Finite Group Databasebeta

← C29×#25493 #20320393

Subgroups — C29×#25493 #20320393

Order 7424.

648 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3166C211yesmaximal, characteristic, complemented
2C29×#3077C211yesmaximal, characteristic
3C2×C29×#478C211yesmaximal, characteristic
4C29×#2962C211yesmaximal, characteristic, complemented
5C29×#2090C211yesmaximal, characteristic, complemented
6C29×#2089C211yesmaximal, characteristic, complemented
7C29×#2063C211yesmaximal, characteristic
8C29×#2063C211yesmaximal, characteristic
9C29×#1998C211yesmaximal, characteristic, complemented
10C29×#1952C211yesmaximal, characteristic, complemented
11C29×#1951C211yesmaximal, characteristic, complemented
12C29×#1950C211yesmaximal, characteristic, complemented
13C29×#1931C211yesmaximal, characteristic
14C29×#1931C211yesmaximal, characteristic
15C4×C29×#100C211yesmaximal, characteristic
16C29×#533C2211yescharacteristic
17C2×C29×#125C2211yescharacteristic
18C2×C4×D4×C29C2211yescharacteristic
19C29×#501—21no—
20C29×#501—21no—
21C29×#499—21no—
22C29×#499—21no—
23C29×#478—21no—
24C29×#478—21no—
25C29×#478—21no—
26C29×#478—21no—
27C29×#478—21no—
28C29×#478—21no—
29C29×#476—21no—
30C29×#474—21no—
31C29×#446—21no—
32C29×#446—21no—
33C29×#446—21no—
34C8×Q8×C29—21no—
35C2×C29×#108C2211yescharacteristic
36C2×C29×#108C2211yescharacteristic
37C29×#428C2211yescharacteristic
38C29×#428C2211yescharacteristic
39C29×#428C2211yescharacteristic
40C29×#428C2211yescharacteristic
41C29×#428C2211yescharacteristic
42C29×#428C2211yescharacteristic
43C2×C29×#107C2211yescharacteristic
44C2×C29×#106C2211yescharacteristic
45C29×#424C2211yescharacteristic
46C29×#424C2211yescharacteristic
47C29×#423C2211yescharacteristic
48C2×C29×C4⋊C8C2211yescharacteristic
49C29×#418C2211yescharacteristic
50C29×#418C2211yescharacteristic
51C2×C29×#102C2211yescharacteristic
52C2×C29×#102C2211yescharacteristic
53C2×C29×#100C2211yescharacteristic
54C2×C29×#100C2211yescharacteristic
55C29×#405C2211yescharacteristic
56C29×#405C2211yescharacteristic
57C4×M16×C29C2211yescharacteristic
58C4×M16×C29C2211yescharacteristic
59C29×#343C2211yescharacteristic
60C29×#343C2211yescharacteristic
61C29×#343C2211yescharacteristic
62C29×#343C2211yescharacteristic
63C29×#343C2211yescharacteristic
64C29×#343C2211yescharacteristic
65C29×#341C2211yescharacteristic
66C29×#341C2211yescharacteristic
67C22×D4×C29C2311yescharacteristic
68C23×C4×C29—21no—
69C2×M16×C29C2311yescharacteristic
70C2×M16×C29C2311yescharacteristic
71C2×M16×C29C2311yescharacteristic
72C2×M16×C29C2311yescharacteristic
73C2×M16×C29C2311yescharacteristic
74C2×M16×C29C2311yescharacteristic
75C22×C8×C29C2311yescharacteristic
76C22×C8×C29C2311yescharacteristic
77C29×C4⋊Q8D411yescharacteristic
78C29×C4⋊Q8D411yescharacteristic
79C29×#125—21no—
80C29×#125—21no—
81C29×#125—21no—
82C29×#125—21no—
83C29×#125D411yescharacteristic
84C29×#125D411yescharacteristic
85C29×C22⋊Q8—21no—
86C29×C22⋊Q8—21no—
87C4×Q8×C29—21no—
88C4×Q8×C29—21no—
89C4×D4×C29—21no—
90C4×D4×C29—21no—
91C4×D4×C29—21no—
92C4×D4×C29—21no—
93C29×#117C2311yescharacteristic
94C29×#117C2311yescharacteristic
95C2×C4⋊C4×C29—21no—
96C2×C4⋊C4×C29—21no—
97C2×C4⋊C4×C29C2311yescharacteristic
98C2×C4⋊C4×C29C2311yescharacteristic
99C2×C4⋊C4×C29C2311yescharacteristic
100C2×C22⋊C4×C29—21no—
101C2×C42×C29C2311yescharacteristic
102C29×#108—22no—
103C29×#108—22no—
104C29×#107—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#107—21no—
108C29×#107—21no—
109C29×#107—21no—
110C29×#107—21no—
111C29×#107—21no—
112C29×#106—21no—
113C29×#106—21no—
114C29×#106—21no—
115C29×#106—21no—
116C29×#106—21no—
