Finite Group Databasebeta

← C29×#29442 #20324342

Subgroups — C29×#29442 #20324342

Order 7424.

660 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2644C211yesmaximal, characteristic
2C29×#2320C211yesmaximal, characteristic, complemented
3C29×#2088C211yesmaximal, characteristic, complemented
4C29×#2066C211yesmaximal, characteristic, complemented
5C29×#2065C211yesmaximal, characteristic
6C29×#2055C211yesmaximal, characteristic
7C29×#1968C211yesmaximal, characteristic
8C29×#1941C211yesmaximal, characteristic, complemented
9C29×#1936C211yesmaximal, characteristic
10C29×#1935C211yesmaximal, characteristic, complemented
11C29×#1926C211yesmaximal, characteristic
12C29×#1920C211yesmaximal, characteristic, complemented
13C29×#1880C211yesmaximal, characteristic
14C29×#1865C211yesmaximal, characteristic, complemented
15C29×#1768C211yesmaximal, characteristic, complemented
16C22×SD16×C29C2211yescharacteristic
17C2×C4×Q8×C29C2211yescharacteristic
18C2×C29×#106C2211yescharacteristic
19C2×C29×#106C2211yescharacteristic
20C2×C29×#106C2211yescharacteristic
21C2×C29×C4⋊C8C2211yescharacteristic
22C2×C29×C4⋊C8C2211yescharacteristic
23C2×C29×#103C2211yescharacteristic
24C2×C29×#103C2211yescharacteristic
25C2×C29×#103C2211yescharacteristic
26C2×C29×#102C2211yescharacteristic
27C2×C29×#102C2211yescharacteristic
28C2×C29×#102C2211yescharacteristic
29C2×C29×#97C2211yescharacteristic
30C2×C4×C8×C29C2211yescharacteristic
31C29×#397—21no—
32C29×#397—21no—
33C29×#397—21no—
34C29×#396—21no—
35C29×#391C2211yescharacteristic
36C29×#391C2211yescharacteristic
37C29×#390C2211yescharacteristic
38C29×#390C2211yescharacteristic
39C29×#390C2211yescharacteristic
40C29×#389C2211yescharacteristic
41C29×#389C2211yescharacteristic
42C29×#389C2211yescharacteristic
43C29×#389C2211yescharacteristic
44C29×#389C2211yescharacteristic
45C29×#387—21no—
46C29×#387—21no—
47C29×#383—21no—
48C29×#382—21no—
49C4×C4⋊C4×C29C2211yescharacteristic
50C29×#376C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×Q8×C29C2311yescharacteristic
60C22×D4×C29C2311yescharacteristic
61C2×SD16×C29—22no—
62C2×SD16×C29—22no—
63C2×SD16×C29—41no—
64C22×C8×C29C2311yescharacteristic
65C22×C8×C29C2311yescharacteristic
66C22×C8×C29C2311yescharacteristic
67C22×C8×C29C2311yescharacteristic
68C4×Q8×C29—22no—
69C4×Q8×C29—22no—
70C2×C4⋊C4×C29—21no—
71C2×C4⋊C4×C29—21no—
72C2×C4⋊C4×C29—21no—
73C2×C4⋊C4×C29—21no—
74C2×C4⋊C4×C29—21no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29C2311yescharacteristic
77C2×C4⋊C4×C29C2311yescharacteristic
78C2×C4⋊C4×C29C2311yescharacteristic
79C2×C4⋊C4×C29C2311yescharacteristic
80C2×C4⋊C4×C29C2311yescharacteristic
81C2×C4⋊C4×C29C2311yescharacteristic
82C2×C22⋊C4×C29—21no—
83C2×C22⋊C4×C29—21no—
84C2×C22⋊C4×C29—21no—
85C2×C22⋊C4×C29—21no—
86C2×C22⋊C4×C29—21no—
87C2×C22⋊C4×C29—21no—
88C2×C42×C29—21no—
89C2×C42×C29—21no—
90C2×C42×C29C2311yescharacteristic
91C2×C42×C29C2311yescharacteristic
92C2×C42×C29C2311yescharacteristic
93C29×#106—22no—
94C29×#106—22no—
95C29×#106—41no—
96C29×C4⋊C8—22no—
97C29×C4⋊C8—22no—
98C29×#103—22no—
99C29×#103—22no—
100C29×#103—41no—
101C29×#102—22no—
102C29×#102—22no—
103C29×#102—41no—
104C29×#97—41no—
105C4×C8×C29—41no—
106C29×#95—21no—
107C29×#95—21no—
108C29×#95—21no—
109C29×#95—21no—
110C29×#95—21no—
111C29×#95—21no—
