Finite Group Databasebeta

← C29×#11078 #20305978

Subgroups — C29×#11078 #20305978

Order 7424.

1078 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C29×#104C211yesmaximal, characteristic
2C2×C29×#417C211yesmaximal, characteristic
3C29×#2311C211yesmaximal, characteristic
4C2×C29×#384C211yesmaximal, characteristic, complemented
5C2×C29×#343C211yesmaximal, characteristic, complemented
6C29×#1736C211yesmaximal, characteristic, complemented
7C2×C29×#339C211yesmaximal, characteristic, complemented
8C22×#41×C29C2211yescharacteristic
9C22×M16×C29C2211yescharacteristic
10C22×M16×C29C2211yescharacteristic
11C2×C29×#117C2211yescharacteristic
12C22×C4⋊C4×C29—22no—
13C22×C4⋊C4×C29C2211yescharacteristic
14C22×C4⋊C4×C29C2211yescharacteristic
15C22×C42×C29C2211yescharacteristic
16C2×C29×#104—22no—
17C2×C29×#104—22no—
18C2×C29×#104C414yescomplemented
19C29×#417—22no—
20C29×#417—22no—
21C2×C29×#103—21no—
22C2×C29×#102—21no—
23C29×#391—21no—
24C29×#390—21no—
25C29×#386—22no—
26C29×#384—22no—
27C29×#384—22no—
28C29×#380—22no—
29C29×#343—22no—
30C29×#340—22no—
31C29×#339—22no—
32C2×#41×C29—21no—
33C2×#41×C29—21no—
34C2×#41×C29—21no—
35C2×#41×C29—21no—
36C2×#41×C29—21no—
37C2×#41×C29—21no—
38C2×#41×C29—21no—
39C2×#41×C29—21no—
40C2×#41×C29—21no—
41C2×#41×C29—21no—
42C2×#41×C29C2×C412yes—
43C2×#41×C29Q812yes—
44C22×Q8×C29D411yescharacteristic
45C22×D4×C29—21no—
46C22×D4×C29D411yescharacteristic
47C23×C4×C29—21no—
48C23×C4×C29—21no—
49C23×C4×C29—21no—
50C23×C4×C29D412yes—
51C23×C4×C29C2311yescharacteristic
52C2×M16×C29—21no—
53C2×M16×C29—21no—
54C2×M16×C29—21no—
55C2×M16×C29—21no—
56C2×M16×C29—21no—
57C2×M16×C29—21no—
58C2×M16×C29—21no—
59C2×M16×C29—21no—
60C2×M16×C29—21no—
61C2×M16×C29—21no—
62C2×M16×C29C2×C412yes—
63C2×M16×C29D412yes—
64C22×C8×C29—21no—
65C22×C8×C29—21no—
66C29×#117—21no—
67C29×#117—21no—
68C29×#117—21no—
69C29×#117—21no—
70C2×C4⋊C4×C29—21no—
71C2×C4⋊C4×C29—21no—
72C2×C4⋊C4×C29—21no—
73C2×C4⋊C4×C29—21no—
74C2×C4⋊C4×C29—28no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29—21no—
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29—21no—
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29—48no—
83C2×C4⋊C4×C29D412yes—
84C2×C4⋊C4×C29D412yes—
85C2×C22⋊C4×C29—21no—
86C2×C22⋊C4×C29—24no—
87C2×C42×C29—21no—
88C2×C42×C29—21no—
89C2×C42×C29—21no—
90C2×C42×C29—21no—
91C2×C42×C29C2×C412yes—
92C2×C42×C29D412yes—
93C2×C42×C29D412yes—
94C29×#104—28no—
95C29×#103—24no—
96C29×#102—24no—
97C29×#95—24no—
98C24×C29—21no—
99C24×C29C2×D411yescharacteristic
100#41×C29—22no—
101#41×C29—22no—
102#41×C29—22no—
103#41×C29—22no—
104#41×C29—22no—
105#41×C29—22no—
106#41×C29—22no—
107#41×C29—22no—
108#41×C29—41no—
109#41×C29—41no—
110#41×C29—41no—
111#41×C29—41no—
112#41×C29—41no—
113#41×C29—41no—
114#41×C29—41no—
115#41×C29—41no—
116C2×Q8×C29—21no—
117C2×Q8×C29—21no—
118C2×Q8×C29—21no—
119C2×Q8×C29—21no—
120C2×Q8×C29—21no—
121C2×Q8×C29C4⋊C412yescomplemented
122C2×D4×C29—22no—
123C2×D4×C29—22no—
124C2×D4×C29—21no—
125C2×D4×C29—21no—
126C2×D4×C29—21no—
127C2×D4×C29—21no—
