Finite Group Databasebeta

← C29×#33595 #20328495

Subgroups — C29×#33595 #20328495

Order 7424.

706 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3414C211yesmaximal, characteristic, complemented
2C2×C29×#509C211yesmaximal, characteristic, complemented
3C29×#3155C211yesmaximal, characteristic, complemented
4C29×#2957C211yesmaximal, characteristic, complemented
5C29×#2213C214yesmaximal, complemented
6C29×#2212C214yesmaximal, complemented
7C29×#2153C211yesmaximal, characteristic, complemented
8C29×#2148C211yesmaximal, characteristic, complemented
9C2×C29×#361C211yesmaximal, characteristic, complemented
10C2×C29×AGL(1,ℤ/8)—21no—
11C2×C29×#135C2211yescharacteristic
12C2×C29×#135C2211yescharacteristic
13C22×D8×C29C2211yescharacteristic
14C29×#568—21no—
15C29×#535—21no—
16C29×#510—21no—
17C29×#510C2212yescomplemented
18C29×#509—22no—
19C29×#509—21no—
20C29×#509C2214yes—
21C29×#509C2212yescomplemented
22C29×#508—22no—
23C2×C29×SD32—21no—
24C2×C29×D16—21no—
25C2×C29×M32C2211yescharacteristic
26C2×C29×M32C2211yescharacteristic
27C29×#496—22no—
28C29×#495C2212yescomplemented
29C29×#493C2212yescomplemented
30C29×#444—22no—
31C29×#443C2214yescomplemented
32C2×C29×#108C2211yescharacteristic
33C29×#421—21no—
34C29×#405C2211yescharacteristic
35C29×#364C2214yescomplemented
36C29×#362C2212yescomplemented
37C29×#361C2214yescomplemented
38C29×#361C2212yescomplemented
39C2×#41×C29—21no—
40C2×#41×C29—21no—
41C22×D4×C29—21no—
42C29×AGL(1,ℤ/8)—42no—
43C29×AGL(1,ℤ/8)—42no—
44C29×#135—21no—
45C29×#135—21no—
46C29×#135—21no—
47C29×#135—21no—
48C29×#135—21no—
49C29×#135—21no—
50C29×#135D412yescomplemented
51C29×#135C2312yes—
52C2×Q16×C29D411yescharacteristic, complemented
53C2×Q16×C29C2311yescharacteristic
54C2×SD16×C29—22no—
55C2×SD16×C29—21no—
56C2×SD16×C29—21no—
57C2×D8×C29—21no—
58C2×D8×C29—21no—
59C2×D8×C29—22no—
60C2×D8×C29—21no—
61C2×D8×C29—21no—
62C2×D8×C29—21no—
63C2×D8×C29D411yescharacteristic, complemented
64C2×D8×C29C2311yescharacteristic
65C2×D8×C29C2312yes—
66C29×#131—24no—
67C29×#131—42no—
68C2×M16×C29—21no—
69C2×M16×C29—42no—
70C2×M16×C29D411yescharacteristic
71C22×C8×C29C2311yescharacteristic
72C29×#127—22no—
73C29×#124—22no—
74C29×#121—42no—
75C29×#120—42no—
76C29×#117D411yescharacteristic
77C29×Q32—22no—
78C29×SD32—24no—
79C29×SD32—22no—
80C29×SD32—22no—
81C29×D16—24no—
82C29×D16—22no—
83C29×M32—21no—
84C29×M32—21no—
85C29×M32C2312yes—
86C29×M32C2312yes—
87C2×C16×C29—21no—
88C2×C16×C29—21no—
89C29×#108—21no—
90C29×#108C2312yes—
91C29×#104—24no—
92C29×#97D412yes—
93C4×C8×C29C2312yes—
94C24×C29—41no—
95#41×C29—22no—
96#41×C29—22no—
97#41×C29—41no—
98#41×C29—41no—
99#41×C29—41no—
100#41×C29—41no—
101#41×C29—41no—
102#41×C29—41no—
103C2×Q8×C29—21no—
104C2×Q8×C29—21no—
105C2×D4×C29—21no—
106C2×D4×C29—22no—
107C2×D4×C29—21no—
108C2×D4×C29—44no—
109C2×D4×C29—41no—
110C2×D4×C29—41no—
111C2×D4×C29—41no—
112C2×D4×C29—41no—
113C2×D4×C29—41no—
