Finite Group Databasebeta

← C29×#19379 #20314279

Subgroups — C29×#19379 #20314279

Order 7424.

572 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3252C211yesmaximal, characteristic
2C29×#3238C211yesmaximal, characteristic
3C29×#3165C211yesmaximal, characteristic, complemented
4C29×#2969C211yesmaximal, characteristic
5C29×#1696C211yesmaximal, characteristic, complemented
6C29×#1695C211yesmaximal, characteristic, complemented
7C29×#1692C211yesmaximal, characteristic, complemented
8C29×#1691C211yesmaximal, characteristic, complemented
9C29×#1676C211yesmaximal, characteristic, complemented
10C29×#1675C211yesmaximal, characteristic, complemented
11C29×#1672C211yesmaximal, characteristic, complemented
12C29×#1671C211yesmaximal, characteristic, complemented
13C29×#1569C211yesmaximal, characteristic, complemented
14C29×#1554C211yesmaximal, characteristic, complemented
15C29×#1548C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C2×C29×C4⋊Q8C2211yescharacteristic
18C29×#529C2211yescharacteristic
19C29×#501—21no—
20C29×#501—21no—
21C29×#501—21no—
22C29×#500C2211yescharacteristic
23C29×#500C2211yescharacteristic
24C29×#498C2211yescharacteristic
25C29×#498C2211yescharacteristic
26C29×#489—21no—
27C29×#483—21no—
28C29×#480—21no—
29C29×#479—21no—
30C29×#477C2211yescharacteristic
31C29×#477C2211yescharacteristic
32C29×#477C2211yescharacteristic
33C29×#476C2211yescharacteristic
34C29×#476C2211yescharacteristic
35C29×#476C2211yescharacteristic
36C29×#470—21no—
37C29×#468—21no—
38C29×#464—21no—
39C29×#462C2211yescharacteristic
40C29×#461C2211yescharacteristic
41C29×#446C2211yescharacteristic
42C8×Q8×C29C2211yescharacteristic
43C29×#436—21no—
44C29×#436C2211yescharacteristic
45C29×#435—21no—
46C8×D4×C29C2211yescharacteristic
47C29×#433—21no—
48C29×#432C2211yescharacteristic
49C29×#431C2211yescharacteristic
50C29×#428—21no—
51C29×#428—21no—
52C29×#423C2211yescharacteristic
53C29×#405—21no—
54C4×M16×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#333C2211yescharacteristic
62C29×#333C2211yescharacteristic
63C29×#333C2211yescharacteristic
64C29×#333C2211yescharacteristic
65C29×#332C2211yescharacteristic
66C29×#332C2211yescharacteristic
67C22×Q8×C29—21no—
68C2×Q16×C29—21no—
69C2×SD16×C29—21no—
70C2×M16×C29—21no—
71C2×M16×C29—21no—
72C2×M16×C29D411yescharacteristic
73C2×M16×C29D411yescharacteristic
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×C4⋊Q8C2311yescharacteristic
82C29×#126—21no—
83C29×#125—21no—
84C29×#125D411yescharacteristic
85C29×#124D411yescharacteristic
86C29×#123—21no—
87C29×C22⋊Q8—21no—
88C29×C22⋊Q8—21no—
89C29×C22⋊Q8D411yescharacteristic
90C29×#121D411yescharacteristic
91C4×Q8×C29—21no—
92C4×Q8×C29—21no—
93C4×Q8×C29C2311yescharacteristic
94C4×D4×C29—21no—
95C4×D4×C29C2311yescharacteristic
96C29×#117—21no—
97C29×#117—21no—
98C2×C4⋊C4×C29—21no—
99C2×C4⋊C4×C29—21no—
100C2×C42×C29C2311yescharacteristic
101C29×#107—21no—
102C29×#107—21no—
103C29×#107—21no—
104C29×#107—21no—
105C29×#107—21no—
106C29×#107—21no—
107C29×#107—21no—
108C29×#106—21no—
109C29×#106—21no—
110C29×#106—21no—
111C29×#106—21no—
112C29×#106—21no—
113C29×#106—21no—
114C29×#106—21no—