128C2×D4×C29—21no—
129C2×D4×C29—41no—
130C2×D4×C29—41no—
131C2×D4×C29—41no—
132C2×D4×C29—41no—
133C2×D4×C29C4⋊C412yescomplemented
134C22×C4×C29—24no—
135C22×C4×C29—24no—
136C22×C4×C29—22no—
137C22×C4×C29—22no—
138C22×C4×C29—22no—
139C22×C4×C29—21no—
140C22×C4×C29—22no—
141C22×C4×C29—22no—
142C22×C4×C29—22no—
143C22×C4×C29—22no—
144C22×C4×C29—22no—
145C22×C4×C29—22no—
146C22×C4×C29—22no—
147C22×C4×C29—41no—
148C22×C4×C29—41no—
149C22×C4×C29—41no—
150C22×C4×C29—41no—
151C22×C4×C29—44no—
152C22×C4×C29—44no—
153C22×C4×C29—41no—
154C22×C4×C29—41no—
155C22×C4×C29C22×C411yescharacteristic
156C22×C4×C29C2×D411yescharacteristic
157C22×C4×C29C2×D411yescharacteristic
158C22×C4×C29C2×D411yescharacteristic
159C22×C4×C29C2×D411yescharacteristic
160C22×C4×C29C2×D411yescharacteristic
161C22×C4×C29C2×D411yescharacteristic
162C22×C4×C29C2×Q811yescharacteristic
163C22×C4×C29#4111yescharacteristic
164C22×C4×C29#4111yescharacteristic
165C22×C4×C29#4111yescharacteristic
166C22×C4×C29#4111yescharacteristic
167C22×C4×C29#4111yescharacteristic
168C22×C4×C29#4111yescharacteristic
169M16×C29—22no—
170M16×C29—22no—
171M16×C29—22no—
172M16×C29—22no—
173M16×C29—41no—
174M16×C29—41no—
175M16×C29—41no—
176M16×C29—41no—
177C2×C8×C29—22no—
178C2×C8×C29—22no—
179C2×C8×C29—41no—
180C2×C8×C29—41no—
181C2×C8×C29—41no—
182C2×C8×C29—41no—
183C4⋊C4×C29—22no—
184C4⋊C4×C29—22no—
185C4⋊C4×C29—22no—
186C4⋊C4×C29—22no—
187C4⋊C4×C29—416no—
188C4⋊C4×C29—41no—
189C4⋊C4×C29—41no—
190C4⋊C4×C29—41no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29—41no—
193C4⋊C4×C29—41no—
194C22⋊C4×C29—41no—
195C22⋊C4×C29—41no—
196C22⋊C4×C29—84no—
197C42×C29—22no—
198C42×C29—22no—
199C42×C29—22no—
200C42×C29—41no—
201C42×C29—41no—
202C42×C29C22⋊C414yescomplemented
203#11078C2911yesmaximal, characteristic, direct product factor, Sylow
204C23×C29—22no—
205C23×C29—22no—
206C23×C29—22no—
207C23×C29—41no—
208C23×C29—41no—
209C23×C29—42no—
210C23×C29—42no—
211C23×C29C4×D411yescharacteristic
212C23×C29#12011yescharacteristic
213C23×C29#12011yescharacteristic
214C23×C29#12111yescharacteristic
215C23×C29#12111yescharacteristic
216C23×C29C22⋊Q811yescharacteristic
217C23×C29#12411yescharacteristic
218Q8×C29—22no—
219Q8×C29—22no—
220Q8×C29—41no—
221Q8×C29—41no—
222D4×C29—22no—
223D4×C29—22no—
224D4×C29—42no—
225D4×C29—42no—
226D4×C29—42no—
227D4×C29—42no—
228D4×C29—41no—
229D4×C29—41no—
230C2×C4×C29—24no—
231C2×C4×C29—28no—
232C2×C4×C29—24no—
233C2×C4×C29—28no—
234C2×C4×C29—24no—
235C2×C4×C29—22no—
236C2×C4×C29—41no—
237C2×C4×C29—41no—
238C2×C4×C29—42no—
239C2×C4×C29—42no—
240C2×C4×C29—42no—
241C2×C4×C29—42no—
242C2×C4×C29—44no—
243C2×C4×C29—44no—
244C2×C4×C29—42no—
245C2×C4×C29—42no—
246C2×C4×C29—42no—
247C2×C4×C29—42no—
248C2×C4×C29—44no—
249C2×C4×C29—42no—
250C2×C4×C29—82no—
251C2×C4×C29—82no—
252C2×C4×C29—82no—
253C2×C4×C29C2×C22⋊C411yescharacteristic
254C2×C4×C29C2×C4⋊C411yescharacteristic
255C2×C4×C29#11711yescharacteristic
256C2×C4×C29C4×D411yescharacteristic
257C2×C4×C29C4×D411yescharacteristic
258C2×C4×C29C4×D411yescharacteristic
