Finite Group Databasebeta

← C29×#9365 #20304265

Subgroups — C29×#9365 #20304265

Order 7424.

802 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3006C211yesmaximal, characteristic
2C29×#2339C211yesmaximal, characteristic, complemented
3C29×#1964C211yesmaximal, characteristic, complemented
4C29×#1789C211yesmaximal, characteristic, complemented
5C29×#1507C211yesmaximal, characteristic, complemented
6C29×#1305C211yesmaximal, characteristic, complemented
7C29×#1297C211yesmaximal, characteristic, complemented
8C22×#41×C29C2211yescharacteristic
9C2×C29×AGL(1,ℤ/8)C412yescomplemented
10C2×C29×#121C2211yescharacteristic
11C2×C4×D4×C29—21no—
12C29×#449—22no—
13C29×#448—21no—
14C29×#447—21no—
15C2×C29×#104—22no—
16C29×#417C412yescomplemented
17C2×C29×#99—22no—
18C29×#407C2211yescharacteristic
19C29×#407C2211yescharacteristic
20C29×#391—21no—
21C29×#386—22no—
22C29×#381—21no—
23C29×#380C2211yescharacteristic
24C4×C22⋊C4×C29C2211yescharacteristic
25C4×C22⋊C4×C29C2211yescharacteristic
26C2×C29×#95—21no—
27C29×#327—21no—
28C29×#327—21no—
29C2×#41×C29—21no—
30C2×#41×C29—21no—
31C2×#41×C29—44no—
32C2×#41×C29C2×C412yes—
33C2×#41×C29D412yes—
34C22×Q8×C29D411yescharacteristic
35C22×D4×C29—21no—
36C22×D4×C29—21no—
37C22×D4×C29C2×C411yescharacteristic, complemented
38C22×D4×C29D411yescharacteristic
39C23×C4×C29—21no—
40C23×C4×C29—22no—
41C23×C4×C29C2311yescharacteristic
42C29×AGL(1,ℤ/8)—44no—
43C2×SD16×C29—22no—
44C2×D8×C29—22no—
45C2×M16×C29—21no—
46C2×M16×C29C2×C412yescomplemented
47C29×#121—21no—
48C29×#121—21no—
49C29×#121—21no—
50C29×#121—21no—
51C4×D4×C29—44no—
52C2×C4⋊C4×C29—21no—
53C2×C4⋊C4×C29C2×C411yescharacteristic, complemented
54C2×C22⋊C4×C29—21no—
55C2×C22⋊C4×C29—22no—
56C2×C22⋊C4×C29—21no—
57C2×C22⋊C4×C29—21no—
58C2×C22⋊C4×C29D412yes—
59C2×C42×C29—21no—
60C2×C42×C29—21no—
61C29×#104—44no—
62C29×#103—22no—
63C29×#102—22no—
64C29×#99—44no—
65C29×C22⋊C8—21no—
66C29×C22⋊C8—21no—
67C29×C22⋊C8—21no—
68C29×C22⋊C8—21no—
69C29×#95—22no—
70C29×#95—22no—
71C29×#95—21no—
72C29×#95—21no—
73C29×#95D411yescharacteristic
74C29×#95D411yescharacteristic
75C24×C29—21no—
76C24×C29—21no—
77C24×C29C2×D411yescharacteristic
78#41×C29—24no—
79#41×C29—24no—
80#41×C29—42no—
81#41×C29—42no—
82#41×C29—44no—
83#41×C29—44no—
84C2×Q8×C29—21no—
85C2×Q8×C29—42no—
86C2×Q8×C29C22⋊C412yes—
87C2×D4×C29—24no—
88C2×D4×C29—22no—
89C2×D4×C29—22no—
90C2×D4×C29—21no—
91C2×D4×C29—21no—
92C2×D4×C29—21no—
93C2×D4×C29—42no—
94C2×D4×C29—44no—
95C2×D4×C29—42no—
96C2×D4×C29—42no—
97C2×D4×C29—41no—
98C2×D4×C29—41no—
99C2×D4×C29C22⋊C412yes—
100C22×C4×C29—21no—
101C22×C4×C29—21no—
102C22×C4×C29—22no—
103C22×C4×C29—22no—
104C22×C4×C29—21no—
105C22×C4×C29—21no—
