Finite Group Databasebeta

← C29×#18428 #20313328

Subgroups — C29×#18428 #20313328

Order 7424.

1104 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3561C211yesmaximal, characteristic, complemented
2C29×#3217C211yesmaximal, characteristic, complemented
3C29×#3208C211yesmaximal, characteristic, complemented
4C29×#2657C211yesmaximal, characteristic, complemented
5C29×#1600C214yesmaximal, complemented
6C29×#1596C214yesmaximal, complemented
7C29×#1506C211yesmaximal, characteristic, complemented
8C29×#1500C211yesmaximal, characteristic, complemented
9C29×#1469C211yesmaximal, characteristic, complemented
10C29×#563—21no—
11C29×#562—21no—
12C29×#556—21no—
13C29×#551—22no—
14D4×Q8×C29—21no—
15C29×#548—21no—
16C29×#546—21no—
17C29×#543C2212yes—
18C29×#542—21no—
19C29×#542—22no—
20C29×#538C2212yes—
21C29×#536—21no—
22C29×#533C2211yescharacteristic
23C2×C29×#127—21no—
24C2×C29×#127C2211yescharacteristic
25C29×#529C2211yescharacteristic
26C2×C29×#124—21no—
27C2×C29×#124C2211yescharacteristic
28C29×#496—21no—
29C29×#492—21no—
30C29×#490—21no—
31C29×#486—21no—
32C29×#460—22no—
33C29×#460—21no—
34C29×#459—21no—
35C29×#450C2214yes—
36C29×#450C2212yes—
37C29×#447C2212yes—
38C29×#432C2211yescharacteristic
39C29×#431C2211yescharacteristic
40C29×#392—22no—
41C29×#392C2214yes—
42C29×#376C2211yescharacteristic
43C29×#328C2212yes—
44C29×#328C2214yes—
45C29×#327C2212yes—
46C29×#323C2214yes—
47C2×#41×C29—21no—
48C22×Q8×C29—21no—
49C22×Q8×C29D411yescharacteristic
50C22×D4×C29—24no—
51C22×D4×C29—21no—
52C22×D4×C29—21no—
53C22×D4×C29D411yescharacteristic
54C22×D4×C29C2312yes—
55C2×SD16×C29—24no—
56C2×SD16×C29—22no—
57C2×D8×C29—22no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8—22no—
60C29×C4⋊Q8D411yescharacteristic, complemented
61C29×C4⋊Q8D411yescharacteristic, complemented
62C29×#127—21no—
63C29×#127—21no—
64C29×#127—21no—
65C29×#127—21no—
66C29×#127—44no—
67C29×#126—22no—
68C29×#126—22no—
69C29×#126—22no—
70C29×#126—21no—
71C29×#125—21no—
72C29×#125D411yescharacteristic, complemented
73C29×#124—21no—
74C29×#124—22no—
75C29×#124—22no—
76C29×#124—21no—
77C29×#124—21no—
78C29×#124—21no—
79C29×#124—21no—
80C29×#124—44no—
81C29×#124D411yescharacteristic, complemented
82C29×#123—22no—
83C29×#123—22no—
84C29×#123—22no—
85C29×#123—21no—
86C29×#123—22no—
87C29×C22⋊Q8—22no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8—22no—
90C29×C22⋊Q8—22no—
91C29×C22⋊Q8—22no—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8—22no—
94C29×C22⋊Q8—22no—
95C29×C22⋊Q8—22no—
96C29×C22⋊Q8C2311yescharacteristic
97C29×C22⋊Q8C2312yes—
98C29×#121—21no—
99C29×#121—22no—
100C29×#121—22no—
101C29×#121C2311yescharacteristic
102C29×#120—22no—