114C2×D4×C29—41no—
115C2×D4×C29—41no—
116C22×C4×C29—41no—
117C22×C4×C29—41no—
118C22×C4×C29C2×D411yescharacteristic
119Q16×C29—21no—
120Q16×C29—21no—
121Q16×C29—21no—
122Q16×C29C2×D412yes—
123SD16×C29—22no—
124SD16×C29—22no—
125SD16×C29—41no—
126SD16×C29—41no—
127SD16×C29—44no—
128D8×C29—21no—
129D8×C29—22no—
130D8×C29—21no—
131D8×C29—22no—
132D8×C29—21no—
133D8×C29—41no—
134D8×C29—41no—
135D8×C29—44no—
136D8×C29C2×D412yes—
137M16×C29—22no—
138M16×C29—41no—
139M16×C29—44no—
140M16×C29D812yes—
141M16×C29D812yes—
142C2×C8×C29—41no—
143C2×C8×C29—44no—
144C2×C8×C29C2×D411yescharacteristic
145C2×C8×C29C2×D411yescharacteristic
146C2×C8×C29C2×D411yescharacteristic
147C2×C8×C29C2×D412yes—
148C2×C8×C29#4111yescharacteristic
149C2×C8×C29#4111yescharacteristic
150C2×C8×C29C2411yescharacteristic
151C4⋊C4×C29—21no—
152C22⋊C4×C29—21no—
153C22⋊C4×C29—44no—
154C42×C29C2×D412yes—
155C16×C29—22no—
156C16×C29—22no—
157#33595C2911yesmaximal, characteristic, direct product factor, Sylow
158C23×C29—41no—
159C23×C29—42no—
160C23×C29—41no—
161C23×C29—81no—
162C23×C29—81no—
163C23×C29—162no—
164C23×C29AGL(1,ℤ/8)11yescharacteristic
165Q8×C29—22no—
166Q8×C29—41no—
167Q8×C29—41no—
168Q8×C29—41no—
169D4×C29—22no—
170D4×C29—42no—
171D4×C29—42no—
172D4×C29—42no—
173D4×C29—41no—
174D4×C29—41no—
175D4×C29—42no—
176D4×C29—41no—
177D4×C29—81no—
178D4×C29—81no—
179D4×C29—81no—
180D4×C29—81no—
181D4×C29—164no—
182C2×C4×C29—22no—
183C2×C4×C29—41no—
184C2×C4×C29—42no—
185C2×C4×C29—42no—
186C2×C4×C29—41no—
187C2×C4×C29—81no—
188C2×C4×C29—81no—
189C2×C4×C29#12111yescharacteristic
190C2×C4×C29#12111yescharacteristic
191C2×C4×C29C2×D811yescharacteristic
192C2×C4×C29C2×D811yescharacteristic
193C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C29C22×D411yescharacteristic
195C8×C29—42no—
196C8×C29#12111yescharacteristic
197C8×C29#12111yescharacteristic
198C8×C29C2×D814yes—
199C8×C29C22×D411yescharacteristic
200C8×C29C2×#4111yescharacteristic
201#3414C2×C2911yescharacteristic, complemented
202C2×#509C2×C2911yescharacteristic, complemented
203#3155C2×C2911yescharacteristic, complemented
204#2957C2×C2911yescharacteristic, complemented
205#2213C2×C2914yescomplemented
206#2212C2×C2914yescomplemented
207#2153C2×C2911yescharacteristic, complemented
208#2148C2×C2911yescharacteristic, complemented
209C2×#361C2×C2911yescharacteristic, complemented
210C22×C29—41no—
211C22×C29—42no—
212C22×C29—82no—
213C22×C29—84no—
214C22×C29—81no—
215C22×C29—82no—
216C22×C29—161no—
217C22×C29—162no—
218C22×C29—162no—
219C22×C29#45911yescharacteristic
220C22×C29#45911yescharacteristic
221C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
222C4×C29—42no—
223C4×C29—42no—
224C4×C29—81no—
225C4×C29#45911yescharacteristic
226C4×C29#45911yescharacteristic
227C4×C29C2×#12111yescharacteristic
228C4×C29C22×D811yescharacteristic
229C2×AGL(1,ℤ/8)—21no—
230C2×#135C22×C2911yescharacteristic
231C2×#135C22×C2911yescharacteristic
