Finite Group Databasebeta

← C29×#9045 #20303945

Subgroups — C29×#9045 #20303945

Order 7424.

678 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#481C211yesmaximal, characteristic
2C29×#2325C211yesmaximal, characteristic
3C29×#1824C211yesmaximal, characteristic, complemented
4C2×C29×#327C211yesmaximal, characteristic
5C29×#1445C211yesmaximal, characteristic, complemented
6C29×#1294C211yesmaximal, characteristic, complemented
7C29×#1280C211yesmaximal, characteristic, complemented
8C2×C29×#121C2211yescharacteristic
9C2×C4×D4×C29—21no—
10C22×C4⋊C4×C29C2211yescharacteristic
11C29×#481—22no—
12C29×#481C414yescomplemented
13C2×C29×#106—21no—
14C2×C29×#102—21no—
15C2×C29×C22⋊C8C2211yescharacteristic
16C2×C29×C22⋊C8C2211yescharacteristic
17C29×#388—21no—
18C29×#387—21no—
19C29×#386—21no—
20C29×#386—21no—
21C29×#385—21no—
22C29×#380C2211yescharacteristic
23C2×C29×#95—21no—
24C2×C29×#95—21no—
25C2×C29×#95C2211yescharacteristic
26C2×C29×#95C2211yescharacteristic
27C29×#340—21no—
28C29×#340—21no—
29C29×#327—22no—
30C22×D4×C29—21no—
31C22×D4×C29D411yescharacteristic
32C23×C4×C29—21no—
33C23×C4×C29—21no—
34C23×C4×C29—21no—
35C23×C4×C29D411yescharacteristic
36C23×C4×C29D411yescharacteristic
37C23×C4×C29C2311yescharacteristic
38C22×C8×C29—21no—
39C22×C8×C29—21no—
40C29×#121—21no—
41C29×#121—21no—
42C29×#121C2×C412yes—
43C29×#121D412yes—
44C4×D4×C29—42no—
45C4×D4×C29—42no—
46C2×C4⋊C4×C29—21no—
47C2×C4⋊C4×C29—21no—
48C2×C4⋊C4×C29—21no—
49C2×C4⋊C4×C29—21no—
50C2×C4⋊C4×C29—21no—
51C2×C4⋊C4×C29—21no—
52C2×C4⋊C4×C29C2×C412yescomplemented
53C2×C4⋊C4×C29D411yescharacteristic
54C2×C4⋊C4×C29D411yescharacteristic
55C2×C4⋊C4×C29D411yescharacteristic
56C2×C22⋊C4×C29—21no—
57C2×C22⋊C4×C29—21no—
58C2×C22⋊C4×C29—21no—
59C2×C22⋊C4×C29—21no—
60C2×C22⋊C4×C29—21no—
61C2×C42×C29—21no—
62C29×#106—24no—
63C29×#102—24no—
64C29×C22⋊C8—21no—
65C29×C22⋊C8—21no—
66C29×C22⋊C8—21no—
67C29×C22⋊C8C2×C412yescomplemented
68C29×#95—21no—
69C29×#95—21no—
70C29×#95—21no—
71C29×#95—21no—
72C29×#95—21no—
73C29×#95—21no—
74C29×#95—21no—
75C29×#95—42no—
76C29×#95—42no—
77C24×C29—21no—
78C24×C29C2×D411yescharacteristic
79C2×D4×C29—22no—
80C2×D4×C29—22no—
81C2×D4×C29—21no—
82C2×D4×C29—41no—
83C2×D4×C29—41no—
84C2×D4×C29—41no—
85C2×D4×C29—41no—
86C2×D4×C29—41no—
87C2×D4×C29—41no—
88C2×D4×C29C22⋊C412yes—
89C22×C4×C29—21no—
90C22×C4×C29—21no—
91C22×C4×C29—21no—
92C22×C4×C29—22no—
93C22×C4×C29—22no—
94C22×C4×C29—21no—
95C22×C4×C29—21no—
96C22×C4×C29—21no—
97C22×C4×C29—21no—
98C22×C4×C29—21no—
99C22×C4×C29—41no—
100C22×C4×C29—41no—
101C22×C4×C29—42no—
102C22×C4×C29—41no—
103C22×C4×C29—41no—
104C22×C4×C29—41no—
105C22×C4×C29—41no—
106C22×C4×C29—41no—
107C22×C4×C29—41no—
108C22×C4×C29—41no—
109C22×C4×C29—41no—
110C22×C4×C29—41no—
111C22×C4×C29—41no—
112C22×C4×C29—41no—
113C22×C4×C29—41no—
