Finite Group Databasebeta

← C29×#33558 #20328458

Subgroups — C29×#33558 #20328458

Order 7424.

1158 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3545C211yesmaximal, characteristic, complemented
2C29×#3026C212yesmaximal, complemented
3C2×C29×#455C211yesmaximal, characteristic, complemented
4C29×#2201C212yesmaximal, complemented
5C29×#2199C212yesmaximal, complemented
6C29×#2197C214yesmaximal, complemented
7C2×C29×#354C211yesmaximal, characteristic, complemented
8C29×#2121C212yesmaximal, complemented
9C2×C29×H(5,𝔽2)C2211yescharacteristic
10C2×C29×#137—21no—
11C29×#563C2211yescharacteristic, complemented
12C29×#562—21no—
13C29×H(3,𝔽4)C2211yescharacteristic, complemented
14C29×#555—21no—
15C29×#551—22no—
16C29×#551C2212yescomplemented
17C29×#546—22no—
18C29×#542—22no—
19C29×#538—22no—
20C29×#536—21no—
21C29×#534—22no—
22C29×#534C2212yes—
23C29×#529—21no—
24C2×C29×#124C2211yescharacteristic
25C29×#458—22no—
26C29×#458C2214yes—
27C29×B(4,𝔽2)—22no—
28C29×B(4,𝔽2)C2214yes—
29C29×#455—21no—
30C29×#455—21no—
31C29×#455C2212yes—
32C29×#455C2212yes—
33C2×C29×#104—21no—
34C2×C29×#100C2211yescharacteristic
35C2×C29×#99—22no—
36C2×C29×#99C2212yes—
37C29×#354C2212yescomplemented
38C29×#354C2212yescomplemented
39C29×#352C2214yescomplemented
40C29×AΣL(1,𝔽16)C2214yescomplemented
41C29×H(5,𝔽2)—22no—
42C29×H(5,𝔽2)—21no—
43C29×H(5,𝔽2)—42no—
44C29×H(5,𝔽2)C2312yes—
45C2×#41×C29—21no—
46C2×#41×C29—21no—
47C2×#41×C29—41no—
48C22×Q8×C29D411yescharacteristic, complemented
49C22×D4×C29—22no—
50C22×D4×C29—41no—
51C22×D4×C29D412yescomplemented
52C22×D4×C29C2311yescharacteristic
53C29×#137—22no—
54C29×#137—22no—
55C29×#137—42no—
56C2×Q16×C29—41no—
57C2×SD16×C29—41no—
58C2×M16×C29—21no—
59C29×C4⋊Q8—21no—
60C29×C4⋊Q8—21no—
61C29×#126—22no—
62C29×#126—22no—
63C29×#126—22no—
64C29×#125—21no—
65C29×#124—21no—
66C29×#124—22no—
67C29×#124—21no—
68C29×#124—22no—
69C29×#124—22no—
70C29×#124—21no—
71C29×#124D411yescharacteristic, complemented
72C29×#124D411yescharacteristic, complemented
73C29×#124C2311yescharacteristic
74C29×#124C2311yescharacteristic
75C29×#123—22no—
76C29×#123—22no—
77C29×#123—22no—
78C29×#123—22no—
79C29×#123—22no—
80C29×#123—24no—
81C29×#123—42no—
82C29×#123D412yescomplemented
83C29×#123C2312yes—
84C29×C22⋊Q8—21no—
85C29×C22⋊Q8—22no—
86C29×C22⋊Q8—22no—
87C29×C22⋊Q8—22no—
88C29×C22⋊Q8—22no—
89C29×#121—21no—
90C29×#121—22no—
91C29×#121—22no—
92C29×#121—22no—
93C29×#121—22no—
94C29×#121—44no—
95C29×#120—22no—
96C29×#120—22no—
97C29×#120—24no—
98C29×#120—42no—
99C29×#120D412yescomplemented
100C29×#120C2312yes—
101C4×Q8×C29—21no—
102C4×D4×C29—21no—
103C4×D4×C29—22no—
104C4×D4×C29—22no—
105C4×D4×C29—22no—
106C29×#117—21no—
107C29×#117—22no—
108C29×#117—22no—
109C2×C22⋊C4×C29—22no—
110C2×C22⋊C4×C29—22no—