232C22×D8C22×C2911yescharacteristic
233#568—21no—
234#535—21no—
235#510—21no—
236#510C22×C2912yescomplemented
237#509—22no—
238#509—21no—
239#509C22×C2914yes—
240#509C22×C2912yescomplemented
241#508—22no—
242C2×SD32—21no—
243C2×D16—21no—
244C2×M32C22×C2911yescharacteristic
245C2×M32C22×C2911yescharacteristic
246#496—22no—
247#495C22×C2912yescomplemented
248#493C22×C2912yescomplemented
249#444—22no—
250#443C22×C2914yescomplemented
251C2×#108C22×C2911yescharacteristic
252#421—21no—
253#405C22×C2911yescharacteristic
254#364C22×C2914yescomplemented
255#362C22×C2912yescomplemented
256#361C22×C2914yescomplemented
257#361C22×C2912yescomplemented
258C2×C29—21no—
259C2×C29—21no—
260C2×C29—21no—
261C2×C29—82no—
262C2×C29—161no—
263C2×C29—162no—
264C2×C29C2×#45911yescharacteristic
265C2×#41—21no—
266C2×#41—21no—
267C22×D4—21no—
268AGL(1,ℤ/8)—42no—
269AGL(1,ℤ/8)—42no—
270#135—21no—
271#135—21no—
272#135—21no—
273#135—21no—
274#135—21no—
275#135—21no—
276#135D4×C2912yescomplemented
277#135C23×C2912yes—
278C2×Q16D4×C2911yescharacteristic, complemented
279C2×Q16C23×C2911yescharacteristic
280C2×SD16—21no—
281C2×SD16—22no—
282C2×SD16—21no—
283C2×D8—21no—
284C2×D8—21no—
285C2×D8—21no—
286C2×D8—22no—
287C2×D8—21no—
288C2×D8—21no—
289C2×D8D4×C2911yescharacteristic, complemented
290C2×D8C23×C2912yes—
291C2×D8C23×C2911yescharacteristic
292#131—24no—
293#131—42no—
294C2×M16—21no—
295C2×M16—42no—
296C2×M16D4×C2911yescharacteristic
297C22×C8C23×C2911yescharacteristic
298#127—22no—
299#124—22no—
300#121—42no—
301#120—42no—
302#117D4×C2911yescharacteristic
303Q32—22no—
304SD32—24no—
305SD32—22no—
306SD32—22no—
307D16—24no—
308D16—22no—
309M32—21no—
310M32—21no—
311M32C23×C2912yes—
312M32C23×C2912yes—
313C2×C16—21no—
314C2×C16—21no—
315#108—21no—
316#108C23×C2912yes—
317#104—24no—
318#97D4×C2912yes—
319C4×C8C23×C2912yes—
320C29#3359511yescharacteristic, direct product factor, Sylow
321C24—41no—
322#41—22no—
323#41—22no—
324#41—41no—
325#41—41no—
326#41—41no—
327#41—41no—
328#41—41no—
329#41—41no—
330C2×Q8—21no—
331C2×Q8—21no—
332C2×D4—21no—
333C2×D4—22no—
334C2×D4—21no—
335C2×D4—44no—
336C2×D4—41no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4C2×D4×C2911yescharacteristic
346Q16—21no—
347Q16—21no—
348Q16—21no—
349Q16C2×D4×C2912yes—
350SD16—22no—
351SD16—22no—
352SD16—41no—
353SD16—41no—
354SD16—44no—
355D8—21no—
356D8—22no—
357D8—21no—
358D8—22no—
359D8—21no—
360D8—41no—
361D8—41no—
362D8—44no—
363D8C2×D4×C2912yes—
364M16—22no—
365M16—41no—
366M16—44no—
367M16D8×C2912yes—
368M16D8×C2912yes—
369C2×C8—41no—
370C2×C8—44no—
371C2×C8C2×D4×C2911yescharacteristic
372C2×C8C2×D4×C2911yescharacteristic
373C2×C8C2×D4×C2911yescharacteristic
374C2×C8C2×D4×C2912yes—
375C2×C8#41×C2911yescharacteristic
376C2×C8#41×C2911yescharacteristic
377C2×C8C24×C2911yescharacteristic
378C4⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—44no—
381C42C2×D4×C2912yes—
382C16—22no—
