Finite Group Databasebeta

← C29×#25317 #20320217

Subgroups — C29×#25317 #20320217

Order 7424.

690 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3140C211yesmaximal, characteristic
2C29×#3078C211yesmaximal, characteristic, complemented
3C2×C29×#464C211yesmaximal, characteristic
4C29×#2962C211yesmaximal, characteristic, complemented
5C29×#2064C211yesmaximal, characteristic, complemented
6C29×#2063C211yesmaximal, characteristic
7C29×#2047C211yesmaximal, characteristic, complemented
8C29×#2046C211yesmaximal, characteristic
9C29×#1979C211yesmaximal, characteristic, complemented
10C29×#1977C211yesmaximal, characteristic
11C29×#1967C211yesmaximal, characteristic
12C29×#1950C211yesmaximal, characteristic, complemented
13C29×#1931C211yesmaximal, characteristic
14C29×#1930C211yesmaximal, characteristic, complemented
15C4×C29×#101C211yesmaximal, characteristic, complemented
16C22×Q16×C29C2211yescharacteristic
17C22×SD16×C29C2211yescharacteristic
18C29×#533C2211yescharacteristic
19C2×C29×#124C2211yescharacteristic
20C2×C4×Q8×C29C2211yescharacteristic
21C29×#489—21no—
22C29×#489—21no—
23C29×#488—21no—
24C29×#488—21no—
25C29×#479—21no—
26C29×#479—21no—
27C29×#477—21no—
28C29×#475—21no—
29C29×#464—21no—
30C29×#464—21no—
31C29×#464—21no—
32C29×#464—21no—
33C29×#446—21no—
34C29×#446—21no—
35C29×#446—21no—
36C8×Q8×C29—21no—
37C2×C29×#108C2211yescharacteristic
38C2×C29×#108C2211yescharacteristic
39C29×#428C2211yescharacteristic
40C29×#428C2211yescharacteristic
41C29×#424C2211yescharacteristic
42C29×#424C2211yescharacteristic
43C29×#423C2211yescharacteristic
44C2×C29×C4⋊C8C2211yescharacteristic
45C29×#419C2211yescharacteristic
46C29×#419C2211yescharacteristic
47C29×#419C2211yescharacteristic
48C29×#419C2211yescharacteristic
49C29×#418C2211yescharacteristic
50C29×#418C2211yescharacteristic
51C2×C29×#103C2211yescharacteristic
52C2×C29×#102C2211yescharacteristic
53C2×C29×#101C2211yescharacteristic
54C2×C29×#101C2211yescharacteristic
55C2×C29×#101C2211yescharacteristic
56C2×C29×#101C2211yescharacteristic
57C2×C29×#100C2211yescharacteristic
58C2×C29×#100C2211yescharacteristic
59C29×#405C2211yescharacteristic
60C29×#405C2211yescharacteristic
61C4×M16×C29C2211yescharacteristic
62C4×M16×C29C2211yescharacteristic
63C29×#343C2211yescharacteristic
64C29×#343C2211yescharacteristic
65C29×#341C2211yescharacteristic
66C29×#341C2211yescharacteristic
67C22×Q8×C29C2311yescharacteristic
68C22×Q8×C29C2311yescharacteristic
69C22×D4×C29C2311yescharacteristic
70C2×Q16×C29—22no—
71C2×Q16×C29—21no—
72C2×Q16×C29—21no—
73C2×Q16×C29—41no—
74C2×SD16×C29—22no—
75C2×SD16×C29—21no—
76C2×SD16×C29—21no—
77C2×SD16×C29—41no—
78C2×M16×C29C2311yescharacteristic
79C2×M16×C29C2311yescharacteristic
80C2×M16×C29C2311yescharacteristic
81C2×M16×C29C2311yescharacteristic
82C2×M16×C29C2311yescharacteristic
83C2×M16×C29C2311yescharacteristic
84C22×C8×C29C2311yescharacteristic
85C22×C8×C29C2311yescharacteristic
86C29×C4⋊Q8D411yescharacteristic
87C29×C4⋊Q8D411yescharacteristic
88C29×#125D411yescharacteristic
89C29×#125D411yescharacteristic
90C29×#124—21no—
91C29×#124—21no—
