Finite Group Databasebeta

← C29×#20455 #20315355

Subgroups — C29×#20455 #20315355

Order 7424.

1126 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#427C211yesmaximal, characteristic
2C22×C29×#107C211yesmaximal, characteristic
3C2×C29×#405C211yesmaximal, characteristic
4C29×#2274C212yesmaximal
5C29×#1776C214yesmaximal, complemented
6C4×C29×#107C214yesmaximal, complemented
7C29×#1736C212yesmaximal
8C22×M16×C29C2211yescharacteristic
9C23×C8×C29C2211yescharacteristic
10C2×C29×#117C2212yes—
11C2×C29×#117C2211yescharacteristic
12C22×C4⋊C4×C29C2212yes—
13C29×#427C418yescomplemented
14C2×C29×#107C418yescomplemented
15C2×C29×#107C2212yes—
16C2×C29×#107C2212yes—
17C2×C29×#107C2212yes—
18C2×C29×#106C2212yes—
19C29×#405C418yescomplemented
20C2×C29×#97C2212yes—
21C2×C4×C8×C29C2212yes—
22C4×C4⋊C4×C29—24no—
23C4×C4⋊C4×C29C2218yes—
24C4×C22⋊C4×C29—24no—
25C29×#340C2218yes—
26C23×C4×C29—22no—
27C23×C4×C29C2311yescharacteristic
28C2×M16×C29—22no—
29C2×M16×C29—22no—
30C2×M16×C29C2×C414yes—
31C22×C8×C29C2×C414yes—
32C22×C8×C29C2×C414yes—
33C22×C8×C29C2×C414yes—
34C22×C8×C29C2312yes—
35C22×C8×C29C2311yescharacteristic
36C22×C8×C29C2311yescharacteristic
37C29×#117—24no—
38C29×#117C2×C418yes—
39C29×#117C2×C414yes—
40C29×#117Q814yes—
41C2×C4⋊C4×C29—22no—
42C2×C4⋊C4×C29—24no—
43C2×C4⋊C4×C29C2×C418yes—
44C2×C4⋊C4×C29D412yes—
45C2×C4⋊C4×C29C2314yes—
46C2×C4⋊C4×C29C2314yes—
47C2×C22⋊C4×C29—22no—
48C2×C22⋊C4×C29D412yes—
49C2×C42×C29—22no—
50C2×C42×C29—28no—
51C2×C42×C29C2312yes—
52C29×#107C2×C418yes—
53C29×#107C2×C418yes—
54C29×#107C2×C418yescomplemented
55C29×#106C2×C418yescomplemented
56C29×#97C2×C418yescomplemented
57C4×C8×C29C2×C418yescomplemented
58C29×#95—28no—
59C24×C29C2×D411yescharacteristic
60C22×C4×C29—24no—
61C22×C4×C29—24no—
62C22×C4×C29—28no—
63C22×C4×C29—84no—
64C22×C4×C29C22×C412yes—
65C22×C4×C29C22×C412yes—
66C22×C4×C29C22×C412yes—
67C22×C4×C29C2×D414yes—
68C22×C4×C29C2×D411yescharacteristic
69C22×C4×C29C2×Q812yes—
70C22×C4×C29#4112yes—
71C22×C4×C29#4112yes—
72C22×C4×C29C2411yescharacteristic
73M16×C29—28no—
74C2×C8×C29—22no—
75C2×C8×C29—22no—
76C2×C8×C29C42116yescomplemented
77C2×C8×C29C22×C414yes—
78C2×C8×C29C22×C412yes—
79C2×C8×C29C22×C412yes—
80C2×C8×C29C22×C412yes—
81C2×C8×C29C22×C412yes—
82C2×C8×C29C22×C412yes—
83C2×C8×C29C22×C412yes—
84C4⋊C4×C29—28no—
85C4⋊C4×C29—24no—
86C4⋊C4×C29—24no—
87C4⋊C4×C29C4⋊C418yes—
88C4⋊C4×C29C22×C418yes—
89C4⋊C4×C29C22×C418yes—
90C22⋊C4×C29—28no—
91C22⋊C4×C29C4⋊C418yes—
92C42×C29—28no—
93C42×C29—88no—
94C42×C29C22×C414yes—
95C42×C29C2×Q814yes—
96#20455C2911yesmaximal, characteristic, direct product factor, Sylow
97C23×C29—22no—
98C23×C29—22no—
99C23×C29C2×C4⋊C412yes—
100C23×C29C4×D412yes—
101C23×C29C4×D412yes—
102C23×C29C22×D411yescharacteristic
103C2×C4×C29—24no—
104C2×C4×C29—24no—
105C2×C4×C29—28no—
106C2×C4×C29—28no—
107C2×C4×C29—44no—
108C2×C4×C29—48no—
109C2×C4×C29—44no—
110C2×C4×C29—88no—
111C2×C4×C29C2×C4214yes—
