Finite Group Databasebeta

← C29×#60140 #20355040

Subgroups — C29×#60140 #20355040

Order 7424.

2722 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C29×#131C212yesmaximal, complemented
2C29×#3449C211yesmaximal, characteristic
3C29×#2932C214yesmaximal, complemented
4C29×#2931C214yesmaximal, complemented
5C29×#2930C218yesmaximal, complemented
6C29×#2929C218yesmaximal, complemented
7C29×#2905C211yesmaximal, characteristic, complemented
8C29×#2879C212yesmaximal, complemented
9C2×C29×#405C211yesmaximal, characteristic, complemented
10C22×#41×C29C2212yes—
11C2×C29×#131—216no—
12C2×C29×#131C2214yes—
13C2×C29×#131C2214yes—
14C2×C29×#131C2214yescomplemented
15C2×C29×#131C2214yescomplemented
16C22×M16×C29C2212yes—
17C22×M16×C29C2211yescharacteristic
18C22×M16×C29C2214yescomplemented
19C23×C8×C29C2211yescharacteristic
20C23×C8×C29C2214yescomplemented
21C29×#537C414yes—
22C29×#536C414yes—
23C29×#535C414yes—
24C29×#534C414yes—
25C29×#532C2214yes—
26C29×#525C2218yes—
27C2×C29×#117C2211yescharacteristic
28C29×#436C22116yescomplemented
29C29×#435C22132yescomplemented
30C8×D4×C29C22116yescomplemented
31C29×#424C2218yescomplemented
32C29×#423C2214yescomplemented
33C29×#408C2218yes—
34C29×#408C2218yescomplemented
35C29×#407C2218yescomplemented
36C29×#405C2214yescomplemented
37C29×#405C2214yescomplemented
38C2×C29×#97C2212yescomplemented
39C2×C4×C8×C29C2212yescomplemented
40C2×#41×C29—28no—
41C2×#41×C29—28no—
42C2×#41×C29C2×C414yes—
43C2×#41×C29C2×C414yes—
44C2×#41×C29C2314yes—
45C2×#41×C29C2314yes—
46C22×Q8×C29C2×C412yes—
47C22×D4×C29C2×C414yes—
48C22×D4×C29C2×C412yes—
49C23×C4×C29C2314yes—
50C23×C4×C29C2311yescharacteristic
51C29×#131—216no—
52C29×#131—216no—
53C29×#131—216no—
54C29×#131—216no—
55C2×M16×C29—28no—
56C2×M16×C29—24no—
57C2×M16×C29—216no—
58C2×M16×C29C2318yes—
59C2×M16×C29C2318yes—
60C2×M16×C29C2314yes—
61C2×M16×C29C2314yes—
62C2×M16×C29C2314yes—
63C22×C8×C29—216no—
64C22×C8×C29D418yescomplemented
65C22×C8×C29C2318yes—
66C22×C8×C29C2314yes—
67C22×C8×C29C2312yes—
68C22×C8×C29C2318yes—
69C22×C8×C29C2312yes—
70C22×C8×C29C2311yescharacteristic
71C22×C8×C29C2312yes—
72C22×C8×C29C2311yescharacteristic
73C29×C4⋊Q8C2×C414yes—
74C29×#127C2×C414yes—
75C29×#124C2×C418yes—
76C29×#123C2×C4116yes—
77C29×C22⋊Q8C2×C4116yes—
78C29×#121C2×C4116yes—
79C29×#121C2×C4116yes—
80C29×#120C2×C4116yes—
81C4×D4×C29C23116yes—
82C29×#117C2×C414yes—
83C29×#117C2314yes—
84C2×C4⋊C4×C29C2×C412yes—
85C2×C22⋊C4×C29C2×C412yes—
86C2×C42×C29C2312yes—
87C29×C4⋊C8C23116yes—
88C29×C22⋊C8C23132yes—
89C29×#97C2318yes—
90C4×C8×C29C2314yes—
91C4×C8×C29C2314yes—
92C24×C29C22×C414yes—
93C24×C29C22×C411yescharacteristic
94#41×C29—216no—
95#41×C29—216no—
96#41×C29—28no—
97#41×C29—28no—
98#41×C29—28no—
99#41×C29—28no—
100C2×Q8×C29—28no—
101C2×Q8×C29C22×C414yes—
102C2×Q8×C29C22×C414yes—
103C2×D4×C29—216no—
104C2×D4×C29—28no—
105C2×D4×C29C22×C418yes—
106C2×D4×C29C22×C418yes—
