Finite Group Databasebeta

← C29×#9083 #20303983

Subgroups — C29×#9083 #20303983

Order 7424.

1100 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#407C211yesmaximal, characteristic, complemented
2C2×C29×#386C211yesmaximal, characteristic
3C29×#1779C211yesmaximal, characteristic, complemented
4C2×C29×#323C212yesmaximal, complemented
5C29×#1280C212yesmaximal, complemented
6C23×D4×C29C411yescharacteristic
7C24×C4×C29C2211yescharacteristic
8C22×M16×C29—21no—
9C22×C22⋊C4×C29C411yescharacteristic
10C22×C22⋊C4×C29C411yescharacteristic
11C22×C22⋊C4×C29C2211yescharacteristic
12C29×#407—24no—
13C2×C29×C22⋊C8—21no—
14C2×C29×C22⋊C8—21no—
15C2×C29×C22⋊C8—21no—
16C2×C29×C22⋊C8C2212yes—
17C2×C29×C22⋊C8C2212yes—
18C29×#386—21no—
19C29×#386—21no—
20C29×#386—21no—
21C29×#386—21no—
22C2×C29×#95C411yescharacteristic
23C2×C29×#95C2211yescharacteristic
24C29×#323—24no—
25C25×C29C2×C411yescharacteristic
26C25×C29C2×C411yescharacteristic
27C22×D4×C29—21no—
28C22×D4×C29—21no—
29C22×D4×C29—22no—
30C22×D4×C29—22no—
31C22×D4×C29—42no—
32C22×D4×C29—42no—
33C23×C4×C29—22no—
34C23×C4×C29—22no—
35C23×C4×C29—42no—
36C23×C4×C29—42no—
37C23×C4×C29C2×C411yescharacteristic
38C23×C4×C29C2×C411yescharacteristic
39C23×C4×C29C2×C411yescharacteristic
40C23×C4×C29C2×C411yescharacteristic
41C23×C4×C29D411yescharacteristic
42C23×C4×C29D411yescharacteristic
43C23×C4×C29D411yescharacteristic
44C23×C4×C29D411yescharacteristic
45C23×C4×C29C2311yescharacteristic
46C2×M16×C29—24no—
47C2×M16×C29—42no—
48C2×M16×C29—42no—
49C22×C8×C29—22no—
50C22×C8×C29—22no—
51C2×C22⋊C4×C29—21no—
52C2×C22⋊C4×C29—21no—
53C2×C22⋊C4×C29—21no—
54C2×C22⋊C4×C29—21no—
55C2×C22⋊C4×C29—22no—
56C2×C22⋊C4×C29—21no—
57C2×C22⋊C4×C29—21no—
58C2×C22⋊C4×C29—22no—
59C2×C22⋊C4×C29—42no—
60C2×C22⋊C4×C29—42no—
61C29×C22⋊C8—24no—
62C29×C22⋊C8—22no—
63C29×C22⋊C8—22no—
64C29×C22⋊C8—22no—
65C29×C22⋊C8—42no—
66C29×C22⋊C8—42no—
67C29×C22⋊C8D414yescomplemented
68C29×#95—21no—
69C29×#95—21no—
70C29×#95—21no—
71C29×#95—21no—
72C24×C29—22no—
73C24×C29—22no—
74C24×C29—21no—
75C24×C29—21no—
76C24×C29—21no—
77C24×C29—22no—
78C24×C29—21no—
79C24×C29—22no—
80C24×C29—22no—
81C24×C29—22no—
82C24×C29—41no—
83C24×C29—41no—
84C24×C29—41no—
85C24×C29—41no—
86C24×C29—41no—
87C24×C29—41no—
88C24×C29C22⋊C411yescharacteristic
89C24×C29C22⋊C411yescharacteristic
90C24×C29M1612yescomplemented
91C24×C29C22×C411yescharacteristic
92C2×D4×C29—24no—
93C2×D4×C29—24no—
94C2×D4×C29—48no—
95C2×D4×C29—42no—
96C2×D4×C29—42no—
97C2×D4×C29—48no—
98C2×D4×C29—42no—
99C2×D4×C29—42no—
100C22×C4×C29—22no—
101C22×C4×C29—22no—
102C22×C4×C29—21no—
103C22×C4×C29—21no—
104C22×C4×C29—22no—
105C22×C4×C29—21no—
106C22×C4×C29—22no—
107C22×C4×C29—21no—
108C22×C4×C29—22no—
109C22×C4×C29—22no—
110C22×C4×C29—21no—
111C22×C4×C29—22no—
112C22×C4×C29—22no—
113C22×C4×C29—21no—
114C22×C4×C29—21no—
115C22×C4×C29—21no—
116C22×C4×C29—22no—
117C22×C4×C29—22no—
118C22×C4×C29—41no—
119C22×C4×C29—41no—
