Finite Group Databasebeta

← C29×#19369 #20314269

Subgroups — C29×#19369 #20314269

Order 7424.

644 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3253C211yesmaximal, characteristic
2C29×#3235C211yesmaximal, characteristic, complemented
3C29×#3182C211yesmaximal, characteristic, complemented
4C29×#2935C211yesmaximal, characteristic, complemented
5C29×#1703C211yesmaximal, characteristic, complemented
6C29×#1697C211yesmaximal, characteristic, complemented
7C29×#1695C211yesmaximal, characteristic, complemented
8C29×#1685C211yesmaximal, characteristic, complemented
9C29×#1683C211yesmaximal, characteristic, complemented
10C29×#1677C211yesmaximal, characteristic, complemented
11C29×#1675C211yesmaximal, characteristic, complemented
12C29×#1665C211yesmaximal, characteristic, complemented
13C29×#1569C211yesmaximal, characteristic, complemented
14C29×#1551C211yesmaximal, characteristic, complemented
15C29×#1550C211yesmaximal, characteristic, complemented
16C2×C29×#131—21no—
17C29×#533C2211yescharacteristic
18C29×#532C2211yescharacteristic
19C29×#532C2211yescharacteristic
20C29×#501—21no—
21C29×#500C2211yescharacteristic
22C29×#492C2211yescharacteristic
23C29×#490—21no—
24C29×#487C2211yescharacteristic
25C29×#486C2211yescharacteristic
26C29×#482—21no—
27C29×#482—21no—
28C29×#476—21no—
29C29×#476C2211yescharacteristic
30C29×#476C2211yescharacteristic
31C29×#476C2211yescharacteristic
32C29×#476C2211yescharacteristic
33C29×#474C2211yescharacteristic
34C29×#474C2211yescharacteristic
35C29×#469—21no—
36C29×#469—21no—
37C29×#468—21no—
38C29×#468—21no—
39C29×#459—21no—
40C29×#459C2211yescharacteristic
41C29×#459C2211yescharacteristic
42C29×#440—21no—
43C29×#440—21no—
44C29×#436C2211yescharacteristic
45C29×#436C2211yescharacteristic
46C29×#435—21no—
47C29×#435—21no—
48C8×D4×C29C2211yescharacteristic
49C8×D4×C29C2211yescharacteristic
50C29×#432C2211yescharacteristic
51C29×#423C2211yescharacteristic
52C2×C29×C4⋊C8C2211yescharacteristic
53C29×#408—21no—
54C4×M16×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#333C2211yescharacteristic
62C29×#333C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29—21no—
69C2×SD16×C29—21no—
70C2×SD16×C29—21no—
71C2×D8×C29—21no—
72C2×D8×C29—21no—
73C29×#131—44no—
74C2×M16×C29—21no—
75C2×M16×C29—21no—
76C2×M16×C29—21no—
77C2×M16×C29D411yescharacteristic
78C2×M16×C29D411yescharacteristic
79C22×C8×C29—21no—
80C22×C8×C29—21no—
81C22×C8×C29—21no—
82C29×C4⋊Q8D411yescharacteristic
83C29×C4⋊Q8C2311yescharacteristic
84C29×C4⋊Q8C2311yescharacteristic
85C29×C4⋊Q8C2311yescharacteristic
86C29×#127D411yescharacteristic
87C29×#127C2311yescharacteristic
88C29×#125—21no—
89C29×#124—21no—
90C29×#124—21no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—21no—
93C29×#121—21no—
94C29×#121—21no—
95C29×#121—21no—
96C29×#121D411yescharacteristic
97C29×#121D411yescharacteristic
98C4×Q8×C29—21no—
99C4×Q8×C29—21no—
100C4×D4×C29—21no—
101C4×D4×C29—21no—
102C4×D4×C29—21no—
103C4×D4×C29C2311yescharacteristic
104C4×D4×C29C2311yescharacteristic
105C29×#117—21no—
106C2×C42×C29C2311yescharacteristic
107C29×#107—21no—
108C29×#107—21no—
109C29×#107—21no—
110C29×#107—21no—
111C29×#106—21no—
112C29×#106—21no—
113C29×#106—21no—
114C29×#106—21no—
115C29×C4⋊C8—21no—
116C29×C4⋊C8—21no—
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×C4⋊C8C2311yescharacteristic
123C29×#103—21no—
124C29×#103—21no—
125C29×#102—21no—
126C29×#102—21no—
