Finite Group Databasebeta

← C29×#32697 #20327597

Subgroups — C29×#32697 #20327597

Order 7424.

528 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2102C211yesmaximal, characteristic, complemented
2C29×#2082C211yesmaximal, characteristic, complemented
3C29×#2082C211yesmaximal, characteristic, complemented
4C29×#2070C211yesmaximal, characteristic, complemented
5C29×#2049C211yesmaximal, characteristic
6C29×#2005C211yesmaximal, characteristic
7C29×#1966C211yesmaximal, characteristic, complemented
8C29×#1932C211yesmaximal, characteristic
9C29×#1915C211yesmaximal, characteristic
10C29×#1912C211yesmaximal, characteristic
11C29×#1902C211yesmaximal, characteristic
12C29×#1886C211yesmaximal, characteristic, complemented
13C29×#1861C211yesmaximal, characteristic
14C29×#1841C211yesmaximal, characteristic, complemented
15C29×#1830C211yesmaximal, characteristic, complemented
16C2×C29×#137C2211yescharacteristic
17C29×#568C2211yescharacteristic
18C29×#536C2211yescharacteristic
19C2×C29×C4⋊Q8C2211yescharacteristic
20C29×#519C2211yescharacteristic
21C29×#430C2211yescharacteristic
22C29×#430C2211yescharacteristic
23C29×#430C2211yescharacteristic
24C29×#423C2211yescharacteristic
25C29×#421C2211yescharacteristic
26C29×#421C2211yescharacteristic
27C2×C29×#104C2211yescharacteristic
28C29×#419C2211yescharacteristic
29C29×#419C2211yescharacteristic
30C29×#419C2211yescharacteristic
31C29×#413C2211yescharacteristic
32C2×C29×#101C2211yescharacteristic
33C2×C29×#101C2211yescharacteristic
34C2×C29×#101C2211yescharacteristic
35C2×C29×#101C2211yescharacteristic
36C2×C29×#101C2211yescharacteristic
37C2×C29×#101C2211yescharacteristic
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×Q8×C29C2311yescharacteristic
54C29×#137—41no—
55C29×#137—41no—
56C2×Q16×C29—21no—
57C2×SD16×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×C4⋊Q8—21no—
71C29×C4⋊Q8—21no—
72C29×C4⋊Q8—41no—
73C29×#124—21no—
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×C4⋊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×#103—41no—
93C29×#103—41no—
94C29×#103—41no—
95C29×#101—21no—
96C29×#101—41no—
97C29×#101—41no—
98C29×#101—41no—
99C29×#101—41no—
100C29×#101—41no—
101C29×#101—41no—
102C29×#100—21no—
103C29×#97—21no—
104C4×C8×C29—21no—
105#41×C29—21no—
106#41×C29—21no—
107#41×C29—21no—
108#41×C29—21no—
109C2×Q8×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—21no—
117C2×Q8×C29—21no—
118C2×Q8×C29—21no—
119C2×Q8×C29—21no—
120C2×Q8×C29—21no—
121C2×Q8×C29#4111yescharacteristic
122C2×D4×C29—21no—
123C2×D4×C29#4111yescharacteristic
124C22×C4×C29—21no—
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29#4112yes—
128C22×C4×C29C2411yescharacteristic
129Q16×C29—42no—
130SD16×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—
162C4⋊C4×C29—42no—
163C4⋊C4×C29—42no—
164C22⋊C4×C29—21no—
165C22⋊C4×C29—21no—
166C22⋊C4×C29—21no—
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#32697C2911yesmaximal, characteristic, direct product factor, Sylow
176C23×C29—21no—
177C23×C29C2×#4111yescharacteristic
178Q8×C29—21no—
179Q8×C29—21no—
180Q8×C29—41no—
181Q8×C29—41no—
182Q8×C29—41no—
183Q8×C29—41no—
184Q8×C29—41no—
185Q8×C29—41no—
186Q8×C29—41no—
187Q8×C29—41no—
188D4×C29—21no—
189D4×C29—21no—
190D4×C29—41no—
191D4×C29—41no—
192C2×C4×C29—21no—
193C2×C4×C29—22no—
194C2×C4×C29—21no—
195C2×C4×C29—22no—
196C2×C4×C29—21no—
197C2×C4×C29—22no—
198C2×C4×C29—42no—
199C2×C4×C29—41no—
200C2×C4×C29—41no—
