Finite Group Databasebeta

← C29×#19159 #20314059

Subgroups — C29×#19159 #20314059

Order 7424.

620 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3167C211yesmaximal, characteristic, complemented
2C29×#3107C211yesmaximal, characteristic, complemented
3C29×#3106C211yesmaximal, characteristic
4C29×#2965C211yesmaximal, characteristic, complemented
5C29×#1704C211yesmaximal, characteristic, complemented
6C29×#1703C211yesmaximal, characteristic, complemented
7C29×#1702C211yesmaximal, characteristic, complemented
8C29×#1701C211yesmaximal, characteristic, complemented
9C29×#1692C211yesmaximal, characteristic, complemented
10C29×#1691C211yesmaximal, characteristic, complemented
11C29×#1686C211yesmaximal, characteristic, complemented
12C29×#1685C211yesmaximal, characteristic, complemented
13C29×#1564C211yesmaximal, characteristic, complemented
14C29×#1544C211yesmaximal, characteristic, complemented
15C29×#1543C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C29×#532C2211yescharacteristic
18C4×#41×C29C2211yescharacteristic
19C29×#498C2211yescharacteristic
20C29×#492C2211yescharacteristic
21C29×#487C2211yescharacteristic
22C29×#486C2211yescharacteristic
23C29×#485—21no—
24C29×#482—21no—
25C29×#477C2211yescharacteristic
26C29×#476C2211yescharacteristic
27C29×#475C2211yescharacteristic
28C29×#474C2211yescharacteristic
29C29×#465—21no—
30C29×#465—21no—
31C29×#462C2211yescharacteristic
32C29×#461C2211yescharacteristic
33C29×#460C2211yescharacteristic
34C29×#459C2211yescharacteristic
35C29×#452—21no—
36C29×#449—21no—
37C29×#446C2211yescharacteristic
38C29×#446C2211yescharacteristic
39C4×Q16×C29—21no—
40C4×SD16×C29—21no—
41C4×SD16×C29—21no—
42C4×SD16×C29—21no—
43C4×SD16×C29—21no—
44C4×D8×C29—21no—
45C29×#436C2211yescharacteristic
46C29×#436C2211yescharacteristic
47C29×#435—21no—
48C29×#435—21no—
49C29×#431—21no—
50C29×#431C2211yescharacteristic
51C29×#431C2211yescharacteristic
52C29×#431C2211yescharacteristic
53C4×M16×C29—21no—
54C2×C4×C8×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C2×#41×C29D411yescharacteristic
69C2×Q16×C29—21no—
70C2×SD16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×D8×C29—21no—
75C2×M16×C29—21no—
76C2×M16×C29—21no—
77C22×C8×C29D411yescharacteristic
78C22×C8×C29D411yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×#127C2311yescharacteristic
83C29×#125—21no—
84C29×#124—21no—
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8—21no—
87C29×#121—21no—
88C29×#121—21no—
89C4×Q8×C29—21no—
90C4×Q8×C29—21no—
91C4×Q8×C29D411yescharacteristic
92C4×Q8×C29C2311yescharacteristic
93C4×D4×C29—21no—
94C4×D4×C29—21no—
95C4×D4×C29—21no—
96C4×D4×C29—21no—
97C4×D4×C29D411yescharacteristic
98C4×D4×C29C2311yescharacteristic
99C29×#117—21no—
100C29×#117—21no—
101C29×#117D411yescharacteristic
102C2×C42×C29—21no—
103C2×C42×C29C2311yescharacteristic
104C29×#107—21no—
105C29×#107—21no—
106C29×#106—21no—
107C29×#106—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×C4⋊C8—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8C2311yescharacteristic
113C29×C4⋊C8C2311yescharacteristic
114C29×C4⋊C8C2311yescharacteristic
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×#103—21no—
119C29×#103—21no—
120C29×#103—21no—
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#102—21no—
125C29×#102—21no—
126C29×#102—21no—
127C29×#102—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×C22⋊C8—21no—
