Finite Group Databasebeta

← C29×#32996 #20327896

Subgroups — C29×#32996 #20327896

Order 7424.

1382 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#520C211yesmaximal, characteristic, complemented
2C29×#3094C211yesmaximal, characteristic, complemented
3C29×#3006C211yesmaximal, characteristic
4C29×#2501C211yesmaximal, characteristic, complemented
5C29×#1883C214yesmaximal, complemented
6C29×#1859C214yesmaximal, complemented
7C29×#1826C211yesmaximal, characteristic, complemented
8C29×#1821C211yesmaximal, characteristic, complemented
9C29×#1789C211yesmaximal, characteristic, complemented
10C22×#41×C29C2211yescharacteristic
11C2×C29×AGL(1,ℤ/8)C2212yes—
12C2×C29×#123—22no—
13C2×C29×#121C2211yescharacteristic
14C29×#520—22no—
15C29×#520—22no—
16C29×#520—22no—
17C29×#520C2214yes—
18C2×C4×Q8×C29—21no—
19C2×C4×D4×C29—21no—
20C2×C4×D4×C29—22no—
21C2×C29×#117—21no—
22C2×C29×#117C2211yescharacteristic
23C22×C4⋊C4×C29—21no—
24C22×C4⋊C4×C29C2211yescharacteristic
25C29×#482—22no—
26C29×#481—21no—
27C29×#480—21no—
28C29×#449—22no—
29C29×#448—21no—
30C29×#447—21no—
31C29×#428C2212yescomplemented
32C2×C29×#104C2214yes—
33C29×#418C2212yescomplemented
34C29×#417C2212yes—
35C29×#407C2211yescharacteristic
36C29×#407C2211yescharacteristic
37C29×#399—22no—
38C29×#390C2212yescomplemented
39C29×#384C2212yescomplemented
40C4×C22⋊C4×C29C2211yescharacteristic
41C29×#343C2214yescomplemented
42C29×#339C2214yescomplemented
43C2×#41×C29—28no—
44C2×#41×C29—21no—
45C2×#41×C29—21no—
46C2×#41×C29D412yes—
47C2×#41×C29C2312yes—
48C22×Q8×C29D411yescharacteristic
49C22×D4×C29—21no—
50C22×D4×C29—21no—
51C22×D4×C29D411yescharacteristic
52C22×D4×C29C2311yescharacteristic
53C23×C4×C29—21no—
54C23×C4×C29—22no—
55C23×C4×C29D412yes—
56C23×C4×C29C2311yescharacteristic
57C29×AGL(1,ℤ/8)—28no—
58C2×SD16×C29—22no—
59C2×D8×C29—22no—
60C2×M16×C29C2312yes—
61C2×M16×C29C2312yes—
62C29×#123—48no—
63C29×#121—21no—
64C29×#121—21no—
65C29×#121—21no—
66C29×#121—21no—
67C4×Q8×C29—24no—
68C4×Q8×C29—24no—
69C4×D4×C29—28no—
70C4×D4×C29—24no—
71C4×D4×C29—24no—
72C4×D4×C29—28no—
73C29×#117—24no—
74C29×#117—21no—
75C29×#117—21no—
76C29×#117—24no—
77C29×#117D412yes—
78C29×#117C2312yes—
79C2×C4⋊C4×C29—22no—
80C2×C4⋊C4×C29—24no—
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29—21no—
84C2×C4⋊C4×C29—21no—
85C2×C4⋊C4×C29—24no—
86C2×C4⋊C4×C29—24no—
87C2×C4⋊C4×C29D412yes—
88C2×C4⋊C4×C29D411yescharacteristic
89C2×C4⋊C4×C29D411yescharacteristic
90C2×C4⋊C4×C29C2311yescharacteristic
91C2×C4⋊C4×C29C2312yes—
92C2×C22⋊C4×C29—22no—
93C2×C22⋊C4×C29—21no—
94C2×C22⋊C4×C29—21no—
95C2×C22⋊C4×C29—21no—
96C2×C22⋊C4×C29—24no—
97C2×C42×C29—22no—
98C2×C42×C29—21no—
99C2×C42×C29C2312yes—
100C29×#107—22no—
101C29×#106—22no—
102C29×#104—28no—
103C29×#103—22no—
104C29×#102—22no—
105C29×#102—22no—
106C29×#102—22no—
107C29×C22⋊C8—21no—
108C29×C22⋊C8—21no—
109C29×C22⋊C8—21no—
110C29×C22⋊C8—21no—
111C29×#95—21no—
112C24×C29—21no—
113C24×C29—21no—
114C24×C29C2×D411yescharacteristic
115#41×C29—28no—
116#41×C29—28no—
117#41×C29—24no—
118#41×C29—24no—
119#41×C29—24no—
120#41×C29#4118yes—
121C2×Q8×C29—24no—
122C2×Q8×C29—21no—
123C2×Q8×C29C2×D412yes—
124C2×D4×C29—28no—
125C2×D4×C29—22no—
