Finite Group Databasebeta

← C29×#9238 #20304138

Subgroups — C29×#9238 #20304138

Order 7424.

512 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3103C211yesmaximal, characteristic
2C29×#2295C211yesmaximal, characteristic, complemented
3C29×#1962C211yesmaximal, characteristic
4C29×#1502C211yesmaximal, characteristic
5C29×#1487C211yesmaximal, characteristic, complemented
6C29×#1303C211yesmaximal, characteristic, complemented
7C29×#1276C211yesmaximal, characteristic, complemented
8C29×#532C2211yescharacteristic
9C2×C4×Q8×C29C2211yescharacteristic
10C29×#481—21no—
11C29×#475C412yescomplemented
12C29×#460C412yescomplemented
13C29×#448—21no—
14C4×SD16×C29—22no—
15C29×#431C2211yescharacteristic
16C29×#431C2211yescharacteristic
17C29×#423C2211yescharacteristic
18C2×C29×#104—21no—
19C2×C29×#104—21no—
20C29×#391—21no—
21C29×#389—21no—
22C29×#387—22no—
23C4×C4⋊C4×C29—21no—
24C4×C4⋊C4×C29C2211yescharacteristic
25C29×#376—21no—
26C43×C29C2211yescharacteristic
27C29×#327—22no—
28C29×Q8⋊C8—22no—
29C2×#41×C29—21no—
30C22×Q8×C29D411yescharacteristic
31C2×SD16×C29—22no—
32C2×M16×C29—21no—
33C29×C4⋊Q8C2×C411yescharacteristic
34C29×#127C2×C411yescharacteristic
35C29×#124—21no—
36C29×#121—21no—
37C29×#121—21no—
38C4×Q8×C29—21no—
39C4×Q8×C29—21no—
40C4×Q8×C29C2×C412yes—
41C4×Q8×C29D412yes—
42C4×D4×C29—21no—
43C4×D4×C29—21no—
44C2×C4⋊C4×C29—21no—
45C2×C4⋊C4×C29—22no—
46C2×C4⋊C4×C29—21no—
47C2×C4⋊C4×C29D411yescharacteristic
48C2×C42×C29—21no—
49C2×C42×C29—21no—
50C2×C42×C29—21no—
51C2×C42×C29—21no—
52C2×C42×C29D411yescharacteristic
53C2×C42×C29D411yescharacteristic
54C2×C42×C29C2311yescharacteristic
55C29×#106—22no—
56C29×C4⋊C8—21no—
57C29×C4⋊C8—21no—
58C29×C4⋊C8—21no—
59C29×C4⋊C8C2×C412yes—
60C29×#104—42no—
61C29×#104—42no—
62C29×#103—22no—
63C29×#102—22no—
64C29×C22⋊C8—21no—
65C29×C22⋊C8—21no—
66C4×C8×C29—21no—
67C4×C8×C29—21no—
68C29×#95—22no—
69C29×#95—22no—
70C29×#95—22no—
71C29×#95D412yes—
72#41×C29—41no—
73#41×C29—41no—
74#41×C29—41no—
75#41×C29—41no—
76C2×Q8×C29—21no—
77C2×Q8×C29—21no—
78C2×Q8×C29—42no—
79C2×Q8×C29C22⋊C412yes—
80C2×D4×C29—21no—
81C2×D4×C29—21no—
82C2×D4×C29—21no—
83C2×D4×C29—41no—
84C22×C4×C29—21no—
85C22×C4×C29—21no—
86C22×C4×C29—21no—
87C22×C4×C29—21no—
88C22×C4×C29—22no—
89C22×C4×C29—41no—
90C22×C4×C29C2×D411yescharacteristic
91C22×C4×C29C2×D411yescharacteristic
92C22×C4×C29C2×D411yescharacteristic
93SD16×C29—44no—
94M16×C29—41no—
95M16×C29—41no—
96C2×C8×C29—22no—
97C2×C8×C29—41no—
98C2×C8×C29—41no—
99C4⋊C4×C29—22no—
100C4⋊C4×C29—22no—
101C4⋊C4×C29—21no—
102C4⋊C4×C29—21no—
103C4⋊C4×C29—21no—
104C4⋊C4×C29—42no—
105C4⋊C4×C29—44no—
106C4⋊C4×C29C22⋊C412yes—
107C22⋊C4×C29—41no—
108C22⋊C4×C29—41no—
109C42×C29—22no—
110C42×C29—22no—
111C42×C29—21no—
112C42×C29—21no—
113C42×C29—21no—
114C42×C29—42no—
115C42×C29—42no—
116C42×C29—41no—
117C42×C29—41no—
118C42×C29SD1612yescomplemented
119C42×C29C22×C411yescharacteristic
120C42×C29C2×D411yescharacteristic
121C42×C29#4111yescharacteristic
122C42×C29#4111yescharacteristic
123#9238C2911yesmaximal, characteristic, direct product factor, Sylow
124C23×C29—41no—
