Finite Group Databasebeta

← C29×#15539 #20310439

Subgroups — C29×#15539 #20310439

Order 7424.

1570 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#397C212yesmaximal
2C2×C29×#397C211yesmaximal, characteristic
3C2×C29×#385C212yesmaximal
4C2×C29×#381C211yesmaximal, characteristic
5C29×#1445C212yesmaximal, complemented
6C29×#1445C212yesmaximal, complemented
7C29×#1444C212yesmaximal, complemented
8C29×#1437C211yesmaximal, characteristic
9C29×C4⋊#95C212yesmaximal, complemented
10C24×C4×C29C2211yescharacteristic
11C22×C4⋊C4×C29C2212yes—
12C22×C4⋊C4×C29C2212yes—
13C22×C4⋊C4×C29C2212yes—
14C22×C4⋊C4×C29C2211yescharacteristic
15C22×C22⋊C4×C29C2211yescharacteristic
16C22×C22⋊C4×C29C2212yes—
17C22×C22⋊C4×C29C2212yes—
18C22×C22⋊C4×C29C2211yescharacteristic
19C22×C42×C29C2211yescharacteristic
20C29×#397—28no—
21C29×#397—24no—
22C29×#385—28no—
23C29×#381—24no—
24C2×C29×#95C2212yes—
25C2×C29×#95C2212yes—
26C2×C29×#95C2212yes—
27C2×C29×#95C2212yes—
28C2×C29×#95C2212yes—
29C2×C29×#95C2212yes—
30C2×C29×#95C2212yes—
31C2×C29×#95C2212yes—
32C2×C29×#95C2212yes—
33C2×C29×#95C2211yescharacteristic
34C2×C29×#95C2211yescharacteristic
35C25×C29C2311yescharacteristic
36C23×C4×C29—22no—
37C23×C4×C29—24no—
38C23×C4×C29—24no—
39C23×C4×C29—41no—
40C23×C4×C29—41no—
41C23×C4×C29C2312yes—
42C23×C4×C29C2312yes—
43C23×C4×C29C2312yes—
44C23×C4×C29C2311yescharacteristic
45C23×C4×C29C2312yes—
46C23×C4×C29C2311yescharacteristic
47C23×C4×C29C2312yes—
48C23×C4×C29C2312yes—
49C2×C4⋊C4×C29—24no—
50C2×C4⋊C4×C29—24no—
51C2×C4⋊C4×C29—22no—
52C2×C4⋊C4×C29—24no—
53C2×C4⋊C4×C29—24no—
54C2×C4⋊C4×C29—24no—
55C2×C4⋊C4×C29—24no—
56C2×C4⋊C4×C29—24no—
57C2×C4⋊C4×C29—42no—
58C2×C4⋊C4×C29—42no—
59C2×C4⋊C4×C29—41no—
60C2×C4⋊C4×C29—41no—
61C2×C22⋊C4×C29—24no—
62C2×C22⋊C4×C29—24no—
63C2×C22⋊C4×C29—22no—
64C2×C22⋊C4×C29—24no—
65C2×C22⋊C4×C29—24no—
66C2×C22⋊C4×C29—24no—
67C2×C22⋊C4×C29—24no—
68C2×C22⋊C4×C29—41no—
69C2×C22⋊C4×C29—41no—
70C2×C22⋊C4×C29D418yes—
71C2×C22⋊C4×C29D414yes—
72C2×C42×C29—24no—
73C2×C42×C29—41no—
74C29×#95—24no—
75C29×#95—24no—
76C29×#95—24no—
77C29×#95—24no—
78C29×#95—24no—
79C29×#95—24no—
80C29×#95—24no—
81C29×#95—22no—
82C29×#95—24no—
83C29×#95—24no—
84C29×#95—41no—
85C24×C29—22no—
86C24×C29—22no—
87C24×C29—22no—
88C24×C29—21no—
89C24×C29—21no—
90C24×C29—22no—
91C24×C29—22no—
92C24×C29C2×D414yes—
93C24×C29C2×D412yes—
94C24×C29C2411yescharacteristic
95C22×C4×C29—22no—
96C22×C4×C29—22no—
97C22×C4×C29—22no—
98C22×C4×C29—22no—
99C22×C4×C29—28no—
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—22no—
107C22×C4×C29—22no—
108C22×C4×C29—22no—
109C22×C4×C29—22no—
110C22×C4×C29—21no—
111C22×C4×C29—21no—
112C22×C4×C29—21no—
113C22×C4×C29—21no—
114C22×C4×C29—22no—
115C22×C4×C29—22no—
116C22×C4×C29—22no—
117C22×C4×C29—22no—