115C29×C4⋊C8—21no—
116C29×C4⋊C8—21no—
117C29×C4⋊C8—21no—
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×C4⋊C8C2311yescharacteristic
123C29×C4⋊C8C2311yescharacteristic
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#102—21no—
130C29×#102—21no—
131C29×#102—21no—
132C29×C22⋊C8—21no—
133C29×C22⋊C8—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8—21no—
136C29×#97—21no—
137C29×#97—21no—
138C29×#97D411yescharacteristic
139C29×#97D411yescharacteristic
140C4×C8×C29—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C2×Q8×C29—21no—
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×C29C2×D411yescharacteristic
153C22×C4×C29—21no—
154C22×C4×C29—41no—
155C22×C4×C29C2×D411yescharacteristic
156C22×C4×C29C2×D411yescharacteristic
157C22×C4×C29#4111yescharacteristic
158Q16×C29—81no—
159SD16×C29—81no—
160M16×C29—22no—
161M16×C29—22no—
162M16×C29—42no—
163M16×C29—81no—
164C2×C8×C29—21no—
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—42no—
171C2×C8×C29C2×D411yescharacteristic
172C2×C8×C29C2×D411yescharacteristic
173C2×C8×C29C2×D411yescharacteristic
174C2×C8×C29C2×D411yescharacteristic
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—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—41no—
188C4⋊C4×C29—41no—
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—
199C42×C29—21no—
200C42×C29—41no—
201C42×C29C2×D411yescharacteristic
202C42×C29C2×D411yescharacteristic
203C42×C29#4111yescharacteristic
204C42×C29C2411yescharacteristic
205#19379C2911yesmaximal, characteristic, direct product factor, Sylow
206C23×C29—21no—
207C23×C29#12111yescharacteristic
208Q8×C29—21no—
209Q8×C29—21no—
210Q8×C29—41no—
211Q8×C29—41no—
212Q8×C29—81no—
213Q8×C29—81no—
214Q8×C29—81no—
215Q8×C29—82no—
216D4×C29—21no—
217D4×C29—21no—
218D4×C29—81no—
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—41no—
227C2×C4×C29—41no—
228C2×C4×C29—41no—
229C2×C4×C29—41no—
230C2×C4×C29—41no—
231C2×C4×C29—41no—
232C2×C4×C29—41no—
233C2×C4×C29—82no—
234C2×C4×C29#12111yescharacteristic
235C2×C4×C29#12111yescharacteristic
236C2×C4×C29#12111yescharacteristic
237C2×C4×C29C22×D411yescharacteristic
238C2×C4×C29C22×D411yescharacteristic
239C2×C4×C29C2×#4111yescharacteristic
240C8×C29—21no—
241C8×C29—21no—
242C8×C29—41no—
243C8×C29—41no—
244C8×C29—41no—
245C8×C29—41no—
246C8×C29—41no—
247C8×C29—41no—
248C8×C29#13712yes—
249C8×C29#13712yes—
250#3252C2×C2911yescharacteristic
251#3238C2×C2911yescharacteristic
252#3165C2×C2911yescharacteristic, complemented
253#2969C2×C2911yescharacteristic
254#1696C2×C2911yescharacteristic, complemented
255#1695C2×C2911yescharacteristic, complemented
256#1692C2×C2911yescharacteristic, complemented
257#1691C2×C2911yescharacteristic, complemented
258#1676C2×C2911yescharacteristic, complemented
259#1675C2×C2911yescharacteristic, complemented
260#1672C2×C2911yescharacteristic, complemented
261#1671C2×C2911yescharacteristic, complemented
262#1569C2×C2911yescharacteristic, complemented
263#1554C2×C2911yescharacteristic, complemented
264#1548C2×C2911yescharacteristic, complemented
265C22×C29—21no—
266C22×C29—21no—
267C22×C29—21no—
268C22×C29—41no—
269C22×C29—41no—
270C22×C29—41no—
