Finite Group Databasebeta

← C29×#9509 #20304409

Subgroups — C29×#9509 #20304409

Order 7424.

524 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2973C211yesmaximal, characteristic
2C29×#2487C211yesmaximal, characteristic
3C29×#1821C212yesmaximal, complemented
4C29×#1465C211yesmaximal, characteristic
5C29×#1305C212yesmaximal, complemented
6C2×C4×D4×C29C2211yescharacteristic
7C22×C4⋊C4×C29C2211yescharacteristic
8C29×#435—24no—
9C29×#432—21no—
10C29×#407C2212yes—
11C29×#407C2212yes—
12C2×C29×C22⋊C8—21no—
13C29×#400—21no—
14C29×#399—21no—
15C29×#389—21no—
16C29×#386C412yes—
17C29×#385C412yes—
18C29×#380—21no—
19C29×#380C2211yescharacteristic
20C29×#343—24no—
21C29×#324—21no—
22C29×#323—21no—
23C22×D4×C29C2×C411yescharacteristic
24C23×C4×C29C2×C412yes—
25C23×C4×C29D411yescharacteristic
26C23×C4×C29C2311yescharacteristic
27C2×M16×C29—22no—
28C2×M16×C29D414yes—
29C22×C8×C29—22no—
30C4×D4×C29—22no—
31C4×D4×C29—22no—
32C2×C4⋊C4×C29—22no—
33C2×C4⋊C4×C29—21no—
34C2×C4⋊C4×C29—21no—
35C2×C4⋊C4×C29—21no—
36C2×C4⋊C4×C29—22no—
37C2×C4⋊C4×C29—22no—
38C2×C4⋊C4×C29D411yescharacteristic
39C2×C22⋊C4×C29—22no—
40C2×C22⋊C4×C29C2×C411yescharacteristic
41C2×C22⋊C4×C29C2×C412yes—
42C2×C22⋊C4×C29D411yescharacteristic
43C2×C42×C29D411yescharacteristic
44C29×C4⋊C8—22no—
45C29×C22⋊C8—22no—
46C29×C22⋊C8—22no—
47C29×C22⋊C8—22no—
48C29×C22⋊C8—22no—
49C29×C22⋊C8—22no—
50C29×#97—22no—
51C29×#95—22no—
52C29×#95—22no—
53C29×#95—21no—
54C24×C29C22⋊C411yescharacteristic
55C24×C29C22×C411yescharacteristic
56C2×D4×C29—22no—
57C2×D4×C29—22no—
58C2×D4×C29—41no—
59C22×C4×C29—21no—
60C22×C4×C29—21no—
61C22×C4×C29—22no—
62C22×C4×C29—22no—
63C22×C4×C29—24no—
64C22×C4×C29—42no—
65C22×C4×C29—42no—
66C22×C4×C29—82no—
67C22×C4×C29C22⋊C411yescharacteristic
68C22×C4×C29C22⋊C411yescharacteristic
69C22×C4×C29C22⋊C411yescharacteristic
70C22×C4×C29C2×D412yes—
71C22×C4×C29C2×D411yescharacteristic
72C22×C4×C29C2×D411yescharacteristic
73C22×C4×C29#4112yes—
74M16×C29—44no—
75M16×C29—44no—
76C2×C8×C29—24no—
77C2×C8×C29—42no—
78C2×C8×C29—82no—
79C4⋊C4×C29—22no—
80C4⋊C4×C29—42no—
81C4⋊C4×C29—41no—
82C4⋊C4×C29—42no—
83C4⋊C4×C29—41no—
84C4⋊C4×C29—82no—
85C22⋊C4×C29—22no—
86C22⋊C4×C29—22no—
87C22⋊C4×C29—42no—
88C22⋊C4×C29—82no—
89C42×C29—21no—
90C42×C29—21no—
91#9509C2911yesmaximal, characteristic, direct product factor, Sylow
92C23×C29—21no—
93C23×C29—21no—
94C23×C29—21no—
95C23×C29—21no—
96C23×C29—41no—
97C23×C29—41no—
98C23×C29—41no—
99C23×C29—41no—
100C23×C29#10112yes—
101C23×C29C2×C22⋊C411yescharacteristic
102C23×C29C4×D412yes—
103D4×C29—44no—
104C2×C4×C29—22no—
105C2×C4×C29—24no—
106C2×C4×C29—21no—
107C2×C4×C29—21no—
108C2×C4×C29—21no—
109C2×C4×C29—21no—
110C2×C4×C29—21no—
111C2×C4×C29—41no—
112C2×C4×C29—42no—
113C2×C4×C29—42no—
114C2×C4×C29—41no—
115C2×C4×C29—41no—
116C2×C4×C29—42no—
117C2×C4×C29—42no—
118C2×C4×C29—42no—
119C2×C4×C29—42no—
120C2×C4×C29—42no—
121C2×C4×C29—42no—
122C2×C4×C29—81no—
123C2×C4×C29—84no—
124C2×C4×C29#12011yescharacteristic
125C2×C4×C29#12112yes—
126C2×C4×C29#12311yescharacteristic
127C8×C29—44no—
128C8×C29—82no—
129#2973C2×C2911yescharacteristic
130#2487C2×C2911yescharacteristic
131#1821C2×C2912yescomplemented
132#1465C2×C2911yescharacteristic
133#1305C2×C2912yescomplemented
134C22×C29—21no—
135C22×C29—21no—
136C22×C29—22no—
137C22×C29—22no—
138C22×C29—22no—
139C22×C29—22no—
140C22×C29—42no—
141C22×C29—42no—
142C22×C29—42no—
143C22×C29—41no—
144C22×C29—41no—