126C2×D4×C29—22no—
127C2×D4×C29—24no—
128C2×D4×C29—21no—
129C2×D4×C29—21no—
130C2×D4×C29—21no—
131C2×D4×C29—24no—
132C2×D4×C29—44no—
133C2×D4×C29—41no—
134C2×D4×C29—41no—
135C2×D4×C29C2×D412yes—
136C22×C4×C29—28no—
137C22×C4×C29—21no—
138C22×C4×C29—22no—
139C22×C4×C29—22no—
140C22×C4×C29—24no—
141C22×C4×C29—21no—
142C22×C4×C29—22no—
143C22×C4×C29—21no—
144C22×C4×C29—22no—
145C22×C4×C29—28no—
146C22×C4×C29—22no—
147C22×C4×C29—21no—
148C22×C4×C29—44no—
149C22×C4×C29—84no—
150C22×C4×C29C2×D411yescharacteristic
151C22×C4×C29C2×D411yescharacteristic
152C22×C4×C29C2×D411yescharacteristic
153C22×C4×C29C2×D411yescharacteristic
154C22×C4×C29C2×D411yescharacteristic
155C22×C4×C29C2×D414yes—
156C22×C4×C29C2411yescharacteristic
157SD16×C29—44no—
158D8×C29—44no—
159M16×C29—24no—
160M16×C29—24no—
161C2×C8×C29—22no—
162C2×C8×C29—22no—
163C4⋊C4×C29—28no—
164C4⋊C4×C29—22no—
165C4⋊C4×C29—21no—
166C4⋊C4×C29—22no—
167C4⋊C4×C29—21no—
168C4⋊C4×C29—22no—
169C4⋊C4×C29—22no—
170C4⋊C4×C29—21no—
171C4⋊C4×C29—21no—
172C4⋊C4×C29—48no—
173C4⋊C4×C29C2×D412yes—
174C4⋊C4×C29C2×D412yes—
175C22⋊C4×C29—28no—
176C22⋊C4×C29—24no—
177C22⋊C4×C29—22no—
178C22⋊C4×C29—22no—
179C22⋊C4×C29—48no—
180C22⋊C4×C29—41no—
181C22⋊C4×C29—41no—
182C42×C29—28no—
183C42×C29—22no—
184C42×C29—22no—
185C42×C29—24no—
186#32996C2911yesmaximal, characteristic, direct product factor, Sylow
187C23×C29—24no—
188C23×C29—22no—
189C23×C29—22no—
190C23×C29—22no—
191C23×C29—41no—
192C23×C29—42no—
193C23×C29—42no—
194C23×C29—42no—
195C23×C29—42no—
196C23×C29—41no—
197C23×C29—42no—
198C23×C29#12011yescharacteristic
199C23×C29#12011yescharacteristic
200C23×C29C22×D411yescharacteristic
201Q8×C29—24no—
202Q8×C29—22no—
203Q8×C29#12314yescomplemented
204D4×C29—28no—
205D4×C29—24no—
206D4×C29—28no—
207D4×C29—22no—
208D4×C29—42no—
209D4×C29—42no—
210D4×C29—82no—
211D4×C29—82no—
212D4×C29#12314yescomplemented
213C2×C4×C29—24no—
214C2×C4×C29—28no—
215C2×C4×C29—22no—
216C2×C4×C29—22no—
217C2×C4×C29—22no—
218C2×C4×C29—22no—
219C2×C4×C29—22no—
220C2×C4×C29—28no—
221C2×C4×C29—22no—
222C2×C4×C29—24no—
223C2×C4×C29—22no—
224C2×C4×C29—24no—
225C2×C4×C29—22no—
226C2×C4×C29—42no—
227C2×C4×C29—42no—
228C2×C4×C29—42no—
229C2×C4×C29—44no—
230C2×C4×C29—42no—
231C2×C4×C29—44no—
232C2×C4×C29—42no—
233C2×C4×C29—41no—
234C2×C4×C29—82no—
235C2×C4×C29—88no—
236C2×C4×C29#12011yescharacteristic
237C2×C4×C29#12011yescharacteristic
238C2×C4×C29C22×D411yescharacteristic
239C2×C4×C29C22×D411yescharacteristic
240C2×C4×C29C2×#4114yes—
241C8×C29—42no—
242C8×C29—42no—
243C2×#520C2×C2911yescharacteristic, complemented
244#3094C2×C2911yescharacteristic, complemented
245#3006C2×C2911yescharacteristic
246#2501C2×C2911yescharacteristic, complemented
247#1883C2×C2914yescomplemented
248#1859C2×C2914yescomplemented
249#1826C2×C2911yescharacteristic, complemented
250#1821C2×C2911yescharacteristic, complemented
251#1789C2×C2911yescharacteristic, complemented
252C22×C29—21no—
253C22×C29—21no—
254C22×C29—21no—
255C22×C29—21no—
256C22×C29—21no—
257C22×C29—24no—
258C22×C29—21no—
259C22×C29—21no—
260C22×C29—44no—
261C22×C29—48no—
262C22×C29—42no—
263C22×C29—42no—
264C22×C29—84no—
265C22×C29—81no—
266C22×C29—81no—
267C22×C29—81no—
