Finite Group Databasebeta

← C29×#12747 #20307647

Subgroups — C29×#12747 #20307647

Order 7424.

886 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3584C211yesmaximal, characteristic
2C29×#2145C211yesmaximal, characteristic, complemented
3C29×#2143C211yesmaximal, characteristic, complemented
4C2×C29×#359C211yesmaximal, characteristic, complemented
5C29×#2138C211yesmaximal, characteristic, complemented
6C2×C29×#350C211yesmaximal, characteristic, complemented
7C29×#1814C211yesmaximal, characteristic, complemented
8C29×#585—21no—
9C29×#578—21no—
10C29×#578C412yescomplemented
11C29×#577—22no—
12C29×#577—22no—
13C29×#576—21no—
14C29×#576C412yescomplemented
15C29×#575—22no—
16C29×#575—21no—
17C2×C29×#135—22no—
18C2×C29×#135C2211yescharacteristic
19C2×C29×#135C2211yescharacteristic
20C2×C29×#131C2211yescharacteristic
21C2×C29×M32C2211yescharacteristic, complemented
22C22×C16×C29C2211yescharacteristic, complemented
23C2×C29×#108C2211yescharacteristic, complemented
24C29×#427C2211yescharacteristic, complemented
25C29×#421—21no—
26C29×#360—22no—
27C29×#359—22no—
28C29×#359—22no—
29C29×#358—21no—
30C29×#357—21no—
31C29×#350—22no—
32C29×#344—21no—
33C29×2−1+4—22no—
34C29×2−1+4—22no—
35C29×2−1+4—41no—
36C29×H(5,𝔽2)—22no—
37C29×H(5,𝔽2)—22no—
38C29×H(5,𝔽2)—42no—
39C29×H(5,𝔽2)—41no—
40C2×#41×C29—24no—
41C2×#41×C29—21no—
42C2×#41×C29—21no—
43C2×#41×C29—42no—
44C2×#41×C29—42no—
45C2×#41×C29D411yescharacteristic
46C29×#137—22no—
47C29×#137—24no—
48C29×#137—24no—
49C29×#137—22no—
50C29×AGL(1,ℤ/8)—22no—
51C29×AGL(1,ℤ/8)—24no—
52C29×AGL(1,ℤ/8)—24no—
53C29×AGL(1,ℤ/8)—22no—
54C29×#135—24no—
55C29×#135—24no—
56C29×#135—22no—
57C29×#135—22no—
58C29×#135—21no—
59C29×#135—21no—
60C29×#135—21no—
61C29×#135—21no—
62C29×#135C2×C412yes—
63C29×#135D412yes—
64C29×#135D412yes—
65C29×#135D412yes—
66C2×Q16×C29—22no—
67C2×Q16×C29C2×C411yescharacteristic
68C2×Q16×C29D411yescharacteristic
69C2×SD16×C29—24no—
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×D8×C29—22no—
73C2×D8×C29C2×C411yescharacteristic
74C2×D8×C29D411yescharacteristic
75C29×#131—21no—
76C29×#131—21no—
77C29×#131C2×C412yes—
78C29×#131D412yes—
79C2×M16×C29—21no—
80C2×M16×C29—21no—
81C2×M16×C29D411yescharacteristic
82C22×C8×C29—21no—
83C22×C8×C29C2311yescharacteristic
84C29×#117—21no—
85C29×M32—21no—
86C29×M32—21no—
87C2×C16×C29—21no—
88C2×C16×C29—21no—
89C2×C16×C29—21no—
90C2×C16×C29—21no—
91C29×#108—21no—
92C29×#108—21no—
93C29×#107—21no—
94C29×#106—21no—
95C29×#104—42no—
96#41×C29—21no—
97#41×C29—21no—
98#41×C29—24no—
99#41×C29—24no—
100#41×C29—22no—
101#41×C29—22no—
102#41×C29—22no—
103#41×C29—22no—
104#41×C29—44no—
105#41×C29—44no—
106#41×C29—44no—
107#41×C29—44no—
108#41×C29—42no—
109#41×C29—42no—
110#41×C29—42no—
111#41×C29—42no—
112#41×C29—41no—
113#41×C29—41no—
114#41×C29—41no—
115#41×C29—41no—
116#41×C29C22⋊C412yes—
117#41×C29D812yes—
118C2×Q8×C29—24no—
119C2×Q8×C29—21no—
120C2×Q8×C29—21no—
121C2×Q8×C29—42no—
122C2×Q8×C29—42no—
123C2×Q8×C29SD1611yescharacteristic
124C2×D4×C29—21no—
125C2×D4×C29—24no—