92C29×#124—21no—
93C29×#124—21no—
94C29×C22⋊Q8—21no—
95C29×C22⋊Q8—21no—
96C4×Q8×C29—21no—
97C4×Q8×C29—21no—
98C4×Q8×C29—21no—
99C4×Q8×C29—21no—
100C4×Q8×C29—21no—
101C4×Q8×C29—21no—
102C29×#117C2311yescharacteristic
103C29×#117C2311yescharacteristic
104C2×C4⋊C4×C29—21no—
105C2×C4⋊C4×C29C2311yescharacteristic
106C2×C22⋊C4×C29—21no—
107C2×C22⋊C4×C29—21no—
108C2×C42×C29—21no—
109C2×C42×C29C2311yescharacteristic
110C29×#108—41no—
111C29×#108—41no—
112C29×#107—21no—
113C29×#107—21no—
114C29×#106—21no—
115C29×#106—21no—
116C29×C4⋊C8—21no—
117C29×C4⋊C8—21no—
118C29×C4⋊C8—21no—
119C29×C4⋊C8—21no—
120C29×C4⋊C8—21no—
121C29×C4⋊C8—21no—
122C29×C4⋊C8D411yescharacteristic
123C29×C4⋊C8D411yescharacteristic
124C29×C4⋊C8D411yescharacteristic
125C29×C4⋊C8D411yescharacteristic
126C29×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#103—21no—
130C29×#103—21no—
131C29×#103—21no—
132C29×#103—21no—
133C29×#103—21no—
134C29×#103—21no—
135C29×#103—21no—
136C29×#102—21no—
137C29×#102—21no—
138C29×#102—21no—
139C29×#102—21no—
140C29×#102—21no—
141C29×#102—21no—
142C29×#101—22no—
143C29×#101—22no—
144C29×#101—22no—
145C29×#101—41no—
146C29×#100—22no—
147C29×#100—41no—
148C29×#97—21no—
149C29×#97—21no—
150C29×#97—21no—
151C29×#97—21no—
152C4×C8×C29—21no—
153C4×C8×C29—21no—
154C4×C8×C29—21no—
155C4×C8×C29—21no—
156C24×C29—21no—
157C2×Q8×C29—21no—
158C2×Q8×C29—21no—
159C2×Q8×C29—21no—
160C2×Q8×C29—21no—
161C2×Q8×C29—21no—
162C2×Q8×C29—21no—
163C2×Q8×C29—21no—
164C2×Q8×C29—21no—
165C2×Q8×C29—21no—
166C2×Q8×C29—21no—
167C2×Q8×C29—21no—
168C2×Q8×C29—21no—
169C2×Q8×C29—21no—
170C2×Q8×C29#4112yes—
171C2×D4×C29—21no—
172C2×D4×C29—21no—
173C2×D4×C29—21no—
174C2×D4×C29—21no—
175C2×D4×C29—21no—
176C2×D4×C29—21no—
177C22×C4×C29—21no—
178C22×C4×C29—21no—
179C22×C4×C29—21no—
180C22×C4×C29#4111yescharacteristic
181C22×C4×C29#4111yescharacteristic
182C22×C4×C29C2411yescharacteristic
183Q16×C29—42no—
184Q16×C29—42no—
185SD16×C29—42no—
186SD16×C29—42no—
187M16×C29—21no—
188M16×C29—21no—
189M16×C29—21no—
190M16×C29—21no—
191M16×C29—21no—
192M16×C29—21no—
193M16×C29—21no—
194M16×C29—21no—
195M16×C29—21no—
196M16×C29—21no—
197M16×C29—21no—
198M16×C29#4112yes—
199C2×C8×C29—21no—
200C2×C8×C29—21no—
201C2×C8×C29—21no—
202C2×C8×C29—21no—
203C2×C8×C29—21no—
204C2×C8×C29—21no—
205C2×C8×C29—21no—
206C2×C8×C29—21no—
207C2×C8×C29—21no—
208C2×C8×C29—21no—
209C2×C8×C29C2×D411yescharacteristic
210C2×C8×C29C2×D411yescharacteristic
211C2×C8×C29C2×D411yescharacteristic
212C2×C8×C29C2×D411yescharacteristic
213C4⋊C4×C29—21no—
214C4⋊C4×C29—21no—
215C4⋊C4×C29—21no—
216C4⋊C4×C29—21no—
217C4⋊C4×C29—21no—
218C4⋊C4×C29—21no—
219C4⋊C4×C29—21no—
220C4⋊C4×C29—21no—
221C4⋊C4×C29—41no—
222C4⋊C4×C29—41no—
223C4⋊C4×C29C2×D411yescharacteristic
224C4⋊C4×C29C2×D411yescharacteristic
225C4⋊C4×C29C2×D411yescharacteristic
226C4⋊C4×C29C2×D411yescharacteristic
227C22⋊C4×C29—21no—
228C22⋊C4×C29—21no—
229C22⋊C4×C29—41no—
230C22⋊C4×C29—41no—
231C22⋊C4×C29—41no—
232C22⋊C4×C29—41no—
233C42×C29—21no—
234C42×C29—21no—
235C42×C29—41no—
236C42×C29—41no—
237C42×C29C2×D411yescharacteristic
238C42×C29C2×D411yescharacteristic
