Finite Group Databasebeta

← C29×#33791 #20328691

Subgroups — C29×#33791 #20328691

Order 7424.

574 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3175C211yesmaximal, characteristic, complemented
2C29×#3156C211yesmaximal, characteristic, complemented
3C29×#2251C211yesmaximal, characteristic, complemented
4C29×#2249C211yesmaximal, characteristic, complemented
5C29×#2243C211yesmaximal, characteristic, complemented
6C29×#2241C211yesmaximal, characteristic, complemented
7C29×#2211C211yesmaximal, characteristic, complemented
8C29×#2210C211yesmaximal, characteristic, complemented
9C29×#2209C211yesmaximal, characteristic, complemented
10C29×#2208C211yesmaximal, characteristic, complemented
11C29×#2189C211yesmaximal, characteristic, complemented
12C29×#2188C211yesmaximal, characteristic, complemented
13C29×#2186C211yesmaximal, characteristic
14C29×#2185C211yesmaximal, characteristic, complemented
15C29×#2164C211yesmaximal, characteristic, complemented
16C2×C29×#137—21no—
17C2×C29×#135C2211yescharacteristic
18C22×Q16×C29C2211yescharacteristic
19C29×#542—21no—
20C29×#536—21no—
21C2×C29×Q32C2211yescharacteristic
22C2×C29×Q32C2211yescharacteristic
23C2×C29×Q32C2211yescharacteristic
24C2×C29×SD32C2211yescharacteristic
25C2×C29×SD32C2211yescharacteristic
26C2×C29×SD32C2211yescharacteristic
27C2×C29×SD32C2211yescharacteristic
28C2×C29×D16C2211yescharacteristic
29C29×#500C2211yescharacteristic
30C29×#497—21no—
31C29×#497—21no—
32C29×#495C2211yescharacteristic
33C29×#495C2211yescharacteristic
34C29×#495C2211yescharacteristic
35C29×#494C2211yescharacteristic
36C29×#494C2211yescharacteristic
37C29×#489—21no—
38C29×#468—21no—
39C29×#467C2211yescharacteristic
40C29×#466C2211yescharacteristic
41C29×#440—21no—
42C4×Q16×C29C2211yescharacteristic
43C4×D8×C29C2211yescharacteristic
44C29×#405C2211yescharacteristic
45C29×C4⋊C16C2211yescharacteristic
46C29×C4⋊C16C2211yescharacteristic
47C29×#358C2211yescharacteristic
48C29×#358C2211yescharacteristic
49C29×#358C2211yescharacteristic
50C29×#358C2211yescharacteristic
51C29×#358C2211yescharacteristic
52C29×#358C2211yescharacteristic
53C29×#357C2211yescharacteristic
54C29×#357C2211yescharacteristic
55C29×C22⋊C16C2211yescharacteristic
56C29×C22⋊C16C2211yescharacteristic
57C29×#346C2211yescharacteristic
58C4×C16×C29C2211yescharacteristic
59C2×#41×C29—21no—
60C22×Q8×C29—21no—
61C29×#137—44no—
62C29×#135—41no—
63C29×#135—41no—
64C2×Q16×C29—21no—
65C2×Q16×C29—21no—
66C2×Q16×C29—21no—
67C2×Q16×C29—41no—
68C2×Q16×C29—41no—
69C2×Q16×C29C2311yescharacteristic
70C2×Q16×C29C2311yescharacteristic
71C2×Q16×C29C2311yescharacteristic
72C2×Q16×C29C2311yescharacteristic
73C2×SD16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29—21no—
76C2×SD16×C29—21no—
77C2×D8×C29C2311yescharacteristic
