Finite Group Databasebeta

← C29×#14629 #20309529

Subgroups — C29×#14629 #20309529

Order 7424.

1130 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#400C211yesmaximal, characteristic
2C2×C29×#389C211yesmaximal, characteristic
3C2×C29×#387C211yesmaximal, characteristic
4C29×#1445C211yesmaximal, characteristic
5C29×#1444C211yesmaximal, characteristic
6C29×#1444C212yesmaximal
7C29×#1443C212yesmaximal
8C29×#1442C212yesmaximal
9C29×#1442C212yesmaximal
10C29×#1441C211yesmaximal, characteristic
11C29×#1434C211yesmaximal, characteristic
12C22×C4⋊C4×C29C2211yescharacteristic
13C22×C4⋊C4×C29C2211yescharacteristic
14C22×C4⋊C4×C29C2211yescharacteristic
15C22×C4⋊C4×C29C2212yes—
16C22×C4⋊C4×C29C2211yescharacteristic
17C22×C4⋊C4×C29C2212yes—
18C22×C42×C29C2211yescharacteristic
19C29×#400C418yescomplemented
20C29×#389—24no—
21C29×#387—24no—
22C2×C29×#95C2211yescharacteristic
23C2×C29×#95C2211yescharacteristic
24C2×C29×#95C2211yescharacteristic
25C2×C29×#95C2212yes—
26C2×C29×#95C2211yescharacteristic
27C2×C29×#95C2211yescharacteristic
28C2×C29×#95C2212yes—
29C2×C29×#95C2212yes—
30C2×C29×#95C2212yes—
31C2×C29×#95C2212yes—
32C2×C29×#95C2212yes—
33C2×C29×#95C2212yes—
34C2×C29×#95C2212yes—
35C2×C29×#95C2211yescharacteristic
36C2×C29×#95C2212yes—
37C2×C29×#95C2212yes—
38C23×C4×C29C2312yes—
39C23×C4×C29C2311yescharacteristic
40C23×C4×C29C2311yescharacteristic
41C23×C4×C29C2312yes—
42C23×C4×C29C2311yescharacteristic
43C23×C4×C29C2312yes—
44C23×C4×C29C2311yescharacteristic
45C23×C4×C29C2312yes—
46C23×C4×C29C2311yescharacteristic
47C23×C4×C29C2311yescharacteristic
48C23×C4×C29C2311yescharacteristic
49C2×C4⋊C4×C29—22no—
50C2×C4⋊C4×C29—22no—
51C2×C4⋊C4×C29—22no—
52C2×C4⋊C4×C29—22no—
53C2×C4⋊C4×C29—22no—
54C2×C4⋊C4×C29—24no—
55C2×C4⋊C4×C29—22no—
56C2×C4⋊C4×C29—42no—
57C2×C4⋊C4×C29—42no—
58C2×C4⋊C4×C29—42no—
59C2×C4⋊C4×C29—42no—
60C2×C4⋊C4×C29—42no—
61C2×C4⋊C4×C29—42no—
62C2×C4⋊C4×C29—42no—
63C2×C4⋊C4×C29C2×C414yes—
64C2×C4⋊C4×C29C2×C414yes—
65C2×C42×C29—42no—
66C2×C42×C29D414yes—
67C29×#95—22no—
68C29×#95—22no—
69C29×#95—22no—
70C29×#95—22no—
71C29×#95—24no—
72C29×#95—22no—
73C29×#95—42no—
74C29×#95—42no—
75C29×#95—42no—
76C29×#95—42no—
77C29×#95—42no—
78C29×#95—42no—
79C29×#95—42no—
80C29×#95C2×C418yes—
81C29×#95C2×C418yes—
82C29×#95C2×C414yes—
83C24×C29C2411yescharacteristic
84C22×C4×C29—22no—
85C22×C4×C29—22no—
86C22×C4×C29—21no—
87C22×C4×C29—22no—
88C22×C4×C29—21no—
89C22×C4×C29—21no—
90C22×C4×C29—21no—
91C22×C4×C29—22no—
92C22×C4×C29—22no—
93C22×C4×C29—22no—
94C22×C4×C29—22no—
95C22×C4×C29—22no—
96C22×C4×C29—22no—
97C22×C4×C29—22no—
98C22×C4×C29—22no—
99C22×C4×C29—22no—
100C22×C4×C29—22no—
101C22×C4×C29—21no—
102C22×C4×C29—21no—
103C22×C4×C29—21no—
104C22×C4×C29—21no—
105C22×C4×C29—22no—
