Finite Group Databasebeta

← C29×#33555 #20328455

Subgroups — C29×#33555 #20328455

Order 7424.

1146 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3540C211yesmaximal, characteristic, complemented
2C29×#3027C211yesmaximal, characteristic, complemented
3C29×#3025C211yesmaximal, characteristic, complemented
4C29×#3022C211yesmaximal, characteristic, complemented
5C29×#2199C214yesmaximal, complemented
6C29×#2197C214yesmaximal, complemented
7C29×#2129C211yesmaximal, characteristic, complemented
8C29×#2122C211yesmaximal, characteristic, complemented
9C29×#2120C211yesmaximal, characteristic, complemented
10C29×#585C2211yescharacteristic
11C2×C29×#137—21no—
12C29×H(3,𝔽4)C2212yescomplemented
13C29×#560—21no—
14C29×#559—21no—
15C29×#556—21no—
16C29×#555—21no—
17C29×#551C2212yescomplemented
18C29×#548—21no—
19C29×#546—21no—
20C29×#542—22no—
21C29×#542—21no—
22C29×#538—22no—
23C29×#536C2211yescharacteristic
24C29×#535—21no—
25C29×#535C2211yescharacteristic
26C29×#525—21no—
27C29×#525—21no—
28C29×#525C2211yescharacteristic
29C29×#458—21no—
30C29×#458C2212yes—
31C29×B(4,𝔽2)—21no—
32C29×B(4,𝔽2)—22no—
33C29×B(4,𝔽2)C2214yes—
34C29×B(4,𝔽2)C2212yes—
35C29×#456—22no—
36C29×#455C2214yes—
37C29×#421—21no—
38C29×#413C2211yescharacteristic
39C29×#410—21no—
40C29×#410—21no—
41C29×#410C2211yescharacteristic
42C29×#410C2211yescharacteristic
43C29×#354C2214yescomplemented
44C29×#352C2212yescomplemented
45C29×AΣL(1,𝔽16)C2214yescomplemented
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, complemented
62C29×#137—24no—
63C29×#137—42no—
64C2×Q16×C29—41no—
65C2×SD16×C29—41no—
66C2×M16×C29—21no—
67C29×C4⋊Q8—21no—
68C29×C4⋊Q8D412yescomplemented
69C29×#127—21no—
70C29×#127—41no—
71C29×#126—22no—
72C29×#126—22no—
73C29×#126—22no—
74C29×#124—22no—
75C29×#124—21no—
76C29×#124—21no—
77C29×#124—22no—
78C29×#124—22no—
79C29×#124—22no—
80C29×#124—22no—
81C29×#124—41no—
82C29×#124C2312yes—
83C29×#123—22no—
84C29×#123—22no—
85C29×#123—21no—
86C29×#123—21no—
87C29×#123—22no—
88C29×#123—22no—
89C29×#123D411yescharacteristic, complemented
90C29×#123C2311yescharacteristic
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—22no—
93C29×C22⋊Q8—21no—
94C29×C22⋊Q8—22no—
95C29×C22⋊Q8—21no—
96C29×C22⋊Q8—21no—
97C29×C22⋊Q8—41no—
98C29×#121—21no—
99C29×#121—22no—
100C29×#121—22no—
101C29×#121—22no—
102C29×#121—21no—
103C29×#121—21no—
104C29×#121—21no—
105C29×#121—42no—
106C29×#121—41no—
107C29×#120—22no—
108C29×#120—22no—
109C29×#120—22no—
110C29×#120—24no—
111C29×#120D411yescharacteristic, complemented
112C29×#120D412yescomplemented
113C29×#120C2311yescharacteristic
114C29×#120C2312yes—
115C4×Q8×C29—21no—
116C4×Q8×C29—22no—
117C4×D4×C29—22no—
118C4×D4×C29—22no—
119C4×D4×C29—21no—
120C4×D4×C29—22no—
121C4×D4×C29—21no—
122C4×D4×C29—21no—
123C4×D4×C29—42no—
124C29×#117—21no—
125C29×#117—22no—
126C29×#117—21no—
127C29×#117—21no—