120C22×C4×C29—41no—
121C22×C4×C29—41no—
122C22×C4×C29—41no—
123C22×C4×C29—41no—
124C22×C4×C29—41no—
125C22×C4×C29—48no—
126C22×C4×C29—48no—
127C22×C4×C29—41no—
128C22×C4×C29—41no—
129C22×C4×C29—41no—
130C22×C4×C29—41no—
131C22×C4×C29—41no—
132C22×C4×C29—41no—
133C22×C4×C29C22⋊C411yescharacteristic
134C22×C4×C29C22⋊C411yescharacteristic
135C22×C4×C29M1612yescomplemented
136C22×C4×C29C2×D411yescharacteristic
137C22×C4×C29C2×D411yescharacteristic
138C22×C4×C29C2×D412yes—
139C22×C4×C29#4112yes—
140M16×C29—48no—
141C2×C8×C29—24no—
142C2×C8×C29—42no—
143C2×C8×C29—42no—
144C2×C8×C29—42no—
145C2×C8×C29—42no—
146C2×C8×C29—42no—
147C22⋊C4×C29—42no—
148C22⋊C4×C29—42no—
149C22⋊C4×C29—42no—
150C22⋊C4×C29—42no—
151C22⋊C4×C29—41no—
152C22⋊C4×C29—42no—
153C22⋊C4×C29—41no—
154#9083C2911yesmaximal, characteristic, direct product factor, Sylow
155C23×C29—21no—
156C23×C29—21no—
157C23×C29—21no—
158C23×C29—21no—
159C23×C29—24no—
160C23×C29—24no—
161C23×C29—21no—
162C23×C29—21no—
163C23×C29—21no—
164C23×C29—21no—
165C23×C29—21no—
166C23×C29—21no—
167C23×C29—21no—
168C23×C29—21no—
169C23×C29—21no—
170C23×C29—21no—
171C23×C29—21no—
172C23×C29—21no—
173C23×C29—22no—
174C23×C29—24no—
175C23×C29—44no—
176C23×C29—44no—
177C23×C29—44no—
178C23×C29—44no—
179C23×C29—42no—
180C23×C29—42no—
181C23×C29—42no—
182C23×C29—42no—
183C23×C29—42no—
184C23×C29—42no—
185C23×C29—42no—
186C23×C29—42no—
187C23×C29—41no—
188C23×C29—41no—
189C23×C29—41no—
190C23×C29—41no—
191C23×C29—41no—
192C23×C29—41no—
193C23×C29—42no—
194C23×C29—82no—
195C23×C29—82no—
196C23×C29—82no—
197C23×C29—82no—
198C23×C29#9912yes—
199C23×C29#10012yes—
200C23×C29C2×C22⋊C411yescharacteristic
201C23×C29C4×D412yes—
202C23×C29C2×M1611yescharacteristic
203C23×C29C2×M1611yescharacteristic
204C23×C29#13112yes—
205D4×C29—48no—
206D4×C29—48no—
207C2×C4×C29—24no—
208C2×C4×C29—24no—
209C2×C4×C29—21no—
210C2×C4×C29—21no—
211C2×C4×C29—21no—
212C2×C4×C29—21no—
213C2×C4×C29—21no—
214C2×C4×C29—21no—
215C2×C4×C29—21no—
216C2×C4×C29—22no—
217C2×C4×C29—21no—
218C2×C4×C29—21no—
219C2×C4×C29—42no—
220C2×C4×C29—42no—
221C2×C4×C29—44no—
222C2×C4×C29—44no—
223C2×C4×C29—44no—
224C2×C4×C29—42no—
225C2×C4×C29—42no—
226C2×C4×C29—42no—
227C2×C4×C29—41no—
228C2×C4×C29—41no—
229C2×C4×C29—42no—
230C2×C4×C29—41no—
231C2×C4×C29—41no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
236C2×C4×C29—82no—
237C2×C4×C29—82no—
238C2×C4×C29#9912yes—
239C2×C4×C29#12011yescharacteristic
240C2×C4×C29#12112yes—
241C2×C4×C29#12311yescharacteristic
242C8×C29—44no—
243C8×C29—82no—
244C2×#407C2×C2911yescharacteristic, complemented
245C2×#386C2×C2911yescharacteristic
246#1779C2×C2911yescharacteristic, complemented
247C2×#323C2×C2912yescomplemented
248#1280C2×C2912yescomplemented
249C22×C29—22no—
250C22×C29—22no—
251C22×C29—21no—
252C22×C29—21no—
253C22×C29—21no—
254C22×C29—21no—
255C22×C29—22no—
256C22×C29—22no—
257C22×C29—22no—
258C22×C29—22no—
