Finite Group Databasebeta

← C29×#9117 #20304017

Subgroups — C29×#9117 #20304017

Order 7424.

1030 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#407C211yesmaximal, characteristic, complemented
2C29×#2847C211yesmaximal, characteristic
3C2×C29×#327C212yesmaximal, complemented
4C29×C22⋊#95C211yesmaximal, characteristic, complemented
5C29×#1294C212yesmaximal, complemented
6C24×C4×C29C2211yescharacteristic
7C22×M16×C29—21no—
8C2×C29×#121C411yescharacteristic, complemented
9C2×C29×#121C411yescharacteristic, complemented
10C2×C29×#121C2211yescharacteristic
11C2×C29×#120—21no—
12C22×C22⋊C4×C29—21no—
13C29×#407—24no—
14C2×C29×C22⋊C8—21no—
15C2×C29×C22⋊C8C2212yes—
16C29×#386—21no—
17C29×#386—21no—
18C29×#386—21no—
19C29×#380C411yescharacteristic, complemented
20C29×#380C411yescharacteristic, complemented
21C29×#380C2211yescharacteristic
22C2×C29×#95—21no—
23C2×C29×#95C2212yes—
24C29×#327—24no—
25C25×C29D411yescharacteristic
26C22×D4×C29—21no—
27C22×D4×C29—21no—
28C22×D4×C29—21no—
29C22×D4×C29C2×C411yescharacteristic
30C23×C4×C29—22no—
31C23×C4×C29—22no—
32C23×C4×C29—22no—
33C23×C4×C29—42no—
34C23×C4×C29—42no—
35C23×C4×C29C2×C411yescharacteristic
36C23×C4×C29C2×C411yescharacteristic
37C23×C4×C29D411yescharacteristic
38C23×C4×C29D411yescharacteristic
39C23×C4×C29D411yescharacteristic
40C23×C4×C29C2311yescharacteristic
41C2×M16×C29—24no—
42C2×M16×C29—42no—
43C2×M16×C29—42no—
44C22×C8×C29—22no—
45C29×#121—22no—
46C29×#121—22no—
47C29×#121—42no—
48C29×#121—42no—
49C29×#120—44no—
50C2×C4⋊C4×C29C2×C411yescharacteristic
51C2×C4⋊C4×C29C2×C411yescharacteristic
52C2×C4⋊C4×C29C2×C411yescharacteristic
53C2×C22⋊C4×C29—24no—
54C2×C22⋊C4×C29—21no—
55C2×C22⋊C4×C29—21no—
56C2×C22⋊C4×C29—21no—
57C2×C22⋊C4×C29—21no—
58C2×C22⋊C4×C29—21no—
59C2×C22⋊C4×C29—21no—
60C2×C22⋊C4×C29—42no—
61C2×C22⋊C4×C29—42no—
62C29×C22⋊C8—24no—
63C29×C22⋊C8—22no—
64C29×C22⋊C8D414yescomplemented
65C29×#95—21no—
66C29×#95—21no—
67C29×#95—21no—
68C29×#95—22no—
69C29×#95—22no—
70C29×#95—42no—
71C24×C29—22no—
72C24×C29—22no—
73C24×C29—21no—
74C24×C29—21no—
75C24×C29—22no—
76C24×C29—22no—
77C24×C29—21no—
78C24×C29—41no—
79C24×C29—41no—
80C24×C29C22⋊C411yescharacteristic
81C24×C29C22⋊C411yescharacteristic
82C24×C29C2×D411yescharacteristic
83C2×D4×C29—22no—
84C2×D4×C29—41no—
85C2×D4×C29—41no—
86C2×D4×C29—42no—
87C2×D4×C29—42no—
88C2×D4×C29—42no—
89C2×D4×C29—42no—
90C2×D4×C29—42no—
91C2×D4×C29—42no—
92C2×D4×C29—42no—
93C2×D4×C29—42no—
94C2×D4×C29—41no—
95C2×D4×C29—41no—
96C22×C4×C29—22no—
97C22×C4×C29—22no—
98C22×C4×C29—21no—
99C22×C4×C29—21no—
100C22×C4×C29—22no—
101C22×C4×C29—22no—
102C22×C4×C29—22no—
103C22×C4×C29—22no—
104C22×C4×C29—22no—
105C22×C4×C29—22no—
106C22×C4×C29—21no—
107C22×C4×C29—21no—
108C22×C4×C29—24no—
109C22×C4×C29—21no—
110C22×C4×C29—21no—
111C22×C4×C29—21no—
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—41no—
119C22×C4×C29—48no—
120C22×C4×C29—48no—
121C22×C4×C29—42no—
122C22×C4×C29—42no—
