Finite Group Databasebeta

← C29×#19478 #20314378

Subgroups — C29×#19478 #20314378

Order 7424.

558 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3231C211yesmaximal, characteristic
2C29×#3104C211yesmaximal, characteristic
3C29×#3078C211yesmaximal, characteristic
4C29×#2984C211yesmaximal, characteristic
5C29×#1704C211yesmaximal, characteristic, complemented
6C29×#1700C211yesmaximal, characteristic, complemented
7C29×#1696C211yesmaximal, characteristic, complemented
8C29×#1692C211yesmaximal, characteristic, complemented
9C29×#1684C211yesmaximal, characteristic, complemented
10C29×#1680C211yesmaximal, characteristic, complemented
11C29×#1676C211yesmaximal, characteristic, complemented
12C29×#1672C211yesmaximal, characteristic, complemented
13C29×#1574C211yesmaximal, characteristic
14C29×#1559C211yesmaximal, characteristic
15C29×#1554C211yesmaximal, characteristic
16C29×#533C2211yescharacteristic
17C29×#533C2211yescharacteristic
18C2×C4×Q8×C29C2211yescharacteristic
19C29×#500C2211yescharacteristic
20C29×#498C2211yescharacteristic
21C29×#487C2211yescharacteristic
22C29×#487C2211yescharacteristic
23C29×#485—21no—
24C29×#485—21no—
25C29×#484—21no—
26C29×#479—21no—
27C29×#479—21no—
28C29×#479—21no—
29C29×#479—21no—
30C29×#477C2211yescharacteristic
31C29×#477C2211yescharacteristic
32C29×#477C2211yescharacteristic
33C29×#477C2211yescharacteristic
34C29×#475C2211yescharacteristic
35C29×#475C2211yescharacteristic
36C29×#462C2211yescharacteristic
37C29×#462C2211yescharacteristic
38C29×#451—21no—
39C29×#446—21no—
40C29×#446—21no—
41C29×#446C2211yescharacteristic
42C29×#446C2211yescharacteristic
43C8×Q8×C29C2211yescharacteristic
44C8×Q8×C29C2211yescharacteristic
45C4×Q16×C29—21no—
46C4×Q16×C29—21no—
47C29×#432—21no—
48C29×#432C2211yescharacteristic
49C29×#431—21no—
50C29×#431C2211yescharacteristic
51C29×#431C2211yescharacteristic
52C29×#428—21no—
53C29×#423C2211yescharacteristic
54C29×#419—21no—
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#333C2211yescharacteristic
62C29×#333C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#332C2211yescharacteristic
66C29×#332C2211yescharacteristic
67C22×Q8×C29D411yescharacteristic
68C2×Q16×C29—21no—
69C2×Q16×C29—21no—
70C2×M16×C29—21no—
71C29×C4⋊Q8C2311yescharacteristic
72C29×C4⋊Q8C2311yescharacteristic
73C29×C4⋊Q8C2311yescharacteristic
74C29×C4⋊Q8C2311yescharacteristic
75C29×#125—21no—
76C29×#125—21no—
77C29×C22⋊Q8—21no—
78C29×C22⋊Q8—21no—
79C29×C22⋊Q8—21no—
80C29×C22⋊Q8—21no—
81C4×Q8×C29—21no—
82C4×Q8×C29—21no—
83C4×Q8×C29—21no—
84C4×Q8×C29—21no—
85C4×Q8×C29—21no—
86C4×Q8×C29—21no—
87C4×Q8×C29D411yescharacteristic
88C4×Q8×C29D411yescharacteristic
89C4×Q8×C29C2311yescharacteristic
90C4×Q8×C29C2311yescharacteristic
91C29×#117—21no—
92C29×#117—21no—
93C2×C4⋊C4×C29—21no—
94C2×C4⋊C4×C29D411yescharacteristic
95C2×C42×C29—21no—
96C2×C42×C29C2311yescharacteristic
97C29×#107—21no—
98C29×#107—21no—
99C29×#107—21no—
100C29×#107—21no—
101C29×#107—21no—
102C29×#107—21no—
103C29×#106—21no—
104C29×#106—21no—
105C29×#106—21no—
106C29×#106—21no—
107C29×C4⋊C8—21no—
108C29×C4⋊C8—21no—
109C29×C4⋊C8—21no—
110C29×C4⋊C8—21no—
111C29×C4⋊C8—21no—
112C29×C4⋊C8D411yescharacteristic
