Finite Group Databasebeta

← C29×#24690 #20319590

Subgroups — C29×#24690 #20319590

Order 7424.

808 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#478C211yesmaximal, characteristic
2C2×C29×#440C211yesmaximal, characteristic
3C29×#2565C211yesmaximal, characteristic, complemented
4C29×#2354C211yesmaximal, characteristic
5C29×#2073C211yesmaximal, characteristic
6C29×#2071C211yesmaximal, characteristic
7C29×#2055C211yesmaximal, characteristic
8C29×#2055C211yesmaximal, characteristic
9C29×#1992C211yesmaximal, characteristic, complemented
10C29×#1949C211yesmaximal, characteristic, complemented
11C29×#1947C211yesmaximal, characteristic, complemented
12C29×#1940C211yesmaximal, characteristic, complemented
13C29×#1928C211yesmaximal, characteristic, complemented
14C29×#1927C211yesmaximal, characteristic, complemented
15C29×#1803C211yesmaximal, characteristic, complemented
16C22×SD16×C29C2211yescharacteristic
17C2×C29×#125C2211yescharacteristic
18C2×C4×Q8×C29C2211yescharacteristic
19C2×C4×D4×C29C2211yescharacteristic
20C2×C29×#117—21no—
21C29×#478—24no—
22C29×#440—24no—
23C2×C29×#107C2211yescharacteristic
24C2×C29×#107C2211yescharacteristic
25C2×C29×#106C2211yescharacteristic
26C2×C29×C4⋊C8C2211yescharacteristic
27C2×C29×C4⋊C8C2211yescharacteristic
28C2×C29×C4⋊C8C2211yescharacteristic
29C2×C29×#103C2211yescharacteristic
30C2×C29×#103C2211yescharacteristic
31C2×C29×#103C2211yescharacteristic
32C2×C29×#102C2211yescharacteristic
33C2×C29×#102C2211yescharacteristic
34C2×C29×#102C2211yescharacteristic
35C2×C29×#97C2211yescharacteristic
36C29×#398—21no—
37C29×#398—21no—
38C29×#391C2211yescharacteristic
39C29×#391C2211yescharacteristic
40C29×#390C2211yescharacteristic
41C29×#390C2211yescharacteristic
42C29×#388—21no—
43C29×#388—21no—
44C29×#387—21no—
45C29×#387—21no—
46C29×#384C2211yescharacteristic
47C29×#384C2211yescharacteristic
48C29×#382C2211yescharacteristic
49C29×#380—21no—
50C4×C4⋊C4×C29C2211yescharacteristic
51C4×C4⋊C4×C29C2211yescharacteristic
52C4×C4⋊C4×C29C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#340C2211yescharacteristic
59C29×#336C2211yescharacteristic
60C29×#336C2211yescharacteristic
61C22×Q8×C29C2311yescharacteristic
62C22×D4×C29C2311yescharacteristic
63C23×C4×C29—21no—
64C2×SD16×C29—22no—
65C2×SD16×C29—22no—
66C2×SD16×C29—22no—
67C22×C8×C29C2311yescharacteristic
68C22×C8×C29C2311yescharacteristic
69C22×C8×C29C2311yescharacteristic
70C22×C8×C29C2311yescharacteristic
71C29×#125—22no—
72C29×#125—22no—
73C4×Q8×C29—22no—
74C4×Q8×C29—22no—
75C4×D4×C29—22no—
76C4×D4×C29D414yes—
77C29×#117—44no—
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29—21no—
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29—21no—
84C2×C4⋊C4×C29—21no—
85C2×C4⋊C4×C29D411yescharacteristic
86C2×C4⋊C4×C29D411yescharacteristic
87C2×C4⋊C4×C29C2311yescharacteristic
88C2×C4⋊C4×C29C2311yescharacteristic
