Finite Group Databasebeta

← C29×#9265 #20304165

Subgroups — C29×#9265 #20304165

Order 7424.

438 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3211C211yesmaximal, characteristic
2C29×#2968C211yesmaximal, characteristic, complemented
3C29×#1532C211yesmaximal, characteristic, complemented
4C2×C29×#329C211yesmaximal, characteristic, complemented
5C29×#1469C211yesmaximal, characteristic, complemented
6C29×#1302C211yesmaximal, characteristic, complemented
7C29×#1281C211yesmaximal, characteristic, complemented
8C29×#529C2211yescharacteristic
9C2×C29×#124C2211yescharacteristic
10C29×#495—21no—
11C29×#488—21no—
12C29×#464—21no—
13C29×#463—21no—
14C29×#451C411yescharacteristic
15C29×#450C411yescharacteristic
16C29×#448C411yescharacteristic
17C29×#447C411yescharacteristic
18C29×#446—21no—
19C29×#435—21no—
20C29×#435—21no—
21C8×D4×C29—21no—
22C29×#433—21no—
23C29×#432C2211yescharacteristic
24C29×#431C2211yescharacteristic
25C29×#431C2211yescharacteristic
26C29×#405—21no—
27C2×C29×#97C2211yescharacteristic
28C2×C29×#97C2211yescharacteristic
29C29×#330—21no—
30C29×#329—21no—
31C29×#329—21no—
32C29×#329—21no—
33C29×#323—21no—
34C29×#323—21no—
35C22×Q8×C29C2×C411yescharacteristic
36C22×D4×C29C2×C411yescharacteristic
37C2×Q16×C29—21no—
38C2×SD16×C29—21no—
39C2×SD16×C29—21no—
40C2×D8×C29—21no—
41C2×M16×C29—21no—
42C22×C8×C29—21no—
43C22×C8×C29—21no—
44C22×C8×C29—21no—
45C29×#126—21no—
46C29×#125D411yescharacteristic
47C29×#124—21no—
48C29×#124—21no—
49C29×#124—21no—
50C29×#124—21no—
51C29×#124D411yescharacteristic
52C29×#123—21no—
53C29×C22⋊Q8C2×C411yescharacteristic
54C29×#121C2×C411yescharacteristic
55C4×Q8×C29D411yescharacteristic
56C4×D4×C29—21no—
57C4×D4×C29D411yescharacteristic
58C29×#117—21no—
59C2×C22⋊C4×C29—21no—
60C2×C22⋊C4×C29—21no—
61C2×C42×C29C2311yescharacteristic
62C29×C4⋊C8—21no—
63C29×C4⋊C8—21no—
64C29×C4⋊C8—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×#103—21no—
68C29×#103—21no—
69C29×#102—21no—
70C29×#102—21no—
71C29×C22⋊C8—21no—
72C29×C22⋊C8—21no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8C2×C411yescharacteristic
75C29×C22⋊C8C2×C411yescharacteristic
76C29×C22⋊C8D411yescharacteristic
77C29×C22⋊C8D411yescharacteristic
78C29×#97—21no—
79C29×#97—21no—
80C29×#97—21no—
81C29×#97—21no—
82C29×#97—21no—
83C29×#97D411yescharacteristic
84C29×#97D411yescharacteristic
85C4×C8×C29—21no—
86C4×C8×C29—21no—
87C4×C8×C29—21no—
88C24×C29—21no—
89C2×Q8×C29—21no—
90C2×Q8×C29—21no—
91C2×Q8×C29—81no—
92C2×Q8×C29C22⋊C411yescharacteristic
93C2×D4×C29—21no—
94C2×D4×C29—21no—
95C2×D4×C29—21no—
96C2×D4×C29—81no—
97C2×D4×C29C22⋊C411yescharacteristic
98C22×C4×C29—21no—
99C22×C4×C29—21no—
100C22×C4×C29C22×C411yescharacteristic
101C22×C4×C29C2×D411yescharacteristic
102C22×C4×C29#4111yescharacteristic
103Q16×C29—81no—
104SD16×C29—81no—
105SD16×C29—81no—
106D8×C29—81no—
107M16×C29—42no—
108C2×C8×C29—21no—
109C2×C8×C29—22no—
110C2×C8×C29—21no—
111C2×C8×C29—21no—
112C2×C8×C29—21no—
113C2×C8×C29—21no—
114C2×C8×C29—21no—
115C2×C8×C29—42no—
116C2×C8×C29—42no—
117C2×C8×C29—41no—
118C2×C8×C29—41no—
119C2×C8×C29—41no—
120C4⋊C4×C29—21no—
121C4⋊C4×C29—21no—
122C4⋊C4×C29—21no—
123C4⋊C4×C29—21no—
124C4⋊C4×C29C22⋊C411yescharacteristic
125C4⋊C4×C29C22⋊C411yescharacteristic
126C22⋊C4×C29—21no—
127C22⋊C4×C29—21no—
