Finite Group Databasebeta

← C29×#19491 #20314391

Subgroups — C29×#19491 #20314391

Order 7424.

614 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3226C211yesmaximal, characteristic, complemented
2C29×#3106C211yesmaximal, characteristic
3C29×#3079C211yesmaximal, characteristic, complemented
4C29×#2990C211yesmaximal, characteristic, complemented
5C29×#1698C212yesmaximal, complemented
6C29×#1696C212yesmaximal, complemented
7C29×#1677C212yesmaximal, complemented
8C29×#1675C212yesmaximal, complemented
9C29×#1574C211yesmaximal, characteristic, complemented
10C29×#1560C211yesmaximal, characteristic, complemented
11C29×#1548C211yesmaximal, characteristic, complemented
12C29×#532C2211yescharacteristic
13C2×C29×C4⋊Q8C2211yescharacteristic
14C4×#41×C29C2211yescharacteristic
15C29×#500C2212yes—
16C29×#486C2212yes—
17C29×#482—21no—
18C29×#480—22no—
19C29×#477C2211yescharacteristic
20C29×#477C2212yes—
21C29×#476C2211yescharacteristic
22C29×#476C2212yes—
23C29×#475—21no—
24C29×#474—21no—
25C29×#474—21no—
26C29×#474—21no—
27C29×#460C2211yescharacteristic
28C29×#459C2211yescharacteristic
29C29×#449—21no—
30C29×#446C2212yes—
31C4×SD16×C29—21no—
32C4×D8×C29—21no—
33C29×#435—22no—
34C8×D4×C29C2212yes—
35C29×#432—21no—
36C29×#431C2211yescharacteristic
37C29×#431C2211yescharacteristic
38C29×#428—21no—
39C29×#423C2211yescharacteristic
40C29×#423C2211yescharacteristic
41C2×C29×C4⋊C8—21no—
42C29×#417—21no—
43C29×#335C2212yes—
44C29×#334C2212yes—
45C29×#333C2212yes—
46C29×#333C2212yes—
47C29×#333C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C2×#41×C29D411yescharacteristic
51C22×Q8×C29—21no—
52C2×SD16×C29—21no—
53C2×D8×C29—21no—
54C2×M16×C29—21no—
55C2×M16×C29—21no—
56C22×C8×C29—22no—
57C29×C4⋊Q8—21no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8—21no—
60C29×C4⋊Q8C2312yes—
61C29×C4⋊Q8C2311yescharacteristic
62C29×#127C2311yescharacteristic
63C29×#124—21no—
64C29×#121—21no—
65C29×#121—21no—
66C4×Q8×C29D411yescharacteristic
67C4×Q8×C29C2311yescharacteristic
68C4×D4×C29—21no—
69C4×D4×C29—21no—
70C4×D4×C29—21no—
71C4×D4×C29—21no—
72C4×D4×C29D411yescharacteristic
73C4×D4×C29C2311yescharacteristic
74C29×#117—21no—
75C29×#117D411yescharacteristic
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29—21no—
78C2×C42×C29—21no—
79C2×C42×C29C2311yescharacteristic
80C29×#107—22no—
81C29×#107—22no—
82C29×#107—22no—
83C29×#107—21no—
84C29×#106—22no—
85C29×#106—21no—
86C29×C4⋊C8—22no—
87C29×C4⋊C8—21no—
88C29×C4⋊C8—21no—
89C29×C4⋊C8D411yescharacteristic
90C29×C4⋊C8D411yescharacteristic
91C29×C4⋊C8C2311yescharacteristic
92C29×C4⋊C8C2311yescharacteristic
93C29×C4⋊C8C2312yes—
94C29×C4⋊C8C2312yes—
95C29×#103—21no—
96C29×#103—22no—
97C29×#102—21no—
98C29×#102—22no—
99C29×#102—22no—
100C29×#102—22no—
101C29×#102—21no—
102C29×#102—21no—
103C29×C22⋊C8—21no—
104C29×C22⋊C8—22no—