128C29×#117D411yescharacteristic, complemented
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—24no—
138C29×#99—22no—
139C29×#99—22no—
140C29×#99C2312yes—
141C29×#99C2312yes—
142C24×C29C2×D412yes—
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—41no—
168C2×Q8×C29—41no—
169C2×Q8×C29—42no—
170C2×Q8×C29C2×D412yes—
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—21no—
182C2×D4×C29—22no—
183C2×D4×C29—21no—
184C2×D4×C29—21no—
185C2×D4×C29—41no—
186C2×D4×C29—41no—
187C2×D4×C29—42no—
188C2×D4×C29—42no—
189C2×D4×C29—42no—
190C2×D4×C29—41no—
191C2×D4×C29—42no—
192C2×D4×C29—44no—
193C2×D4×C29C2×D411yescharacteristic
194C2×D4×C29C2×D411yescharacteristic
195C2×D4×C29C2411yescharacteristic
196C22×C4×C29—22no—
197C22×C4×C29—22no—
198C22×C4×C29—22no—
199C22×C4×C29—22no—
200C22×C4×C29—21no—
201C22×C4×C29—21no—
202C22×C4×C29—21no—
203C22×C4×C29—41no—
204C22×C4×C29—41no—
205C22×C4×C29—41no—
206C22×C4×C29C2×D411yescharacteristic
207C22×C4×C29C2×D411yescharacteristic
208C22×C4×C29C2×D411yescharacteristic
209C22×C4×C29C2×D411yescharacteristic
210Q16×C29—44no—
211SD16×C29—44no—
212M16×C29—22no—
213M16×C29—41no—
214C2×C8×C29—41no—
215C4⋊C4×C29—22no—
216C4⋊C4×C29—22no—
217C4⋊C4×C29—22no—
218C4⋊C4×C29—21no—
219C4⋊C4×C29—21no—
220C4⋊C4×C29—22no—
221C4⋊C4×C29—22no—
222C4⋊C4×C29—21no—
223C4⋊C4×C29—21no—
224C4⋊C4×C29—21no—
225C4⋊C4×C29—41no—
226C4⋊C4×C29—41no—
227C4⋊C4×C29—42no—
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—21no—
236C22⋊C4×C29—21no—
237C22⋊C4×C29—22no—
238C22⋊C4×C29—22no—
239C22⋊C4×C29—21no—
240C22⋊C4×C29—22no—
241C22⋊C4×C29—22no—
242C22⋊C4×C29—21no—
243C22⋊C4×C29—22no—
244C22⋊C4×C29—22no—
245C22⋊C4×C29—42no—
246C22⋊C4×C29—44no—
247C22⋊C4×C29—42no—
248C22⋊C4×C29C2×D412yes—
249C22⋊C4×C29C2×D411yescharacteristic
250C22⋊C4×C29C2×D411yescharacteristic
251C42×C29—22no—
252C42×C29—22no—
253C42×C29—21no—
254C42×C29—21no—
255C42×C29—41no—
256C42×C29—41no—
257C42×C29C2×D412yes—
258#33555C2911yesmaximal, characteristic, direct product factor, Sylow
259C23×C29—22no—
260C23×C29—22no—
261C23×C29—22no—
262C23×C29—21no—
263C23×C29—41no—
264C23×C29—41no—
265C23×C29—42no—
266C23×C29—81no—
267C23×C29—82no—
268C23×C29#12011yescharacteristic
269C23×C29C22×D411yescharacteristic
270C23×C29C22×D411yescharacteristic
271Q8×C29—22no—
272Q8×C29—41no—
273Q8×C29—42no—
274Q8×C29—41no—
275Q8×C29—41no—
276Q8×C29—41no—
277Q8×C29—41no—
278Q8×C29—41no—
279Q8×C29—82no—
280D4×C29—22no—
281D4×C29—41no—
282D4×C29—41no—
283D4×C29—41no—
284D4×C29—41no—
285D4×C29—41no—
286D4×C29—42no—
287D4×C29—42no—
288D4×C29—42no—
289D4×C29—42no—
290D4×C29—41no—
291D4×C29—41no—
292D4×C29—41no—
293D4×C29—81no—
294D4×C29—81no—
295D4×C29—82no—
296D4×C29—82no—
297D4×C29—82no—
298D4×C29—81no—
299D4×C29—82no—
300D4×C29—84no—
301D4×C29—164no—
302C2×C4×C29—21no—
303C2×C4×C29—21no—
304C2×C4×C29—21no—
305C2×C4×C29—21no—
