Finite Group Databasebeta

← C29×#9054 #20303954

Subgroups — C29×#9054 #20303954

Order 7424.

470 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3167C211yesmaximal, characteristic
2C29×#2962C211yesmaximal, characteristic, complemented
3C29×#1980C211yesmaximal, characteristic
4C29×#1503C211yesmaximal, characteristic, complemented
5C29×#1480C211yesmaximal, characteristic
6C29×#1279C211yesmaximal, characteristic, complemented
7C29×#1278C211yesmaximal, characteristic, complemented
8C29×#533C2211yescharacteristic
9C29×#532C2211yescharacteristic
10C29×#498C411yescharacteristic, complemented
11C29×#492C411yescharacteristic, complemented
12C29×#487C411yescharacteristic, complemented
13C29×#486C411yescharacteristic, complemented
14C29×#465—22no—
15C29×#446—21no—
16C29×#446—22no—
17C8×Q8×C29—21no—
18C4×SD16×C29—22no—
19C29×#431C2211yescharacteristic
20C29×#424—21no—
21C2×C29×C4⋊C8C2211yescharacteristic
22C2×C29×#104—21no—
23C2×C29×#104—21no—
24C29×#405—21no—
25C4×M16×C29C2211yescharacteristic
26C2×C4×C8×C29C2211yescharacteristic
27C4×C4⋊C4×C29C2211yescharacteristic
28C29×#328—22no—
29C29×D4⋊C8—21no—
30C29×D4⋊C8—21no—
31C2×#41×C29—21no—
32C2×SD16×C29—22no—
33C2×M16×C29D411yescharacteristic
34C2×M16×C29D411yescharacteristic
35C22×C8×C29—21no—
36C22×C8×C29—21no—
37C29×C4⋊Q8C2×C411yescharacteristic
38C29×C4⋊Q8C2×C411yescharacteristic
39C29×C4⋊Q8C2×C411yescharacteristic
40C29×#127C2×C411yescharacteristic
41C29×#125—21no—
42C29×#124—21no—
43C29×C22⋊Q8—21no—
44C29×C22⋊Q8D412yes—
45C29×#121—21no—
46C29×#121—21no—
47C4×Q8×C29—21no—
48C4×Q8×C29D412yes—
49C4×D4×C29—21no—
50C4×D4×C29—21no—
51C29×#117—21no—
52C2×C4⋊C4×C29—21no—
53C2×C42×C29—21no—
54C2×C42×C29C2311yescharacteristic
55C29×#106—22no—
56C29×C4⋊C8—22no—
57C29×C4⋊C8—22no—
58C29×C4⋊C8—21no—
59C29×C4⋊C8—21no—
60C29×C4⋊C8D411yescharacteristic
61C29×C4⋊C8D411yescharacteristic
62C29×#104—42no—
63C29×#104—42no—
64C29×#103—22no—
65C29×#102—22no—
66C29×C22⋊C8—21no—
67C29×#97—22no—
68C29×#97—21no—
69C4×C8×C29—22no—
70C4×C8×C29—21no—
71C4×C8×C29—21no—
72C4×C8×C29—21no—
73C4×C8×C29C2×C411yescharacteristic
74C4×C8×C29C2×C411yescharacteristic
75C29×#95—21no—
76#41×C29—41no—
77#41×C29—41no—
78#41×C29—41no—
79#41×C29—41no—
80C2×Q8×C29—21no—
81C2×Q8×C29—21no—
82C2×Q8×C29C22⋊C412yes—
83C2×D4×C29—21no—
84C2×D4×C29—21no—
85C2×D4×C29—21no—
86C2×D4×C29—41no—
87C22×C4×C29—41no—
88C22×C4×C29—41no—
89C22×C4×C29C2×D411yescharacteristic
90C22×C4×C29C2×D411yescharacteristic
91C22×C4×C29#4111yescharacteristic
92SD16×C29—44no—
93M16×C29—21no—
94M16×C29—21no—
95M16×C29—21no—
96M16×C29SD1612yescomplemented
97C2×C8×C29—21no—
98C2×C8×C29—21no—
99C2×C8×C29—21no—
100C2×C8×C29—21no—
101C2×C8×C29—21no—
102C2×C8×C29—21no—
103C2×C8×C29—42no—
104C2×C8×C29—41no—
105C2×C8×C29—41no—
106C2×C8×C29—41no—
107C4⋊C4×C29—21no—
108C4⋊C4×C29—21no—
109C4⋊C4×C29—21no—
110C4⋊C4×C29—22no—
111C4⋊C4×C29—22no—
112C4⋊C4×C29—22no—
113C4⋊C4×C29—21no—
114C4⋊C4×C29—21no—
115C4⋊C4×C29—41no—
116C4⋊C4×C29C22⋊C412yes—
117C22⋊C4×C29—22no—
118C22⋊C4×C29—41no—
119C22⋊C4×C29—41no—
120C42×C29—22no—
121C42×C29—41no—
122C42×C29—41no—
123C42×C29C22×C411yescharacteristic
124C42×C29C2×D411yescharacteristic
125C42×C29C2×D411yescharacteristic
126C42×C29#4111yescharacteristic
127#9054C2911yesmaximal, characteristic, direct product factor, Sylow
128C23×C29—41no—
