Finite Group Databasebeta

← C29×#14652 #20309552

Subgroups — C29×#14652 #20309552

Order 7424.

1226 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#397C211yesmaximal, characteristic
2C29×#1442C212yesmaximal, complemented
3C29×#1442C212yesmaximal, complemented
4C29×#1441C212yesmaximal, complemented
5C29×#1440C211yesmaximal, characteristic
6C29×#1439C212yesmaximal
7C29×#1439C212yesmaximal
8C29×#1437C211yesmaximal, characteristic
9C29×#1436C212yesmaximal, complemented
10C22×C4⋊C4×C29C2212yes—
11C22×C4⋊C4×C29C2212yes—
12C22×C4⋊C4×C29C2211yescharacteristic
13C22×C22⋊C4×C29C2212yes—
14C22×C22⋊C4×C29C2211yescharacteristic
15C22×C22⋊C4×C29C2211yescharacteristic
16C22×C22⋊C4×C29C2211yescharacteristic
17C22×C22⋊C4×C29C2212yes—
18C22×C42×C29C2211yescharacteristic
19C29×#397C418yescomplemented
20C2×C29×#95C2212yes—
21C2×C29×#95C2212yes—
22C2×C29×#95C2212yes—
23C2×C29×#95C2212yes—
24C2×C29×#95C2212yes—
25C2×C29×#95C2211yescharacteristic
26C2×C29×#95C2212yes—
27C2×C29×#95C2212yes—
28C2×C29×#95C2212yes—
29C2×C29×#95C2212yes—
30C2×C29×#95C2212yes—
31C2×C29×#95C2211yescharacteristic
32C25×C29C2311yescharacteristic
33C23×C4×C29C2312yes—
34C23×C4×C29C2312yes—
35C23×C4×C29C2312yes—
36C23×C4×C29C2311yescharacteristic
37C23×C4×C29C2312yes—
38C23×C4×C29C2311yescharacteristic
39C23×C4×C29C2312yes—
40C23×C4×C29C2312yes—
41C2×C4⋊C4×C29—24no—
42C2×C4⋊C4×C29—41no—
43C2×C4⋊C4×C29—41no—
44C2×C4⋊C4×C29—42no—
45C2×C4⋊C4×C29—42no—
46C2×C4⋊C4×C29—42no—
47C2×C4⋊C4×C29—42no—
48C2×C4⋊C4×C29—42no—
49C2×C4⋊C4×C29C2×C414yes—
50C2×C22⋊C4×C29—24no—
51C2×C22⋊C4×C29—41no—
52C2×C22⋊C4×C29—42no—
53C2×C22⋊C4×C29—41no—
54C2×C22⋊C4×C29—42no—
55C2×C22⋊C4×C29—42no—
56C2×C22⋊C4×C29—42no—
57C2×C22⋊C4×C29—41no—
58C2×C22⋊C4×C29—42no—
59C2×C22⋊C4×C29—41no—
60C2×C22⋊C4×C29—42no—
61C2×C22⋊C4×C29C2×C414yes—
62C2×C22⋊C4×C29C2×C418yes—
63C2×C42×C29—41no—
64C2×C42×C29—42no—
65C29×#95—24no—
66C29×#95—42no—
67C29×#95—42no—
68C29×#95—42no—
69C29×#95—42no—
70C29×#95—42no—
71C29×#95—41no—
72C29×#95—42no—
73C29×#95—42no—
74C29×#95—42no—
75C29×#95C2×C418yes—
76C29×#95C2×C414yes—
77C24×C29—22no—
78C24×C29—22no—
79C24×C29—21no—
80C24×C29—21no—
81C24×C29—22no—
82C24×C29—22no—
83C24×C29—22no—
84C24×C29—22no—
85C24×C29C22×C412yes—
86C24×C29C2411yescharacteristic
87C22×C4×C29—22no—
88C22×C4×C29—22no—
89C22×C4×C29—21no—
90C22×C4×C29—22no—
91C22×C4×C29—22no—
92C22×C4×C29—22no—
93C22×C4×C29—22no—
94C22×C4×C29—21no—
95C22×C4×C29—21no—
96C22×C4×C29—22no—
97C22×C4×C29—22no—
98C22×C4×C29—22no—
99C22×C4×C29—22no—
100C22×C4×C29—21no—
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—22no—
111C22×C4×C29—22no—
112C22×C4×C29—22no—
113C22×C4×C29—22no—
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×C29C22×C414yes—
135C22×C4×C29C22×C412yes—
136C22×C4×C29C22×C412yes—
137C22×C4×C29C22×C414yes—
138C22×C4×C29#4114yes—
139C4⋊C4×C29—44no—
140C4⋊C4×C29—48no—
141C4⋊C4×C29—48no—
142C22⋊C4×C29—44no—
143C22⋊C4×C29—48no—
144C22⋊C4×C29—48no—
145C22⋊C4×C29—44no—
146C22⋊C4×C29—44no—
147C42×C29—44no—
148#14652C2911yesmaximal, characteristic, direct product factor, Sylow
149C23×C29—22no—
150C23×C29—22no—
151C23×C29—22no—
152C23×C29—24no—
153C23×C29—24no—
154C23×C29—42no—
155C23×C29—42no—
156C23×C29—42no—
157C23×C29—42no—
158C23×C29—42no—
159C23×C29—42no—
160C23×C29—41no—
161C23×C29—42no—
162C23×C29—41no—
163C23×C29—42no—
164C23×C29—42no—
165C23×C29—42no—
166C23×C29—42no—
167C23×C29—42no—
168C23×C29—41no—
169C23×C29—41no—