114C22×C4×C29—41no—
115C22×C4×C29—41no—
116C22×C4×C29—41no—
117C22×C4×C29—41no—
118C22×C4×C29—81no—
119C22×C4×C29—81no—
120C22×C4×C29SD1612yes—
121C22×C4×C29C22×C411yescharacteristic
122C22×C4×C29C2×D411yescharacteristic
123C22×C4×C29C2×D411yescharacteristic
124C22×C4×C29C2×D411yescharacteristic
125C22×C4×C29#4111yescharacteristic
126C22×C4×C29#4111yescharacteristic
127C2×C8×C29—22no—
128C2×C8×C29—41no—
129C2×C8×C29—41no—
130C2×C8×C29—41no—
131C2×C8×C29—41no—
132C2×C8×C29—41no—
133C4⋊C4×C29—21no—
134C4⋊C4×C29—22no—
135C4⋊C4×C29—22no—
136C4⋊C4×C29—41no—
137C4⋊C4×C29—41no—
138C4⋊C4×C29—42no—
139C4⋊C4×C29—41no—
140C4⋊C4×C29—41no—
141C4⋊C4×C29C22⋊C412yes—
142C22⋊C4×C29—22no—
143C22⋊C4×C29—22no—
144C22⋊C4×C29—42no—
145C22⋊C4×C29—41no—
146C22⋊C4×C29—41no—
147C22⋊C4×C29—81no—
148C22⋊C4×C29—81no—
149C42×C29—42no—
150#9045C2911yesmaximal, characteristic, direct product factor, Sylow
151C23×C29—21no—
152C23×C29—21no—
153C23×C29—21no—
154C23×C29—21no—
155C23×C29—22no—
156C23×C29—41no—
157C23×C29—41no—
158C23×C29—41no—
159C23×C29—41no—
160C23×C29—41no—
161C23×C29—41no—
162C23×C29C4×D411yescharacteristic
163C23×C29#12011yescharacteristic
164C23×C29#12111yescharacteristic
165C23×C29C2×SD1611yescharacteristic
166C23×C29#13511yescharacteristic
167C23×C29AGL(1,ℤ/8)11yescharacteristic
168C23×C29#13711yescharacteristic
169D4×C29—42no—
170D4×C29—42no—
171D4×C29—42no—
172D4×C29—42no—
173D4×C29—42no—
174D4×C29—81no—
175C2×C4×C29—21no—
176C2×C4×C29—21no—
177C2×C4×C29—21no—
178C2×C4×C29—21no—
179C2×C4×C29—22no—
180C2×C4×C29—22no—
181C2×C4×C29—41no—
182C2×C4×C29—41no—
183C2×C4×C29—41no—
184C2×C4×C29—41no—
185C2×C4×C29—41no—
186C2×C4×C29—41no—
187C2×C4×C29—41no—
188C2×C4×C29—41no—
189C2×C4×C29—42no—
190C2×C4×C29—42no—
191C2×C4×C29—42no—
192C2×C4×C29—42no—
193C2×C4×C29—42no—
194C2×C4×C29—42no—
195C2×C4×C29—42no—
196C2×C4×C29—42no—
197C2×C4×C29—41no—
198C2×C4×C29—41no—
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—81no—
207C2×C4×C29—84no—
208C2×C4×C29—81no—
209C2×C4×C29—81no—
210C2×C4×C29—81no—
211C2×C4×C29—81no—
212C2×C4×C29—81no—
213C2×C4×C29—81no—
214C2×C4×C29—81no—
215C2×C4×C29—81no—
216C2×C4×C29—81no—
217C2×C4×C29C2×C22⋊C411yescharacteristic
218C2×C4×C29C4×D411yescharacteristic
219C2×C4×C29#12111yescharacteristic
220C2×C4×C29#12311yescharacteristic
221C8×C29—42no—
222C8×C29—81no—
223C2×#481C2×C2911yescharacteristic
224#2325C2×C2911yescharacteristic
225#1824C2×C2911yescharacteristic, complemented
226C2×#327C2×C2911yescharacteristic
227#1445C2×C2911yescharacteristic, complemented
228#1294C2×C2911yescharacteristic, complemented
229#1280C2×C2911yescharacteristic, complemented
230C22×C29—21no—
231C22×C29—21no—
232C22×C29—21no—
233C22×C29—21no—
234C22×C29—21no—
235C22×C29—21no—
236C22×C29—21no—
237C22×C29—21no—
238C22×C29—21no—
239C22×C29—21no—
240C22×C29—21no—
