Finite Group Databasebeta

← C29×#19485 #20314385

Subgroups — C29×#19485 #20314385

Order 7424.

604 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3209C211yesmaximal, characteristic, complemented
2C29×#3107C211yesmaximal, characteristic
3C29×#3079C211yesmaximal, characteristic
4C29×#2990C211yesmaximal, characteristic
5C29×#1700C212yesmaximal, complemented
6C29×#1690C212yesmaximal, complemented
7C29×#1679C212yesmaximal, complemented
8C29×#1669C212yesmaximal, complemented
9C29×#1574C211yesmaximal, characteristic, complemented
10C29×#1561C211yesmaximal, characteristic, complemented
11C29×#1546C211yesmaximal, characteristic, complemented
12C29×#533C2211yescharacteristic
13C2×C29×C4⋊Q8C2211yescharacteristic
14C4×#41×C29C2211yescharacteristic
15C29×#494C2212yes—
16C29×#487C2212yes—
17C29×#485—21no—
18C29×#477—21no—
19C29×#476—21no—
20C29×#475C2211yescharacteristic
21C29×#475C2212yes—
22C29×#474C2211yescharacteristic
23C29×#474C2212yes—
24C29×#462—21no—
25C29×#462—21no—
26C29×#462C2211yescharacteristic
27C29×#461C2211yescharacteristic
28C29×#452—21no—
29C29×#451—22no—
30C29×#446C2212yes—
31C4×Q16×C29—21no—
32C4×SD16×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×#332C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#332C2212yes—
49C2×#41×C29D411yescharacteristic
50C22×Q8×C29—21no—
51C2×Q16×C29—21no—
52C2×Q16×C29—22no—
53C2×Q16×C29—22no—
54C2×SD16×C29—21no—
55C2×M16×C29—21no—
56C2×M16×C29—21no—
57C22×C8×C29—22no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8—21no—
60C29×C4⋊Q8—21no—
61C29×C4⋊Q8C2311yescharacteristic
62C29×C4⋊Q8C2312yes—
63C29×C4⋊Q8C2311yescharacteristic
64C29×#125—21no—
65C29×C22⋊Q8—21no—
66C29×C22⋊Q8—21no—
67C4×Q8×C29—21no—
68C4×Q8×C29—21no—
69C4×Q8×C29D411yescharacteristic
70C4×Q8×C29C2311yescharacteristic
71C4×D4×C29—21no—
72C4×D4×C29—21no—
73C4×D4×C29D411yescharacteristic
74C4×D4×C29C2311yescharacteristic
75C29×#117—21no—
76C29×#117—21no—
77C29×#117D411yescharacteristic
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29—21no—
80C2×C42×C29—21no—
81C2×C42×C29C2311yescharacteristic
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×#103—22no—
98C29×#103—22no—
99C29×#103—21no—
100C29×#103—21no—
101C29×#102—21no—
102C29×#102—22no—
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—
111C2×Q8×C29—21no—
112C2×Q8×C29—21no—
113C2×Q8×C29—22no—
114C2×Q8×C29—41no—
115C2×Q8×C29—81no—
116C2×Q8×C29—81no—
117C2×Q8×C29C2×D411yescharacteristic
118C2×D4×C29—21no—
119C2×D4×C29C2×D411yescharacteristic
120C22×C4×C29—21no—
121C22×C4×C29—21no—
122C22×C4×C29—21no—
123C22×C4×C29—41no—
124C22×C4×C29C2×D411yescharacteristic
125C22×C4×C29C2×D411yescharacteristic
126C22×C4×C29#4111yescharacteristic
127Q16×C29—42no—
128Q16×C29—82no—
129Q16×C29—82no—
130SD16×C29—42no—
131M16×C29—42no—
132M16×C29—81no—
133C2×C8×C29—22no—
134C2×C8×C29—22no—
135C2×C8×C29—21no—
136C2×C8×C29—21no—
137C2×C8×C29—82no—
138C2×C8×C29C2×D412yes—
139C2×C8×C29C2×D412yes—
140C4⋊C4×C29—21no—
141C4⋊C4×C29—21no—
142C4⋊C4×C29—22no—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—21no—
145C4⋊C4×C29—22no—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—41no—
149C4⋊C4×C29—41no—
150C4⋊C4×C29—41no—
151C4⋊C4×C29—41no—
152C4⋊C4×C29C2×D411yescharacteristic
153C4⋊C4×C29C2×D411yescharacteristic
154C22⋊C4×C29—21no—
155C22⋊C4×C29—21no—
156C22⋊C4×C29—21no—
157C22⋊C4×C29—41no—
158C42×C29—21no—
159C42×C29—21no—
160C42×C29—21no—
161C42×C29—41no—
162C42×C29C2×D411yescharacteristic