106C22×C4×C29—21no—
107C22×C4×C29—22no—
108C22×C4×C29—22no—
109C22×C4×C29—22no—
110C22×C4×C29—22no—
111C22×C4×C29—22no—
112C22×C4×C29—21no—
113C22×C4×C29—21no—
114C22×C4×C29—22no—
115C22×C4×C29—21no—
116C22×C4×C29—22no—
117C22×C4×C29—21no—
118C22×C4×C29—21no—
119C22×C4×C29—22no—
120C22×C4×C29—22no—
121C22×C4×C29—22no—
122C22×C4×C29—22no—
123C22×C4×C29—21no—
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—21no—
133C22×C4×C29—22no—
134C22×C4×C29—21no—
135C22×C4×C29—22no—
136C22×C4×C29—21no—
137C22×C4×C29—22no—
138C22×C4×C29—22no—
139C22×C4×C29—22no—
140C22×C4×C29C22×C412yes—
141C22×C4×C29C22×C412yes—
142C22×C4×C29C22×C414yes—
143C22×C4×C29C22×C414yes—
144C22×C4×C29C22×C412yes—
145C22×C4×C29C2×D412yes—
146C22×C4×C29C2×D412yes—
147C22×C4×C29C2×D412yes—
148C22×C4×C29#4112yes—
149C4⋊C4×C29—28no—
150C4⋊C4×C29—28no—
151C4⋊C4×C29—44no—
152C4⋊C4×C29—44no—
153C4⋊C4×C29—48no—
154C4⋊C4×C29—48no—
155C42×C29—44no—
156#14629C2911yesmaximal, characteristic, direct product factor, Sylow
157C23×C29C23×C411yescharacteristic
158C23×C29C22×D411yescharacteristic
159C23×C29C2×#4111yescharacteristic
160C23×C29H(5,𝔽2)12yes—
161C23×C29H(5,𝔽2)12yes—
162C23×C29H(5,𝔽2)11yescharacteristic
163C23×C292−1+411yescharacteristic
164C23×C292−1+411yescharacteristic
165C23×C292−1+412yes—
166C23×C292−1+411yescharacteristic
167C23×C292−1+412yes—
168C2×C4×C29—24no—
169C2×C4×C29—22no—
170C2×C4×C29—22no—
171C2×C4×C29—24no—
172C2×C4×C29—22no—
173C2×C4×C29—22no—
174C2×C4×C29—24no—
175C2×C4×C29—22no—
176C2×C4×C29—24no—
177C2×C4×C29—22no—
178C2×C4×C29—24no—
179C2×C4×C29—24no—
180C2×C4×C29—24no—
181C2×C4×C29—24no—
182C2×C4×C29—24no—
183C2×C4×C29—22no—
184C2×C4×C29—22no—
185C2×C4×C29—22no—
186C2×C4×C29—22no—
187C2×C4×C29—22no—
188C2×C4×C29—22no—
189C2×C4×C29—41no—
190C2×C4×C29—42no—
191C2×C4×C29—41no—
192C2×C4×C29—41no—
193C2×C4×C29—42no—
194C2×C4×C29—41no—
195C2×C4×C29—42no—
196C2×C4×C29—41no—
197C2×C4×C29—41no—
198C2×C4×C29—42no—
199C2×C4×C29—42no—
200C2×C4×C29—42no—
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—42no—
209C2×C4×C29—41no—
210C2×C4×C29—42no—
211C2×C4×C29—41no—
212C2×C4×C29—41no—
213C2×C4×C29—41no—
214C2×C4×C29—41no—
215C2×C4×C29—42no—
216C2×C4×C29—41no—
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×C4×C29—42no—
232C2×C4×C29C4×D414yes—
233C2×#400C2×C2911yescharacteristic
234C2×#389C2×C2911yescharacteristic
235C2×#387C2×C2911yescharacteristic
236#1445C2×C2911yescharacteristic
237#1444C2×C2911yescharacteristic
238#1444C2×C2912yes—
239#1443C2×C2912yes—
240#1442C2×C2912yes—
241#1442C2×C2912yes—
242#1441C2×C2911yescharacteristic
243#1434C2×C2911yescharacteristic
244C22×C29C2×C4×D411yescharacteristic
245C22×C29#51911yescharacteristic
246C22×C29#52012yes—
247C22×C29#52011yescharacteristic
