Finite Group Databasebeta

← C29×#60143 #20355043

Subgroups — C29×#60143 #20355043

Order 7424.

2706 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#568C212yesmaximal, complemented
2C29×#3449C211yesmaximal, characteristic
3C29×#2933C2116yesmaximal, complemented
4C29×#2932C214yesmaximal, complemented
5C29×#2931C214yesmaximal, complemented
6C29×#2905C211yesmaximal, characteristic, complemented
7C2×C29×#408C212yesmaximal, complemented
8C2×C29×#405C211yesmaximal, characteristic, complemented
9C22×#41×C29C2212yes—
10C29×#568—216no—
11C2×C29×#131C2218yes—
12C2×C29×#131C2218yescomplemented
13C22×M16×C29C2212yes—
14C22×M16×C29C2211yescharacteristic
15C22×M16×C29C2218yescomplemented
16C23×C8×C29C2211yescharacteristic
17C29×#537C414yes—
18C29×#536C414yes—
19C29×#535C414yes—
20C29×#534C414yes—
21C29×#532C2214yes—
22C29×#525C2218yes—
23C2×C29×#117C2211yescharacteristic
24C29×#436C22116yescomplemented
25C29×#435C22132yescomplemented
26C8×D4×C29C22116yescomplemented
27C29×#424C2218yescomplemented
28C29×#423C2214yescomplemented
29C29×#408C2218yes—
30C29×#408C2214yescomplemented
31C29×#408C2214yescomplemented
32C2×C29×C22⋊C8C2218yescomplemented
33C29×#405C2218yescomplemented
34C2×C29×#97C2212yescomplemented
35C2×C4×C8×C29C2212yescomplemented
36C2×#41×C29—28no—
37C2×#41×C29—28no—
38C2×#41×C29C2×C414yes—
39C2×#41×C29C2×C414yes—
40C2×#41×C29C2314yes—
41C2×#41×C29C2314yes—
42C22×Q8×C29C2×C412yes—
43C22×D4×C29C2×C414yes—
44C22×D4×C29C2×C412yes—
45C23×C4×C29C2314yes—
46C23×C4×C29C2311yescharacteristic
47C29×#131—232no—
48C29×#131—232no—
49C2×M16×C29—28no—
50C2×M16×C29—232no—
51C2×M16×C29D418yescomplemented
52C2×M16×C29C23116yes—
53C2×M16×C29C2314yes—
54C2×M16×C29C2314yes—
55C2×M16×C29C2314yes—
56C22×C8×C29—24no—
57C22×C8×C29C23116yes—
58C22×C8×C29C2311yescharacteristic
59C22×C8×C29C2311yescharacteristic
60C22×C8×C29C2314yes—
61C22×C8×C29C2314yes—
62C22×C8×C29C2312yes—
63C29×C4⋊Q8C2×C414yes—
64C29×#127C2×C414yes—
65C29×#124C2×C418yes—
66C29×#123C2×C4116yes—
67C29×C22⋊Q8C2×C4116yes—
68C29×#121C2×C4116yes—
69C29×#121C2×C4116yes—
70C29×#120C2×C4116yes—
71C4×D4×C29C23116yes—
72C29×#117C2×C414yes—
73C29×#117C2314yes—
74C2×C4⋊C4×C29C2×C412yes—
75C2×C22⋊C4×C29C2×C412yes—
76C2×C42×C29C2312yes—
77C29×C4⋊C8C23116yes—
78C29×C22⋊C8C23116yes—
79C29×C22⋊C8C23116yes—
80C29×#97C2318yes—
81C4×C8×C29C2318yes—
82C24×C29C22×C414yes—
83C24×C29C22×C411yescharacteristic
84#41×C29—216no—
85#41×C29—216no—
86#41×C29—28no—
87#41×C29—28no—
88#41×C29—28no—
89#41×C29—28no—
90C2×Q8×C29—28no—
91C2×Q8×C29C22×C414yes—
92C2×Q8×C29C22×C414yes—
93C2×D4×C29—216no—
94C2×D4×C29—28no—
95C2×D4×C29C22×C418yes—
96C2×D4×C29C22×C418yes—
97C2×D4×C29C22×C414yes—