170C23×C29C23×C411yescharacteristic
171C23×C29C2×#4112yes—
172C23×C29H(5,𝔽2)11yescharacteristic
173C23×C29H(5,𝔽2)12yes—
174C23×C29H(5,𝔽2)11yescharacteristic
175C23×C29H(5,𝔽2)12yes—
176C23×C29H(5,𝔽2)12yes—
177C23×C292−1+412yes—
178C23×C292−1+412yes—
179C2×C4×C29—24no—
180C2×C4×C29—22no—
181C2×C4×C29—24no—
182C2×C4×C29—24no—
183C2×C4×C29—22no—
184C2×C4×C29—24no—
185C2×C4×C29—24no—
186C2×C4×C29—24no—
187C2×C4×C29—24no—
188C2×C4×C29—24no—
189C2×C4×C29—24no—
190C2×C4×C29—24no—
191C2×C4×C29—24no—
192C2×C4×C29—42no—
193C2×C4×C29—42no—
194C2×C4×C29—42no—
195C2×C4×C29—42no—
196C2×C4×C29—42no—
197C2×C4×C29—42no—
198C2×C4×C29—41no—
199C2×C4×C29—42no—
200C2×C4×C29—41no—
201C2×C4×C29—42no—
202C2×C4×C29—42no—
203C2×C4×C29—42no—
204C2×C4×C29—42no—
205C2×C4×C29—42no—
206C2×C4×C29—42no—
207C2×C4×C29—42no—
208C2×C4×C29—41no—
209C2×C4×C29—41no—
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—42no—
218C2×C4×C29—42no—
219C2×C4×C29—42no—
220C2×C4×C29—42no—
221C2×C4×C29—42no—
222C2×C4×C29—42no—
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×#397C2×C2911yescharacteristic
232#1442C2×C2912yescomplemented
233#1442C2×C2912yescomplemented
234#1441C2×C2912yescomplemented
235#1440C2×C2911yescharacteristic
236#1439C2×C2912yes—
237#1439C2×C2912yes—
238#1437C2×C2911yescharacteristic
239#1436C2×C2912yescomplemented
240C22×C29—42no—
241C22×C29—44no—
242C22×C29—44no—
243C22×C29—42no—
244C22×C29—42no—
245C22×C29—82no—
246C22×C29—82no—
247C22×C29—82no—
248C22×C29—82no—
249C22×C29C4×#4111yescharacteristic
250C22×C29#51811yescharacteristic
251C22×C29#51811yescharacteristic
252C22×C29#52012yes—
253C22×C29#52012yes—
254C22×C29#53812yes—
255C22×C29#53812yes—
256C22×C29#53912yes—
257C22×C29#54012yes—
258C22×C29#54112yes—
259C22×C29#54212yes—
260C22×C29#56012yes—
261C22×C29#56011yescharacteristic
262C22×C29H(3,𝔽4)11yescharacteristic
263C22×C29#56212yes—
264C22×C29#56212yes—
265C22×C29#56212yes—
266C22×C29#56212yes—
267C22×C29#56311yescharacteristic
268C22×C29#56312yes—
269C22×C29#56311yescharacteristic
270C4×C29—44no—
271C4×C29—44no—
272C4×C29—42no—
273C4×C29—44no—
274C4×C29—42no—
275C4×C29—82no—
276C4×C29—82no—
277C4×C29—82no—
278C22×C4⋊C4C22×C2912yes—
279C22×C4⋊C4C22×C2912yes—
280C22×C4⋊C4C22×C2911yescharacteristic
281C22×C22⋊C4C22×C2912yes—
282C22×C22⋊C4C22×C2911yescharacteristic
283C22×C22⋊C4C22×C2911yescharacteristic
284C22×C22⋊C4C22×C2911yescharacteristic
285C22×C22⋊C4C22×C2912yes—
286C22×C42C22×C2911yescharacteristic
287#397C4×C2918yescomplemented
288C2×#95C22×C2912yes—
289C2×#95C22×C2912yes—
290C2×#95C22×C2912yes—
291C2×#95C22×C2912yes—
292C2×#95C22×C2912yes—
293C2×#95C22×C2911yescharacteristic
294C2×#95C22×C2912yes—
295C2×#95C22×C2912yes—
296C2×#95C22×C2912yes—
297C2×#95C22×C2912yes—
298C2×#95C22×C2912yes—
299C2×#95C22×C2911yescharacteristic
300C2×C29—82no—
301C2×C29#233311yescharacteristic
302C2×C29#233412yes—
303C2×C29#237612yes—
304C2×C29#237611yescharacteristic
305C2×C29#237911yescharacteristic
306C2×C29#282412yes—
307C2×C29#282912yes—
308C2×C29#283112yes—
309C2×C29#283612yes—
310C25C23×C2911yescharacteristic
311C23×C4C23×C2912yes—
312C23×C4C23×C2912yes—
313C23×C4C23×C2912yes—
314C23×C4C23×C2912yes—
315C23×C4C23×C2911yescharacteristic
316C23×C4C23×C2912yes—
317C23×C4C23×C2911yescharacteristic
318C23×C4C23×C2912yes—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—41no—
321C2×C4⋊C4—41no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4C2×C4×C2914yes—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—42no—