112C2×C4×C29C2×C4⋊C418yes—
113C2×C4×C29C2×C4⋊C412yes—
114C2×C4×C29#11714yes—
115C2×C4×C29C4×D412yes—
116C2×C4×C29C4×D412yes—
117C2×C4×C29C4×Q814yes—
118C2×C4×C29C4×Q814yes—
119C2×C4×C29C23×C411yescharacteristic
120C2×C4×C29C23×C411yescharacteristic
121C2×C4×C29C23×C411yescharacteristic
122C2×C4×C29C22×Q811yescharacteristic
123C2×C4×C29C2×#4111yescharacteristic
124C2×C4×C29C2×#4111yescharacteristic
125C8×C29—24no—
126C8×C29C2×C4214yes—
127C8×C29C2×C4214yes—
128C2×#427C2×C2911yescharacteristic
129C22×#107C2×C2911yescharacteristic
130C2×#405C2×C2911yescharacteristic
131#2274C2×C2912yes—
132#1776C2×C2914yescomplemented
133C4×#107C2×C2914yescomplemented
134#1736C2×C2912yes—
135C22×C29—24no—
136C22×C29—22no—
137C22×C29—22no—
138C22×C29—24no—
139C22×C29C4×C4⋊C414yes—
140C22×C29C22×C4⋊C411yescharacteristic
141C22×C29C2×C4×D411yescharacteristic
142C22×C29C2×C4×D411yescharacteristic
143C22×C29#57612yes—
144C22×C29#57812yes—
145C4×C29—28no—
146C4×C29—48no—
147C4×C29—48no—
148C4×C29C4×C4⋊C414yes—
149C4×C29C22×C4211yescharacteristic
150C4×C29C2×#11711yescharacteristic
151C4×C29C2×C4×Q811yescharacteristic
152C4×C29C2×C4×Q811yescharacteristic
153C22×M16C22×C2911yescharacteristic
154C23×C8C22×C2911yescharacteristic
155C2×#117C22×C2912yes—
156C2×#117C22×C2911yescharacteristic
157C22×C4⋊C4C22×C2912yes—
158#427C4×C2918yescomplemented
159C2×#107C4×C2918yescomplemented
160C2×#107C22×C2912yes—
161C2×#107C22×C2912yes—
162C2×#107C22×C2912yes—
163C2×#106C22×C2912yes—
164#405C4×C2918yescomplemented
165C2×#97C22×C2912yes—
166C2×C4×C8C22×C2912yes—
167C4×C4⋊C4—24no—
168C4×C4⋊C4C22×C2918yes—
169C4×C22⋊C4—24no—
170#340C22×C2918yes—
171C2×C29—24no—
172C2×C29C2×C4×C4⋊C411yescharacteristic
173C2×C29#291312yes—
174C2×C29#294811yescharacteristic
175C2×C29#295011yescharacteristic
176C2×C29#295112yes—
177C23×C4—22no—
178C23×C4C23×C2911yescharacteristic
179C2×M16—22no—
180C2×M16—22no—
181C2×M16C2×C4×C2914yes—
182C22×C8C2×C4×C2914yes—
183C22×C8C2×C4×C2914yes—
184C22×C8C2×C4×C2914yes—
185C22×C8C23×C2912yes—
186C22×C8C23×C2911yescharacteristic
187C22×C8C23×C2911yescharacteristic
188#117—24no—
189#117C2×C4×C2918yes—
190#117C2×C4×C2914yes—
191#117Q8×C2914yes—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4C2×C4×C2918yes—
195C2×C4⋊C4D4×C2912yes—
196C2×C4⋊C4C23×C2914yes—
197C2×C4⋊C4C23×C2914yes—
198C2×C22⋊C4—22no—
199C2×C22⋊C4D4×C2912yes—
200C2×C42—22no—
201C2×C42—28no—
202C2×C42C23×C2912yes—
203#107C2×C4×C2918yes—
204#107C2×C4×C2918yes—
205#107C2×C4×C2918yescomplemented
206#106C2×C4×C2918yescomplemented
207#97C2×C4×C2918yescomplemented
208C4×C8C2×C4×C2918yescomplemented
209#95—28no—
210C29#2045511yescharacteristic, direct product factor, Sylow
211C24C2×D4×C2911yescharacteristic
212C22×C4—24no—
213C22×C4—24no—
214C22×C4—28no—
215C22×C4—84no—
216C22×C4C22×C4×C2912yes—
217C22×C4C22×C4×C2912yes—
218C22×C4C22×C4×C2912yes—
219C22×C4C2×D4×C2914yes—
220C22×C4C2×D4×C2911yescharacteristic
221C22×C4C2×Q8×C2912yes—
