Finite Group Databasebeta

← C29×#33020 #20327920

Subgroups — C29×#33020 #20327920

Order 7424.

1824 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#518C211yesmaximal, characteristic, complemented
2C29×#2405C212yesmaximal, complemented
3C29×#2403C211yesmaximal, characteristic
4C29×#1889C214yesmaximal, complemented
5C29×#1867C214yesmaximal, complemented
6C29×#1819C212yesmaximal, complemented
7C29×#1781C211yesmaximal, characteristic, complemented
8C23×D4×C29C2211yescharacteristic
9C23×D4×C29C2211yescharacteristic
10C2×C29×#123—22no—
11C2×C29×#120—21no—
12C2×C29×#120C2212yes—
13C29×#518—22no—
14C29×#518—24no—
15C29×#518C2214yes—
16C2×C4×D4×C29—22no—
17C2×C4×D4×C29—22no—
18C2×C29×#117—21no—
19C22×C22⋊C4×C29—21no—
20C22×C22⋊C4×C29C2212yes—
21C2×C29×#99C2214yes—
22C29×#394—24no—
23C29×#392—22no—
24C29×#386—21no—
25C29×#386—22no—
26C29×#386C2212yes—
27C29×#385C2214yescomplemented
28C29×#379C2212yes—
29C29×#379C2211yescharacteristic
30C29×#379C2214yescomplemented
31C29×#342C2218yescomplemented
32C25×C29D411yescharacteristic
33C25×C29C2311yescharacteristic
34C25×C29C2311yescharacteristic
35C22×D4×C29—22no—
36C22×D4×C29—22no—
37C22×D4×C29—28no—
38C22×D4×C29—21no—
39C22×D4×C29—22no—
40C22×D4×C29—21no—
41C22×D4×C29—22no—
42C22×D4×C29—22no—
43C22×D4×C29—44no—
44C22×D4×C29D412yes—
45C22×D4×C29C2312yes—
46C23×C4×C29—21no—
47C23×C4×C29—21no—
48C23×C4×C29D411yescharacteristic
49C23×C4×C29D412yescomplemented
50C23×C4×C29D412yescomplemented
51C23×C4×C29C2311yescharacteristic
52C29×#123—48no—
53C29×#120—28no—
54C29×#120—44no—
55C4×D4×C29—28no—
56C4×D4×C29—28no—
57C4×D4×C29—28no—
58C4×D4×C29—28no—
59C29×#117—24no—
60C29×#117—24no—
61C2×C4⋊C4×C29—21no—
62C2×C4⋊C4×C29—21no—
63C2×C4⋊C4×C29—24no—
64C2×C22⋊C4×C29—22no—
65C2×C22⋊C4×C29—24no—
66C2×C22⋊C4×C29—22no—
67C2×C22⋊C4×C29—24no—
68C2×C22⋊C4×C29—22no—
69C2×C22⋊C4×C29—22no—
70C2×C22⋊C4×C29—22no—
71C2×C22⋊C4×C29—21no—
72C2×C22⋊C4×C29—22no—
73C2×C22⋊C4×C29—22no—
74C2×C22⋊C4×C29—22no—
75C2×C22⋊C4×C29—24no—
76C2×C22⋊C4×C29—21no—
77C2×C22⋊C4×C29—22no—
78C2×C22⋊C4×C29—24no—
79C2×C22⋊C4×C29D414yescomplemented
80C2×C22⋊C4×C29C2312yes—
81C2×C22⋊C4×C29C2314yes—
82C2×C22⋊C4×C29C2314yes—
83C2×C42×C29—22no—
84C29×#99—28no—
85C29×#95—24no—
86C29×#95—22no—
87C24×C29—21no—
88C24×C29—21no—
89C24×C29—24no—
90C24×C29—24no—
91C24×C29—22no—
92C24×C29—21no—
93C24×C29—24no—
94C24×C29—42no—
95C24×C29—42no—
96C24×C29—42no—
97C24×C29—81no—
98C24×C29—81no—
99C24×C29—81no—
100C24×C29C2×D411yescharacteristic
101C24×C29C2×D412yes—
102C24×C29C2×D411yescharacteristic
103C24×C29C2×D412yes—
104C24×C29C2×D412yes—
105C24×C29C2411yescharacteristic
106C2×D4×C29—216no—
107C2×D4×C29—216no—
108C2×D4×C29—24no—
109C2×D4×C29—24no—
110C2×D4×C29—24no—
111C2×D4×C29—24no—
112C2×D4×C29—24no—
113C2×D4×C29—28no—
114C2×D4×C29—24no—
115C2×D4×C29—42no—
116C2×D4×C29—44no—
117C2×D4×C29—44no—
118C2×D4×C29—42no—
119C2×D4×C29—44no—
120C2×D4×C29—42no—
121C2×D4×C29—41no—
122C2×D4×C29—42no—
123C2×D4×C29—41no—
124C2×D4×C29—44no—
125C2×D4×C29—44no—
126C2×D4×C29—82no—
127C2×D4×C29#4118yes—
128C22×C4×C29—21no—
129C22×C4×C29—21no—
130C22×C4×C29—24no—
131C22×C4×C29—22no—