78C2×D8×C29C2311yescharacteristic
79C2×M16×C29D411yescharacteristic
80C22×C8×C29C2311yescharacteristic
81C29×C4⋊Q8—21no—
82C29×C4⋊Q8—21no—
83C29×C4⋊Q8—21no—
84C29×#126—41no—
85C29×#124—21no—
86C29×#124—21no—
87C29×#124—21no—
88C29×#124—41no—
89C29×#123—41no—
90C29×#123—41no—
91C29×#123—41no—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8—41no—
94C29×C22⋊Q8—41no—
95C29×C22⋊Q8—41no—
96C29×#121—21no—
97C4×Q8×C29—21no—
98C4×D4×C29—21no—
99C29×#117D411yescharacteristic
100C29×Q32—41no—
101C29×Q32—41no—
102C29×Q32—41no—
103C29×SD32—41no—
104C29×SD32—41no—
105C29×SD32—41no—
106C29×SD32—41no—
107C29×D16—41no—
108C2×C16×C29C2311yescharacteristic
109C2×C16×C29C2311yescharacteristic
110C2×C16×C29C2311yescharacteristic
111C2×C16×C29C2311yescharacteristic
112C29×#107—21no—
113C29×#107C2311yescharacteristic
114C29×#107C2311yescharacteristic
115C29×#103—21no—
116C29×#103—21no—
117C29×#102—21no—
118C29×#102—21no—
119C29×#97D411yescharacteristic
120C29×#97D411yescharacteristic
121C4×C8×C29C2311yescharacteristic
122C4×C8×C29C2311yescharacteristic
123#41×C29—42no—
124#41×C29—42no—
125C2×Q8×C29—21no—
126C2×Q8×C29—21no—
127C2×Q8×C29—21no—
128C2×Q8×C29—21no—
129C2×Q8×C29—42no—
130C2×Q8×C29—42no—
131C2×Q8×C29—41no—
132C2×Q8×C29—41no—
133C2×D4×C29—21no—
134C2×D4×C29—21no—
135C2×D4×C29—41no—
136C2×D4×C29—41no—
137C22×C4×C29—41no—
138C22×C4×C29—41no—
139C22×C4×C29—41no—
140C22×C4×C29C2×D411yescharacteristic
141Q16×C29—21no—
142Q16×C29—21no—
143Q16×C29—21no—
144Q16×C29—21no—
145Q16×C29—21no—
146Q16×C29—21no—
147Q16×C29—21no—
148Q16×C29—21no—
149Q16×C29—42no—
150Q16×C29—42no—
151Q16×C29—42no—
152SD16×C29—42no—
153SD16×C29—42no—
154SD16×C29—42no—
155SD16×C29—42no—
156D8×C29—21no—
157D8×C29—21no—
158D8×C29—21no—
159D8×C29—21no—
160M16×C29—22no—
161C2×C8×C29—21no—
162C2×C8×C29—21no—
163C2×C8×C29C2×D411yescharacteristic
164C2×C8×C29C2×D411yescharacteristic
165C2×C8×C29C2×D411yescharacteristic
166C2×C8×C29C2411yescharacteristic
167C4⋊C4×C29—21no—
168C4⋊C4×C29—21no—
169C4⋊C4×C29—41no—
170C4⋊C4×C29—41no—
171C4⋊C4×C29—41no—
172C4⋊C4×C29—41no—
173C4⋊C4×C29—41no—
174C4⋊C4×C29—41no—
175C4⋊C4×C29—41no—
176C4⋊C4×C29D811yescharacteristic
177C4⋊C4×C29D811yescharacteristic
178C22⋊C4×C29—41no—
179C22⋊C4×C29—41no—
180C22⋊C4×C29—41no—
181C22⋊C4×C29—41no—
182C22⋊C4×C29—41no—
183C22⋊C4×C29—41no—
184C22⋊C4×C29—41no—
185C22⋊C4×C29—41no—
186C22⋊C4×C29—41no—
187C22⋊C4×C29D811yescharacteristic
188C22⋊C4×C29D811yescharacteristic
189C42×C29—41no—
190C42×C29C2×D411yescharacteristic
191C42×C29C2×D411yescharacteristic
192C16×C29—21no—
193C16×C29—21no—
194C16×C29—21no—
195C16×C29—21no—
196#33791C2911yesmaximal, characteristic, direct product factor, Sylow
197C23×C29—41no—
198C23×C29—41no—
199C23×C29C2×D811yescharacteristic
200Q8×C29—41no—
201Q8×C29—41no—
202Q8×C29—41no—
203Q8×C29—41no—
