Finite Group Databasebeta

← C29×#12752 #20307652

Subgroups — C29×#12752 #20307652

Order 7424.

888 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×#3584C211yesmaximal, characteristic
2C29×#2148C211yesmaximal, characteristic, complemented
3C2×C29×#360C211yesmaximal, characteristic, complemented
4C2×C29×#360C211yesmaximal, characteristic, complemented
5C29×#2143C211yesmaximal, characteristic, complemented
6C29×#2117C211yesmaximal, characteristic, complemented
7C29×#1815C211yesmaximal, 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
22C2×C29×M32C2211yescharacteristic, complemented
23C2×C29×#108C2211yescharacteristic, complemented
24C2×C29×#106C2211yescharacteristic, complemented
25C29×#417—21no—
26C29×#362—21no—
27C29×#361—21no—
28C29×#360—22no—
29C29×#360—22no—
30C29×#359—22no—
31C29×#350—22no—
32C29×#343—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
84C2×C4⋊C4×C29—21no—
85C29×M32—21no—
86C29×M32—21no—
87C29×M32—21no—
88C29×M32—21no—
89C2×C16×C29—21no—
90C2×C16×C29—21no—
91C29×#108—21no—
92C29×#108—21no—
93C29×#106—21no—
94C29×#106—21no—
95C29×#103—41no—
96C29×#102—41no—
97#41×C29—21no—
98#41×C29—21no—
99#41×C29—24no—
100#41×C29—24no—
101#41×C29—22no—
102#41×C29—22no—
103#41×C29—22no—
104#41×C29—22no—
105#41×C29—44no—
106#41×C29—44no—
107#41×C29—44no—
108#41×C29—44no—
109#41×C29—42no—
110#41×C29—42no—
111#41×C29—42no—
112#41×C29—42no—
113#41×C29—41no—
114#41×C29—41no—
115#41×C29—41no—
116#41×C29—41no—
117#41×C29C22⋊C412yes—
118#41×C29SD1612yes—
119C2×Q8×C29—24no—
120C2×Q8×C29—21no—
121C2×Q8×C29—21no—
122C2×Q8×C29—42no—
123C2×Q8×C29—42no—
124C2×Q8×C29D811yescharacteristic
125C2×D4×C29—21no—
126C2×D4×C29—24no—
127C2×D4×C29—21no—
128C2×D4×C29—21no—
129C2×D4×C29—44no—
130C2×D4×C29—44no—
131C2×D4×C29—42no—
132C2×D4×C29—44no—
133C2×D4×C29—41no—
134C2×D4×C29—41no—
135C2×D4×C29—42no—
136C2×D4×C29D811yescharacteristic
137C22×C4×C29—21no—
138C22×C4×C29—44no—
139C22×C4×C29—41no—
140C22×C4×C29—41no—
141C22×C4×C29—41no—
142C22×C4×C29C2×D411yescharacteristic
143Q16×C29—24no—
144Q16×C29—21no—
145Q16×C29—21no—
146Q16×C29C22⋊C412yes—
147Q16×C29C22⋊C412yes—
148SD16×C29—24no—
149SD16×C29—24no—
150SD16×C29—22no—
151SD16×C29—22no—
152SD16×C29—22no—
153SD16×C29—22no—
154D8×C29—24no—
155D8×C29—21no—
156D8×C29—21no—
157D8×C29C22⋊C412yes—
158D8×C29C22⋊C412yes—
159M16×C29—21no—
160M16×C29—22no—
161M16×C29—22no—
162M16×C29—41no—
163M16×C29—41no—
164M16×C29C22⋊C412yes—
165C2×C8×C29—21no—
166C2×C8×C29—22no—
167C2×C8×C29—22no—
168C2×C8×C29—41no—
169C2×C8×C29C22×C411yescharacteristic
170C2×C8×C29C2×D411yescharacteristic
171C2×C8×C29C2×D411yescharacteristic
172C2×C8×C29C2×D411yescharacteristic
173C2×C8×C29C2×D411yescharacteristic