132C22×C4×C29—22no—
133C22×C4×C29—21no—
134C22×C4×C29—22no—
135C22×C4×C29—24no—
136C22×C4×C29—24no—
137C22×C4×C29—22no—
138C22×C4×C29—22no—
139C22×C4×C29—24no—
140C22×C4×C29—22no—
141C22×C4×C29—42no—
142C22×C4×C29—44no—
143C22×C4×C29—82no—
144C22×C4×C29—82no—
145C22×C4×C29—82no—
146C22×C4×C29C2×D412yes—
147C22×C4×C29C2×D414yes—
148C22×C4×C29C2×D414yes—
149C4⋊C4×C29—24no—
150C4⋊C4×C29—24no—
151C4⋊C4×C29—48no—
152C22⋊C4×C29—28no—
153C22⋊C4×C29—24no—
154C22⋊C4×C29—24no—
155C22⋊C4×C29—24no—
156C22⋊C4×C29—24no—
157C22⋊C4×C29—24no—
158C22⋊C4×C29—28no—
159C22⋊C4×C29—44no—
160C22⋊C4×C29—42no—
161C22⋊C4×C29—48no—
162C22⋊C4×C29—44no—
163C22⋊C4×C29—44no—
164C22⋊C4×C29—84no—
165C22⋊C4×C29—82no—
166C22⋊C4×C29—81no—
167C42×C29—28no—
168#33020C2911yesmaximal, characteristic, direct product factor, Sylow
169C23×C29—24no—
170C23×C29—24no—
171C23×C29—22no—
172C23×C29—22no—
173C23×C29—24no—
174C23×C29—24no—
175C23×C29—22no—
176C23×C29—22no—
177C23×C29—22no—
178C23×C29—24no—
179C23×C29—24no—
180C23×C29—22no—
181C23×C29—41no—
182C23×C29—42no—
183C23×C29—41no—
184C23×C29—41no—
185C23×C29—42no—
186C23×C29—41no—
187C23×C29—42no—
188C23×C29—41no—
189C23×C29—42no—
190C23×C29—42no—
191C23×C29—42no—
192C23×C29—44no—
193C23×C29—42no—
194C23×C29—41no—
195C23×C29—42no—
196C23×C29—42no—
197C23×C29—41no—
198C23×C29—42no—
199C23×C29—44no—
200C23×C29—81no—
201C23×C29—81no—
202C23×C29—88no—
203C23×C29—88no—
204C23×C29—88no—
205C23×C29#12011yescharacteristic
206C23×C29#12012yes—
207C23×C29#12011yescharacteristic
208C23×C29#12314yescomplemented
209C23×C29C22×D411yescharacteristic
210C23×C29C22×D412yes—
211C23×C29C2×#4114yes—
212D4×C29—216no—
213D4×C29—216no—
214D4×C29—48no—
215D4×C29—44no—
216D4×C29—44no—
217D4×C29—88no—
218C2×C4×C29—24no—
219C2×C4×C29—24no—
220C2×C4×C29—22no—
221C2×C4×C29—22no—
222C2×C4×C29—22no—
223C2×C4×C29—24no—
224C2×C4×C29—24no—
225C2×C4×C29—24no—
226C2×C4×C29—42no—
227C2×C4×C29—41no—
228C2×C4×C29—44no—
229C2×C4×C29—41no—
230C2×C4×C29—44no—
231C2×C4×C29—44no—
232C2×C4×C29—44no—
233C2×C4×C29—44no—
234C2×C4×C29—42no—
235C2×C4×C29—44no—
236C2×C4×C29—42no—
237C2×C4×C29—42no—
238C2×C4×C29—44no—
239C2×C4×C29—82no—
240C2×C4×C29—82no—
241C2×C4×C29—84no—
242C2×C4×C29—84no—
243C2×C4×C29#12314yescomplemented
244C2×#518C2×C2911yescharacteristic, complemented
245#2405C2×C2912yescomplemented
246#2403C2×C2911yescharacteristic
247#1889C2×C2914yescomplemented
248#1867C2×C2914yescomplemented
249#1819C2×C2912yescomplemented
250#1781C2×C2911yescharacteristic, complemented
251C22×C29—21no—
252C22×C29—22no—
253C22×C29—21no—
254C22×C29—21no—
255C22×C29—22no—
256C22×C29—21no—
257C22×C29—21no—
258C22×C29—22no—
259C22×C29—24no—
260C22×C29—22no—
261C22×C29—21no—
262C22×C29—22no—
263C22×C29—21no—
264C22×C29—44no—
265C22×C29—48no—
266C22×C29—44no—
267C22×C29—44no—
268C22×C29—48no—
269C22×C29—44no—
270C22×C29—48no—
271C22×C29—42no—
272C22×C29—42no—
273C22×C29—42no—
274C22×C29—82no—
275C22×C29—82no—
276C22×C29—84no—
277C22×C29—82no—
278C22×C29—84no—
279C22×C29—84no—
280C22×C29—81no—
281C22×C29—81no—
282C22×C29B(4,𝔽2)12yes—
283C22×C29C2×#12011yescharacteristic
284C22×C29C2×#12312yes—