107C2×D4×C29C22×C414yes—
108C2×D4×C29C22×C414yes—
109C2×D4×C29C22×C4116yes—
110C22×C4×C29—28no—
111C22×C4×C29—28no—
112C22×C4×C29C22×C418yes—
113C22×C4×C29C22×C414yes—
114C22×C4×C29C22×C414yes—
115C22×C4×C29C22×C411yescharacteristic
116C22×C4×C29C22×C412yes—
117C22×C4×C29C2×D414yes—
118C22×C4×C29#4114yes—
119C22×C4×C29C2418yes—
120C22×C4×C29C2411yescharacteristic
121C22×C4×C29C2412yes—
122M16×C29—28no—
123M16×C29—28no—
124M16×C29—28no—
125M16×C29—216no—
126M16×C29—216no—
127C2×C8×C29—28no—
128C2×C8×C29—24no—
129C2×C8×C29—216no—
130C2×C8×C29—216no—
131C2×C8×C29C2×D418yes—
132C2×C8×C29C2×D418yes—
133C2×C8×C29C2×D414yes—
134C2×C8×C29C2×D414yes—
135C2×C8×C29C2418yes—
136C2×C8×C29C2414yes—
137C2×C8×C29C2412yes—
138C2×C8×C29C2411yescharacteristic
139C2×C8×C29C2411yescharacteristic
140C4⋊C4×C29C22×C418yes—
141C4⋊C4×C29C22×C4116yes—
142C22⋊C4×C29C22×C418yes—
143C22⋊C4×C29C22×C4132yes—
144C42×C29C22×C414yes—
145C42×C29C2414yes—
146#60140C2911yesmaximal, characteristic, direct product factor, Sylow
147C23×C29—28no—
148C23×C29—42no—
149C23×C29—48no—
150C23×C29C4×D414yes—
151C23×C29C23×C418yes—
152C23×C29C23×C412yes—
153C23×C29C23×C411yescharacteristic
154Q8×C29—28no—
155Q8×C29—28no—
156D4×C29—216no—
157D4×C29—216no—
158D4×C29—28no—
159D4×C29—28no—
160D4×C29—416no—
161C2×C4×C29—28no—
162C2×C4×C29—216no—
163C2×C4×C29—28no—
164C2×C4×C29—28no—
165C2×C4×C29—44no—
166C2×C4×C29C4×D418yes—
167C2×C4×C29C4×D414yes—
168C2×C4×C29C23×C418yes—
169C2×C4×C29C23×C418yes—
170C2×C4×C29C23×C411yescharacteristic
171C2×C4×C29C23×C412yes—
172C2×C4×C29C22×D414yes—
173C2×C4×C29C22×D412yes—
174C2×C4×C29C2×#4112yes—
175C2×C4×C29C2×#4114yes—
176C2×C4×C29C2511yescharacteristic
177C8×C29—28no—
178C8×C29—24no—
179C8×C29C22×D412yes—
180C8×C29C22×D414yes—
181C8×C29C22×D412yes—
182C22×#131C2×C2912yescomplemented
183#3449C2×C2911yescharacteristic
184#2932C2×C2914yescomplemented
185#2931C2×C2914yescomplemented
186#2930C2×C2918yescomplemented
187#2929C2×C2918yescomplemented
188#2905C2×C2911yescharacteristic, complemented
189#2879C2×C2912yescomplemented
190C2×#405C2×C2911yescharacteristic, complemented
191C22×C29—22no—
192C22×C29—24no—
193C22×C29—28no—
194C22×C29—216no—
195C22×C29—44no—
196C22×C29—416no—
197C22×C29C2×C4×D414yes—
198C22×C29C2×C4×D412yes—
199C22×C29C24×C411yescharacteristic
200C4×C29—28no—
201C4×C29—28no—
202C4×C29C2×C4×D414yes—
203C4×C29C2×C4×D412yes—
204C4×C29C23×D411yescharacteristic
205C4×C29C22×#4111yescharacteristic
206C22×#41C22×C2912yes—
207C2×#131—216no—
208C2×#131C22×C2914yes—
209C2×#131C22×C2914yes—
210C2×#131C22×C2914yescomplemented
211C2×#131C22×C2914yescomplemented
212C22×M16C22×C2911yescharacteristic
213C22×M16C22×C2912yes—
214C22×M16C22×C2914yescomplemented
215C23×C8C22×C2911yescharacteristic
216C23×C8C22×C2914yescomplemented
217#537C4×C2914yes—
218#536C4×C2914yes—
219#535C4×C2914yes—
220#534C4×C2914yes—
221#532C22×C2914yes—
222#525C22×C2918yes—