174C2×C8×C29C2×D411yescharacteristic
175C4⋊C4×C29—41no—
176C4⋊C4×C29—41no—
177C16×C29—41no—
178C16×C29—41no—
179#12752C2911yesmaximal, characteristic, direct product factor, Sylow
180C23×C29—21no—
181C23×C29—44no—
182C23×C29—41no—
183C23×C29—41no—
184C23×C29AGL(1,ℤ/8)11yescharacteristic
185Q8×C29—21no—
186Q8×C29—22no—
187Q8×C29—22no—
188Q8×C29—44no—
189Q8×C29—41no—
190Q8×C29—41no—
191Q8×C29#10212yes—
192D4×C29—22no—
193D4×C29—22no—
194D4×C29—22no—
195D4×C29—22no—
196D4×C29—21no—
197D4×C29—44no—
198D4×C29—44no—
199D4×C29—44no—
200D4×C29—42no—
201D4×C29—42no—
202D4×C29—42no—
203D4×C29—42no—
204D4×C29—41no—
205D4×C29—41no—
206D4×C29#10212yes—
207C2×C4×C29—21no—
208C2×C4×C29—22no—
209C2×C4×C29—22no—
210C2×C4×C29—44no—
211C2×C4×C29—44no—
212C2×C4×C29—44no—
213C2×C4×C29—41no—
214C2×C4×C29—41no—
215C2×C4×C29—42no—
216C2×C4×C29—42no—
217C2×C4×C29—42no—
218C2×C4×C29—42no—
219C2×C4×C29—81no—
220C2×C4×C29—161no—
221C2×C4×C29C2×C22⋊C411yescharacteristic
222C2×C4×C29#12011yescharacteristic
223C2×C4×C29#12011yescharacteristic
224C2×C4×C29C2×D811yescharacteristic
225C2×C4×C29C2×SD1611yescharacteristic
226C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
227C8×C29—22no—
228C8×C29—81no—
229C8×C29C2×C22⋊C411yescharacteristic
230C8×C29C2×C22⋊C411yescharacteristic
231C8×C29#12011yescharacteristic
232C8×C29#12011yescharacteristic
233#3584C2×C2911yescharacteristic
234#2148C2×C2911yescharacteristic, complemented
235C2×#360C2×C2911yescharacteristic, complemented
236C2×#360C2×C2911yescharacteristic, complemented
237#2143C2×C2911yescharacteristic, complemented
238#2117C2×C2911yescharacteristic, complemented
239#1815C2×C2911yescharacteristic, complemented
240C22×C29—22no—
241C22×C29—41no—
242C22×C29—42no—
243C22×C29—42no—
244C22×C29—81no—
245C22×C29—161no—
246C22×C29—161no—
247C22×C29—164no—
248C22×C29#41811yescharacteristic
249C22×C29#44711yescharacteristic
250C22×C29#45011yescharacteristic
251C4×C29—22no—
252C4×C29—42no—
253C4×C29—42no—
254C4×C29—161no—
255C4×C29#37911yescharacteristic
256C4×C29C2×#10211yescharacteristic
257C4×C29#44711yescharacteristic
258C4×C29#45011yescharacteristic
259#585—21no—
260#578—21no—
261#578C4×C2912yescomplemented
262#577—22no—
263#577—22no—
264#576—21no—
265#576C4×C2912yescomplemented
266#575—22no—
267#575—21no—
268C2×#135—22no—
269C2×#135C22×C2911yescharacteristic
270C2×#135C22×C2911yescharacteristic
271C2×#131C22×C2911yescharacteristic
272C2×M32C22×C2911yescharacteristic, complemented
273C2×M32C22×C2911yescharacteristic, complemented
274C2×#108C22×C2911yescharacteristic, complemented
275C2×#106C22×C2911yescharacteristic, complemented
276#417—21no—
277#362—21no—
278#361—21no—
279#360—22no—
280#360—22no—
