Finite Group Databasebeta

← C29×#33556 #20328456

Subgroups — C29×#33556 #20328456

Order 7424.

1134 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3540C211yesmaximal, characteristic, complemented
2C29×#3028C211yesmaximal, characteristic, complemented
3C29×#3025C211yesmaximal, characteristic, complemented
4C29×#3021C211yesmaximal, characteristic, complemented
5C29×#2200C214yesmaximal, complemented
6C29×#2198C214yesmaximal, complemented
7C29×#2128C211yesmaximal, characteristic, complemented
8C29×#2123C211yesmaximal, characteristic, complemented
9C29×#2120C211yesmaximal, characteristic, complemented
10C29×#585C2211yescharacteristic
11C2×C29×AGL(1,ℤ/8)—21no—
12C29×H(3,𝔽4)—21no—
13C29×#560C2212yescomplemented
14C29×#559C2212yescomplemented
15C29×#556—21no—
16C29×#555—21no—
17C29×#551—21no—
18C29×#548—21no—
19C29×#546—21no—
20C29×#542—22no—
21C29×#542—21no—
22C29×#538—22no—
23C29×#536—21no—
24C29×#536C2211yescharacteristic
25C29×#535C2211yescharacteristic
26C29×#525—21no—
27C29×#525—21no—
28C29×#525C2211yescharacteristic
29C29×#458—21no—
30C29×#458—22no—
31C29×#458C2212yescomplemented
32C29×#458C2214yescomplemented
33C29×B(4,𝔽2)—21no—
34C29×B(4,𝔽2)C2212yescomplemented
35C29×#454—22no—
36C29×#453C2214yes—
37C29×#421—21no—
38C29×#413C2211yescharacteristic
39C29×#410—21no—
40C29×#410—21no—
41C29×#410C2211yescharacteristic
42C29×#410C2211yescharacteristic
43C29×#353C2214yescomplemented
44C29×#352C2212yescomplemented
45C29×#352C2214yescomplemented
46C29×AΣL(1,𝔽16)C2212yescomplemented
47C29×2−1+4—21no—
48C29×2−1+4—41no—
49C29×H(5,𝔽2)—21no—
50C29×H(5,𝔽2)—21no—
51C29×H(5,𝔽2)—41no—
52C29×H(5,𝔽2)C2312yes—
53C2×#41×C29—21no—
54C2×#41×C29—21no—
55C2×#41×C29—21no—
56C2×#41×C29—21no—
57C2×#41×C29—42no—
58C2×#41×C29C2311yescharacteristic
59C22×Q8×C29D411yescharacteristic, complemented
60C22×D4×C29D411yescharacteristic, complemented
61C23×C4×C29D411yescharacteristic
62C29×AGL(1,ℤ/8)—24no—
63C29×AGL(1,ℤ/8)—42no—
64C2×SD16×C29—41no—
65C2×D8×C29—41no—
66C2×M16×C29—21no—
67C29×C4⋊Q8—21no—
68C29×C4⋊Q8—21no—
69C29×C4⋊Q8—41no—
70C29×#127C2312yes—
71C29×#126—22no—
72C29×#126—22no—
73C29×#126—22no—
74C29×#124—22no—
75C29×#124—21no—
76C29×#124—22no—
77C29×#124—22no—
78C29×#124—21no—
79C29×#124—22no—
80C29×#124—22no—
81C29×#124—41no—
82C29×#124D412yescomplemented
83C29×#123—22no—
84C29×#123—22no—
85C29×#123—22no—
86C29×#123—22no—
87C29×#123—24no—
88C29×#123D411yescharacteristic
89C29×#123D412yescomplemented
90C29×#123C2311yescharacteristic
91C29×#123C2312yes—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8—22no—
94C29×C22⋊Q8—22no—
95C29×C22⋊Q8—21no—
96C29×C22⋊Q8—21no—
97C29×C22⋊Q8—21no—
98C29×C22⋊Q8—42no—
99C29×C22⋊Q8—41no—
100C29×#121—21no—
101C29×#121—21no—
102C29×#121—22no—
103C29×#121—21no—
104C29×#121—21no—
105C29×#121—22no—
106C29×#121—22no—
107C29×#121—41no—
108C29×#120—22no—
109C29×#120—22no—
110C29×#120—21no—
111C29×#120—21no—
112C29×#120—22no—
113C29×#120D411yescharacteristic
114C29×#120C2311yescharacteristic
115C4×Q8×C29—21no—
116C4×Q8×C29—22no—
117C4×D4×C29—22no—
118C4×D4×C29—21no—
119C4×D4×C29—22no—
120C4×D4×C29—21no—
121C4×D4×C29—21no—