118C22×C4×C29—22no—
119C22×C4×C29—22no—
120C22×C4×C29—22no—
121C22×C4×C29—22no—
122C22×C4×C29—22no—
123C22×C4×C29—22no—
124C22×C4×C29—22no—
125C22×C4×C29—22no—
126C22×C4×C29—22no—
127C22×C4×C29—22no—
128C22×C4×C29—22no—
129C22×C4×C29—22no—
130C22×C4×C29—22no—
131C22×C4×C29—22no—
132C22×C4×C29—22no—
133C22×C4×C29—22no—
134C22×C4×C29—22no—
135C22×C4×C29—22no—
136C22×C4×C29—22no—
137C22×C4×C29—22no—
138C22×C4×C29—22no—
139C22×C4×C29—22no—
140C22×C4×C29—22no—
141C22×C4×C29—48no—
142C22×C4×C29—48no—
143C22×C4×C29—44no—
144C22×C4×C29—44no—
145C22×C4×C29C2×D414yes—
146C22×C4×C29C2×D412yes—
147C22×C4×C29C2×D412yes—
148C22×C4×C29C2×D414yes—
149C22×C4×C29#4114yes—
150C22×C4×C29#4114yes—
151C22×C4×C29#4114yes—
152C4⋊C4×C29—48no—
153C4⋊C4×C29—48no—
154C4⋊C4×C29—44no—
155C4⋊C4×C29—48no—
156C22⋊C4×C29—216no—
157C22⋊C4×C29—44no—
158C22⋊C4×C29—44no—
159C22⋊C4×C29—48no—
160C42×C29—44no—
161#15539C2911yesmaximal, characteristic, direct product factor, Sylow
162C23×C29—24no—
163C23×C29—22no—
164C23×C29—22no—
165C23×C29—24no—
166C23×C29—24no—
167C23×C29—24no—
168C23×C29—24no—
169C23×C29—24no—
170C23×C29—24no—
171C23×C29—24no—
172C23×C29—42no—
173C23×C29—42no—
174C23×C29—42no—
175C23×C29—42no—
176C23×C29—41no—
177C23×C29—42no—
178C23×C29—42no—
179C23×C29—41no—
180C23×C29—41no—
181C23×C29—41no—
182C23×C29#12714yes—
183C23×C29C22×D412yes—
184C23×C29C22×D411yescharacteristic
185C23×C29C2×#4112yes—
186C23×C29C2×#4112yes—
187C23×C29C2×#4112yes—
188C23×C29H(5,𝔽2)11yescharacteristic
189C23×C29H(5,𝔽2)11yescharacteristic
190C23×C292−1+412yes—
191C23×C292−1+412yes—
192C2×C4×C29—24no—
193C2×C4×C29—24no—
194C2×C4×C29—24no—
195C2×C4×C29—24no—
196C2×C4×C29—24no—
197C2×C4×C29—24no—
198C2×C4×C29—24no—
199C2×C4×C29—24no—
200C2×C4×C29—22no—
201C2×C4×C29—22no—
202C2×C4×C29—24no—
203C2×C4×C29—24no—
204C2×C4×C29—24no—
205C2×C4×C29—24no—
206C2×C4×C29—24no—
207C2×C4×C29—24no—
208C2×C4×C29—416no—
209C2×C4×C29—42no—
210C2×C4×C29—42no—
211C2×C4×C29—42no—
212C2×C4×C29—42no—
213C2×C4×C29—42no—
214C2×C4×C29—42no—
215C2×C4×C29—42no—
216C2×C4×C29—42no—
217C2×C4×C29—41no—
218C2×C4×C29—42no—
219C2×C4×C29—42no—
220C2×C4×C29—41no—
221C2×C4×C29—41no—
222C2×C4×C29—41no—
223C2×C4×C29—42no—
224C2×C4×C29—42no—
225C2×C4×C29—42no—
226C2×C4×C29—42no—
227C2×C4×C29—42no—
228C2×C4×C29—42no—
229C2×C4×C29—42no—
230C2×C4×C29—42no—
231C2×C4×C29—42no—
232C2×C4×C29—42no—
233C2×C4×C29—42no—
234C2×C4×C29—42no—
235C2×C4×C29—42no—
236C2×C4×C29—42no—
237C2×C4×C29—42no—
238C2×C4×C29—42no—
239C2×C4×C29—42no—
240C2×C4×C29—42no—
241C2×C4×C29—42no—
242C2×C4×C29—42no—
243C2×C4×C29—42no—
244C2×C4×C29#12318yes—
245C2×#397C2×C2912yes—
246C2×#397C2×C2911yescharacteristic
247C2×#385C2×C2912yes—
248C2×#381C2×C2911yescharacteristic
249#1445C2×C2912yescomplemented