306C2×C4×C29—21no—
307C2×C4×C29—21no—
308C2×C4×C29—22no—
309C2×C4×C29—22no—
310C2×C4×C29—21no—
311C2×C4×C29—22no—
312C2×C4×C29—21no—
313C2×C4×C29—22no—
314C2×C4×C29—22no—
315C2×C4×C29—21no—
316C2×C4×C29—42no—
317C2×C4×C29—42no—
318C2×C4×C29—42no—
319C2×C4×C29—41no—
320C2×C4×C29—42no—
321C2×C4×C29—41no—
322C2×C4×C29—41no—
323C2×C4×C29—41no—
324C2×C4×C29—42no—
325C2×C4×C29—42no—
326C2×C4×C29—81no—
327C2×C4×C29—81no—
328C2×C4×C29—82no—
329C2×C4×C29—82no—
330C2×C4×C29#12011yescharacteristic
331C2×C4×C29#12011yescharacteristic
332C2×C4×C29#12011yescharacteristic
333C2×C4×C29C22×D411yescharacteristic
334C8×C29—42no—
335#3540C2×C2911yescharacteristic, complemented
336#3027C2×C2911yescharacteristic, complemented
337#3025C2×C2911yescharacteristic, complemented
338#3022C2×C2911yescharacteristic, complemented
339#2199C2×C2914yescomplemented
340#2197C2×C2914yescomplemented
341#2129C2×C2911yescharacteristic, complemented
342#2122C2×C2911yescharacteristic, complemented
343#2120C2×C2911yescharacteristic, complemented
344C22×C29—21no—
345C22×C29—21no—
346C22×C29—21no—
347C22×C29—41no—
348C22×C29—41no—
349C22×C29—41no—
350C22×C29—42no—
351C22×C29—41no—
352C22×C29—41no—
353C22×C29—42no—
354C22×C29—42no—
355C22×C29—42no—
356C22×C29—41no—
357C22×C29—42no—
358C22×C29—82no—
359C22×C29—82no—
360C22×C29—84no—
361C22×C29—81no—
362C22×C29—161no—
363C22×C29C2×#12011yescharacteristic
364C4×C29—21no—
365C4×C29—21no—
366C4×C29—21no—
367C4×C29—41no—
368C4×C29—42no—
369C4×C29—42no—
370C4×C29—41no—
371C4×C29—42no—
372C4×C29—41no—
373C4×C29—42no—
374C4×C29—82no—
375C4×C29—82no—
376C4×C29B(4,𝔽2)11yescharacteristic
377C4×C29B(4,𝔽2)11yescharacteristic
378#585C22×C2911yescharacteristic
379C2×#137—21no—
380H(3,𝔽4)C22×C2912yescomplemented
381#560—21no—
382#559—21no—
383#556—21no—
384#555—21no—
385#551C22×C2912yescomplemented
386#548—21no—
387#546—21no—
388#542—22no—
389#542—21no—
390#538—22no—
391#536C22×C2911yescharacteristic
392#535—21no—
393#535C22×C2911yescharacteristic
394#525—21no—
395#525—21no—
396#525C22×C2911yescharacteristic
397#458—21no—
398#458C22×C2912yes—
399B(4,𝔽2)—21no—
400B(4,𝔽2)—22no—
401B(4,𝔽2)C22×C2914yes—
402B(4,𝔽2)C22×C2912yes—
403#456—22no—
404#455C22×C2914yes—
405#421—21no—
406#413C22×C2911yescharacteristic
407#410—21no—
408#410—21no—
409#410C22×C2911yescharacteristic
410#410C22×C2911yescharacteristic
411#354C22×C2914yescomplemented
412#352C22×C2912yescomplemented
413AΣL(1,𝔽16)C22×C2912yescomplemented
414AΣL(1,𝔽16)C22×C2914yescomplemented
415C2×C29—21no—
416C2×C29—41no—
417C2×C29—41no—
418C2×C29—41no—
419C2×C29—81no—
420C2×C29—82no—
421C2×C29—82no—
422C2×C29C2×B(4,𝔽2)11yescharacteristic
4232−1+4—21no—
4242−1+4—41no—
425H(5,𝔽2)—21no—
426H(5,𝔽2)—21no—
427H(5,𝔽2)—41no—
428H(5,𝔽2)C23×C2912yes—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—42no—
434C2×#41C23×C2911yescharacteristic