204Q8×C29—41no—
205Q8×C29—41no—
206Q8×C29—41no—
207Q8×C29—41no—
208Q8×C29—82no—
209Q8×C29—161no—
210D4×C29—41no—
211D4×C29—41no—
212D4×C29—41no—
213D4×C29—41no—
214D4×C29—82no—
215D4×C29—161no—
216C2×C4×C29—21no—
217C2×C4×C29—21no—
218C2×C4×C29—41no—
219C2×C4×C29—41no—
220C2×C4×C29—41no—
221C2×C4×C29—41no—
222C2×C4×C29—41no—
223C2×C4×C29—41no—
224C2×C4×C29—82no—
225C2×C4×C29—82no—
226C2×C4×C29—161no—
227C2×C4×C29C2×D811yescharacteristic
228C2×C4×C29C2×D811yescharacteristic
229C2×C4×C29C2×D811yescharacteristic
230C2×C4×C29C2×D811yescharacteristic
231C2×C4×C29C2×D811yescharacteristic
232C2×C4×C29C22×D411yescharacteristic
233C8×C29—21no—
234C8×C29—21no—
235C8×C29AGL(1,ℤ/8)12yes—
236C8×C29H(5,𝔽2)11yescharacteristic
237C8×C29H(5,𝔽2)11yescharacteristic
238#3175C2×C2911yescharacteristic, complemented
239#3156C2×C2911yescharacteristic, complemented
240#2251C2×C2911yescharacteristic, complemented
241#2249C2×C2911yescharacteristic, complemented
242#2243C2×C2911yescharacteristic, complemented
243#2241C2×C2911yescharacteristic, complemented
244#2211C2×C2911yescharacteristic, complemented
245#2210C2×C2911yescharacteristic, complemented
246#2209C2×C2911yescharacteristic, complemented
247#2208C2×C2911yescharacteristic, complemented
248#2189C2×C2911yescharacteristic, complemented
249#2188C2×C2911yescharacteristic, complemented
250#2186C2×C2911yescharacteristic
251#2185C2×C2911yescharacteristic, complemented
252#2164C2×C2911yescharacteristic, complemented
253C22×C29—21no—
254C22×C29—21no—
255C22×C29—21no—
256C22×C29—81no—
257C22×C29—81no—
258C22×C29—81no—
259C22×C29—81no—
260C22×C29—81no—
261C22×C29—81no—
262C22×C29C22×D811yescharacteristic
263C4×C29—21no—
264C4×C29—21no—
265C4×C29—21no—
266C4×C29—21no—
267C4×C29—21no—
268C4×C29—81no—
269C4×C29—81no—
270C4×C29—81no—
271C4×C29—81no—
272C4×C29—81no—
273C4×C29—81no—
274C4×C29#53511yescharacteristic
275C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
276C2×#137—21no—
277C2×#135C22×C2911yescharacteristic
278C22×Q16C22×C2911yescharacteristic
279#542—21no—
280#536—21no—
281C2×Q32C22×C2911yescharacteristic
282C2×Q32C22×C2911yescharacteristic
283C2×Q32C22×C2911yescharacteristic
284C2×SD32C22×C2911yescharacteristic
285C2×SD32C22×C2911yescharacteristic
286C2×SD32C22×C2911yescharacteristic
287C2×SD32C22×C2911yescharacteristic
288C2×D16C22×C2911yescharacteristic
289#500C22×C2911yescharacteristic
290#497—21no—
291#497—21no—
292#495C22×C2911yescharacteristic
293#495C22×C2911yescharacteristic
294#495C22×C2911yescharacteristic
295#494C22×C2911yescharacteristic
296#494C22×C2911yescharacteristic
297#489—21no—
298#468—21no—
299#467C22×C2911yescharacteristic
300#466C22×C2911yescharacteristic
301#440—21no—
302C4×Q16C22×C2911yescharacteristic
303C4×D8C22×C2911yescharacteristic
