22no—
34C2×C4⋊C4×C29—22no—
35C2×C4⋊C4×C29—22no—
36C2×C42×C29—22no—
37C2×C42×C29C2311yescharacteristic
38C29×C4⋊C8—22no—
39C29×C22⋊C8—22no—
40C29×#97—21no—
41C29×#97—22no—
42C4×C8×C29C2×C412yes—
43C29×#95—24no—
44C29×#95—22no—
45C29×#95—22no—
46C29×#95D414yes—
47#41×C29—42no—
48#41×C29—42no—
49C2×Q8×C29—22no—
50C2×Q8×C29—21no—
51C2×Q8×C29—42no—
52C2×Q8×C29—42no—
53C2×Q8×C29C22⋊C414yes—
54C2×D4×C29—21no—
55C2×D4×C29—22no—
56C2×D4×C29—41no—
57C22×C4×C29—22no—
58C22×C4×C29—24no—
59C22×C4×C29—41no—
60C22×C4×C29C2×D411yescharacteristic
61C22×C4×C29C2×D412yes—
62Q16×C29—48no—
63SD16×C29—48no—
64M16×C29—24no—
65C2×C8×C29—22no—
66C2×C8×C29—42no—
67C4⋊C4×C29—24no—
68C4⋊C4×C29—24no—
69C4⋊C4×C29—22no—
70C4⋊C4×C29—82no—
71C22⋊C4×C29—42no—
72C42×C29—82no—
73C42×C29C22×C411yescharacteristic
74C42×C29C2×D411yescharacteristic
75C42×C29#4112yes—
76#9429C2911yesmaximal, characteristic, direct product factor, Sylow
77C23×C29—41no—
78C23×C29#12011yescharacteristic
79Q8×C29—44no—
80Q8×C29—42no—
81Q8×C29—82no—
82D4×C29—42no—
83D4×C29—82no—
84D4×C29—82no—
85C2×C4×C29—22no—
86C2×C4×C29—24no—
87C2×C4×C29—42no—
88C2×C4×C29—42no—
89C2×C4×C29—42no—
90C2×C4×C29—48no—
91C2×C4×C29—41no—
92C2×C4×C29—44no—
93C2×C4×C29—81no—
94C2×C4×C29—81no—
95C2×C4×C29C2×C22⋊C411yescharacteristic
96C2×C4×C29C4×D412yes—
97C2×C4×C29#12112yes—
98C2×C4×C29#12311yescharacteristic
99C8×C29—24no—
100C8×C29—82no—
101#3152C2×C2911yescharacteristic
102#2381C2×C2911yescharacteristic, complemented
103#1558C2×C2911yescharacteristic, complemented
104#1514C2×C2912yes—
105#1288C2×C2912yescomplemented
106C22×C29—22no—
107C22×C29—81no—
108C22×C29—82no—
109C22×C29#38611yescharacteristic
110C22×C29#45312yes—
111C4×C29—21no—
112C4×C29—21no—
113C4×C29—22no—
114C4×C29—22no—
115C4×C29—44no—
116C4×C29—84no—
117C4×C29—81no—
118C2×#137—22no—
119#532C22×C2911yescharacteristic
120C2×C4⋊Q8C22×C2911yescharacteristic
121#497—22no—
122#494C4×C2912yescomplemented
123#492C4×C2912yescomplemented
124#432C22×C2912yes—
125C4×M16C22×C2911yescharacteristic
126#391—22no—
127#387—24no—
128#383C22×C2912yes—
129#333—22no—
130#327—24no—
131C2×C29—22no—
132C2×C29—161no—
133C2×C29#188711yescharacteristic
134C2×C29#190512yes—
135C2×#41—21no—
136C22×Q8D4×C2912yes—
137#137—44no—
138#137—44no—
139C2×Q16—24no—
140C2×SD16—24no—
141C2×M16—21no—
142C4⋊Q8—22no—
143C4⋊Q8C2×C4×C2911yescharacteristic
144C4⋊Q8C2×C4×C2912yes—
145C4⋊Q8D4×C2912yes—
146#127C2×C4×C2911yescharacteristic
147#124—21no—
148#121—22no—
149C4×D4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C42—22no—
153C2×C42C23×C2911yescharacteristic
154C4⋊C8—22no—
155C22⋊C8—22no—
156#97—21no—
157#97—22no—
158C4×C8C2×C4×C2912yes—
159#95—24no—
160#95—22no—
161#95—22no—
162#95D4×C2914yes—
163C29#942911yescharacteristic, direct product factor, Sylow
164#41—42no—
165#41—42no—
166C2×Q8—22no—
167C2×Q8—21no—
168C2×Q8—42no—
169C2×Q8—42no—
170C2×Q8C22⋊C4×C2914yes—
171C2×D4—21no—
172C2×D4—22no—
173C2×D4—41no—
174C22×C4—22no—
175C22×C4—24no—
176C22×C4—41no—
177C22×C4C2×D4×C2911yescharacteristic
178C22×C4C2×D4×C2912yes—
179Q16—48no—
180SD16—48no—
181M16—24no—
182C2×C8—22no—
183C2×C8—42no—
184C4⋊C4—24no—
185C4⋊C4—24no—
186C4⋊C4—22no—
187C4⋊C4—82no—
188C22⋊C4—42no—
189C42—82no—
190C42C22×C4×C2911yescharacteristic
191C42C2×D4×C2911yescharacteristic
192C42#41×C2912yes—
193C23—41no—
194C23C29×#12011yescharacteristic
195Q8—44no—
196Q8—42no—
197Q8—82no—
198D4—42no—
199D4—82no—
200D4—82no—
201C2×C4—22no—
202C2×C4—24no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—48no—
207C2×C4—44no—
208C2×C4—41no—
209C2×C4—81no—
210C2×C4—81no—
211C2×C4C2×C22⋊C4×C2911yescharacteristic
212C2×C4C4×D4×C2912yes—
213C2×C4C29×#12112yes—
214C2×C4C29×#12311yescharacteristic
215C8—24no—
216C8—82no—
217C22—22no—
218C22—82no—
219C22—81no—
220C22C29×#38611yescharacteristic
221C22C29×#45312yes—
222C4—22no—
223C4—22no—
224C4—21no—
225C4—21no—
226C4—44no—
227C4—84no—
228C4—81no—
229C2—22no—
230C2—161no—
231C2C29×#188711yescharacteristic
232C2C29×#190512yes—
subgroupG/H
center, socleC22×C29#386
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2381C2semidirect
3. C29×#1558C2semidirect
5. C29×#1288C2semidirect
10. C29×#494C4semidirect
11. C29×#492C4semidirect
76. #9429C29direct (N × H)
102. #2381C2×C29semidirect
103. #1558C2×C29semidirect
105. #1288C2×C29semidirect
122. #494C4×C29semidirect
123. #492C4×C29semidirect
163. C29#9429direct (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×#23812
C29×#15582
C29×#15142
C29×#12882
#942929