127C29×#102—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×C22⋊C8—21no—
136C29×C22⋊C8—21no—
137C29×C22⋊C8—21no—
138C29×C22⋊C8—21no—
139C29×C22⋊C8—21no—
140C29×#97—21no—
141C29×#97D411yescharacteristic
142C29×#97D411yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C4×C8×C29C2311yescharacteristic
145#41×C29—42no—
146#41×C29—42no—
147#41×C29—82no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—21no—
159C2×D4×C29—41no—
160C2×D4×C29C2×D411yescharacteristic
161C2×D4×C29C2×D411yescharacteristic
162C22×C4×C29—21no—
163C22×C4×C29—21no—
164C22×C4×C29—41no—
165C22×C4×C29C2×D411yescharacteristic
166C22×C4×C29C2×D411yescharacteristic
167C22×C4×C29#4111yescharacteristic
168SD16×C29—42no—
169SD16×C29—42no—
170D8×C29—81no—
171D8×C29—81no—
172M16×C29—22no—
173M16×C29—41no—
174M16×C29—42no—
175M16×C29—42no—
176M16×C29—81no—
177C2×C8×C29—21no—
178C2×C8×C29—21no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29—21no—
182C2×C8×C29—21no—
183C2×C8×C29—42no—
184C2×C8×C29—42no—
185C2×C8×C29—42no—
186C2×C8×C29C2×D411yescharacteristic
187C2×C8×C29C2×D411yescharacteristic
188C2×C8×C29C2×D411yescharacteristic
189C2×C8×C29C2×D411yescharacteristic
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—41no—
198C4⋊C4×C29—41no—
199C4⋊C4×C29C2×D411yescharacteristic
200C4⋊C4×C29C2×D411yescharacteristic
201C22⋊C4×C29—21no—
202C22⋊C4×C29—21no—
203C22⋊C4×C29—21no—
204C22⋊C4×C29—21no—
205C22⋊C4×C29—41no—
206C22⋊C4×C29—41no—
207C22⋊C4×C29—41no—
208C42×C29—41no—
209C42×C29C2×D411yescharacteristic
210C42×C29C2×D411yescharacteristic
211C42×C29#4111yescharacteristic
212C42×C29C2411yescharacteristic
213#19369C2911yesmaximal, characteristic, direct product factor, Sylow
214C23×C29—21no—
215C23×C29—21no—
216C23×C29—41no—
217C23×C29#12111yescharacteristic
218Q8×C29—42no—
219Q8×C29—41no—
220Q8×C29—41no—
221Q8×C29—81no—
222Q8×C29—81no—
223D4×C29—21no—
224D4×C29—21no—
225D4×C29—21no—
226D4×C29—21no—
227D4×C29—42no—
228D4×C29—42no—
229D4×C29—42no—
230D4×C29—41no—
231D4×C29—41no—
232D4×C29—41no—
233D4×C29—41no—
234D4×C29—81no—
235D4×C29—81no—
236D4×C29—82no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
242C2×C4×C29—21no—
243C2×C4×C29—41no—
244C2×C4×C29—41no—
245C2×C4×C29—41no—
246C2×C4×C29—41no—
247C2×C4×C29—41no—
248C2×C4×C29—41no—
249C2×C4×C29—41no—
250C2×C4×C29—41no—
251C2×C4×C29—82no—
252C2×C4×C29#12111yescharacteristic
253C2×C4×C29#12111yescharacteristic
254C2×C4×C29#12111yescharacteristic
255C2×C4×C29C22×D411yescharacteristic
256C2×C4×C29C22×D411yescharacteristic
257C2×C4×C29C2×#4111yescharacteristic
258C8×C29—21no—
259C8×C29—21no—
260C8×C29—21no—
261C8×C29—41no—
262C8×C29—41no—
263C8×C29—41no—
264C8×C29—41no—
265C8×C29—41no—
266C8×C29—41no—
267C8×C29AGL(1,ℤ/8)12yes—
268#3253C2×C2911yescharacteristic
269#3235C2×C2911yescharacteristic, complemented
270#3182C2×C2911yescharacteristic, complemented
271#2935C2×C2911yescharacteristic, complemented
272#1703C2×C2911yescharacteristic, complemented
273#1697C2×C2911yescharacteristic, complemented
274#1695C2×C2911yescharacteristic, complemented
275#1685C2×C2911yescharacteristic, complemented
276#1683C2×C2911yescharacteristic, complemented
277#1677C2×C2911yescharacteristic, complemented
278#1675C2×C2911yescharacteristic, complemented
279#1665C2×C2911yescharacteristic, complemented
280#1569C2×C2911yescharacteristic, complemented
281#1551C2×C2911yescharacteristic, complemented
282#1550C2×C2911yescharacteristic, complemented