330C2×C22⋊C4—41no—
331C2×C22⋊C4—41no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—42no—
334C2×C22⋊C4—42no—
335C2×C22⋊C4—41no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—41no—
339C2×C22⋊C4C2×C4×C2914yes—
340C2×C22⋊C4C2×C4×C2918yes—
341C2×C42—42no—
342C2×C42—41no—
343#95—24no—
344#95—42no—
345#95—42no—
346#95—42no—
347#95—42no—
348#95—42no—
349#95—41no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95C2×C4×C2918yes—
354#95C2×C4×C2914yes—
355C29#1465211yescharacteristic, direct product factor, Sylow
356C24—22no—
357C24—22no—
358C24—21no—
359C24—21no—
360C24—22no—
361C24—22no—
362C24—22no—
363C24—22no—
364C24C22×C4×C2912yes—
365C24C24×C2911yescharacteristic
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—21no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
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—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4C22×C4×C2914yes—
414C22×C4C22×C4×C2912yes—
415C22×C4C22×C4×C2914yes—
416C22×C4C22×C4×C2912yes—
417C22×C4#41×C2914yes—
418C4⋊C4—44no—
419C4⋊C4—48no—
420C4⋊C4—48no—
421C22⋊C4—44no—
422C22⋊C4—48no—
423C22⋊C4—48no—
424C22⋊C4—44no—
425C22⋊C4—44no—
426C42—44no—
427C23—22no—
428C23—22no—
429C23—22no—
430C23—24no—
431C23—24no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—41no—
439C23—42no—
440C23—41no—
441C23—42no—
442C23—42no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—41no—
447C23—41no—
448C23C23×C4×C2911yescharacteristic
449C23C2×#41×C2912yes—
450C23C29×H(5,𝔽2)11yescharacteristic
451C23C29×H(5,𝔽2)12yes—
452C23C29×H(5,𝔽2)11yescharacteristic
453C23C29×H(5,𝔽2)12yes—
454C23C29×H(5,𝔽2)12yes—
455C23C29×2−1+412yes—
456C23C29×2−1+412yes—
457C2×C4—24no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—41no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C22—42no—
510C22—44no—
511C22—44no—
512C22—42no—
513C22—42no—
514C22—82no—
515C22—82no—
516C22—82no—
517C22—82no—
518C22C4×#41×C2911yescharacteristic
519C22C29×#51811yescharacteristic
520C22C29×#51811yescharacteristic
521C22C29×#52012yes—
522C22C29×#52012yes—
523C22C29×#53812yes—
524C22C29×#53812yes—
525C22C29×#53912yes—
526C22C29×#54012yes—
527C22C29×#54112yes—
528C22C29×#54212yes—
529C22C29×#56012yes—
530C22C29×#56011yescharacteristic
531C22C29×H(3,𝔽4)11yescharacteristic
532C22C29×#56212yes—
533C22C29×#56212yes—
534C22C29×#56212yes—
535C22C29×#56212yes—
536C22C29×#56311yescharacteristic
537C22C29×#56312yes—
538C22C29×#56311yescharacteristic
539C4—44no—
540C4—44no—
541C4—42no—
542C4—44no—
543C4—42no—
544C4—82no—
545C4—82no—
546C4—82no—
547C2—82no—
548C2C29×#233311yescharacteristic
549C2C29×#233412yes—
550C2C29×#237612yes—
551C2C29×#237611yescharacteristic
552C2C29×#237911yescharacteristic
553C2C29×#282412yes—
554C2C29×#282912yes—
555C2C29×#283112yes—
556C2C29×#283612yes—
subgroupG/H
center, socleC24×C29C24
commutatorC23C23×C4×C29
Frattini, cosocleC24C24×C29
prime radicalC25×C29C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#1442C2semidirect
3. C29×#1442C2semidirect
4. C29×#1441C2semidirect
9. C29×#1436C2semidirect
19. C29×#397C4semidirect
148. #14652C29direct (N × H)
232. #1442C2×C29semidirect
233. #1442C2×C29semidirect
234. #1441C2×C29semidirect
239. #1436C2×C29semidirect
287. #397C4×C29semidirect
355. C29#14652direct (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
C29×#14422
C29×#14412
C29×#14402
C29×#14392
C29×#14372
C29×#14362
#1465229