129C23×C29#12111yescharacteristic
130Q8×C29—42no—
131Q8×C29—41no—
132Q8×C29—41no—
133Q8×C29—41no—
134Q8×C29—41no—
135D4×C29—42no—
136D4×C29—41no—
137D4×C29—41no—
138D4×C29—41no—
139D4×C29—41no—
140D4×C29—81no—
141D4×C29—81no—
142C2×C4×C29—21no—
143C2×C4×C29—21no—
144C2×C4×C29—22no—
145C2×C4×C29—22no—
146C2×C4×C29—41no—
147C2×C4×C29—42no—
148C2×C4×C29—41no—
149C2×C4×C29—81no—
150C2×C4×C29—81no—
151C2×C4×C29—81no—
152C2×C4×C29—81no—
153C2×C4×C29C2×C22⋊C411yescharacteristic
154C2×C4×C29C4×D411yescharacteristic
155C2×C4×C29C4×D411yescharacteristic
156C2×C4×C29#12011yescharacteristic
157C2×C4×C29#12111yescharacteristic
158C2×C4×C29#12311yescharacteristic
159C2×C4×C29C2×SD1611yescharacteristic
160C2×C4×C29#13511yescharacteristic
161C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C29#13711yescharacteristic
163C8×C29—22no—
164C8×C29—22no—
165C8×C29—41no—
166C8×C29—41no—
167C8×C29—41no—
168C8×C29—41no—
169C8×C29—81no—
170#3167C2×C2911yescharacteristic
171#2962C2×C2911yescharacteristic, complemented
172#1980C2×C2911yescharacteristic
173#1503C2×C2911yescharacteristic, complemented
174#1480C2×C2911yescharacteristic
175#1279C2×C2911yescharacteristic, complemented
176#1278C2×C2911yescharacteristic, complemented
177C22×C29—21no—
178C22×C29—21no—
179C22×C29—81no—
180C22×C29—81no—
181C22×C29—81no—
182C22×C29#38611yescharacteristic
183C22×C29#46011yescharacteristic
184C22×C29#46411yescharacteristic
185C4×C29—21no—
186C4×C29—21no—
187C4×C29—21no—
188C4×C29—42no—
189C4×C29—42no—
190C4×C29—82no—
191C4×C29—81no—
192C4×C29C4×SD1611yescharacteristic
193C4×C29#44011yescharacteristic
194C4×C29#44311yescharacteristic
195C4×C29#44411yescharacteristic
196C4×C29#44811yescharacteristic
197C4×C29#44911yescharacteristic
198#533C22×C2911yescharacteristic
199#532C22×C2911yescharacteristic
200#498C4×C2911yescharacteristic, complemented
201#492C4×C2911yescharacteristic, complemented
202#487C4×C2911yescharacteristic, complemented
203#486C4×C2911yescharacteristic, complemented
204#465—22no—
205#446—22no—
206#446—21no—
207C8×Q8—21no—
208C4×SD16—22no—
209#431C22×C2911yescharacteristic
210#424—21no—
211C2×C4⋊C8C22×C2911yescharacteristic
212C2×#104—21no—
213C2×#104—21no—
214#405—21no—
215C4×M16C22×C2911yescharacteristic
216C2×C4×C8C22×C2911yescharacteristic
217C4×C4⋊C4C22×C2911yescharacteristic
218#328—22no—
219D4⋊C8—21no—
220D4⋊C8—21no—
221C2×C29—21no—
222C2×C29—21no—
223C2×C29—161no—
224C2×C29#187611yescharacteristic
225C2×C29#188011yescharacteristic
226C2×C29#188411yescharacteristic
227C2×#41—21no—
228C2×SD16—22no—
229C2×M16D4×C2911yescharacteristic
230C2×M16D4×C2911yescharacteristic
231C22×C8—21no—
232C22×C8—21no—
233C4⋊Q8C2×C4×C2911yescharacteristic
234C4⋊Q8C2×C4×C2911yescharacteristic
235C4⋊Q8C2×C4×C2911yescharacteristic
236#127C2×C4×C2911yescharacteristic
237#125—21no—
238#124—21no—
239C22⋊Q8—21no—
240C22⋊Q8D4×C2912yes—
241#121—21no—
242#121—21no—
243C4×Q8—21no—
244C4×Q8D4×C2912yes—
245C4×D4—21no—
246C4×D4—21no—
247#117—21no—
248C2×C4⋊C4—21no—
249C2×C42—21no—
250C2×C42C23×C2911yescharacteristic
251#106—22no—
252C4⋊C8—22no—
253C4⋊C8—22no—
254C4⋊C8—21no—
255C4⋊C8—21no—
256C4⋊C8D4×C2911yescharacteristic
257C4⋊C8D4×C2911yescharacteristic
258#104—42no—
259#104—42no—
260#103—22no—
261#102—22no—
262C22⋊C8—21no—
263#97—22no—
264#97—21no—
265C4×C8—22no—
266C4×C8—21no—
