Finite Group Databasebeta

← C29×#18259 #20313159

Subgroups — C29×#18259 #20313159

Order 7424.

1132 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3538C211yesmaximal, characteristic
2C29×#3004C211yesmaximal, characteristic
3C2×C29×#451C211yesmaximal, characteristic, complemented
4C29×#2434C211yesmaximal, characteristic, complemented
5C29×#1605C214yesmaximal, complemented
6C29×#1603C214yesmaximal, complemented
7C29×#1508C211yesmaximal, characteristic, complemented
8C29×#1501C211yesmaximal, characteristic
9C29×#1472C211yesmaximal, characteristic, complemented
10C23×Q8×C29C2211yescharacteristic
11C2×C29×#137—21no—
12C22×Q16×C29—21no—
13C29×#563—22no—
14C29×#552—21no—
15C29×#552—21no—
16C29×#551—22no—
17D4×Q8×C29—21no—
18D4×Q8×C29—21no—
19C29×#544—21no—
20C29×#544C2212yes—
21C29×#541—21no—
22C29×#539—21no—
23C29×#539C2212yes—
24C29×#536—21no—
25C2×C29×C4⋊Q8—21no—
26C29×#525C2211yescharacteristic
27C2×C29×C22⋊Q8C2211yescharacteristic
28C2×C29×C22⋊Q8C2211yescharacteristic
29C29×#451—22no—
30C29×#451—21no—
31C29×#451C2214yes—
32C29×#451C2212yes—
33C29×#448—21no—
34C29×#448C2212yes—
35C29×#419—21no—
36C2×C29×#103—21no—
37C29×#407C2211yescharacteristic
38C2×C29×C22⋊C8C2211yescharacteristic
39C29×#395C2214yes—
40C29×#391—21no—
41C29×#385—22no—
42C4×C22⋊C4×C29C2211yescharacteristic
43C29×#328C2212yes—
44C29×#328C2214yes—
45C29×#327C2212yes—
46C29×#324C2214yes—
47C2×#41×C29D411yescharacteristic
48C22×Q8×C29—21no—
49C22×Q8×C29—21no—
50C22×Q8×C29—21no—
51C22×Q8×C29—21no—
52C22×Q8×C29—21no—
53C22×Q8×C29—21no—
54C22×Q8×C29—44no—
55C22×Q8×C29D411yescharacteristic
56C22×Q8×C29D411yescharacteristic
57C22×Q8×C29C2312yes—
58C23×C4×C29—21no—
59C23×C4×C29C2311yescharacteristic
60C29×#137—44no—
61C2×Q16×C29—24no—
62C2×Q16×C29—22no—
63C2×Q16×C29—44no—
64C2×SD16×C29—22no—
65C2×M16×C29—21no—
66C22×C8×C29—21no—
67C29×C4⋊Q8—21no—
68C29×C4⋊Q8—22no—
69C29×C4⋊Q8—22no—
70C29×C4⋊Q8—22no—
71C29×C4⋊Q8—44no—
72C29×#126—22no—
73C29×#126—22no—
74C29×#126—22no—
75C29×#126—22no—
76C29×#125—21no—
77C29×#125—22no—
78C29×#125—22no—
79C29×#125—22no—
80C29×#125—22no—
81C29×#124—22no—
82C29×#123—22no—
83C29×#123—22no—
84C29×#123—22no—
85C29×#123—21no—
86C29×#123—22no—
87C29×C22⋊Q8—21no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8—22no—
90C29×C22⋊Q8—22no—
91C29×C22⋊Q8—22no—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8—21no—
94C29×C22⋊Q8—21no—
95C29×C22⋊Q8—21no—
96C29×C22⋊Q8—21no—
97C29×C22⋊Q8—21no—
98C29×C22⋊Q8—22no—
99C29×C22⋊Q8D412yes—
100C29×C22⋊Q8D411yescharacteristic
101C29×C22⋊Q8C2312yes—
102C29×C22⋊Q8C2311yescharacteristic
103C29×#121D411yescharacteristic
104C29×#121C2311yescharacteristic
105C29×#120—21no—
106C4×Q8×C29—21no—
107C4×Q8×C29—21no—
108C4×D4×C29—22no—
109C4×D4×C29—21no—
110C4×D4×C29—21no—
111C4×D4×C29—22no—
112C29×#117—21no—
113C29×#117—22no—
114C29×#117—22no—
115C29×#117D411yescharacteristic
116C2×C4⋊C4×C29—21no—
117C2×C4⋊C4×C29—24no—
118C2×C4⋊C4×C29D411yescharacteristic
119C2×C4⋊C4×C29D411yescharacteristic
120C2×C4⋊C4×C29C2312yes—
121C2×C22⋊C4×C29—21no—
122C2×C22⋊C4×C29—21no—
123C2×C22⋊C4×C29D412yes—
124C2×C42×C29—21no—
125C29×#103—22no—
126C29×#103—22no—
127C29×#103—24no—
128C29×C22⋊C8—21no—
129C29×C22⋊C8—21no—
130C29×C22⋊C8C2312yes—
131C29×C22⋊C8C2312yes—
132C29×#95—24no—
133C29×#95C2312yes—