250#1445C2×C2912yescomplemented
251#1444C2×C2912yescomplemented
252#1437C2×C2911yescharacteristic
253C4⋊#95C2×C2912yescomplemented
254C22×C29—28no—
255C22×C29—24no—
256C22×C29—44no—
257C22×C29—44no—
258C22×C29—44no—
259C22×C29—44no—
260C22×C29—42no—
261C22×C29—42no—
262C22×C29—44no—
263C22×C29C2×#12312yes—
264C22×C29#52511yescharacteristic
265C22×C29#52912yes—
266C22×C29C2×#12711yescharacteristic
267C22×C29#53411yescharacteristic
268C22×C29#53612yes—
269C22×C29#53912yes—
270C22×C29#54112yes—
271C22×C29#54212yes—
272C22×C29#54612yes—
273C22×C29#54612yes—
274C22×C29#54712yes—
275C22×C29#54712yes—
276C22×C29#54712yes—
277C22×C29#54712yes—
278C22×C29#55111yescharacteristic
279C22×C29#55212yes—
280C22×C29#55612yes—
281C22×C29#55911yescharacteristic
282C22×C29#56311yescharacteristic
283C22×C29#56311yescharacteristic
284C4×C29—28no—
285C4×C29—44no—
286C4×C29—42no—
287C4×C29—42no—
288C4×C29—44no—
289C4×C29—82no—
290C4×C29—82no—
291C4×C29—82no—
292C24×C4C22×C2911yescharacteristic
293C22×C4⋊C4C22×C2912yes—
294C22×C4⋊C4C22×C2912yes—
295C22×C4⋊C4C22×C2912yes—
296C22×C4⋊C4C22×C2911yescharacteristic
297C22×C22⋊C4C22×C2911yescharacteristic
298C22×C22⋊C4C22×C2912yes—
299C22×C22⋊C4C22×C2912yes—
300C22×C22⋊C4C22×C2911yescharacteristic
301C22×C42C22×C2911yescharacteristic
302#397—28no—
303#397—24no—
304#385—28no—
305#381—24no—
306C2×#95C22×C2912yes—
307C2×#95C22×C2912yes—
308C2×#95C22×C2912yes—
309C2×#95C22×C2911yescharacteristic
310C2×#95C22×C2912yes—
311C2×#95C22×C2912yes—
312C2×#95C22×C2912yes—
313C2×#95C22×C2912yes—
314C2×#95C22×C2912yes—
315C2×#95C22×C2912yes—
316C2×#95C22×C2911yescharacteristic
317C2×C29—44no—
318C2×C29#241912yes—
319C2×C29#244712yes—
320C2×C29#247812yes—
321C2×C29#250112yes—
322C2×C29#253911yescharacteristic
323C2×C29#268912yes—
324C2×C29#269812yes—
325C2×C29#271711yescharacteristic
326C2×C29#272411yescharacteristic
327C25C23×C2911yescharacteristic
328C23×C4—22no—
329C23×C4—24no—
330C23×C4—24no—
331C23×C4—41no—
332C23×C4—41no—
333C23×C4C23×C2912yes—
334C23×C4C23×C2912yes—
335C23×C4C23×C2912yes—
336C23×C4C23×C2911yescharacteristic
337C23×C4C23×C2912yes—
338C23×C4C23×C2911yescharacteristic
339C23×C4C23×C2912yes—
340C23×C4C23×C2912yes—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—41no—
352C2×C4⋊C4—41no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—41no—
361C2×C22⋊C4—41no—
362C2×C22⋊C4D4×C2918yes—
363C2×C22⋊C4D4×C2914yes—
364C2×C42—24no—
365C2×C42—41no—
366#95—24no—
367#95—24no—
368#95—24no—
369#95—24no—
370#95—22no—
371#95—24no—
372#95—24no—
373#95—24no—
374#95—24no—
375#95—24no—
376#95—41no—
377C29#1553911yescharacteristic, direct product factor, Sylow
378C24—22no—
379C24—22no—
380C24—22no—
381C24—21no—
382C24—21no—
383C24—22no—
384C24—22no—
385C24C2×D4×C2914yes—
