Finite Group Databasebeta

← C29×#9412 #20304312

Subgroups — C29×#9412 #20304312

Order 7424.

526 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2583C211yesmaximal, characteristic
2C29×#2313C211yesmaximal, characteristic
3C29×#1508C212yesmaximal
4C29×#1463C211yesmaximal, characteristic
5C29×#1297C212yesmaximal
6C2×C29×C22⋊Q8C2211yescharacteristic
7C22×C4⋊C4×C29C2211yescharacteristic
8C29×#407C2212yes—
9C29×#398C412yescomplemented
10C29×#395C412yescomplemented
11C29×#389—22no—
12C29×#387—24no—
13C29×#385—21no—
14C29×#385—21no—
15C29×#381—21no—
16C29×#380—21no—
17C4×C22⋊C4×C29C2211yescharacteristic
18C4×C22⋊C4×C29C2212yes—
19C29×#328—24no—
20C29×#324—22no—
21C22×Q8×C29C2×C411yescharacteristic
22C23×C4×C29D411yescharacteristic
23C23×C4×C29D411yescharacteristic
24C23×C4×C29C2311yescharacteristic
25C2×M16×C29—22no—
26C29×C22⋊Q8—22no—
27C29×C22⋊Q8—22no—
28C2×C4⋊C4×C29—22no—
29C2×C4⋊C4×C29—22no—
30C2×C4⋊C4×C29—22no—
31C2×C4⋊C4×C29—21no—
32C2×C4⋊C4×C29—22no—
33C2×C4⋊C4×C29—22no—
34C2×C4⋊C4×C29C2×C411yescharacteristic
35C2×C4⋊C4×C29C2×C412yes—
36C2×C4⋊C4×C29D412yes—
37C2×C22⋊C4×C29—21no—
38C2×C22⋊C4×C29—21no—
39C2×C22⋊C4×C29—22no—
40C2×C42×C29—22no—
41C2×C42×C29—21no—
42C29×C22⋊C8—22no—
43C29×C22⋊C8—22no—
44C29×#95—22no—
45C29×#95—24no—
46C29×#95—22no—
47C29×#95—22no—
48C29×#95C2×C412yes—
49C29×#95D414yes—
50C24×C29C2×D411yescharacteristic
51C2×Q8×C29—22no—
52C2×Q8×C29—81no—
53C22×C4×C29—22no—
54C22×C4×C29—21no—
55C22×C4×C29—21no—
56C22×C4×C29—21no—
57C22×C4×C29—21no—
58C22×C4×C29—21no—
59C22×C4×C29—21no—
60C22×C4×C29—24no—
61C22×C4×C29—42no—
62C22×C4×C29—81no—
63C22×C4×C29—81no—
64C22×C4×C29C22⋊C412yes—
65C22×C4×C29C22⋊C412yes—
66C22×C4×C29C22×C411yescharacteristic
67C22×C4×C29C2×D412yes—
68C22×C4×C29C2×D411yescharacteristic
69C22×C4×C29#4112yes—
70M16×C29—82no—
71C2×C8×C29—42no—
72C4⋊C4×C29—24no—
73C4⋊C4×C29—24no—
74C4⋊C4×C29—22no—
75C4⋊C4×C29—44no—
76C4⋊C4×C29—42no—
77C4⋊C4×C29—82no—
78C4⋊C4×C29—82no—
79C22⋊C4×C29—24no—
80C22⋊C4×C29—44no—
81C22⋊C4×C29—41no—
82C22⋊C4×C29—41no—
83C42×C29—81no—
84C42×C29—82no—
85#9412C2911yesmaximal, characteristic, direct product factor, Sylow
86C23×C29—22no—
87C23×C29—22no—
88C23×C29—41no—
89C23×C29C2×C22⋊C411yescharacteristic
90C23×C29#12011yescharacteristic
91C23×C29#12311yescharacteristic
92Q8×C29—82no—
93C2×C4×C29—24no—
94C2×C4×C29—22no—
95C2×C4×C29—22no—
96C2×C4×C29—22no—
97C2×C4×C29—22no—
98C2×C4×C29—41no—
99C2×C4×C29—42no—
100C2×C4×C29—42no—
101C2×C4×C29—41no—
102C2×C4×C29—42no—
103C2×C4×C29—42no—
104C2×C4×C29—42no—
105C2×C4×C29—42no—
106C2×C4×C29—42no—
107C2×C4×C29—42no—
108C2×C4×C29—44no—
109C2×C4×C29—44no—
110C2×C4×C29—42no—
111C2×C4×C29—41no—
112C2×C4×C29—41no—
113C2×C4×C29—42no—
114C2×C4×C29—44no—
115C2×C4×C29—81no—
116C2×C4×C29C4×D412yes—
117C2×C4×C29#12112yes—
118C8×C29—82no—
119#2583C2×C2911yescharacteristic
120#2313C2×C2911yescharacteristic
121#1508C2×C2912yes—
122#1463C2×C2911yescharacteristic
123#1297C2×C2912yes—
124C22×C29—21no—
125C22×C29—21no—
126C22×C29—21no—
127C22×C29—21no—
128C22×C29—21no—
129C22×C29—21no—
130C22×C29—21no—
