Finite Group Databasebeta

← C29×#19591 #20314491

Subgroups — C29×#19591 #20314491

Order 7424.

590 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3247C211yesmaximal, characteristic
2C29×#3238C211yesmaximal, characteristic, complemented
3C29×#3226C211yesmaximal, characteristic, complemented
4C29×#2994C211yesmaximal, characteristic, complemented
5C29×#1698C211yesmaximal, characteristic, complemented
6C29×#1697C211yesmaximal, characteristic, complemented
7C29×#1696C211yesmaximal, characteristic, complemented
8C29×#1695C211yesmaximal, characteristic, complemented
9C29×#1678C211yesmaximal, characteristic, complemented
10C29×#1677C211yesmaximal, characteristic, complemented
11C29×#1676C211yesmaximal, characteristic, complemented
12C29×#1675C211yesmaximal, characteristic, complemented
13C29×#1573C211yesmaximal, characteristic, complemented
14C29×#1551C211yesmaximal, characteristic, complemented
15C2×C29×#333C211yesmaximal, characteristic, complemented
16C29×#532C2211yescharacteristic
17C2×C29×C4⋊Q8C2211yescharacteristic
18C29×#529C2211yescharacteristic
19C29×#501—21no—
20C29×#500C2211yescharacteristic
21C29×#500C2211yescharacteristic
22C29×#489—21no—
23C29×#486C2211yescharacteristic
24C29×#486C2211yescharacteristic
25C29×#483—21no—
26C29×#480—21no—
27C29×#480—21no—
28C29×#480—21no—
29C29×#478—21no—
30C29×#477C2211yescharacteristic
31C29×#477C2211yescharacteristic
32C29×#477C2211yescharacteristic
33C29×#476C2211yescharacteristic
34C29×#476C2211yescharacteristic
35C29×#476C2211yescharacteristic
36C29×#474—21no—
37C29×#474—21no—
38C29×#466—21no—
39C29×#465—21no—
40C29×#463—21no—
41C29×#460C2211yescharacteristic
42C29×#459C2211yescharacteristic
43C29×#446C2211yescharacteristic
44C8×Q8×C29C2211yescharacteristic
45C29×#436C2211yescharacteristic
46C29×#435—21no—
47C8×D4×C29—21no—
48C8×D4×C29C2211yescharacteristic
49C29×#433—21no—
50C29×#432C2211yescharacteristic
51C29×#431C2211yescharacteristic
52C29×#424—21no—
53C2×C29×C4⋊C8C2211yescharacteristic
54C2×C29×C4⋊C8C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#333C2211yescharacteristic
62C29×#333C2211yescharacteristic
63C29×#333C2211yescharacteristic
64C29×#333C2211yescharacteristic
65C29×#331C2211yescharacteristic
66C29×#331C2211yescharacteristic
67C2×#41×C29—21no—
68C22×Q8×C29—21no—
69C2×SD16×C29—21no—
70C2×D8×C29—21no—
71C2×M16×C29—21no—
72C22×C8×C29—21no—
73C22×C8×C29—21no—
74C22×C8×C29—21no—
75C29×C4⋊Q8—21no—
76C29×C4⋊Q8—21no—
77C29×C4⋊Q8—21no—
78C29×C4⋊Q8C2311yescharacteristic
79C29×C4⋊Q8C2311yescharacteristic
80C29×C4⋊Q8C2311yescharacteristic
81C29×#127C2311yescharacteristic
82C29×#126—21no—
83C29×#125D411yescharacteristic
84C29×#124—21no—
85C29×#124D411yescharacteristic
86C29×#123—21no—
87C29×C22⋊Q8D411yescharacteristic
88C29×#121—21no—
89C29×#121—21no—
90C29×#121D411yescharacteristic
91C4×Q8×C29C2311yescharacteristic
92C4×D4×C29—21no—
93C4×D4×C29—21no—
94C4×D4×C29—21no—
95C4×D4×C29C2311yescharacteristic
96C29×#117—21no—
97C2×C4⋊C4×C29—21no—
98C2×C4⋊C4×C29—21no—
99C2×C42×C29C2311yescharacteristic
100C29×#107—21no—
101C29×#107—21no—
102C29×#107—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#106—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×C4⋊C8—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8—21no—
113C29×C4⋊C8—21no—
114C29×C4⋊C8D411yescharacteristic
115C29×C4⋊C8D411yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#102—21no—