103C4×Q8×C29—21no—
104C4×Q8×C29—21no—
105C4×Q8×C29D411yescharacteristic, complemented
106C4×Q8×C29D412yescomplemented
107C4×D4×C29—21no—
108C4×D4×C29—22no—
109C4×D4×C29—21no—
110C4×D4×C29—22no—
111C4×D4×C29D411yescharacteristic, complemented
112C29×#117—22no—
113C29×#117—21no—
114C29×#117—21no—
115C2×C22⋊C4×C29—22no—
116C2×C22⋊C4×C29—24no—
117C2×C22⋊C4×C29D412yes—
118C2×C22⋊C4×C29C2312yes—
119C2×C42×C29—21no—
120C2×C42×C29C2311yescharacteristic
121C29×C4⋊C8—21no—
122C29×C4⋊C8—21no—
123C29×#102—22no—
124C29×#102—22no—
125C29×#102—24no—
126C29×C22⋊C8C2312yes—
127C29×C22⋊C8C2312yes—
128C29×#97—21no—
129C4×C8×C29—21no—
130C29×#95—21no—
131C29×#95C2312yes—
132C24×C29—22no—
133C24×C29C2×D412yes—
134#41×C29—82no—
135C2×Q8×C29—22no—
136C2×Q8×C29—21no—
137C2×Q8×C29—21no—
138C2×Q8×C29—21no—
139C2×Q8×C29—42no—
140C2×Q8×C29—82no—
141C2×Q8×C29C2×D411yescharacteristic
142C2×Q8×C29C2×D412yes—
143C2×D4×C29—21no—
144C2×D4×C29—22no—
145C2×D4×C29—22no—
146C2×D4×C29—21no—
147C2×D4×C29—21no—
148C2×D4×C29—22no—
149C2×D4×C29—22no—
150C2×D4×C29—42no—
151C2×D4×C29—42no—
152C2×D4×C29—42no—
153C2×D4×C29—48no—
154C2×D4×C29—41no—
155C2×D4×C29—41no—
156C2×D4×C29—41no—
157C2×D4×C29—41no—
158C2×D4×C29—82no—
159C2×D4×C29—82no—
160C2×D4×C29—84no—
161C2×D4×C29—84no—
162C2×D4×C29C2×D411yescharacteristic
163C22×C4×C29—22no—
164C22×C4×C29—22no—
165C22×C4×C29—22no—
166C22×C4×C29—22no—
167C22×C4×C29—21no—
168C22×C4×C29C2×D411yescharacteristic
169C22×C4×C29C2×D411yescharacteristic
170C22×C4×C29C2×D412yes—
171C22×C4×C29C2411yescharacteristic
172SD16×C29—82no—
173SD16×C29—84no—
174D8×C29—82no—
175C2×C8×C29—22no—
176C2×C8×C29—22no—
177C4⋊C4×C29—22no—
178C4⋊C4×C29—22no—
179C4⋊C4×C29—22no—
180C4⋊C4×C29—22no—
181C4⋊C4×C29—21no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—22no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—22no—
190C4⋊C4×C29C2×D411yescharacteristic
191C4⋊C4×C29C2×D411yescharacteristic
192C4⋊C4×C29C2×D412yes—
193C22⋊C4×C29—22no—
194C22⋊C4×C29—22no—
195C22⋊C4×C29—22no—
196C22⋊C4×C29—22no—
197C22⋊C4×C29—22no—
198C22⋊C4×C29—21no—
199C22⋊C4×C29—22no—
200C22⋊C4×C29—22no—
201C22⋊C4×C29—22no—
202C22⋊C4×C29—21no—
203C22⋊C4×C29—21no—
204C22⋊C4×C29—21no—
205C22⋊C4×C29—22no—
206C22⋊C4×C29—22no—
207C22⋊C4×C29—21no—
208C22⋊C4×C29—48no—
209C42×C29—24no—
210C42×C29—22no—
211C42×C29—22no—
212C42×C29—21no—
213C42×C29C2×D411yescharacteristic
214C42×C29C2×D411yescharacteristic
215C42×C29C2×D411yescharacteristic
216C42×C29C2×D411yescharacteristic
217#18428C2911yesmaximal, characteristic, direct product factor, Sylow
218C23×C29—22no—
219C23×C29—21no—
220C23×C29—24no—
221C23×C29—42no—
222C23×C29—42no—
223C23×C29—42no—
224C23×C29—42no—
225C23×C29—44no—