163C42×C29C2×D411yescharacteristic
164C42×C29#4111yescharacteristic
165C42×C29C2411yescharacteristic
166#19485C2911yesmaximal, characteristic, direct product factor, Sylow
167C23×C29—21no—
168C23×C29#12111yescharacteristic
169Q8×C29—21no—
170Q8×C29—21no—
171Q8×C29—41no—
172Q8×C29—41no—
173Q8×C29—41no—
174Q8×C29—42no—
175Q8×C29—41no—
176Q8×C29—42no—
177Q8×C29—82no—
178D4×C29—21no—
179D4×C29—42no—
180D4×C29#13712yes—
181C2×C4×C29—21no—
182C2×C4×C29—21no—
183C2×C4×C29—21no—
184C2×C4×C29—21no—
185C2×C4×C29—22no—
186C2×C4×C29—21no—
187C2×C4×C29—21no—
188C2×C4×C29—21no—
189C2×C4×C29—42no—
190C2×C4×C29—41no—
191C2×C4×C29—41no—
192C2×C4×C29—42no—
193C2×C4×C29—41no—
194C2×C4×C29—41no—
195C2×C4×C29—42no—
196C2×C4×C29—82no—
197C2×C4×C29#12111yescharacteristic
198C2×C4×C29#12111yescharacteristic
199C2×C4×C29#12111yescharacteristic
200C2×C4×C29C22×D411yescharacteristic
201C2×C4×C29C22×D411yescharacteristic
202C2×C4×C29C2×#4111yescharacteristic
203C8×C29—22no—
204C8×C29—22no—
205C8×C29—41no—
206C8×C29—42no—
207C8×C29—41no—
208C8×C29—42no—
209#3209C2×C2911yescharacteristic, complemented
210#3107C2×C2911yescharacteristic
211#3079C2×C2911yescharacteristic
212#2990C2×C2911yescharacteristic
213#1700C2×C2912yescomplemented
214#1690C2×C2912yescomplemented
215#1679C2×C2912yescomplemented
216#1669C2×C2912yescomplemented
217#1574C2×C2911yescharacteristic, complemented
218#1561C2×C2911yescharacteristic, complemented
219#1546C2×C2911yescharacteristic, complemented
220C22×C29—21no—
221C22×C29—21no—
222C22×C29—22no—
223C22×C29—21no—
224C22×C29—41no—
225C22×C29—41no—
226C22×C29C2×#12111yescharacteristic
227C4×C29—21no—
228C4×C29—21no—
229C4×C29—21no—
230C4×C29—41no—
231C4×C29—41no—
232C4×C29—41no—
233C4×C29—82no—
234C4×C29—81no—
235C4×C29—81no—
236C4×C29#47312yes—
237C4×C29C2×#13711yescharacteristic
238C4×C29#57511yescharacteristic
239C4×C29#57611yescharacteristic
240C4×C29#57711yescharacteristic
241#533C22×C2911yescharacteristic
242C2×C4⋊Q8C22×C2911yescharacteristic
243C4×#41C22×C2911yescharacteristic
244#494C22×C2912yes—
245#487C22×C2912yes—
246#485—21no—
247#477—21no—
248#476—21no—
249#475C22×C2912yes—
250#475C22×C2911yescharacteristic
251#474C22×C2912yes—
252#474C22×C2911yescharacteristic
253#462—21no—
254#462—21no—
255#462C22×C2911yescharacteristic
256#461C22×C2911yescharacteristic
257#452—21no—
258#451—22no—
259#446C22×C2912yes—
260C4×Q16—21no—
261C4×SD16—21no—
262#435—22no—
263C8×D4C22×C2912yes—
264#432—21no—
265#431C22×C2911yescharacteristic
266#431C22×C2911yescharacteristic
267#428—21no—
268#423C22×C2911yescharacteristic
269#423C22×C2911yescharacteristic
270C2×C4⋊C8—21no—
271#417—21no—
272#335C22×C2912yes—
273#334C22×C2912yes—
274#332C22×C2912yes—
275#332C22×C2912yes—
276#332C22×C2912yes—
277#332C22×C2912yes—
278C2×C29—41no—
279C2×C29—42no—
280C2×C29#304511yescharacteristic
281C2×C29#305611yescharacteristic
282C2×C29C2×#47311yescharacteristic
283C2×#41D4×C2911yescharacteristic
284C22×Q8—21no—
285C2×Q16—21no—
286C2×Q16—22no—
287C2×Q16—22no—
288C2×SD16—21no—
289C2×M16—21no—
290C2×M16—21no—
291C22×C8—22no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8C23×C2912yes—
296C4⋊Q8C23×C2911yescharacteristic
297C4⋊Q8C23×C2911yescharacteristic
298#125—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8D4×C2911yescharacteristic
304C4×Q8C23×C2911yescharacteristic
305C4×D4—21no—
306C4×D4—21no—
307C4×D4D4×C2911yescharacteristic
308C4×D4C23×C2911yescharacteristic
309#117—21no—
310#117—21no—