134C24×C29C2×D411yescharacteristic
135#41×C29—42no—
136C2×Q8×C29—24no—
137C2×Q8×C29—22no—
138C2×Q8×C29—21no—
139C2×Q8×C29—21no—
140C2×Q8×C29—21no—
141C2×Q8×C29—24no—
142C2×Q8×C29—24no—
143C2×Q8×C29—22no—
144C2×Q8×C29—22no—
145C2×Q8×C29—44no—
146C2×Q8×C29—42no—
147C2×Q8×C29—42no—
148C2×Q8×C29—42no—
149C2×Q8×C29—42no—
150C2×Q8×C29—42no—
151C2×Q8×C29—44no—
152C2×Q8×C29—44no—
153C2×Q8×C29—41no—
154C2×Q8×C29—41no—
155C2×Q8×C29—82no—
156C2×Q8×C29C2×D412yes—
157C2×Q8×C29C2×D411yescharacteristic
158C2×D4×C29—21no—
159C2×D4×C29—21no—
160C2×D4×C29—21no—
161C2×D4×C29C2×D411yescharacteristic
162C22×C4×C29—21no—
163C22×C4×C29—22no—
164C22×C4×C29—22no—
165C22×C4×C29—22no—
166C22×C4×C29—21no—
167C22×C4×C29—21no—
168C22×C4×C29—42no—
169C22×C4×C29—44no—
170C22×C4×C29—41no—
171C22×C4×C29—41no—
172C22×C4×C29C2×D412yes—
173C22×C4×C29C2×D411yescharacteristic
174C22×C4×C29C2×D411yescharacteristic
175C22×C4×C29C2×D411yescharacteristic
176C22×C4×C29C2×D412yes—
177C22×C4×C29C2×D411yescharacteristic
178C22×C4×C29C2×D411yescharacteristic
179C22×C4×C29C2411yescharacteristic
180Q16×C29—48no—
181Q16×C29—44no—
182SD16×C29—44no—
183M16×C29—42no—
184C2×C8×C29—22no—
185C2×C8×C29—22no—
186C2×C8×C29—42no—
187C4⋊C4×C29—22no—
188C4⋊C4×C29—22no—
189C4⋊C4×C29—22no—
190C4⋊C4×C29—22no—
191C4⋊C4×C29—22no—
192C4⋊C4×C29—22no—
193C4⋊C4×C29—22no—
194C4⋊C4×C29—22no—
195C4⋊C4×C29—22no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—22no—
201C4⋊C4×C29—22no—
202C4⋊C4×C29—22no—
203C4⋊C4×C29—21no—
204C4⋊C4×C29—48no—
205C4⋊C4×C29C2×D412yes—
206C4⋊C4×C29C2×D411yescharacteristic
207C4⋊C4×C29C2×D411yescharacteristic
208C22⋊C4×C29—24no—
209C22⋊C4×C29—22no—
210C22⋊C4×C29—22no—
211C22⋊C4×C29—22no—
212C22⋊C4×C29—22no—
213C22⋊C4×C29—22no—
214C22⋊C4×C29—22no—
215C22⋊C4×C29—21no—
216C22⋊C4×C29—21no—
217C22⋊C4×C29—22no—
218C22⋊C4×C29—21no—
219C22⋊C4×C29—21no—
220C22⋊C4×C29—21no—
221C42×C29—22no—
222C42×C29—22no—
223C42×C29—22no—
224C42×C29—21no—
225C42×C29—42no—
226#18259C2911yesmaximal, characteristic, direct product factor, Sylow
227C23×C29—22no—
228C23×C29—22no—
229C23×C29—21no—
230C23×C29—41no—
231C23×C29#12011yescharacteristic
232C23×C29#12011yescharacteristic
233C23×C29C22×D411yescharacteristic
234Q8×C29—24no—
235Q8×C29—24no—
236Q8×C29—42no—
237Q8×C29—41no—
238Q8×C29—42no—
239Q8×C29—42no—
240Q8×C29—44no—
241Q8×C29—44no—
242Q8×C29—42no—
243Q8×C29—42no—
244Q8×C29—81no—
245Q8×C29—82no—
246D4×C29—41no—
247D4×C29—42no—
248D4×C29—42no—
249D4×C29—81no—
250C2×C4×C29—22no—
251C2×C4×C29—22no—
252C2×C4×C29—22no—
253C2×C4×C29—24no—
254C2×C4×C29—24no—
255C2×C4×C29—21no—
256C2×C4×C29—21no—
257C2×C4×C29—22no—
258C2×C4×C29—22no—
259C2×C4×C29—21no—
260C2×C4×C29—22no—
261C2×C4×C29—22no—
262C2×C4×C29—24no—
263C2×C4×C29—41no—
264C2×C4×C29—41no—
265C2×C4×C29—41no—
266C2×C4×C29—42no—
267C2×C4×C29—42no—
268C2×C4×C29—44no—
269C2×C4×C29—44no—
270C2×C4×C29—42no—
271C2×C4×C29—42no—
272C2×C4×C29—42no—
273C2×C4×C29—42no—
274C2×C4×C29—42no—
275C2×C4×C29—81no—
276C2×C4×C29—82no—
277C2×C4×C29#12011yescharacteristic
278C2×C4×C29#12011yescharacteristic
279C2×C4×C29C22×D411yescharacteristic
280C2×C4×C29C22×D411yescharacteristic
281C8×C29—42no—
282C8×C29—42no—
283#3538C2×C2911yescharacteristic
284#3004C2×C2911yescharacteristic
285C2×#451C2×C2911yescharacteristic, complemented
286#2434C2×C2911yescharacteristic, complemented