111C2×C22⋊C4×C29—22no—
112C2×C22⋊C4×C29D412yescomplemented
113C2×C42×C29D411yescharacteristic, complemented
114C29×#104—22no—
115C29×#104—22no—
116C29×#100—21no—
117C29×#100C2312yes—
118C29×#99—22no—
119C29×#99—24no—
120C29×#99—24no—
121C29×#99C2314yes—
122C24×C29—22no—
123C24×C29C2×D412yes—
124C24×C29C2×D412yes—
125#41×C29—22no—
126#41×C29—22no—
127#41×C29—42no—
128#41×C29—41no—
129#41×C29—44no—
130#41×C29—42no—
131#41×C29—41no—
132#41×C29—81no—
133#41×C29—81no—
134C2×Q8×C29—21no—
135C2×Q8×C29—21no—
136C2×Q8×C29—21no—
137C2×Q8×C29—21no—
138C2×Q8×C29—41no—
139C2×Q8×C29—41no—
140C2×Q8×C29C2×D411yescharacteristic
141C2×Q8×C29C2×D411yescharacteristic
142C2×D4×C29—21no—
143C2×D4×C29—24no—
144C2×D4×C29—22no—
145C2×D4×C29—24no—
146C2×D4×C29—21no—
147C2×D4×C29—21no—
148C2×D4×C29—22no—
149C2×D4×C29—22no—
150C2×D4×C29—22no—
151C2×D4×C29—41no—
152C2×D4×C29—41no—
153C2×D4×C29—42no—
154C2×D4×C29—42no—
155C2×D4×C29—42no—
156C2×D4×C29—42no—
157C2×D4×C29—44no—
158C2×D4×C29—42no—
159C2×D4×C29—41no—
160C2×D4×C29—42no—
161C2×D4×C29—42no—
162C2×D4×C29—44no—
163C2×D4×C29C2×D412yes—
164C2×D4×C29C2×D411yescharacteristic
165C2×D4×C29C2411yescharacteristic
166C22×C4×C29—22no—
167C22×C4×C29—21no—
168C22×C4×C29—22no—
169C22×C4×C29—22no—
170C22×C4×C29—22no—
171C22×C4×C29—21no—
172C22×C4×C29—41no—
173C22×C4×C29—42no—
174C22×C4×C29C2×D411yescharacteristic
175C22×C4×C29C2×D412yes—
176Q16×C29—42no—
177Q16×C29—42no—
178SD16×C29—42no—
179SD16×C29—42no—
180M16×C29—22no—
181M16×C29—41no—
182C2×C8×C29—41no—
183C4⋊C4×C29—22no—
184C4⋊C4×C29—22no—
185C4⋊C4×C29—22no—
186C4⋊C4×C29—22no—
187C4⋊C4×C29—22no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—22no—
191C4⋊C4×C29—22no—
192C4⋊C4×C29—44no—
193C22⋊C4×C29—22no—
194C22⋊C4×C29—22no—
195C22⋊C4×C29—22no—
196C22⋊C4×C29—22no—
197C22⋊C4×C29—22no—
198C22⋊C4×C29—22no—
199C22⋊C4×C29—22no—
200C22⋊C4×C29—22no—
201C22⋊C4×C29—22no—
202C22⋊C4×C29—22no—
203C22⋊C4×C29—22no—
204C22⋊C4×C29—22no—
205C22⋊C4×C29—22no—
206C22⋊C4×C29—24no—
207C22⋊C4×C29—44no—
208C22⋊C4×C29—42no—
209C22⋊C4×C29—44no—
210C22⋊C4×C29C2×D412yes—
211C22⋊C4×C29C2×D412yes—
212C42×C29—21no—
213C42×C29—22no—
214C42×C29—21no—
215C42×C29—21no—
216C42×C29C2×D411yescharacteristic
217C42×C29C2×D411yescharacteristic
218#33558C2911yesmaximal, characteristic, direct product factor, Sylow
219C23×C29—22no—
220C23×C29—22no—
221C23×C29—24no—
222C23×C29—22no—
223C23×C29—42no—
224C23×C29—42no—
225C23×C29—41no—
226C23×C29—82no—
227C23×C29—82no—
228C23×C29—162no—
229C23×C29#12012yes—
230C23×C29#12011yescharacteristic
231C23×C29C22×D412yes—
232Q8×C29—22no—
233Q8×C29—41no—
234Q8×C29—41no—
235Q8×C29—41no—
236Q8×C29—81no—
237Q8×C29—81no—
238Q8×C29—81no—
239D4×C29—22no—
240D4×C29—41no—
241D4×C29—42no—
242D4×C29—41no—
243D4×C29—41no—
