Finite Group Databasebeta

← C29×#20347 #20315247

Subgroups — C29×#20347 #20315247

Order 7424.

2270 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×M16×C29C211yesmaximal, characteristic
2C22×C29×#117C212yesmaximal
3C29×#1736C218yesmaximal, complemented
4C29×#1735C214yesmaximal, complemented
5C24×C4×C29C2211yescharacteristic
6C22×M16×C29—28no—
7C22×M16×C29C418yescomplemented
8C22×M16×C29C2214yes—
9C23×C8×C29C2212yes—
10C2×C29×#117—28no—
11C2×C29×#117—22no—
12C2×C29×#117—22no—
13C2×C29×#117C4116yescomplemented
14C2×C29×#117C2214yes—
15C2×C29×#117C2214yes—
16C22×C4⋊C4×C29C2214yes—
17C22×C22⋊C4×C29—22no—
18C22×C42×C29—22no—
19C29×#340C22116yescomplemented
20C25×C29D411yescharacteristic
21C23×C4×C29—24no—
22C23×C4×C29C2×C414yes—
23C23×C4×C29C2×C418yes—
24C23×C4×C29D411yescharacteristic
25C23×C4×C29D412yes—
26C23×C4×C29D418yes—
27C23×C4×C29Q814yes—
28C23×C4×C29C2312yes—
29C23×C4×C29C2311yescharacteristic
30C2×M16×C29—232no—
31C2×M16×C29—28no—
32C2×M16×C29—28no—
33C2×M16×C29C2×C4116yescomplemented
34C22×C8×C29—28no—
35C22×C8×C29C2×C418yescomplemented
36C22×C8×C29C2314yes—
37C29×#117—216no—
38C29×#117—216no—
39C29×#117—28no—
40C29×#117—28no—
41C29×#117C2×C4116yes—
42C29×#117C2×C4116yescomplemented
43C2×C4⋊C4×C29—24no—
44C2×C4⋊C4×C29—28no—
45C2×C4⋊C4×C29C2×C4116yescomplemented
46C2×C4⋊C4×C29C2318yes—
47C2×C22⋊C4×C29—216no—
48C2×C22⋊C4×C29—24no—
49C2×C22⋊C4×C29—24no—
50C2×C42×C29—216no—
51C2×C42×C29—24no—
52C2×C42×C29—24no—
53C24×C29—44no—
54C24×C29C22⋊C418yes—
55C24×C29C4⋊C414yes—
56C24×C29C2×D411yescharacteristic
57C24×C29C2×D412yes—
58C22×C4×C29—216no—
59C22×C4×C29—28no—
60C22×C4×C29—416no—
61C22×C4×C29C42116yes—
62C22×C4×C29C22⋊C418yes—
63C22×C4×C29C22⋊C418yes—
64C22×C4×C29C22⋊C418yes—
65C22×C4×C29C22⋊C4116yes—
66C22×C4×C29C4⋊C414yes—
67C22×C4×C29C4⋊C418yes—
68C22×C4×C29C4⋊C4132yes—
69C22×C4×C29C22×C412yes—
70C22×C4×C29C22×C414yes—
71C22×C4×C29C22×C414yes—
72C22×C4×C29C22×C414yes—
73C22×C4×C29C22×C414yes—
74C22×C4×C29C2×D412yes—
75C22×C4×C29C2×D414yes—
76C22×C4×C29C2×D414yes—
77C22×C4×C29C2×D414yes—
78C22×C4×C29C2×D411yescharacteristic
79C22×C4×C29C2×Q814yes—
80C22×C4×C29C2×Q812yes—
81C22×C4×C29C2411yescharacteristic
82M16×C29—232no—
83C2×C8×C29—216no—
84C2×C8×C29—28no—
85C2×C8×C29C22×C418yes—
86C4⋊C4×C29—216no—
87C4⋊C4×C29—28no—
88C4⋊C4×C29C22×C4116yes—
89C22⋊C4×C29—216no—
90C22⋊C4×C29—216no—
91C42×C29—216no—
92C42×C29—216no—
93#20347C2911yesmaximal, characteristic, direct product factor, Sylow
94C23×C29—28no—
95C23×C29—24no—
96C23×C29—416no—
97C23×C29—48no—
98C23×C29#95116yes—
99C23×C29C2×C22⋊C414yes—
100C23×C29C2×C22⋊C414yes—
101C23×C29C2×C22⋊C414yes—
102C23×C29C2×C4⋊C412yes—
103C23×C29C2×C4⋊C414yes—
104C23×C29C22×D411yescharacteristic
105C2×C4×C29—216no—
106C2×C4×C29—432no—
