Finite Group Databasebeta

← C29×#19308 #20314208

Subgroups — C29×#19308 #20314208

Order 7424.

632 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×#3182C211yesmaximal, characteristic
2C29×#3113C211yesmaximal, characteristic, complemented
3C29×#3037C211yesmaximal, characteristic
4Q8×M16×C29C211yesmaximal, characteristic, complemented
5C29×#1702C211yesmaximal, characteristic, complemented
6C29×#1700C211yesmaximal, characteristic, complemented
7C29×#1694C211yesmaximal, characteristic, complemented
8C29×#1686C211yesmaximal, characteristic, complemented
9C29×#1682C211yesmaximal, characteristic, complemented
10C29×#1680C211yesmaximal, characteristic, complemented
11C29×#1674C211yesmaximal, characteristic, complemented
12C29×#1666C211yesmaximal, characteristic, complemented
13C29×#1569C211yesmaximal, characteristic, complemented
14C29×#1561C211yesmaximal, characteristic, complemented
15C29×#1557C211yesmaximal, characteristic
16C2×C29×#137—21no—
17C29×#533C2211yescharacteristic
18C29×#532C2211yescharacteristic
19C2×C4×Q8×C29C2211yescharacteristic
20C29×#500C2211yescharacteristic
21C29×#492C2211yescharacteristic
22C29×#487C2211yescharacteristic
23C29×#486C2211yescharacteristic
24C29×#483—21no—
25C29×#475C2211yescharacteristic
26C29×#475C2211yescharacteristic
27C29×#468—21no—
28C29×#468—21no—
29C29×#464—21no—
30C29×#464—21no—
31C29×#462C2211yescharacteristic
32C29×#462C2211yescharacteristic
33C29×#462C2211yescharacteristic
34C29×#462C2211yescharacteristic
35C29×#460C2211yescharacteristic
36C29×#460C2211yescharacteristic
37C29×#451—21no—
38C29×#446—21no—
39C29×#446—21no—
40C29×#446C2211yescharacteristic
41C29×#446C2211yescharacteristic
42C8×Q8×C29C2211yescharacteristic
43C8×Q8×C29C2211yescharacteristic
44C29×#441—21no—
45C29×#441—21no—
46C29×#440—21no—
47C29×#440—21no—
48C29×#432C2211yescharacteristic
49C29×#423—21no—
50C29×#423C2211yescharacteristic
51C29×#423C2211yescharacteristic
52C29×#417—21no—
53C4×M16×C29—21no—
54C4×M16×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#332C2211yescharacteristic
60C29×#332C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C22×Q8×C29D411yescharacteristic
69C29×#137—44no—
70C2×Q16×C29—21no—
71C2×Q16×C29—21no—
72C2×Q16×C29—21no—
73C2×Q16×C29—21no—
74C2×SD16×C29—21no—
75C2×SD16×C29—21no—
76C2×SD16×C29—21no—
77C2×SD16×C29—21no—
78C2×M16×C29—21no—
79C2×M16×C29—21no—
80C2×M16×C29D411yescharacteristic
81C2×M16×C29D411yescharacteristic
82C29×C4⋊Q8C2311yescharacteristic
83C29×C4⋊Q8C2311yescharacteristic
84C29×C4⋊Q8C2311yescharacteristic
85C29×#127C2311yescharacteristic
86C29×#125—21no—
87C29×#124—21no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8—21no—
90C29×#121—21no—
91C29×#121—21no—
92C4×Q8×C29—21no—
93C4×Q8×C29—21no—
94C4×Q8×C29—21no—
95C4×Q8×C29—21no—
96C4×Q8×C29D411yescharacteristic
97C4×Q8×C29D411yescharacteristic
98C4×Q8×C29C2311yescharacteristic
99C4×Q8×C29C2311yescharacteristic
100C4×D4×C29—21no—
101C4×D4×C29—21no—
102C29×#117—21no—
103C2×C4⋊C4×C29—21no—
104C2×C4⋊C4×C29D411yescharacteristic
105C2×C42×C29—21no—
106C2×C42×C29C2311yescharacteristic
107C29×#107—21no—
108C29×#107—21no—
109C29×#106—21no—
110C29×#106—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8—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×#103—21no—
126C29×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#103—21no—
130C29×#103—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×C22⋊C8—21no—