311#117D4×C2911yescharacteristic
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C42—21no—
315C2×C42C23×C2911yescharacteristic
316#107—22no—
317#107—21no—
318#106—22no—
319#106—21no—
320C4⋊C8—22no—
321C4⋊C8—21no—
322C4⋊C8—21no—
323C4⋊C8D4×C2911yescharacteristic
324C4⋊C8D4×C2911yescharacteristic
325C4⋊C8C23×C2912yes—
326C4⋊C8C23×C2911yescharacteristic
327C4⋊C8C23×C2912yes—
328C4⋊C8C23×C2911yescharacteristic
329#103—22no—
330#103—21no—
331#103—22no—
332#103—22no—
333#103—21no—
334#103—21no—
335#102—22no—
336#102—21no—
337C22⋊C8—21no—
338C22⋊C8—22no—
339C22⋊C8D4×C2912yes—
340#97—22no—
341C4×C8—21no—
342C4×C8C23×C2912yes—
343C29#1948511yescharacteristic, direct product factor, Sylow
344#41—22no—
345#41—41no—
346C2×Q8—21no—
347C2×Q8—22no—
348C2×Q8—21no—
349C2×Q8—41no—
350C2×Q8—81no—
351C2×Q8—81no—
352C2×Q8C2×D4×C2911yescharacteristic
353C2×D4—21no—
354C2×D4C2×D4×C2911yescharacteristic
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—41no—
359C22×C4C2×D4×C2911yescharacteristic
360C22×C4C2×D4×C2911yescharacteristic
361C22×C4#41×C2911yescharacteristic
362Q16—42no—
363Q16—82no—
364Q16—82no—
365SD16—42no—
366M16—42no—
367M16—81no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—82no—
373C2×C8C2×D4×C2912yes—
374C2×C8C2×D4×C2912yes—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4C2×D4×C2911yescharacteristic
388C4⋊C4C2×D4×C2911yescharacteristic
389C22⋊C4—21no—
390C22⋊C4—21no—
391C22⋊C4—21no—
392C22⋊C4—41no—
393C42—21no—
394C42—21no—
395C42—21no—
396C42—41no—
397C42C2×D4×C2911yescharacteristic
398C42C2×D4×C2911yescharacteristic
399C42#41×C2911yescharacteristic
400C42C24×C2911yescharacteristic
401C23—21no—
402C23C29×#12111yescharacteristic
403Q8—21no—
404Q8—21no—
405Q8—41no—
406Q8—41no—
407Q8—41no—
408Q8—42no—
409Q8—41no—
410Q8—42no—
411Q8—82no—
412D4—21no—
413D4—42no—
414D4C29×#13712yes—
415C2×C4—22no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—82no—
431C2×C4C29×#12111yescharacteristic
432C2×C4C29×#12111yescharacteristic
433C2×C4C29×#12111yescharacteristic
434C2×C4C22×D4×C2911yescharacteristic
435C2×C4C22×D4×C2911yescharacteristic
436C2×C4C2×#41×C2911yescharacteristic
437C8—22no—
438C8—22no—
439C8—41no—
440C8—42no—
441C8—41no—
442C8—42no—
443C22—21no—
444C22—21no—
445C22—22no—
446C22—21no—
447C22—41no—
448C22—41no—
449C22C2×C29×#12111yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—41no—
454C4—41no—
455C4—41no—
456C4—82no—
457C4—81no—
458C4—81no—
459C4C29×#47312yes—
460C4C2×C29×#13711yescharacteristic
461C4C29×#57511yescharacteristic
462C4C29×#57611yescharacteristic
463C4C29×#57711yescharacteristic
464C2—41no—
465C2—42no—
466C2C29×#304511yescharacteristic
467C2C29×#305611yescharacteristic
468C2C2×C29×#47311yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC2×#41×C29D4
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×#3209C2semidirect
5. C29×#1700C2semidirect
6. C29×#1690C2semidirect
7. C29×#1679C2semidirect
8. C29×#1669C2semidirect
9. C29×#1574C2semidirect
10. C29×#1561C2semidirect
11. C29×#1546C2semidirect
166. #19485C29direct (N × H)
209. #3209C2×C29semidirect
213. #1700C2×C29semidirect
214. #1690C2×C29semidirect
215. #1679C2×C29semidirect
216. #1669C2×C29semidirect
217. #1574C2×C29semidirect
218. #1561C2×C29semidirect
219. #1546C2×C29semidirect
343. C29#19485direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32092
C29×#31072
C29×#30792
C29×#29902
C29×#17002
C29×#16902
C29×#16792
C29×#16692
C29×#15742
C29×#15612
C29×#15462
#1948529