89C2×C4⋊C4×C29C2311yescharacteristic
90C2×C4⋊C4×C29C2311yescharacteristic
91C2×C4⋊C4×C29C2311yescharacteristic
92C2×C4⋊C4×C29C2311yescharacteristic
93C2×C22⋊C4×C29—21no—
94C2×C22⋊C4×C29—21no—
95C2×C22⋊C4×C29—21no—
96C2×C22⋊C4×C29—21no—
97C2×C22⋊C4×C29—21no—
98C2×C42×C29—21no—
99C2×C42×C29—21no—
100C2×C42×C29—21no—
101C2×C42×C29C2311yescharacteristic
102C2×C42×C29C2311yescharacteristic
103C2×C42×C29C2311yescharacteristic
104C29×#107—22no—
105C29×#107—22no—
106C29×#106—22no—
107C29×C4⋊C8—22no—
108C29×C4⋊C8—22no—
109C29×C4⋊C8—22no—
110C29×#103—22no—
111C29×#103—22no—
112C29×#103—22no—
113C29×#102—22no—
114C29×#102—22no—
115C29×#102—22no—
116C29×#97—22no—
117C29×#95—21no—
118C29×#95—21no—
119C29×#95—21no—
120C29×#95—21no—
121C29×#95—21no—
122C29×#95—21no—
123C29×#95—21no—
124C29×#95—21no—
125C29×#95D411yescharacteristic
126C29×#95D411yescharacteristic
127C24×C29—21no—
128C2×Q8×C29—21no—
129C2×Q8×C29—21no—
130C2×Q8×C29—21no—
131C2×Q8×C29—21no—
132C2×Q8×C29—21no—
133C2×Q8×C29#4112yes—
134C2×D4×C29—21no—
135C2×D4×C29—21no—
136C2×D4×C29—21no—
137C2×D4×C29—21no—
138C2×D4×C29—21no—
139C2×D4×C29C2×D412yes—
140C22×C4×C29—21no—
141C22×C4×C29—21no—
142C22×C4×C29—24no—
143C22×C4×C29—21no—
144C22×C4×C29—21no—
145C22×C4×C29—21no—
146C22×C4×C29—21no—
147C22×C4×C29—21no—
148C22×C4×C29—42no—
149C22×C4×C29—42no—
150C22×C4×C29C2×D411yescharacteristic
151C22×C4×C29C2×D411yescharacteristic
152C22×C4×C29C2×D411yescharacteristic
153C22×C4×C29C2×D411yescharacteristic
154C22×C4×C29C2×D411yescharacteristic
155C22×C4×C29C2×D411yescharacteristic
156C22×C4×C29C2411yescharacteristic
157SD16×C29—28no—
158C2×C8×C29—21no—
159C2×C8×C29—21no—
160C2×C8×C29—21no—
161C2×C8×C29—21no—
162C2×C8×C29—21no—
163C2×C8×C29—21no—
164C2×C8×C29—21no—
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29#4112yes—
170C4⋊C4×C29—22no—
171C4⋊C4×C29—21no—
172C4⋊C4×C29—21no—
173C4⋊C4×C29—21no—
174C4⋊C4×C29—21no—
175C4⋊C4×C29—21no—
176C4⋊C4×C29—21no—
177C4⋊C4×C29—21no—
178C4⋊C4×C29—21no—
179C4⋊C4×C29—21no—
180C4⋊C4×C29—21no—
181C4⋊C4×C29—21no—
182C4⋊C4×C29—41no—
183C4⋊C4×C29—42no—
184C4⋊C4×C29—42no—
185C4⋊C4×C29—42no—
186C4⋊C4×C29—42no—
187C4⋊C4×C29—42no—
188C4⋊C4×C29—42no—
189C4⋊C4×C29—81no—
190C4⋊C4×C29C2×D412yes—
191C22⋊C4×C29—24no—
192C22⋊C4×C29—42no—
193C22⋊C4×C29—42no—
194C22⋊C4×C29—81no—
195C22⋊C4×C29—81no—
196C42×C29—21no—
197C42×C29—21no—
198C42×C29—21no—
199C42×C29—21no—
200C42×C29—42no—
201C42×C29—42no—
202C42×C29—42no—
203C42×C29C2×D412yes—
204C42×C29#4112yes—
205#24690C2911yesmaximal, characteristic, direct product factor, Sylow
206C23×C29—22no—
207C23×C29—41no—
208C23×C29—41no—
209C23×C29—41no—
210C23×C29—41no—
211C23×C29—41no—
212C23×C29—41no—
213C23×C29C22×D411yescharacteristic
214Q8×C29—22no—
215Q8×C29—22no—
216Q8×C29—41no—
217Q8×C29—41no—
218D4×C29—22no—
219D4×C29—22no—
220D4×C29—41no—
221D4×C29—41no—
222C2×C4×C29—21no—
223C2×C4×C29—21no—