105C29×C22⋊C8D412yes—
106C29×#97—22no—
107C4×C8×C29—21no—
108C4×C8×C29C2312yes—
109#41×C29—22no—
110#41×C29—41no—
111#41×C29—82no—
112C2×Q8×C29—21no—
113C2×Q8×C29—22no—
114C2×Q8×C29—41no—
115C2×Q8×C29—82no—
116C2×Q8×C29C2×D411yescharacteristic
117C2×D4×C29—21no—
118C2×D4×C29—21no—
119C2×D4×C29—21no—
120C2×D4×C29—21no—
121C2×D4×C29—41no—
122C2×D4×C29C2×D411yescharacteristic
123C22×C4×C29—21no—
124C22×C4×C29—21no—
125C22×C4×C29—21no—
126C22×C4×C29—41no—
127C22×C4×C29—41no—
128C22×C4×C29C2×D411yescharacteristic
129C22×C4×C29C2×D411yescharacteristic
130C22×C4×C29#4111yescharacteristic
131SD16×C29—42no—
132D8×C29—42no—
133M16×C29—42no—
134M16×C29—81no—
135C2×C8×C29—22no—
136C2×C8×C29—22no—
137C2×C8×C29—21no—
138C2×C8×C29—21no—
139C2×C8×C29—82no—
140C2×C8×C29C2×D412yes—
141C2×C8×C29C2×D412yes—
142C4⋊C4×C29—21no—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—22no—
145C4⋊C4×C29—22no—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—41no—
149C4⋊C4×C29—41no—
150C4⋊C4×C29C2×D411yescharacteristic
151C4⋊C4×C29C2×D411yescharacteristic
152C22⋊C4×C29—21no—
153C22⋊C4×C29—21no—
154C22⋊C4×C29—21no—
155C22⋊C4×C29—41no—
156C22⋊C4×C29—41no—
157C42×C29—21no—
158C42×C29—21no—
159C42×C29—21no—
160C42×C29C2×D411yescharacteristic
161C42×C29C2×D411yescharacteristic
162C42×C29#4111yescharacteristic
163C42×C29C2411yescharacteristic
164#19491C2911yesmaximal, characteristic, direct product factor, Sylow
165C23×C29—21no—
166C23×C29—41no—
167C23×C29#12111yescharacteristic
168Q8×C29—21no—
169Q8×C29—21no—
170Q8×C29—82no—
171Q8×C29—81no—
172Q8×C29—82no—
173D4×C29—21no—
174D4×C29—42no—
175D4×C29—41no—
176D4×C29—41no—
177D4×C29—41no—
178D4×C29—41no—
179D4×C29—81no—
180D4×C29—82no—
181D4×C29#13712yes—
182C2×C4×C29—21no—
183C2×C4×C29—21no—
184C2×C4×C29—21no—
185C2×C4×C29—21no—
186C2×C4×C29—22no—
187C2×C4×C29—21no—
188C2×C4×C29—21no—
189C2×C4×C29—21no—
190C2×C4×C29—42no—
191C2×C4×C29—41no—
192C2×C4×C29—41no—
193C2×C4×C29—42no—
194C2×C4×C29—41no—
195C2×C4×C29—42no—
196C2×C4×C29—82no—
197C2×C4×C29—82no—
198C2×C4×C29#12111yescharacteristic
199C2×C4×C29#12111yescharacteristic
200C2×C4×C29#12111yescharacteristic
201C2×C4×C29C22×D411yescharacteristic
202C2×C4×C29C22×D411yescharacteristic
203C2×C4×C29C2×#4111yescharacteristic
204C8×C29—22no—
205C8×C29—22no—
206C8×C29—41no—
207C8×C29—42no—
208C8×C29—41no—
209C8×C29—42no—
210#3226C2×C2911yescharacteristic, complemented
211#3106C2×C2911yescharacteristic
212#3079C2×C2911yescharacteristic, complemented
213#2990C2×C2911yescharacteristic, complemented
214#1698C2×C2912yescomplemented
215#1696C2×C2912yescomplemented
216#1677C2×C2912yescomplemented
217#1675C2×C2912yescomplemented
218#1574C2×C2911yescharacteristic, complemented
219#1560C2×C2911yescharacteristic, complemented
220#1548C2×C2911yescharacteristic, complemented
221C22×C29—21no—
222C22×C29—21no—