126C2×D4×C29—21no—
127C2×D4×C29—21no—
128C2×D4×C29—44no—
129C2×D4×C29—44no—
130C2×D4×C29—42no—
131C2×D4×C29—44no—
132C2×D4×C29—41no—
133C2×D4×C29—41no—
134C2×D4×C29—42no—
135C2×D4×C29SD1611yescharacteristic
136C22×C4×C29—21no—
137C22×C4×C29—44no—
138C22×C4×C29—41no—
139C22×C4×C29—41no—
140C22×C4×C29C2×D411yescharacteristic
141Q16×C29—24no—
142Q16×C29—21no—
143Q16×C29—21no—
144Q16×C29C22⋊C412yes—
145Q16×C29C22⋊C412yes—
146SD16×C29—24no—
147SD16×C29—24no—
148SD16×C29—22no—
149SD16×C29—22no—
150SD16×C29—22no—
151SD16×C29—22no—
152D8×C29—24no—
153D8×C29—21no—
154D8×C29—21no—
155D8×C29C22⋊C412yes—
156D8×C29C22⋊C412yes—
157M16×C29—21no—
158M16×C29—22no—
159M16×C29—22no—
160M16×C29—41no—
161M16×C29—41no—
162M16×C29C22⋊C412yes—
163C2×C8×C29—21no—
164C2×C8×C29—22no—
165C2×C8×C29—22no—
166C2×C8×C29—41no—
167C2×C8×C29C22×C411yescharacteristic
168C2×C8×C29C2×D411yescharacteristic
169C2×C8×C29C2×D411yescharacteristic
170C2×C8×C29C2×D411yescharacteristic
171C2×C8×C29C2×D411yescharacteristic
172C2×C8×C29C2×D411yescharacteristic
173C4⋊C4×C29—41no—
174C22⋊C4×C29—41no—
175C42×C29—41no—
176C16×C29—41no—
177C16×C29—41no—
178#12747C2911yesmaximal, characteristic, direct product factor, Sylow
179C23×C29—21no—
180C23×C29—44no—
181C23×C29—41no—
182C23×C29—41no—
183C23×C29AGL(1,ℤ/8)11yescharacteristic
184Q8×C29—21no—
185Q8×C29—22no—
186Q8×C29—22no—
187Q8×C29—44no—
188Q8×C29—41no—
189Q8×C29—41no—
190Q8×C29#10212yes—
191D4×C29—22no—
192D4×C29—22no—
193D4×C29—22no—
194D4×C29—22no—
195D4×C29—21no—
196D4×C29—44no—
197D4×C29—44no—
198D4×C29—44no—
199D4×C29—42no—
200D4×C29—42no—
201D4×C29—42no—
202D4×C29—42no—
203D4×C29—41no—
204D4×C29—41no—
205D4×C29#10212yes—
206C2×C4×C29—21no—
207C2×C4×C29—22no—
208C2×C4×C29—22no—
209C2×C4×C29—44no—
210C2×C4×C29—44no—
211C2×C4×C29—44no—
212C2×C4×C29—41no—
213C2×C4×C29—41no—
214C2×C4×C29—42no—
215C2×C4×C29—42no—
216C2×C4×C29—42no—
217C2×C4×C29—42no—
218C2×C4×C29—81no—
219C2×C4×C29C2×C22⋊C411yescharacteristic
220C2×C4×C29#12011yescharacteristic
221C2×C4×C29#12011yescharacteristic
222C2×C4×C29C2×D811yescharacteristic
223C2×C4×C29C2×SD1611yescharacteristic
224C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
225C8×C29—22no—
226C8×C29—81no—
227C8×C29C2×C22⋊C411yescharacteristic
228C8×C29C2×C22⋊C411yescharacteristic
229C8×C29#12011yescharacteristic
230C8×C29#12011yescharacteristic
231#3584C2×C2911yescharacteristic
232#2145C2×C2911yescharacteristic, complemented
233#2143C2×C2911yescharacteristic, complemented
234C2×#359C2×C2911yescharacteristic, complemented
235#2138C2×C2911yescharacteristic, complemented
236C2×#350C2×C2911yescharacteristic, complemented
237#1814C2×C2911yescharacteristic, complemented
238C22×C29—22no—
239C22×C29—41no—
240C22×C29—42no—
241C22×C29—42no—
242C22×C29—81no—
243C22×C29—161no—
244C22×C29—161no—
245C22×C29—164no—
246C22×C29#41811yescharacteristic
247C22×C29#44711yescharacteristic
248C22×C29#45011yescharacteristic
249C4×C29—22no—
250C4×C29—42no—
251C4×C29—42no—
252C4×C29—161no—
253C4×C29#37911yescharacteristic