259C22×C29—22no—
260C22×C29—22no—
261C22×C29—22no—
262C22×C29—22no—
263C22×C29—48no—
264C22×C29—48no—
265C22×C29—41no—
266C22×C29—41no—
267C22×C29—41no—
268C22×C29—41no—
269C22×C29—41no—
270C22×C29—41no—
271C22×C29—41no—
272C22×C29—41no—
273C22×C29—42no—
274C22×C29—42no—
275C22×C29—42no—
276C22×C29—84no—
277C22×C29—84no—
278C22×C29—81no—
279C22×C29—81no—
280C22×C29—81no—
281C22×C29—81no—
282C22×C29#38611yescharacteristic
283C22×C29#40711yescharacteristic
284C22×C29#40811yescharacteristic
285C22×C29C2×#9911yescharacteristic
286C22×C29C2×#9911yescharacteristic
287C22×C29C2×#10011yescharacteristic
288C22×C29#41311yescharacteristic
289C22×C29#43512yes—
290C22×C29#43612yes—
291C4×C29—21no—
292C4×C29—22no—
293C4×C29—22no—
294C4×C29—21no—
295C4×C29—41no—
296C4×C29—42no—
297C4×C29—81no—
298C4×C29—81no—
299C23×D4C4×C2911yescharacteristic
300C24×C4C22×C2911yescharacteristic
301C22×M16—21no—
302C22×C22⋊C4C4×C2911yescharacteristic
303C22×C22⋊C4C4×C2911yescharacteristic
304C22×C22⋊C4C22×C2911yescharacteristic
305#407—24no—
306C2×C22⋊C8—21no—
307C2×C22⋊C8—21no—
308C2×C22⋊C8—21no—
309C2×C22⋊C8C22×C2912yes—
310C2×C22⋊C8C22×C2912yes—
311#386—21no—
312#386—21no—
313#386—21no—
314#386—21no—
315C2×#95C4×C2911yescharacteristic
316C2×#95C22×C2911yescharacteristic
317#323—24no—
318C2×C29—22no—
319C2×C29—22no—
320C2×C29—42no—
321C2×C29—42no—
322C2×C29—82no—
323C2×C29#146211yescharacteristic
324C2×C29#146511yescharacteristic
325C2×C29#146811yescharacteristic
326C2×C29#147111yescharacteristic
327C2×C29#187011yescharacteristic
328C2×C29#189811yescharacteristic
329C2×C29#190011yescharacteristic
330C25C2×C4×C2911yescharacteristic
331C25C2×C4×C2911yescharacteristic
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—42no—
337C22×D4—42no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—42no—
341C23×C4—42no—
342C23×C4C2×C4×C2911yescharacteristic
343C23×C4C2×C4×C2911yescharacteristic
344C23×C4C2×C4×C2911yescharacteristic
345C23×C4C2×C4×C2911yescharacteristic
346C23×C4D4×C2911yescharacteristic
347C23×C4D4×C2911yescharacteristic
348C23×C4D4×C2911yescharacteristic
349C23×C4D4×C2911yescharacteristic
350C23×C4C23×C2911yescharacteristic
351C2×M16—24no—
352C2×M16—42no—
353C2×M16—42no—
354C22×C8—22no—
355C22×C8—22no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C22⋊C8—24no—
367C22⋊C8—22no—
368C22⋊C8—22no—
369C22⋊C8—22no—
370C22⋊C8—42no—
371C22⋊C8—42no—
372C22⋊C8D4×C2914yescomplemented
373#95—21no—
374#95—21no—
375#95—21no—
376#95—21no—
377C29#908311yescharacteristic, direct product factor, Sylow
378C24—21no—
379C24—21no—
380C24—22no—
381C24—22no—
382C24—21no—
383C24—22no—
384C24—21no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24—41no—
394C24C22⋊C4×C2911yescharacteristic
395C24C22⋊C4×C2911yescharacteristic
396C24M16×C2912yescomplemented
397C24C22×C4×C2911yescharacteristic
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—48no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—48no—