126C29×#102—21no—
127C29×#102—21no—
128C29×#102—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×#102—21no—
133C29×#102—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8—21no—
136C29×C22⋊C8—21no—
137C29×C22⋊C8D411yescharacteristic
138C29×C22⋊C8D411yescharacteristic
139C29×#97—21no—
140C29×#97—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144#41×C29—82no—
145C2×Q8×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—41no—
149C2×Q8×C29—82no—
150C2×Q8×C29C2×D411yescharacteristic
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—41no—
156C2×D4×C29C2×D411yescharacteristic
157C22×C4×C29—21no—
158C22×C4×C29—41no—
159C22×C4×C29—41no—
160C22×C4×C29C2×D411yescharacteristic
161C22×C4×C29C2×D411yescharacteristic
162C22×C4×C29#4111yescharacteristic
163SD16×C29—81no—
164D8×C29—81no—
165M16×C29—81no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—81no—
173C2×C8×C29—81no—
174C2×C8×C29—81no—
175C2×C8×C29C2×D411yescharacteristic
176C2×C8×C29C2×D411yescharacteristic
177C2×C8×C29C2×D411yescharacteristic
178C2×C8×C29C2×D411yescharacteristic
179C4⋊C4×C29—21no—
180C4⋊C4×C29—21no—
181C4⋊C4×C29—21no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—41no—
190C4⋊C4×C29—41no—
191C4⋊C4×C29C2×D411yescharacteristic
192C4⋊C4×C29C2×D411yescharacteristic
193C22⋊C4×C29—21no—
194C22⋊C4×C29—21no—
195C22⋊C4×C29—21no—
196C22⋊C4×C29—21no—
197C22⋊C4×C29—21no—
198C22⋊C4×C29—41no—
199C22⋊C4×C29—41no—
200C42×C29—21no—
201C42×C29C2×D411yescharacteristic
202C42×C29C2×D411yescharacteristic
203C42×C29#4111yescharacteristic
204C42×C29C2411yescharacteristic
205#19591C2911yesmaximal, characteristic, direct product factor, Sylow
206C23×C29—21no—
207C23×C29—41no—
208C23×C29#12111yescharacteristic
209Q8×C29—21no—
210Q8×C29—21no—
211Q8×C29—81no—
212Q8×C29—81no—
213Q8×C29—81no—
214Q8×C29—82no—
215D4×C29—21no—
216D4×C29—21no—
217D4×C29—42no—
218D4×C29—41no—
219D4×C29—41no—
220D4×C29—41no—
221D4×C29—41no—
222D4×C29—81no—
223D4×C29—82no—
224C2×C4×C29—22no—
225C2×C4×C29—21no—
226C2×C4×C29—21no—
227C2×C4×C29—21no—
228C2×C4×C29—21no—
229C2×C4×C29—21no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
236C2×C4×C29—41no—
237C2×C4×C29—82no—
238C2×C4×C29—82no—
239C2×C4×C29#12111yescharacteristic
240C2×C4×C29#12111yescharacteristic
241C2×C4×C29#12111yescharacteristic
242C2×C4×C29C22×D411yescharacteristic
243C2×C4×C29C22×D411yescharacteristic
244C2×C4×C29C2×#4111yescharacteristic
245C8×C29—21no—
246C8×C29—21no—
247C8×C29—21no—
248C8×C29—21no—
249C8×C29—41no—
250C8×C29—41no—
251C8×C29—41no—
252C8×C29—41no—
253C8×C29—41no—
254C8×C29—41no—
255#3247C2×C2911yescharacteristic
256#3238C2×C2911yescharacteristic, complemented
257#3226C2×C2911yescharacteristic, complemented
258#2994C2×C2911yescharacteristic, complemented
259#1698C2×C2911yescharacteristic, complemented
260#1697C2×C2911yescharacteristic, complemented
261#1696C2×C2911yescharacteristic, complemented
262#1695C2×C2911yescharacteristic, complemented
263#1678C2×C2911yescharacteristic, complemented
264#1677C2×C2911yescharacteristic, complemented
265#1676C2×C2911yescharacteristic, complemented
266#1675C2×C2911yescharacteristic, complemented
267#1573C2×C2911yescharacteristic, complemented
268#1551C2×C2911yescharacteristic, complemented
269C2×#333C2×C2911yescharacteristic, complemented
270C22×C29—21no—
271C22×C29—21no—