223C22×C29—22no—
224C22×C29—21no—
225C22×C29—41no—
226C22×C29—41no—
227C22×C29—81no—
228C22×C29—81no—
229C22×C29—81no—
230C22×C29C2×#12111yescharacteristic
231C4×C29—21no—
232C4×C29—21no—
233C4×C29—21no—
234C4×C29—41no—
235C4×C29—41no—
236C4×C29—41no—
237C4×C29—81no—
238C4×C29—82no—
239C4×C29#47212yes—
240C4×C29C2×#13711yescharacteristic
241C4×C29#57511yescharacteristic
242C4×C29#57711yescharacteristic
243C4×C29#57811yescharacteristic
244#532C22×C2911yescharacteristic
245C2×C4⋊Q8C22×C2911yescharacteristic
246C4×#41C22×C2911yescharacteristic
247#500C22×C2912yes—
248#486C22×C2912yes—
249#482—21no—
250#480—22no—
251#477C22×C2912yes—
252#477C22×C2911yescharacteristic
253#476C22×C2912yes—
254#476C22×C2911yescharacteristic
255#475—21no—
256#474—21no—
257#474—21no—
258#474—21no—
259#460C22×C2911yescharacteristic
260#459C22×C2911yescharacteristic
261#449—21no—
262#446C22×C2912yes—
263C4×SD16—21no—
264C4×D8—21no—
265#435—22no—
266C8×D4C22×C2912yes—
267#432—21no—
268#431C22×C2911yescharacteristic
269#431C22×C2911yescharacteristic
270#428—21no—
271#423C22×C2911yescharacteristic
272#423C22×C2911yescharacteristic
273C2×C4⋊C8—21no—
274#417—21no—
275#335C22×C2912yes—
276#334C22×C2912yes—
277#333C22×C2912yes—
278#333C22×C2912yes—
279#333C22×C2912yes—
280#331C22×C2912yes—
281C2×C29—41no—
282C2×C29—42no—
283C2×C29—161no—
284C2×C29#304611yescharacteristic
285C2×C29#305611yescharacteristic
286C2×C29C2×#47211yescharacteristic
287C2×#41—21no—
288C2×#41D4×C2911yescharacteristic
289C22×Q8—21no—
290C2×SD16—21no—
291C2×D8—21no—
292C2×M16—21no—
293C2×M16—21no—
294C22×C8—22no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8C23×C2912yes—
299C4⋊Q8C23×C2911yescharacteristic
300#127C23×C2911yescharacteristic
301#124—21no—
302#121—21no—
303#121—21no—
304C4×Q8D4×C2911yescharacteristic
305C4×Q8C23×C2911yescharacteristic
306C4×D4—21no—
307C4×D4—21no—
308C4×D4—21no—
309C4×D4—21no—
310C4×D4D4×C2911yescharacteristic
311C4×D4C23×C2911yescharacteristic
312#117—21no—
313#117D4×C2911yescharacteristic
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C42—21no—
317C2×C42C23×C2911yescharacteristic
318#107—22no—
319#107—22no—
320#107—22no—
321#107—21no—
322#106—22no—
323#106—21no—
324C4⋊C8—22no—
325C4⋊C8—21no—
326C4⋊C8—21no—
327C4⋊C8D4×C2911yescharacteristic
328C4⋊C8D4×C2911yescharacteristic
329C4⋊C8C23×C2912yes—
330C4⋊C8C23×C2912yes—
331C4⋊C8C23×C2911yescharacteristic
332C4⋊C8C23×C2911yescharacteristic
333#103—22no—
334#103—21no—
335#102—22no—
336#102—21no—
337#102—22no—
338#102—22no—
339#102—21no—
340#102—21no—
341C22⋊C8—21no—
342C22⋊C8—22no—
343C22⋊C8D4×C2912yes—
344#97—22no—
345C4×C8—21no—
346C4×C8C23×C2912yes—
347C29#1949111yescharacteristic, direct product factor, Sylow
348#41—22no—
349#41—41no—
350#41—82no—
351C2×Q8—21no—
352C2×Q8—22no—
353C2×Q8—41no—
354C2×Q8—82no—
355C2×Q8C2×D4×C2911yescharacteristic