113C29×C4⋊C8D411yescharacteristic
114C29×C4⋊C8C2311yescharacteristic
115C29×C4⋊C8C2311yescharacteristic
116C29×C4⋊C8C2311yescharacteristic
117C29×C4⋊C8C2311yescharacteristic
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×#103—21no—
121C29×#103—21no—
122C29×#103—21no—
123C29×#103—21no—
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#103—21no—
130C29×#103—21no—
131C29×#103—21no—
132C29×C22⋊C8—21no—
133C29×C22⋊C8—21no—
134C29×C22⋊C8D411yescharacteristic
135C29×C22⋊C8D411yescharacteristic
136C29×#97—21no—
137C29×#97—21no—
138C29×#97—21no—
139C4×C8×C29—21no—
140C4×C8×C29—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C2×Q8×C29—21no—
145C2×Q8×C29—22no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29—41no—
151C2×Q8×C29C2×D411yescharacteristic
152C2×Q8×C29C2×D411yescharacteristic
153C22×C4×C29—21no—
154C22×C4×C29—21no—
155C22×C4×C29C2×D411yescharacteristic
156C22×C4×C29C2×D411yescharacteristic
157C22×C4×C29#4111yescharacteristic
158Q16×C29—42no—
159Q16×C29—42no—
160M16×C29—42no—
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×C29C2×D411yescharacteristic
168C2×C8×C29C2×D411yescharacteristic
169C2×C8×C29C2×D411yescharacteristic
170C2×C8×C29C2×D411yescharacteristic
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—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—41no—
185C4⋊C4×C29—41no—
186C4⋊C4×C29—41no—
187C4⋊C4×C29—41no—
188C4⋊C4×C29C2×D411yescharacteristic
189C4⋊C4×C29C2×D411yescharacteristic
190C22⋊C4×C29—41no—
191C22⋊C4×C29—41no—
192C42×C29—21no—
193C42×C29—21no—
194C42×C29—21no—
195C42×C29—21no—
196C42×C29—41no—
197C42×C29—41no—
198C42×C29C2×D411yescharacteristic
199C42×C29C2×D411yescharacteristic
200C42×C29#4111yescharacteristic
201C42×C29C2411yescharacteristic
202#19478C2911yesmaximal, characteristic, direct product factor, Sylow
203C23×C29#12111yescharacteristic
204Q8×C29—21no—
205Q8×C29—21no—
206Q8×C29—21no—
207Q8×C29—42no—
208Q8×C29—41no—
209Q8×C29—41no—
210Q8×C29—41no—
211Q8×C29—41no—
212Q8×C29—81no—
213Q8×C29—81no—
214Q8×C29#13712yes—
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—41no—
224C2×C4×C29—42no—
225C2×C4×C29—42no—
226C2×C4×C29—41no—
227C2×C4×C29—41no—
228C2×C4×C29—41no—
229C2×C4×C29—41no—
230C2×C4×C29#12111yescharacteristic
231C2×C4×C29#12111yescharacteristic
232C2×C4×C29#12111yescharacteristic
233C2×C4×C29C22×D411yescharacteristic
234C2×C4×C29C22×D411yescharacteristic
235C2×C4×C29C2×#4111yescharacteristic
236C8×C29—21no—
237C8×C29—21no—
238C8×C29—21no—
239C8×C29—21no—
240C8×C29—41no—
241C8×C29—41no—
242C8×C29—41no—
243C8×C29—41no—
244C8×C29—41no—
245C8×C29—41no—
246#3231C2×C2911yescharacteristic
247#3104C2×C2911yescharacteristic
248#3078C2×C2911yescharacteristic
249#2984C2×C2911yescharacteristic
250#1704C2×C2911yescharacteristic, complemented
251#1700C2×C2911yescharacteristic, complemented
252#1696C2×C2911yescharacteristic, complemented
253#1692C2×C2911yescharacteristic, complemented
254#1684C2×C2911yescharacteristic, complemented
255#1680C2×C2911yescharacteristic, complemented
256#1676C2×C2911yescharacteristic, complemented
257#1672C2×C2911yescharacteristic, complemented
258#1574C2×C2911yescharacteristic
259#1559C2×C2911yescharacteristic