226C23×C29—42no—
227C23×C29—44no—
228C23×C29C22×D411yescharacteristic
229Q8×C29—41no—
230Q8×C29—42no—
231Q8×C29—42no—
232Q8×C29—42no—
233Q8×C29—81no—
234Q8×C29—82no—
235D4×C29—41no—
236D4×C29—42no—
237D4×C29—42no—
238D4×C29—44no—
239D4×C29—42no—
240D4×C29—42no—
241D4×C29—81no—
242D4×C29—82no—
243D4×C29—82no—
244D4×C29—82no—
245D4×C29—82no—
246D4×C29—82no—
247D4×C29—816no—
248D4×C29—82no—
249C2×C4×C29—22no—
250C2×C4×C29—22no—
251C2×C4×C29—24no—
252C2×C4×C29—21no—
253C2×C4×C29—22no—
254C2×C4×C29—21no—
255C2×C4×C29—22no—
256C2×C4×C29—22no—
257C2×C4×C29—21no—
258C2×C4×C29—41no—
259C2×C4×C29—42no—
260C2×C4×C29—42no—
261C2×C4×C29—42no—
262C2×C4×C29—42no—
263C2×C4×C29—82no—
264C2×C4×C29—82no—
265C2×C4×C29—82no—
266C2×C4×C29#12011yescharacteristic
267C2×C4×C29#12011yescharacteristic
268C2×C4×C29#12011yescharacteristic
269C2×C4×C29#12011yescharacteristic
270C2×C4×C29C22×D411yescharacteristic
271C2×C4×C29C22×D411yescharacteristic
272C8×C29—42no—
273C8×C29—42no—
274#3561C2×C2911yescharacteristic, complemented
275#3217C2×C2911yescharacteristic, complemented
276#3208C2×C2911yescharacteristic, complemented
277#2657C2×C2911yescharacteristic, complemented
278#1600C2×C2914yescomplemented
279#1596C2×C2914yescomplemented
280#1506C2×C2911yescharacteristic, complemented
281#1500C2×C2911yescharacteristic, complemented
282#1469C2×C2911yescharacteristic, complemented
283C22×C29—21no—
284C22×C29—21no—
285C22×C29—41no—
286C22×C29—42no—
287C22×C29—41no—
288C22×C29—42no—
289C22×C29—42no—
290C22×C29—41no—
291C22×C29—84no—
292C22×C29—84no—
293C22×C29—84no—
294C22×C29—82no—
295C22×C29—82no—
296C22×C29—82no—
297C22×C29C2×#12011yescharacteristic
298C22×C29#57712yes—
299C4×C29—21no—
300C4×C29—21no—
301C4×C29—21no—
302C4×C29—21no—
303C4×C29—21no—
304C4×C29—44no—
305C4×C29—41no—
306C4×C29—41no—
307C4×C29—42no—
308C4×C29—42no—
309C4×C29—41no—
310C4×C29—42no—
311C4×C29#45312yes—
312#563—21no—
313#562—21no—
314#556—21no—
315#551—22no—
316D4×Q8—21no—
317#548—21no—
318#546—21no—
319#543C22×C2912yes—
320#542—21no—
321#542—22no—
322#538C22×C2912yes—
323#536—21no—
324#533C22×C2911yescharacteristic
325C2×#127—21no—
326C2×#127C22×C2911yescharacteristic
327#529C22×C2911yescharacteristic
328C2×#124—21no—
329C2×#124C22×C2911yescharacteristic
330#496—21no—
331#492—21no—
332#490—21no—
333#486—21no—
334#460—22no—
335#460—21no—
336#459—21no—
337#450C22×C2912yes—
338#450C22×C2914yes—
339#447C22×C2912yes—
340#432C22×C2911yescharacteristic
341#431C22×C2911yescharacteristic
342#392—22no—
343#392C22×C2914yes—
344#376C22×C2911yescharacteristic
345#328C22×C2912yes—
346#328C22×C2914yes—
347#327C22×C2912yes—
348#323C22×C2914yes—
349C2×C29—22no—
350C2×C29—81no—
351C2×C29—82no—