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—41no—
361C2×D4C2×D4×C2911yescharacteristic
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4C2×D4×C2911yescharacteristic
368C22×C4C2×D4×C2911yescharacteristic
369C22×C4#41×C2911yescharacteristic
370SD16—42no—
371D8—42no—
372M16—42no—
373M16—81no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—82no—
379C2×C8C2×D4×C2912yes—
380C2×C8C2×D4×C2912yes—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4C2×D4×C2911yescharacteristic
390C4⋊C4C2×D4×C2911yescharacteristic
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—21no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C42—21no—
397C42—21no—
398C42—21no—
399C42C2×D4×C2911yescharacteristic
400C42C2×D4×C2911yescharacteristic
401C42#41×C2911yescharacteristic
402C42C24×C2911yescharacteristic
403C23—21no—
404C23—41no—
405C23C29×#12111yescharacteristic
406Q8—21no—
407Q8—21no—
408Q8—82no—
409Q8—81no—
410Q8—82no—
411D4—21no—
412D4—42no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—41no—
417D4—81no—
418D4—82no—
419D4C29×#13712yes—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4C29×#12111yescharacteristic
437C2×C4C29×#12111yescharacteristic
438C2×C4C29×#12111yescharacteristic
439C2×C4C22×D4×C2911yescharacteristic
440C2×C4C22×D4×C2911yescharacteristic
441C2×C4C2×#41×C2911yescharacteristic
442C8—22no—
443C8—22no—
444C8—41no—
445C8—42no—
446C8—41no—
447C8—42no—
448C22—21no—
449C22—21no—
450C22—22no—
451C22—21no—
452C22—41no—
453C22—41no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22C2×C29×#12111yescharacteristic
458C4—21no—
459C4—21no—
460C4—21no—
461C4—41no—
462C4—41no—
463C4—41no—
464C4—81no—
465C4—82no—
466C4C29×#47212yes—
467C4C2×C29×#13711yescharacteristic
468C4C29×#57511yescharacteristic
469C4C29×#57711yescharacteristic
470C4C29×#57811yescharacteristic
471C2—41no—
472C2—42no—
473C2—161no—
474C2C29×#304611yescharacteristic
475C2C29×#305611yescharacteristic
476C2C2×C29×#47211yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3106C2
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
1. C29×#3226C2semidirect
3. C29×#3079C2semidirect
4. C29×#2990C2semidirect
5. C29×#1698C2semidirect
6. C29×#1696C2semidirect
7. C29×#1677C2semidirect
8. C29×#1675C2semidirect
9. C29×#1574C2semidirect
10. C29×#1560C2semidirect
11. C29×#1548C2semidirect
164. #19491C29direct (N × H)
210. #3226C2×C29semidirect
212. #3079C2×C29semidirect
213. #2990C2×C29semidirect
214. #1698C2×C29semidirect
215. #1696C2×C29semidirect
216. #1677C2×C29semidirect
217. #1675C2×C29semidirect
218. #1574C2×C29semidirect
219. #1560C2×C29semidirect
220. #1548C2×C29semidirect
347. C29#19491direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32262
C29×#31062
C29×#30792
C29×#29902
C29×#16982
C29×#16962
C29×#16772
C29×#16752
C29×#15742
C29×#15602
C29×#15482
#1949129