122C4×D4×C29—22no—
123C4×D4×C29—42no—
124C29×#117—21no—
125C29×#117—22no—
126C29×#117—21no—
127C29×#117—21no—
128C29×#117D411yescharacteristic
129C29×#117D411yescharacteristic, complemented
130C29×#117D411yescharacteristic, complemented
131C2×C22⋊C4×C29—22no—
132C29×#104—24no—
133C29×#101—21no—
134C29×#100C2312yes—
135C29×#99—21no—
136C29×#99—21no—
137C29×#99—22no—
138C29×#99—22no—
139C29×#99—24no—
140C29×#99C2312yes—
141C29×#99C2312yes—
142C24×C29—21no—
143C24×C29C2×D411yescharacteristic
144#41×C29—22no—
145#41×C29—22no—
146#41×C29—41no—
147#41×C29—41no—
148#41×C29—42no—
149#41×C29—41no—
150#41×C29—41no—
151#41×C29—41no—
152#41×C29—41no—
153#41×C29—41no—
154#41×C29—42no—
155#41×C29—42no—
156#41×C29—42no—
157#41×C29—41no—
158#41×C29—41no—
159#41×C29—41no—
160#41×C29—81no—
161#41×C29—81no—
162C2×Q8×C29—21no—
163C2×Q8×C29—21no—
164C2×Q8×C29—22no—
165C2×Q8×C29—21no—
166C2×Q8×C29—21no—
167C2×Q8×C29—21no—
168C2×Q8×C29—41no—
169C2×Q8×C29—41no—
170C2×Q8×C29—42no—
171C2×Q8×C29C2×D411yescharacteristic
172C2×D4×C29—21no—
173C2×D4×C29—21no—
174C2×D4×C29—21no—
175C2×D4×C29—22no—
176C2×D4×C29—22no—
177C2×D4×C29—22no—
178C2×D4×C29—22no—
179C2×D4×C29—21no—
180C2×D4×C29—22no—
181C2×D4×C29—22no—
182C2×D4×C29—21no—
183C2×D4×C29—21no—
184C2×D4×C29—41no—
185C2×D4×C29—41no—
186C2×D4×C29—42no—
187C2×D4×C29—42no—
188C2×D4×C29—42no—
189C2×D4×C29—41no—
190C2×D4×C29—42no—
191C2×D4×C29C2×D411yescharacteristic
192C2×D4×C29C2×D411yescharacteristic
193C2×D4×C29C2×D412yes—
194C2×D4×C29C2411yescharacteristic
195C22×C4×C29—22no—
196C22×C4×C29—22no—
197C22×C4×C29—22no—
198C22×C4×C29—22no—
199C22×C4×C29—21no—
200C22×C4×C29—21no—
201C22×C4×C29—41no—
202C22×C4×C29—41no—
203C22×C4×C29—41no—
204C22×C4×C29C2×D411yescharacteristic
205C22×C4×C29C2×D411yescharacteristic
206C22×C4×C29C2×D411yescharacteristic
207C22×C4×C29C2×D411yescharacteristic
208C22×C4×C29C2×D412yes—
209SD16×C29—44no—
210D8×C29—44no—
211M16×C29—22no—
212M16×C29—41no—
213C2×C8×C29—41no—
214C4⋊C4×C29—22no—
215C4⋊C4×C29—22no—
216C4⋊C4×C29—22no—
217C4⋊C4×C29—21no—
218C4⋊C4×C29—21no—
219C4⋊C4×C29—22no—
220C4⋊C4×C29—21no—
221C4⋊C4×C29—21no—
222C4⋊C4×C29—21no—
223C4⋊C4×C29—22no—
224C4⋊C4×C29—41no—
225C4⋊C4×C29—41no—
226C4⋊C4×C29—42no—
227C4⋊C4×C29—44no—
228C22⋊C4×C29—22no—
229C22⋊C4×C29—22no—
230C22⋊C4×C29—22no—
231C22⋊C4×C29—22no—
232C22⋊C4×C29—22no—
233C22⋊C4×C29—22no—
234C22⋊C4×C29—21no—
235C22⋊C4×C29—22no—
236C22⋊C4×C29—21no—
237C22⋊C4×C29—21no—
238C22⋊C4×C29—22no—
239C22⋊C4×C29—22no—
240C22⋊C4×C29—22no—
241C22⋊C4×C29—21no—
242C22⋊C4×C29—21no—
243C22⋊C4×C29—22no—
244C22⋊C4×C29—22no—
245C22⋊C4×C29—42no—
246C22⋊C4×C29—42no—
247C22⋊C4×C29—44no—
248C22⋊C4×C29C2×D411yescharacteristic
249C22⋊C4×C29C2×D411yescharacteristic
250C22⋊C4×C29C2×D412yes—
251C42×C29—22no—
252C42×C29—22no—
253C42×C29—21no—
254C42×C29—21no—
255C42×C29—41no—
256C42×C29—41no—
257C42×C29C2×D412yes—
258#33556C2911yesmaximal, characteristic, direct product factor, Sylow
259C23×C29—22no—
260C23×C29—22no—
261C23×C29—21no—
262C23×C29—22no—
263C23×C29—41no—
264C23×C29—41no—
265C23×C29—81no—
266C23×C29—81no—
267C23×C29—82no—
268C23×C29#12011yescharacteristic