271C22×C29C2×#12111yescharacteristic
272C4×C29—21no—
273C4×C29—21no—
274C4×C29—21no—
275C4×C29—21no—
276C4×C29—41no—
277C4×C29—41no—
278C4×C29—41no—
279C4×C29—81no—
280C4×C29—81no—
281C4×C29—81no—
282C4×C29—81no—
283C4×C29C2×#13711yescharacteristic
284C4×C29C2×#13711yescharacteristic
285C4×C29#57711yescharacteristic
286C4×C29#57811yescharacteristic
287#533C22×C2911yescharacteristic
288C2×C4⋊Q8C22×C2911yescharacteristic
289#529C22×C2911yescharacteristic
290#501—21no—
291#501—21no—
292#501—21no—
293#500C22×C2911yescharacteristic
294#500C22×C2911yescharacteristic
295#498C22×C2911yescharacteristic
296#498C22×C2911yescharacteristic
297#489—21no—
298#483—21no—
299#480—21no—
300#479—21no—
301#477C22×C2911yescharacteristic
302#477C22×C2911yescharacteristic
303#477C22×C2911yescharacteristic
304#476C22×C2911yescharacteristic
305#476C22×C2911yescharacteristic
306#476C22×C2911yescharacteristic
307#470—21no—
308#468—21no—
309#464—21no—
310#462C22×C2911yescharacteristic
311#461C22×C2911yescharacteristic
312#446C22×C2911yescharacteristic
313C8×Q8C22×C2911yescharacteristic
314#436—21no—
315#436C22×C2911yescharacteristic
316#435—21no—
317C8×D4C22×C2911yescharacteristic
318#433—21no—
319#432C22×C2911yescharacteristic
320#431C22×C2911yescharacteristic
321#428—21no—
322#428—21no—
323#423C22×C2911yescharacteristic
324#405—21no—
325C4×M16C22×C2911yescharacteristic
326#335C22×C2911yescharacteristic
327#335C22×C2911yescharacteristic
328#334C22×C2911yescharacteristic
329#334C22×C2911yescharacteristic
330#333C22×C2911yescharacteristic
331#333C22×C2911yescharacteristic
332#333C22×C2911yescharacteristic
333#333C22×C2911yescharacteristic
334#333C22×C2911yescharacteristic
335#333C22×C2911yescharacteristic
336#332C22×C2911yescharacteristic
337#332C22×C2911yescharacteristic
338C2×C29—41no—
339C2×C29—81no—
340C2×C29#303911yescharacteristic
341C2×C29#306311yescharacteristic
342C2×C29#306811yescharacteristic
343C22×Q8—21no—
344C2×Q16—21no—
345C2×SD16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16D4×C2911yescharacteristic
349C2×M16D4×C2911yescharacteristic
350C22×C8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8C23×C2911yescharacteristic
355C4⋊Q8C23×C2911yescharacteristic
356C4⋊Q8C23×C2911yescharacteristic
357C4⋊Q8C23×C2911yescharacteristic
358#126—21no—
359#125—21no—
360#125D4×C2911yescharacteristic
361#124D4×C2911yescharacteristic
362#123—21no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8D4×C2911yescharacteristic
366#121D4×C2911yescharacteristic
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8C23×C2911yescharacteristic
370C4×D4—21no—
371C4×D4C23×C2911yescharacteristic
372#117—21no—
373#117—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C42C23×C2911yescharacteristic
377#107—21no—
378#107—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8C23×C2911yescharacteristic
395C4⋊C8C23×C2911yescharacteristic
396C4⋊C8C23×C2911yescharacteristic
397C4⋊C8C23×C2911yescharacteristic
398C4⋊C8C23×C2911yescharacteristic
399C4⋊C8C23×C2911yescharacteristic
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#102—21no—
406#102—21no—
407#102—21no—
408C22⋊C8—21no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412#97—21no—
