Finite Group Databasebeta

← C29×#9241 #20304141

Subgroups — C29×#9241 #20304141

Order 7424.

712 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#449C211yesmaximal, characteristic
2C29×#2880C211yesmaximal, characteristic, complemented
3C29×#1789C211yesmaximal, characteristic, complemented
4C29×#1507C211yesmaximal, characteristic, complemented
5C29×#1471C211yesmaximal, characteristic, complemented
6C29×#1293C211yesmaximal, characteristic, complemented
7C29×#1282C211yesmaximal, characteristic, complemented
8C22×#41×C29C2211yescharacteristic
9C22×SD16×C29C411yescharacteristic, complemented
10C22×D8×C29C411yescharacteristic, complemented
11C2×C29×#131—21no—
12C2×C29×#121C2211yescharacteristic
13C29×#449—21no—
14C29×#449—21no—
15C29×#449—21no—
16C29×#449—21no—
17C2×C29×#104—21no—
18C2×C29×#104—21no—
19C2×C29×#103C411yescharacteristic, complemented
20C2×C29×#102C411yescharacteristic, complemented
21C29×#408—22no—
22C29×#408—21no—
23C29×#407—21no—
24C29×#407C2211yescharacteristic
25C29×#407C2211yescharacteristic
26C2×C29×C22⋊C8—21no—
27C2×C29×C22⋊C8C2211yescharacteristic
28C2×C29×C22⋊C8C2211yescharacteristic
29C4×C22⋊C4×C29C2211yescharacteristic
30C29×#327—22no—
31C29×#323—21no—
32C29×#323—21no—
33C2×#41×C29—21no—
34C2×#41×C29—21no—
35C2×#41×C29—42no—
36C2×#41×C29—42no—
37C2×#41×C29D411yescharacteristic
38C2×#41×C29D411yescharacteristic
39C2×#41×C29D411yescharacteristic
40C2×#41×C29D411yescharacteristic
41C22×Q8×C29C2×C411yescharacteristic
42C22×D4×C29—21no—
43C22×D4×C29—21no—
44C22×D4×C29C2×C411yescharacteristic
45C22×D4×C29C2×C411yescharacteristic
46C23×C4×C29—21no—
47C23×C4×C29C2311yescharacteristic
48C2×SD16×C29—21no—
49C2×SD16×C29—21no—
50C2×SD16×C29—42no—
51C2×D8×C29—21no—
52C2×D8×C29—21no—
53C2×D8×C29—42no—
54C29×#131—42no—
55C29×#131—42no—
56C2×M16×C29—22no—
57C2×M16×C29—21no—
58C2×M16×C29—21no—
59C22×C8×C29—22no—
60C22×C8×C29—21no—
61C22×C8×C29C2×C411yescharacteristic
62C22×C8×C29C2×C411yescharacteristic
63C29×#121—21no—
64C29×#121—21no—
65C29×#121—21no—
66C29×#121—21no—
67C2×C4⋊C4×C29C2×C411yescharacteristic
68C2×C22⋊C4×C29—21no—
69C2×C22⋊C4×C29—21no—
70C2×C42×C29—21no—
71C29×#104—42no—
72C29×#104—42no—
73C29×#103—21no—
74C29×#103—21no—
75C29×#102—21no—
76C29×#102—21no—
77C29×C22⋊C8—22no—
78C29×C22⋊C8—22no—
79C29×C22⋊C8—21no—
80C29×C22⋊C8—21no—
81C29×C22⋊C8—21no—
82C29×C22⋊C8—21no—
83C29×C22⋊C8—21no—
84C29×C22⋊C8—21no—
85C29×C22⋊C8D411yescharacteristic
86C29×C22⋊C8D411yescharacteristic
87C29×C22⋊C8D412yes—
88C29×#95—21no—
89C24×C29—21no—
90C24×C29—21no—
91C24×C29#4111yescharacteristic
92#41×C29—22no—
93#41×C29—22no—
94#41×C29—22no—
95#41×C29—22no—
96#41×C29—41no—
97#41×C29—41no—
98#41×C29—41no—
99#41×C29—41no—
100#41×C29—44no—
101#41×C29—44no—
102C2×Q8×C29—21no—
103C2×Q8×C29—22no—
104C2×Q8×C29—41no—
105C2×Q8×C29C22⋊C411yescharacteristic
106C2×Q8×C29C22⋊C411yescharacteristic
107C2×D4×C29—21no—
108C2×D4×C29—22no—
109C2×D4×C29—21no—
110C2×D4×C29—21no—
111C2×D4×C29—21no—
112C2×D4×C29—21no—
113C2×D4×C29—21no—
114C2×D4×C29—21no—
115C2×D4×C29—41no—
116C2×D4×C29—41no—