106C22×C4×C29—22no—
107C22×C4×C29—42no—
108C22×C4×C29—44no—
109C22×C4×C29—44no—
110C22×C4×C29—44no—
111C22×C4×C29—41no—
112C22×C4×C29—82no—
113C22×C4×C29C22×C411yescharacteristic
114C22×C4×C29C2×D411yescharacteristic
115C22×C4×C29C2×D411yescharacteristic
116C22×C4×C29C2×D411yescharacteristic
117C22×C4×C29#4111yescharacteristic
118C22×C4×C29#4111yescharacteristic
119SD16×C29—44no—
120D8×C29—44no—
121M16×C29—42no—
122M16×C29—42no—
123C2×C8×C29—22no—
124C2×C8×C29—41no—
125C4⋊C4×C29—21no—
126C4⋊C4×C29—21no—
127C4⋊C4×C29—42no—
128C22⋊C4×C29—22no—
129C22⋊C4×C29—42no—
130C22⋊C4×C29—41no—
131C22⋊C4×C29—44no—
132C22⋊C4×C29—41no—
133C22⋊C4×C29—41no—
134C22⋊C4×C29—42no—
135C42×C29—42no—
136C42×C29—42no—
137#9365C2911yesmaximal, characteristic, direct product factor, Sylow
138C23×C29—24no—
139C23×C29—22no—
140C23×C29—21no—
141C23×C29—21no—
142C23×C29—41no—
143C23×C29—41no—
144C23×C29—42no—
145C23×C29—42no—
146C23×C29—41no—
147C23×C29—41no—
148C23×C29—41no—
149C23×C29—81no—
150C23×C29—81no—
151C23×C29C4×D411yescharacteristic
152C23×C29#12011yescharacteristic
153C23×C29#12111yescharacteristic
154Q8×C29—22no—
155Q8×C29—22no—
156Q8×C29—42no—
157D4×C29—24no—
158D4×C29—22no—
159D4×C29—44no—
160D4×C29—44no—
161D4×C29—42no—
162D4×C29—81no—
163D4×C29—82no—
164D4×C29—81no—
165D4×C29—81no—
166D4×C29#9914yescomplemented
167C2×C4×C29—22no—
168C2×C4×C29—22no—
169C2×C4×C29—22no—
170C2×C4×C29—22no—
171C2×C4×C29—22no—
172C2×C4×C29—41no—
173C2×C4×C29—41no—
174C2×C4×C29—41no—
175C2×C4×C29—44no—
176C2×C4×C29—44no—
177C2×C4×C29—41no—
178C2×C4×C29—42no—
179C2×C4×C29—41no—
180C2×C4×C29—41no—
181C2×C4×C29—42no—
182C2×C4×C29—42no—
183C2×C4×C29—41no—
184C2×C4×C29—42no—
185C2×C4×C29—42no—
186C2×C4×C29—41no—
187C2×C4×C29—42no—
188C2×C4×C29—41no—
189C2×C4×C29—88no—
190C2×C4×C29—81no—
191C2×C4×C29—81no—
192C2×C4×C29C2×C22⋊C411yescharacteristic
193C2×C4×C29C4×D411yescharacteristic
194C2×C4×C29#12111yescharacteristic
195C2×C4×C29#12311yescharacteristic
196C8×C29—42no—
197C8×C29—81no—
198#3006C2×C2911yescharacteristic
199#2339C2×C2911yescharacteristic, complemented
200#1964C2×C2911yescharacteristic, complemented
201#1789C2×C2911yescharacteristic, complemented
202#1507C2×C2911yescharacteristic, complemented
203#1305C2×C2911yescharacteristic, complemented
204#1297C2×C2911yescharacteristic, complemented
205C22×C29—21no—
206C22×C29—21no—
207C22×C29—21no—
208C22×C29—21no—
209C22×C29—21no—
210C22×C29—21no—
211C22×C29—24no—
212C22×C29—21no—
213C22×C29—21no—
214C22×C29—44no—
215C22×C29—44no—
216C22×C29—42no—
217C22×C29—42no—
218C22×C29—81no—
219C22×C29—81no—
220C22×C29—81no—
221C22×C29—81no—
222C22×C29—81no—
223C22×C29—162no—
224C22×C29#38611yescharacteristic