260#1554C2×C2911yescharacteristic
261C22×C29—21no—
262C22×C29—21no—
263C22×C29—21no—
264C22×C29C2×#12111yescharacteristic
265C4×C29—21no—
266C4×C29—21no—
267C4×C29—22no—
268C4×C29—21no—
269C4×C29—21no—
270C4×C29—41no—
271C4×C29—41no—
272C4×C29—41no—
273C4×C29—81no—
274C4×C29—81no—
275C4×C29—81no—
276C4×C29—81no—
277C4×C29C2×#13711yescharacteristic
278C4×C29#57511yescharacteristic
279C4×C29#57811yescharacteristic
280C4×C29#57811yescharacteristic
281#533C22×C2911yescharacteristic
282#533C22×C2911yescharacteristic
283C2×C4×Q8C22×C2911yescharacteristic
284#500C22×C2911yescharacteristic
285#498C22×C2911yescharacteristic
286#487C22×C2911yescharacteristic
287#487C22×C2911yescharacteristic
288#485—21no—
289#485—21no—
290#484—21no—
291#479—21no—
292#479—21no—
293#479—21no—
294#479—21no—
295#477C22×C2911yescharacteristic
296#477C22×C2911yescharacteristic
297#477C22×C2911yescharacteristic
298#477C22×C2911yescharacteristic
299#475C22×C2911yescharacteristic
300#475C22×C2911yescharacteristic
301#462C22×C2911yescharacteristic
302#462C22×C2911yescharacteristic
303#451—21no—
304#446—21no—
305#446—21no—
306#446C22×C2911yescharacteristic
307#446C22×C2911yescharacteristic
308C8×Q8C22×C2911yescharacteristic
309C8×Q8C22×C2911yescharacteristic
310C4×Q16—21no—
311C4×Q16—21no—
312#432—21no—
313#432C22×C2911yescharacteristic
314#431—21no—
315#431C22×C2911yescharacteristic
316#431C22×C2911yescharacteristic
317#428—21no—
318#423C22×C2911yescharacteristic
319#419—21no—
320#335C22×C2911yescharacteristic
321#335C22×C2911yescharacteristic
322#334C22×C2911yescharacteristic
323#334C22×C2911yescharacteristic
324#333C22×C2911yescharacteristic
325#333C22×C2911yescharacteristic
326#333C22×C2911yescharacteristic
327#333C22×C2911yescharacteristic
328#332C22×C2911yescharacteristic
329#332C22×C2911yescharacteristic
330#332C22×C2911yescharacteristic
331#332C22×C2911yescharacteristic
332C2×C29—41no—
333C2×C29#304411yescharacteristic
334C2×C29#305611yescharacteristic
335C2×C29#306711yescharacteristic
336C22×Q8D4×C2911yescharacteristic
337C2×Q16—21no—
338C2×Q16—21no—
339C2×M16—21no—
340C4⋊Q8C23×C2911yescharacteristic
341C4⋊Q8C23×C2911yescharacteristic
342C4⋊Q8C23×C2911yescharacteristic
343C4⋊Q8C23×C2911yescharacteristic
344#125—21no—
345#125—21no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8—21no—
350C4×Q8—21no—
351C4×Q8—21no—
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8D4×C2911yescharacteristic
357C4×Q8D4×C2911yescharacteristic
358C4×Q8C23×C2911yescharacteristic
359C4×Q8C23×C2911yescharacteristic
360#117—21no—
361#117—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4D4×C2911yescharacteristic
364C2×C42—21no—
365C2×C42C23×C2911yescharacteristic
366#107—21no—
367#107—21no—
368#107—21no—
369#107—21no—
370#107—21no—
371#107—21no—
372#106—21no—
373#106—21no—
374#106—21no—
375#106—21no—
376C4⋊C8—21no—
377C4⋊C8—21no—
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8D4×C2911yescharacteristic
382C4⋊C8D4×C2911yescharacteristic
383C4⋊C8C23×C2911yescharacteristic
384C4⋊C8C23×C2911yescharacteristic
385C4⋊C8C23×C2911yescharacteristic
386C4⋊C8C23×C2911yescharacteristic
387C4⋊C8C23×C2911yescharacteristic
388C4⋊C8C23×C2911yescharacteristic