201C2×C4×C29—41no—
202C2×C4×C29—41no—
203C2×C4×C29—41no—
204C2×C4×C29—41no—
205C2×C4×C29—41no—
206C2×C4×C29—41no—
207C2×C4×C29C2×#4111yescharacteristic
208C2×C4×C29C2×#4111yescharacteristic
209C2×C4×C29H(5,𝔽2)11yescharacteristic
210C2×C4×C29H(5,𝔽2)11yescharacteristic
211C2×C4×C29H(5,𝔽2)11yescharacteristic
212C2×C4×C29H(5,𝔽2)11yescharacteristic
213C8×C29—41no—
214C8×C29—41no—
215C8×C29—41no—
216C8×C29—41no—
217C8×C29—41no—
218C8×C29—41no—
219C8×C29—41no—
220C8×C29—41no—
221#2102C2×C2911yescharacteristic, complemented
222#2082C2×C2911yescharacteristic, complemented
223#2082C2×C2911yescharacteristic, complemented
224#2070C2×C2911yescharacteristic, complemented
225#2049C2×C2911yescharacteristic
226#2005C2×C2911yescharacteristic
227#1966C2×C2911yescharacteristic, complemented
228#1932C2×C2911yescharacteristic
229#1915C2×C2911yescharacteristic
230#1912C2×C2911yescharacteristic
231#1902C2×C2911yescharacteristic
232#1886C2×C2911yescharacteristic, complemented
233#1861C2×C2911yescharacteristic
234#1841C2×C2911yescharacteristic, complemented
235#1830C2×C2911yescharacteristic, complemented
236C22×C29—41no—
237C22×C29—41no—
238C22×C29—81no—
239C22×C29#53811yescharacteristic
240C22×C29#55111yescharacteristic
241C22×C29#55111yescharacteristic
242C4×C29—22no—
243C4×C29—41no—
244C4×C29—42no—
245C4×C29—41no—
246C4×C29—81no—
247C4×C29—81no—
248C4×C29—81no—
249C4×C29—81no—
250C4×C29#53811yescharacteristic
251C4×C29#54011yescharacteristic
252C4×C29#55311yescharacteristic
253C4×C29#56011yescharacteristic
254C2×#137C22×C2911yescharacteristic
255#568C22×C2911yescharacteristic
256#536C22×C2911yescharacteristic
257C2×C4⋊Q8C22×C2911yescharacteristic
258#519C22×C2911yescharacteristic
259#430C22×C2911yescharacteristic
260#430C22×C2911yescharacteristic
261#430C22×C2911yescharacteristic
262#423C22×C2911yescharacteristic
263#421C22×C2911yescharacteristic
264#421C22×C2911yescharacteristic
265C2×#104C22×C2911yescharacteristic
266#419C22×C2911yescharacteristic
267#419C22×C2911yescharacteristic
268#419C22×C2911yescharacteristic
269#413C22×C2911yescharacteristic
270C2×#101C22×C2911yescharacteristic
271C2×#101C22×C2911yescharacteristic
272C2×#101C22×C2911yescharacteristic
273C2×#101C22×C2911yescharacteristic
274C2×#101C22×C2911yescharacteristic
275C2×#101C22×C2911yescharacteristic
276C4×M16C22×C2911yescharacteristic
277#344C22×C2911yescharacteristic
278#344C22×C2911yescharacteristic
279#344C22×C2911yescharacteristic
280#344C22×C2911yescharacteristic
281#344C22×C2911yescharacteristic
282#344C22×C2911yescharacteristic
283#339C22×C2911yescharacteristic
284#339C22×C2911yescharacteristic
285#339C22×C2911yescharacteristic
286#338C22×C2911yescharacteristic
287H(3,ℤ/4)C22×C2911yescharacteristic
288H(3,ℤ/4)C22×C2911yescharacteristic
289C2×C29—21no—
290C2×C29—21no—
291C2×C29—21no—
292C2×C29—81no—
293C2×C29#274911yescharacteristic
294C2×#41C23×C2911yescharacteristic
295C22×Q8C23×C2911yescharacteristic
296C22×Q8C23×C2911yescharacteristic
297#137—41no—
298#137—41no—
299C2×Q16—21no—
300C2×SD16—21no—
301#131—41no—
302#131—41no—
303C2×M16—41no—
304C2×M16C23×C2911yescharacteristic
305C2×M16C23×C2911yescharacteristic
306C2×M16C23×C2911yescharacteristic
307C2×M16C23×C2911yescharacteristic
308C2×M16C23×C2911yescharacteristic
309C2×M16C23×C2911yescharacteristic
310C2×M16C23×C2911yescharacteristic
311C2×M16C23×C2911yescharacteristic
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—41no—