112C29×#95—21no—
113C29×#95—21no—
114C29×#95—21no—
115C29×#95—21no—
116C29×#95D411yescharacteristic
117C29×#95D411yescharacteristic
118C29×#95D411yescharacteristic
119C29×#95D411yescharacteristic
120C24×C29—21no—
121C2×Q8×C29—21no—
122C2×Q8×C29—21no—
123C2×Q8×C29—21no—
124C2×Q8×C29—21no—
125C2×Q8×C29—21no—
126C2×Q8×C29#4112yes—
127C2×D4×C29—21no—
128C2×D4×C29—21no—
129C2×D4×C29—21no—
130C2×D4×C29—21no—
131C2×D4×C29—21no—
132C2×D4×C29—21no—
133C22×C4×C29—21no—
134C22×C4×C29—21no—
135C22×C4×C29—21no—
136C22×C4×C29—21no—
137C22×C4×C29—21no—
138C22×C4×C29—21no—
139C22×C4×C29—21no—
140C22×C4×C29C2×D411yescharacteristic
141C22×C4×C29C2×D411yescharacteristic
142C22×C4×C29C2×D411yescharacteristic
143C22×C4×C29C2×D411yescharacteristic
144C22×C4×C29C2×D411yescharacteristic
145C22×C4×C29C2×D411yescharacteristic
146C22×C4×C29C2411yescharacteristic
147SD16×C29—44no—
148C2×C8×C29—21no—
149C2×C8×C29—21no—
150C2×C8×C29—21no—
151C2×C8×C29—21no—
152C2×C8×C29—21no—
153C2×C8×C29—21no—
154C2×C8×C29—21no—
155C2×C8×C29—21no—
156C2×C8×C29—21no—
157C2×C8×C29—21no—
158C2×C8×C29#4112yes—
159C2×C8×C29#4112yes—
160C4⋊C4×C29—24no—
161C4⋊C4×C29—21no—
162C4⋊C4×C29—21no—
163C4⋊C4×C29—21no—
164C4⋊C4×C29—21no—
165C4⋊C4×C29—21no—
166C4⋊C4×C29—21no—
167C4⋊C4×C29—21no—
168C4⋊C4×C29—21no—
169C4⋊C4×C29—21no—
170C4⋊C4×C29—21no—
171C4⋊C4×C29—21no—
172C4⋊C4×C29—81no—
173C4⋊C4×C29—81no—
174C4⋊C4×C29—81no—
175C4⋊C4×C29—81no—
176C4⋊C4×C29—81no—
177C4⋊C4×C29#4112yes—
178C22⋊C4×C29—81no—
179C22⋊C4×C29—81no—
180C22⋊C4×C29—81no—
181C22⋊C4×C29—81no—
182C22⋊C4×C29—81no—
183C22⋊C4×C29—81no—
184C42×C29—24no—
185C42×C29—21no—
186C42×C29—21no—
187C42×C29—21no—
188C42×C29—21no—
189C42×C29—21no—
190C42×C29—21no—
191C42×C29—81no—
192#29442C2911yesmaximal, characteristic, direct product factor, Sylow
193C23×C29—41no—
194C23×C29—41no—
195C23×C29—41no—
196C23×C29—41no—
197C23×C29—41no—
198C23×C29—41no—
199C23×C29—41no—
200C23×C29C22×D411yescharacteristic
201Q8×C29—22no—
202Q8×C29—22no—
203Q8×C29—41no—
204Q8×C29—41no—
205D4×C29—41no—
206D4×C29—41no—
207D4×C29—41no—
208D4×C29—41no—
209C2×C4×C29—21no—
210C2×C4×C29—21no—
211C2×C4×C29—22no—
212C2×C4×C29—22no—
213C2×C4×C29—21no—
214C2×C4×C29—21no—
215C2×C4×C29—21no—
216C2×C4×C29—21no—
217C2×C4×C29—21no—
218C2×C4×C29—21no—
219C2×C4×C29—21no—
220C2×C4×C29—21no—
221C2×C4×C29—21no—
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—21no—
229C2×C4×C29—41no—
230C2×C4×C29—41no—
231C2×C4×C29—41no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
236C2×C4×C29—41no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—41no—
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×C29C2×#4111yescharacteristic
249C2×C4×C29C2×#4111yescharacteristic
250C2×C4×C29C2×#4111yescharacteristic
251C2×C4×C29C2×#4111yescharacteristic
252C2×C4×C29H(5,𝔽2)11yescharacteristic
253C2×C4×C292−1+411yescharacteristic
254C8×C29—22no—
255C8×C29—22no—
256C8×C29—41no—
257C8×C29—41no—
258#2644C2×C2911yescharacteristic
259#2320C2×C2911yescharacteristic, complemented
260#2088C2×C2911yescharacteristic, complemented
261#2066C2×C2911yescharacteristic, complemented
262#2065C2×C2911yescharacteristic
263#2055C2×C2911yescharacteristic
264#1968C2×C2911yescharacteristic
265#1941C2×C2911yescharacteristic, complemented
266#1936C2×C2911yescharacteristic
267#1935C2×C2911yescharacteristic, complemented