117C2×D4×C29—41no—
118C2×D4×C29—44no—
119C2×D4×C29—41no—
120C2×D4×C29—41no—
121C2×D4×C29—82no—
122C2×D4×C29C22⋊C411yescharacteristic
123C2×D4×C29C22⋊C411yescharacteristic
124C22×C4×C29—21no—
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29—21no—
128C22×C4×C29—21no—
129C22×C4×C29—21no—
130C22×C4×C29—41no—
131C22×C4×C29—41no—
132C22×C4×C29—44no—
133C22×C4×C29—41no—
134C22×C4×C29C22×C411yescharacteristic
135C22×C4×C29C2×D411yescharacteristic
136C22×C4×C29C2×D411yescharacteristic
137C22×C4×C29C2×D411yescharacteristic
138C22×C4×C29C2×D411yescharacteristic
139C22×C4×C29#4111yescharacteristic
140SD16×C29—42no—
141SD16×C29—42no—
142D8×C29—42no—
143D8×C29—42no—
144M16×C29—44no—
145M16×C29—41no—
146M16×C29—41no—
147M16×C29—41no—
148M16×C29—41no—
149C2×C8×C29—21no—
150C2×C8×C29—21no—
151C2×C8×C29—21no—
152C2×C8×C29—22no—
153C2×C8×C29—21no—
154C2×C8×C29—44no—
155C2×C8×C29—41no—
156C2×C8×C29—41no—
157C2×C8×C29—41no—
158C2×C8×C29—41no—
159C2×C8×C29—41no—
160C4⋊C4×C29—21no—
161C4⋊C4×C29—21no—
162C22⋊C4×C29—22no—
163C22⋊C4×C29—41no—
164C22⋊C4×C29—41no—
165C22⋊C4×C29—41no—
166C42×C29—41no—
167C42×C29—41no—
168#9241C2911yesmaximal, characteristic, direct product factor, Sylow
169C23×C29—21no—
170C23×C29—21no—
171C23×C29—21no—
172C23×C29—21no—
173C23×C29—41no—
174C23×C29—41no—
175C23×C29—42no—
176C23×C29—41no—
177C23×C29—41no—
178C23×C29—41no—
179C23×C29—41no—
180C23×C29—41no—
181C23×C29—81no—
182C23×C29—81no—
183C23×C29—81no—
184C23×C29C4×D411yescharacteristic
185C23×C29#12111yescharacteristic
186C23×C29#12311yescharacteristic
187Q8×C29—21no—
188Q8×C29—21no—
189Q8×C29—21no—
190Q8×C29—42no—
191Q8×C29#9912yes—
192D4×C29—24no—
193D4×C29—21no—
194D4×C29—21no—
195D4×C29—21no—
196D4×C29—42no—
197D4×C29—42no—
198D4×C29—42no—
199D4×C29—42no—
200D4×C29—41no—
201D4×C29—41no—
202D4×C29—81no—
203D4×C29—82no—
204D4×C29—82no—
205D4×C29#9912yes—
206C2×C4×C29—24no—
207C2×C4×C29—21no—
208C2×C4×C29—21no—
209C2×C4×C29—21no—
210C2×C4×C29—21no—
211C2×C4×C29—21no—
212C2×C4×C29—21no—
213C2×C4×C29—21no—
214C2×C4×C29—21no—
215C2×C4×C29—41no—
216C2×C4×C29—41no—
217C2×C4×C29—41no—
218C2×C4×C29—42no—
219C2×C4×C29—42no—
220C2×C4×C29—42no—
221C2×C4×C29—42no—
222C2×C4×C29—42no—
223C2×C4×C29—41no—
224C2×C4×C29—81no—
225C2×C4×C29—81no—
226C2×C4×C29—81no—
227C2×C4×C29C2×C22⋊C411yescharacteristic
228C2×C4×C29C4×D411yescharacteristic
229C2×C4×C29#12011yescharacteristic
230C2×C4×C29#12111yescharacteristic
231C8×C29—41no—
232C8×C29—42no—
233C8×C29—41no—
234C8×C29—41no—
235C8×C29—41no—
236C8×C29—81no—
237C2×#449C2×C2911yescharacteristic
238#2880C2×C2911yescharacteristic, complemented
239#1789C2×C2911yescharacteristic, complemented
240#1507C2×C2911yescharacteristic, complemented
241#1471C2×C2911yescharacteristic, complemented
242#1293C2×C2911yescharacteristic, complemented
243#1282C2×C2911yescharacteristic, complemented
244C22×C29—21no—
245C22×C29—21no—
246C22×C29—21no—
247C22×C29—21no—
248C22×C29—21no—
249C22×C29—21no—
250C22×C29—22no—
251C22×C29—21no—
252C22×C29—21no—
253C22×C29—41no—
254C22×C29—41no—
255C22×C29—41no—