269C23×C29C22×D411yescharacteristic
270C23×C29C22×D411yescharacteristic
271Q8×C29—22no—
272Q8×C29—41no—
273Q8×C29—41no—
274Q8×C29—41no—
275Q8×C29—41no—
276Q8×C29—41no—
277Q8×C29—41no—
278Q8×C29—81no—
279Q8×C29—82no—
280D4×C29—22no—
281D4×C29—41no—
282D4×C29—41no—
283D4×C29—41no—
284D4×C29—42no—
285D4×C29—41no—
286D4×C29—41no—
287D4×C29—42no—
288D4×C29—42no—
289D4×C29—42no—
290D4×C29—42no—
291D4×C29—41no—
292D4×C29—41no—
293D4×C29—41no—
294D4×C29—81no—
295D4×C29—82no—
296D4×C29—82no—
297D4×C29—82no—
298D4×C29—81no—
299D4×C29—82no—
300D4×C29—84no—
301C2×C4×C29—21no—
302C2×C4×C29—21no—
303C2×C4×C29—21no—
304C2×C4×C29—21no—
305C2×C4×C29—21no—
306C2×C4×C29—21no—
307C2×C4×C29—22no—
308C2×C4×C29—22no—
309C2×C4×C29—21no—
310C2×C4×C29—22no—
311C2×C4×C29—22no—
312C2×C4×C29—21no—
313C2×C4×C29—22no—
314C2×C4×C29—21no—
315C2×C4×C29—42no—
316C2×C4×C29—42no—
317C2×C4×C29—42no—
318C2×C4×C29—41no—
319C2×C4×C29—42no—
320C2×C4×C29—41no—
321C2×C4×C29—41no—
322C2×C4×C29—41no—
323C2×C4×C29—42no—
324C2×C4×C29—42no—
325C2×C4×C29—42no—
326C2×C4×C29—81no—
327C2×C4×C29—82no—
328C2×C4×C29—82no—
329C2×C4×C29#12011yescharacteristic
330C2×C4×C29#12011yescharacteristic
331C2×C4×C29#12011yescharacteristic
332C2×C4×C29C22×D411yescharacteristic
333C8×C29—42no—
334#3540C2×C2911yescharacteristic, complemented
335#3028C2×C2911yescharacteristic, complemented
336#3025C2×C2911yescharacteristic, complemented
337#3021C2×C2911yescharacteristic, complemented
338#2200C2×C2914yescomplemented
339#2198C2×C2914yescomplemented
340#2128C2×C2911yescharacteristic, complemented
341#2123C2×C2911yescharacteristic, complemented
342#2120C2×C2911yescharacteristic, complemented
343C22×C29—21no—
344C22×C29—21no—
345C22×C29—21no—
346C22×C29—41no—
347C22×C29—41no—
348C22×C29—41no—
349C22×C29—42no—
350C22×C29—41no—
351C22×C29—41no—
352C22×C29—42no—
353C22×C29—42no—
354C22×C29—42no—
355C22×C29—41no—
356C22×C29—42no—
357C22×C29—82no—
358C22×C29—82no—
359C22×C29—81no—
360C22×C29—161no—
361C22×C29—162no—
362C22×C29C2×#12011yescharacteristic
363C4×C29—21no—
364C4×C29—21no—
365C4×C29—21no—
366C4×C29—41no—
367C4×C29—42no—
368C4×C29—42no—
369C4×C29—41no—
370C4×C29—42no—
371C4×C29—41no—
372C4×C29—42no—
373C4×C29—82no—
374C4×C29—82no—
375C4×C29B(4,𝔽2)11yescharacteristic
376C4×C29B(4,𝔽2)11yescharacteristic
377#585C22×C2911yescharacteristic
378C2×AGL(1,ℤ/8)—21no—
379H(3,𝔽4)—21no—
380#560C22×C2912yescomplemented
381#559C22×C2912yescomplemented
382#556—21no—
383#555—21no—
384#551—21no—
385#548—21no—
386#546—21no—
387#542—22no—
388#542—21no—
389#538—22no—
390#536—21no—
391#536C22×C2911yescharacteristic
392#535C22×C2911yescharacteristic
393#525—21no—
394#525—21no—
395#525C22×C2911yescharacteristic
396#458—21no—
397#458—22no—
398#458C22×C2912yescomplemented
399#458C22×C2914yescomplemented
400B(4,𝔽2)—21no—
401B(4,𝔽2)C22×C2912yescomplemented
402#454—22no—
403#453C22×C2914yes—
404#421—21no—
405#413C22×C2911yescharacteristic
406#410—21no—
407#410—21no—
408#410C22×C2911yescharacteristic
409#410C22×C2911yescharacteristic
410#353C22×C2914yescomplemented
411#352C22×C2912yescomplemented
412#352C22×C2914yescomplemented