131C22×C29—44no—
132C22×C29#38611yescharacteristic
133C22×C29#42112yes—
134C22×C29#45612yes—
135C4×C29—22no—
136C4×C29—22no—
137C4×C29—44no—
138C4×C29—42no—
139C4×C29—42no—
140C4×C29—84no—
141C4×C29—81no—
142C4×C29—81no—
143C2×C22⋊Q8C22×C2911yescharacteristic
144C22×C4⋊C4C22×C2911yescharacteristic
145#407C22×C2912yes—
146#398C4×C2912yescomplemented
147#395C4×C2912yescomplemented
148#389—22no—
149#387—24no—
150#385—21no—
151#385—21no—
152#381—21no—
153#380—21no—
154C4×C22⋊C4C22×C2911yescharacteristic
155C4×C22⋊C4C22×C2912yes—
156#328—24no—
157#324—22no—
158C2×C29—22no—
159C2×C29—22no—
160C2×C29—41no—
161C2×C29#188611yescharacteristic
162C2×C29#189711yescharacteristic
163C2×C29#191311yescharacteristic
164C22×Q8C2×C4×C2911yescharacteristic
165C23×C4D4×C2911yescharacteristic
166C23×C4D4×C2911yescharacteristic
167C23×C4C23×C2911yescharacteristic
168C2×M16—22no—
169C22⋊Q8—22no—
170C22⋊Q8—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4C2×C4×C2911yescharacteristic
178C2×C4⋊C4C2×C4×C2912yes—
179C2×C4⋊C4D4×C2912yes—
180C2×C22⋊C4—21no—
181C2×C22⋊C4—21no—
182C2×C22⋊C4—22no—
183C2×C42—22no—
184C2×C42—21no—
185C22⋊C8—22no—
186C22⋊C8—22no—
187#95—22no—
188#95—24no—
189#95—22no—
190#95—22no—
191#95C2×C4×C2912yes—
192#95D4×C2914yes—
193C29#941211yescharacteristic, direct product factor, Sylow
194C24C2×D4×C2911yescharacteristic
195C2×Q8—22no—
196C2×Q8—81no—
197C22×C4—22no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—24no—
205C22×C4—42no—
206C22×C4—81no—
207C22×C4—81no—
208C22×C4C22⋊C4×C2912yes—
209C22×C4C22⋊C4×C2912yes—
210C22×C4C22×C4×C2911yescharacteristic
211C22×C4C2×D4×C2912yes—
212C22×C4C2×D4×C2911yescharacteristic
213C22×C4#41×C2912yes—
214M16—82no—
215C2×C8—42no—
216C4⋊C4—24no—
217C4⋊C4—24no—
218C4⋊C4—22no—
219C4⋊C4—44no—
220C4⋊C4—42no—
221C4⋊C4—82no—
222C4⋊C4—82no—
223C22⋊C4—24no—
224C22⋊C4—44no—
225C22⋊C4—41no—
226C22⋊C4—41no—
227C42—81no—
228C42—82no—
229C23—22no—
230C23—22no—
231C23—41no—
232C23C2×C22⋊C4×C2911yescharacteristic
233C23C29×#12011yescharacteristic
234C23C29×#12311yescharacteristic
235Q8—82no—
236C2×C4—24no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—44no—
252C2×C4—44no—
253C2×C4—42no—
254C2×C4—44no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—42no—
258C2×C4—81no—
259C2×C4C4×D4×C2912yes—
260C2×C4C29×#12112yes—
261C8—82no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—44no—
270C22C29×#38611yescharacteristic
271C22C29×#42112yes—
272C22C29×#45612yes—
273C4—22no—
274C4—22no—
275C4—44no—
276C4—42no—
277C4—42no—
278C4—84no—
279C4—81no—
280C4—81no—
281C2—22no—
282C2—22no—
283C2—41no—
284C2C29×#188611yescharacteristic
285C2C29×#189711yescharacteristic
286C2C29×#191311yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC24×C29C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
9. C29×#398C4semidirect
10. C29×#395C4semidirect
85. #9412C29direct (N × H)
146. #398C4×C29semidirect
147. #395C4×C29semidirect
193. C29#9412direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#25832
C29×#23132
C29×#15082
C29×#14632
C29×#12972
#941229