283C22×C29—21no—
284C22×C29—21no—
285C22×C29—21no—
286C22×C29—41no—
287C22×C29—41no—
288C22×C29—41no—
289C22×C29—41no—
290C22×C29—41no—
291C22×C29—41no—
292C22×C29—81no—
293C22×C29—81no—
294C22×C29—81no—
295C22×C29C2×#12111yescharacteristic
296C4×C29—21no—
297C4×C29—21no—
298C4×C29—21no—
299C4×C29—21no—
300C4×C29—41no—
301C4×C29—41no—
302C4×C29—81no—
303C4×C29—81no—
304C4×C29—81no—
305C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
306C4×C29#57511yescharacteristic
307C4×C29#57711yescharacteristic
308C4×C29#57811yescharacteristic
309C2×#131—21no—
310#533C22×C2911yescharacteristic
311#532C22×C2911yescharacteristic
312#532C22×C2911yescharacteristic
313#501—21no—
314#500C22×C2911yescharacteristic
315#492C22×C2911yescharacteristic
316#490—21no—
317#487C22×C2911yescharacteristic
318#486C22×C2911yescharacteristic
319#482—21no—
320#482—21no—
321#476—21no—
322#476C22×C2911yescharacteristic
323#476C22×C2911yescharacteristic
324#476C22×C2911yescharacteristic
325#476C22×C2911yescharacteristic
326#474C22×C2911yescharacteristic
327#474C22×C2911yescharacteristic
328#469—21no—
329#469—21no—
330#468—21no—
331#468—21no—
332#459—21no—
333#459C22×C2911yescharacteristic
334#459C22×C2911yescharacteristic
335#440—21no—
336#440—21no—
337#436C22×C2911yescharacteristic
338#436C22×C2911yescharacteristic
339#435—21no—
340#435—21no—
341C8×D4C22×C2911yescharacteristic
342C8×D4C22×C2911yescharacteristic
343#432C22×C2911yescharacteristic
344#423C22×C2911yescharacteristic
345C2×C4⋊C8C22×C2911yescharacteristic
346#408—21no—
347C4×M16C22×C2911yescharacteristic
348#335C22×C2911yescharacteristic
349#335C22×C2911yescharacteristic
350#334C22×C2911yescharacteristic
351#334C22×C2911yescharacteristic
352#333C22×C2911yescharacteristic
353#333C22×C2911yescharacteristic
354#333C22×C2911yescharacteristic
355#333C22×C2911yescharacteristic
356#332C22×C2911yescharacteristic
357#332C22×C2911yescharacteristic
358#331C22×C2911yescharacteristic
359#331C22×C2911yescharacteristic
360C2×C29—41no—
361C2×C29—81no—
362C2×C29—81no—
363C2×C29—161no—
364C2×C29#303611yescharacteristic
365C2×C29#306311yescharacteristic
366C2×C29#306811yescharacteristic
367C2×#41—21no—
368C2×#41—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×D8—21no—
372C2×D8—21no—
373#131—44no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16D4×C2911yescharacteristic
378C2×M16D4×C2911yescharacteristic
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—21no—
382C4⋊Q8D4×C2911yescharacteristic
383C4⋊Q8C23×C2911yescharacteristic
384C4⋊Q8C23×C2911yescharacteristic
385C4⋊Q8C23×C2911yescharacteristic
386#127D4×C2911yescharacteristic
387#127C23×C2911yescharacteristic
388#125—21no—
389#124—21no—
390#124—21no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393#121—21no—
394#121—21no—
395#121—21no—
396#121D4×C2911yescharacteristic
397#121D4×C2911yescharacteristic
398C4×Q8—21no—
399C4×Q8—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4C23×C2911yescharacteristic
404C4×D4C23×C2911yescharacteristic
405#117—21no—
406C2×C42C23×C2911yescharacteristic
407#107—21no—
408#107—21no—
409#107—21no—
410#107—21no—
411#106—21no—
412#106—21no—
413#106—21no—
414#106—21no—
415C4⋊C8—21no—
416C4⋊C8—21no—
417C4⋊C8C23×C2911yescharacteristic
418C4⋊C8C23×C2911yescharacteristic
419C4⋊C8C23×C2911yescharacteristic
420C4⋊C8C23×C2911yescharacteristic
421C4⋊C8C23×C2911yescharacteristic
422C4⋊C8C23×C2911yescharacteristic