136C29×#97—21no—
137C29×#97—21no—
138C29×#97—21no—
139C29×#97D411yescharacteristic
140C29×#97D411yescharacteristic
141C4×C8×C29—21no—
142C4×C8×C29—21no—
143C4×C8×C29C2311yescharacteristic
144C4×C8×C29C2311yescharacteristic
145#41×C29—42no—
146#41×C29—42no—
147C2×Q8×C29—21no—
148C2×Q8×C29—22no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29—21no—
152C2×Q8×C29—41no—
153C2×Q8×C29C2×D411yescharacteristic
154C2×Q8×C29C2×D411yescharacteristic
155C2×D4×C29—21no—
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—41no—
159C22×C4×C29—21no—
160C22×C4×C29—21no—
161C22×C4×C29—41no—
162C22×C4×C29C2×D411yescharacteristic
163C22×C4×C29C2×D411yescharacteristic
164C22×C4×C29#4111yescharacteristic
165Q16×C29—42no—
166Q16×C29—42no—
167Q16×C29—42no—
168Q16×C29—42no—
169SD16×C29—42no—
170SD16×C29—42no—
171SD16×C29—42no—
172SD16×C29—42no—
173M16×C29—22no—
174M16×C29—41no—
175M16×C29—42no—
176M16×C29—42no—
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×C29C2×D411yescharacteristic
184C2×C8×C29C2×D411yescharacteristic
185C2×C8×C29C2×D411yescharacteristic
186C2×C8×C29C2×D411yescharacteristic
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
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—21no—
198C4⋊C4×C29—41no—
199C4⋊C4×C29—41no—
200C4⋊C4×C29C2×D411yescharacteristic
201C4⋊C4×C29C2×D411yescharacteristic
202C22⋊C4×C29—41no—
203C22⋊C4×C29—41no—
204C22⋊C4×C29—41no—
205C42×C29—21no—
206C42×C29—21no—
207C42×C29—21no—
208C42×C29—21no—
209C42×C29—41no—
210C42×C29C2×D411yescharacteristic
211C42×C29C2×D411yescharacteristic
212C42×C29#4111yescharacteristic
213C42×C29C2411yescharacteristic
214#19308C2911yesmaximal, characteristic, direct product factor, Sylow
215C23×C29—41no—
216C23×C29#12111yescharacteristic
217Q8×C29—21no—
218Q8×C29—21no—
219Q8×C29—21no—
220Q8×C29—42no—
221Q8×C29—41no—
222Q8×C29—41no—
223Q8×C29—41no—
224Q8×C29—41no—
225Q8×C29—41no—
226Q8×C29—41no—
227Q8×C29AGL(1,ℤ/8)12yes—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—41no—
231D4×C29—41no—
232D4×C29—81no—
233D4×C29—82no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
242C2×C4×C29—41no—
243C2×C4×C29—42no—
244C2×C4×C29—41no—
245C2×C4×C29—41no—
246C2×C4×C29—41no—
247C2×C4×C29—82no—
248C2×C4×C29—81no—
249C2×C4×C29#12111yescharacteristic
250C2×C4×C29#12111yescharacteristic
251C2×C4×C29#12111yescharacteristic
252C2×C4×C29C22×D411yescharacteristic
253C2×C4×C29C22×D411yescharacteristic
254C2×C4×C29C2×#4111yescharacteristic
255C8×C29—21no—
256C8×C29—21no—
257C8×C29—21no—
258C8×C29—41no—
259C8×C29—41no—
260C8×C29—41no—
261C8×C29—41no—
262C8×C29—41no—
263C8×C29—41no—
264C8×C29#13712yescomplemented
265#3182C2×C2911yescharacteristic
266#3113C2×C2911yescharacteristic, complemented
267#3037C2×C2911yescharacteristic
268Q8×M16C2×C2911yescharacteristic, complemented
269#1702C2×C2911yescharacteristic, complemented
270#1700C2×C2911yescharacteristic, complemented
271#1694C2×C2911yescharacteristic, complemented
272#1686C2×C2911yescharacteristic, complemented
273#1682C2×C2911yescharacteristic, complemented
274#1680C2×C2911yescharacteristic, complemented
275#1674C2×C2911yescharacteristic, complemented
276#1666C2×C2911yescharacteristic, complemented
277#1569C2×C2911yescharacteristic, complemented
278#1561C2×C2911yescharacteristic, complemented
279#1557C2×C2911yescharacteristic
280C22×C29—21no—
281C22×C29—21no—
282C22×C29—21no—
283C22×C29—81no—