256C22×C29—41no—
257C22×C29—41no—
258C22×C29—81no—
259C22×C29—81no—
260C22×C29—82no—
261C22×C29—82no—
262C22×C29—81no—
263C22×C29—81no—
264C22×C29—81no—
265C22×C29—161no—
266C22×C29—161no—
267C22×C29#38611yescharacteristic
268C22×C29#44311yescharacteristic
269C22×C29#44411yescharacteristic
270C4×C29—21no—
271C4×C29—21no—
272C4×C29—22no—
273C4×C29—21no—
274C4×C29—41no—
275C4×C29—82no—
276C4×C29—81no—
277C4×C29C2×#9911yescharacteristic
278C4×C29C2×#9911yescharacteristic
279C22×#41C22×C2911yescharacteristic
280C22×SD16C4×C2911yescharacteristic, complemented
281C22×D8C4×C2911yescharacteristic, complemented
282C2×#131—21no—
283C2×#121C22×C2911yescharacteristic
284#449—21no—
285#449—21no—
286#449—21no—
287#449—21no—
288C2×#104—21no—
289C2×#104—21no—
290C2×#103C4×C2911yescharacteristic, complemented
291C2×#102C4×C2911yescharacteristic, complemented
292#408—21no—
293#408—22no—
294#407—21no—
295#407C22×C2911yescharacteristic
296#407C22×C2911yescharacteristic
297C2×C22⋊C8—21no—
298C2×C22⋊C8C22×C2911yescharacteristic
299C2×C22⋊C8C22×C2911yescharacteristic
300C4×C22⋊C4C22×C2911yescharacteristic
301#327—22no—
302#323—21no—
303#323—21no—
304C2×C29—21no—
305C2×C29—21no—
306C2×C29—41no—
307C2×C29—41no—
308C2×C29—42no—
309C2×C29—81no—
310C2×C29—161no—
311C2×C29#187611yescharacteristic
312C2×C29#189811yescharacteristic
313C2×C29#190311yescharacteristic
314C2×#41—21no—
315C2×#41—21no—
316C2×#41—42no—
317C2×#41—42no—
318C2×#41D4×C2911yescharacteristic
319C2×#41D4×C2911yescharacteristic
320C2×#41D4×C2911yescharacteristic
321C2×#41D4×C2911yescharacteristic
322C22×Q8C2×C4×C2911yescharacteristic
323C22×D4—21no—
324C22×D4—21no—
325C22×D4C2×C4×C2911yescharacteristic
326C22×D4C2×C4×C2911yescharacteristic
327C23×C4—21no—
328C23×C4C23×C2911yescharacteristic
329C2×SD16—21no—
330C2×SD16—21no—
331C2×SD16—42no—
332C2×D8—21no—
333C2×D8—21no—
334C2×D8—42no—
335#131—42no—
336#131—42no—
337C2×M16—22no—
338C2×M16—21no—
339C2×M16—21no—
340C22×C8—22no—
341C22×C8—21no—
342C22×C8C2×C4×C2911yescharacteristic
343C22×C8C2×C4×C2911yescharacteristic
344#121—21no—
345#121—21no—
346#121—21no—
347#121—21no—
348C2×C4⋊C4C2×C4×C2911yescharacteristic
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C42—21no—
352#104—42no—
353#104—42no—
354#103—21no—
355#103—21no—
356#102—21no—
357#102—21no—
358C22⋊C8—22no—
359C22⋊C8—22no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C22⋊C8—21no—
365C22⋊C8—21no—
366C22⋊C8D4×C2911yescharacteristic
367C22⋊C8D4×C2911yescharacteristic
368C22⋊C8D4×C2912yes—
369#95—21no—
370C29#924111yescharacteristic, direct product factor, Sylow
371C24—21no—
372C24—21no—
373C24#41×C2911yescharacteristic
374#41—22no—
375#41—22no—
376#41—22no—
377#41—22no—
378#41—41no—
379#41—41no—
380#41—41no—
381#41—41no—
382#41—44no—
383#41—44no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—41no—
387C2×Q8C22⋊C4×C2911yescharacteristic
388C2×Q8C22⋊C4×C2911yescharacteristic
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—44no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—82no—
404C2×D4C22⋊C4×C2911yescharacteristic
