Finite Group Databasebeta

← C29×#32698 #20327598

Subgroups — C29×#32698 #20327598

Order 7424.

594 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2102C211yesmaximal, characteristic, complemented
2C29×#2081C211yesmaximal, characteristic, complemented
3C29×#2081C211yesmaximal, characteristic, complemented
4C29×#2069C211yesmaximal, characteristic, complemented
5C29×#2048C211yesmaximal, characteristic, complemented
6C29×#2002C211yesmaximal, characteristic
7C29×#1965C211yesmaximal, characteristic, complemented
8C29×#1932C211yesmaximal, characteristic, complemented
9C29×#1914C211yesmaximal, characteristic, complemented
10C29×#1911C211yesmaximal, characteristic, complemented
11C29×#1903C211yesmaximal, characteristic, complemented
12C29×#1887C211yesmaximal, characteristic, complemented
13C29×#1861C211yesmaximal, characteristic, complemented
14C29×#1841C211yesmaximal, characteristic, complemented
15C29×#1829C211yesmaximal, characteristic, complemented
16C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
17C29×#568C2211yescharacteristic
18C29×#535C2211yescharacteristic
19C2×C29×#127C2211yescharacteristic
20C29×#518C2211yescharacteristic
21C29×#430C2211yescharacteristic
22C29×#430C2211yescharacteristic
23C29×#430C2211yescharacteristic
24C29×#423C2211yescharacteristic
25C29×#421C2211yescharacteristic
26C29×#421C2211yescharacteristic
27C2×C29×#104C2211yescharacteristic
28C29×#418C2211yescharacteristic
29C29×#418C2211yescharacteristic
30C29×#418C2211yescharacteristic
31C29×#413C2211yescharacteristic
32C2×C29×#100C2211yescharacteristic
33C2×C29×#100C2211yescharacteristic
34C2×C29×#100C2211yescharacteristic
35C2×C29×#100C2211yescharacteristic
36C2×C29×#100C2211yescharacteristic
37C2×C29×#100C2211yescharacteristic
38C4×M16×C29C2211yescharacteristic
39C29×#344C2211yescharacteristic
40C29×#344C2211yescharacteristic
41C29×#344C2211yescharacteristic
42C29×#344C2211yescharacteristic
43C29×#344C2211yescharacteristic
44C29×#344C2211yescharacteristic
45C29×#339C2211yescharacteristic
46C29×#339C2211yescharacteristic
47C29×#339C2211yescharacteristic
48C29×#338C2211yescharacteristic
49C29×H(3,ℤ/4)C2211yescharacteristic
50C29×H(3,ℤ/4)C2211yescharacteristic
51C2×#41×C29C2311yescharacteristic
52C22×D4×C29—22no—
53C22×D4×C29C2311yescharacteristic
54C22×D4×C29C2311yescharacteristic
55C29×AGL(1,ℤ/8)—41no—
56C29×AGL(1,ℤ/8)—41no—
57C2×SD16×C29—21no—
58C2×D8×C29—21no—
59C29×#131—41no—
60C29×#131—41no—
61C2×M16×C29—41no—
62C2×M16×C29C2311yescharacteristic
63C2×M16×C29C2311yescharacteristic
64C2×M16×C29C2311yescharacteristic
65C2×M16×C29C2311yescharacteristic
66C2×M16×C29C2311yescharacteristic
67C2×M16×C29C2311yescharacteristic
68C2×M16×C29C2311yescharacteristic
69C2×M16×C29C2311yescharacteristic
70C29×#127—21no—
71C29×#127—21no—
72C29×#127—21no—
73C29×#127—41no—
74C29×#124—21no—
75C29×#121—41no—
76C29×#120—22no—
77C4×D4×C29—41no—
78C4×D4×C29—41no—
79C29×#117C2311yescharacteristic
80C29×#117C2311yescharacteristic
81C29×#117C2311yescharacteristic
82C2×C22⋊C4×C29—22no—
83C2×C42×C29C2311yescharacteristic
84C29×#108—41no—
85C29×#108—41no—
86C29×#108—41no—
87C29×C4⋊C8—41no—
88C29×#104—21no—
89C29×#104—21no—
90C29×#104—41no—
91C29×#104—41no—
92C29×#102—41no—
93C29×#102—41no—
94C29×#102—41no—
95C29×#101—21no—
96C29×#100—21no—
97C29×#100—41no—
98C29×#100—41no—