128C22⋊C4×C29—21no—
129C22⋊C4×C29—21no—
130C22⋊C4×C29—21no—
131C22⋊C4×C29—41no—
132C22⋊C4×C29—41no—
133C22⋊C4×C29—41no—
134C22⋊C4×C29—41no—
135C42×C29—21no—
136C42×C29C2×D411yescharacteristic
137C42×C29C2×D411yescharacteristic
138C42×C29C2×D411yescharacteristic
139C42×C29#4111yescharacteristic
140#9265C2911yesmaximal, characteristic, direct product factor, Sylow
141C23×C29—21no—
142C23×C29—41no—
143C23×C29—41no—
144C23×C29—41no—
145C23×C29—81no—
146C23×C29—81no—
147C23×C29C4×D411yescharacteristic
148Q8×C29—41no—
149Q8×C29—41no—
150Q8×C29—41no—
151Q8×C29—81no—
152D4×C29—41no—
153D4×C29—41no—
154D4×C29—41no—
155D4×C29—41no—
156D4×C29—41no—
157D4×C29—81no—
158C2×C4×C29—21no—
159C2×C4×C29—21no—
160C2×C4×C29—21no—
161C2×C4×C29—21no—
162C2×C4×C29—21no—
163C2×C4×C29—41no—
164C2×C4×C29—41no—
165C2×C4×C29—41no—
166C2×C4×C29—41no—
167C2×C4×C29—41no—
168C2×C4×C29—81no—
169C2×C4×C29C2×C22⋊C411yescharacteristic
170C2×C4×C29C4×D411yescharacteristic
171C2×C4×C29#12011yescharacteristic
172C2×C4×C29#12111yescharacteristic
173C2×C4×C29#12111yescharacteristic
174C2×C4×C29#12311yescharacteristic
175C8×C29—22no—
176C8×C29—42no—
177C8×C29—41no—
178C8×C29—41no—
179C8×C29—41no—
180C8×C29—41no—
181C8×C29—41no—
182C8×C29—81no—
183#3211C2×C2911yescharacteristic
184#2968C2×C2911yescharacteristic, complemented
185#1532C2×C2911yescharacteristic, complemented
186C2×#329C2×C2911yescharacteristic, complemented
187#1469C2×C2911yescharacteristic, complemented
188#1302C2×C2911yescharacteristic, complemented
189#1281C2×C2911yescharacteristic, complemented
190C22×C29—21no—
191C22×C29—21no—
192C22×C29—41no—
193C22×C29—41no—
194C22×C29—41no—
195C22×C29—81no—
196C22×C29—81no—
197C22×C29—81no—
198C22×C29—161no—
199C22×C29—161no—
200C22×C29#38611yescharacteristic
201C22×C29#44311yescharacteristic
202C22×C29#44411yescharacteristic
203C4×C29—21no—
204C4×C29—21no—
205C4×C29—21no—
206C4×C29—21no—
207C4×C29—21no—
208C4×C29—21no—
209C4×C29—41no—
210C4×C29—41no—
211C4×C29—41no—
212C4×C29—81no—
213#529C22×C2911yescharacteristic
214C2×#124C22×C2911yescharacteristic
215#495—21no—
216#488—21no—
217#464—21no—
218#463—21no—
219#451C4×C2911yescharacteristic
220#450C4×C2911yescharacteristic
221#448C4×C2911yescharacteristic
222#447C4×C2911yescharacteristic
223#446—21no—
224#435—21no—
225#435—21no—
226C8×D4—21no—
227#433—21no—
228#432C22×C2911yescharacteristic
229#431C22×C2911yescharacteristic
230#431C22×C2911yescharacteristic
231#405—21no—
232C2×#97C22×C2911yescharacteristic
233C2×#97C22×C2911yescharacteristic
234#330—21no—
235#329—21no—
236#329—21no—
237#329—21no—
238#323—21no—
239#323—21no—
240C2×C29—21no—
241C2×C29—21no—
242C2×C29—81no—
243C2×C29—161no—
244C2×C29#187611yescharacteristic
245C2×C29#190611yescharacteristic
246C2×C29#191411yescharacteristic
247C22×Q8C2×C4×C2911yescharacteristic
248C22×D4C2×C4×C2911yescharacteristic
249C2×Q16—21no—
250C2×SD16—21no—
251C2×SD16—21no—
252C2×D8—21no—
253C2×M16—21no—
254C22×C8—21no—
255C22×C8—21no—
256C22×C8—21no—
257#126—21no—
258#125D4×C2911yescharacteristic
259#124—21no—
260#124—21no—
261#124—21no—
262#124—21no—
263#124D4×C2911yescharacteristic
264#123—21no—
265C22⋊Q8C2×C4×C2911yescharacteristic
266#121C2×C4×C2911yescharacteristic
267C4×Q8D4×C2911yescharacteristic
268C4×D4—21no—