254C4×C29C2×#10211yescharacteristic
255C4×C29#44711yescharacteristic
256C4×C29#45011yescharacteristic
257#585—21no—
258#578—21no—
259#578C4×C2912yescomplemented
260#577—22no—
261#577—22no—
262#576—21no—
263#576C4×C2912yescomplemented
264#575—22no—
265#575—21no—
266C2×#135—22no—
267C2×#135C22×C2911yescharacteristic
268C2×#135C22×C2911yescharacteristic
269C2×#131C22×C2911yescharacteristic
270C2×M32C22×C2911yescharacteristic, complemented
271C22×C16C22×C2911yescharacteristic, complemented
272C2×#108C22×C2911yescharacteristic, complemented
273#427C22×C2911yescharacteristic, complemented
274#421—21no—
275#360—22no—
276#359—22no—
277#359—22no—
278#358—21no—
279#357—21no—
280#350—22no—
281#344—21no—
282C2×C29—21no—
283C2×C29—21no—
284C2×C29—21no—
285C2×C29—42no—
286C2×C29—82no—
287C2×C29—82no—
288C2×C29#178611yescharacteristic
2892−1+4—22no—
2902−1+4—22no—
2912−1+4—41no—
292H(5,𝔽2)—22no—
293H(5,𝔽2)—22no—
294H(5,𝔽2)—42no—
295H(5,𝔽2)—41no—
296C2×#41—24no—
297C2×#41—21no—
298C2×#41—21no—
299C2×#41—42no—
300C2×#41—42no—
301C2×#41D4×C2911yescharacteristic
302#137—22no—
303#137—24no—
304#137—24no—
305#137—22no—
306AGL(1,ℤ/8)—22no—
307AGL(1,ℤ/8)—24no—
308AGL(1,ℤ/8)—24no—
309AGL(1,ℤ/8)—22no—
310#135—24no—
311#135—24no—
312#135—22no—
313#135—22no—
314#135—21no—
315#135—21no—
316#135—21no—
317#135—21no—
318#135C2×C4×C2912yes—
319#135D4×C2912yes—
320#135D4×C2912yes—
321#135D4×C2912yes—
322C2×Q16—22no—
323C2×Q16C2×C4×C2911yescharacteristic
324C2×Q16D4×C2911yescharacteristic
325C2×SD16—24no—
326C2×SD16—21no—
327C2×SD16—21no—
328C2×D8—22no—
329C2×D8C2×C4×C2911yescharacteristic
330C2×D8D4×C2911yescharacteristic
331#131—21no—
332#131—21no—
333#131C2×C4×C2912yes—
334#131D4×C2912yes—
335C2×M16—21no—
336C2×M16—21no—
337C2×M16D4×C2911yescharacteristic
338C22×C8—21no—
339C22×C8C23×C2911yescharacteristic
340#117—21no—
341M32—21no—
342M32—21no—
343C2×C16—21no—
344C2×C16—21no—
345C2×C16—21no—
346C2×C16—21no—
347#108—21no—
348#108—21no—
349#107—21no—
350#106—21no—
351#104—42no—
352C29#1274711yescharacteristic, direct product factor, Sylow
353#41—21no—
354#41—21no—
355#41—24no—
356#41—24no—
357#41—22no—
358#41—22no—
359#41—22no—
360#41—22no—
361#41—44no—
362#41—44no—
363#41—44no—
364#41—44no—
365#41—42no—
366#41—42no—
367#41—42no—
368#41—42no—
369#41—41no—
370#41—41no—
371#41—41no—
372#41—41no—
373#41C22⋊C4×C2912yes—
374#41D8×C2912yes—
375C2×Q8—24no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—42no—
379C2×Q8—42no—
380C2×Q8SD16×C2911yescharacteristic
381C2×D4—21no—
382C2×D4—24no—
383C2×D4—21no—
384C2×D4—21no—
385C2×D4—44no—
386C2×D4—44no—
387C2×D4—42no—
388C2×D4—44no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—42no—
392C2×D4SD16×C2911yescharacteristic
393C22×C4—21no—
394C22×C4—44no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4C2×D4×C2911yescharacteristic
398Q16—24no—
399Q16—21no—
400Q16—21no—
401Q16C22⋊C4×C2912yes—
402Q16C22⋊C4×C2912yes—
403SD16—24no—
404SD16—24no—
405SD16—22no—
406SD16—22no—
407SD16—22no—
408SD16—22no—
409D8—24no—
410D8—21no—
411D8—21no—