287#1605C2×C2914yescomplemented
288#1603C2×C2914yescomplemented
289#1508C2×C2911yescharacteristic, complemented
290#1501C2×C2911yescharacteristic
291#1472C2×C2911yescharacteristic, complemented
292C22×C29—21no—
293C22×C29—21no—
294C22×C29—21no—
295C22×C29—21no—
296C22×C29—21no—
297C22×C29—21no—
298C22×C29—21no—
299C22×C29—44no—
300C22×C29—41no—
301C22×C29—41no—
302C22×C29—41no—
303C22×C29#45612yes—
304C22×C29C2×#12011yescharacteristic
305C22×C29#57812yes—
306C4×C29—21no—
307C4×C29—21no—
308C4×C29—21no—
309C4×C29—44no—
310C4×C29—42no—
311C4×C29—41no—
312C4×C29—42no—
313C4×C29—41no—
314C4×C29—44no—
315C4×C29—41no—
316C4×C29—42no—
317C4×C29—42no—
318C4×C29B(4,𝔽2)12yes—
319C23×Q8C22×C2911yescharacteristic
320C2×#137—21no—
321C22×Q16—21no—
322#563—22no—
323#552—21no—
324#552—21no—
325#551—22no—
326D4×Q8—21no—
327D4×Q8—21no—
328#544—21no—
329#544C22×C2912yes—
330#541—21no—
331#539—21no—
332#539C22×C2912yes—
333#536—21no—
334C2×C4⋊Q8—21no—
335#525C22×C2911yescharacteristic
336C2×C22⋊Q8C22×C2911yescharacteristic
337C2×C22⋊Q8C22×C2911yescharacteristic
338#451—22no—
339#451—21no—
340#451C22×C2914yes—
341#451C22×C2912yes—
342#448—21no—
343#448C22×C2912yes—
344#419—21no—
345C2×#103—21no—
346#407C22×C2911yescharacteristic
347C2×C22⋊C8C22×C2911yescharacteristic
348#395C22×C2914yes—
349#391—21no—
350#385—22no—
351C4×C22⋊C4C22×C2911yescharacteristic
352#328C22×C2914yes—
353#328C22×C2912yes—
354#327C22×C2912yes—
355#324C22×C2914yes—
356C2×C29—22no—
357C2×C29—22no—
358C2×C29—41no—
359C2×C29—81no—
360C2×C29#301111yescharacteristic
361C2×C29C2×#45611yescharacteristic
362C2×C29C2×B(4,𝔽2)11yescharacteristic
363C2×#41D4×C2911yescharacteristic
364C22×Q8—21no—
365C22×Q8—21no—
366C22×Q8—21no—
367C22×Q8—21no—
368C22×Q8—21no—
369C22×Q8—21no—
370C22×Q8—44no—
371C22×Q8D4×C2911yescharacteristic
372C22×Q8D4×C2911yescharacteristic
373C22×Q8C23×C2912yes—
374C23×C4—21no—
375C23×C4C23×C2911yescharacteristic
376#137—44no—
377C2×Q16—24no—
378C2×Q16—22no—
379C2×Q16—44no—
380C2×SD16—22no—
381C2×M16—21no—
382C22×C8—21no—
383C4⋊Q8—21no—
384C4⋊Q8—22no—
385C4⋊Q8—22no—
386C4⋊Q8—22no—
387C4⋊Q8—44no—
388#126—22no—
389#126—22no—
390#126—22no—
391#126—22no—
392#125—21no—
393#125—22no—
394#125—22no—
395#125—22no—
396#125—22no—
397#124—22no—
398#123—22no—
399#123—22no—
400#123—22no—
401#123—21no—
402#123—22no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—22no—
406C22⋊Q8—22no—
407C22⋊Q8—22no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8—22no—
415C22⋊Q8D4×C2912yes—
416C22⋊Q8D4×C2911yescharacteristic
417C22⋊Q8C23×C2912yes—
418C22⋊Q8C23×C2911yescharacteristic
419#121D4×C2911yescharacteristic
420#121C23×C2911yescharacteristic
421#120—21no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×D4—22no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—22no—
428#117—21no—
429#117—22no—
430#117—22no—
431#117D4×C2911yescharacteristic
432C2×C4⋊C4—21no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4D4×C2911yescharacteristic
435C2×C4⋊C4D4×C2911yescharacteristic
436C2×C4⋊C4C23×C2912yes—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4D4×C2912yes—
440C2×C42—21no—
441#103—24no—
442#103—22no—
443#103—22no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446C22⋊C8C23×C2912yes—
447C22⋊C8C23×C2912yes—
448#95—24no—
449#95C23×C2912yes—