272C22×C29—41no—
273C22×C29—41no—
274C22×C29—41no—
275C22×C29—81no—
276C22×C29—81no—
277C22×C29—81no—
278C22×C29#47212yes—
279C22×C29C2×#12111yescharacteristic
280C4×C29—21no—
281C4×C29—21no—
282C4×C29—21no—
283C4×C29—21no—
284C4×C29—41no—
285C4×C29—41no—
286C4×C29—41no—
287C4×C29—81no—
288C4×C29—81no—
289C4×C29—81no—
290C4×C29#57711yescharacteristic
291C4×C29#57711yescharacteristic
292C4×C29#57811yescharacteristic
293C4×C29#57811yescharacteristic
294#532C22×C2911yescharacteristic
295C2×C4⋊Q8C22×C2911yescharacteristic
296#529C22×C2911yescharacteristic
297#501—21no—
298#500C22×C2911yescharacteristic
299#500C22×C2911yescharacteristic
300#489—21no—
301#486C22×C2911yescharacteristic
302#486C22×C2911yescharacteristic
303#483—21no—
304#480—21no—
305#480—21no—
306#480—21no—
307#478—21no—
308#477C22×C2911yescharacteristic
309#477C22×C2911yescharacteristic
310#477C22×C2911yescharacteristic
311#476C22×C2911yescharacteristic
312#476C22×C2911yescharacteristic
313#476C22×C2911yescharacteristic
314#474—21no—
315#474—21no—
316#466—21no—
317#465—21no—
318#463—21no—
319#460C22×C2911yescharacteristic
320#459C22×C2911yescharacteristic
321#446C22×C2911yescharacteristic
322C8×Q8C22×C2911yescharacteristic
323#436C22×C2911yescharacteristic
324#435—21no—
325C8×D4—21no—
326C8×D4C22×C2911yescharacteristic
327#433—21no—
328#432C22×C2911yescharacteristic
329#431C22×C2911yescharacteristic
330#424—21no—
331C2×C4⋊C8C22×C2911yescharacteristic
332C2×C4⋊C8C22×C2911yescharacteristic
333#335C22×C2911yescharacteristic
334#335C22×C2911yescharacteristic
335#334C22×C2911yescharacteristic
336#334C22×C2911yescharacteristic
337#333C22×C2911yescharacteristic
338#333C22×C2911yescharacteristic
339#333C22×C2911yescharacteristic
340#333C22×C2911yescharacteristic
341#333C22×C2911yescharacteristic
342#333C22×C2911yescharacteristic
343#331C22×C2911yescharacteristic
344#331C22×C2911yescharacteristic
345C2×C29—22no—
346C2×C29—81no—
347C2×C29—161no—
348C2×C29#304611yescharacteristic
349C2×C29#306311yescharacteristic
350C2×C29C2×#47211yescharacteristic
351C2×#41—21no—
352C22×Q8—21no—
353C2×SD16—21no—
354C2×D8—21no—
355C2×M16—21no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—21no—
359C4⋊Q8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8C23×C2911yescharacteristic
363C4⋊Q8C23×C2911yescharacteristic
364C4⋊Q8C23×C2911yescharacteristic
365#127C23×C2911yescharacteristic
366#126—21no—
367#125D4×C2911yescharacteristic
368#124—21no—
369#124D4×C2911yescharacteristic
370#123—21no—
371C22⋊Q8D4×C2911yescharacteristic
372#121—21no—
373#121—21no—
374#121D4×C2911yescharacteristic
375C4×Q8C23×C2911yescharacteristic
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4C23×C2911yescharacteristic
380#117—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C42C23×C2911yescharacteristic
384#107—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#107—21no—
390#107—21no—
391#106—21no—
392#106—21no—
393#106—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8D4×C2911yescharacteristic
399C4⋊C8D4×C2911yescharacteristic
400C4⋊C8C23×C2911yescharacteristic
401C4⋊C8C23×C2911yescharacteristic
402C4⋊C8C23×C2911yescharacteristic
403C4⋊C8C23×C2911yescharacteristic
404C4⋊C8C23×C2911yescharacteristic
405C4⋊C8C23×C2911yescharacteristic
406#103—21no—
407#103—21no—
408#103—21no—
409#102—21no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8D4×C2911yescharacteristic