117C29×#106—21no—
118C29×#106—21no—
119C29×#106—21no—
120C29×C4⋊C8—21no—
121C29×C4⋊C8—21no—
122C29×C4⋊C8—21no—
123C29×C4⋊C8—21no—
124C29×C4⋊C8—21no—
125C29×C4⋊C8—21no—
126C29×C4⋊C8D411yescharacteristic
127C29×C4⋊C8D411yescharacteristic
128C29×C4⋊C8D411yescharacteristic
129C29×C4⋊C8D411yescharacteristic
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×#102—21no—
135C29×#102—21no—
136C29×#102—21no—
137C29×#102—21no—
138C29×#100—22no—
139C29×#100Q814yescomplemented
140C29×#97—21no—
141C29×#97—21no—
142C29×#97—21no—
143C29×#97—21no—
144C4×C8×C29—21no—
145C4×C8×C29—21no—
146C4×C8×C29—21no—
147C4×C8×C29—21no—
148C24×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
156C2×D4×C29C2×Q812yes—
157C22×C4×C29—21no—
158C22×C4×C29—21no—
159C22×C4×C29—21no—
160C22×C4×C29—41no—
161C22×C4×C29—41no—
162C22×C4×C29—82no—
163C22×C4×C29#4111yescharacteristic
164C22×C4×C29#4111yescharacteristic
165C22×C4×C29C2411yescharacteristic
166M16×C29—21no—
167M16×C29—21no—
168M16×C29—21no—
169M16×C29—21no—
170M16×C29—21no—
171M16×C29—21no—
172M16×C29—21no—
173M16×C29—21no—
174M16×C29—21no—
175M16×C29C2×Q812yes—
176M16×C29C2×Q812yes—
177M16×C29#4112yes—
178C2×C8×C29—21no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29—21no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29—21no—
187C2×C8×C29—21no—
188C2×C8×C29C2×D411yescharacteristic
189C2×C8×C29C2×D411yescharacteristic
190C2×C8×C29C2×D411yescharacteristic
191C2×C8×C29C2×D411yescharacteristic
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—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—21no—
201C4⋊C4×C29—21no—
202C4⋊C4×C29—21no—
203C4⋊C4×C29—21no—
204C4⋊C4×C29—41no—
205C4⋊C4×C29—41no—
206C4⋊C4×C29—41no—
207C4⋊C4×C29—41no—
208C4⋊C4×C29C2×D411yescharacteristic
209C4⋊C4×C29C2×D411yescharacteristic
210C4⋊C4×C29C2×D411yescharacteristic
211C4⋊C4×C29C2×D411yescharacteristic
212C22⋊C4×C29—21no—
213C22⋊C4×C29—21no—
214C22⋊C4×C29—41no—
215C22⋊C4×C29—41no—
216C42×C29—21no—
217C42×C29—21no—
218C42×C29C2×D411yescharacteristic
219C42×C29C2×D411yescharacteristic
220C42×C29C2×D411yescharacteristic
221C42×C29C2×D411yescharacteristic
222#25493C2911yesmaximal, characteristic, direct product factor, Sylow
223C23×C29—22no—
224C23×C29—41no—
225C23×C29—41no—
226C23×C29—81no—
227C23×C29—81no—
228C23×C29C2×#4111yescharacteristic
229Q8×C29—42no—
230Q8×C29—81no—
231D4×C29—22no—
232D4×C29—22no—
233D4×C29—41no—
234D4×C29—41no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
241C2×C4×C29—41no—
242C2×C4×C29—41no—
243C2×C4×C29—41no—
244C2×C4×C29—82no—
245C2×C4×C29—82no—
246C2×C4×C29—81no—
247C2×C4×C29—81no—
248C2×C4×C29—81no—
249C2×C4×C29#12111yescharacteristic
250C2×C4×C29#12111yescharacteristic
251C2×C4×C29#12111yescharacteristic
252C2×C4×C29#12111yescharacteristic
253C2×C4×C29C22×D411yescharacteristic
254C2×C4×C29C22×D411yescharacteristic
255C2×C4×C29C22×Q811yescharacteristic
256C2×C4×C29C2×#4111yescharacteristic
257C2×C4×C292−1+411yescharacteristic
258C2×C4×C292−1+411yescharacteristic
259C8×C29—21no—
260C8×C29—21no—
261C8×C29—21no—
262C8×C29—21no—
263C8×C29—22no—
264C8×C29—22no—
265C8×C29—22no—
266C8×C29—41no—
267C8×C29—41no—
268C8×C29—41no—
269#3166C2×C2911yescharacteristic, complemented
270#3077C2×C2911yescharacteristic
271C2×#478C2×C2911yescharacteristic
272#2962C2×C2911yescharacteristic, complemented
273#2090C2×C2911yescharacteristic, complemented
274#2089C2×C2911yescharacteristic, complemented
275#2063C2×C2911yescharacteristic
276#2063C2×C2911yescharacteristic
277#1998C2×C2911yescharacteristic, complemented
278#1952C2×C2911yescharacteristic, complemented
279#1951C2×C2911yescharacteristic, complemented