435C22×Q8D4×C2911yescharacteristic, complemented
436C22×D4D4×C2911yescharacteristic, complemented
437C23×C4D4×C2911yescharacteristic, complemented
438#137—24no—
439#137—42no—
440C2×Q16—41no—
441C2×SD16—41no—
442C2×M16—21no—
443C4⋊Q8—21no—
444C4⋊Q8D4×C2912yescomplemented
445#127—21no—
446#127—41no—
447#126—22no—
448#126—22no—
449#126—22no—
450#124—22no—
451#124—21no—
452#124—21no—
453#124—22no—
454#124—22no—
455#124—22no—
456#124—22no—
457#124—41no—
458#124C23×C2912yes—
459#123—22no—
460#123—22no—
461#123—21no—
462#123—21no—
463#123—22no—
464#123—22no—
465#123D4×C2911yescharacteristic, complemented
466#123C23×C2911yescharacteristic
467C22⋊Q8—21no—
468C22⋊Q8—22no—
469C22⋊Q8—21no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—41no—
474#121—21no—
475#121—22no—
476#121—22no—
477#121—22no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—42no—
482#121—41no—
483#120—22no—
484#120—22no—
485#120—22no—
486#120—24no—
487#120D4×C2911yescharacteristic, complemented
488#120D4×C2912yescomplemented
489#120C23×C2911yescharacteristic
490#120C23×C2912yes—
491C4×Q8—21no—
492C4×Q8—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—21no—
496C4×D4—22no—
497C4×D4—21no—
498C4×D4—21no—
499C4×D4—42no—
500#117—21no—
501#117—22no—
502#117—21no—
503#117—21no—
504#117D4×C2911yescharacteristic, complemented
505#117D4×C2911yescharacteristic, complemented
506#117D4×C2911yescharacteristic, complemented
507C2×C22⋊C4—22no—
508#104—24no—
509#101—21no—
510#100C23×C2912yes—
511#99—21no—
512#99—21no—
513#99—24no—
514#99—22no—
515#99—22no—
516#99C23×C2912yes—
517#99C23×C2912yes—
518C29#3355511yescharacteristic, direct product factor, Sylow
519C24C2×D4×C2912yes—
520C24C2×D4×C2911yescharacteristic
521#41—22no—
522#41—22no—
523#41—41no—
524#41—41no—
525#41—42no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—42no—
532#41—42no—
533#41—42no—
534#41—41no—
535#41—41no—
536#41—41no—
537#41—81no—
538#41—81no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—22no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C2912yes—
548C2×Q8C2×D4×C2911yescharacteristic
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—41no—
568C2×D4—42no—
569C2×D4—44no—
570C2×D4C2×D4×C2911yescharacteristic
571C2×D4C2×D4×C2911yescharacteristic
572C2×D4C24×C2911yescharacteristic
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4C2×D4×C2911yescharacteristic
584C22×C4C2×D4×C2911yescharacteristic
585C22×C4C2×D4×C2911yescharacteristic
586C22×C4C2×D4×C2911yescharacteristic
587Q16—44no—
588SD16—44no—
589M16—22no—
590M16—41no—
591C2×C8—41no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—42no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—21no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4—42no—
625C22⋊C4C2×D4×C2912yes—
626C22⋊C4C2×D4×C2911yescharacteristic
627C22⋊C4C2×D4×C2911yescharacteristic
628C42—22no—
629C42—22no—
630C42—21no—