422C22⋊C8D4×C2911yescharacteristic
423#97—21no—
424#97—21no—
425C4×C8—21no—
426C4×C8C23×C2911yescharacteristic
427C4×C8C23×C2911yescharacteristic
428C29#1959111yescharacteristic, direct product factor, Sylow
429#41—82no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—41no—
434C2×Q8—82no—
435C2×Q8C2×D4×C2911yescharacteristic
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—41no—
441C2×D4C2×D4×C2911yescharacteristic
442C22×C4—21no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4C2×D4×C2911yescharacteristic
446C22×C4C2×D4×C2911yescharacteristic
447C22×C4#41×C2911yescharacteristic
448SD16—81no—
449D8—81no—
450M16—81no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—81no—
458C2×C8—81no—
459C2×C8—81no—
460C2×C8C2×D4×C2911yescharacteristic
461C2×C8C2×D4×C2911yescharacteristic
462C2×C8C2×D4×C2911yescharacteristic
463C2×C8C2×D4×C2911yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4C2×D4×C2911yescharacteristic
477C4⋊C4C2×D4×C2911yescharacteristic
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C42—21no—
486C42C2×D4×C2911yescharacteristic
487C42C2×D4×C2911yescharacteristic
488C42#41×C2911yescharacteristic
489C42C24×C2911yescharacteristic
490C23—21no—
491C23—41no—
492C23C29×#12111yescharacteristic
493Q8—21no—
494Q8—21no—
495Q8—81no—
496Q8—81no—
497Q8—81no—
498Q8—82no—
499D4—21no—
500D4—21no—
501D4—42no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—81no—
507D4—82no—
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—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4C29×#12111yescharacteristic
524C2×C4C29×#12111yescharacteristic
525C2×C4C29×#12111yescharacteristic
526C2×C4C22×D4×C2911yescharacteristic
527C2×C4C22×D4×C2911yescharacteristic
528C2×C4C2×#41×C2911yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C22—21no—
540C22—21no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22C29×#47212yes—
548C22C2×C29×#12111yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4—81no—
559C4C29×#57711yescharacteristic
560C4C29×#57711yescharacteristic
561C4C29×#57811yescharacteristic
562C4C29×#57811yescharacteristic
563C2—22no—
564C2—81no—
565C2—161no—
566C2C29×#304611yescharacteristic
567C2C29×#306311yescharacteristic
568C2C2×C29×#47211yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3247C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3238C2semidirect
3. C29×#3226C2semidirect
4. C29×#2994C2semidirect
5. C29×#1698C2semidirect
6. C29×#1697C2semidirect
7. C29×#1696C2semidirect
8. C29×#1695C2semidirect
9. C29×#1678C2semidirect
10. C29×#1677C2semidirect
11. C29×#1676C2semidirect
12. C29×#1675C2semidirect
13. C29×#1573C2semidirect
14. C29×#1551C2semidirect
15. C2×C29×#333C2semidirect
205. #19591C29direct (N × H)
256. #3238C2×C29semidirect
257. #3226C2×C29semidirect
258. #2994C2×C29semidirect
259. #1698C2×C29semidirect
260. #1697C2×C29semidirect
261. #1696C2×C29semidirect
262. #1695C2×C29semidirect
263. #1678C2×C29semidirect
264. #1677C2×C29semidirect
265. #1676C2×C29semidirect
266. #1675C2×C29semidirect
267. #1573C2×C29semidirect
268. #1551C2×C29semidirect
269. C2×#333C2×C29semidirect
428. C29#19591direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32472
C29×#32382
C29×#32262
C29×#29942
C29×#16982
C29×#16972
C29×#16962
C29×#16952
C29×#16782
C29×#16772
C29×#16762
C29×#16752
C29×#15732
C29×#15512
C2×C29×#3332
#1959129