412D8C22⋊C4×C2912yes—
413D8C22⋊C4×C2912yes—
414M16—21no—
415M16—22no—
416M16—22no—
417M16—41no—
418M16—41no—
419M16C22⋊C4×C2912yes—
420C2×C8—21no—
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—41no—
424C2×C8C22×C4×C2911yescharacteristic
425C2×C8C2×D4×C2911yescharacteristic
426C2×C8C2×D4×C2911yescharacteristic
427C2×C8C2×D4×C2911yescharacteristic
428C2×C8C2×D4×C2911yescharacteristic
429C2×C8C2×D4×C2911yescharacteristic
430C4⋊C4—41no—
431C22⋊C4—41no—
432C42—41no—
433C16—41no—
434C16—41no—
435C23—21no—
436C23—44no—
437C23—41no—
438C23—41no—
439C23C29×AGL(1,ℤ/8)11yescharacteristic
440Q8—21no—
441Q8—22no—
442Q8—22no—
443Q8—44no—
444Q8—41no—
445Q8—41no—
446Q8C29×#10212yes—
447D4—22no—
448D4—22no—
449D4—21no—
450D4—22no—
451D4—22no—
452D4—44no—
453D4—44no—
454D4—44no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—42no—
459D4—41no—
460D4—41no—
461D4C29×#10212yes—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—44no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—81no—
475C2×C4C2×C22⋊C4×C2911yescharacteristic
476C2×C4C29×#12011yescharacteristic
477C2×C4C29×#12011yescharacteristic
478C2×C4C2×D8×C2911yescharacteristic
479C2×C4C2×SD16×C2911yescharacteristic
480C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
481C8—22no—
482C8—81no—
483C8C2×C22⋊C4×C2911yescharacteristic
484C8C2×C22⋊C4×C2911yescharacteristic
485C8C29×#12011yescharacteristic
486C8C29×#12011yescharacteristic
487C22—22no—
488C22—41no—
489C22—42no—
490C22—42no—
491C22—81no—
492C22—161no—
493C22—161no—
494C22—164no—
495C22C29×#41811yescharacteristic
496C22C29×#44711yescharacteristic
497C22C29×#45011yescharacteristic
498C4—22no—
499C4—42no—
500C4—42no—
501C4—161no—
502C4C29×#37911yescharacteristic
503C4C2×C29×#10211yescharacteristic
504C4C29×#44711yescharacteristic
505C4C29×#45011yescharacteristic
506C2—21no—
507C2—21no—
508C2—21no—
509C2—42no—
510C2—82no—
511C2—82no—
512C2C29×#178611yescharacteristic
subgroupG/H
centerC4×C29#447
commutatorC2×C8C22×C4×C29
Frattini, cosocleC22×C8C23×C29
socleC2×C29#1786
prime radicalC29×#3584C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C29 ◁ C22×C4×C29 ◁ C2×C29×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2145C2semidirect
3. C29×#2143C2semidirect
4. C2×C29×#359C2semidirect
5. C29×#2138C2semidirect
6. C2×C29×#350C2semidirect
7. C29×#1814C2semidirect
10. C29×#578C4semidirect
14. C29×#576C4semidirect
21. C2×C29×M32C22semidirect
22. C22×C16×C29C22semidirect
23. C2×C29×#108C22semidirect
24. C29×#427C22semidirect
178. #12747C29direct (N × H)
232. #2145C2×C29semidirect
233. #2143C2×C29semidirect
234. C2×#359C2×C29semidirect
235. #2138C2×C29semidirect
236. C2×#350C2×C29semidirect
237. #1814C2×C29semidirect
259. #578C4×C29semidirect
263. #576C4×C29semidirect
270. C2×M32C22×C29semidirect
271. C22×C16C22×C29semidirect
272. C2×#108C22×C29semidirect
273. #427C22×C29semidirect
352. C29#12747direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35842
C29×#21452
C29×#21432
C2×C29×#3592
C29×#21382
C2×C29×#3502
C29×#18142
#1274729