268#1926C2×C2911yescharacteristic
269#1920C2×C2911yescharacteristic, complemented
270#1880C2×C2911yescharacteristic
271#1865C2×C2911yescharacteristic, complemented
272#1768C2×C2911yescharacteristic, complemented
273C22×C29—81no—
274C22×C29—81no—
275C22×C29—81no—
276C22×C29—81no—
277C22×C29—81no—
278C22×C29—81no—
279C22×C29—81no—
280C22×C29#52511yescharacteristic
281C22×C29#53211yescharacteristic
282C22×C29#53711yescharacteristic
283C22×C29#57711yescharacteristic
284C22×C29#57711yescharacteristic
285C22×C29#57711yescharacteristic
286C22×C29#57711yescharacteristic
287C4×C29—42no—
288C4×C29—41no—
289C4×C29—42no—
290C4×C29—41no—
291C4×C29—41no—
292C4×C29—41no—
293C4×C29—41no—
294C4×C29—41no—
295C4×C29—81no—
296C4×C29—81no—
297C4×C29—81no—
298C4×C29—81no—
299C4×C29—81no—
300C4×C29#55111yescharacteristic
301C4×C29#55211yescharacteristic
302C4×C29#55311yescharacteristic
303C4×C29#55611yescharacteristic
304C22×SD16C22×C2911yescharacteristic
305C2×C4×Q8C22×C2911yescharacteristic
306C2×#106C22×C2911yescharacteristic
307C2×#106C22×C2911yescharacteristic
308C2×#106C22×C2911yescharacteristic
309C2×C4⋊C8C22×C2911yescharacteristic
310C2×C4⋊C8C22×C2911yescharacteristic
311C2×#103C22×C2911yescharacteristic
312C2×#103C22×C2911yescharacteristic
313C2×#103C22×C2911yescharacteristic
314C2×#102C22×C2911yescharacteristic
315C2×#102C22×C2911yescharacteristic
316C2×#102C22×C2911yescharacteristic
317C2×#97C22×C2911yescharacteristic
318C2×C4×C8C22×C2911yescharacteristic
319#397—21no—
320#397—21no—
321#397—21no—
322#396—21no—
323#391C22×C2911yescharacteristic
324#391C22×C2911yescharacteristic
325#390C22×C2911yescharacteristic
326#390C22×C2911yescharacteristic
327#390C22×C2911yescharacteristic
328#389C22×C2911yescharacteristic
329#389C22×C2911yescharacteristic
330#389C22×C2911yescharacteristic
331#389C22×C2911yescharacteristic
332#389C22×C2911yescharacteristic
333#387—21no—
334#387—21no—
335#383—21no—
336#382—21no—
337C4×C4⋊C4C22×C2911yescharacteristic
338#376C22×C2911yescharacteristic
339#340C22×C2911yescharacteristic
340#340C22×C2911yescharacteristic
341#340C22×C2911yescharacteristic
342#340C22×C2911yescharacteristic
343#340C22×C2911yescharacteristic
344#340C22×C2911yescharacteristic
345#336C22×C2911yescharacteristic
346#336C22×C2911yescharacteristic
347C2×C29—161no—
348C2×C29#260111yescharacteristic
349C2×C29#312511yescharacteristic
350C2×C29#312611yescharacteristic
351C2×C29#317311yescharacteristic
352C2×C29#317411yescharacteristic
353C2×C29#326011yescharacteristic
354C2×C29#326311yescharacteristic
355C22×Q8C23×C2911yescharacteristic
356C22×D4C23×C2911yescharacteristic
357C2×SD16—22no—
358C2×SD16—22no—
359C2×SD16—41no—
360C22×C8C23×C2911yescharacteristic
361C22×C8C23×C2911yescharacteristic
362C22×C8C23×C2911yescharacteristic
363C22×C8C23×C2911yescharacteristic
364C4×Q8—22no—
365C4×Q8—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4C23×C2911yescharacteristic
373C2×C4⋊C4C23×C2911yescharacteristic
374C2×C4⋊C4C23×C2911yescharacteristic
375C2×C4⋊C4C23×C2911yescharacteristic
376C2×C4⋊C4C23×C2911yescharacteristic
377C2×C4⋊C4C23×C2911yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42C23×C2911yescharacteristic
387C2×C42C23×C2911yescharacteristic
388C2×C42C23×C2911yescharacteristic
389#106—22no—
390#106—22no—