131C29×C22⋊C8—21no—
132C29×C22⋊C8—21no—
133C29×C22⋊C8—21no—
134C29×C22⋊C8—21no—
135C29×#97—21no—
136C29×#97—21no—
137C4×C8×C29—21no—
138C4×C8×C29—21no—
139C4×C8×C29—21no—
140C4×C8×C29D411yescharacteristic
141C4×C8×C29D411yescharacteristic
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—41no—
145#41×C29—41no—
146#41×C29—82no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29C2×D411yescharacteristic
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—41no—
156C2×D4×C29C2×D411yescharacteristic
157C22×C4×C29—21no—
158C22×C4×C29—21no—
159C22×C4×C29—21no—
160C22×C4×C29—41no—
161C22×C4×C29C2×D411yescharacteristic
162C22×C4×C29C2×D411yescharacteristic
163C22×C4×C29#4111yescharacteristic
164Q16×C29—42no—
165SD16×C29—42no—
166SD16×C29—42no—
167SD16×C29—42no—
168SD16×C29—42no—
169D8×C29—42no—
170M16×C29—42no—
171M16×C29—42no—
172C2×C8×C29—22no—
173C2×C8×C29—21no—
174C2×C8×C29—21no—
175C2×C8×C29—21no—
176C2×C8×C29—21no—
177C2×C8×C29—21no—
178C2×C8×C29—21no—
179C2×C8×C29—41no—
180C2×C8×C29C2×D411yescharacteristic
181C2×C8×C29C2×D411yescharacteristic
182C2×C8×C29C2×D411yescharacteristic
183C2×C8×C29C2×D411yescharacteristic
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—41no—
193C4⋊C4×C29—41no—
194C4⋊C4×C29C2×D411yescharacteristic
195C4⋊C4×C29C2×D411yescharacteristic
196C22⋊C4×C29—21no—
197C22⋊C4×C29—21no—
198C22⋊C4×C29—21no—
199C22⋊C4×C29—41no—
200C22⋊C4×C29—41no—
201C22⋊C4×C29—41no—
202C42×C29—21no—
203C42×C29—21no—
204C42×C29—21no—
205C42×C29—41no—
206C42×C29C2×D411yescharacteristic
207C42×C29C2×D411yescharacteristic
208C42×C29#4111yescharacteristic
209C42×C29C2411yescharacteristic
210#19159C2911yesmaximal, characteristic, direct product factor, Sylow
211C23×C29—21no—
212C23×C29—41no—
213C23×C29#12111yescharacteristic
214Q8×C29—21no—
215Q8×C29—21no—
216Q8×C29—41no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29—41no—
220Q8×C29—81no—
221D4×C29—21no—
222D4×C29—21no—
223D4×C29—42no—
224D4×C29—41no—
225D4×C29—41no—
226D4×C29—41no—
227D4×C29—41no—
228D4×C29—81no—
229D4×C29—82no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
233C2×C4×C29—21no—
234C2×C4×C29—22no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—42no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
241C2×C4×C29—42no—
242C2×C4×C29—41no—
243C2×C4×C29—41no—
244C2×C4×C29—41no—
245C2×C4×C29—82no—
246C2×C4×C29#12111yescharacteristic
247C2×C4×C29#12111yescharacteristic
248C2×C4×C29#12111yescharacteristic
249C2×C4×C29C22×D411yescharacteristic
250C2×C4×C29C22×D411yescharacteristic
251C2×C4×C29C2×#4111yescharacteristic
252C8×C29—21no—
253C8×C29—21no—
254C8×C29—21no—
255C8×C29—41no—
256C8×C29—41no—
257C8×C29—41no—
258C8×C29—41no—
259C8×C29—41no—
260C8×C29—41no—
261C8×C29#13512yes—
262#3167C2×C2911yescharacteristic, complemented
263#3107C2×C2911yescharacteristic, complemented
264#3106C2×C2911yescharacteristic
265#2965C2×C2911yescharacteristic, complemented
266#1704C2×C2911yescharacteristic, complemented
267#1703C2×C2911yescharacteristic, complemented
268#1702C2×C2911yescharacteristic, complemented
269#1701C2×C2911yescharacteristic, complemented
270#1692C2×C2911yescharacteristic, complemented
271#1691C2×C2911yescharacteristic, complemented
272#1686C2×C2911yescharacteristic, complemented
273#1685C2×C2911yescharacteristic, complemented
274#1564C2×C2911yescharacteristic, complemented
275#1544C2×C2911yescharacteristic, complemented