248C22×C29#52012yes—
249C22×C29#53411yescharacteristic
250C22×C29#53511yescharacteristic
251C22×C29#53611yescharacteristic
252C22×C29#53611yescharacteristic
253C22×C29#53611yescharacteristic
254C22×C29#53711yescharacteristic
255C22×C29#53912yes—
256C22×C29#54111yescharacteristic
257C22×C29#54211yescharacteristic
258C22×C29#54212yes—
259C22×C29#56012yes—
260C22×C29#56212yes—
261C22×C29#56312yes—
262C22×C29#56312yes—
263C22×C29#56312yes—
264C22×C29#56312yes—
265C22×C29#56312yes—
266C22×C29#56412yes—
267C4×C29—24no—
268C4×C29—42no—
269C4×C29—42no—
270C4×C29—42no—
271C4×C29—44no—
272C4×C29—44no—
273C4×C29—42no—
274C4×C29—81no—
275C4×C29—82no—
276C4×C29—82no—
277C4×C29—81no—
278C22×C4⋊C4C22×C2911yescharacteristic
279C22×C4⋊C4C22×C2911yescharacteristic
280C22×C4⋊C4C22×C2911yescharacteristic
281C22×C4⋊C4C22×C2912yes—
282C22×C4⋊C4C22×C2911yescharacteristic
283C22×C4⋊C4C22×C2912yes—
284C22×C42C22×C2911yescharacteristic
285#400C4×C2918yescomplemented
286#389—24no—
287#387—24no—
288C2×#95C22×C2911yescharacteristic
289C2×#95C22×C2911yescharacteristic
290C2×#95C22×C2911yescharacteristic
291C2×#95C22×C2912yes—
292C2×#95C22×C2911yescharacteristic
293C2×#95C22×C2911yescharacteristic
294C2×#95C22×C2912yes—
295C2×#95C22×C2912yes—
296C2×#95C22×C2912yes—
297C2×#95C22×C2912yes—
298C2×#95C22×C2912yes—
299C2×#95C22×C2912yes—
300C2×#95C22×C2912yes—
301C2×#95C22×C2911yescharacteristic
302C2×#95C22×C2912yes—
303C2×#95C22×C2912yes—
304C2×C29#232211yescharacteristic
305C2×C29#232311yescharacteristic
306C2×C29#232611yescharacteristic
307C2×C29#238212yes—
308C2×C29#238312yes—
309C2×C29#281311yescharacteristic
310C2×C29#281711yescharacteristic
311C2×C29#282111yescharacteristic
312C2×C29#282211yescharacteristic
313C2×C29#283812yes—
314C2×C29#283912yes—
315C23×C4C23×C2911yescharacteristic
316C23×C4C23×C2912yes—
317C23×C4C23×C2911yescharacteristic
318C23×C4C23×C2912yes—
319C23×C4C23×C2911yescharacteristic
320C23×C4C23×C2912yes—
321C23×C4C23×C2911yescharacteristic
322C23×C4C23×C2912yes—
323C23×C4C23×C2911yescharacteristic
324C23×C4C23×C2911yescharacteristic
325C23×C4C23×C2911yescharacteristic
326C2×C4⋊C4—22no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—22no—
333C2×C4⋊C4—42no—
334C2×C4⋊C4—42no—
335C2×C4⋊C4—42no—
336C2×C4⋊C4—42no—
337C2×C4⋊C4—42no—
338C2×C4⋊C4—42no—
339C2×C4⋊C4—42no—
340C2×C4⋊C4C2×C4×C2914yes—
341C2×C4⋊C4C2×C4×C2914yes—
342C2×C42—42no—
343C2×C42D4×C2914yes—
344#95—22no—
345#95—22no—
346#95—22no—
347#95—22no—
348#95—24no—
349#95—22no—
350#95—42no—
351#95—42no—
352#95—42no—
353#95—42no—
354#95—42no—
355#95—42no—
356#95—42no—
357#95C2×C4×C2914yes—
358#95C2×C4×C2918yes—
359#95C2×C4×C2918yes—
360C29#1462911yescharacteristic, direct product factor, Sylow