241C22×C29—21no—
242C22×C29—42no—
243C22×C29—42no—
244C22×C29—42no—
245C22×C29—81no—
246C22×C29—81no—
247C22×C29—81no—
248C22×C29—81no—
249C22×C29#38611yescharacteristic
250C22×C29C4×SD1611yescharacteristic
251C22×C29#44011yescharacteristic
252C22×C29#45011yescharacteristic
253C22×C29#45211yescharacteristic
254C22×C29#45311yescharacteristic
255C22×C29#45411yescharacteristic
256C22×C29#45811yescharacteristic
257C22×C29#45811yescharacteristic
258C22×C29#46111yescharacteristic
259C22×C29#46311yescharacteristic
260C4×C29—21no—
261C4×C29—21no—
262C4×C29—21no—
263C4×C29—21no—
264C4×C29—42no—
265C4×C29—42no—
266C4×C29—82no—
267C4×C29—81no—
268C4×C29—81no—
269C4×C29—81no—
270C4×C29—82no—
271C2×#121C22×C2911yescharacteristic
272C2×C4×D4—21no—
273C22×C4⋊C4C22×C2911yescharacteristic
274#481—22no—
275#481C4×C2914yescomplemented
276C2×#106—21no—
277C2×#102—21no—
278C2×C22⋊C8C22×C2911yescharacteristic
279C2×C22⋊C8C22×C2911yescharacteristic
280#388—21no—
281#387—21no—
282#386—21no—
283#386—21no—
284#385—21no—
285#380C22×C2911yescharacteristic
286C2×#95—21no—
287C2×#95—21no—
288C2×#95C22×C2911yescharacteristic
289C2×#95C22×C2911yescharacteristic
290#340—21no—
291#340—21no—
292#327—22no—
293C2×C29—21no—
294C2×C29—21no—
295C2×C29—21no—
296C2×C29—21no—
297C2×C29—82no—
298C2×C29#161311yescharacteristic
299C2×C29#161511yescharacteristic
300C2×C29#161611yescharacteristic
301C2×C29#161811yescharacteristic
302C2×C29#187711yescharacteristic
303C2×C29#188311yescharacteristic
304C2×C29#189011yescharacteristic
305C22×D4—21no—
306C22×D4D4×C2911yescharacteristic
307C23×C4—21no—
308C23×C4—21no—
309C23×C4—21no—
310C23×C4D4×C2911yescharacteristic
311C23×C4D4×C2911yescharacteristic
312C23×C4C23×C2911yescharacteristic
313C22×C8—21no—
314C22×C8—21no—
315#121—21no—
316#121—21no—
317#121C2×C4×C2912yes—
318#121D4×C2912yes—
319C4×D4—42no—
320C4×D4—42no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4C2×C4×C2912yescomplemented
328C2×C4⋊C4D4×C2911yescharacteristic
329C2×C4⋊C4D4×C2911yescharacteristic
330C2×C4⋊C4D4×C2911yescharacteristic
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C42—21no—
337#106—24no—
338#102—24no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8C2×C4×C2912yescomplemented
343#95—21no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—42no—
351#95—42no—
352C29#904511yescharacteristic, direct product factor, Sylow
353C24—21no—
354C24C2×D4×C2911yescharacteristic
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—21no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4C22⋊C4×C2912yes—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—42no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—81no—
395C22×C4—81no—
396C22×C4SD16×C2912yes—
397C22×C4C22×C4×C2911yescharacteristic
398C22×C4C2×D4×C2911yescharacteristic