413#97—21no—
414#97D4×C2911yescharacteristic
415#97D4×C2911yescharacteristic
416C4×C8—21no—
417C4×C8—21no—
418C4×C8C23×C2911yescharacteristic
419C4×C8C23×C2911yescharacteristic
420C29#1937911yescharacteristic, direct product factor, Sylow
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—41no—
426C2×Q8—82no—
427C2×Q8C2×D4×C2911yescharacteristic
428C2×D4—21no—
429C2×D4C2×D4×C2911yescharacteristic
430C22×C4—21no—
431C22×C4—41no—
432C22×C4C2×D4×C2911yescharacteristic
433C22×C4C2×D4×C2911yescharacteristic
434C22×C4#41×C2911yescharacteristic
435Q16—81no—
436SD16—81no—
437M16—22no—
438M16—22no—
439M16—42no—
440M16—81no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
448C2×C8C2×D4×C2911yescharacteristic
449C2×C8C2×D4×C2911yescharacteristic
450C2×C8C2×D4×C2911yescharacteristic
451C2×C8C2×D4×C2911yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4C2×D4×C2911yescharacteristic
469C4⋊C4C2×D4×C2911yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—41no—
476C42—21no—
477C42—41no—
478C42C2×D4×C2911yescharacteristic
479C42C2×D4×C2911yescharacteristic
480C42#41×C2911yescharacteristic
481C42C24×C2911yescharacteristic
482C23—21no—
483C23C29×#12111yescharacteristic
484Q8—21no—
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—81no—
489Q8—81no—
490Q8—81no—
491Q8—82no—
492D4—21no—
493D4—21no—
494D4—81no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—82no—
510C2×C4C29×#12111yescharacteristic
511C2×C4C29×#12111yescharacteristic
512C2×C4C29×#12111yescharacteristic
513C2×C4C22×D4×C2911yescharacteristic
514C2×C4C22×D4×C2911yescharacteristic
515C2×C4C2×#41×C2911yescharacteristic
516C8—21no—
517C8—21no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8C29×#13712yes—
525C8C29×#13712yes—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22C2×C29×#12111yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4—81no—
544C4C2×C29×#13711yescharacteristic
545C4C2×C29×#13711yescharacteristic
546C4C29×#57711yescharacteristic
547C4C29×#57811yescharacteristic
548C2—41no—
549C2—81no—
550C2C29×#303911yescharacteristic
551C2C29×#306311yescharacteristic
552C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#121D4
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
3. C29×#3165C2semidirect
5. C29×#1696C2semidirect
6. C29×#1695C2semidirect
7. C29×#1692C2semidirect
8. C29×#1691C2semidirect
9. C29×#1676C2semidirect
10. C29×#1675C2semidirect
11. C29×#1672C2semidirect
12. C29×#1671C2semidirect
13. C29×#1569C2semidirect
14. C29×#1554C2semidirect
15. C29×#1548C2semidirect
205. #19379C29direct (N × H)
252. #3165C2×C29semidirect
254. #1696C2×C29semidirect
255. #1695C2×C29semidirect
256. #1692C2×C29semidirect
257. #1691C2×C29semidirect
258. #1676C2×C29semidirect
259. #1675C2×C29semidirect
260. #1672C2×C29semidirect
261. #1671C2×C29semidirect
262. #1569C2×C29semidirect
263. #1554C2×C29semidirect
264. #1548C2×C29semidirect
420. C29#19379direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32522
C29×#32382
C29×#31652
C29×#29692
C29×#16962
C29×#16952
C29×#16922
C29×#16912
C29×#16762
C29×#16752
C29×#16722
C29×#16712
C29×#15692
C29×#15542
C29×#15482
#1937929