269C4×D4D4×C2911yescharacteristic
270#117—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C42C23×C2911yescharacteristic
274C4⋊C8—21no—
275C4⋊C8—21no—
276C4⋊C8—21no—
277C4⋊C8—21no—
278C4⋊C8—21no—
279#103—21no—
280#103—21no—
281#102—21no—
282#102—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8C2×C4×C2911yescharacteristic
287C22⋊C8C2×C4×C2911yescharacteristic
288C22⋊C8D4×C2911yescharacteristic
289C22⋊C8D4×C2911yescharacteristic
290#97—21no—
291#97—21no—
292#97—21no—
293#97—21no—
294#97—21no—
295#97D4×C2911yescharacteristic
296#97D4×C2911yescharacteristic
297C4×C8—21no—
298C4×C8—21no—
299C4×C8—21no—
300C29#926511yescharacteristic, direct product factor, Sylow
301C24—21no—
302C2×Q8—21no—
303C2×Q8—21no—
304C2×Q8—81no—
305C2×Q8C22⋊C4×C2911yescharacteristic
306C2×D4—21no—
307C2×D4—21no—
308C2×D4—21no—
309C2×D4—81no—
310C2×D4C22⋊C4×C2911yescharacteristic
311C22×C4—21no—
312C22×C4—21no—
313C22×C4C22×C4×C2911yescharacteristic
314C22×C4C2×D4×C2911yescharacteristic
315C22×C4#41×C2911yescharacteristic
316Q16—81no—
317SD16—81no—
318SD16—81no—
319D8—81no—
320M16—42no—
321C2×C8—21no—
322C2×C8—22no—
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—21no—
327C2×C8—21no—
328C2×C8—42no—
329C2×C8—42no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8—41no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4C22⋊C4×C2911yescharacteristic
338C4⋊C4C22⋊C4×C2911yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—21no—
343C22⋊C4—21no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C42—21no—
349C42C2×D4×C2911yescharacteristic
350C42C2×D4×C2911yescharacteristic
351C42C2×D4×C2911yescharacteristic
352C42#41×C2911yescharacteristic
353C23—21no—
354C23—41no—
355C23—41no—
356C23—41no—
357C23—81no—
358C23—81no—
359C23C4×D4×C2911yescharacteristic
360Q8—41no—
361Q8—41no—
362Q8—41no—
363Q8—81no—
364D4—41no—
365D4—41no—
366D4—41no—
367D4—41no—
368D4—41no—
369D4—81no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—81no—
381C2×C4C2×C22⋊C4×C2911yescharacteristic
382C2×C4C4×D4×C2911yescharacteristic
383C2×C4C29×#12011yescharacteristic
384C2×C4C29×#12111yescharacteristic
385C2×C4C29×#12111yescharacteristic
386C2×C4C29×#12311yescharacteristic
387C8—22no—
388C8—41no—
389C8—41no—
390C8—42no—
391C8—41no—
392C8—41no—
393C8—41no—
394C8—81no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—81no—
401C22—81no—
402C22—81no—
403C22—161no—
404C22—161no—
405C22C29×#38611yescharacteristic
406C22C29×#44311yescharacteristic
407C22C29×#44411yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—41no—
417C4—81no—
418C2—21no—
419C2—21no—
420C2—81no—
421C2—161no—
422C2C29×#187611yescharacteristic
423C2C29×#190611yescharacteristic
424C2C29×#191411yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#447C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2968C2semidirect
3. C29×#1532C2semidirect
4. C2×C29×#329C2semidirect
5. C29×#1469C2semidirect
6. C29×#1302C2semidirect
7. C29×#1281C2semidirect
140. #9265C29direct (N × H)
184. #2968C2×C29semidirect
185. #1532C2×C29semidirect
186. C2×#329C2×C29semidirect
187. #1469C2×C29semidirect
188. #1302C2×C29semidirect
189. #1281C2×C29semidirect
300. C29#9265direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32112
C29×#29682
C29×#15322
C2×C29×#3292
C29×#14692
C29×#13022
C29×#12812
#926529