383C16—22no—
384C23—41no—
385C23—42no—
386C23—41no—
387C23—81no—
388C23—81no—
389C23—162no—
390C23C29×AGL(1,ℤ/8)11yescharacteristic
391Q8—22no—
392Q8—41no—
393Q8—41no—
394Q8—41no—
395D4—22no—
396D4—42no—
397D4—42no—
398D4—41no—
399D4—42no—
400D4—41no—
401D4—41no—
402D4—42no—
403D4—81no—
404D4—81no—
405D4—81no—
406D4—81no—
407D4—164no—
408C2×C4—22no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—41no—
413C2×C4—81no—
414C2×C4—81no—
415C2×C4C29×#12111yescharacteristic
416C2×C4C29×#12111yescharacteristic
417C2×C4C2×D8×C2911yescharacteristic
418C2×C4C2×D8×C2911yescharacteristic
419C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
420C2×C4C22×D4×C2911yescharacteristic
421C8—42no—
422C8C29×#12111yescharacteristic
423C8C29×#12111yescharacteristic
424C8C2×D8×C2914yes—
425C8C22×D4×C2911yescharacteristic
426C8C2×#41×C2911yescharacteristic
427C22—41no—
428C22—42no—
429C22—82no—
430C22—84no—
431C22—81no—
432C22—82no—
433C22—161no—
434C22—162no—
435C22—162no—
436C22C29×#45911yescharacteristic
437C22C29×#45911yescharacteristic
438C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
439C4—42no—
440C4—42no—
441C4—81no—
442C4C29×#45911yescharacteristic
443C4C29×#45911yescharacteristic
444C4C2×C29×#12111yescharacteristic
445C4C22×D8×C2911yescharacteristic
446C2—21no—
447C2—21no—
448C2—21no—
449C2—82no—
450C2—162no—
451C2—161no—
452C2C2×C29×#45911yescharacteristic
subgroupG/H
center, socleC2×C29C2×#459
commutator, Frattini, cosocleC2×C8C24×C29
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C22×C4×C29 ◁ C29×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3414C2semidirect
2. C2×C29×#509C2semidirect
3. C29×#3155C2semidirect
4. C29×#2957C2semidirect
5. C29×#2213C2semidirect
6. C29×#2212C2semidirect
7. C29×#2153C2semidirect
8. C29×#2148C2semidirect
9. C2×C29×#361C2semidirect
17. C29×#510C22semidirect
21. C29×#509C22semidirect
28. C29×#495C22semidirect
29. C29×#493C22semidirect
31. C29×#443C22semidirect
35. C29×#364C22semidirect
36. C29×#362C22semidirect
37. C29×#361C22semidirect
38. C29×#361C22semidirect
50. C29×#135D4semidirect
52. C2×Q16×C29D4semidirect
63. C2×D8×C29D4semidirect
157. #33595C29direct (N × H)
201. #3414C2×C29semidirect
202. C2×#509C2×C29semidirect
203. #3155C2×C29semidirect
204. #2957C2×C29semidirect
205. #2213C2×C29semidirect
206. #2212C2×C29semidirect
207. #2153C2×C29semidirect
208. #2148C2×C29semidirect
209. C2×#361C2×C29semidirect
236. #510C22×C29semidirect
240. #509C22×C29semidirect
247. #495C22×C29semidirect
248. #493C22×C29semidirect
250. #443C22×C29semidirect
254. #364C22×C29semidirect
255. #362C22×C29semidirect
256. #361C22×C29semidirect
257. #361C22×C29semidirect
276. #135D4×C29semidirect
278. C2×Q16D4×C29semidirect
289. C2×D8D4×C29semidirect
320. C29#33595direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34142
C2×C29×#5092
C29×#31552
C29×#29572
C29×#22132
C29×#22122
C29×#21532
C29×#21482
C2×C29×#3612
#3359529