239C42×C29C2×D411yescharacteristic
240C42×C29C2×D411yescharacteristic
241#25317C2911yesmaximal, characteristic, direct product factor, Sylow
242C23×C29—41no—
243C23×C29—41no—
244C23×C29—41no—
245C23×C29—81no—
246C23×C29—81no—
247C23×C29C2×#4111yescharacteristic
248Q8×C29—22no—
249Q8×C29—22no—
250Q8×C29—42no—
251Q8×C29—41no—
252Q8×C29—41no—
253Q8×C29—41no—
254Q8×C29—41no—
255Q8×C29—41no—
256Q8×C29—41no—
257Q8×C29—81no—
258D4×C29—41no—
259D4×C29—41no—
260D4×C29—41no—
261D4×C29—41no—
262C2×C4×C29—21no—
263C2×C4×C29—21no—
264C2×C4×C29—21no—
265C2×C4×C29—21no—
266C2×C4×C29—22no—
267C2×C4×C29—41no—
268C2×C4×C29—41no—
269C2×C4×C29—41no—
270C2×C4×C29—41no—
271C2×C4×C29—41no—
272C2×C4×C29—41no—
273C2×C4×C29—41no—
274C2×C4×C29—41no—
275C2×C4×C29—81no—
276C2×C4×C29#12111yescharacteristic
277C2×C4×C29#12111yescharacteristic
278C2×C4×C29#12111yescharacteristic
279C2×C4×C29#12111yescharacteristic
280C2×C4×C29C22×D411yescharacteristic
281C2×C4×C29C22×D411yescharacteristic
282C2×C4×C29C2×#4111yescharacteristic
283C2×C4×C29C2×#4111yescharacteristic
284C2×C4×C29H(5,𝔽2)11yescharacteristic
285C2×C4×C292−1+411yescharacteristic
286C8×C29—21no—
287C8×C29—21no—
288C8×C29—21no—
289C8×C29—21no—
290C8×C29—22no—
291C8×C29—41no—
292C8×C29—41no—
293C8×C29—41no—
294C8×C29—41no—
295C8×C29—41no—
296#3140C2×C2911yescharacteristic
297#3078C2×C2911yescharacteristic, complemented
298C2×#464C2×C2911yescharacteristic
299#2962C2×C2911yescharacteristic, complemented
300#2064C2×C2911yescharacteristic, complemented
301#2063C2×C2911yescharacteristic
302#2047C2×C2911yescharacteristic, complemented
303#2046C2×C2911yescharacteristic
304#1979C2×C2911yescharacteristic, complemented
305#1977C2×C2911yescharacteristic
306#1967C2×C2911yescharacteristic
307#1950C2×C2911yescharacteristic, complemented
308#1931C2×C2911yescharacteristic
309#1930C2×C2911yescharacteristic, complemented
310C4×#101C2×C2911yescharacteristic, complemented
311C22×C29—21no—
312C22×C29—21no—
313C22×C29—81no—
314C22×C29—81no—
315C22×C29—81no—
316C22×C29—161no—
317C22×C29—161no—
318C22×C29C2×#12111yescharacteristic
319C22×C29#52911yescharacteristic
320C22×C29#54211yescharacteristic
321C4×C29—21no—
322C4×C29—21no—
323C4×C29—21no—
324C4×C29—21no—
325C4×C29—42no—
326C4×C29—41no—
327C4×C29—41no—
328C4×C29—41no—
329C4×C29—41no—
330C4×C29—81no—
331C4×C29—81no—
332C4×C29#54611yescharacteristic
333C4×C29#54811yescharacteristic
334C4×C29#54811yescharacteristic
335C4×C29#55011yescharacteristic
336C22×Q16C22×C2911yescharacteristic
337C22×SD16C22×C2911yescharacteristic
338#533C22×C2911yescharacteristic
339C2×#124C22×C2911yescharacteristic
340C2×C4×Q8C22×C2911yescharacteristic
341#489—21no—
342#489—21no—
343#488—21no—
344#488—21no—
345#479—21no—
346#479—21no—
347#477—21no—
348#475—21no—
349#464—21no—
350#464—21no—
351#464—21no—
352#464—21no—
353#446—21no—
354#446—21no—
355#446—21no—
356C8×Q8—21no—
357C2×#108C22×C2911yescharacteristic
358C2×#108C22×C2911yescharacteristic
359#428C22×C2911yescharacteristic
360#428C22×C2911yescharacteristic
361#424C22×C2911yescharacteristic
362#424C22×C2911yescharacteristic