413AΣL(1,𝔽16)C22×C2912yescomplemented
414C2×C29—21no—
415C2×C29—41no—
416C2×C29—41no—
417C2×C29—41no—
418C2×C29—81no—
419C2×C29—82no—
420C2×C29—82no—
421C2×C29C2×B(4,𝔽2)11yescharacteristic
4222−1+4—21no—
4232−1+4—41no—
424H(5,𝔽2)—21no—
425H(5,𝔽2)—21no—
426H(5,𝔽2)—41no—
427H(5,𝔽2)C23×C2912yes—
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—42no—
433C2×#41C23×C2911yescharacteristic
434C22×Q8D4×C2911yescharacteristic, complemented
435C22×D4D4×C2911yescharacteristic, complemented
436C23×C4D4×C2911yescharacteristic
437AGL(1,ℤ/8)—24no—
438AGL(1,ℤ/8)—42no—
439C2×SD16—41no—
440C2×D8—41no—
441C2×M16—21no—
442C4⋊Q8—21no—
443C4⋊Q8—21no—
444C4⋊Q8—41no—
445#127C23×C2912yes—
446#126—22no—
447#126—22no—
448#126—22no—
449#124—22no—
450#124—21no—
451#124—22no—
452#124—22no—
453#124—21no—
454#124—22no—
455#124—22no—
456#124—41no—
457#124D4×C2912yescomplemented
458#123—22no—
459#123—22no—
460#123—22no—
461#123—22no—
462#123—24no—
463#123D4×C2911yescharacteristic
464#123D4×C2912yescomplemented
465#123C23×C2911yescharacteristic
466#123C23×C2912yes—
467C22⋊Q8—21no—
468C22⋊Q8—22no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—42no—
474C22⋊Q8—41no—
475#121—21no—
476#121—21no—
477#121—22no—
478#121—21no—
479#121—21no—
480#121—22no—
481#121—22no—
482#121—41no—
483#120—22no—
484#120—22no—
485#120—21no—
486#120—21no—
487#120—22no—
488#120D4×C2911yescharacteristic
489#120C23×C2911yescharacteristic
490C4×Q8—21no—
491C4×Q8—22no—
492C4×D4—22no—
493C4×D4—21no—
494C4×D4—22no—
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—22no—
498C4×D4—42no—
499#117—21no—
500#117—22no—
501#117—21no—
502#117—21no—
503#117D4×C2911yescharacteristic
504#117D4×C2911yescharacteristic, complemented
505#117D4×C2911yescharacteristic, complemented
506C2×C22⋊C4—22no—
507#104—24no—
508#101—21no—
509#100C23×C2912yes—
510#99—21no—
511#99—21no—
512#99—22no—
513#99—22no—
514#99—24no—
515#99C23×C2912yes—
516#99C23×C2912yes—
517C29#3355611yescharacteristic, direct product factor, Sylow
518C24—21no—
519C24C2×D4×C2911yescharacteristic
520#41—22no—
521#41—22no—
522#41—41no—
523#41—41no—
524#41—42no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—42no—
531#41—42no—
532#41—42no—
533#41—41no—
534#41—41no—
535#41—41no—
536#41—81no—
537#41—81no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—22no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C2911yescharacteristic
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—41no—
566C2×D4—42no—
567C2×D4C2×D4×C2911yescharacteristic
568C2×D4C2×D4×C2911yescharacteristic
569C2×D4C2×D4×C2912yes—
570C2×D4C24×C2911yescharacteristic
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4C2×D4×C2911yescharacteristic
581C22×C4C2×D4×C2911yescharacteristic
582C22×C4C2×D4×C2911yescharacteristic
583C22×C4C2×D4×C2911yescharacteristic
584C22×C4C2×D4×C2912yes—
585SD16—44no—
586D8—44no—
587M16—22no—
588M16—41no—
589C2×C8—41no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—42no—
603C4⋊C4—44no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—21no—
611C22⋊C4—22no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4C2×D4×C2911yescharacteristic
