Finite Group Databasebeta

← C29×#32699 #20327599

Subgroups — C29×#32699 #20327599

Order 7424.

538 conjugacy classes of subgroups.

The subgroup lattice has 498 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×#2070C211yesmaximal, characteristic, complemented
5C29×#2048C211yesmaximal, characteristic
6C29×#2003C211yesmaximal, characteristic
7C29×#1967C211yesmaximal, characteristic, complemented
8C29×#1932C211yesmaximal, characteristic, complemented
9C29×#1915C211yesmaximal, characteristic, complemented
10C29×#1912C211yesmaximal, characteristic, complemented
11C29×#1903C211yesmaximal, characteristic
12C29×#1888C211yesmaximal, characteristic, complemented
13C29×#1861C211yesmaximal, characteristic, complemented
14C29×#1841C211yesmaximal, characteristic, complemented
15C29×#1830C211yesmaximal, characteristic, complemented
16C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
17C29×#568C2211yescharacteristic
18C29×#536C2211yescharacteristic
19C2×C29×#124C2211yescharacteristic
20C29×#519C2211yescharacteristic
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×#101C2211yescharacteristic
33C2×C29×#101C2211yescharacteristic
34C2×C29×#101C2211yescharacteristic
35C2×C29×#101C2211yescharacteristic
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×Q8×C29C2311yescharacteristic
53C22×D4×C29C2311yescharacteristic
54C29×AGL(1,ℤ/8)—41no—
55C29×AGL(1,ℤ/8)—41no—
56C2×SD16×C29—21no—
57C2×D8×C29—21no—
58C29×#131—41no—
59C29×#131—41no—
60C2×M16×C29—41no—
61C2×M16×C29C2311yescharacteristic
62C2×M16×C29C2311yescharacteristic
63C2×M16×C29C2311yescharacteristic
64C2×M16×C29C2311yescharacteristic
65C2×M16×C29C2311yescharacteristic
66C2×M16×C29C2311yescharacteristic
67C2×M16×C29C2311yescharacteristic
68C2×M16×C29C2311yescharacteristic
69C29×C4⋊Q8—21no—
70C29×#124—21no—
71C29×#124—21no—
72C29×#124—21no—
73C29×#124—41no—
74C29×#123—22no—
75C29×C22⋊Q8—41no—
76C4×Q8×C29—41no—
77C4×Q8×C29—41no—
78C29×#117—22no—
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×#101—41no—
97C29×#101—41no—
98C29×#101—41no—
99C29×#101—41no—
100C29×#100—21no—
101C29×#100—41no—
102C29×#100—41no—
103C29×#97—21no—
104C4×C8×C29—21no—
105C24×C29—21no—
106#41×C29—21no—
107#41×C29—21no—
108#41×C29—21no—
109#41×C29—21no—
110C2×Q8×C29—21no—
111C2×Q8×C29—21no—
112C2×Q8×C29—21no—
113C2×Q8×C29—21no—
114C2×Q8×C29—21no—
115C2×Q8×C29—21no—
116C2×Q8×C29#4111yescharacteristic
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#4111yescharacteristic
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29#4112yes—
128C22×C4×C29C2411yescharacteristic
129SD16×C29—42no—
130D8×C29—42no—
131M16×C29—21no—
132M16×C29—21no—
133M16×C29—21no—
134M16×C29—21no—
135M16×C29—21no—
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—42no—
148C2×C8×C29—21no—
149C2×C8×C29—21no—
150C2×C8×C29—21no—
151C2×C8×C29—21no—
152C2×C8×C29—21no—
153C2×C8×C29—21no—
154C2×C8×C29—21no—
155C2×C8×C29—21no—
156C2×C8×C29—42no—
157C4⋊C4×C29—21no—
158C4⋊C4×C29—21no—
159C4⋊C4×C29—21no—
160C4⋊C4×C29—42no—
161C4⋊C4×C29—42no—
162C22⋊C4×C29—21no—
163C22⋊C4×C29—21no—
164C22⋊C4×C29—21no—
165C22⋊C4×C29—42no—
166C22⋊C4×C29—42no—
167C22⋊C4×C29—42no—
168C42×C29—21no—
169C42×C29—21no—
170C42×C29—21no—
171C42×C29—21no—
172C42×C29—42no—
173C42×C29#4111yescharacteristic
174C42×C29#4111yescharacteristic
175#32699C2911yesmaximal, characteristic, direct product factor, Sylow
176C23×C29—21no—
177C23×C29—41no—
178C23×C29—41no—
179C23×C29—41no—
180C23×C29—82no—
181C23×C29C2×#4111yescharacteristic
182Q8×C29—21no—
183Q8×C29—21no—
184Q8×C29—41no—
185Q8×C29—41no—
186Q8×C29—41no—
187Q8×C29—41no—
188D4×C29—21no—
189D4×C29—21no—
190D4×C29—41no—
191D4×C29—41no—
192D4×C29—41no—
193D4×C29—41no—
194D4×C29—41no—
195D4×C29—41no—
