Finite Group Databasebeta

← C29×#25833 #20320733

Subgroups — C29×#25833 #20320733

Order 7424.

934 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3504C211yesmaximal, characteristic
2C29×#3165C211yesmaximal, characteristic, complemented
3C29×#3079C211yesmaximal, characteristic
4C29×#2660C211yesmaximal, characteristic, complemented
5C29×#2061C212yesmaximal, complemented
6C29×#2060C212yesmaximal, complemented
7C29×#1998C211yesmaximal, characteristic, complemented
8C29×#1995C211yesmaximal, characteristic, complemented
9C29×#1860C212yesmaximal
10C29×#1859C212yesmaximal
11C29×#1759C211yesmaximal, characteristic
12C29×#557—21no—
13C29×#557—21no—
14C29×#554—21no—
15C29×#554—21no—
16C29×#554—22no—
17C29×#554—22no—
18C29×#544—21no—
19C29×#544—21no—
20C29×#544C2211yescharacteristic
21C29×#544C2211yescharacteristic
22C29×#533—21no—
23C29×#533C2211yescharacteristic
24C2×C29×C4⋊Q8C2211yescharacteristic
25C2×C29×#125—21no—
26C2×C29×#125C2211yescharacteristic
27C29×#520C2211yescharacteristic
28C29×#520C2211yescharacteristic
29C4×#41×C29C2211yescharacteristic
30C29×#501—21no—
31C29×#501—21no—
32C29×#500—21no—
33C29×#498—21no—
34C29×#477—21no—
35C29×#476—21no—
36C29×#475—21no—
37C29×#474—21no—
38C29×#428C2212yes—
39C29×#428C2212yes—
40C29×#428C2212yes—
41C29×#423C2211yescharacteristic
42C2×C29×#104C2212yes—
43C29×#417C2212yes—
44C4×M16×C29C2211yescharacteristic
45C29×#398—22no—
46C29×#395—22no—
47C29×#384C2212yes—
48C29×#382C2212yes—
49C29×#376C2211yescharacteristic
50C29×#343C2212yes—
51C29×#343C2212yes—
52C29×#339C2212yes—
53C29×#339C2212yes—
54C29×#339C2212yes—
55C2×#41×C29C2311yescharacteristic
56C22×Q8×C29—21no—
57C2×M16×C29C2312yes—
58C2×M16×C29C2312yes—
59C29×C4⋊Q8—22no—
60C29×C4⋊Q8—22no—
61C29×C4⋊Q8—21no—
62C29×C4⋊Q8—21no—
63C29×C4⋊Q8—21no—
64C29×C4⋊Q8—21no—
65C29×C4⋊Q8—21no—
66C29×C4⋊Q8—21no—
67C29×C4⋊Q8—21no—
68C29×C4⋊Q8—21no—
69C29×C4⋊Q8D411yescharacteristic
70C29×C4⋊Q8D411yescharacteristic
71C29×#125—22no—
72C29×#125—22no—
73C29×#125—22no—
74C29×#125—22no—
75C29×#125—21no—
76C29×#125—21no—
77C29×#125—21no—
78C29×#125—21no—
79C29×#125—21no—
80C29×#125—21no—
81C29×#125—21no—
82C29×#125—21no—
83C29×#125D411yescharacteristic
84C29×#125D411yescharacteristic
85C29×C22⋊Q8—22no—
86C29×C22⋊Q8—22no—
87C29×C22⋊Q8—22no—
88C29×C22⋊Q8—22no—
89C29×C22⋊Q8—22no—
90C29×C22⋊Q8—22no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8—22no—
94C29×C22⋊Q8—22no—
95C4×Q8×C29—22no—
96C4×Q8×C29—22no—
97C4×Q8×C29—21no—
98C4×Q8×C29—21no—
99C4×Q8×C29—21no—
100C4×Q8×C29—21no—
101C4×Q8×C29D411yescharacteristic
102C4×Q8×C29D411yescharacteristic
103C4×D4×C29—21no—
104C4×D4×C29—21no—
105C4×D4×C29—21no—
106C4×D4×C29—21no—
107C4×D4×C29—22no—
108C4×D4×C29—22no—
109C4×D4×C29D411yescharacteristic
110C4×D4×C29D411yescharacteristic
111C29×#117—21no—
112C29×#117—21no—
113C29×#117—21no—
114C29×#117C2311yescharacteristic
115C29×#117C2311yescharacteristic
116C29×#117C2311yescharacteristic
117C2×C4⋊C4×C29—22no—
118C2×C4⋊C4×C29—22no—
119C2×C4⋊C4×C29—21no—
120C2×C4⋊C4×C29—21no—
121C2×C4⋊C4×C29—21no—
122C2×C4⋊C4×C29—24no—
123C2×C4⋊C4×C29D412yes—
124C2×C4⋊C4×C29D412yes—
125C2×C4⋊C4×C29C2312yes—
126C2×C4⋊C4×C29C2311yescharacteristic
127C2×C4⋊C4×C29C2311yescharacteristic
128C2×C42×C29—21no—
129C2×C42×C29C2312yes—
130C2×C42×C29C2311yescharacteristic