225C22×C29#45311yescharacteristic
226C22×C29#45411yescharacteristic
227C4×C29—21no—
228C4×C29—21no—
229C4×C29—21no—
230C4×C29—42no—
231C4×C29—42no—
232C4×C29—81no—
233C4×C29—82no—
234C4×C29—82no—
235C4×C29—81no—
236C4×C29C2×#9912yes—
237C22×#41C22×C2911yescharacteristic
238C2×AGL(1,ℤ/8)C4×C2912yescomplemented
239C2×#121C22×C2911yescharacteristic
240C2×C4×D4—21no—
241#449—22no—
242#448—21no—
243#447—21no—
244C2×#104—22no—
245#417C4×C2912yescomplemented
246C2×#99—22no—
247#407C22×C2911yescharacteristic
248#407C22×C2911yescharacteristic
249#391—21no—
250#386—22no—
251#381—21no—
252#380C22×C2911yescharacteristic
253C4×C22⋊C4C22×C2911yescharacteristic
254C4×C22⋊C4C22×C2911yescharacteristic
255C2×#95—21no—
256#327—21no—
257#327—21no—
258C2×C29—21no—
259C2×C29—21no—
260C2×C29—41no—
261C2×C29—41no—
262C2×C29—44no—
263C2×C29—161no—
264C2×C29#188311yescharacteristic
265C2×C29#189811yescharacteristic
266C2×C29#190611yescharacteristic
267C2×#41—21no—
268C2×#41—21no—
269C2×#41—44no—
270C2×#41C2×C4×C2912yes—
271C2×#41D4×C2912yes—
272C22×Q8D4×C2911yescharacteristic
273C22×D4—21no—
274C22×D4—21no—
275C22×D4C2×C4×C2911yescharacteristic, complemented
276C22×D4D4×C2911yescharacteristic
277C23×C4—21no—
278C23×C4—22no—
279C23×C4C23×C2911yescharacteristic
280AGL(1,ℤ/8)—44no—
281C2×SD16—22no—
282C2×D8—22no—
283C2×M16—21no—
284C2×M16C2×C4×C2912yescomplemented
285#121—21no—
286#121—21no—
287#121—21no—
288#121—21no—
289C4×D4—44no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4C2×C4×C2911yescharacteristic, complemented
292C2×C22⋊C4—21no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—21no—
295C2×C22⋊C4—21no—
296C2×C22⋊C4D4×C2912yes—
297C2×C42—21no—
298C2×C42—21no—
299#104—44no—
300#103—22no—
301#102—22no—
302#99—44no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307#95—22no—
308#95—22no—
309#95—21no—
310#95—21no—
311#95D4×C2911yescharacteristic
312#95D4×C2911yescharacteristic
313C29#936511yescharacteristic, direct product factor, Sylow
314C24—21no—
315C24—21no—
316C24C2×D4×C2911yescharacteristic
317#41—24no—
318#41—24no—
319#41—42no—
320#41—42no—
321#41—44no—
322#41—44no—
323C2×Q8—21no—
324C2×Q8—42no—
325C2×Q8C22⋊C4×C2912yes—
326C2×D4—24no—
327C2×D4—22no—
328C2×D4—22no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—42no—
333C2×D4—44no—
334C2×D4—42no—
335C2×D4—42no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4C22⋊C4×C2912yes—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—42no—
347C22×C4—44no—
348C22×C4—44no—
349C22×C4—44no—
350C22×C4—41no—
351C22×C4—82no—
352C22×C4C22×C4×C2911yescharacteristic
353C22×C4C2×D4×C2911yescharacteristic
354C22×C4C2×D4×C2911yescharacteristic