98C2×D4×C29C22×C414yes—
99C2×D4×C29C22×C4116yes—
100C22×C4×C29—28no—
101C22×C4×C29—28no—
102C22×C4×C29C22×C418yes—
103C22×C4×C29C22×C414yes—
104C22×C4×C29C22×C414yes—
105C22×C4×C29C22×C411yescharacteristic
106C22×C4×C29C22×C412yes—
107C22×C4×C29C2×D414yes—
108C22×C4×C29#4114yes—
109C22×C4×C29C2418yes—
110C22×C4×C29C2411yescharacteristic
111C22×C4×C29C2412yes—
112M16×C29—28no—
113M16×C29—28no—
114M16×C29—232no—
115M16×C29C2×D4116yes—
116C2×C8×C29—28no—
117C2×C8×C29—28no—
118C2×C8×C29—22no—
119C2×C8×C29—22no—
120C2×C8×C29—232no—
121C2×C8×C29C2×D418yes—
122C2×C8×C29C2418yes—
123C2×C8×C29C2412yes—
124C2×C8×C29C2412yes—
125C2×C8×C29C2414yes—
126C4⋊C4×C29C22×C418yes—
127C4⋊C4×C29C22×C4116yes—
128C22⋊C4×C29C22×C418yes—
129C22⋊C4×C29C22×C4132yes—
130C42×C29C22×C414yes—
131C42×C29C2414yes—
132#60143C2911yesmaximal, characteristic, direct product factor, Sylow
133C23×C29—28no—
134C23×C29—42no—
135C23×C29—48no—
136C23×C29C4×D414yes—
137C23×C29C23×C418yes—
138C23×C29C23×C412yes—
139C23×C29C23×C411yescharacteristic
140Q8×C29—28no—
141Q8×C29—28no—
142D4×C29—216no—
143D4×C29—216no—
144D4×C29—28no—
145D4×C29—28no—
146D4×C29—416no—
147C2×C4×C29—28no—
148C2×C4×C29—216no—
149C2×C4×C29—28no—
150C2×C4×C29—28no—
151C2×C4×C29—44no—
152C2×C4×C29C4×D418yes—
153C2×C4×C29C4×D414yes—
154C2×C4×C29C23×C418yes—
155C2×C4×C29C23×C418yes—
156C2×C4×C29C23×C411yescharacteristic
157C2×C4×C29C23×C412yes—
158C2×C4×C29C22×D414yes—
159C2×C4×C29C22×D412yes—
160C2×C4×C29C2×#4114yes—
161C2×C4×C29C2×#4112yes—
162C2×C4×C29C2511yescharacteristic
163C8×C29—28no—
164C8×C29—22no—
165C8×C29—22no—
166C8×C29C22×D418yes—
167C2×#568C2×C2912yescomplemented
168#3449C2×C2911yescharacteristic
169#2933C2×C29116yescomplemented
170#2932C2×C2914yescomplemented
171#2931C2×C2914yescomplemented
172#2905C2×C2911yescharacteristic, complemented
173C2×#408C2×C2912yescomplemented
174C2×#405C2×C2911yescharacteristic, complemented
175C22×C29—22no—
176C22×C29—24no—
177C22×C29—28no—
178C22×C29—216no—
179C22×C29—44no—
180C22×C29—88no—
181C22×C29C2×C4×D414yes—
182C22×C29C2×C4×D412yes—
183C22×C29C24×C411yescharacteristic
184C4×C29—28no—
185C4×C29—28no—
186C4×C29C2×C4×D414yes—
187C4×C29C2×C4×D412yes—
188C4×C29C23×D411yescharacteristic
189C4×C29C22×#4111yescharacteristic
190C22×#41C22×C2912yes—
191#568—216no—
192C2×#131C22×C2918yes—
193C2×#131C22×C2918yescomplemented
194C22×M16C22×C2912yes—
195C22×M16C22×C2911yescharacteristic
196C22×M16C22×C2918yescomplemented
197C23×C8C22×C2911yescharacteristic
198#537C4×C2914yes—
199#536C4×C2914yes—
200#535C4×C2914yes—
201#534C4×C2914yes—
202#532C22×C2914yes—
203#525C22×C2918yes—
204C2×#117C22×C2911yescharacteristic