224C2×C4×C29—21no—
225C2×C4×C29—21no—
226C2×C4×C29—21no—
227C2×C4×C29—21no—
228C2×C4×C29—22no—
229C2×C4×C29—21no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—22no—
233C2×C4×C29—21no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—48no—
240C2×C4×C29—41no—
241C2×C4×C29—41no—
242C2×C4×C29—41no—
243C2×C4×C29—41no—
244C2×C4×C29—41no—
245C2×C4×C29—41no—
246C2×C4×C29—41no—
247C2×C4×C29—41no—
248C2×C4×C29—41no—
249C2×C4×C29—41no—
250C2×C4×C29—41no—
251C2×C4×C29—41no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
254C2×C4×C29—41no—
255C2×C4×C29—41no—
256C2×C4×C29—41no—
257C2×C4×C29—41no—
258C2×C4×C29—41no—
259C2×C4×C29#12112yes—
260C2×C4×C29#12112yes—
261C2×C4×C29AGL(1,ℤ/8)12yes—
262C2×C4×C29C22×D411yescharacteristic
263C2×C4×C29C2×#4111yescharacteristic
264C2×C4×C29C2×#4111yescharacteristic
265C2×C4×C29C2×#4111yescharacteristic
266C2×C4×C292−1+411yescharacteristic
267C2×C4×C292−1+411yescharacteristic
268C8×C29—22no—
269C8×C29—41no—
270C8×C29—41no—
271C8×C29—41no—
272C2×#478C2×C2911yescharacteristic
273C2×#440C2×C2911yescharacteristic
274#2565C2×C2911yescharacteristic, complemented
275#2354C2×C2911yescharacteristic
276#2073C2×C2911yescharacteristic
277#2071C2×C2911yescharacteristic
278#2055C2×C2911yescharacteristic
279#2055C2×C2911yescharacteristic
280#1992C2×C2911yescharacteristic, complemented
281#1949C2×C2911yescharacteristic, complemented
282#1947C2×C2911yescharacteristic, complemented
283#1940C2×C2911yescharacteristic, complemented
284#1928C2×C2911yescharacteristic, complemented
285#1927C2×C2911yescharacteristic, complemented
286#1803C2×C2911yescharacteristic, complemented
287C22×C29—42no—
288C22×C29—42no—
289C22×C29—42no—
290C22×C29—81no—
291C22×C29—81no—
292C22×C29—81no—
293C22×C29—81no—
294C22×C29C2×#12111yescharacteristic
295C22×C29#54711yescharacteristic
296C22×C29#54811yescharacteristic
297C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
298C22×C29#57511yescharacteristic
299C22×C29#57711yescharacteristic
300C22×C29#57811yescharacteristic
301C4×C29—22no—
302C4×C29—22no—
303C4×C29—22no—
304C4×C29—41no—
305C4×C29—41no—
306C4×C29—41no—
307C4×C29—42no—
308C4×C29—42no—
309C4×C29—81no—
310C4×C29—81no—
311C4×C29—81no—
312C4×C29—81no—
313C4×C29—81no—
314C4×C29#52511yescharacteristic
315C4×C29#53611yescharacteristic
316C4×C29#55211yescharacteristic
317C4×C29#55611yescharacteristic
318C22×SD16C22×C2911yescharacteristic
319C2×#125C22×C2911yescharacteristic
320C2×C4×Q8C22×C2911yescharacteristic
321C2×C4×D4C22×C2911yescharacteristic
322C2×#117—21no—
323#478—24no—
324#440—24no—
325C2×#107C22×C2911yescharacteristic
326C2×#107C22×C2911yescharacteristic
327C2×#106C22×C2911yescharacteristic
328C2×C4⋊C8C22×C2911yescharacteristic
329C2×C4⋊C8C22×C2911yescharacteristic
330C2×C4⋊C8C22×C2911yescharacteristic
331C2×#103C22×C2911yescharacteristic
332C2×#103C22×C2911yescharacteristic