284C22×C29—81no—
285C22×C29—81no—
286C22×C29C2×#12111yescharacteristic
287C4×C29—21no—
288C4×C29—21no—
289C4×C29—22no—
290C4×C29—21no—
291C4×C29—21no—
292C4×C29—41no—
293C4×C29—41no—
294C4×C29—41no—
295C4×C29—81no—
296C4×C29—81no—
297C4×C29—81no—
298C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C29C2×#13711yescharacteristic
300C4×C29#57511yescharacteristic
301C4×C29#57511yescharacteristic
302C2×#137—21no—
303#533C22×C2911yescharacteristic
304#532C22×C2911yescharacteristic
305C2×C4×Q8C22×C2911yescharacteristic
306#500C22×C2911yescharacteristic
307#492C22×C2911yescharacteristic
308#487C22×C2911yescharacteristic
309#486C22×C2911yescharacteristic
310#483—21no—
311#475C22×C2911yescharacteristic
312#475C22×C2911yescharacteristic
313#468—21no—
314#468—21no—
315#464—21no—
316#464—21no—
317#462C22×C2911yescharacteristic
318#462C22×C2911yescharacteristic
319#462C22×C2911yescharacteristic
320#462C22×C2911yescharacteristic
321#460C22×C2911yescharacteristic
322#460C22×C2911yescharacteristic
323#451—21no—
324#446—21no—
325#446—21no—
326#446C22×C2911yescharacteristic
327#446C22×C2911yescharacteristic
328C8×Q8C22×C2911yescharacteristic
329C8×Q8C22×C2911yescharacteristic
330#441—21no—
331#441—21no—
332#440—21no—
333#440—21no—
334#432C22×C2911yescharacteristic
335#423—21no—
336#423C22×C2911yescharacteristic
337#423C22×C2911yescharacteristic
338#417—21no—
339C4×M16—21no—
340C4×M16C22×C2911yescharacteristic
341#335C22×C2911yescharacteristic
342#335C22×C2911yescharacteristic
343#334C22×C2911yescharacteristic
344#334C22×C2911yescharacteristic
345#332C22×C2911yescharacteristic
346#332C22×C2911yescharacteristic
347#332C22×C2911yescharacteristic
348#332C22×C2911yescharacteristic
349#332C22×C2911yescharacteristic
350#332C22×C2911yescharacteristic
351#331C22×C2911yescharacteristic
352#331C22×C2911yescharacteristic
353C2×C29—41no—
354C2×C29—161no—
355C2×C29#303711yescharacteristic
356C2×C29#305511yescharacteristic
357C2×C29#306911yescharacteristic
358C2×#41—21no—
359C22×Q8D4×C2911yescharacteristic
360#137—44no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×Q16—21no—
364C2×Q16—21no—
365C2×SD16—21no—
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16D4×C2911yescharacteristic
372C2×M16D4×C2911yescharacteristic
373C4⋊Q8C23×C2911yescharacteristic
374C4⋊Q8C23×C2911yescharacteristic
375C4⋊Q8C23×C2911yescharacteristic
376#127C23×C2911yescharacteristic
377#125—21no—
378#124—21no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381#121—21no—
382#121—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8D4×C2911yescharacteristic
388C4×Q8D4×C2911yescharacteristic
389C4×Q8C23×C2911yescharacteristic
390C4×Q8C23×C2911yescharacteristic
391C4×D4—21no—
392C4×D4—21no—
393#117—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4D4×C2911yescharacteristic
396C2×C42—21no—
397C2×C42C23×C2911yescharacteristic
398#107—21no—
399#107—21no—
400#106—21no—
401#106—21no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8—21no—
408C4⋊C8C23×C2911yescharacteristic
409C4⋊C8C23×C2911yescharacteristic
410C4⋊C8C23×C2911yescharacteristic
411C4⋊C8C23×C2911yescharacteristic
412C4⋊C8C23×C2911yescharacteristic
413C4⋊C8C23×C2911yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426C22⋊C8—21no—
427#97—21no—
428#97—21no—
429#97—21no—
430#97D4×C2911yescharacteristic
431#97D4×C2911yescharacteristic
432C4×C8—21no—
433C4×C8—21no—
434C4×C8C23×C2911yescharacteristic