205#436C22×C29116yescomplemented
206#435C22×C29132yescomplemented
207C8×D4C22×C29116yescomplemented
208#424C22×C2918yescomplemented
209#423C22×C2914yescomplemented
210#408C22×C2918yes—
211#408C22×C2914yescomplemented
212#408C22×C2914yescomplemented
213C2×C22⋊C8C22×C2918yescomplemented
214#405C22×C2918yescomplemented
215C2×#97C22×C2912yescomplemented
216C2×C4×C8C22×C2912yescomplemented
217C2×C29—24no—
218C2×C29—22no—
219C2×C29—48no—
220C2×C29C22×C4×D411yescharacteristic
221C2×C29#357312yes—
222C2×#41—28no—
223C2×#41—28no—
224C2×#41C2×C4×C2914yes—
225C2×#41C2×C4×C2914yes—
226C2×#41C23×C2914yes—
227C2×#41C23×C2914yes—
228C22×Q8C2×C4×C2912yes—
229C22×D4C2×C4×C2914yes—
230C22×D4C2×C4×C2912yes—
231C23×C4C23×C2914yes—
232C23×C4C23×C2911yescharacteristic
233#131—232no—
234#131—232no—
235C2×M16—28no—
236C2×M16—232no—
237C2×M16D4×C2918yescomplemented
238C2×M16C23×C2914yes—
239C2×M16C23×C2914yes—
240C2×M16C23×C29116yes—
241C2×M16C23×C2914yes—
242C22×C8—24no—
243C22×C8C23×C2911yescharacteristic
244C22×C8C23×C2911yescharacteristic
245C22×C8C23×C2914yes—
246C22×C8C23×C2914yes—
247C22×C8C23×C29116yes—
248C22×C8C23×C2912yes—
249C4⋊Q8C2×C4×C2914yes—
250#127C2×C4×C2914yes—
251#124C2×C4×C2918yes—
252#123C2×C4×C29116yes—
253C22⋊Q8C2×C4×C29116yes—
254#121C2×C4×C29116yes—
255#121C2×C4×C29116yes—
256#120C2×C4×C29116yes—
257C4×D4C23×C29116yes—
258#117C2×C4×C2914yes—
259#117C23×C2914yes—
260C2×C4⋊C4C2×C4×C2912yes—
261C2×C22⋊C4C2×C4×C2912yes—
262C2×C42C23×C2912yes—
263C4⋊C8C23×C29116yes—
264C22⋊C8C23×C29116yes—
265C22⋊C8C23×C29116yes—
266#97C23×C2918yes—
267C4×C8C23×C2918yes—
268C29#6014311yescharacteristic, direct product factor, Sylow
269C24C22×C4×C2914yes—
270C24C22×C4×C2911yescharacteristic
271#41—216no—
272#41—216no—
273#41—28no—
274#41—28no—
275#41—28no—
276#41—28no—
277C2×Q8—28no—
278C2×Q8C22×C4×C2914yes—
279C2×Q8C22×C4×C2914yes—
280C2×D4—216no—
281C2×D4—28no—
282C2×D4C22×C4×C2918yes—
283C2×D4C22×C4×C2918yes—
284C2×D4C22×C4×C2914yes—
285C2×D4C22×C4×C2914yes—
286C2×D4C22×C4×C29116yes—
287C22×C4—28no—
288C22×C4—28no—
289C22×C4C22×C4×C2918yes—
290C22×C4C22×C4×C2914yes—
291C22×C4C22×C4×C2914yes—
292C22×C4C22×C4×C2911yescharacteristic
293C22×C4C22×C4×C2912yes—
294C22×C4C2×D4×C2914yes—
295C22×C4#41×C2914yes—
296C22×C4C24×C2918yes—
297C22×C4C24×C2911yescharacteristic
298C22×C4C24×C2912yes—
299M16—28no—
300M16—28no—
301M16—232no—
302M16C2×D4×C29116yes—
303C2×C8—28no—
304C2×C8—28no—
305C2×C8—22no—
306C2×C8—22no—
307C2×C8—232no—
308C2×C8C2×D4×C2918yes—
309C2×C8C24×C2912yes—
310C2×C8C24×C2912yes—
311C2×C8C24×C2918yes—
312C2×C8C24×C2914yes—
313C4⋊C4C22×C4×C2918yes—
314C4⋊C4C22×C4×C29116yes—
315C22⋊C4C22×C4×C2918yes—
316C22⋊C4C22×C4×C29132yes—