281#359—22no—
282#350—22no—
283#343—21no—
284C2×C29—21no—
285C2×C29—21no—
286C2×C29—21no—
287C2×C29—42no—
288C2×C29—82no—
289C2×C29—82no—
290C2×C29#178611yescharacteristic
2912−1+4—22no—
2922−1+4—22no—
2932−1+4—41no—
294H(5,𝔽2)—22no—
295H(5,𝔽2)—22no—
296H(5,𝔽2)—42no—
297H(5,𝔽2)—41no—
298C2×#41—24no—
299C2×#41—21no—
300C2×#41—21no—
301C2×#41—42no—
302C2×#41—42no—
303C2×#41D4×C2911yescharacteristic
304#137—22no—
305#137—24no—
306#137—24no—
307#137—22no—
308AGL(1,ℤ/8)—22no—
309AGL(1,ℤ/8)—24no—
310AGL(1,ℤ/8)—24no—
311AGL(1,ℤ/8)—22no—
312#135—24no—
313#135—24no—
314#135—22no—
315#135—22no—
316#135—21no—
317#135—21no—
318#135—21no—
319#135—21no—
320#135C2×C4×C2912yes—
321#135D4×C2912yes—
322#135D4×C2912yes—
323#135D4×C2912yes—
324C2×Q16—22no—
325C2×Q16C2×C4×C2911yescharacteristic
326C2×Q16D4×C2911yescharacteristic
327C2×SD16—24no—
328C2×SD16—21no—
329C2×SD16—21no—
330C2×D8—22no—
331C2×D8C2×C4×C2911yescharacteristic
332C2×D8D4×C2911yescharacteristic
333#131—21no—
334#131—21no—
335#131C2×C4×C2912yes—
336#131D4×C2912yes—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16D4×C2911yescharacteristic
340C22×C8—21no—
341C22×C8C23×C2911yescharacteristic
342C2×C4⋊C4—21no—
343M32—21no—
344M32—21no—
345M32—21no—
346M32—21no—
347C2×C16—21no—
348C2×C16—21no—
349#108—21no—
350#108—21no—
351#106—21no—
352#106—21no—
353#103—41no—
354#102—41no—
355C29#1275211yescharacteristic, direct product factor, Sylow
356#41—21no—
357#41—21no—
358#41—24no—
359#41—24no—
360#41—22no—
361#41—22no—
362#41—22no—
363#41—22no—
364#41—44no—
365#41—44no—
366#41—44no—
367#41—44no—
368#41—42no—
369#41—42no—
370#41—42no—
371#41—42no—
372#41—41no—
373#41—41no—
374#41—41no—
375#41—41no—
376#41C22⋊C4×C2912yes—
377#41SD16×C2912yes—
378C2×Q8—24no—
379C2×Q8—21no—
380C2×Q8—21no—
381C2×Q8—42no—
382C2×Q8—42no—
383C2×Q8D8×C2911yescharacteristic
384C2×D4—21no—
385C2×D4—24no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—44no—
389C2×D4—44no—
390C2×D4—42no—
391C2×D4—44no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—42no—
395C2×D4D8×C2911yescharacteristic
396C22×C4—21no—
397C22×C4—44no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4C2×D4×C2911yescharacteristic
402Q16—24no—
403Q16—21no—
404Q16—21no—
405Q16C22⋊C4×C2912yes—
406Q16C22⋊C4×C2912yes—
407SD16—24no—
408SD16—24no—
409SD16—22no—
410SD16—22no—
411SD16—22no—
412SD16—22no—
413D8—24no—
414D8—21no—
415D8—21no—
416D8C22⋊C4×C2912yes—
417D8C22⋊C4×C2912yes—
418M16—21no—
419M16—22no—
420M16—22no—
421M16—41no—
422M16—41no—
423M16C22⋊C4×C2912yes—
424C2×C8—21no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—41no—
428C2×C8C22×C4×C2911yescharacteristic
429C2×C8C2×D4×C2911yescharacteristic