223C2×#117C22×C2911yescharacteristic
224#436C22×C29116yescomplemented
225#435C22×C29132yescomplemented
226C8×D4C22×C29116yescomplemented
227#424C22×C2918yescomplemented
228#423C22×C2914yescomplemented
229#408C22×C2918yes—
230#408C22×C2918yescomplemented
231#407C22×C2918yescomplemented
232#405C22×C2914yescomplemented
233#405C22×C2914yescomplemented
234C2×#97C22×C2912yescomplemented
235C2×C4×C8C22×C2912yescomplemented
236C2×C29—24no—
237C2×C29—22no—
238C2×C29—48no—
239C2×C29C22×C4×D411yescharacteristic
240C2×C29#357312yes—
241C2×#41—28no—
242C2×#41—28no—
243C2×#41C2×C4×C2914yes—
244C2×#41C2×C4×C2914yes—
245C2×#41C23×C2914yes—
246C2×#41C23×C2914yes—
247C22×Q8C2×C4×C2912yes—
248C22×D4C2×C4×C2914yes—
249C22×D4C2×C4×C2912yes—
250C23×C4C23×C2914yes—
251C23×C4C23×C2911yescharacteristic
252#131—216no—
253#131—216no—
254#131—216no—
255#131—216no—
256C2×M16—28no—
257C2×M16—24no—
258C2×M16—216no—
259C2×M16C23×C2914yes—
260C2×M16C23×C2914yes—
261C2×M16C23×C2914yes—
262C2×M16C23×C2918yes—
263C2×M16C23×C2918yes—
264C22×C8—216no—
265C22×C8D4×C2918yescomplemented
266C22×C8C23×C2914yes—
267C22×C8C23×C2918yes—
268C22×C8C23×C2918yes—
269C22×C8C23×C2912yes—
270C22×C8C23×C2912yes—
271C22×C8C23×C2912yes—
272C22×C8C23×C2911yescharacteristic
273C22×C8C23×C2911yescharacteristic
274C4⋊Q8C2×C4×C2914yes—
275#127C2×C4×C2914yes—
276#124C2×C4×C2918yes—
277#123C2×C4×C29116yes—
278C22⋊Q8C2×C4×C29116yes—
279#121C2×C4×C29116yes—
280#121C2×C4×C29116yes—
281#120C2×C4×C29116yes—
282C4×D4C23×C29116yes—
283#117C2×C4×C2914yes—
284#117C23×C2914yes—
285C2×C4⋊C4C2×C4×C2912yes—
286C2×C22⋊C4C2×C4×C2912yes—
287C2×C42C23×C2912yes—
288C4⋊C8C23×C29116yes—
289C22⋊C8C23×C29132yes—
290#97C23×C2918yes—
291C4×C8C23×C2914yes—
292C4×C8C23×C2914yes—
293C29#6014011yescharacteristic, direct product factor, Sylow
294C24C22×C4×C2914yes—
295C24C22×C4×C2911yescharacteristic
296#41—216no—
297#41—216no—
298#41—28no—
299#41—28no—
300#41—28no—
301#41—28no—
302C2×Q8—28no—
303C2×Q8C22×C4×C2914yes—
304C2×Q8C22×C4×C2914yes—
305C2×D4—216no—
306C2×D4—28no—
307C2×D4C22×C4×C2918yes—
308C2×D4C22×C4×C2918yes—
309C2×D4C22×C4×C2914yes—
310C2×D4C22×C4×C2914yes—
311C2×D4C22×C4×C29116yes—
312C22×C4—28no—
313C22×C4—28no—
314C22×C4C22×C4×C2918yes—
315C22×C4C22×C4×C2914yes—
316C22×C4C22×C4×C2914yes—
317C22×C4C22×C4×C2911yescharacteristic
318C22×C4C22×C4×C2912yes—
319C22×C4C2×D4×C2914yes—
320C22×C4#41×C2914yes—
321C22×C4C24×C2918yes—
322C22×C4C24×C2911yescharacteristic
323C22×C4C24×C2912yes—
324M16—28no—
325M16—28no—
326M16—28no—
327M16—216no—
328M16—216no—
329C2×C8—28no—
330C2×C8—24no—
331C2×C8—216no—
332C2×C8—216no—
333C2×C8C2×D4×C2918yes—
334C2×C8C2×D4×C2918yes—
335C2×C8C2×D4×C2914yes—
336C2×C8C2×D4×C2914yes—
337C2×C8C24×C2914yes—
338C2×C8C24×C2918yes—
339C2×C8C24×C2911yescharacteristic
340C2×C8C24×C2911yescharacteristic
341C2×C8C24×C2912yes—
342C4⋊C4C22×C4×C2918yes—
343C4⋊C4C22×C4×C29116yes—