304#405C22×C2911yescharacteristic
305C4⋊C16C22×C2911yescharacteristic
306C4⋊C16C22×C2911yescharacteristic
307#358C22×C2911yescharacteristic
308#358C22×C2911yescharacteristic
309#358C22×C2911yescharacteristic
310#358C22×C2911yescharacteristic
311#358C22×C2911yescharacteristic
312#358C22×C2911yescharacteristic
313#357C22×C2911yescharacteristic
314#357C22×C2911yescharacteristic
315C22⋊C16C22×C2911yescharacteristic
316C22⋊C16C22×C2911yescharacteristic
317#346C22×C2911yescharacteristic
318C4×C16C22×C2911yescharacteristic
319C2×C29—41no—
320C2×C29—161no—
321C2×C29—161no—
322C2×C29#320511yescharacteristic
323C2×C29#341611yescharacteristic
324C2×C29#341711yescharacteristic
325C2×#41—21no—
326C22×Q8—21no—
327#137—44no—
328#135—41no—
329#135—41no—
330C2×Q16—21no—
331C2×Q16—21no—
332C2×Q16—21no—
333C2×Q16—41no—
334C2×Q16—41no—
335C2×Q16C23×C2911yescharacteristic
336C2×Q16C23×C2911yescharacteristic
337C2×Q16C23×C2911yescharacteristic
338C2×Q16C23×C2911yescharacteristic
339C2×SD16—21no—
340C2×SD16—21no—
341C2×SD16—21no—
342C2×SD16—21no—
343C2×D8C23×C2911yescharacteristic
344C2×D8C23×C2911yescharacteristic
345C2×M16D4×C2911yescharacteristic
346C22×C8C23×C2911yescharacteristic
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350#126—41no—
351#124—21no—
352#124—21no—
353#124—21no—
354#124—41no—
355#123—41no—
356#123—41no—
357#123—41no—
358C22⋊Q8—21no—
359C22⋊Q8—41no—
360C22⋊Q8—41no—
361C22⋊Q8—41no—
362#121—21no—
363C4×Q8—21no—
364C4×D4—21no—
365#117D4×C2911yescharacteristic
366Q32—41no—
367Q32—41no—
368Q32—41no—
369SD32—41no—
370SD32—41no—
371SD32—41no—
372SD32—41no—
373D16—41no—
374C2×C16C23×C2911yescharacteristic
375C2×C16C23×C2911yescharacteristic
376C2×C16C23×C2911yescharacteristic
377C2×C16C23×C2911yescharacteristic
378#107—21no—
379#107C23×C2911yescharacteristic
380#107C23×C2911yescharacteristic
381#103—21no—
382#103—21no—
383#102—21no—
384#102—21no—
385#97D4×C2911yescharacteristic
386#97D4×C2911yescharacteristic
387C4×C8C23×C2911yescharacteristic
388C4×C8C23×C2911yescharacteristic
389C29#3379111yescharacteristic, direct product factor, Sylow
390#41—42no—
391#41—42no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—42no—
397C2×Q8—42no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—41no—
403C2×D4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4C2×D4×C2911yescharacteristic
408Q16—21no—
409Q16—21no—
410Q16—21no—
411Q16—21no—
412Q16—21no—
413Q16—21no—
414Q16—21no—
415Q16—21no—
416Q16—42no—
417Q16—42no—
418Q16—42no—
419SD16—42no—
420SD16—42no—
421SD16—42no—
422SD16—42no—
423D8—21no—
424D8—21no—
425D8—21no—
426D8—21no—
427M16—22no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8C2×D4×C2911yescharacteristic
431C2×C8C2×D4×C2911yescharacteristic
432C2×C8C2×D4×C2911yescharacteristic
433C2×C8C24×C2911yescharacteristic