363#423C22×C2911yescharacteristic
364C2×C4⋊C8C22×C2911yescharacteristic
365#419C22×C2911yescharacteristic
366#419C22×C2911yescharacteristic
367#419C22×C2911yescharacteristic
368#419C22×C2911yescharacteristic
369#418C22×C2911yescharacteristic
370#418C22×C2911yescharacteristic
371C2×#103C22×C2911yescharacteristic
372C2×#102C22×C2911yescharacteristic
373C2×#101C22×C2911yescharacteristic
374C2×#101C22×C2911yescharacteristic
375C2×#101C22×C2911yescharacteristic
376C2×#101C22×C2911yescharacteristic
377C2×#100C22×C2911yescharacteristic
378C2×#100C22×C2911yescharacteristic
379#405C22×C2911yescharacteristic
380#405C22×C2911yescharacteristic
381C4×M16C22×C2911yescharacteristic
382C4×M16C22×C2911yescharacteristic
383#343C22×C2911yescharacteristic
384#343C22×C2911yescharacteristic
385#341C22×C2911yescharacteristic
386#341C22×C2911yescharacteristic
387C2×C29—21no—
388C2×C29—21no—
389C2×C29—161no—
390C2×C29#242611yescharacteristic
391C2×C29#306711yescharacteristic
392C2×C29#306911yescharacteristic
393C22×Q8C23×C2911yescharacteristic
394C22×Q8C23×C2911yescharacteristic
395C22×D4C23×C2911yescharacteristic
396C2×Q16—22no—
397C2×Q16—21no—
398C2×Q16—21no—
399C2×Q16—41no—
400C2×SD16—22no—
401C2×SD16—21no—
402C2×SD16—21no—
403C2×SD16—41no—
404C2×M16C23×C2911yescharacteristic
405C2×M16C23×C2911yescharacteristic
406C2×M16C23×C2911yescharacteristic
407C2×M16C23×C2911yescharacteristic
408C2×M16C23×C2911yescharacteristic
409C2×M16C23×C2911yescharacteristic
410C22×C8C23×C2911yescharacteristic
411C22×C8C23×C2911yescharacteristic
412C4⋊Q8D4×C2911yescharacteristic
413C4⋊Q8D4×C2911yescharacteristic
414#125D4×C2911yescharacteristic
415#125D4×C2911yescharacteristic
416#124—21no—
417#124—21no—
418#124—21no—
419#124—21no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×Q8—21no—
428#117C23×C2911yescharacteristic
429#117C23×C2911yescharacteristic
430C2×C4⋊C4—21no—
431C2×C4⋊C4C23×C2911yescharacteristic
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C42—21no—
435C2×C42C23×C2911yescharacteristic
436#108—41no—
437#108—41no—
438#107—21no—
439#107—21no—
440#106—21no—
441#106—21no—
442C4⋊C8—21no—
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—21no—
446C4⋊C8—21no—
447C4⋊C8—21no—
448C4⋊C8D4×C2911yescharacteristic
449C4⋊C8D4×C2911yescharacteristic
450C4⋊C8D4×C2911yescharacteristic
451C4⋊C8D4×C2911yescharacteristic
452#103—21no—
453#103—21no—
454#103—21no—
455#103—21no—
456#103—21no—
457#103—21no—
458#103—21no—
459#103—21no—
460#103—21no—
461#103—21no—
462#102—21no—
463#102—21no—
464#102—21no—
465#102—21no—
466#102—21no—
467#102—21no—
468#101—22no—
469#101—22no—
470#101—22no—
471#101—41no—
472#100—22no—
473#100—41no—
474#97—21no—
475#97—21no—
476#97—21no—
477#97—21no—
478C4×C8—21no—
479C4×C8—21no—
480C4×C8—21no—
481C4×C8—21no—
482C29#2531711yescharacteristic, direct product factor, Sylow
483C24—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8#41×C2912yes—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4#41×C2911yescharacteristic
508C22×C4#41×C2911yescharacteristic
509C22×C4C24×C2911yescharacteristic
510Q16—42no—
511Q16—42no—
512SD16—42no—