268C22×C29#45312yes—
269C22×C29C2×#12011yescharacteristic
270C22×C29#52512yes—
271C4×C29—21no—
272C4×C29—24no—
273C4×C29—21no—
274C4×C29—44no—
275C4×C29—44no—
276C4×C29—42no—
277C4×C29—42no—
278C4×C29—81no—
279C4×C29C2×#12312yes—
280C4×C29#52512yes—
281C22×#41C22×C2911yescharacteristic
282C2×AGL(1,ℤ/8)C22×C2912yes—
283C2×#123—22no—
284C2×#121C22×C2911yescharacteristic
285#520—22no—
286#520—22no—
287#520—22no—
288#520C22×C2914yes—
289C2×C4×Q8—21no—
290C2×C4×D4—21no—
291C2×C4×D4—22no—
292C2×#117—21no—
293C2×#117C22×C2911yescharacteristic
294C22×C4⋊C4—21no—
295C22×C4⋊C4C22×C2911yescharacteristic
296#482—22no—
297#481—21no—
298#480—21no—
299#449—22no—
300#448—21no—
301#447—21no—
302#428C22×C2912yescomplemented
303C2×#104C22×C2914yes—
304#418C22×C2912yescomplemented
305#417C22×C2912yes—
306#407C22×C2911yescharacteristic
307#407C22×C2911yescharacteristic
308#399—22no—
309#390C22×C2912yescomplemented
310#384C22×C2912yescomplemented
311C4×C22⋊C4C22×C2911yescharacteristic
312#343C22×C2914yescomplemented
313#339C22×C2914yescomplemented
314C2×C29—22no—
315C2×C29—22no—
316C2×C29—41no—
317C2×C29—44no—
318C2×C29—161no—
319C2×C29#284911yescharacteristic
320C2×C29C2×#45311yescharacteristic
321C2×C29#302011yescharacteristic
322C2×#41—28no—
323C2×#41—21no—
324C2×#41—21no—
325C2×#41D4×C2912yes—
326C2×#41C23×C2912yes—
327C22×Q8D4×C2911yescharacteristic
328C22×D4—21no—
329C22×D4—21no—
330C22×D4D4×C2911yescharacteristic
331C22×D4C23×C2911yescharacteristic
332C23×C4—21no—
333C23×C4—22no—
334C23×C4D4×C2912yes—
335C23×C4C23×C2911yescharacteristic
336AGL(1,ℤ/8)—28no—
337C2×SD16—22no—
338C2×D8—22no—
339C2×M16C23×C2912yes—
340C2×M16C23×C2912yes—
341#123—48no—
342#121—21no—
343#121—21no—
344#121—21no—
345#121—21no—
346C4×Q8—24no—
347C4×Q8—24no—
348C4×D4—28no—
349C4×D4—24no—
350C4×D4—24no—
351C4×D4—28no—
352#117—24no—
353#117—21no—
354#117—21no—
355#117—24no—
356#117D4×C2912yes—
357#117C23×C2912yes—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—24no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—24no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4D4×C2912yes—
367C2×C4⋊C4D4×C2911yescharacteristic
368C2×C4⋊C4D4×C2911yescharacteristic
369C2×C4⋊C4C23×C2911yescharacteristic
370C2×C4⋊C4C23×C2912yes—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—24no—
376C2×C42—22no—
377C2×C42—21no—
378C2×C42C23×C2912yes—
379#107—22no—
380#106—22no—
381#104—28no—
382#103—22no—
383#102—22no—
384#102—22no—
385#102—22no—
386C22⋊C8—21no—
387C22⋊C8—21no—
388C22⋊C8—21no—
389C22⋊C8—21no—
390#95—21no—
391C29#3299611yescharacteristic, direct product factor, Sylow
392C24—21no—
393C24—21no—
394C24C2×D4×C2911yescharacteristic
395#41—28no—
396#41—28no—
397#41—24no—
398#41—24no—
399#41—24no—
400#41#41×C2918yes—
401C2×Q8—24no—
402C2×Q8—21no—
403C2×Q8C2×D4×C2912yes—
404C2×D4—28no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—24no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—24no—
412C2×D4—44no—
413C2×D4—41no—
414C2×D4—41no—
415C2×D4C2×D4×C2912yes—
416C22×C4—28no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—28no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—44no—
429C22×C4—84no—
430C22×C4C2×D4×C2911yescharacteristic