196C2×C4×C29—22no—
197C2×C4×C29—21no—
198C2×C4×C29—21no—
199C2×C4×C29—22no—
200C2×C4×C29—22no—
201C2×C4×C29—21no—
202C2×C4×C29—41no—
203C2×C4×C29—41no—
204C2×C4×C29—41no—
205C2×C4×C29—41no—
206C2×C4×C29—41no—
207C2×C4×C29—81no—
208C2×C4×C29C2×#4111yescharacteristic
209C2×C4×C29C2×#4111yescharacteristic
210C2×C4×C29H(5,𝔽2)11yescharacteristic
211C2×C4×C29H(5,𝔽2)11yescharacteristic
212C2×C4×C29H(5,𝔽2)11yescharacteristic
213C2×C4×C29H(5,𝔽2)11yescharacteristic
214C8×C29—41no—
215C8×C29—41no—
216C8×C29—41no—
217C8×C29—41no—
218C8×C29—41no—
219C8×C29—41no—
220C8×C29—41no—
221C8×C29—41no—
222#2102C2×C2911yescharacteristic, complemented
223#2081C2×C2911yescharacteristic, complemented
224#2081C2×C2911yescharacteristic, complemented
225#2070C2×C2911yescharacteristic, complemented
226#2048C2×C2911yescharacteristic
227#2003C2×C2911yescharacteristic
228#1967C2×C2911yescharacteristic, complemented
229#1932C2×C2911yescharacteristic, complemented
230#1915C2×C2911yescharacteristic, complemented
231#1912C2×C2911yescharacteristic, complemented
232#1903C2×C2911yescharacteristic
233#1888C2×C2911yescharacteristic, complemented
234#1861C2×C2911yescharacteristic, complemented
235#1841C2×C2911yescharacteristic, complemented
236#1830C2×C2911yescharacteristic, complemented
237C22×C29—41no—
238C22×C29—41no—
239C22×C29—81no—
240C22×C29—82no—
241C22×C29—81no—
242C22×C29—161no—
243C22×C29—161no—
244C22×C29#53811yescharacteristic
245C22×C29#55111yescharacteristic
246C22×C29#55111yescharacteristic
247C4×C29—41no—
248C4×C29—41no—
249C4×C29—42no—
250C4×C29—41no—
251C4×C29—81no—
252C4×C29—81no—
253C4×C29—81no—
254C4×C29#53811yescharacteristic
255C4×C29#54011yescharacteristic
256C4×C29#55311yescharacteristic
257C4×C29#56011yescharacteristic
258C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
259#568C22×C2911yescharacteristic
260#536C22×C2911yescharacteristic
261C2×#124C22×C2911yescharacteristic
262#519C22×C2911yescharacteristic
263#430C22×C2911yescharacteristic
264#430C22×C2911yescharacteristic
265#430C22×C2911yescharacteristic
266#423C22×C2911yescharacteristic
267#421C22×C2911yescharacteristic
268#421C22×C2911yescharacteristic
269C2×#104C22×C2911yescharacteristic
270#418C22×C2911yescharacteristic
271#418C22×C2911yescharacteristic
272#418C22×C2911yescharacteristic
273#413C22×C2911yescharacteristic
274C2×#101C22×C2911yescharacteristic
275C2×#101C22×C2911yescharacteristic
276C2×#101C22×C2911yescharacteristic
277C2×#101C22×C2911yescharacteristic
278C2×#100C22×C2911yescharacteristic
279C2×#100C22×C2911yescharacteristic
280C4×M16C22×C2911yescharacteristic
281#344C22×C2911yescharacteristic
282#344C22×C2911yescharacteristic
283#344C22×C2911yescharacteristic
284#344C22×C2911yescharacteristic
285#344C22×C2911yescharacteristic
286#344C22×C2911yescharacteristic
287#339C22×C2911yescharacteristic
288#339C22×C2911yescharacteristic
289#339C22×C2911yescharacteristic
290#338C22×C2911yescharacteristic
291H(3,ℤ/4)C22×C2911yescharacteristic
292H(3,ℤ/4)C22×C2911yescharacteristic
293C2×C29—21no—
294C2×C29—21no—
295C2×C29—21no—
296C2×C29—81no—
297C2×C29—161no—
298C2×C29#274911yescharacteristic
299C2×#41C23×C2911yescharacteristic
300C22×Q8C23×C2911yescharacteristic
301C22×D4C23×C2911yescharacteristic
302AGL(1,ℤ/8)—41no—
303AGL(1,ℤ/8)—41no—
304C2×SD16—21no—
305C2×D8—21no—
306#131—41no—
307#131—41no—
308C2×M16—41no—
309C2×M16C23×C2911yescharacteristic
310C2×M16C23×C2911yescharacteristic
311C2×M16C23×C2911yescharacteristic
312C2×M16C23×C2911yescharacteristic
313C2×M16C23×C2911yescharacteristic
314C2×M16C23×C2911yescharacteristic
315C2×M16C23×C2911yescharacteristic
316C2×M16C23×C2911yescharacteristic
317C4⋊Q8—21no—
318#124—21no—
319#124—21no—
320#124—21no—
321#124—41no—