361C24C24×C2911yescharacteristic
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
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—21no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4C22×C4×C2914yes—
419C22×C4C22×C4×C2912yes—
420C22×C4C22×C4×C2912yes—
421C22×C4C22×C4×C2914yes—
422C22×C4C22×C4×C2912yes—
423C22×C4C2×D4×C2912yes—
424C22×C4C2×D4×C2912yes—
425C22×C4C2×D4×C2912yes—
426C22×C4#41×C2912yes—
427C4⋊C4—28no—
428C4⋊C4—28no—
429C4⋊C4—44no—
430C4⋊C4—44no—
431C4⋊C4—48no—
432C4⋊C4—48no—
433C42—44no—
434C23C23×C4×C2911yescharacteristic
435C23C22×D4×C2911yescharacteristic
436C23C2×#41×C2911yescharacteristic
437C23C29×H(5,𝔽2)12yes—
438C23C29×H(5,𝔽2)12yes—
439C23C29×H(5,𝔽2)11yescharacteristic
440C23C29×2−1+411yescharacteristic
441C23C29×2−1+411yescharacteristic
442C23C29×2−1+412yes—
443C23C29×2−1+411yescharacteristic
444C23C29×2−1+412yes—
445C2×C4—24no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—24no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—24no—
454C2×C4—22no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—42no—
471C2×C4—41no—
472C2×C4—42no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
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—
509C2×C4C4×D4×C2914yes—
510C22C2×C4×D4×C2911yescharacteristic
511C22C29×#51911yescharacteristic
512C22C29×#52012yes—
513C22C29×#52011yescharacteristic
514C22C29×#52012yes—
515C22C29×#53411yescharacteristic
516C22C29×#53511yescharacteristic
517C22C29×#53611yescharacteristic
518C22C29×#53611yescharacteristic
519C22C29×#53611yescharacteristic
520C22C29×#53711yescharacteristic
521C22C29×#53912yes—
522C22C29×#54111yescharacteristic
523C22C29×#54211yescharacteristic
524C22C29×#54212yes—
525C22C29×#56012yes—
526C22C29×#56212yes—
527C22C29×#56312yes—
528C22C29×#56312yes—
529C22C29×#56312yes—
530C22C29×#56312yes—
531C22C29×#56312yes—
532C22C29×#56412yes—
533C4—24no—
534C4—42no—
535C4—42no—
536C4—42no—
537C4—42no—
538C4—44no—
539C4—44no—
540C4—82no—
541C4—81no—
542C4—81no—
543C4—82no—
544C2C29×#232211yescharacteristic
545C2C29×#232311yescharacteristic
546C2C29×#232611yescharacteristic
547C2C29×#238212yes—
548C2C29×#238312yes—
549C2C29×#281311yescharacteristic
550C2C29×#281711yescharacteristic
551C2C29×#282111yescharacteristic
552C2C29×#282211yescharacteristic
553C2C29×#283812yes—
554C2C29×#283912yes—
subgroupG/H
center, socle, prime radicalC24×C29C24
commutatorC23C23×C4×C29
Frattini, cosocleC24C24×C29
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
19. C29×#400C4semidirect
156. #14629C29direct (N × H)
285. #400C4×C29semidirect
360. C29#14629direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4002
C2×C29×#3892
C2×C29×#3872
C29×#14452
C29×#14442
C29×#14432
C29×#14422
C29×#14412
C29×#14342
#1462929