317C42C22×C4×C2914yes—
318C42C24×C2914yes—
319C23—28no—
320C23—42no—
321C23—48no—
322C23C4×D4×C2914yes—
323C23C23×C4×C2918yes—
324C23C23×C4×C2912yes—
325C23C23×C4×C2911yescharacteristic
326Q8—28no—
327Q8—28no—
328D4—216no—
329D4—216no—
330D4—28no—
331D4—28no—
332D4—416no—
333C2×C4—28no—
334C2×C4—216no—
335C2×C4—28no—
336C2×C4—28no—
337C2×C4—44no—
338C2×C4C4×D4×C2918yes—
339C2×C4C4×D4×C2914yes—
340C2×C4C23×C4×C2918yes—
341C2×C4C23×C4×C2918yes—
342C2×C4C23×C4×C2911yescharacteristic
343C2×C4C23×C4×C2912yes—
344C2×C4C22×D4×C2914yes—
345C2×C4C22×D4×C2912yes—
346C2×C4C2×#41×C2914yes—
347C2×C4C2×#41×C2912yes—
348C2×C4C25×C2911yescharacteristic
349C8—28no—
350C8—22no—
351C8—22no—
352C8C22×D4×C2918yes—
353C22—22no—
354C22—24no—
355C22—216no—
356C22—28no—
357C22—44no—
358C22—88no—
359C22C2×C4×D4×C2914yes—
360C22C2×C4×D4×C2912yes—
361C22C24×C4×C2911yescharacteristic
362C4—28no—
363C4—28no—
364C4C2×C4×D4×C2914yes—
365C4C2×C4×D4×C2912yes—
366C4C23×D4×C2911yescharacteristic
367C4C22×#41×C2911yescharacteristic
368C2—24no—
369C2—22no—
370C2—48no—
371C2C22×C4×D4×C2911yescharacteristic
372C2C29×#357312yes—
subgroupG/H
centerC2×C4×C29C25
commutatorC22C24×C4×C29
Frattini, cosocleC2×C4C25×C29
socleC22×C29C24×C4
prime radicalC29×#3449C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#568C2semidirect
3. C29×#2933C2semidirect
4. C29×#2932C2semidirect
5. C29×#2931C2semidirect
6. C29×#2905C2semidirect
7. C2×C29×#408C2semidirect
8. C2×C29×#405C2semidirect
12. C2×C29×#131C22semidirect
15. C22×M16×C29C22semidirect
24. C29×#436C22semidirect
25. C29×#435C22semidirect
26. C8×D4×C29C22semidirect
27. C29×#424C22semidirect
28. C29×#423C22semidirect
30. C29×#408C22semidirect
31. C29×#408C22semidirect
32. C2×C29×C22⋊C8C22semidirect
33. C29×#405C22semidirect
34. C2×C29×#97C22semidirect
35. C2×C4×C8×C29C22semidirect
51. C2×M16×C29D4semidirect
132. #60143C29direct (N × H)
167. C2×#568C2×C29semidirect
169. #2933C2×C29semidirect
170. #2932C2×C29semidirect
171. #2931C2×C29semidirect
172. #2905C2×C29semidirect
173. C2×#408C2×C29semidirect
174. C2×#405C2×C29semidirect
193. C2×#131C22×C29semidirect
196. C22×M16C22×C29semidirect
205. #436C22×C29semidirect
206. #435C22×C29semidirect
207. C8×D4C22×C29semidirect
208. #424C22×C29semidirect
209. #423C22×C29semidirect
211. #408C22×C29semidirect
212. #408C22×C29semidirect
213. C2×C22⋊C8C22×C29semidirect
214. #405C22×C29semidirect
215. C2×#97C22×C29semidirect
216. C2×C4×C8C22×C29semidirect
237. C2×M16D4×C29semidirect
268. C29#60143direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5682
C29×#34492
C29×#29332
C29×#29322
C29×#29312
C29×#29052
C2×C29×#4082
C2×C29×#4052
#6014329