391#106—41no—
392C4⋊C8—22no—
393C4⋊C8—22no—
394#103—22no—
395#103—22no—
396#103—41no—
397#102—22no—
398#102—22no—
399#102—41no—
400#97—41no—
401C4×C8—41no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95D4×C2911yescharacteristic
413#95D4×C2911yescharacteristic
414#95D4×C2911yescharacteristic
415#95D4×C2911yescharacteristic
416C29#2944211yescharacteristic, direct product factor, Sylow
417C24—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8#41×C2912yes—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4C2×D4×C2911yescharacteristic
438C22×C4C2×D4×C2911yescharacteristic
439C22×C4C2×D4×C2911yescharacteristic
440C22×C4C2×D4×C2911yescharacteristic
441C22×C4C2×D4×C2911yescharacteristic
442C22×C4C2×D4×C2911yescharacteristic
443C22×C4C24×C2911yescharacteristic
444SD16—44no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8#41×C2912yes—
456C2×C8#41×C2912yes—
457C4⋊C4—24no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4—81no—
474C4⋊C4#41×C2912yes—
475C22⋊C4—81no—
476C22⋊C4—81no—
477C22⋊C4—81no—
478C22⋊C4—81no—
479C22⋊C4—81no—
480C22⋊C4—81no—
481C42—24no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—81no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23C22×D4×C2911yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—41no—
500Q8—41no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—41no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4C2×#41×C2911yescharacteristic
545C2×C4C2×#41×C2911yescharacteristic
546C2×C4C2×#41×C2911yescharacteristic
547C2×C4C2×#41×C2911yescharacteristic
548C2×C4C29×H(5,𝔽2)11yescharacteristic
549C2×C4C29×2−1+411yescharacteristic
550C8—22no—
551C8—22no—
552C8—41no—
553C8—41no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22C29×#52511yescharacteristic
562C22C29×#53211yescharacteristic
563C22C29×#53711yescharacteristic
564C22C29×#57711yescharacteristic
565C22C29×#57711yescharacteristic
566C22C29×#57711yescharacteristic
567C22C29×#57711yescharacteristic
568C4—41no—
569C4—41no—
570C4—42no—
571C4—41no—
572C4—42no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4C29×#55111yescharacteristic
582C4C29×#55211yescharacteristic
583C4C29×#55311yescharacteristic
584C4C29×#55611yescharacteristic
585C2—161no—
586C2C29×#260111yescharacteristic
587C2C29×#312511yescharacteristic
588C2C29×#312611yescharacteristic
589C2C29×#317311yescharacteristic
590C2C29×#317411yescharacteristic
591C2C29×#326011yescharacteristic
592C2C29×#326311yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D4×C29C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C29×#376 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2320C2semidirect
3. C29×#2088C2semidirect
4. C29×#2066C2semidirect
8. C29×#1941C2semidirect
10. C29×#1935C2semidirect
12. C29×#1920C2semidirect
14. C29×#1865C2semidirect
15. C29×#1768C2semidirect
192. #29442C29direct (N × H)
259. #2320C2×C29semidirect
260. #2088C2×C29semidirect
261. #2066C2×C29semidirect
265. #1941C2×C29semidirect
267. #1935C2×C29semidirect
269. #1920C2×C29semidirect
271. #1865C2×C29semidirect
272. #1768C2×C29semidirect
416. C29#29442direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#26442
C29×#23202
C29×#20882
C29×#20662
C29×#20652
C29×#20552
C29×#19682
C29×#19412
C29×#19362
C29×#19352
C29×#19262
C29×#19202
C29×#18802
C29×#18652
C29×#17682
#2944229