423#103—21no—
424#103—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435C22⋊C8—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440#97—21no—
441#97D4×C2911yescharacteristic
442#97D4×C2911yescharacteristic
443C4×C8C23×C2911yescharacteristic
444C4×C8C23×C2911yescharacteristic
445C29#1936911yescharacteristic, direct product factor, Sylow
446#41—42no—
447#41—42no—
448#41—82no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4C2×D4×C2911yescharacteristic
462C2×D4C2×D4×C2911yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4C2×D4×C2911yescharacteristic
467C22×C4C2×D4×C2911yescharacteristic
468C22×C4#41×C2911yescharacteristic
469SD16—42no—
470SD16—42no—
471D8—81no—
472D8—81no—
473M16—22no—
474M16—41no—
475M16—42no—
476M16—42no—
477M16—81no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—42no—
485C2×C8—42no—
486C2×C8—42no—
487C2×C8C2×D4×C2911yescharacteristic
488C2×C8C2×D4×C2911yescharacteristic
489C2×C8C2×D4×C2911yescharacteristic
490C2×C8C2×D4×C2911yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4C2×D4×C2911yescharacteristic
501C4⋊C4C2×D4×C2911yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C42—41no—
510C42C2×D4×C2911yescharacteristic
511C42C2×D4×C2911yescharacteristic
512C42#41×C2911yescharacteristic
513C42C24×C2911yescharacteristic
514C23—21no—
515C23—21no—
516C23—41no—
517C23C29×#12111yescharacteristic
518Q8—42no—
519Q8—41no—
520Q8—41no—
521Q8—81no—
522Q8—81no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—42no—
528D4—42no—
529D4—42no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—81no—
535D4—81no—
536D4—82no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—82no—
552C2×C4C29×#12111yescharacteristic
553C2×C4C29×#12111yescharacteristic
554C2×C4C29×#12111yescharacteristic
555C2×C4C22×D4×C2911yescharacteristic
556C2×C4C22×D4×C2911yescharacteristic
557C2×C4C2×#41×C2911yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8C29×AGL(1,ℤ/8)12yes—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22C2×C29×#12111yescharacteristic
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
591C4C29×#57511yescharacteristic
592C4C29×#57711yescharacteristic
593C4C29×#57811yescharacteristic
594C2—41no—
595C2—81no—
596C2—81no—
597C2—161no—
598C2C29×#303611yescharacteristic
599C2C29×#306311yescharacteristic
600C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3253C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3235C2semidirect
3. C29×#3182C2semidirect
4. C29×#2935C2semidirect
5. C29×#1703C2semidirect
6. C29×#1697C2semidirect
7. C29×#1695C2semidirect
8. C29×#1685C2semidirect
9. C29×#1683C2semidirect
10. C29×#1677C2semidirect
11. C29×#1675C2semidirect
12. C29×#1665C2semidirect
13. C29×#1569C2semidirect
14. C29×#1551C2semidirect
15. C29×#1550C2semidirect
213. #19369C29direct (N × H)
269. #3235C2×C29semidirect
270. #3182C2×C29semidirect
271. #2935C2×C29semidirect
272. #1703C2×C29semidirect
273. #1697C2×C29semidirect
274. #1695C2×C29semidirect
275. #1685C2×C29semidirect
276. #1683C2×C29semidirect
277. #1677C2×C29semidirect
278. #1675C2×C29semidirect
279. #1665C2×C29semidirect
280. #1569C2×C29semidirect
281. #1551C2×C29semidirect
282. #1550C2×C29semidirect
445. C29#19369direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32532
C29×#32352
C29×#31822
C29×#29352
C29×#17032
C29×#16972
C29×#16952
C29×#16852
C29×#16832
C29×#16772
C29×#16752
C29×#16652
C29×#15692
C29×#15512
C29×#15502
#1936929