244D4×C29—44no—
245D4×C29—44no—
246D4×C29—42no—
247D4×C29—42no—
248D4×C29—42no—
249D4×C29—42no—
250D4×C29—82no—
251D4×C29—82no—
252D4×C29—82no—
253D4×C29—81no—
254D4×C29—81no—
255D4×C29—164no—
256C2×C4×C29—21no—
257C2×C4×C29—21no—
258C2×C4×C29—24no—
259C2×C4×C29—21no—
260C2×C4×C29—21no—
261C2×C4×C29—22no—
262C2×C4×C29—21no—
263C2×C4×C29—22no—
264C2×C4×C29—22no—
265C2×C4×C29—21no—
266C2×C4×C29—42no—
267C2×C4×C29—42no—
268C2×C4×C29—42no—
269C2×C4×C29—41no—
270C2×C4×C29—41no—
271C2×C4×C29—41no—
272C2×C4×C29—42no—
273C2×C4×C29—44no—
274C2×C4×C29—82no—
275C2×C4×C29—81no—
276C2×C4×C29—82no—
277C2×C4×C29—82no—
278C2×C4×C29—162no—
279C2×C4×C29#12011yescharacteristic
280C2×C4×C29C22×D411yescharacteristic
281C8×C29—42no—
282#3545C2×C2911yescharacteristic, complemented
283#3026C2×C2912yescomplemented
284C2×#455C2×C2911yescharacteristic, complemented
285#2201C2×C2912yescomplemented
286#2199C2×C2912yescomplemented
287#2197C2×C2914yescomplemented
288C2×#354C2×C2911yescharacteristic, complemented
289#2121C2×C2912yescomplemented
290C22×C29—22no—
291C22×C29—22no—
292C22×C29—41no—
293C22×C29—42no—
294C22×C29—42no—
295C22×C29—42no—
296C22×C29—42no—
297C22×C29—42no—
298C22×C29—42no—
299C22×C29—82no—
300C22×C29—82no—
301C22×C29—82no—
302C22×C29—84no—
303C22×C29—84no—
304C22×C29—162no—
305C22×C29B(4,𝔽2)11yescharacteristic
306C22×C29B(4,𝔽2)11yescharacteristic
307C22×C29C2×#12011yescharacteristic
308C4×C29—21no—
309C4×C29—21no—
310C4×C29—41no—
311C4×C29—42no—
312C4×C29—42no—
313C4×C29—41no—
314C4×C29—42no—
315C4×C29—41no—
316C4×C29—41no—
317C4×C29—42no—
318C4×C29—84no—
319C2×H(5,𝔽2)C22×C2911yescharacteristic
320C2×#137—21no—
321#563C22×C2911yescharacteristic, complemented
322#562—21no—
323H(3,𝔽4)C22×C2911yescharacteristic, complemented
324#555—21no—
325#551—22no—
326#551C22×C2912yescomplemented
327#546—22no—
328#542—22no—
329#538—22no—
330#536—21no—
331#534—22no—
332#534C22×C2912yes—
333#529—21no—
334C2×#124C22×C2911yescharacteristic
335#458—22no—
336#458C22×C2914yes—
337B(4,𝔽2)—22no—
338B(4,𝔽2)C22×C2914yes—
339#455—21no—
340#455—21no—
341#455C22×C2912yes—
342#455C22×C2912yes—
343C2×#104—21no—
344C2×#100C22×C2911yescharacteristic
345C2×#99—22no—
346C2×#99C22×C2912yes—
347#354C22×C2912yescomplemented
348#354C22×C2912yescomplemented
349#352C22×C2914yescomplemented
350AΣL(1,𝔽16)C22×C2914yescomplemented
351C2×C29—21no—
352C2×C29—21no—
353C2×C29—21no—
354C2×C29—42no—
355C2×C29—42no—
356C2×C29—82no—
357C2×C29—82no—
358C2×C29C2×B(4,𝔽2)11yescharacteristic
359H(5,𝔽2)—22no—
360H(5,𝔽2)—21no—
361H(5,𝔽2)—42no—
362H(5,𝔽2)C23×C2912yes—
363C2×#41—21no—
364C2×#41—21no—
365C2×#41—41no—
366C22×Q8D4×C2911yescharacteristic, complemented
367C22×D4—22no—
368C22×D4—41no—
369C22×D4D4×C2912yescomplemented
370C22×D4C23×C2911yescharacteristic