280#1950C2×C2911yescharacteristic, complemented
281#1931C2×C2911yescharacteristic
282#1931C2×C2911yescharacteristic
283C4×#100C2×C2911yescharacteristic
284C22×C29—21no—
285C22×C29—21no—
286C22×C29—42no—
287C22×C29—82no—
288C22×C29—82no—
289C22×C29—81no—
290C22×C29—81no—
291C22×C29C2×#12111yescharacteristic
292C22×C29#53311yescharacteristic
293C22×C29#54111yescharacteristic
294C4×C29—21no—
295C4×C29—21no—
296C4×C29—21no—
297C4×C29—21no—
298C4×C29—41no—
299C4×C29—41no—
300C4×C29—41no—
301C4×C29—41no—
302C4×C29—81no—
303C4×C29—81no—
304C4×C29—81no—
305C4×C29#54711yescharacteristic
306C4×C29#54811yescharacteristic
307C4×C29D4×Q811yescharacteristic
308C4×C29D4×Q811yescharacteristic
309#533C22×C2911yescharacteristic
310C2×#125C22×C2911yescharacteristic
311C2×C4×D4C22×C2911yescharacteristic
312#501—21no—
313#501—21no—
314#499—21no—
315#499—21no—
316#478—21no—
317#478—21no—
318#478—21no—
319#478—21no—
320#478—21no—
321#478—21no—
322#476—21no—
323#474—21no—
324#446—21no—
325#446—21no—
326#446—21no—
327C8×Q8—21no—
328C2×#108C22×C2911yescharacteristic
329C2×#108C22×C2911yescharacteristic
330#428C22×C2911yescharacteristic
331#428C22×C2911yescharacteristic
332#428C22×C2911yescharacteristic
333#428C22×C2911yescharacteristic
334#428C22×C2911yescharacteristic
335#428C22×C2911yescharacteristic
336C2×#107C22×C2911yescharacteristic
337C2×#106C22×C2911yescharacteristic
338#424C22×C2911yescharacteristic
339#424C22×C2911yescharacteristic
340#423C22×C2911yescharacteristic
341C2×C4⋊C8C22×C2911yescharacteristic
342#418C22×C2911yescharacteristic
343#418C22×C2911yescharacteristic
344C2×#102C22×C2911yescharacteristic
345C2×#102C22×C2911yescharacteristic
346C2×#100C22×C2911yescharacteristic
347C2×#100C22×C2911yescharacteristic
348#405C22×C2911yescharacteristic
349#405C22×C2911yescharacteristic
350C4×M16C22×C2911yescharacteristic
351C4×M16C22×C2911yescharacteristic
352#343C22×C2911yescharacteristic
353#343C22×C2911yescharacteristic
354#343C22×C2911yescharacteristic
355#343C22×C2911yescharacteristic
356#343C22×C2911yescharacteristic
357#343C22×C2911yescharacteristic
358#341C22×C2911yescharacteristic
359#341C22×C2911yescharacteristic
360C2×C29—21no—
361C2×C29—21no—
362C2×C29—82no—
363C2×C29#242911yescharacteristic
364C2×C29#306711yescharacteristic
365C2×C29#306811yescharacteristic
366C22×D4C23×C2911yescharacteristic
367C23×C4—21no—
368C2×M16C23×C2911yescharacteristic
369C2×M16C23×C2911yescharacteristic
370C2×M16C23×C2911yescharacteristic
371C2×M16C23×C2911yescharacteristic
372C2×M16C23×C2911yescharacteristic
373C2×M16C23×C2911yescharacteristic
374C22×C8C23×C2911yescharacteristic
375C22×C8C23×C2911yescharacteristic
376C4⋊Q8D4×C2911yescharacteristic
377C4⋊Q8D4×C2911yescharacteristic
378#125—21no—
379#125—21no—
380#125—21no—
381#125—21no—
382#125D4×C2911yescharacteristic
383#125D4×C2911yescharacteristic
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C4×Q8—21no—
387C4×Q8—21no—
388C4×D4—21no—
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392#117C23×C2911yescharacteristic
393#117C23×C2911yescharacteristic
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4C23×C2911yescharacteristic
397C2×C4⋊C4C23×C2911yescharacteristic
398C2×C4⋊C4C23×C2911yescharacteristic
399C2×C22⋊C4—21no—
400C2×C42C23×C2911yescharacteristic
401#108—22no—
402#108—22no—
403#107—21no—
404#107—21no—
405#107—21no—
406#107—21no—
407#107—21no—
408#107—21no—
409#107—21no—
410#107—21no—
411#106—21no—
412#106—21no—
413#106—21no—
414#106—21no—
415#106—21no—
416#106—21no—
417#106—21no—
418#106—21no—
419C4⋊C8—21no—
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8—21no—