259C2×C4×C29#12011yescharacteristic
260C2×C4×C29#12111yescharacteristic
261C2×C4×C29#12111yescharacteristic
262C2×C4×C29#12111yescharacteristic
263C2×C4×C29#12111yescharacteristic
264C2×C4×C29#12111yescharacteristic
265C2×C4×C29#12111yescharacteristic
266C2×C4×C29C22⋊Q811yescharacteristic
267C2×C4×C29C22⋊Q811yescharacteristic
268C2×C4×C29C22⋊Q811yescharacteristic
269C2×C4×C29C22⋊Q811yescharacteristic
270C2×C4×C29C22⋊Q811yescharacteristic
271C2×C4×C29#12311yescharacteristic
272C2×C4×C29#12311yescharacteristic
273C2×C4×C29#12311yescharacteristic
274C2×C4×C29#12311yescharacteristic
275C2×C4×C29#12311yescharacteristic
276C2×C4×C29#12411yescharacteristic
277C2×C4×C29#12411yescharacteristic
278C2×C4×C29#12611yescharacteristic
279C2×C4×C29#12611yescharacteristic
280C2×C4×C29#12711yescharacteristic
281C8×C29—42no—
282C8×C29—42no—
283C22×#104C2×C2911yescharacteristic
284C2×#417C2×C2911yescharacteristic
285#2311C2×C2911yescharacteristic
286C2×#384C2×C2911yescharacteristic, complemented
287C2×#343C2×C2911yescharacteristic, complemented
288#1736C2×C2911yescharacteristic, complemented
289C2×#339C2×C2911yescharacteristic, complemented
290C22×C29—22no—
291C22×C29—22no—
292C22×C29—21no—
293C22×C29—21no—
294C22×C29—21no—
295C22×C29—21no—
296C22×C29—22no—
297C22×C29—22no—
298C22×C29—44no—
299C22×C29—42no—
300C22×C29—81no—
301C22×C29—81no—
302C22×C29—82no—
303C22×C29#38511yescharacteristic
304C22×C29#38611yescharacteristic
305C22×C29#38811yescharacteristic
306C22×C29#39211yescharacteristic
307C22×C29#39311yescharacteristic
308C22×C29#39411yescharacteristic
309C22×C29#39611yescharacteristic
310C22×C29#45312yes—
311C22×C29#45612yes—
312C4×C29—28no—
313C4×C29—42no—
314C4×C29—82no—
315C4×C29—82no—
316C4×C29—82no—
317C4×C29#38011yescharacteristic
318C4×C29#38511yescharacteristic
319C4×C29#38811yescharacteristic
320C4×C29#39011yescharacteristic
321C4×C29#39411yescharacteristic
322C4×C29#39611yescharacteristic
323C4×C29#39711yescharacteristic
324C4×C29#39911yescharacteristic
325C22×#41C22×C2911yescharacteristic
326C22×M16C22×C2911yescharacteristic
327C22×M16C22×C2911yescharacteristic
328C2×#117C22×C2911yescharacteristic
329C22×C4⋊C4—22no—
330C22×C4⋊C4C22×C2911yescharacteristic
331C22×C4⋊C4C22×C2911yescharacteristic
332C22×C42C22×C2911yescharacteristic
333C2×#104—22no—
334C2×#104—22no—
335C2×#104C4×C2914yescomplemented
336#417—22no—
337#417—22no—
338C2×#103—21no—
339C2×#102—21no—
340#391—21no—
341#390—21no—
342#386—22no—
343#384—22no—
344#384—22no—
345#380—22no—
346#343—22no—
347#340—22no—
348#339—22no—
349C2×C29—21no—
350C2×C29—21no—
351C2×C29—21no—
352C2×C29—21no—
353C2×C29—82no—
354C2×C29#143911yescharacteristic
355C2×C29#185912yes—
356C2×C29#200211yescharacteristic
357C2×C29#200511yescharacteristic
358C2×C29#203912yes—
359C2×#41—21no—
360C2×#41—21no—
361C2×#41—21no—
362C2×#41—21no—
363C2×#41—21no—
364C2×#41—21no—
365C2×#41—21no—
366C2×#41—21no—
367C2×#41—21no—
368C2×#41—21no—
369C2×#41C2×C4×C2912yes—
370C2×#41Q8×C2912yes—
371C22×Q8D4×C2911yescharacteristic
372C22×D4—21no—