386C24C2×D4×C2912yes—
387C24C24×C2911yescharacteristic
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—28no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—48no—
435C22×C4—48no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4C2×D4×C2912yes—
439C22×C4C2×D4×C2914yes—
440C22×C4C2×D4×C2912yes—
441C22×C4C2×D4×C2914yes—
442C22×C4#41×C2914yes—
443C22×C4#41×C2914yes—
444C22×C4#41×C2914yes—
445C4⋊C4—48no—
446C4⋊C4—48no—
447C4⋊C4—44no—
448C4⋊C4—48no—
449C22⋊C4—216no—
450C22⋊C4—44no—
451C22⋊C4—44no—
452C22⋊C4—48no—
453C42—44no—
454C23—24no—
455C23—22no—
456C23—22no—
457C23—24no—
458C23—24no—
459C23—24no—
460C23—24no—
461C23—24no—
462C23—24no—
463C23—24no—
464C23—42no—
465C23—42no—
466C23—42no—
467C23—42no—
468C23—41no—
469C23—42no—
470C23—42no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23C29×#12714yes—
475C23C22×D4×C2912yes—
476C23C22×D4×C2911yescharacteristic
477C23C2×#41×C2912yes—
478C23C2×#41×C2912yes—
479C23C2×#41×C2912yes—
480C23C29×H(5,𝔽2)11yescharacteristic
481C23C29×H(5,𝔽2)11yescharacteristic
482C23C29×2−1+412yes—
483C23C29×2−1+412yes—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—416no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4C29×#12318yes—
537C22—28no—
538C22—24no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22—44no—
543C22—42no—
544C22—42no—
545C22—44no—
546C22C2×C29×#12312yes—
547C22C29×#52511yescharacteristic
548C22C29×#52912yes—
549C22C2×C29×#12711yescharacteristic
550C22C29×#53411yescharacteristic
551C22C29×#53612yes—
552C22C29×#53912yes—
553C22C29×#54112yes—
554C22C29×#54212yes—
555C22C29×#54612yes—
556C22C29×#54612yes—
557C22C29×#54712yes—
558C22C29×#54712yes—
559C22C29×#54712yes—
560C22C29×#54712yes—
561C22C29×#55111yescharacteristic
562C22C29×#55212yes—
563C22C29×#55612yes—
564C22C29×#55911yescharacteristic
565C22C29×#56311yescharacteristic
566C22C29×#56311yescharacteristic
567C4—28no—
568C4—44no—
569C4—42no—
570C4—42no—
571C4—44no—
572C4—82no—
573C4—82no—
574C4—82no—
575C2—44no—
576C2C29×#241912yes—
577C2C29×#244712yes—
578C2C29×#247812yes—
579C2C29×#250112yes—
580C2C29×#253911yescharacteristic
581C2C29×#268912yes—
582C2C29×#269812yes—
583C2C29×#271711yescharacteristic
584C2C29×#272411yescharacteristic
subgroupG/H
center, socleC24×C29C24
commutator, Frattini, cosocleC24C24×C29
prime radicalC25×C29C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
5. C29×#1445C2semidirect
6. C29×#1445C2semidirect
7. C29×#1444C2semidirect
9. C29×C4⋊#95C2semidirect
161. #15539C29direct (N × H)
249. #1445C2×C29semidirect
250. #1445C2×C29semidirect
251. #1444C2×C29semidirect
253. C4⋊#95C2×C29semidirect
377. C29#15539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#3972
C2×C29×#3852
C2×C29×#3812
C29×#14452
C29×#14442
C29×#14372
C29×C4⋊#952
#1553929