123C22×C4×C29—42no—
124C22×C4×C29—42no—
125C22×C4×C29—42no—
126C22×C4×C29—42no—
127C22×C4×C29C22⋊C411yescharacteristic
128C22×C4×C29C22⋊C411yescharacteristic
129C22×C4×C29C22×C411yescharacteristic
130C22×C4×C29C2×D411yescharacteristic
131C22×C4×C29C2×D412yes—
132C22×C4×C29#4112yes—
133M16×C29—48no—
134C2×C8×C29—24no—
135C2×C8×C29—42no—
136C2×C8×C29—42no—
137C4⋊C4×C29—22no—
138C4⋊C4×C29—41no—
139C4⋊C4×C29—41no—
140C22⋊C4×C29—42no—
141C22⋊C4×C29—48no—
142C22⋊C4×C29—42no—
143C22⋊C4×C29—42no—
144C22⋊C4×C29—42no—
145C22⋊C4×C29—42no—
146C22⋊C4×C29—41no—
147C22⋊C4×C29—41no—
148#9117C2911yesmaximal, characteristic, direct product factor, Sylow
149C23×C29—21no—
150C23×C29—21no—
151C23×C29—21no—
152C23×C29—21no—
153C23×C29—24no—
154C23×C29—24no—
155C23×C29—21no—
156C23×C29—21no—
157C23×C29—21no—
158C23×C29—21no—
159C23×C29—21no—
160C23×C29—21no—
161C23×C29—21no—
162C23×C29—21no—
163C23×C29—21no—
164C23×C29—21no—
165C23×C29—21no—
166C23×C29—21no—
167C23×C29—44no—
168C23×C29—44no—
169C23×C29—44no—
170C23×C29—44no—
171C23×C29—42no—
172C23×C29—42no—
173C23×C29—42no—
174C23×C29—42no—
175C23×C29—41no—
176C23×C29—41no—
177C23×C29—41no—
178C23×C29—41no—
179C23×C29—41no—
180C23×C29—41no—
181C23×C29—41no—
182C23×C29#9912yes—
183C23×C29#10412yes—
184C23×C29C2×C22⋊C411yescharacteristic
185C23×C29#12112yes—
186C23×C29AGL(1,ℤ/8)11yescharacteristic
187C23×C29AGL(1,ℤ/8)12yes—
188C23×C29#13711yescharacteristic
189D4×C29—82no—
190D4×C29—84no—
191D4×C29—84no—
192D4×C29—82no—
193D4×C29—82no—
194C2×C4×C29—24no—
195C2×C4×C29—24no—
196C2×C4×C29—21no—
197C2×C4×C29—21no—
198C2×C4×C29—21no—
199C2×C4×C29—21no—
200C2×C4×C29—21no—
201C2×C4×C29—21no—
202C2×C4×C29—21no—
203C2×C4×C29—21no—
204C2×C4×C29—21no—
205C2×C4×C29—42no—
206C2×C4×C29—42no—
207C2×C4×C29—44no—
208C2×C4×C29—44no—
209C2×C4×C29—44no—
210C2×C4×C29—42no—
211C2×C4×C29—42no—
212C2×C4×C29—44no—
213C2×C4×C29—44no—
214C2×C4×C29—44no—
215C2×C4×C29—41no—
216C2×C4×C29—41no—
217C2×C4×C29—41no—
218C2×C4×C29—41no—
219C2×C4×C29—41no—
220C2×C4×C29—41no—
221C2×C4×C29—41no—
222C2×C4×C29—41no—
223C2×C4×C29—41no—
224C2×C4×C29—82no—
225C2×C4×C29—82no—
226C2×C4×C29—82no—
227C2×C4×C29—82no—
228C2×C4×C29#9912yes—
229C2×C4×C29C4×D412yes—
230C2×C4×C29#12011yescharacteristic
231C2×C4×C29#12311yescharacteristic
232C8×C29—44no—
233C2×#407C2×C2911yescharacteristic, complemented
234#2847C2×C2911yescharacteristic
235C2×#327C2×C2912yescomplemented
236C22⋊#95C2×C2911yescharacteristic, complemented
237#1294C2×C2912yescomplemented
238C22×C29—22no—
239C22×C29—22no—
240C22×C29—21no—
241C22×C29—21no—
242C22×C29—22no—
243C22×C29—22no—
244C22×C29—21no—
245C22×C29—21no—
246C22×C29—22no—
247C22×C29—22no—
248C22×C29—22no—
249C22×C29—22no—
250C22×C29—22no—
251C22×C29—22no—
252C22×C29—48no—
253C22×C29—48no—
254C22×C29—41no—
255C22×C29—41no—
256C22×C29—41no—
257C22×C29—41no—
258C22×C29—41no—
259C22×C29—41no—
260C22×C29—41no—
261C22×C29—41no—
262C22×C29—81no—
263C22×C29—81no—
264C22×C29—81no—