285C22×C29#52514yes—
286C4×C29—24no—
287C4×C29—42no—
288C4×C29—44no—
289C4×C29—44no—
290C4×C29—84no—
291C4×C29—82no—
292C23×D4C22×C2911yescharacteristic
293C23×D4C22×C2911yescharacteristic
294C2×#123—22no—
295C2×#120—21no—
296C2×#120C22×C2912yes—
297#518—22no—
298#518—24no—
299#518C22×C2914yes—
300C2×C4×D4—22no—
301C2×C4×D4—22no—
302C2×#117—21no—
303C22×C22⋊C4—21no—
304C22×C22⋊C4C22×C2912yes—
305C2×#99C22×C2914yes—
306#394—24no—
307#392—22no—
308#386—21no—
309#386—22no—
310#386C22×C2912yes—
311#385C22×C2914yescomplemented
312#379C22×C2911yescharacteristic
313#379C22×C2912yes—
314#379C22×C2914yescomplemented
315#342C22×C2918yescomplemented
316C2×C29—22no—
317C2×C29—24no—
318C2×C29—22no—
319C2×C29—42no—
320C2×C29—41no—
321C2×C29—44no—
322C2×C29—82no—
323C2×C29#284911yescharacteristic
324C2×C29C2×B(4,𝔽2)11yescharacteristic
325C2×C29#302611yescharacteristic
326C25D4×C2911yescharacteristic
327C25C23×C2911yescharacteristic
328C25C23×C2911yescharacteristic
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—28no—
332C22×D4—21no—
333C22×D4—22no—
334C22×D4—21no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—44no—
338C22×D4D4×C2912yes—
339C22×D4C23×C2912yes—
340C23×C4—21no—
341C23×C4—21no—
342C23×C4D4×C2911yescharacteristic
343C23×C4D4×C2912yescomplemented
344C23×C4D4×C2912yescomplemented
345C23×C4C23×C2911yescharacteristic
346#123—48no—
347#120—28no—
348#120—44no—
349C4×D4—28no—
350C4×D4—28no—
351C4×D4—28no—
352C4×D4—28no—
353#117—24no—
354#117—24no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—24no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—24no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—24no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—22no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4D4×C2914yescomplemented
374C2×C22⋊C4C23×C2912yes—
375C2×C22⋊C4C23×C2914yes—
376C2×C22⋊C4C23×C2914yes—
377C2×C42—22no—
378#99—28no—
379#95—24no—
380#95—22no—
381C29#3302011yescharacteristic, direct product factor, Sylow
382C24—21no—
383C24—21no—
384C24—24no—
385C24—24no—
386C24—22no—
387C24—21no—
388C24—24no—
389C24—42no—
390C24—42no—
391C24—42no—
392C24—81no—
393C24—81no—
394C24—81no—
395C24C2×D4×C2911yescharacteristic
396C24C2×D4×C2912yes—
397C24C2×D4×C2911yescharacteristic
398C24C2×D4×C2912yes—
399C24C2×D4×C2912yes—
400C24C24×C2911yescharacteristic
401C2×D4—216no—
402C2×D4—216no—
403C2×D4—24no—
404C2×D4—24no—
405C2×D4—24no—
406C2×D4—24no—
407C2×D4—24no—
408C2×D4—28no—
409C2×D4—24no—
410C2×D4—42no—
411C2×D4—44no—
412C2×D4—44no—
413C2×D4—42no—
414C2×D4—44no—
415C2×D4—42no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—41no—
419C2×D4—44no—
420C2×D4—44no—
421C2×D4—82no—
422C2×D4#41×C2918yes—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—24no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—42no—
437C22×C4—44no—
438C22×C4—82no—
439C22×C4—82no—
440C22×C4—82no—
441C22×C4C2×D4×C2912yes—
442C22×C4C2×D4×C2914yes—
443C22×C4C2×D4×C2914yes—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—48no—
447C22⋊C4—28no—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—24no—
452C22⋊C4—28no—