222C22×C4#41×C2912yes—
223C22×C4#41×C2912yes—
224C22×C4C24×C2911yescharacteristic
225M16—28no—
226C2×C8—22no—
227C2×C8—22no—
228C2×C8C42×C29116yescomplemented
229C2×C8C22×C4×C2914yes—
230C2×C8C22×C4×C2912yes—
231C2×C8C22×C4×C2912yes—
232C2×C8C22×C4×C2912yes—
233C2×C8C22×C4×C2912yes—
234C2×C8C22×C4×C2912yes—
235C2×C8C22×C4×C2912yes—
236C4⋊C4—28no—
237C4⋊C4—24no—
238C4⋊C4—24no—
239C4⋊C4C4⋊C4×C2918yes—
240C4⋊C4C22×C4×C2918yes—
241C4⋊C4C22×C4×C2918yes—
242C22⋊C4—28no—
243C22⋊C4C4⋊C4×C2918yes—
244C42—28no—
245C42—88no—
246C42C22×C4×C2914yes—
247C42C2×Q8×C2914yes—
248C23—22no—
249C23—22no—
250C23C2×C4⋊C4×C2912yes—
251C23C4×D4×C2912yes—
252C23C4×D4×C2912yes—
253C23C22×D4×C2911yescharacteristic
254C2×C4—24no—
255C2×C4—24no—
256C2×C4—28no—
257C2×C4—28no—
258C2×C4—44no—
259C2×C4—48no—
260C2×C4—44no—
261C2×C4—88no—
262C2×C4C2×C42×C2914yes—
263C2×C4C2×C4⋊C4×C2918yes—
264C2×C4C2×C4⋊C4×C2912yes—
265C2×C4C29×#11714yes—
266C2×C4C4×D4×C2912yes—
267C2×C4C4×D4×C2912yes—
268C2×C4C4×Q8×C2914yes—
269C2×C4C4×Q8×C2914yes—
270C2×C4C23×C4×C2911yescharacteristic
271C2×C4C23×C4×C2911yescharacteristic
272C2×C4C23×C4×C2911yescharacteristic
273C2×C4C22×Q8×C2911yescharacteristic
274C2×C4C2×#41×C2911yescharacteristic
275C2×C4C2×#41×C2911yescharacteristic
276C8—24no—
277C8C2×C42×C2914yes—
278C8C2×C42×C2914yes—
279C22—22no—
280C22—22no—
281C22—24no—
282C22—24no—
283C22C4×C4⋊C4×C2914yes—
284C22C22×C4⋊C4×C2911yescharacteristic
285C22C2×C4×D4×C2911yescharacteristic
286C22C2×C4×D4×C2911yescharacteristic
287C22C29×#57612yes—
288C22C29×#57812yes—
289C4—28no—
290C4—48no—
291C4—48no—
292C4C4×C4⋊C4×C2914yes—
293C4C22×C42×C2911yescharacteristic
294C4C2×C29×#11711yescharacteristic
295C4C2×C4×Q8×C2911yescharacteristic
296C4C2×C4×Q8×C2911yescharacteristic
297C2—24no—
298C2C2×C4×C4⋊C4×C2911yescharacteristic
299C2C29×#291312yes—
300C2C29×#294811yescharacteristic
301C2C29×#295011yescharacteristic
302C2C29×#295112yes—
subgroupG/H
center, socleC23×C29C22×D4
commutatorC4C22×C42×C29
Frattini, cosocleC22×C4C24×C29
prime radicalC24×C29C2×D4
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C29×#117 ◁ G

Complements

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

NH ≅ G/Ntype
5. C29×#1776C2semidirect
6. C4×C29×#107C2semidirect
13. C29×#427C4semidirect
14. C2×C29×#107C4semidirect
19. C29×#405C4semidirect
54. C29×#107C2×C4semidirect
55. C29×#106C2×C4semidirect
56. C29×#97C2×C4semidirect
57. C4×C8×C29C2×C4semidirect
76. C2×C8×C29C42semidirect
96. #20455C29direct (N × H)
132. #1776C2×C29semidirect
133. C4×#107C2×C29semidirect
158. #427C4×C29semidirect
159. C2×#107C4×C29semidirect
164. #405C4×C29semidirect
205. #107C2×C4×C29semidirect
206. #106C2×C4×C29semidirect
207. #97C2×C4×C29semidirect
208. C4×C8C2×C4×C29semidirect
210. C29#20455direct (N × H)
228. C2×C8C42×C29semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#4272
C22×C29×#1072
C2×C29×#4052
C29×#22742
C29×#17762
C4×C29×#1072
C29×#17362
#2045529