107C2×C4×C29—416no—
108C2×C4×C29#95132yes—
109C2×C4×C29#95116yes—
110C2×C4×C29C2×C4214yes—
111C2×C4×C29C2×C4218yes—
112C2×C4×C29C2×C22⋊C414yes—
113C2×C4×C29C2×C22⋊C418yes—
114C2×C4×C29C2×C22⋊C414yes—
115C2×C4×C29C2×C22⋊C414yes—
116C2×C4×C29C2×C22⋊C414yes—
117C2×C4×C29C2×C4⋊C418yes—
118C2×C4×C29C2×C4⋊C418yes—
119C2×C4×C29C2×C4⋊C418yes—
120C2×C4×C29C2×C4⋊C414yes—
121C2×C4×C29C2×C4⋊C412yes—
122C2×C4×C29C23×C411yescharacteristic
123C2×C4×C29C23×C412yes—
124C2×C4×C29C22×D412yes—
125C2×C4×C29C22×Q811yescharacteristic
126C8×C29—28no—
127C23×M16C2×C2911yescharacteristic
128C22×#117C2×C2912yes—
129#1736C2×C2918yescomplemented
130#1735C2×C2914yescomplemented
131C22×C29—28no—
132C22×C29—28no—
133C22×C29—28no—
134C22×C29—28no—
135C22×C29—24no—
136C22×C29—416no—
137C22×C29C2×#9514yes—
138C22×C29C2×#9518yes—
139C22×C29C22×C22⋊C412yes—
140C22×C29C22×C4⋊C411yescharacteristic
141C22×C29#57514yes—
142C4×C29—416no—
143C4×C29C2×#9514yes—
144C4×C29C2×#9518yes—
145C4×C29C22×C4211yescharacteristic
146C4×C29C22×C22⋊C411yescharacteristic
147C4×C29C22×C4⋊C412yes—
148C24×C4C22×C2911yescharacteristic
149C22×M16—28no—
150C22×M16C4×C2918yescomplemented
151C22×M16C22×C2914yes—
152C23×C8C22×C2912yes—
153C2×#117—28no—
154C2×#117—22no—
155C2×#117—22no—
156C2×#117C4×C29116yescomplemented
157C2×#117C22×C2914yes—
158C2×#117C22×C2914yes—
159C22×C4⋊C4C22×C2914yes—
160C22×C22⋊C4—22no—
161C22×C42—22no—
162#340C22×C29116yescomplemented
163C2×C29—28no—
164C2×C29—24no—
165C2×C29C22×#9511yescharacteristic
166C2×C29#289614yes—
167C2×C29#291112yes—
168C25D4×C2911yescharacteristic
169C23×C4—24no—
170C23×C4C2×C4×C2914yes—
171C23×C4C2×C4×C2918yes—
172C23×C4D4×C2911yescharacteristic
173C23×C4D4×C2912yes—
174C23×C4D4×C2918yes—
175C23×C4Q8×C2914yes—
176C23×C4C23×C2912yes—
177C23×C4C23×C2911yescharacteristic
178C2×M16—232no—
179C2×M16—28no—
180C2×M16—28no—
181C2×M16C2×C4×C29116yescomplemented
182C22×C8—28no—
183C22×C8C2×C4×C2918yescomplemented
184C22×C8C23×C2914yes—
185#117—216no—
186#117—216no—
187#117—28no—
188#117—28no—
189#117C2×C4×C29116yes—
190#117C2×C4×C29116yescomplemented
191C2×C4⋊C4—24no—
192C2×C4⋊C4—28no—
193C2×C4⋊C4C2×C4×C29116yescomplemented
194C2×C4⋊C4C23×C2918yes—
195C2×C22⋊C4—216no—
196C2×C22⋊C4—24no—
197C2×C22⋊C4—24no—
198C2×C42—216no—
199C2×C42—24no—
200C2×C42—24no—
201C29#2034711yescharacteristic, direct product factor, Sylow
202C24—44no—
203C24C22⋊C4×C2918yes—
204C24C4⋊C4×C2914yes—
205C24C2×D4×C2911yescharacteristic
206C24C2×D4×C2912yes—
207C22×C4—216no—
208C22×C4—28no—
209C22×C4—416no—
210C22×C4C42×C29116yes—
211C22×C4C22⋊C4×C29116yes—
212C22×C4C22⋊C4×C2918yes—
213C22×C4C22⋊C4×C2918yes—
214C22×C4C22⋊C4×C2918yes—
215C22×C4C4⋊C4×C29132yes—
216C22×C4C4⋊C4×C2914yes—
217C22×C4C4⋊C4×C2918yes—
218C22×C4C22×C4×C2912yes—