333C2×#103C22×C2911yescharacteristic
334C2×#102C22×C2911yescharacteristic
335C2×#102C22×C2911yescharacteristic
336C2×#102C22×C2911yescharacteristic
337C2×#97C22×C2911yescharacteristic
338#398—21no—
339#398—21no—
340#391C22×C2911yescharacteristic
341#391C22×C2911yescharacteristic
342#390C22×C2911yescharacteristic
343#390C22×C2911yescharacteristic
344#388—21no—
345#388—21no—
346#387—21no—
347#387—21no—
348#384C22×C2911yescharacteristic
349#384C22×C2911yescharacteristic
350#382C22×C2911yescharacteristic
351#380—21no—
352C4×C4⋊C4C22×C2911yescharacteristic
353C4×C4⋊C4C22×C2911yescharacteristic
354C4×C4⋊C4C22×C2911yescharacteristic
355#340C22×C2911yescharacteristic
356#340C22×C2911yescharacteristic
357#340C22×C2911yescharacteristic
358#340C22×C2911yescharacteristic
359#340C22×C2911yescharacteristic
360#340C22×C2911yescharacteristic
361#336C22×C2911yescharacteristic
362#336C22×C2911yescharacteristic
363C2×C29—82no—
364C2×C29#241511yescharacteristic
365C2×C29#303611yescharacteristic
366C2×C29#304611yescharacteristic
367C2×C29#334311yescharacteristic
368C2×C29#334811yescharacteristic
369C2×C29#336811yescharacteristic
370C2×C29#337711yescharacteristic
371C22×Q8C23×C2911yescharacteristic
372C22×D4C23×C2911yescharacteristic
373C23×C4—21no—
374C2×SD16—22no—
375C2×SD16—22no—
376C2×SD16—22no—
377C22×C8C23×C2911yescharacteristic
378C22×C8C23×C2911yescharacteristic
379C22×C8C23×C2911yescharacteristic
380C22×C8C23×C2911yescharacteristic
381#125—22no—
382#125—22no—
383C4×Q8—22no—
384C4×Q8—22no—
385C4×D4—22no—
386C4×D4D4×C2914yes—
387#117—44no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4D4×C2911yescharacteristic
396C2×C4⋊C4D4×C2911yescharacteristic
397C2×C4⋊C4C23×C2911yescharacteristic
398C2×C4⋊C4C23×C2911yescharacteristic
399C2×C4⋊C4C23×C2911yescharacteristic
400C2×C4⋊C4C23×C2911yescharacteristic
401C2×C4⋊C4C23×C2911yescharacteristic
402C2×C4⋊C4C23×C2911yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C42—21no—
409C2×C42—21no—
410C2×C42—21no—
411C2×C42C23×C2911yescharacteristic
412C2×C42C23×C2911yescharacteristic
413C2×C42C23×C2911yescharacteristic
414#107—22no—
415#107—22no—
416#106—22no—
417C4⋊C8—22no—
418C4⋊C8—22no—
419C4⋊C8—22no—
420#103—22no—
421#103—22no—
422#103—22no—
423#102—22no—
424#102—22no—
425#102—22no—
426#97—22no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95D4×C2911yescharacteristic
436#95D4×C2911yescharacteristic
437C29#2469011yescharacteristic, direct product factor, Sylow
438C24—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8#41×C2912yes—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4C2×D4×C2912yes—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—24no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4C2×D4×C2911yescharacteristic
462C22×C4C2×D4×C2911yescharacteristic
463C22×C4C2×D4×C2911yescharacteristic
464C22×C4C2×D4×C2911yescharacteristic
465C22×C4C2×D4×C2911yescharacteristic