373C22×D4D4×C2911yescharacteristic
374C23×C4—21no—
375C23×C4—21no—
376C23×C4—21no—
377C23×C4D4×C2912yes—
378C23×C4C23×C2911yescharacteristic
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C2×M16—21no—
384C2×M16—21no—
385C2×M16—21no—
386C2×M16—21no—
387C2×M16—21no—
388C2×M16—21no—
389C2×M16C2×C4×C2912yes—
390C2×M16D4×C2912yes—
391C22×C8—21no—
392C22×C8—21no—
393#117—21no—
394#117—21no—
395#117—21no—
396#117—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—28no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—48no—
410C2×C4⋊C4D4×C2912yes—
411C2×C4⋊C4D4×C2912yes—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—24no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42—21no—
418C2×C42C2×C4×C2912yes—
419C2×C42D4×C2912yes—
420C2×C42D4×C2912yes—
421#104—28no—
422#103—24no—
423#102—24no—
424#95—24no—
425C29#1107811yescharacteristic, direct product factor, Sylow
426C24—21no—
427C24C2×D4×C2911yescharacteristic
428#41—22no—
429#41—22no—
430#41—22no—
431#41—22no—
432#41—22no—
433#41—22no—
434#41—22no—
435#41—22no—
436#41—41no—
437#41—41no—
438#41—41no—
439#41—41no—
440#41—41no—
441#41—41no—
442#41—41no—
443#41—41no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8C4⋊C4×C2912yescomplemented
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—41no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4C4⋊C4×C2912yescomplemented
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—41no—
476C22×C4—41no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—44no—
480C22×C4—44no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4C22×C4×C2911yescharacteristic
484C22×C4C2×D4×C2911yescharacteristic
485C22×C4C2×D4×C2911yescharacteristic
486C22×C4C2×D4×C2911yescharacteristic
487C22×C4C2×D4×C2911yescharacteristic
488C22×C4C2×D4×C2911yescharacteristic
489C22×C4C2×D4×C2911yescharacteristic
490C22×C4C2×Q8×C2911yescharacteristic
491C22×C4#41×C2911yescharacteristic
492C22×C4#41×C2911yescharacteristic
493C22×C4#41×C2911yescharacteristic
494C22×C4#41×C2911yescharacteristic
495C22×C4#41×C2911yescharacteristic
496C22×C4#41×C2911yescharacteristic
497M16—22no—
498M16—22no—
499M16—22no—
500M16—22no—
501M16—41no—
502M16—41no—
503M16—41no—
504M16—41no—
505C2×C8—22no—
506C2×C8—22no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C2×C8—41no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—416no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—84no—
525C42—22no—
526C42—22no—
527C42—22no—
528C42—41no—
529C42—41no—
530C42C22⋊C4×C2914yescomplemented
531C23—22no—
532C23—22no—
533C23—22no—
534C23—42no—
535C23—42no—
536C23—41no—
537C23—41no—
538C23C4×D4×C2911yescharacteristic
539C23C29×#12011yescharacteristic
540C23C29×#12011yescharacteristic
541C23C29×#12111yescharacteristic
542C23C29×#12111yescharacteristic
543C23C29×C22⋊Q811yescharacteristic
544C23C29×#12411yescharacteristic
545Q8—22no—
546Q8—22no—
547Q8—41no—
548Q8—41no—
549D4—22no—
550D4—22no—
551D4—42no—
552D4—42no—
553D4—42no—
554D4—42no—
555D4—41no—
556D4—41no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—28no—