267C4×C8—21no—
268C4×C8—21no—
269C4×C8C2×C4×C2911yescharacteristic
270C4×C8C2×C4×C2911yescharacteristic
271#95—21no—
272C29#905411yescharacteristic, direct product factor, Sylow
273#41—41no—
274#41—41no—
275#41—41no—
276#41—41no—
277C2×Q8—21no—
278C2×Q8—21no—
279C2×Q8C22⋊C4×C2912yes—
280C2×D4—21no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—41no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4C2×D4×C2911yescharacteristic
287C22×C4C2×D4×C2911yescharacteristic
288C22×C4#41×C2911yescharacteristic
289SD16—44no—
290M16—21no—
291M16—21no—
292M16—21no—
293M16SD16×C2912yescomplemented
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—42no—
301C2×C8—41no—
302C2×C8—41no—
303C2×C8—41no—
304C4⋊C4—21no—
305C4⋊C4—21no—
306C4⋊C4—21no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—22no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4C22⋊C4×C2912yes—
314C22⋊C4—22no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C42—22no—
318C42—41no—
319C42—41no—
320C42C22×C4×C2911yescharacteristic
321C42C2×D4×C2911yescharacteristic
322C42C2×D4×C2911yescharacteristic
323C42#41×C2911yescharacteristic
324C23—41no—
325C23C29×#12111yescharacteristic
326Q8—42no—
327Q8—41no—
328Q8—41no—
329Q8—41no—
330Q8—41no—
331D4—42no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—41no—
336D4—81no—
337D4—81no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—81no—
346C2×C4—81no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4C2×C22⋊C4×C2911yescharacteristic
350C2×C4C4×D4×C2911yescharacteristic
351C2×C4C4×D4×C2911yescharacteristic
352C2×C4C29×#12011yescharacteristic
353C2×C4C29×#12111yescharacteristic
354C2×C4C29×#12311yescharacteristic
355C2×C4C2×SD16×C2911yescharacteristic
356C2×C4C29×#13511yescharacteristic
357C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
358C2×C4C29×#13711yescharacteristic
359C8—22no—
360C8—22no—
361C8—41no—
362C8—41no—
363C8—41no—
364C8—41no—
365C8—81no—
366C22—21no—
367C22—21no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22C29×#38611yescharacteristic
372C22C29×#46011yescharacteristic
373C22C29×#46411yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—42no—
378C4—42no—
379C4—82no—
380C4—81no—
381C4C4×SD16×C2911yescharacteristic
382C4C29×#44011yescharacteristic
383C4C29×#44311yescharacteristic
384C4C29×#44411yescharacteristic
385C4C29×#44811yescharacteristic
386C4C29×#44911yescharacteristic
387C2—21no—
388C2—21no—
389C2—161no—
390C2C29×#187611yescharacteristic
391C2C29×#188011yescharacteristic
392C2C29×#188411yescharacteristic
subgroupG/H
centerC2×C4×C29#120
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC29×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2962C2semidirect
4. C29×#1503C2semidirect
6. C29×#1279C2semidirect
7. C29×#1278C2semidirect
10. C29×#498C4semidirect
11. C29×#492C4semidirect
12. C29×#487C4semidirect
13. C29×#486C4semidirect
96. M16×C29SD16semidirect
127. #9054C29direct (N × H)
171. #2962C2×C29semidirect
173. #1503C2×C29semidirect
175. #1279C2×C29semidirect
176. #1278C2×C29semidirect
200. #498C4×C29semidirect
201. #492C4×C29semidirect
202. #487C4×C29semidirect
203. #486C4×C29semidirect
272. C29#9054direct (N × H)
293. M16SD16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#31672
C29×#29622
C29×#19802
C29×#15032
C29×#14802
C29×#12792
C29×#12782
#905429