145C22×C29—81no—
146C22×C29#38611yescharacteristic
147C22×C29C2×#10111yescharacteristic
148C22×C29#41311yescharacteristic
149C4×C29—22no—
150C4×C29—21no—
151C4×C29—41no—
152C4×C29—41no—
153C4×C29—41no—
154C4×C29—82no—
155C4×C29—82no—
156C4×C29#45812yes—
157C2×C4×D4C22×C2911yescharacteristic
158C22×C4⋊C4C22×C2911yescharacteristic
159#435—24no—
160#432—21no—
161#407C22×C2912yes—
162#407C22×C2912yes—
163C2×C22⋊C8—21no—
164#400—21no—
165#399—21no—
166#389—21no—
167#386C4×C2912yes—
168#385C4×C2912yes—
169#380—21no—
170#380C22×C2911yescharacteristic
171#343—24no—
172#324—21no—
173#323—21no—
174C2×C29—21no—
175C2×C29—21no—
176C2×C29—42no—
177C2×C29—42no—
178C2×C29#189011yescharacteristic
179C2×C29#190111yescharacteristic
180C2×C29#191411yescharacteristic
181C22×D4C2×C4×C2911yescharacteristic
182C23×C4C2×C4×C2912yes—
183C23×C4D4×C2911yescharacteristic
184C23×C4C23×C2911yescharacteristic
185C2×M16—22no—
186C2×M16D4×C2914yes—
187C22×C8—22no—
188C4×D4—22no—
189C4×D4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4D4×C2911yescharacteristic
197C2×C22⋊C4—22no—
198C2×C22⋊C4C2×C4×C2911yescharacteristic
199C2×C22⋊C4C2×C4×C2912yes—
200C2×C22⋊C4D4×C2911yescharacteristic
201C2×C42D4×C2911yescharacteristic
202C4⋊C8—22no—
203C22⋊C8—22no—
204C22⋊C8—22no—
205C22⋊C8—22no—
206C22⋊C8—22no—
207C22⋊C8—22no—
208#97—22no—
209#95—22no—
210#95—22no—
211#95—21no—
212C29#950911yescharacteristic, direct product factor, Sylow
213C24C22⋊C4×C2911yescharacteristic
214C24C22×C4×C2911yescharacteristic
215C2×D4—22no—
216C2×D4—22no—
217C2×D4—41no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—24no—
223C22×C4—42no—
224C22×C4—42no—
225C22×C4—82no—
226C22×C4C22⋊C4×C2911yescharacteristic
227C22×C4C22⋊C4×C2911yescharacteristic
228C22×C4C22⋊C4×C2911yescharacteristic
229C22×C4C2×D4×C2912yes—
230C22×C4C2×D4×C2911yescharacteristic
231C22×C4C2×D4×C2911yescharacteristic
232C22×C4#41×C2912yes—
233M16—44no—
234M16—44no—
235C2×C8—24no—
236C2×C8—42no—
237C2×C8—82no—
238C4⋊C4—22no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—41no—
243C4⋊C4—82no—
244C22⋊C4—22no—
245C22⋊C4—22no—
246C22⋊C4—42no—
247C22⋊C4—82no—
248C42—21no—
249C42—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23—41no—
258C23C29×#10112yes—
259C23C2×C22⋊C4×C2911yescharacteristic
260C23C4×D4×C2912yes—
261D4—44no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—81no—
281C2×C4—84no—
282C2×C4C29×#12011yescharacteristic
283C2×C4C29×#12112yes—
284C2×C4C29×#12311yescharacteristic
285C8—44no—
286C8—82no—
287C22—21no—
288C22—21no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—22no—
293C22—42no—
294C22—42no—
295C22—42no—
296C22—41no—
297C22—41no—
298C22—81no—
299C22C29×#38611yescharacteristic
300C22C2×C29×#10111yescharacteristic
301C22C29×#41311yescharacteristic
302C4—22no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—82no—
308C4—82no—
309C4C29×#45812yes—
310C2—21no—
311C2—21no—
312C2—42no—
313C2—42no—
314C2C29×#189011yescharacteristic
315C2C29×#190111yescharacteristic
316C2C29×#191411yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC24C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC22×D4×C29C2×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1821C2semidirect
5. C29×#1305C2semidirect
91. #9509C29direct (N × H)
131. #1821C2×C29semidirect
133. #1305C2×C29semidirect
212. C29#9509direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#29732
C29×#24872
C29×#18212
C29×#14652
C29×#13052
#950929