513SD16—42no—
514M16—21no—
515M16—21no—
516M16—21no—
517M16—21no—
518M16—21no—
519M16—21no—
520M16—21no—
521M16—21no—
522M16—21no—
523M16—21no—
524M16—21no—
525M16#41×C2912yes—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8C2×D4×C2911yescharacteristic
537C2×C8C2×D4×C2911yescharacteristic
538C2×C8C2×D4×C2911yescharacteristic
539C2×C8C2×D4×C2911yescharacteristic
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—41no—
549C4⋊C4—41no—
550C4⋊C4C2×D4×C2911yescharacteristic
551C4⋊C4C2×D4×C2911yescharacteristic
552C4⋊C4C2×D4×C2911yescharacteristic
553C4⋊C4C2×D4×C2911yescharacteristic
554C22⋊C4—21no—
555C22⋊C4—21no—
556C22⋊C4—41no—
557C22⋊C4—41no—
558C22⋊C4—41no—
559C22⋊C4—41no—
560C42—21no—
561C42—21no—
562C42—41no—
563C42—41no—
564C42C2×D4×C2911yescharacteristic
565C42C2×D4×C2911yescharacteristic
566C42C2×D4×C2911yescharacteristic
567C42C2×D4×C2911yescharacteristic
568C23—41no—
569C23—41no—
570C23—41no—
571C23—81no—
572C23—81no—
573C23C2×#41×C2911yescharacteristic
574Q8—22no—
575Q8—22no—
576Q8—42no—
577Q8—41no—
578Q8—41no—
579Q8—41no—
580Q8—41no—
581Q8—41no—
582Q8—41no—
583Q8—81no—
584D4—41no—
585D4—41no—
586D4—41no—
587D4—41no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—81no—
602C2×C4C29×#12111yescharacteristic
603C2×C4C29×#12111yescharacteristic
604C2×C4C29×#12111yescharacteristic
605C2×C4C29×#12111yescharacteristic
606C2×C4C22×D4×C2911yescharacteristic
607C2×C4C22×D4×C2911yescharacteristic
608C2×C4C2×#41×C2911yescharacteristic
609C2×C4C2×#41×C2911yescharacteristic
610C2×C4C29×H(5,𝔽2)11yescharacteristic
611C2×C4C29×2−1+411yescharacteristic
612C8—21no—
613C8—21no—
614C8—21no—
615C8—21no—
616C8—22no—
617C8—41no—
618C8—41no—
619C8—41no—
620C8—41no—
621C8—41no—
622C22—21no—
623C22—21no—
624C22—81no—
625C22—81no—
626C22—81no—
627C22—161no—
628C22—161no—
629C22C2×C29×#12111yescharacteristic
630C22C29×#52911yescharacteristic
631C22C29×#54211yescharacteristic
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—42no—
637C4—41no—
638C4—41no—
639C4—41no—
640C4—41no—
641C4—81no—
642C4—81no—
643C4C29×#54611yescharacteristic
644C4C29×#54811yescharacteristic
645C4C29×#54811yescharacteristic
646C4C29×#55011yescharacteristic
647C2—21no—
648C2—21no—
649C2—161no—
650C2C29×#242611yescharacteristic
651C2C29×#306711yescharacteristic
652C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D4×C29C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3078C2semidirect
4. C29×#2962C2semidirect
5. C29×#2064C2semidirect
7. C29×#2047C2semidirect
9. C29×#1979C2semidirect
12. C29×#1950C2semidirect
14. C29×#1930C2semidirect
15. C4×C29×#101C2semidirect
241. #25317C29direct (N × H)
297. #3078C2×C29semidirect
299. #2962C2×C29semidirect
300. #2064C2×C29semidirect
302. #2047C2×C29semidirect
304. #1979C2×C29semidirect
307. #1950C2×C29semidirect
309. #1930C2×C29semidirect
310. C4×#101C2×C29semidirect
482. C29#25317direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31402
C29×#30782
C2×C29×#4642
C29×#29622
C29×#20642
C29×#20632
C29×#20472
C29×#20462
C29×#19792
C29×#19772
C29×#19672
C29×#19502
C29×#19312
C29×#19302
C4×C29×#1012
#2531729