131C29×#107—22no—
132C29×#107—22no—
133C29×#107—22no—
134C29×#106—22no—
135C29×#106—22no—
136C29×#106—22no—
137C29×C4⋊C8—21no—
138C29×C4⋊C8—21no—
139C29×#104Q818yescomplemented
140C29×#103—22no—
141C29×#102—22no—
142C29×#97—21no—
143C4×C8×C29—21no—
144C29×#95—21no—
145C29×#95—21no—
146C29×#95—24no—
147#41×C29—22no—
148#41×C29C2×Q814yes—
149C2×Q8×C29—22no—
150C2×Q8×C29—22no—
151C2×Q8×C29—21no—
152C2×Q8×C29—21no—
153C2×Q8×C29—41no—
154C2×Q8×C29—41no—
155C2×Q8×C29—82no—
156C2×Q8×C29C2×D411yescharacteristic
157C2×D4×C29—21no—
158C2×D4×C29C2×D411yescharacteristic
159C22×C4×C29—21no—
160C22×C4×C29—22no—
161C22×C4×C29—22no—
162C22×C4×C29—22no—
163C22×C4×C29—21no—
164C22×C4×C29—21no—
165C22×C4×C29—22no—
166C22×C4×C29C2×D412yes—
167C22×C4×C29C2×D412yes—
168C22×C4×C29C2×D411yescharacteristic
169C22×C4×C29C2×D411yescharacteristic
170C22×C4×C29C2411yescharacteristic
171M16×C29—22no—
172M16×C29—24no—
173M16×C29C2×Q814yes—
174C2×C8×C29—22no—
175C2×C8×C29—22no—
176C4⋊C4×C29—22no—
177C4⋊C4×C29—22no—
178C4⋊C4×C29—22no—
179C4⋊C4×C29—22no—
180C4⋊C4×C29—22no—
181C4⋊C4×C29—22no—
182C4⋊C4×C29—22no—
183C4⋊C4×C29—22no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—22no—
187C4⋊C4×C29—22no—
188C4⋊C4×C29—22no—
189C4⋊C4×C29—22no—
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—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—22no—
201C4⋊C4×C29—22no—
202C4⋊C4×C29—41no—
203C4⋊C4×C29—41no—
204C4⋊C4×C29—84no—
205C4⋊C4×C29C2×D411yescharacteristic
206C4⋊C4×C29C2×D411yescharacteristic
207C4⋊C4×C29C2×D411yescharacteristic
208C4⋊C4×C29C2×D411yescharacteristic
209C4⋊C4×C29C2×D411yescharacteristic
210C4⋊C4×C29C2×D411yescharacteristic
211C22⋊C4×C29—22no—
212C22⋊C4×C29—22no—
213C22⋊C4×C29—21no—
214C22⋊C4×C29—21no—
215C22⋊C4×C29—21no—
216C22⋊C4×C29—21no—
217C22⋊C4×C29—21no—
218C42×C29—22no—
219C42×C29—22no—
220C42×C29—21no—
221C42×C29—21no—
222C42×C29—21no—
223C42×C29—21no—
224C42×C29—21no—
225C42×C29—22no—
226C42×C29C2×D411yescharacteristic
227C42×C29C2×D411yescharacteristic
228C42×C29C2×D411yescharacteristic
229C42×C29C2×D411yescharacteristic
230C42×C29C2×Q814yes—
231#25833C2911yesmaximal, characteristic, direct product factor, Sylow
232C23×C29—21no—
233C23×C29C22×D411yescharacteristic
234Q8×C29—21no—
235Q8×C29—81no—
236Q8×C29—81no—
237Q8×C29—82no—
238Q8×C29—82no—
239Q8×C29—82no—
240Q8×C29—82no—
241Q8×C29C4⋊Q812yes—
242D4×C29—24no—
243D4×C29—21no—
244D4×C29C4⋊Q812yes—
245C2×C4×C29—21no—
246C2×C4×C29—24no—
247C2×C4×C29—21no—
248C2×C4×C29—21no—
249C2×C4×C29—21no—
250C2×C4×C29—21no—
251C2×C4×C29—22no—
252C2×C4×C29—22no—
253C2×C4×C29—21no—
254C2×C4×C29—21no—
255C2×C4×C29—24no—
256C2×C4×C29—41no—
257C2×C4×C29—41no—
258C2×C4×C29—42no—
259C2×C4×C29—42no—
260C2×C4×C29—42no—
261C2×C4×C29—42no—
262C2×C4×C29—44no—
263C2×C4×C29—42no—
264C2×C4×C29—81no—
265C2×C4×C29—81no—
266C2×C4×C29—82no—
267C2×C4×C29—82no—
268C2×C4×C29#12011yescharacteristic
269C2×C4×C29#12011yescharacteristic
270C2×C4×C29#12011yescharacteristic
271C2×C4×C29#12011yescharacteristic
272C2×C4×C29C22×D411yescharacteristic
273C2×C4×C29C22×D411yescharacteristic
274C2×C4×C29C22×Q812yes—
275C2×C4×C292−1+412yes—
276C8×C29—24no—
277C8×C29—42no—
278#3504C2×C2911yescharacteristic
279#3165C2×C2911yescharacteristic, complemented
280#3079C2×C2911yescharacteristic