430C2×C8C2×D4×C2911yescharacteristic
431C2×C8C2×D4×C2911yescharacteristic
432C2×C8C2×D4×C2911yescharacteristic
433C2×C8C2×D4×C2911yescharacteristic
434C4⋊C4—41no—
435C4⋊C4—41no—
436C16—41no—
437C16—41no—
438C23—21no—
439C23—44no—
440C23—41no—
441C23—41no—
442C23C29×AGL(1,ℤ/8)11yescharacteristic
443Q8—21no—
444Q8—22no—
445Q8—22no—
446Q8—44no—
447Q8—41no—
448Q8—41no—
449Q8C29×#10212yes—
450D4—22no—
451D4—22no—
452D4—21no—
453D4—22no—
454D4—22no—
455D4—44no—
456D4—44no—
457D4—44no—
458D4—42no—
459D4—42no—
460D4—42no—
461D4—42no—
462D4—41no—
463D4—41no—
464D4C29×#10212yes—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—44no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—81no—
478C2×C4—161no—
479C2×C4C2×C22⋊C4×C2911yescharacteristic
480C2×C4C29×#12011yescharacteristic
481C2×C4C29×#12011yescharacteristic
482C2×C4C2×D8×C2911yescharacteristic
483C2×C4C2×SD16×C2911yescharacteristic
484C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
485C8—22no—
486C8—81no—
487C8C2×C22⋊C4×C2911yescharacteristic
488C8C2×C22⋊C4×C2911yescharacteristic
489C8C29×#12011yescharacteristic
490C8C29×#12011yescharacteristic
491C22—22no—
492C22—41no—
493C22—42no—
494C22—42no—
495C22—81no—
496C22—161no—
497C22—161no—
498C22—164no—
499C22C29×#41811yescharacteristic
500C22C29×#44711yescharacteristic
501C22C29×#45011yescharacteristic
502C4—22no—
503C4—42no—
504C4—42no—
505C4—161no—
506C4C29×#37911yescharacteristic
507C4C2×C29×#10211yescharacteristic
508C4C29×#44711yescharacteristic
509C4C29×#45011yescharacteristic
510C2—21no—
511C2—21no—
512C2—21no—
513C2—42no—
514C2—82no—
515C2—82no—
516C2C29×#178611yescharacteristic
subgroupG/H
center, socleC2×C29#1786
commutatorC2×C8C22×C4×C29
Frattini, cosocleC22×C8C23×C29
prime radicalC29×#3584C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C22×C4×C29 ◁ C2×C29×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2148C2semidirect
3. C2×C29×#360C2semidirect
4. C2×C29×#360C2semidirect
5. C29×#2143C2semidirect
6. C29×#2117C2semidirect
7. C29×#1815C2semidirect
10. C29×#578C4semidirect
14. C29×#576C4semidirect
21. C2×C29×M32C22semidirect
22. C2×C29×M32C22semidirect
23. C2×C29×#108C22semidirect
24. C2×C29×#106C22semidirect
179. #12752C29direct (N × H)
234. #2148C2×C29semidirect
235. C2×#360C2×C29semidirect
236. C2×#360C2×C29semidirect
237. #2143C2×C29semidirect
238. #2117C2×C29semidirect
239. #1815C2×C29semidirect
261. #578C4×C29semidirect
265. #576C4×C29semidirect
272. C2×M32C22×C29semidirect
273. C2×M32C22×C29semidirect
274. C2×#108C22×C29semidirect
275. C2×#106C22×C29semidirect
355. C29#12752direct (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×#21482
C2×C29×#3602
C29×#21432
C29×#21172
C29×#18152
#1275229