625C22⋊C4C2×D4×C2911yescharacteristic
626C22⋊C4C2×D4×C2912yes—
627C42—22no—
628C42—22no—
629C42—21no—
630C42—21no—
631C42—41no—
632C42—41no—
633C42C2×D4×C2912yes—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—81no—
641C23—81no—
642C23—82no—
643C23C29×#12011yescharacteristic
644C23C22×D4×C2911yescharacteristic
645C23C22×D4×C2911yescharacteristic
646Q8—22no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—81no—
654Q8—82no—
655D4—22no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—42no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—82no—
670D4—81no—
671D4—82no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—84no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—81no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4C29×#12011yescharacteristic
705C2×C4C29×#12011yescharacteristic
706C2×C4C29×#12011yescharacteristic
707C2×C4C22×D4×C2911yescharacteristic
708C8—42no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—82no—
724C22—82no—
725C22—81no—
726C22—161no—
727C22—162no—
728C22C2×C29×#12011yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—41no—
733C4—42no—
734C4—42no—
735C4—41no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—82no—
740C4—82no—
741C4C29×B(4,𝔽2)11yescharacteristic
742C4C29×B(4,𝔽2)11yescharacteristic
743C2—21no—
744C2—41no—
745C2—41no—
746C2—41no—
747C2—81no—
748C2—82no—
749C2—82no—
750C2C2×C29×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C29C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C29
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C2×#41×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3540C2semidirect
2. C29×#3028C2semidirect
3. C29×#3025C2semidirect
4. C29×#3021C2semidirect
5. C29×#2200C2semidirect
6. C29×#2198C2semidirect
7. C29×#2128C2semidirect
8. C29×#2123C2semidirect
9. C29×#2120C2semidirect
13. C29×#560C22semidirect
14. C29×#559C22semidirect
31. C29×#458C22semidirect
32. C29×#458C22semidirect
34. C29×B(4,𝔽2)C22semidirect
43. C29×#353C22semidirect
44. C29×#352C22semidirect
45. C29×#352C22semidirect
46. C29×AΣL(1,𝔽16)C22semidirect
59. C22×Q8×C29D4semidirect
60. C22×D4×C29D4semidirect
82. C29×#124D4semidirect
89. C29×#123D4semidirect
129. C29×#117D4semidirect
130. C29×#117D4semidirect
258. #33556C29direct (N × H)
334. #3540C2×C29semidirect
335. #3028C2×C29semidirect
336. #3025C2×C29semidirect
337. #3021C2×C29semidirect
338. #2200C2×C29semidirect
339. #2198C2×C29semidirect
340. #2128C2×C29semidirect
341. #2123C2×C29semidirect
342. #2120C2×C29semidirect
380. #560C22×C29semidirect
381. #559C22×C29semidirect
398. #458C22×C29semidirect
399. #458C22×C29semidirect
401. B(4,𝔽2)C22×C29semidirect
410. #353C22×C29semidirect
411. #352C22×C29semidirect
412. #352C22×C29semidirect
413. AΣL(1,𝔽16)C22×C29semidirect
434. C22×Q8D4×C29semidirect
435. C22×D4D4×C29semidirect
457. #124D4×C29semidirect
464. #123D4×C29semidirect
504. #117D4×C29semidirect
505. #117D4×C29semidirect
517. C29#33556direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35402
C29×#30282
C29×#30252
C29×#30212
C29×#22002
C29×#21982
C29×#21282
C29×#21232
C29×#21202
#3355629