371#137—22no—
372#137—22no—
373#137—42no—
374C2×Q16—41no—
375C2×SD16—41no—
376C2×M16—21no—
377C4⋊Q8—21no—
378C4⋊Q8—21no—
379#126—22no—
380#126—22no—
381#126—22no—
382#125—21no—
383#124—21no—
384#124—22no—
385#124—21no—
386#124—22no—
387#124—22no—
388#124—21no—
389#124D4×C2911yescharacteristic, complemented
390#124D4×C2911yescharacteristic, complemented
391#124C23×C2911yescharacteristic
392#124C23×C2911yescharacteristic
393#123—22no—
394#123—22no—
395#123—22no—
396#123—22no—
397#123—22no—
398#123—24no—
399#123—42no—
400#123D4×C2912yescomplemented
401#123C23×C2912yes—
402C22⋊Q8—21no—
403C22⋊Q8—22no—
404C22⋊Q8—22no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407#121—21no—
408#121—22no—
409#121—22no—
410#121—22no—
411#121—22no—
412#121—44no—
413#120—22no—
414#120—22no—
415#120—24no—
416#120—42no—
417#120D4×C2912yescomplemented
418#120C23×C2912yes—
419C4×Q8—21no—
420C4×D4—21no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—22no—
424#117—21no—
425#117—22no—
426#117—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4D4×C2912yescomplemented
431C2×C42D4×C2911yescharacteristic, complemented
432#104—22no—
433#104—22no—
434#100—21no—
435#100C23×C2912yes—
436#99—22no—
437#99—24no—
438#99—24no—
439#99C23×C2914yes—
440C29#3355811yescharacteristic, direct product factor, Sylow
441C24—22no—
442C24C2×D4×C2912yes—
443C24C2×D4×C2912yes—
444#41—22no—
445#41—22no—
446#41—42no—
447#41—41no—
448#41—44no—
449#41—42no—
450#41—41no—
451#41—81no—
452#41—81no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—41no—
458C2×Q8—41no—
459C2×Q8C2×D4×C2911yescharacteristic
460C2×Q8C2×D4×C2911yescharacteristic
461C2×D4—21no—
462C2×D4—24no—
463C2×D4—22no—
464C2×D4—24no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—22no—
468C2×D4—22no—
469C2×D4—22no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—44no—
477C2×D4—41no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—42no—
481C2×D4—44no—
482C2×D4C2×D4×C2912yes—
483C2×D4C2×D4×C2911yescharacteristic
484C2×D4C24×C2911yescharacteristic
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—41no—
492C22×C4—42no—
493C22×C4C2×D4×C2911yescharacteristic
494C22×C4C2×D4×C2912yes—
495Q16—42no—
496Q16—42no—
497SD16—42no—
498SD16—42no—
499M16—22no—
500M16—41no—
501C2×C8—41no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—44no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—24no—
526C22⋊C4—44no—
527C22⋊C4—42no—
528C22⋊C4—44no—
529C22⋊C4C2×D4×C2912yes—
530C22⋊C4C2×D4×C2912yes—
531C42—21no—
532C42—22no—
533C42—21no—
534C42—21no—
535C42C2×D4×C2911yescharacteristic
536C42C2×D4×C2911yescharacteristic
537C23—22no—
538C23—22no—
539C23—24no—
540C23—22no—
541C23—42no—
542C23—42no—
543C23—41no—
544C23—82no—
545C23—82no—
546C23—162no—
547C23C29×#12012yes—