276#1543C2×C2911yescharacteristic, complemented
277C22×C29—21no—
278C22×C29—21no—
279C22×C29—21no—
280C22×C29—41no—
281C22×C29—41no—
282C22×C29—41no—
283C22×C29—81no—
284C22×C29—81no—
285C22×C29—81no—
286C22×C29C2×#12111yescharacteristic
287C4×C29—21no—
288C4×C29—21no—
289C4×C29—21no—
290C4×C29—41no—
291C4×C29—41no—
292C4×C29—41no—
293C4×C29—81no—
294C4×C29—81no—
295C4×C29—81no—
296C4×C29#47112yes—
297C4×C29C2×#13511yescharacteristic
298C4×C29#57511yescharacteristic
299C4×C29#57511yescharacteristic
300C4×C29#57511yescharacteristic
301#533C22×C2911yescharacteristic
302#532C22×C2911yescharacteristic
303C4×#41C22×C2911yescharacteristic
304#498C22×C2911yescharacteristic
305#492C22×C2911yescharacteristic
306#487C22×C2911yescharacteristic
307#486C22×C2911yescharacteristic
308#485—21no—
309#482—21no—
310#477C22×C2911yescharacteristic
311#476C22×C2911yescharacteristic
312#475C22×C2911yescharacteristic
313#474C22×C2911yescharacteristic
314#465—21no—
315#465—21no—
316#462C22×C2911yescharacteristic
317#461C22×C2911yescharacteristic
318#460C22×C2911yescharacteristic
319#459C22×C2911yescharacteristic
320#452—21no—
321#449—21no—
322#446C22×C2911yescharacteristic
323#446C22×C2911yescharacteristic
324C4×Q16—21no—
325C4×SD16—21no—
326C4×SD16—21no—
327C4×SD16—21no—
328C4×SD16—21no—
329C4×D8—21no—
330#436C22×C2911yescharacteristic
331#436C22×C2911yescharacteristic
332#435—21no—
333#435—21no—
334#431—21no—
335#431C22×C2911yescharacteristic
336#431C22×C2911yescharacteristic
337#431C22×C2911yescharacteristic
338C4×M16—21no—
339C2×C4×C8C22×C2911yescharacteristic
340#335C22×C2911yescharacteristic
341#335C22×C2911yescharacteristic
342#334C22×C2911yescharacteristic
343#334C22×C2911yescharacteristic
344#333C22×C2911yescharacteristic
345#333C22×C2911yescharacteristic
346#332C22×C2911yescharacteristic
347#332C22×C2911yescharacteristic
348#332C22×C2911yescharacteristic
349#332C22×C2911yescharacteristic
350#331C22×C2911yescharacteristic
351#331C22×C2911yescharacteristic
352C2×C29—41no—
353C2×C29—81no—
354C2×C29—161no—
355C2×C29#303511yescharacteristic
356C2×C29#305411yescharacteristic
357C2×C29C2×#47111yescharacteristic
358C2×#41—21no—
359C2×#41D4×C2911yescharacteristic
360C2×Q16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×D8—21no—
366C2×M16—21no—
367C2×M16—21no—
368C22×C8D4×C2911yescharacteristic
369C22×C8D4×C2911yescharacteristic
370C4⋊Q8C23×C2911yescharacteristic
371C4⋊Q8C23×C2911yescharacteristic
372C4⋊Q8C23×C2911yescharacteristic
373#127C23×C2911yescharacteristic
374#125—21no—
375#124—21no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378#121—21no—
379#121—21no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8D4×C2911yescharacteristic
383C4×Q8C23×C2911yescharacteristic
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4D4×C2911yescharacteristic
389C4×D4C23×C2911yescharacteristic
390#117—21no—
391#117—21no—
392#117D4×C2911yescharacteristic
393C2×C42—21no—
394C2×C42C23×C2911yescharacteristic
395#107—21no—
396#107—21no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8C23×C2911yescharacteristic
404C4⋊C8C23×C2911yescharacteristic
405C4⋊C8C23×C2911yescharacteristic
406C4⋊C8C23×C2911yescharacteristic
407C4⋊C8C23×C2911yescharacteristic
408C4⋊C8C23×C2911yescharacteristic
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—21no—
426#97—21no—
427#97—21no—
428C4×C8—21no—
429C4×C8—21no—
430C4×C8—21no—
431C4×C8D4×C2911yescharacteristic