265C22×C29—81no—
266C22×C29—81no—
267C22×C29—81no—
268C22×C29—81no—
269C22×C29#38611yescharacteristic
270C22×C29C2×#9911yescharacteristic
271C22×C29C2×#9911yescharacteristic
272C22×C29#41711yescharacteristic
273C22×C29#41811yescharacteristic
274C22×C29C2×#10411yescharacteristic
275C22×C29#42111yescharacteristic
276C22×C29#46812yes—
277C22×C29#46912yes—
278C4×C29—21no—
279C4×C29—22no—
280C4×C29—21no—
281C4×C29—22no—
282C4×C29—41no—
283C4×C29—84no—
284C4×C29—81no—
285C4×C29—81no—
286C4×C29—81no—
287C24×C4C22×C2911yescharacteristic
288C22×M16—21no—
289C2×#121C4×C2911yescharacteristic, complemented
290C2×#121C4×C2911yescharacteristic, complemented
291C2×#121C22×C2911yescharacteristic
292C2×#120—21no—
293C22×C22⋊C4—21no—
294#407—24no—
295C2×C22⋊C8—21no—
296C2×C22⋊C8C22×C2912yes—
297#386—21no—
298#386—21no—
299#386—21no—
300#380C4×C2911yescharacteristic, complemented
301#380C4×C2911yescharacteristic, complemented
302#380C22×C2911yescharacteristic
303C2×#95—21no—
304C2×#95C22×C2912yes—
305#327—24no—
306C2×C29—22no—
307C2×C29—22no—
308C2×C29—42no—
309C2×C29—42no—
310C2×C29—161no—
311C2×C29#150411yescharacteristic
312C2×C29#150711yescharacteristic
313C2×C29#151011yescharacteristic
314C2×C29#151311yescharacteristic
315C2×C29#187111yescharacteristic
316C2×C29#189511yescharacteristic
317C2×C29#189811yescharacteristic
318C25D4×C2911yescharacteristic
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4C2×C4×C2911yescharacteristic
323C23×C4—22no—
324C23×C4—22no—
325C23×C4—22no—
326C23×C4—42no—
327C23×C4—42no—
328C23×C4C2×C4×C2911yescharacteristic
329C23×C4C2×C4×C2911yescharacteristic
330C23×C4D4×C2911yescharacteristic
331C23×C4D4×C2911yescharacteristic
332C23×C4D4×C2911yescharacteristic
333C23×C4C23×C2911yescharacteristic
334C2×M16—24no—
335C2×M16—42no—
336C2×M16—42no—
337C22×C8—22no—
338#121—22no—
339#121—22no—
340#121—42no—
341#121—42no—
342#120—44no—
343C2×C4⋊C4C2×C4×C2911yescharacteristic
344C2×C4⋊C4C2×C4×C2911yescharacteristic
345C2×C4⋊C4C2×C4×C2911yescharacteristic
346C2×C22⋊C4—24no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—42no—
354C2×C22⋊C4—42no—
355C22⋊C8—24no—
356C22⋊C8—22no—
357C22⋊C8D4×C2914yescomplemented
358#95—21no—
359#95—21no—
360#95—21no—
361#95—22no—
362#95—22no—
363#95—42no—
364C29#911711yescharacteristic, direct product factor, Sylow
365C24—21no—
366C24—21no—
367C24—22no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—21no—
372C24—41no—
373C24—41no—
374C24C22⋊C4×C2911yescharacteristic
375C24C22⋊C4×C2911yescharacteristic
376C24C2×D4×C2911yescharacteristic
377C2×D4—22no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—42no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—42no—
389C2×D4—42no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—48no—
414C22×C4—48no—
415C22×C4—42no—
416C22×C4—42no—
417C22×C4—42no—
418C22×C4—42no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4C22⋊C4×C2911yescharacteristic
422C22×C4C22⋊C4×C2911yescharacteristic