219C22×C4C22×C4×C2914yes—
220C22×C4C22×C4×C2914yes—
221C22×C4C22×C4×C2914yes—
222C22×C4C22×C4×C2914yes—
223C22×C4C2×D4×C2911yescharacteristic
224C22×C4C2×D4×C2912yes—
225C22×C4C2×D4×C2914yes—
226C22×C4C2×D4×C2914yes—
227C22×C4C2×D4×C2914yes—
228C22×C4C2×Q8×C2914yes—
229C22×C4C2×Q8×C2912yes—
230C22×C4C24×C2911yescharacteristic
231M16—232no—
232C2×C8—216no—
233C2×C8—28no—
234C2×C8C22×C4×C2918yes—
235C4⋊C4—216no—
236C4⋊C4—28no—
237C4⋊C4C22×C4×C29116yes—
238C22⋊C4—216no—
239C22⋊C4—216no—
240C42—216no—
241C42—216no—
242C23—28no—
243C23—24no—
244C23—416no—
245C23—48no—
246C23C29×#95116yes—
247C23C2×C22⋊C4×C2914yes—
248C23C2×C22⋊C4×C2914yes—
249C23C2×C22⋊C4×C2914yes—
250C23C2×C4⋊C4×C2912yes—
251C23C2×C4⋊C4×C2914yes—
252C23C22×D4×C2911yescharacteristic
253C2×C4—216no—
254C2×C4—432no—
255C2×C4—416no—
256C2×C4C29×#95132yes—
257C2×C4C29×#95116yes—
258C2×C4C2×C42×C2914yes—
259C2×C4C2×C42×C2918yes—
260C2×C4C2×C22⋊C4×C2914yes—
261C2×C4C2×C22⋊C4×C2918yes—
262C2×C4C2×C22⋊C4×C2914yes—
263C2×C4C2×C22⋊C4×C2914yes—
264C2×C4C2×C22⋊C4×C2914yes—
265C2×C4C2×C4⋊C4×C2918yes—
266C2×C4C2×C4⋊C4×C2918yes—
267C2×C4C2×C4⋊C4×C2918yes—
268C2×C4C2×C4⋊C4×C2912yes—
269C2×C4C2×C4⋊C4×C2914yes—
270C2×C4C23×C4×C2911yescharacteristic
271C2×C4C23×C4×C2912yes—
272C2×C4C22×D4×C2912yes—
273C2×C4C22×Q8×C2911yescharacteristic
274C8—28no—
275C22—28no—
276C22—28no—
277C22—28no—
278C22—28no—
279C22—24no—
280C22—416no—
281C22C2×C29×#9514yes—
282C22C2×C29×#9518yes—
283C22C22×C22⋊C4×C2912yes—
284C22C22×C4⋊C4×C2911yescharacteristic
285C22C29×#57514yes—
286C4—416no—
287C4C2×C29×#9514yes—
288C4C2×C29×#9518yes—
289C4C22×C42×C2911yescharacteristic
290C4C22×C22⋊C4×C2911yescharacteristic
291C4C22×C4⋊C4×C2912yes—
292C2—28no—
293C2—24no—
294C2C22×C29×#9511yescharacteristic
295C2C29×#289614yes—
296C2C29×#291112yes—
subgroupG/H
centerC22×C4×C29C2×D4
commutatorC4C22×C42×C29
Frattini, cosocleC22×C4C24×C29
socleC23×C29C22×D4
prime radicalC25×C29D4
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C29 ◁ C24×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1736C2semidirect
4. C29×#1735C2semidirect
7. C22×M16×C29C4semidirect
13. C2×C29×#117C4semidirect
19. C29×#340C22semidirect
33. C2×M16×C29C2×C4semidirect
35. C22×C8×C29C2×C4semidirect
42. C29×#117C2×C4semidirect
45. C2×C4⋊C4×C29C2×C4semidirect
93. #20347C29direct (N × H)
129. #1736C2×C29semidirect
130. #1735C2×C29semidirect
150. C22×M16C4×C29semidirect
156. C2×#117C4×C29semidirect
162. #340C22×C29semidirect
181. C2×M16C2×C4×C29semidirect
183. C22×C8C2×C4×C29semidirect
190. #117C2×C4×C29semidirect
193. C2×C4⋊C4C2×C4×C29semidirect
201. C29#20347direct (N × H)

Maximal subgroups

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

subgroupindex
C23×M16×C292
C22×C29×#1172
C29×#17362
C29×#17352
#2034729