316#124—21no—
317#123—22no—
318C22⋊Q8—41no—
319C4×Q8—41no—
320C4×Q8—41no—
321#117—22no—
322#117C23×C2911yescharacteristic
323#117C23×C2911yescharacteristic
324#117C23×C2911yescharacteristic
325C2×C4⋊C4—22no—
326C2×C42C23×C2911yescharacteristic
327#108—41no—
328#108—41no—
329#108—41no—
330C4⋊C8—41no—
331#104—21no—
332#104—21no—
333#104—41no—
334#104—41no—
335#103—41no—
336#103—41no—
337#103—41no—
338#101—21no—
339#101—41no—
340#101—41no—
341#101—41no—
342#101—41no—
343#101—41no—
344#101—41no—
345#100—21no—
346#97—21no—
347C4×C8—21no—
348C29#3269711yescharacteristic, direct product factor, Sylow
349#41—21no—
350#41—21no—
351#41—21no—
352#41—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—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#41×C2911yescharacteristic
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4#41×C2912yes—
372C22×C4C24×C2911yescharacteristic
373Q16—42no—
374SD16—42no—
375M16—21no—
376M16—21no—
377M16—21no—
378M16—21no—
379M16—21no—
380M16—21no—
381M16—21no—
382M16—21no—
383M16—21no—
384M16—21no—
385M16—21no—
386M16—21no—
387M16—21no—
388M16—21no—
389M16—21no—
390M16—21no—
391M16—42no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—42no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—42no—
407C4⋊C4—42no—
408C22⋊C4—21no—
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—42no—
412C42—21no—
413C42—21no—
414C42—21no—
415C42—21no—
416C42—42no—
417C42#41×C2911yescharacteristic
418C42#41×C2911yescharacteristic
419C23—21no—
420C23C2×#41×C2911yescharacteristic
421Q8—21no—
422Q8—21no—
423Q8—41no—
424Q8—41no—
425Q8—41no—
426Q8—41no—
427Q8—41no—
428Q8—41no—
429Q8—41no—
430Q8—41no—
431D4—21no—
432D4—21no—
433D4—41no—
434D4—41no—
435C2×C4—21no—
436C2×C4—22no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—21no—
440C2×C4—22no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4C2×#41×C2911yescharacteristic
451C2×C4C2×#41×C2911yescharacteristic
452C2×C4C29×H(5,𝔽2)11yescharacteristic
453C2×C4C29×H(5,𝔽2)11yescharacteristic
454C2×C4C29×H(5,𝔽2)11yescharacteristic
455C2×C4C29×H(5,𝔽2)11yescharacteristic
456C8—41no—
457C8—41no—
458C8—41no—
459C8—41no—
460C8—41no—
461C8—41no—
462C8—41no—
463C8—41no—
464C22—41no—
465C22—41no—
466C22—81no—
467C22C29×#53811yescharacteristic
468C22C29×#55111yescharacteristic
469C22C29×#55111yescharacteristic
470C4—22no—
471C4—41no—
472C4—42no—
473C4—41no—
474C4—81no—
475C4—81no—
476C4—81no—
477C4—81no—
478C4C29×#53811yescharacteristic
479C4C29×#54011yescharacteristic
480C4C29×#55311yescharacteristic
481C4C29×#56011yescharacteristic
482C2—21no—
483C2—21no—
484C2—21no—
485C2—81no—
486C2C29×#274911yescharacteristic
subgroupG/H
center, socleC2×C29#2749
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×#41×C29C23
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×#2082C2semidirect
3. C29×#2082C2semidirect
4. C29×#2070C2semidirect
7. C29×#1966C2semidirect
12. C29×#1886C2semidirect
14. C29×#1841C2semidirect
15. C29×#1830C2semidirect
175. #32697C29direct (N × H)
221. #2102C2×C29semidirect
222. #2082C2×C29semidirect
223. #2082C2×C29semidirect
224. #2070C2×C29semidirect
227. #1966C2×C29semidirect
232. #1886C2×C29semidirect
234. #1841C2×C29semidirect
235. #1830C2×C29semidirect
348. C29#32697direct (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×#20822
C29×#20702
C29×#20492
C29×#20052
C29×#19662
C29×#19322
C29×#19152
C29×#19122
C29×#19022
C29×#18862
C29×#18612
C29×#18412
C29×#18302
#3269729