355C22×C4C2×D4×C2911yescharacteristic
356C22×C4#41×C2911yescharacteristic
357C22×C4#41×C2911yescharacteristic
358SD16—44no—
359D8—44no—
360M16—42no—
361M16—42no—
362C2×C8—22no—
363C2×C8—41no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—42no—
367C22⋊C4—22no—
368C22⋊C4—42no—
369C22⋊C4—44no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—42no—
374C42—42no—
375C42—42no—
376C23—24no—
377C23—22no—
378C23—21no—
379C23—21no—
380C23—41no—
381C23—41no—
382C23—42no—
383C23—42no—
384C23—41no—
385C23—41no—
386C23—41no—
387C23—81no—
388C23—81no—
389C23C4×D4×C2911yescharacteristic
390C23C29×#12011yescharacteristic
391C23C29×#12111yescharacteristic
392Q8—22no—
393Q8—22no—
394Q8—42no—
395D4—24no—
396D4—22no—
397D4—44no—
398D4—44no—
399D4—42no—
400D4—81no—
401D4—82no—
402D4—81no—
403D4—81no—
404D4C29×#9914yescomplemented
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—88no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4C2×C22⋊C4×C2911yescharacteristic
431C2×C4C4×D4×C2911yescharacteristic
432C2×C4C29×#12111yescharacteristic
433C2×C4C29×#12311yescharacteristic
434C8—42no—
435C8—81no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—24no—
445C22—44no—
446C22—44no—
447C22—42no—
448C22—42no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—162no—
455C22C29×#38611yescharacteristic
456C22C29×#45311yescharacteristic
457C22C29×#45411yescharacteristic
458C4—21no—
459C4—21no—
460C4—21no—
461C4—42no—
462C4—42no—
463C4—82no—
464C4—81no—
465C4—82no—
466C4—81no—
467C4C2×C29×#9912yes—
468C2—21no—
469C2—21no—
470C2—41no—
471C2—41no—
472C2—44no—
473C2—161no—
474C2C29×#188311yescharacteristic
475C2C29×#189811yescharacteristic
476C2C29×#190611yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC29×#3006C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2339C2semidirect
3. C29×#1964C2semidirect
4. C29×#1789C2semidirect
5. C29×#1507C2semidirect
6. C29×#1305C2semidirect
7. C29×#1297C2semidirect
9. C2×C29×AGL(1,ℤ/8)C4semidirect
16. C29×#417C4semidirect
37. C22×D4×C29C2×C4semidirect
46. C2×M16×C29C2×C4semidirect
53. C2×C4⋊C4×C29C2×C4semidirect
137. #9365C29direct (N × H)
166. D4×C29#99semidirect
199. #2339C2×C29semidirect
200. #1964C2×C29semidirect
201. #1789C2×C29semidirect
202. #1507C2×C29semidirect
203. #1305C2×C29semidirect
204. #1297C2×C29semidirect
238. C2×AGL(1,ℤ/8)C4×C29semidirect
245. #417C4×C29semidirect
275. C22×D4C2×C4×C29semidirect
284. C2×M16C2×C4×C29semidirect
291. C2×C4⋊C4C2×C4×C29semidirect
313. C29#9365direct (N × H)
404. D4C29×#99semidirect

Maximal subgroups

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

subgroupindex
C29×#30062
C29×#23392
C29×#19642
C29×#17892
C29×#15072
C29×#13052
C29×#12972
#936529