125C23×C29#12011yescharacteristic
126Q8×C29—22no—
127Q8×C29—22no—
128Q8×C29—42no—
129Q8×C29—41no—
130Q8×C29—41no—
131D4×C29—42no—
132D4×C29—41no—
133D4×C29—41no—
134D4×C29—81no—
135D4×C29—81no—
136D4×C29—81no—
137C2×C4×C29—22no—
138C2×C4×C29—22no—
139C2×C4×C29—22no—
140C2×C4×C29—22no—
141C2×C4×C29—22no—
142C2×C4×C29—41no—
143C2×C4×C29—41no—
144C2×C4×C29—41no—
145C2×C4×C29—41no—
146C2×C4×C29—42no—
147C2×C4×C29—42no—
148C2×C4×C29—41no—
149C2×C4×C29—42no—
150C2×C4×C29—42no—
151C2×C4×C29—41no—
152C2×C4×C29—42no—
153C2×C4×C29—81no—
154C2×C4×C29—81no—
155C2×C4×C29C2×C22⋊C411yescharacteristic
156C2×C4×C29C4×D411yescharacteristic
157C2×C4×C29C4×D411yescharacteristic
158C2×C4×C29#12111yescharacteristic
159C2×C4×C29#12111yescharacteristic
160C2×C4×C29#12311yescharacteristic
161C2×C4×C29C2×SD1611yescharacteristic
162C2×C4×C29#13511yescharacteristic
163C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C29#13711yescharacteristic
165C8×C29—42no—
166C8×C29—81no—
167C8×C29—81no—
168#3103C2×C2911yescharacteristic
169#2295C2×C2911yescharacteristic, complemented
170#1962C2×C2911yescharacteristic
171#1502C2×C2911yescharacteristic
172#1487C2×C2911yescharacteristic, complemented
173#1303C2×C2911yescharacteristic, complemented
174#1276C2×C2911yescharacteristic, complemented
175C22×C29—21no—
176C22×C29—21no—
177C22×C29—81no—
178C22×C29—81no—
179C22×C29—81no—
180C22×C29#38611yescharacteristic
181C22×C29#44811yescharacteristic
182C22×C29#44911yescharacteristic
183C4×C29—21no—
184C4×C29—21no—
185C4×C29—21no—
186C4×C29—42no—
187C4×C29—42no—
188C4×C29—42no—
189C4×C29—42no—
190C4×C29—82no—
191C4×C29—81no—
192C4×C29#42112yes—
193C4×C29C4×SD1611yescharacteristic
194C4×C29#44011yescharacteristic
195C4×C29#46011yescharacteristic
196C4×C29#46411yescharacteristic
197#532C22×C2911yescharacteristic
198C2×C4×Q8C22×C2911yescharacteristic
199#481—21no—
200#475C4×C2912yescomplemented
201#460C4×C2912yescomplemented
202#448—21no—
203C4×SD16—22no—
204#431C22×C2911yescharacteristic
205#431C22×C2911yescharacteristic
206#423C22×C2911yescharacteristic
207C2×#104—21no—
208C2×#104—21no—
209#391—21no—
210#389—21no—
211#387—22no—
212C4×C4⋊C4—21no—
213C4×C4⋊C4C22×C2911yescharacteristic
214#376—21no—
215C43C22×C2911yescharacteristic
216#327—22no—
217Q8⋊C8—22no—
218C2×C29—21no—
219C2×C29—21no—
220C2×C29—161no—
221C2×C29#188011yescharacteristic
222C2×C29#189711yescharacteristic
223C2×C29#190611yescharacteristic
224C2×#41—21no—
225C22×Q8D4×C2911yescharacteristic
226C2×SD16—22no—
227C2×M16—21no—
228C4⋊Q8C2×C4×C2911yescharacteristic
229#127C2×C4×C2911yescharacteristic
230#124—21no—
231#121—21no—
232#121—21no—
233C4×Q8—21no—
234C4×Q8—21no—
235C4×Q8C2×C4×C2912yes—
236C4×Q8D4×C2912yes—
237C4×D4—21no—
238C4×D4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4D4×C2911yescharacteristic
243C2×C42—21no—
244C2×C42—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42D4×C2911yescharacteristic
248C2×C42D4×C2911yescharacteristic
249C2×C42C23×C2911yescharacteristic
250#106—22no—
251C4⋊C8—21no—
252C4⋊C8—21no—
253C4⋊C8—21no—
254C4⋊C8C2×C4×C2912yes—
255#104—42no—
256#104—42no—