432C4×C8D4×C2911yescharacteristic
433C4×C8C23×C2911yescharacteristic
434C4×C8C23×C2911yescharacteristic
435C29#1915911yescharacteristic, direct product factor, Sylow
436#41—41no—
437#41—41no—
438#41—82no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C2×D4×C2911yescharacteristic
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—41no—
448C2×D4C2×D4×C2911yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—41no—
453C22×C4C2×D4×C2911yescharacteristic
454C22×C4C2×D4×C2911yescharacteristic
455C22×C4#41×C2911yescharacteristic
456Q16—42no—
457SD16—42no—
458SD16—42no—
459SD16—42no—
460SD16—42no—
461D8—42no—
462M16—42no—
463M16—42no—
464C2×C8—22no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—41no—
472C2×C8C2×D4×C2911yescharacteristic
473C2×C8C2×D4×C2911yescharacteristic
474C2×C8C2×D4×C2911yescharacteristic
475C2×C8C2×D4×C2911yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4C2×D4×C2911yescharacteristic
487C4⋊C4C2×D4×C2911yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—41no—
498C42C2×D4×C2911yescharacteristic
499C42C2×D4×C2911yescharacteristic
500C42#41×C2911yescharacteristic
501C42C24×C2911yescharacteristic
502C23—21no—
503C23—41no—
504C23C29×#12111yescharacteristic
505Q8—21no—
506Q8—21no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—81no—
512D4—21no—
513D4—21no—
514D4—42no—
515D4—41no—
516D4—41no—
517D4—41no—
518D4—41no—
519D4—81no—
520D4—82no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4C29×#12111yescharacteristic
538C2×C4C29×#12111yescharacteristic
539C2×C4C29×#12111yescharacteristic
540C2×C4C22×D4×C2911yescharacteristic
541C2×C4C22×D4×C2911yescharacteristic
542C2×C4C2×#41×C2911yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8C29×#13512yes—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22C2×C29×#12111yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—41no—
567C4—41no—
568C4—41no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4C29×#47112yes—
573C4C2×C29×#13511yescharacteristic
574C4C29×#57511yescharacteristic
575C4C29×#57511yescharacteristic
576C4C29×#57511yescharacteristic
577C2—41no—
578C2—81no—
579C2—161no—
580C2C29×#303511yescharacteristic
581C2C29×#305411yescharacteristic
582C2C2×C29×#47111yescharacteristic
subgroupG/H
centerC2×C4×C29#121
commutator, Frattini, cosocleC42C24×C29
socleC22×C29C2×#121
prime radicalC29×#3106C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3167C2semidirect
2. C29×#3107C2semidirect
4. C29×#2965C2semidirect
5. C29×#1704C2semidirect
6. C29×#1703C2semidirect
7. C29×#1702C2semidirect
8. C29×#1701C2semidirect
9. C29×#1692C2semidirect
10. C29×#1691C2semidirect
11. C29×#1686C2semidirect
12. C29×#1685C2semidirect
13. C29×#1564C2semidirect
14. C29×#1544C2semidirect
15. C29×#1543C2semidirect
210. #19159C29direct (N × H)
262. #3167C2×C29semidirect
263. #3107C2×C29semidirect
265. #2965C2×C29semidirect
266. #1704C2×C29semidirect
267. #1703C2×C29semidirect
268. #1702C2×C29semidirect
269. #1701C2×C29semidirect
270. #1692C2×C29semidirect
271. #1691C2×C29semidirect
272. #1686C2×C29semidirect
273. #1685C2×C29semidirect
274. #1564C2×C29semidirect
275. #1544C2×C29semidirect
276. #1543C2×C29semidirect
435. C29#19159direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31672
C29×#31072
C29×#31062
C29×#29652
C29×#17042
C29×#17032
C29×#17022
C29×#17012
C29×#16922
C29×#16912
C29×#16862
C29×#16852
C29×#15642
C29×#15442
C29×#15432
#1915929