389#103—21no—
390#103—21no—
391#103—21no—
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401C22⋊C8—21no—
402C22⋊C8—21no—
403C22⋊C8D4×C2911yescharacteristic
404C22⋊C8D4×C2911yescharacteristic
405#97—21no—
406#97—21no—
407#97—21no—
408C4×C8—21no—
409C4×C8—21no—
410C4×C8—21no—
411C4×C8C23×C2911yescharacteristic
412C4×C8C23×C2911yescharacteristic
413C29#1947811yescharacteristic, direct product factor, Sylow
414C2×Q8—21no—
415C2×Q8—22no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—41no—
421C2×Q8C2×D4×C2911yescharacteristic
422C2×Q8C2×D4×C2911yescharacteristic
423C22×C4—21no—
424C22×C4—21no—
425C22×C4C2×D4×C2911yescharacteristic
426C22×C4C2×D4×C2911yescharacteristic
427C22×C4#41×C2911yescharacteristic
428Q16—42no—
429Q16—42no—
430M16—42no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8C2×D4×C2911yescharacteristic
438C2×C8C2×D4×C2911yescharacteristic
439C2×C8C2×D4×C2911yescharacteristic
440C2×C8C2×D4×C2911yescharacteristic
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4C2×D4×C2911yescharacteristic
459C4⋊C4C2×D4×C2911yescharacteristic
460C22⋊C4—41no—
461C22⋊C4—41no—
462C42—21no—
463C42—21no—
464C42—21no—
465C42—21no—
466C42—41no—
467C42—41no—
468C42C2×D4×C2911yescharacteristic
469C42C2×D4×C2911yescharacteristic
470C42#41×C2911yescharacteristic
471C42C24×C2911yescharacteristic
472C23C29×#12111yescharacteristic
473Q8—21no—
474Q8—21no—
475Q8—21no—
476Q8—42no—
477Q8—41no—
478Q8—41no—
479Q8—41no—
480Q8—41no—
481Q8—81no—
482Q8—81no—
483Q8C29×#13712yes—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4C29×#12111yescharacteristic
500C2×C4C29×#12111yescharacteristic
501C2×C4C29×#12111yescharacteristic
502C2×C4C22×D4×C2911yescharacteristic
503C2×C4C22×D4×C2911yescharacteristic
504C2×C4C2×#41×C2911yescharacteristic
505C8—21no—
506C8—21no—
507C8—21no—
508C8—21no—
509C8—41no—
510C8—41no—
511C8—41no—
512C8—41no—
513C8—41no—
514C8—41no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22C2×C29×#12111yescharacteristic
519C4—21no—
520C4—21no—
521C4—22no—
522C4—21no—
523C4—21no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—81no—
528C4—81no—
529C4—81no—
530C4—81no—
531C4C2×C29×#13711yescharacteristic
532C4C29×#57511yescharacteristic
533C4C29×#57811yescharacteristic
534C4C29×#57811yescharacteristic
535C2—41no—
536C2C29×#304411yescharacteristic
537C2C29×#305611yescharacteristic
538C2C29×#306711yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC23×C29#121
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
5. C29×#1704C2semidirect
6. C29×#1700C2semidirect
7. C29×#1696C2semidirect
8. C29×#1692C2semidirect
9. C29×#1684C2semidirect
10. C29×#1680C2semidirect
11. C29×#1676C2semidirect
12. C29×#1672C2semidirect
202. #19478C29direct (N × H)
250. #1704C2×C29semidirect
251. #1700C2×C29semidirect
252. #1696C2×C29semidirect
253. #1692C2×C29semidirect
254. #1684C2×C29semidirect
255. #1680C2×C29semidirect
256. #1676C2×C29semidirect
257. #1672C2×C29semidirect
413. C29#19478direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32312
C29×#31042
C29×#30782
C29×#29842
C29×#17042
C29×#17002
C29×#16962
C29×#16922
C29×#16842
C29×#16802
C29×#16762
C29×#16722
C29×#15742
C29×#15592
C29×#15542
#1947829