257#103—22no—
258#102—22no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C4×C8—21no—
262C4×C8—21no—
263#95—22no—
264#95—22no—
265#95—22no—
266#95D4×C2912yes—
267C29#923811yescharacteristic, direct product factor, Sylow
268#41—41no—
269#41—41no—
270#41—41no—
271#41—41no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—42no—
275C2×Q8C22⋊C4×C2912yes—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—41no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—41no—
286C22×C4C2×D4×C2911yescharacteristic
287C22×C4C2×D4×C2911yescharacteristic
288C22×C4C2×D4×C2911yescharacteristic
289SD16—44no—
290M16—41no—
291M16—41no—
292C2×C8—22no—
293C2×C8—41no—
294C2×C8—41no—
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—21no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—42no—
301C4⋊C4—44no—
302C4⋊C4C22⋊C4×C2912yes—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C42—22no—
306C42—22no—
307C42—21no—
308C42—21no—
309C42—21no—
310C42—42no—
311C42—42no—
312C42—41no—
313C42—41no—
314C42SD16×C2912yescomplemented
315C42C22×C4×C2911yescharacteristic
316C42C2×D4×C2911yescharacteristic
317C42#41×C2911yescharacteristic
318C42#41×C2911yescharacteristic
319C23—41no—
320C23C29×#12011yescharacteristic
321Q8—22no—
322Q8—22no—
323Q8—42no—
324Q8—41no—
325Q8—41no—
326D4—41no—
327D4—41no—
328D4—42no—
329D4—81no—
330D4—81no—
331D4—81no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—42no—
346C2×C4—42no—
347C2×C4—41no—
348C2×C4—81no—
349C2×C4—81no—
350C2×C4C2×C22⋊C4×C2911yescharacteristic
351C2×C4C4×D4×C2911yescharacteristic
352C2×C4C4×D4×C2911yescharacteristic
353C2×C4C29×#12111yescharacteristic
354C2×C4C29×#12111yescharacteristic
355C2×C4C29×#12311yescharacteristic
356C2×C4C2×SD16×C2911yescharacteristic
357C2×C4C29×#13511yescharacteristic
358C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
359C2×C4C29×#13711yescharacteristic
360C8—42no—
361C8—81no—
362C8—81no—
363C22—21no—
364C22—21no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22C29×#38611yescharacteristic
369C22C29×#44811yescharacteristic
370C22C29×#44911yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—42no—
376C4—42no—
377C4—42no—
378C4—82no—
379C4—81no—
380C4C29×#42112yes—
381C4C4×SD16×C2911yescharacteristic
382C4C29×#44011yescharacteristic
383C4C29×#46011yescharacteristic
384C4C29×#46411yescharacteristic
385C2—21no—
386C2—21no—
387C2—161no—
388C2C29×#188011yescharacteristic
389C2C29×#189711yescharacteristic
390C2C29×#190611yescharacteristic
subgroupG/H
centerC2×C4×C29#121
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×#2295C2semidirect
5. C29×#1487C2semidirect
6. C29×#1303C2semidirect
7. C29×#1276C2semidirect
11. C29×#475C4semidirect
12. C29×#460C4semidirect
118. C42×C29SD16semidirect
123. #9238C29direct (N × H)
169. #2295C2×C29semidirect
172. #1487C2×C29semidirect
173. #1303C2×C29semidirect
174. #1276C2×C29semidirect
200. #475C4×C29semidirect
201. #460C4×C29semidirect
267. C29#9238direct (N × H)
314. C42SD16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#31032
C29×#22952
C29×#19622
C29×#15022
C29×#14872
C29×#13032
C29×#12762
#923829