352C2×C29—162no—
353C2×C29#301011yescharacteristic
354C2×C29C2×#45311yescharacteristic
355C2×C29#302711yescharacteristic
356C2×#41—21no—
357C22×Q8—21no—
358C22×Q8D4×C2911yescharacteristic
359C22×D4—24no—
360C22×D4—21no—
361C22×D4—21no—
362C22×D4D4×C2911yescharacteristic
363C22×D4C23×C2912yes—
364C2×SD16—24no—
365C2×SD16—22no—
366C2×D8—22no—
367C4⋊Q8—21no—
368C4⋊Q8—22no—
369C4⋊Q8D4×C2911yescharacteristic, complemented
370C4⋊Q8D4×C2911yescharacteristic, complemented
371#127—21no—
372#127—21no—
373#127—21no—
374#127—21no—
375#127—44no—
376#126—22no—
377#126—22no—
378#126—22no—
379#126—21no—
380#125—21no—
381#125D4×C2911yescharacteristic, complemented
382#124—21no—
383#124—22no—
384#124—22no—
385#124—21no—
386#124—21no—
387#124—21no—
388#124—21no—
389#124—44no—
390#124D4×C2911yescharacteristic, complemented
391#123—22no—
392#123—22no—
393#123—22no—
394#123—21no—
395#123—22no—
396C22⋊Q8—22no—
397C22⋊Q8—21no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—21no—
402C22⋊Q8—22no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405C22⋊Q8C23×C2911yescharacteristic
406C22⋊Q8C23×C2912yes—
407#121—21no—
408#121—22no—
409#121—22no—
410#121C23×C2911yescharacteristic
411#120—22no—
412C4×Q8—21no—
413C4×Q8—21no—
414C4×Q8D4×C2911yescharacteristic, complemented
415C4×Q8D4×C2912yescomplemented
416C4×D4—21no—
417C4×D4—22no—
418C4×D4—21no—
419C4×D4—22no—
420C4×D4D4×C2911yescharacteristic, complemented
421#117—22no—
422#117—21no—
423#117—21no—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—24no—
426C2×C22⋊C4D4×C2912yes—
427C2×C22⋊C4C23×C2912yes—
428C2×C42—21no—
429C2×C42C23×C2911yescharacteristic
430C4⋊C8—21no—
431C4⋊C8—21no—
432#102—22no—
433#102—22no—
434#102—24no—
435C22⋊C8C23×C2912yes—
436C22⋊C8C23×C2912yes—
437#97—21no—
438C4×C8—21no—
439#95—21no—
440#95C23×C2912yes—
441C29#1842811yescharacteristic, direct product factor, Sylow
442C24—22no—
443C24C2×D4×C2912yes—
444#41—82no—
445C2×Q8—22no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—42no—
450C2×Q8—82no—
451C2×Q8C2×D4×C2911yescharacteristic
452C2×Q8C2×D4×C2912yes—
453C2×D4—21no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—48no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—82no—
469C2×D4—82no—
470C2×D4—84no—
471C2×D4—84no—
472C2×D4C2×D4×C2911yescharacteristic
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4C2×D4×C2911yescharacteristic
479C22×C4C2×D4×C2911yescharacteristic
480C22×C4C2×D4×C2912yes—
481C22×C4C24×C2911yescharacteristic
482SD16—82no—
483SD16—84no—
484D8—82no—
485C2×C8—22no—
486C2×C8—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4C2×D4×C2911yescharacteristic
501C4⋊C4C2×D4×C2911yescharacteristic