631C42—21no—
632C42—41no—
633C42—41no—
634C42C2×D4×C2912yes—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—21no—
639C23—41no—
640C23—41no—
641C23—42no—
642C23—81no—
643C23—82no—
644C23C29×#12011yescharacteristic
645C23C22×D4×C2911yescharacteristic
646C23C22×D4×C2911yescharacteristic
647Q8—22no—
648Q8—41no—
649Q8—42no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—82no—
656D4—22no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—81no—
670D4—82no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—82no—
675D4—81no—
676D4—84no—
677D4—164no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4C29×#12011yescharacteristic
707C2×C4C29×#12011yescharacteristic
708C2×C4C29×#12011yescharacteristic
709C2×C4C22×D4×C2911yescharacteristic
710C8—42no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—42no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—82no—
726C22—82no—
727C22—84no—
728C22—81no—
729C22—161no—
730C22C2×C29×#12011yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—41no—
735C4—42no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—42no—
741C4—82no—
742C4—82no—
743C4C29×B(4,𝔽2)11yescharacteristic
744C4C29×B(4,𝔽2)11yescharacteristic
745C2—21no—
746C2—41no—
747C2—41no—
748C2—41no—
749C2—81no—
750C2—82no—
751C2—82no—
752C2C2×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×#3027C2semidirect
3. C29×#3025C2semidirect
4. C29×#3022C2semidirect
5. C29×#2199C2semidirect
6. C29×#2197C2semidirect
7. C29×#2129C2semidirect
8. C29×#2122C2semidirect
9. C29×#2120C2semidirect
12. C29×H(3,𝔽4)C22semidirect
17. C29×#551C22semidirect
43. C29×#354C22semidirect
44. C29×#352C22semidirect
45. C29×AΣL(1,𝔽16)C22semidirect
46. C29×AΣL(1,𝔽16)C22semidirect
59. C22×Q8×C29D4semidirect
60. C22×D4×C29D4semidirect
61. C23×C4×C29D4semidirect
68. C29×C4⋊Q8D4semidirect
89. C29×#123D4semidirect
111. C29×#120D4semidirect
112. C29×#120D4semidirect
128. C29×#117D4semidirect
129. C29×#117D4semidirect
130. C29×#117D4semidirect
258. #33555C29direct (N × H)
335. #3540C2×C29semidirect
336. #3027C2×C29semidirect
337. #3025C2×C29semidirect
338. #3022C2×C29semidirect
339. #2199C2×C29semidirect
340. #2197C2×C29semidirect
341. #2129C2×C29semidirect
342. #2122C2×C29semidirect
343. #2120C2×C29semidirect
380. H(3,𝔽4)C22×C29semidirect
385. #551C22×C29semidirect
411. #354C22×C29semidirect
412. #352C22×C29semidirect
413. AΣL(1,𝔽16)C22×C29semidirect
414. AΣL(1,𝔽16)C22×C29semidirect
435. C22×Q8D4×C29semidirect
436. C22×D4D4×C29semidirect
437. C23×C4D4×C29semidirect
444. C4⋊Q8D4×C29semidirect
465. #123D4×C29semidirect
487. #120D4×C29semidirect
488. #120D4×C29semidirect
504. #117D4×C29semidirect
505. #117D4×C29semidirect
506. #117D4×C29semidirect
518. C29#33555direct (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×#30272
C29×#30252
C29×#30222
C29×#21992
C29×#21972
C29×#21292
C29×#21222
C29×#21202
#3355529