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4—41no—
442C4⋊C4—41no—
443C4⋊C4D8×C2911yescharacteristic
444C4⋊C4D8×C2911yescharacteristic
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C22⋊C4D8×C2911yescharacteristic
455C22⋊C4D8×C2911yescharacteristic
456C42—41no—
457C42C2×D4×C2911yescharacteristic
458C42C2×D4×C2911yescharacteristic
459C16—21no—
460C16—21no—
461C16—21no—
462C16—21no—
463C23—41no—
464C23—41no—
465C23C2×D8×C2911yescharacteristic
466Q8—41no—
467Q8—41no—
468Q8—41no—
469Q8—41no—
470Q8—41no—
471Q8—41no—
472Q8—41no—
473Q8—41no—
474Q8—82no—
475Q8—161no—
476D4—41no—
477D4—41no—
478D4—41no—
479D4—41no—
480D4—82no—
481D4—161no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—82no—
491C2×C4—82no—
492C2×C4—161no—
493C2×C4C2×D8×C2911yescharacteristic
494C2×C4C2×D8×C2911yescharacteristic
495C2×C4C2×D8×C2911yescharacteristic
496C2×C4C2×D8×C2911yescharacteristic
497C2×C4C2×D8×C2911yescharacteristic
498C2×C4C22×D4×C2911yescharacteristic
499C8—21no—
500C8—21no—
501C8C29×AGL(1,ℤ/8)12yes—
502C8C29×H(5,𝔽2)11yescharacteristic
503C8C29×H(5,𝔽2)11yescharacteristic
504C22—21no—
505C22—21no—
506C22—21no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22C22×D8×C2911yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—21no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4—81no—
524C4—81no—
525C4C29×#53511yescharacteristic
526C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
527C2—41no—
528C2—161no—
529C2—161no—
530C2C29×#320511yescharacteristic
531C2C29×#341611yescharacteristic
532C2C29×#341711yescharacteristic
subgroupG/H
center, socleC22×C29C22×D8
commutator, Frattini, cosocleC2×C8C24×C29
prime radicalC29×#2186C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C29×#117 ◁ C29×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3175C2semidirect
2. C29×#3156C2semidirect
3. C29×#2251C2semidirect
4. C29×#2249C2semidirect
5. C29×#2243C2semidirect
6. C29×#2241C2semidirect
7. C29×#2211C2semidirect
8. C29×#2210C2semidirect
9. C29×#2209C2semidirect
10. C29×#2208C2semidirect
11. C29×#2189C2semidirect
12. C29×#2188C2semidirect
14. C29×#2185C2semidirect
15. C29×#2164C2semidirect
196. #33791C29direct (N × H)
238. #3175C2×C29semidirect
239. #3156C2×C29semidirect
240. #2251C2×C29semidirect
241. #2249C2×C29semidirect
242. #2243C2×C29semidirect
243. #2241C2×C29semidirect
244. #2211C2×C29semidirect
245. #2210C2×C29semidirect
246. #2209C2×C29semidirect
247. #2208C2×C29semidirect
248. #2189C2×C29semidirect
249. #2188C2×C29semidirect
251. #2185C2×C29semidirect
252. #2164C2×C29semidirect
389. C29#33791direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31752
C29×#31562
C29×#22512
C29×#22492
C29×#22432
C29×#22412
C29×#22112
C29×#22102
C29×#22092
C29×#22082
C29×#21892
C29×#21882
C29×#21862
C29×#21852
C29×#21642
#3379129