99C29×#100—41no—
100C29×#100—41no—
101C29×#100—41no—
102C29×#100—41no—
103C29×#97—21no—
104C4×C8×C29—21no—
105C24×C29—21no—
106C24×C29#4112yes—
107#41×C29—21no—
108#41×C29—21no—
109#41×C29—21no—
110#41×C29—21no—
111C2×Q8×C29#4111yescharacteristic
112C2×D4×C29—21no—
113C2×D4×C29—21no—
114C2×D4×C29—21no—
115C2×D4×C29—21no—
116C2×D4×C29—21no—
117C2×D4×C29—21no—
118C2×D4×C29—21no—
119C2×D4×C29—21no—
120C2×D4×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29—21no—
123C2×D4×C29—21no—
124C2×D4×C29—21no—
125C2×D4×C29—42no—
126C2×D4×C29—42no—
127C2×D4×C29—42no—
128C2×D4×C29—84no—
129C2×D4×C29#4111yescharacteristic
130C22×C4×C29—21no—
131C22×C4×C29—21no—
132C22×C4×C29—42no—
133C22×C4×C29C2411yescharacteristic
134SD16×C29—42no—
135D8×C29—42no—
136M16×C29—21no—
137M16×C29—21no—
138M16×C29—21no—
139M16×C29—21no—
140M16×C29—21no—
141M16×C29—21no—
142M16×C29—21no—
143M16×C29—21no—
144M16×C29—21no—
145M16×C29—21no—
146M16×C29—21no—
147M16×C29—21no—
148M16×C29—21no—
149M16×C29—21no—
150M16×C29—21no—
151M16×C29—21no—
152M16×C29—42no—
153C2×C8×C29—21no—
154C2×C8×C29—21no—
155C2×C8×C29—21no—
156C2×C8×C29—21no—
157C2×C8×C29—21no—
158C2×C8×C29—21no—
159C2×C8×C29—21no—
160C2×C8×C29—21no—
161C2×C8×C29—42no—
162C4⋊C4×C29—21no—
163C4⋊C4×C29—21no—
164C4⋊C4×C29—21no—
165C22⋊C4×C29—21no—
166C22⋊C4×C29—21no—
167C22⋊C4×C29—21no—
168C22⋊C4×C29—42no—
169C22⋊C4×C29—42no—
170C42×C29—21no—
171C42×C29—21no—
172C42×C29—21no—
173C42×C29—21no—
174C42×C29#4111yescharacteristic
175C42×C29#4111yescharacteristic
176#32698C2911yesmaximal, characteristic, direct product factor, Sylow
177C23×C29—22no—
178C23×C29—22no—
179C23×C29—21no—
180C23×C29—22no—
181C23×C29—41no—
182C23×C29—41no—
183C23×C29—41no—
184C23×C29—82no—
185C23×C29—82no—
186C23×C29C2×#4111yescharacteristic
187Q8×C29—21no—
188Q8×C29—21no—
189D4×C29—21no—
190D4×C29—21no—
191D4×C29—41no—
192D4×C29—41no—
193D4×C29—41no—
194D4×C29—41no—
195D4×C29—41no—
196D4×C29—41no—
197D4×C29—41no—
198D4×C29—41no—
199D4×C29—41no—
200D4×C29—41no—
201D4×C29—84no—
202D4×C29—84no—
203D4×C29—162no—
204C2×C4×C29—21no—
205C2×C4×C29—21no—
206C2×C4×C29—21no—
207C2×C4×C29—42no—
208C2×C4×C29—41no—
209C2×C4×C29—41no—
210C2×C4×C29—41no—
211C2×C4×C29—41no—
212C2×C4×C29—41no—
213C2×C4×C29—162no—
214C2×C4×C29C2×#4111yescharacteristic
215C2×C4×C29C2×#4111yescharacteristic
216C2×C4×C29H(5,𝔽2)11yescharacteristic
217C2×C4×C29H(5,𝔽2)11yescharacteristic
218C2×C4×C29H(5,𝔽2)11yescharacteristic
219C2×C4×C29H(5,𝔽2)11yescharacteristic
220C8×C29—41no—
221C8×C29—41no—
222C8×C29—41no—
223C8×C29—41no—
224C8×C29—41no—
225C8×C29—41no—
226C8×C29—41no—
227C8×C29—41no—
228#2102C2×C2911yescharacteristic, complemented
229#2081C2×C2911yescharacteristic, complemented
230#2081C2×C2911yescharacteristic, complemented
231#2069C2×C2911yescharacteristic, complemented
232#2048C2×C2911yescharacteristic, complemented
233#2002C2×C2911yescharacteristic
234#1965C2×C2911yescharacteristic, complemented
235#1932C2×C2911yescharacteristic, complemented
236#1914C2×C2911yescharacteristic, complemented
237#1911C2×C2911yescharacteristic, complemented
238#1903C2×C2911yescharacteristic, complemented
239#1887C2×C2911yescharacteristic, complemented
240#1861C2×C2911yescharacteristic, complemented
241#1841C2×C2911yescharacteristic, complemented
242#1829C2×C2911yescharacteristic, complemented