423C22×C4C22×C4×C2911yescharacteristic
424C22×C4C2×D4×C2911yescharacteristic
425C22×C4C2×D4×C2912yes—
426C22×C4#41×C2912yes—
427M16—48no—
428C2×C8—24no—
429C2×C8—42no—
430C2×C8—42no—
431C4⋊C4—22no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C22⋊C4—42no—
435C22⋊C4—48no—
436C22⋊C4—42no—
437C22⋊C4—42no—
438C22⋊C4—42no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—42no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—21no—
446C23—24no—
447C23—24no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—44no—
461C23—44no—
462C23—44no—
463C23—44no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23C29×#9912yes—
476C23C29×#10412yes—
477C23C2×C22⋊C4×C2911yescharacteristic
478C23C29×#12112yes—
479C23C29×AGL(1,ℤ/8)12yes—
480C23C29×AGL(1,ℤ/8)11yescharacteristic
481C23C29×#13711yescharacteristic
482D4—82no—
483D4—84no—
484D4—84no—
485D4—82no—
486D4—82no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—44no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—44no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4C29×#9912yes—
522C2×C4C4×D4×C2912yes—
523C2×C4C29×#12011yescharacteristic
524C2×C4C29×#12311yescharacteristic
525C8—44no—
526C22—21no—
527C22—21no—
528C22—22no—
529C22—22no—
530C22—21no—
531C22—21no—
532C22—22no—
533C22—22no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22—48no—
541C22—48no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C29×#38611yescharacteristic
558C22C2×C29×#9911yescharacteristic
559C22C2×C29×#9911yescharacteristic
560C22C29×#41711yescharacteristic
561C22C29×#41811yescharacteristic
562C22C2×C29×#10411yescharacteristic
563C22C29×#42111yescharacteristic
564C22C29×#46812yes—
565C22C29×#46912yes—
566C4—21no—
567C4—21no—
568C4—22no—
569C4—22no—
570C4—41no—
571C4—84no—
572C4—81no—
573C4—81no—
574C4—81no—
575C2—22no—
576C2—22no—
577C2—42no—
578C2—42no—
579C2—161no—
580C2C29×#150411yescharacteristic
581C2C29×#150711yescharacteristic
582C2C29×#151011yescharacteristic
583C2C29×#151311yescharacteristic
584C2C29×#187111yescharacteristic
585C2C29×#189511yescharacteristic
586C2C29×#189811yescharacteristic
subgroupG/H
center, socleC23×C29C2×C22⋊C4
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC29×#2847C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ C24×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#407C2semidirect
3. C2×C29×#327C2semidirect
4. C29×C22⋊#95C2semidirect
5. C29×#1294C2semidirect
8. C2×C29×#121C4semidirect
9. C2×C29×#121C4semidirect
19. C29×#380C4semidirect
20. C29×#380C4semidirect
64. C29×C22⋊C8D4semidirect
148. #9117C29direct (N × H)
233. C2×#407C2×C29semidirect
235. C2×#327C2×C29semidirect
236. C22⋊#95C2×C29semidirect
237. #1294C2×C29semidirect
289. C2×#121C4×C29semidirect
290. C2×#121C4×C29semidirect
300. #380C4×C29semidirect
301. #380C4×C29semidirect
357. C22⋊C8D4×C29semidirect
364. C29#9117direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4072
C29×#28472
C2×C29×#3272
C29×C22⋊#952
C29×#12942
#911729