399C22×C4C2×D4×C2911yescharacteristic
400C22×C4C2×D4×C2911yescharacteristic
401C22×C4#41×C2911yescharacteristic
402C22×C4#41×C2911yescharacteristic
403C2×C8—22no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—41no—
407C2×C8—41no—
408C2×C8—41no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—42no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4C22⋊C4×C2912yes—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—42no—
421C22⋊C4—41no—
422C22⋊C4—41no—
423C22⋊C4—81no—
424C22⋊C4—81no—
425C42—42no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—22no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23C4×D4×C2911yescharacteristic
438C23C29×#12011yescharacteristic
439C23C29×#12111yescharacteristic
440C23C2×SD16×C2911yescharacteristic
441C23C29×#13511yescharacteristic
442C23C29×AGL(1,ℤ/8)11yescharacteristic
443C23C29×#13711yescharacteristic
444D4—42no—
445D4—42no—
446D4—42no—
447D4—42no—
448D4—42no—
449D4—81no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—81no—
482C2×C4—84no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—81no—
492C2×C4C2×C22⋊C4×C2911yescharacteristic
493C2×C4C4×D4×C2911yescharacteristic
494C2×C4C29×#12111yescharacteristic
495C2×C4C29×#12311yescharacteristic
496C8—42no—
497C8—81no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22C29×#38611yescharacteristic
518C22C4×SD16×C2911yescharacteristic
519C22C29×#44011yescharacteristic
520C22C29×#45011yescharacteristic
521C22C29×#45211yescharacteristic
522C22C29×#45311yescharacteristic
523C22C29×#45411yescharacteristic
524C22C29×#45811yescharacteristic
525C22C29×#45811yescharacteristic
526C22C29×#46111yescharacteristic
527C22C29×#46311yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—42no—
533C4—42no—
534C4—82no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4—82no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—82no—
544C2C29×#161311yescharacteristic
545C2C29×#161511yescharacteristic
546C2C29×#161611yescharacteristic
547C2C29×#161811yescharacteristic
548C2C29×#187711yescharacteristic
549C2C29×#188311yescharacteristic
550C2C29×#189011yescharacteristic
subgroupG/H
center, socleC23×C29#120
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC2×C29×#121C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#1824C2semidirect
5. C29×#1445C2semidirect
6. C29×#1294C2semidirect
7. C29×#1280C2semidirect
12. C29×#481C4semidirect
52. C2×C4⋊C4×C29C2×C4semidirect
67. C29×C22⋊C8C2×C4semidirect
150. #9045C29direct (N × H)
225. #1824C2×C29semidirect
227. #1445C2×C29semidirect
228. #1294C2×C29semidirect
229. #1280C2×C29semidirect
275. #481C4×C29semidirect
327. C2×C4⋊C4C2×C4×C29semidirect
342. C22⋊C8C2×C4×C29semidirect
352. C29#9045direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4812
C29×#23252
C29×#18242
C2×C29×#3272
C29×#14452
C29×#12942
C29×#12802
#904529