243C22×C29—41no—
244C22×C29—41no—
245C22×C29—42no—
246C22×C29—82no—
247C22×C29—82no—
248C22×C29—81no—
249C22×C29—82no—
250C22×C29—82no—
251C22×C29—81no—
252C22×C29—161no—
253C22×C29—161no—
254C22×C29#53811yescharacteristic
255C22×C29#55111yescharacteristic
256C22×C29#55111yescharacteristic
257C4×C29—22no—
258C4×C29—41no—
259C4×C29—41no—
260C4×C29—81no—
261C4×C29—81no—
262C4×C29—81no—
263C4×C29#53811yescharacteristic
264C4×C29#54011yescharacteristic
265C4×C29#55311yescharacteristic
266C4×C29#56011yescharacteristic
267C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
268#568C22×C2911yescharacteristic
269#535C22×C2911yescharacteristic
270C2×#127C22×C2911yescharacteristic
271#518C22×C2911yescharacteristic
272#430C22×C2911yescharacteristic
273#430C22×C2911yescharacteristic
274#430C22×C2911yescharacteristic
275#423C22×C2911yescharacteristic
276#421C22×C2911yescharacteristic
277#421C22×C2911yescharacteristic
278C2×#104C22×C2911yescharacteristic
279#418C22×C2911yescharacteristic
280#418C22×C2911yescharacteristic
281#418C22×C2911yescharacteristic
282#413C22×C2911yescharacteristic
283C2×#100C22×C2911yescharacteristic
284C2×#100C22×C2911yescharacteristic
285C2×#100C22×C2911yescharacteristic
286C2×#100C22×C2911yescharacteristic
287C2×#100C22×C2911yescharacteristic
288C2×#100C22×C2911yescharacteristic
289C4×M16C22×C2911yescharacteristic
290#344C22×C2911yescharacteristic
291#344C22×C2911yescharacteristic
292#344C22×C2911yescharacteristic
293#344C22×C2911yescharacteristic
294#344C22×C2911yescharacteristic
295#344C22×C2911yescharacteristic
296#339C22×C2911yescharacteristic
297#339C22×C2911yescharacteristic
298#339C22×C2911yescharacteristic
299#338C22×C2911yescharacteristic
300H(3,ℤ/4)C22×C2911yescharacteristic
301H(3,ℤ/4)C22×C2911yescharacteristic
302C2×C29—21no—
303C2×C29—21no—
304C2×C29—21no—
305C2×C29—81no—
306C2×C29—82no—
307C2×C29—161no—
308C2×C29#274911yescharacteristic
309C2×#41C23×C2911yescharacteristic
310C22×D4—22no—
311C22×D4C23×C2911yescharacteristic
312C22×D4C23×C2911yescharacteristic
313AGL(1,ℤ/8)—41no—
314AGL(1,ℤ/8)—41no—
315C2×SD16—21no—
316C2×D8—21no—
317#131—41no—
318#131—41no—
319C2×M16—41no—
320C2×M16C23×C2911yescharacteristic
321C2×M16C23×C2911yescharacteristic
322C2×M16C23×C2911yescharacteristic
323C2×M16C23×C2911yescharacteristic
324C2×M16C23×C2911yescharacteristic
325C2×M16C23×C2911yescharacteristic
326C2×M16C23×C2911yescharacteristic
327C2×M16C23×C2911yescharacteristic
328#127—21no—
329#127—21no—
330#127—21no—
331#127—41no—
332#124—21no—
333#121—41no—
334#120—22no—
335C4×D4—41no—
336C4×D4—41no—
337#117C23×C2911yescharacteristic
338#117C23×C2911yescharacteristic
339#117C23×C2911yescharacteristic
340C2×C22⋊C4—22no—
341C2×C42C23×C2911yescharacteristic
342#108—41no—
343#108—41no—
344#108—41no—
345C4⋊C8—41no—
346#104—21no—
347#104—21no—
348#104—41no—
349#104—41no—
350#102—41no—
351#102—41no—
352#102—41no—
353#101—21no—
354#100—21no—
355#100—41no—
356#100—41no—
357#100—41no—
358#100—41no—
359#100—41no—
360#100—41no—
361#97—21no—
362C4×C8—21no—
363C29#3269811yescharacteristic, direct product factor, Sylow
364C24—21no—
365C24#41×C2912yes—
366#41—21no—
367#41—21no—
368#41—21no—
369#41—21no—
370C2×Q8#41×C2911yescharacteristic
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—21no—