453C22⋊C4—24no—
454C22⋊C4—44no—
455C22⋊C4—42no—
456C22⋊C4—48no—
457C22⋊C4—44no—
458C22⋊C4—44no—
459C22⋊C4—84no—
460C22⋊C4—82no—
461C22⋊C4—81no—
462C42—28no—
463C23—24no—
464C23—24no—
465C23—24no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—24no—
470C23—22no—
471C23—22no—
472C23—24no—
473C23—24no—
474C23—22no—
475C23—41no—
476C23—42no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—41no—
481C23—42no—
482C23—41no—
483C23—42no—
484C23—42no—
485C23—42no—
486C23—44no—
487C23—42no—
488C23—41no—
489C23—42no—
490C23—42no—
491C23—41no—
492C23—42no—
493C23—44no—
494C23—81no—
495C23—81no—
496C23—88no—
497C23—88no—
498C23—88no—
499C23C29×#12011yescharacteristic
500C23C29×#12012yes—
501C23C29×#12011yescharacteristic
502C23C29×#12314yescomplemented
503C23C22×D4×C2911yescharacteristic
504C23C22×D4×C2912yes—
505C23C2×#41×C2914yes—
506D4—216no—
507D4—216no—
508D4—48no—
509D4—44no—
510D4—44no—
511D4—88no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—44no—
523C2×C4—44no—
524C2×C4—41no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—42no—
529C2×C4—44no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—82no—
534C2×C4—82no—
535C2×C4—84no—
536C2×C4—84no—
537C2×C4C29×#12314yescomplemented
538C22—22no—
539C22—21no—
540C22—21no—
541C22—22no—
542C22—21no—
543C22—21no—
544C22—22no—
545C22—21no—
546C22—22no—
547C22—21no—
548C22—21no—
549C22—22no—
550C22—24no—
551C22—44no—
552C22—44no—
553C22—48no—
554C22—44no—
555C22—48no—
556C22—44no—
557C22—48no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22—82no—
562C22—82no—
563C22—84no—
564C22—82no—
565C22—84no—
566C22—84no—
567C22—81no—
568C22—81no—
569C22C29×B(4,𝔽2)12yes—
570C22C2×C29×#12011yescharacteristic
571C22C2×C29×#12312yes—
572C22C29×#52514yes—
573C4—24no—
574C4—42no—
575C4—44no—
576C4—44no—
577C4—82no—
578C4—84no—
579C2—22no—
580C2—24no—
581C2—22no—
582C2—41no—
583C2—42no—
584C2—44no—
585C2—82no—
586C2C29×#284911yescharacteristic
587C2C2×C29×B(4,𝔽2)11yescharacteristic
588C2C29×#302611yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC24C24×C29
prime radicalC29×#2403C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C25×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#518C2semidirect
2. C29×#2405C2semidirect
4. C29×#1889C2semidirect
5. C29×#1867C2semidirect
6. C29×#1819C2semidirect
7. C29×#1781C2semidirect
27. C29×#385C22semidirect
30. C29×#379C22semidirect
31. C29×#342C22semidirect
49. C23×C4×C29D4semidirect
50. C23×C4×C29D4semidirect
79. C2×C22⋊C4×C29D4semidirect
168. #33020C29direct (N × H)
208. C23×C29#123semidirect
243. C2×C4×C29#123semidirect
244. C2×#518C2×C29semidirect
245. #2405C2×C29semidirect
247. #1889C2×C29semidirect
248. #1867C2×C29semidirect
249. #1819C2×C29semidirect
250. #1781C2×C29semidirect
311. #385C22×C29semidirect
314. #379C22×C29semidirect
315. #342C22×C29semidirect
343. C23×C4D4×C29semidirect
344. C23×C4D4×C29semidirect
373. C2×C22⋊C4D4×C29semidirect
381. C29#33020direct (N × H)
502. C23C29×#123semidirect
537. C2×C4C29×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#5182
C29×#24052
C29×#24032
C29×#18892
C29×#18672
C29×#18192
C29×#17812
#3302029