281#2660C2×C2911yescharacteristic, complemented
282#2061C2×C2912yescomplemented
283#2060C2×C2912yescomplemented
284#1998C2×C2911yescharacteristic, complemented
285#1995C2×C2911yescharacteristic, complemented
286#1860C2×C2912yes—
287#1859C2×C2912yes—
288#1759C2×C2911yescharacteristic
289C22×C29—21no—
290C22×C29—21no—
291C22×C29—22no—
292C22×C29—41no—
293C22×C29—41no—
294C22×C29C2×#12011yescharacteristic
295C22×C29D4×Q812yes—
296C4×C29—22no—
297C4×C29—21no—
298C4×C29—21no—
299C4×C29—21no—
300C4×C29—21no—
301C4×C29—44no—
302C4×C29—42no—
303C4×C29—41no—
304C4×C29—41no—
305C4×C29—41no—
306C4×C29—42no—
307C4×C29—41no—
308C4×C29—41no—
309C4×C29—41no—
310C4×C29—82no—
311C4×C29C2×C4⋊Q811yescharacteristic
312C4×C29#53611yescharacteristic
313C4×C29D4×Q812yes—
314#557—21no—
315#557—21no—
316#554—21no—
317#554—21no—
318#554—22no—
319#554—22no—
320#544—21no—
321#544—21no—
322#544C22×C2911yescharacteristic
323#544C22×C2911yescharacteristic
324#533—21no—
325#533C22×C2911yescharacteristic
326C2×C4⋊Q8C22×C2911yescharacteristic
327C2×#125—21no—
328C2×#125C22×C2911yescharacteristic
329#520C22×C2911yescharacteristic
330#520C22×C2911yescharacteristic
331C4×#41C22×C2911yescharacteristic
332#501—21no—
333#501—21no—
334#500—21no—
335#498—21no—
336#477—21no—
337#476—21no—
338#475—21no—
339#474—21no—
340#428C22×C2912yes—
341#428C22×C2912yes—
342#428C22×C2912yes—
343#423C22×C2911yescharacteristic
344C2×#104C22×C2912yes—
345#417C22×C2912yes—
346C4×M16C22×C2911yescharacteristic
347#398—22no—
348#395—22no—
349#384C22×C2912yes—
350#382C22×C2912yes—
351#376C22×C2911yescharacteristic
352#343C22×C2912yes—
353#343C22×C2912yes—
354#339C22×C2912yes—
355#339C22×C2912yes—
356#339C22×C2912yes—
357C2×C29—22no—
358C2×C29—42no—
359C2×C29#243411yescharacteristic
360C2×C29#302111yescharacteristic
361C2×C29#302211yescharacteristic
362C2×#41C23×C2911yescharacteristic
363C22×Q8—21no—
364C2×M16C23×C2912yes—
365C2×M16C23×C2912yes—
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8—21no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8D4×C2911yescharacteristic
377C4⋊Q8D4×C2911yescharacteristic
378#125—22no—
379#125—22no—
380#125—22no—
381#125—22no—
382#125—21no—
383#125—21no—
384#125—21no—
385#125—21no—
386#125—21no—
387#125—21no—
388#125—21no—
389#125—21no—
390#125D4×C2911yescharacteristic
391#125D4×C2911yescharacteristic
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395C22⋊Q8—22no—
396C22⋊Q8—22no—
397C22⋊Q8—22no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C4×Q8—22no—
403C4×Q8—22no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8D4×C2911yescharacteristic
409C4×Q8D4×C2911yescharacteristic
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4—21no—
414C4×D4—22no—
415C4×D4—22no—
416C4×D4D4×C2911yescharacteristic
417C4×D4D4×C2911yescharacteristic
418#117—21no—
419#117—21no—
420#117—21no—
421#117C23×C2911yescharacteristic
422#117C23×C2911yescharacteristic
423#117C23×C2911yescharacteristic
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4D4×C2912yes—
431C2×C4⋊C4D4×C2912yes—
432C2×C4⋊C4C23×C2912yes—
433C2×C4⋊C4C23×C2911yescharacteristic
434C2×C4⋊C4C23×C2911yescharacteristic
435C2×C42—21no—
436C2×C42C23×C2912yes—
437C2×C42C23×C2911yescharacteristic
438#107—22no—
439#107—22no—
440#107—22no—
441#106—22no—
442#106—22no—
443#106—22no—
444C4⋊C8—21no—