383C2×D4—21no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—84no—
388C2×D4#41×C2911yescharacteristic
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—42no—
392C22×C4C24×C2911yescharacteristic
393SD16—42no—
394D8—42no—
395M16—21no—
396M16—21no—
397M16—21no—
398M16—21no—
399M16—21no—
400M16—21no—
401M16—21no—
402M16—21no—
403M16—21no—
404M16—21no—
405M16—21no—
406M16—21no—
407M16—21no—
408M16—21no—
409M16—21no—
410M16—21no—
411M16—42no—
412C2×C8—21no—
413C2×C8—21no—
414C2×C8—21no—
415C2×C8—21no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—42no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C22⋊C4—21no—
425C22⋊C4—21no—
426C22⋊C4—21no—
427C22⋊C4—42no—
428C22⋊C4—42no—
429C42—21no—
430C42—21no—
431C42—21no—
432C42—21no—
433C42#41×C2911yescharacteristic
434C42#41×C2911yescharacteristic
435C23—22no—
436C23—22no—
437C23—21no—
438C23—22no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—82no—
443C23—82no—
444C23C2×#41×C2911yescharacteristic
445Q8—21no—
446Q8—21no—
447D4—21no—
448D4—21no—
449D4—41no—
450D4—41no—
451D4—41no—
452D4—41no—
453D4—41no—
454D4—41no—
455D4—41no—
456D4—41no—
457D4—41no—
458D4—41no—
459D4—84no—
460D4—84no—
461D4—162no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—162no—
472C2×C4C2×#41×C2911yescharacteristic
473C2×C4C2×#41×C2911yescharacteristic
474C2×C4C29×H(5,𝔽2)11yescharacteristic
475C2×C4C29×H(5,𝔽2)11yescharacteristic
476C2×C4C29×H(5,𝔽2)11yescharacteristic
477C2×C4C29×H(5,𝔽2)11yescharacteristic
478C8—41no—
479C8—41no—
480C8—41no—
481C8—41no—
482C8—41no—
483C8—41no—
484C8—41no—
485C8—41no—
486C22—41no—
487C22—41no—
488C22—42no—
489C22—82no—
490C22—82no—
491C22—81no—
492C22—82no—
493C22—82no—
494C22—81no—
495C22—161no—
496C22—161no—
497C22C29×#53811yescharacteristic
498C22C29×#55111yescharacteristic
499C22C29×#55111yescharacteristic
500C4—22no—
501C4—41no—
502C4—41no—
503C4—81no—
504C4—81no—
505C4—81no—
506C4C29×#53811yescharacteristic
507C4C29×#54011yescharacteristic
508C4C29×#55311yescharacteristic
509C4C29×#56011yescharacteristic
510C2—21no—
511C2—21no—
512C2—21no—
513C2—82no—
514C2—81no—
515C2—161no—
516C2C29×#274911yescharacteristic
subgroupG/H
center, socleC2×C29#2749
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#2002C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C22×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2102C2semidirect
2. C29×#2081C2semidirect
3. C29×#2081C2semidirect
4. C29×#2069C2semidirect
5. C29×#2048C2semidirect
7. C29×#1965C2semidirect
8. C29×#1932C2semidirect
9. C29×#1914C2semidirect
10. C29×#1911C2semidirect
11. C29×#1903C2semidirect
12. C29×#1887C2semidirect
13. C29×#1861C2semidirect
14. C29×#1841C2semidirect
15. C29×#1829C2semidirect
176. #32698C29direct (N × H)
228. #2102C2×C29semidirect
229. #2081C2×C29semidirect
230. #2081C2×C29semidirect
231. #2069C2×C29semidirect
232. #2048C2×C29semidirect
234. #1965C2×C29semidirect
235. #1932C2×C29semidirect
236. #1914C2×C29semidirect
237. #1911C2×C29semidirect
238. #1903C2×C29semidirect
239. #1887C2×C29semidirect
240. #1861C2×C29semidirect
241. #1841C2×C29semidirect
242. #1829C2×C29semidirect
363. C29#32698direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#21022
C29×#20812
C29×#20692
C29×#20482
C29×#20022
C29×#19652
C29×#19322
C29×#19142
C29×#19112
C29×#19032
C29×#18872
C29×#18612
C29×#18412
C29×#18292
#3269829