466C22×C4C2×D4×C2911yescharacteristic
467C22×C4C24×C2911yescharacteristic
468SD16—28no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8#41×C2912yes—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—41no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—81no—
501C4⋊C4C2×D4×C2912yes—
502C22⋊C4—24no—
503C22⋊C4—42no—
504C22⋊C4—42no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—42no—
512C42—42no—
513C42—42no—
514C42C2×D4×C2912yes—
515C42#41×C2912yes—
516C23—22no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—41no—
522C23—41no—
523C23C22×D4×C2911yescharacteristic
524Q8—22no—
525Q8—22no—
526Q8—41no—
527Q8—41no—
528D4—22no—
529D4—22no—
530D4—41no—
531D4—41no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—48no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4C29×#12112yes—
570C2×C4C29×#12112yes—
571C2×C4C29×AGL(1,ℤ/8)12yes—
572C2×C4C22×D4×C2911yescharacteristic
573C2×C4C2×#41×C2911yescharacteristic
574C2×C4C2×#41×C2911yescharacteristic
575C2×C4C2×#41×C2911yescharacteristic
576C2×C4C29×2−1+411yescharacteristic
577C2×C4C29×2−1+411yescharacteristic
578C8—22no—
579C8—41no—
580C8—41no—
581C8—41no—
582C22—42no—
583C22—42no—
584C22—42no—
585C22—81no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22C2×C29×#12111yescharacteristic
590C22C29×#54711yescharacteristic
591C22C29×#54811yescharacteristic
592C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
593C22C29×#57511yescharacteristic
594C22C29×#57711yescharacteristic
595C22C29×#57811yescharacteristic
596C4—22no—
597C4—22no—
598C4—22no—
599C4—42no—
600C4—42no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4—81no—
608C4—81no—
609C4C29×#52511yescharacteristic
610C4C29×#53611yescharacteristic
611C4C29×#55211yescharacteristic
612C4C29×#55611yescharacteristic
613C2—82no—
614C2C29×#241511yescharacteristic
615C2C29×#303611yescharacteristic
616C2C29×#304611yescharacteristic
617C2C29×#334311yescharacteristic
618C2C29×#334811yescharacteristic
619C2C29×#336811yescharacteristic
620C2C29×#337711yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D4×C29C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C4⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#2565C2semidirect
9. C29×#1992C2semidirect
10. C29×#1949C2semidirect
11. C29×#1947C2semidirect
12. C29×#1940C2semidirect
13. C29×#1928C2semidirect
14. C29×#1927C2semidirect
15. C29×#1803C2semidirect
205. #24690C29direct (N × H)
274. #2565C2×C29semidirect
280. #1992C2×C29semidirect
281. #1949C2×C29semidirect
282. #1947C2×C29semidirect
283. #1940C2×C29semidirect
284. #1928C2×C29semidirect
285. #1927C2×C29semidirect
286. #1803C2×C29semidirect
437. C29#24690direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4782
C2×C29×#4402
C29×#25652
C29×#23542
C29×#20732
C29×#20712
C29×#20552
C29×#19922
C29×#19492
C29×#19472
C29×#19402
C29×#19282
C29×#19272
C29×#18032
#2469029