435C4×C8C23×C2911yescharacteristic
436C29#1930811yescharacteristic, direct product factor, Sylow
437#41—42no—
438#41—42no—
439C2×Q8—21no—
440C2×Q8—22no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—41no—
445C2×Q8C2×D4×C2911yescharacteristic
446C2×Q8C2×D4×C2911yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—41no—
454C22×C4C2×D4×C2911yescharacteristic
455C22×C4C2×D4×C2911yescharacteristic
456C22×C4#41×C2911yescharacteristic
457Q16—42no—
458Q16—42no—
459Q16—42no—
460Q16—42no—
461SD16—42no—
462SD16—42no—
463SD16—42no—
464SD16—42no—
465M16—22no—
466M16—41no—
467M16—42no—
468M16—42no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8C2×D4×C2911yescharacteristic
476C2×C8C2×D4×C2911yescharacteristic
477C2×C8C2×D4×C2911yescharacteristic
478C2×C8C2×D4×C2911yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C2911yescharacteristic
493C4⋊C4C2×D4×C2911yescharacteristic
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C42—21no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—41no—
502C42C2×D4×C2911yescharacteristic
503C42C2×D4×C2911yescharacteristic
504C42#41×C2911yescharacteristic
505C42C24×C2911yescharacteristic
506C23—41no—
507C23C29×#12111yescharacteristic
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—42no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8C29×AGL(1,ℤ/8)12yes—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—81no—
524D4—82no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4—81no—
540C2×C4C29×#12111yescharacteristic
541C2×C4C29×#12111yescharacteristic
542C2×C4C29×#12111yescharacteristic
543C2×C4C22×D4×C2911yescharacteristic
544C2×C4C22×D4×C2911yescharacteristic
545C2×C4C2×#41×C2911yescharacteristic
546C8—21no—
547C8—21no—
548C8—21no—
549C8—41no—
550C8—41no—
551C8—41no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8C29×#13712yescomplemented
556C22—21no—
557C22—21no—
558C22—21no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22C2×C29×#12111yescharacteristic
563C4—21no—
564C4—21no—
565C4—22no—
566C4—21no—
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
575C4C2×C29×#13711yescharacteristic
576C4C29×#57511yescharacteristic
577C4C29×#57511yescharacteristic
578C2—41no—
579C2—161no—
580C2C29×#303711yescharacteristic
581C2C29×#305511yescharacteristic
582C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#532C22
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×#3113C2semidirect
4. Q8×M16×C29C2semidirect
5. C29×#1702C2semidirect
6. C29×#1700C2semidirect
7. C29×#1694C2semidirect
8. C29×#1686C2semidirect
9. C29×#1682C2semidirect
10. C29×#1680C2semidirect
11. C29×#1674C2semidirect
12. C29×#1666C2semidirect
13. C29×#1569C2semidirect
14. C29×#1561C2semidirect
214. #19308C29direct (N × H)
264. C8×C29#137semidirect
266. #3113C2×C29semidirect
268. Q8×M16C2×C29semidirect
269. #1702C2×C29semidirect
270. #1700C2×C29semidirect
271. #1694C2×C29semidirect
272. #1686C2×C29semidirect
273. #1682C2×C29semidirect
274. #1680C2×C29semidirect
275. #1674C2×C29semidirect
276. #1666C2×C29semidirect
277. #1569C2×C29semidirect
278. #1561C2×C29semidirect
436. C29#19308direct (N × H)
555. C8C29×#137semidirect

Maximal subgroups

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

subgroupindex
C29×#31822
C29×#31132
C29×#30372
Q8×M16×C292
C29×#17022
C29×#17002
C29×#16942
C29×#16862
C29×#16822
C29×#16802
C29×#16742
C29×#16662
C29×#15692
C29×#15612
C29×#15572
#1930829