502C4⋊C4C2×D4×C2912yes—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—21no—
509C22⋊C4—22no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—21no—
518C22⋊C4—48no—
519C42—24no—
520C42—22no—
521C42—22no—
522C42—21no—
523C42C2×D4×C2911yescharacteristic
524C42C2×D4×C2911yescharacteristic
525C42C2×D4×C2911yescharacteristic
526C42C2×D4×C2911yescharacteristic
527C23—22no—
528C23—21no—
529C23—24no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23—42no—
534C23—44no—
535C23—42no—
536C23—44no—
537C23C22×D4×C2911yescharacteristic
538Q8—41no—
539Q8—42no—
540Q8—42no—
541Q8—42no—
542Q8—81no—
543Q8—82no—
544D4—41no—
545D4—42no—
546D4—42no—
547D4—44no—
548D4—42no—
549D4—42no—
550D4—81no—
551D4—82no—
552D4—82no—
553D4—82no—
554D4—82no—
555D4—82no—
556D4—816no—
557D4—82no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4C29×#12011yescharacteristic
576C2×C4C29×#12011yescharacteristic
577C2×C4C29×#12011yescharacteristic
578C2×C4C29×#12011yescharacteristic
579C2×C4C22×D4×C2911yescharacteristic
580C2×C4C22×D4×C2911yescharacteristic
581C8—42no—
582C8—42no—
583C22—21no—
584C22—21no—
585C22—41no—
586C22—42no—
587C22—41no—
588C22—42no—
589C22—42no—
590C22—41no—
591C22—84no—
592C22—84no—
593C22—84no—
594C22—82no—
595C22—82no—
596C22—82no—
597C22C2×C29×#12011yescharacteristic
598C22C29×#57712yes—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—44no—
605C4—41no—
606C4—41no—
607C4—42no—
608C4—42no—
609C4—41no—
610C4—42no—
611C4C29×#45312yes—
612C2—22no—
613C2—82no—
614C2—81no—
615C2—162no—
616C2C29×#301011yescharacteristic
617C2C2×C29×#45311yescharacteristic
618C2C29×#302711yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3561C2semidirect
2. C29×#3217C2semidirect
3. C29×#3208C2semidirect
4. C29×#2657C2semidirect
5. C29×#1600C2semidirect
6. C29×#1596C2semidirect
7. C29×#1506C2semidirect
8. C29×#1500C2semidirect
9. C29×#1469C2semidirect
60. C29×C4⋊Q8D4semidirect
61. C29×C4⋊Q8D4semidirect
72. C29×#125D4semidirect
81. C29×#124D4semidirect
105. C4×Q8×C29D4semidirect
106. C4×Q8×C29D4semidirect
111. C4×D4×C29D4semidirect
217. #18428C29direct (N × H)
274. #3561C2×C29semidirect
275. #3217C2×C29semidirect
276. #3208C2×C29semidirect
277. #2657C2×C29semidirect
278. #1600C2×C29semidirect
279. #1596C2×C29semidirect
280. #1506C2×C29semidirect
281. #1500C2×C29semidirect
282. #1469C2×C29semidirect
369. C4⋊Q8D4×C29semidirect
370. C4⋊Q8D4×C29semidirect
381. #125D4×C29semidirect
390. #124D4×C29semidirect
414. C4×Q8D4×C29semidirect
415. C4×Q8D4×C29semidirect
420. C4×D4D4×C29semidirect
441. C29#18428direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35612
C29×#32172
C29×#32082
C29×#26572
C29×#16002
C29×#15962
C29×#15062
C29×#15002
C29×#14692
#1842829