450C29#1825911yescharacteristic, direct product factor, Sylow
451C24C2×D4×C2911yescharacteristic
452#41—42no—
453C2×Q8—24no—
454C2×Q8—22no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—24no—
459C2×Q8—24no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—44no—
463C2×Q8—42no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—44no—
469C2×Q8—44no—
470C2×Q8—41no—
471C2×Q8—41no—
472C2×Q8—82no—
473C2×Q8C2×D4×C2912yes—
474C2×Q8C2×D4×C2911yescharacteristic
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4C2×D4×C2911yescharacteristic
479C22×C4—21no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—42no—
486C22×C4—44no—
487C22×C4—41no—
488C22×C4—41no—
489C22×C4C2×D4×C2912yes—
490C22×C4C2×D4×C2911yescharacteristic
491C22×C4C2×D4×C2911yescharacteristic
492C22×C4C2×D4×C2911yescharacteristic
493C22×C4C2×D4×C2912yes—
494C22×C4C2×D4×C2911yescharacteristic
495C22×C4C2×D4×C2911yescharacteristic
496C22×C4C24×C2911yescharacteristic
497Q16—48no—
498Q16—44no—
499SD16—44no—
500M16—42no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—42no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—48no—
522C4⋊C4C2×D4×C2912yes—
523C4⋊C4C2×D4×C2911yescharacteristic
524C4⋊C4C2×D4×C2911yescharacteristic
525C22⋊C4—24no—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—22no—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—22no—
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—21no—
538C42—22no—
539C42—22no—
540C42—22no—
541C42—21no—
542C42—42no—
543C23—22no—
544C23—22no—
545C23—21no—
546C23—41no—
547C23C29×#12011yescharacteristic
548C23C29×#12011yescharacteristic
549C23C22×D4×C2911yescharacteristic
550Q8—24no—
551Q8—24no—
552Q8—42no—
553Q8—41no—
554Q8—42no—
555Q8—42no—
556Q8—44no—
557Q8—44no—
558Q8—42no—
559Q8—42no—
560Q8—81no—
561Q8—82no—
562D4—41no—
563D4—42no—
564D4—42no—
565D4—81no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—44no—
585C2×C4—44no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—81no—
592C2×C4—82no—
593C2×C4C29×#12011yescharacteristic
594C2×C4C29×#12011yescharacteristic
595C2×C4C22×D4×C2911yescharacteristic
596C2×C4C22×D4×C2911yescharacteristic
597C8—42no—
598C8—42no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—44no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22C29×#45612yes—
611C22C2×C29×#12011yescharacteristic
612C22C29×#57812yes—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—44no—
617C4—42no—
618C4—41no—
619C4—42no—
620C4—41no—
621C4—44no—
622C4—41no—
623C4—42no—
624C4—42no—
625C4C29×B(4,𝔽2)12yes—
626C2—22no—
627C2—22no—
628C2—41no—
629C2—81no—
630C2C29×#301111yescharacteristic
631C2C2×C29×#45611yescharacteristic
632C2C2×C29×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#525C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C29×#451C2semidirect
4. C29×#2434C2semidirect
5. C29×#1605C2semidirect
6. C29×#1603C2semidirect
7. C29×#1508C2semidirect
9. C29×#1472C2semidirect
226. #18259C29direct (N × H)
285. C2×#451C2×C29semidirect
286. #2434C2×C29semidirect
287. #1605C2×C29semidirect
288. #1603C2×C29semidirect
289. #1508C2×C29semidirect
291. #1472C2×C29semidirect
450. C29#18259direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35382
C29×#30042
C2×C29×#4512
C29×#24342
C29×#16052
C29×#16032
C29×#15082
C29×#15012
C29×#14722
#1825929