344C22⋊C4C22×C4×C2918yes—
345C22⋊C4C22×C4×C29132yes—
346C42C22×C4×C2914yes—
347C42C24×C2914yes—
348C23—28no—
349C23—42no—
350C23—48no—
351C23C4×D4×C2914yes—
352C23C23×C4×C2918yes—
353C23C23×C4×C2912yes—
354C23C23×C4×C2911yescharacteristic
355Q8—28no—
356Q8—28no—
357D4—216no—
358D4—216no—
359D4—28no—
360D4—28no—
361D4—416no—
362C2×C4—28no—
363C2×C4—216no—
364C2×C4—28no—
365C2×C4—28no—
366C2×C4—44no—
367C2×C4C4×D4×C2918yes—
368C2×C4C4×D4×C2914yes—
369C2×C4C23×C4×C2918yes—
370C2×C4C23×C4×C2918yes—
371C2×C4C23×C4×C2911yescharacteristic
372C2×C4C23×C4×C2912yes—
373C2×C4C22×D4×C2914yes—
374C2×C4C22×D4×C2912yes—
375C2×C4C2×#41×C2912yes—
376C2×C4C2×#41×C2914yes—
377C2×C4C25×C2911yescharacteristic
378C8—28no—
379C8—24no—
380C8C22×D4×C2912yes—
381C8C22×D4×C2914yes—
382C8C22×D4×C2912yes—
383C22—22no—
384C22—24no—
385C22—216no—
386C22—28no—
387C22—44no—
388C22—416no—
389C22C2×C4×D4×C2914yes—
390C22C2×C4×D4×C2912yes—
391C22C24×C4×C2911yescharacteristic
392C4—28no—
393C4—28no—
394C4C2×C4×D4×C2914yes—
395C4C2×C4×D4×C2912yes—
396C4C23×D4×C2911yescharacteristic
397C4C22×#41×C2911yescharacteristic
398C2—24no—
399C2—22no—
400C2—48no—
401C2C22×C4×D4×C2911yescharacteristic
402C2C29×#357312yes—
subgroupG/H
centerC2×C8×C29C24
commutatorC22C24×C4×C29
Frattini, cosocleC2×C4C25×C29
socleC22×C29C24×C4
prime radicalC29×#3449C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C29×#131C2semidirect
3. C29×#2932C2semidirect
4. C29×#2931C2semidirect
5. C29×#2930C2semidirect
6. C29×#2929C2semidirect
7. C29×#2905C2semidirect
8. C29×#2879C2semidirect
9. C2×C29×#405C2semidirect
14. C2×C29×#131C22semidirect
15. C2×C29×#131C22semidirect
18. C22×M16×C29C22semidirect
20. C23×C8×C29C22semidirect
28. C29×#436C22semidirect
29. C29×#435C22semidirect
30. C8×D4×C29C22semidirect
31. C29×#424C22semidirect
32. C29×#423C22semidirect
34. C29×#408C22semidirect
35. C29×#407C22semidirect
36. C29×#405C22semidirect
37. C29×#405C22semidirect
38. C2×C29×#97C22semidirect
39. C2×C4×C8×C29C22semidirect
64. C22×C8×C29D4semidirect
146. #60140C29direct (N × H)
182. C22×#131C2×C29semidirect
184. #2932C2×C29semidirect
185. #2931C2×C29semidirect
186. #2930C2×C29semidirect
187. #2929C2×C29semidirect
188. #2905C2×C29semidirect
189. #2879C2×C29semidirect
190. C2×#405C2×C29semidirect
210. C2×#131C22×C29semidirect
211. C2×#131C22×C29semidirect
214. C22×M16C22×C29semidirect
216. C23×C8C22×C29semidirect
224. #436C22×C29semidirect
225. #435C22×C29semidirect
226. C8×D4C22×C29semidirect
227. #424C22×C29semidirect
228. #423C22×C29semidirect
230. #408C22×C29semidirect
231. #407C22×C29semidirect
232. #405C22×C29semidirect
233. #405C22×C29semidirect
234. C2×#97C22×C29semidirect
235. C2×C4×C8C22×C29semidirect
265. C22×C8D4×C29semidirect
293. C29#60140direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C29×#1312
C29×#34492
C29×#29322
C29×#29312
C29×#29302
C29×#29292
C29×#29052
C29×#28792
C2×C29×#4052
#6014029