424C4⋊C8—21no—
425C4⋊C8D4×C2911yescharacteristic
426C4⋊C8D4×C2911yescharacteristic
427C4⋊C8D4×C2911yescharacteristic
428C4⋊C8D4×C2911yescharacteristic
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#100—22no—
438#100Q8×C2914yescomplemented
439#97—21no—
440#97—21no—
441#97—21no—
442#97—21no—
443C4×C8—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8—21no—
447C29#2549311yescharacteristic, direct product factor, Sylow
448C24—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4C2×Q8×C2912yes—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—82no—
463C22×C4#41×C2911yescharacteristic
464C22×C4#41×C2911yescharacteristic
465C22×C4C24×C2911yescharacteristic
466M16—21no—
467M16—21no—
468M16—21no—
469M16—21no—
470M16—21no—
471M16—21no—
472M16—21no—
473M16—21no—
474M16—21no—
475M16C2×Q8×C2912yes—
476M16C2×Q8×C2912yes—
477M16#41×C2912yes—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8C2×D4×C2911yescharacteristic
489C2×C8C2×D4×C2911yescharacteristic
490C2×C8C2×D4×C2911yescharacteristic
491C2×C8C2×D4×C2911yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4C2×D4×C2911yescharacteristic
509C4⋊C4C2×D4×C2911yescharacteristic
510C4⋊C4C2×D4×C2911yescharacteristic
511C4⋊C4C2×D4×C2911yescharacteristic
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C42—21no—
517C42—21no—
518C42C2×D4×C2911yescharacteristic
519C42C2×D4×C2911yescharacteristic
520C42C2×D4×C2911yescharacteristic
521C42C2×D4×C2911yescharacteristic
522C23—22no—
523C23—41no—
524C23—41no—
525C23—81no—
526C23—81no—
527C23C2×#41×C2911yescharacteristic
528Q8—42no—
529Q8—81no—
530D4—22no—
531D4—22no—
532D4—41no—
533D4—41no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—82no—
544C2×C4—82no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4C29×#12111yescharacteristic
549C2×C4C29×#12111yescharacteristic
550C2×C4C29×#12111yescharacteristic
551C2×C4C29×#12111yescharacteristic
552C2×C4C22×D4×C2911yescharacteristic
553C2×C4C22×D4×C2911yescharacteristic
554C2×C4C22×Q8×C2911yescharacteristic
555C2×C4C2×#41×C2911yescharacteristic
556C2×C4C29×2−1+411yescharacteristic
557C2×C4C29×2−1+411yescharacteristic
558C8—21no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—22no—
563C8—22no—
564C8—22no—
565C8—41no—
566C8—41no—
567C8—41no—
568C22—21no—
569C22—21no—
570C22—42no—
571C22—82no—
572C22—82no—
573C22—81no—
574C22—81no—
575C22C2×C29×#12111yescharacteristic
576C22C29×#53311yescharacteristic
577C22C29×#54111yescharacteristic
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—81no—
587C4—81no—
588C4—81no—
589C4C29×#54711yescharacteristic
590C4C29×#54811yescharacteristic
591C4D4×Q8×C2911yescharacteristic
592C4D4×Q8×C2911yescharacteristic
593C2—21no—
594C2—21no—
595C2—82no—
596C2C29×#242911yescharacteristic
597C2C29×#306711yescharacteristic
598C2C29×#306811yescharacteristic
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
1. C29×#3166C2semidirect
4. C29×#2962C2semidirect
5. C29×#2090C2semidirect
6. C29×#2089C2semidirect
9. C29×#1998C2semidirect
10. C29×#1952C2semidirect
11. C29×#1951C2semidirect
12. C29×#1950C2semidirect
139. C29×#100Q8semidirect
222. #25493C29direct (N × H)
269. #3166C2×C29semidirect
272. #2962C2×C29semidirect
273. #2090C2×C29semidirect
274. #2089C2×C29semidirect
277. #1998C2×C29semidirect
278. #1952C2×C29semidirect
279. #1951C2×C29semidirect
280. #1950C2×C29semidirect
438. #100Q8×C29semidirect
447. C29#25493direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31662
C29×#30772
C2×C29×#4782
C29×#29622
C29×#20902
C29×#20892
C29×#20632
C29×#19982
C29×#19522
C29×#19512
C29×#19502
C29×#19312
C4×C29×#1002
#2549329