431C22×C4C2×D4×C2911yescharacteristic
432C22×C4C2×D4×C2911yescharacteristic
433C22×C4C2×D4×C2911yescharacteristic
434C22×C4C2×D4×C2911yescharacteristic
435C22×C4C2×D4×C2914yes—
436C22×C4C24×C2911yescharacteristic
437SD16—44no—
438D8—44no—
439M16—24no—
440M16—24no—
441C2×C8—22no—
442C2×C8—22no—
443C4⋊C4—28no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—48no—
453C4⋊C4C2×D4×C2912yes—
454C4⋊C4C2×D4×C2912yes—
455C22⋊C4—28no—
456C22⋊C4—24no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—48no—
460C22⋊C4—41no—
461C22⋊C4—41no—
462C42—28no—
463C42—22no—
464C42—22no—
465C42—24no—
466C23—24no—
467C23—22no—
468C23—22no—
469C23—22no—
470C23—41no—
471C23—42no—
472C23—42no—
473C23—42no—
474C23—42no—
475C23—41no—
476C23—42no—
477C23C29×#12011yescharacteristic
478C23C29×#12011yescharacteristic
479C23C22×D4×C2911yescharacteristic
480Q8—24no—
481Q8—22no—
482Q8C29×#12314yescomplemented
483D4—28no—
484D4—24no—
485D4—28no—
486D4—22no—
487D4—42no—
488D4—42no—
489D4—82no—
490D4—82no—
491D4C29×#12314yescomplemented
492C2×C4—24no—
493C2×C4—28no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—28no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—44no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—44no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—82no—
514C2×C4—88no—
515C2×C4C29×#12011yescharacteristic
516C2×C4C29×#12011yescharacteristic
517C2×C4C22×D4×C2911yescharacteristic
518C2×C4C22×D4×C2911yescharacteristic
519C2×C4C2×#41×C2914yes—
520C8—42no—
521C8—42no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—24no—
530C22—44no—
531C22—48no—
532C22—42no—
533C22—42no—
534C22—84no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22C29×#45312yes—
539C22C2×C29×#12011yescharacteristic
540C22C29×#52512yes—
541C4—21no—
542C4—24no—
543C4—21no—
544C4—44no—
545C4—44no—
546C4—42no—
547C4—42no—
548C4—81no—
549C4C2×C29×#12312yes—
550C4C29×#52512yes—
551C2—22no—
552C2—22no—
553C2—41no—
554C2—44no—
555C2—161no—
556C2C29×#284911yescharacteristic
557C2C2×C29×#45311yescharacteristic
558C2C29×#302011yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#3006C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#520C2semidirect
2. C29×#3094C2semidirect
4. C29×#2501C2semidirect
5. C29×#1883C2semidirect
6. C29×#1859C2semidirect
7. C29×#1826C2semidirect
8. C29×#1821C2semidirect
9. C29×#1789C2semidirect
31. C29×#428C22semidirect
33. C29×#418C22semidirect
38. C29×#390C22semidirect
39. C29×#384C22semidirect
41. C29×#343C22semidirect
42. C29×#339C22semidirect
186. #32996C29direct (N × H)
203. Q8×C29#123semidirect
212. D4×C29#123semidirect
243. C2×#520C2×C29semidirect
244. #3094C2×C29semidirect
246. #2501C2×C29semidirect
247. #1883C2×C29semidirect
248. #1859C2×C29semidirect
249. #1826C2×C29semidirect
250. #1821C2×C29semidirect
251. #1789C2×C29semidirect
302. #428C22×C29semidirect
304. #418C22×C29semidirect
309. #390C22×C29semidirect
310. #384C22×C29semidirect
312. #343C22×C29semidirect
313. #339C22×C29semidirect
391. C29#32996direct (N × H)
482. Q8C29×#123semidirect
491. D4C29×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#5202
C29×#30942
C29×#30062
C29×#25012
C29×#18832
C29×#18592
C29×#18262
C29×#18212
C29×#17892
#3299629