548C23C29×#12011yescharacteristic
549C23C22×D4×C2912yes—
550Q8—22no—
551Q8—41no—
552Q8—41no—
553Q8—41no—
554Q8—81no—
555Q8—81no—
556Q8—81no—
557D4—22no—
558D4—41no—
559D4—42no—
560D4—41no—
561D4—41no—
562D4—44no—
563D4—44no—
564D4—42no—
565D4—42no—
566D4—42no—
567D4—42no—
568D4—82no—
569D4—81no—
570D4—82no—
571D4—82no—
572D4—81no—
573D4—164no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—24no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—42no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—42no—
591C2×C4—44no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—81no—
595C2×C4—82no—
596C2×C4—162no—
597C2×C4C29×#12011yescharacteristic
598C2×C4C22×D4×C2911yescharacteristic
599C8—42no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—82no—
610C22—82no—
611C22—82no—
612C22—84no—
613C22—84no—
614C22—162no—
615C22C29×B(4,𝔽2)11yescharacteristic
616C22C29×B(4,𝔽2)11yescharacteristic
617C22C2×C29×#12011yescharacteristic
618C4—21no—
619C4—21no—
620C4—41no—
621C4—42no—
622C4—42no—
623C4—41no—
624C4—42no—
625C4—41no—
626C4—41no—
627C4—42no—
628C4—84no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—42no—
633C2—42no—
634C2—82no—
635C2—82no—
636C2C2×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 ◁ C23×C29 ◁ C22×D4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3545C2semidirect
2. C29×#3026C2semidirect
3. C2×C29×#455C2semidirect
4. C29×#2201C2semidirect
5. C29×#2199C2semidirect
6. C29×#2197C2semidirect
7. C2×C29×#354C2semidirect
8. C29×#2121C2semidirect
11. C29×#563C22semidirect
13. C29×H(3,𝔽4)C22semidirect
16. C29×#551C22semidirect
37. C29×#354C22semidirect
38. C29×#354C22semidirect
39. C29×#352C22semidirect
40. C29×AΣL(1,𝔽16)C22semidirect
48. C22×Q8×C29D4semidirect
51. C22×D4×C29D4semidirect
71. C29×#124D4semidirect
72. C29×#124D4semidirect
82. C29×#123D4semidirect
99. C29×#120D4semidirect
112. C2×C22⋊C4×C29D4semidirect
113. C2×C42×C29D4semidirect
218. #33558C29direct (N × H)
282. #3545C2×C29semidirect
283. #3026C2×C29semidirect
284. C2×#455C2×C29semidirect
285. #2201C2×C29semidirect
286. #2199C2×C29semidirect
287. #2197C2×C29semidirect
288. C2×#354C2×C29semidirect
289. #2121C2×C29semidirect
321. #563C22×C29semidirect
323. H(3,𝔽4)C22×C29semidirect
326. #551C22×C29semidirect
347. #354C22×C29semidirect
348. #354C22×C29semidirect
349. #352C22×C29semidirect
350. AΣL(1,𝔽16)C22×C29semidirect
366. C22×Q8D4×C29semidirect
369. C22×D4D4×C29semidirect
389. #124D4×C29semidirect
390. #124D4×C29semidirect
400. #123D4×C29semidirect
417. #120D4×C29semidirect
430. C2×C22⋊C4D4×C29semidirect
431. C2×C42D4×C29semidirect
440. C29#33558direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35452
C29×#30262
C2×C29×#4552
C29×#22012
C29×#21992
C29×#21972
C2×C29×#3542
C29×#21212
#3355829