322#123—22no—
323C22⋊Q8—41no—
324C4×Q8—41no—
325C4×Q8—41no—
326#117—22no—
327#117C23×C2911yescharacteristic
328#117C23×C2911yescharacteristic
329#117C23×C2911yescharacteristic
330C2×C22⋊C4—22no—
331C2×C42C23×C2911yescharacteristic
332#108—41no—
333#108—41no—
334#108—41no—
335C4⋊C8—41no—
336#104—21no—
337#104—21no—
338#104—41no—
339#104—41no—
340#102—41no—
341#102—41no—
342#102—41no—
343#101—21no—
344#101—41no—
345#101—41no—
346#101—41no—
347#101—41no—
348#100—21no—
349#100—41no—
350#100—41no—
351#97—21no—
352C4×C8—21no—
353C29#3269911yescharacteristic, direct product factor, Sylow
354C24—21no—
355#41—21no—
356#41—21no—
357#41—21no—
358#41—21no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8#41×C2911yescharacteristic
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4#41×C2911yescharacteristic
374C22×C4—21no—
375C22×C4—21no—
376C22×C4#41×C2912yes—
377C22×C4C24×C2911yescharacteristic
378SD16—42no—
379D8—42no—
380M16—21no—
381M16—21no—
382M16—21no—
383M16—21no—
384M16—21no—
385M16—21no—
386M16—21no—
387M16—21no—
388M16—21no—
389M16—21no—
390M16—21no—
391M16—21no—
392M16—21no—
393M16—21no—
394M16—21no—
395M16—21no—
396M16—42no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—42no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C22⋊C4—21no—
412C22⋊C4—21no—
413C22⋊C4—21no—
414C22⋊C4—42no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C42—21no—
418C42—21no—
419C42—21no—
420C42—21no—
421C42—42no—
422C42#41×C2911yescharacteristic
423C42#41×C2911yescharacteristic
424C23—21no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—82no—
429C23C2×#41×C2911yescharacteristic
430Q8—21no—
431Q8—21no—
432Q8—41no—
433Q8—41no—
434Q8—41no—
435Q8—41no—
436D4—21no—
437D4—21no—
438D4—41no—
439D4—41no—
440D4—41no—
441D4—41no—
442D4—41no—
443D4—41no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—21no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—81no—
456C2×C4C2×#41×C2911yescharacteristic
457C2×C4C2×#41×C2911yescharacteristic
458C2×C4C29×H(5,𝔽2)11yescharacteristic
459C2×C4C29×H(5,𝔽2)11yescharacteristic
460C2×C4C29×H(5,𝔽2)11yescharacteristic
461C2×C4C29×H(5,𝔽2)11yescharacteristic
462C8—41no—
463C8—41no—
464C8—41no—
465C8—41no—
466C8—41no—
467C8—41no—
468C8—41no—
469C8—41no—
470C22—41no—
471C22—41no—
472C22—81no—
473C22—82no—
474C22—81no—
475C22—161no—
476C22—161no—
477C22C29×#53811yescharacteristic
478C22C29×#55111yescharacteristic
479C22C29×#55111yescharacteristic
480C4—41no—
481C4—41no—
482C4—42no—
483C4—41no—
484C4—81no—
485C4—81no—
486C4—81no—
487C4C29×#53811yescharacteristic
488C4C29×#54011yescharacteristic
489C4C29×#55311yescharacteristic
490C4C29×#56011yescharacteristic
491C2—21no—
492C2—21no—
493C2—21no—
494C2—81no—
495C2—161no—
496C2C29×#274911yescharacteristic
subgroupG/H
center, socleC2×C29#2749
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×AGL(1,ℤ/8)C22
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×#2070C2semidirect
7. C29×#1967C2semidirect
8. C29×#1932C2semidirect
9. C29×#1915C2semidirect
10. C29×#1912C2semidirect
12. C29×#1888C2semidirect
13. C29×#1861C2semidirect
14. C29×#1841C2semidirect
15. C29×#1830C2semidirect
175. #32699C29direct (N × H)
222. #2102C2×C29semidirect
223. #2081C2×C29semidirect
224. #2081C2×C29semidirect
225. #2070C2×C29semidirect
228. #1967C2×C29semidirect
229. #1932C2×C29semidirect
230. #1915C2×C29semidirect
231. #1912C2×C29semidirect
233. #1888C2×C29semidirect
234. #1861C2×C29semidirect
235. #1841C2×C29semidirect
236. #1830C2×C29semidirect
353. C29#32699direct (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×#20702
C29×#20482
C29×#20032
C29×#19672
C29×#19322
C29×#19152
C29×#19122
C29×#19032
C29×#18882
C29×#18612
C29×#18412
C29×#18302
#3269929