405C2×D4C22⋊C4×C2911yescharacteristic
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—44no—
415C22×C4—41no—
416C22×C4C22×C4×C2911yescharacteristic
417C22×C4C2×D4×C2911yescharacteristic
418C22×C4C2×D4×C2911yescharacteristic
419C22×C4C2×D4×C2911yescharacteristic
420C22×C4C2×D4×C2911yescharacteristic
421C22×C4#41×C2911yescharacteristic
422SD16—42no—
423SD16—42no—
424D8—42no—
425D8—42no—
426M16—44no—
427M16—41no—
428M16—41no—
429M16—41no—
430M16—41no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—22no—
435C2×C8—21no—
436C2×C8—44no—
437C2×C8—41no—
438C2×C8—41no—
439C2×C8—41no—
440C2×C8—41no—
441C2×C8—41no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C22⋊C4—22no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C42—41no—
449C42—41no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—81no—
463C23—81no—
464C23—81no—
465C23C4×D4×C2911yescharacteristic
466C23C29×#12111yescharacteristic
467C23C29×#12311yescharacteristic
468Q8—21no—
469Q8—21no—
470Q8—21no—
471Q8—42no—
472Q8C29×#9912yes—
473D4—24no—
474D4—21no—
475D4—21no—
476D4—21no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—42no—
481D4—41no—
482D4—41no—
483D4—81no—
484D4—82no—
485D4—82no—
486D4C29×#9912yes—
487C2×C4—24no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—81no—
506C2×C4—81no—
507C2×C4—81no—
508C2×C4C2×C22⋊C4×C2911yescharacteristic
509C2×C4C4×D4×C2911yescharacteristic
510C2×C4C29×#12011yescharacteristic
511C2×C4C29×#12111yescharacteristic
512C8—41no—
513C8—42no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—81no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—22no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—81no—
534C22—82no—
535C22—82no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—161no—
540C22—161no—
541C22C29×#38611yescharacteristic
542C22C29×#44311yescharacteristic
543C22C29×#44411yescharacteristic
544C4—21no—
545C4—21no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—82no—
550C4—81no—
551C4C2×C29×#9911yescharacteristic
552C4C2×C29×#9911yescharacteristic
553C2—21no—
554C2—21no—
555C2—41no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—161no—
560C2C29×#187611yescharacteristic
561C2C29×#189811yescharacteristic
562C2C29×#190311yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC2×C29×#449C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2880C2semidirect
3. C29×#1789C2semidirect
4. C29×#1507C2semidirect
5. C29×#1471C2semidirect
6. C29×#1293C2semidirect
7. C29×#1282C2semidirect
9. C22×SD16×C29C4semidirect
10. C22×D8×C29C4semidirect
19. C2×C29×#103C4semidirect
20. C2×C29×#102C4semidirect
168. #9241C29direct (N × H)
238. #2880C2×C29semidirect
239. #1789C2×C29semidirect
240. #1507C2×C29semidirect
241. #1471C2×C29semidirect
242. #1293C2×C29semidirect
243. #1282C2×C29semidirect
280. C22×SD16C4×C29semidirect
281. C22×D8C4×C29semidirect
290. C2×#103C4×C29semidirect
291. C2×#102C4×C29semidirect
370. C29#9241direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4492
C29×#28802
C29×#17892
C29×#15072
C29×#14712
C29×#12932
C29×#12822
#924129