560C2×C4—28no—
561C2×C4—24no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—44no—
571C2×C4—42no—
572C2×C4—44no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4—82no—
580C2×C4C2×C22⋊C4×C2911yescharacteristic
581C2×C4C2×C4⋊C4×C2911yescharacteristic
582C2×C4C29×#11711yescharacteristic
583C2×C4C4×D4×C2911yescharacteristic
584C2×C4C4×D4×C2911yescharacteristic
585C2×C4C4×D4×C2911yescharacteristic
586C2×C4C29×#12011yescharacteristic
587C2×C4C29×#12111yescharacteristic
588C2×C4C29×#12111yescharacteristic
589C2×C4C29×#12111yescharacteristic
590C2×C4C29×#12111yescharacteristic
591C2×C4C29×#12111yescharacteristic
592C2×C4C29×#12111yescharacteristic
593C2×C4C29×C22⋊Q811yescharacteristic
594C2×C4C29×C22⋊Q811yescharacteristic
595C2×C4C29×C22⋊Q811yescharacteristic
596C2×C4C29×C22⋊Q811yescharacteristic
597C2×C4C29×C22⋊Q811yescharacteristic
598C2×C4C29×#12311yescharacteristic
599C2×C4C29×#12311yescharacteristic
600C2×C4C29×#12311yescharacteristic
601C2×C4C29×#12311yescharacteristic
602C2×C4C29×#12311yescharacteristic
603C2×C4C29×#12411yescharacteristic
604C2×C4C29×#12411yescharacteristic
605C2×C4C29×#12611yescharacteristic
606C2×C4C29×#12611yescharacteristic
607C2×C4C29×#12711yescharacteristic
608C8—42no—
609C8—42no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—42no—
619C22—44no—
620C22—81no—
621C22—81no—
622C22—82no—
623C22C29×#38511yescharacteristic
624C22C29×#38611yescharacteristic
625C22C29×#38811yescharacteristic
626C22C29×#39211yescharacteristic
627C22C29×#39311yescharacteristic
628C22C29×#39411yescharacteristic
629C22C29×#39611yescharacteristic
630C22C29×#45312yes—
631C22C29×#45612yes—
632C4—28no—
633C4—42no—
634C4—82no—
635C4—82no—
636C4—82no—
637C4C29×#38011yescharacteristic
638C4C29×#38511yescharacteristic
639C4C29×#38811yescharacteristic
640C4C29×#39011yescharacteristic
641C4C29×#39411yescharacteristic
642C4C29×#39611yescharacteristic
643C4C29×#39711yescharacteristic
644C4C29×#39911yescharacteristic
645C2—21no—
646C2—21no—
647C2—21no—
648C2—21no—
649C2—82no—
650C2C29×#143911yescharacteristic
651C2C29×#185912yes—
652C2C29×#200211yescharacteristic
653C2C29×#200511yescharacteristic
654C2C29×#203912yes—
subgroupG/H
center, socleC23×C29#120
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC22×#41×C29C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C29×#384C2semidirect
5. C2×C29×#343C2semidirect
6. C29×#1736C2semidirect
7. C2×C29×#339C2semidirect
18. C2×C29×#104C4semidirect
121. C2×Q8×C29C4⋊C4semidirect
133. C2×D4×C29C4⋊C4semidirect
202. C42×C29C22⋊C4semidirect
203. #11078C29direct (N × H)
286. C2×#384C2×C29semidirect
287. C2×#343C2×C29semidirect
288. #1736C2×C29semidirect
289. C2×#339C2×C29semidirect
335. C2×#104C4×C29semidirect
425. C29#11078direct (N × H)
449. C2×Q8C4⋊C4×C29semidirect
461. C2×D4C4⋊C4×C29semidirect
530. C42C22⋊C4×C29semidirect

Maximal subgroups

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

subgroupindex
C22×C29×#1042
C2×C29×#4172
C29×#23112
C2×C29×#3842
C2×C29×#3432
C29×#17362
C2×C29×#3392
#1107829