445C4⋊C8—21no—
446#104Q8×C2918yescomplemented
447#103—22no—
448#102—22no—
449#97—21no—
450C4×C8—21no—
451#95—21no—
452#95—21no—
453#95—24no—
454C29#2583311yescharacteristic, direct product factor, Sylow
455#41—22no—
456#41C2×Q8×C2914yes—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—41no—
462C2×Q8—41no—
463C2×Q8—82no—
464C2×Q8C2×D4×C2911yescharacteristic
465C2×D4—21no—
466C2×D4C2×D4×C2911yescharacteristic
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4C2×D4×C2912yes—
475C22×C4C2×D4×C2912yes—
476C22×C4C2×D4×C2911yescharacteristic
477C22×C4C2×D4×C2911yescharacteristic
478C22×C4C24×C2911yescharacteristic
479M16—22no—
480M16—24no—
481M16C2×Q8×C2914yes—
482C2×C8—22no—
483C2×C8—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—84no—
513C4⋊C4C2×D4×C2911yescharacteristic
514C4⋊C4C2×D4×C2911yescharacteristic
515C4⋊C4C2×D4×C2911yescharacteristic
516C4⋊C4C2×D4×C2911yescharacteristic
517C4⋊C4C2×D4×C2911yescharacteristic
518C4⋊C4C2×D4×C2911yescharacteristic
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C42—22no—
527C42—22no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—22no—
534C42C2×D4×C2911yescharacteristic
535C42C2×D4×C2911yescharacteristic
536C42C2×D4×C2911yescharacteristic
537C42C2×D4×C2911yescharacteristic
538C42C2×Q8×C2914yes—
539C23—21no—
540C23C22×D4×C2911yescharacteristic
541Q8—21no—
542Q8—81no—
543Q8—81no—
544Q8—82no—
545Q8—82no—
546Q8—82no—
547Q8—82no—
548Q8C29×C4⋊Q812yes—
549D4—24no—
550D4—21no—
551D4C29×C4⋊Q812yes—
552C2×C4—21no—
553C2×C4—24no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—24no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—42no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—42no—
571C2×C4—81no—
572C2×C4—81no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4C29×#12011yescharacteristic
576C2×C4C29×#12011yescharacteristic
577C2×C4C29×#12011yescharacteristic
578C2×C4C29×#12011yescharacteristic
579C2×C4C22×D4×C2911yescharacteristic
580C2×C4C22×D4×C2911yescharacteristic
581C2×C4C22×Q8×C2912yes—
582C2×C4C29×2−1+412yes—
583C8—24no—
584C8—42no—
585C22—21no—
586C22—21no—
587C22—22no—
588C22—41no—
589C22—41no—
590C22C2×C29×#12011yescharacteristic
591C22D4×Q8×C2912yes—
592C4—22no—
593C4—21no—
594C4—21no—
595C4—21no—
596C4—21no—
597C4—44no—
598C4—42no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—42no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—82no—
607C4C2×C29×C4⋊Q811yescharacteristic
608C4C29×#53611yescharacteristic
609C4D4×Q8×C2912yes—
610C2—22no—
611C2—42no—
612C2C29×#243411yescharacteristic
613C2C29×#302111yescharacteristic
614C2C29×#302211yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×#41×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×#3165C2semidirect
4. C29×#2660C2semidirect
5. C29×#2061C2semidirect
6. C29×#2060C2semidirect
7. C29×#1998C2semidirect
8. C29×#1995C2semidirect
139. C29×#104Q8semidirect
231. #25833C29direct (N × H)
279. #3165C2×C29semidirect
281. #2660C2×C29semidirect
282. #2061C2×C29semidirect
283. #2060C2×C29semidirect
284. #1998C2×C29semidirect
285. #1995C2×C29semidirect
446. #104Q8×C29semidirect
454. C29#25833direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35042
C29×#31652
C29×#30792
C29×#26602
C29×#20612
C29×#20602
C29×#19982
C29×#19952
C29×#18602
C29×#18592
C29×#17592
#2583329