404C2×D4—42no—
405C2×D4—42no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—48no—
432C22×C4—48no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4C22⋊C4×C2911yescharacteristic
440C22×C4C22⋊C4×C2911yescharacteristic
441C22×C4M16×C2912yescomplemented
442C22×C4C2×D4×C2911yescharacteristic
443C22×C4C2×D4×C2911yescharacteristic
444C22×C4C2×D4×C2912yes—
445C22×C4#41×C2912yes—
446M16—48no—
447C2×C8—24no—
448C2×C8—42no—
449C2×C8—42no—
450C2×C8—42no—
451C2×C8—42no—
452C2×C8—42no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—42no—
456C22⋊C4—41no—
457C22⋊C4—42no—
458C22⋊C4—41no—
459C22⋊C4—42no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—24no—
465C23—24no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—22no—
479C23—24no—
480C23—44no—
481C23—44no—
482C23—44no—
483C23—44no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—82no—
500C23—82no—
501C23—82no—
502C23—82no—
503C23C29×#9912yes—
504C23C29×#10012yes—
505C23C2×C22⋊C4×C2911yescharacteristic
506C23C4×D4×C2912yes—
507C23C2×M16×C2911yescharacteristic
508C23C2×M16×C2911yescharacteristic
509C23C29×#13112yes—
510D4—48no—
511D4—48no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4C29×#9912yes—
544C2×C4C29×#12011yescharacteristic
545C2×C4C29×#12112yes—
546C2×C4C29×#12311yescharacteristic
547C8—44no—
548C8—82no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—48no—
564C22—48no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—84no—
577C22—84no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22C29×#38611yescharacteristic
583C22C29×#40711yescharacteristic
584C22C29×#40811yescharacteristic
585C22C2×C29×#9911yescharacteristic
586C22C2×C29×#9911yescharacteristic
587C22C2×C29×#10011yescharacteristic
588C22C29×#41311yescharacteristic
589C22C29×#43512yes—
590C22C29×#43612yes—
591C4—21no—
592C4—22no—
593C4—21no—
594C4—22no—
595C4—42no—
596C4—41no—
597C4—81no—
598C4—81no—
599C2—22no—
600C2—22no—
601C2—42no—
602C2—42no—
603C2—82no—
604C2C29×#146211yescharacteristic
605C2C29×#146511yescharacteristic
606C2C29×#146811yescharacteristic
607C2C29×#147111yescharacteristic
608C2C29×#187011yescharacteristic
609C2C29×#189811yescharacteristic
610C2C29×#190011yescharacteristic
subgroupG/H
center, socleC23×C29C2×C22⋊C4
commutatorC24C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC23×D4×C29C4
LCSG ▷ C24 ▷ C2 ▷ 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. C29×#1779C2semidirect
4. C2×C29×#323C2semidirect
5. C29×#1280C2semidirect
67. C29×C22⋊C8D4semidirect
90. C24×C29M16semidirect
135. C22×C4×C29M16semidirect
154. #9083C29direct (N × H)
244. C2×#407C2×C29semidirect
246. #1779C2×C29semidirect
247. C2×#323C2×C29semidirect
248. #1280C2×C29semidirect
372. C22⋊C8D4×C29semidirect
377. C29#9083direct (N × H)
396. C24M16×C29semidirect
441. C22×C4M16×C29semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#4072
C2×C29×#3862
C29×#17792
C2×C29×#3232
C29×#12802
#908329