Finite Group Databasebeta

← C29×#19318 #20314218

Subgroups — C29×#19318 #20314218

Order 7424.

620 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×#3141C211yesmaximal, characteristic, complemented
2C29×#3115C211yesmaximal, characteristic
3C29×#3079C211yesmaximal, characteristic, complemented
4C29×#2970C211yesmaximal, characteristic, complemented
5C29×#1704C212yesmaximal, complemented
6C29×#1698C212yesmaximal, complemented
7C29×#1683C212yesmaximal, complemented
8C29×#1677C212yesmaximal, complemented
9C29×#1569C211yesmaximal, characteristic, complemented
10C29×#1558C211yesmaximal, characteristic, complemented
11C29×#1557C211yesmaximal, characteristic, complemented
12C29×#532C2211yescharacteristic
13C2×C29×C4⋊Q8C2211yescharacteristic
14C4×#41×C29C2211yescharacteristic
15C29×#489—21no—
16C29×#489—21no—
17C29×#487C2212yes—
18C29×#486C2212yes—
19C29×#482—21no—
20C29×#477C2212yes—
21C29×#476C2212yes—
22C29×#475—21no—
23C29×#475C2211yescharacteristic
24C29×#474—21no—
25C29×#474C2211yescharacteristic
26C29×#460C2211yescharacteristic
27C29×#459C2211yescharacteristic
28C29×#449—21no—
29C29×#446C2212yes—
30C29×#442—21no—
31C29×#440—21no—
32C29×#435—22no—
33C8×D4×C29C2212yes—
34C29×#432—21no—
35C29×#432C2211yescharacteristic
36C29×#432C2211yescharacteristic
37C29×#428—21no—
38C29×#423C2211yescharacteristic
39C29×#417—21no—
40C29×#417—22no—
41C4×M16×C29C2211yescharacteristic
42C2×C29×#97—21no—
43C29×#335C2212yes—
44C29×#334C2212yes—
45C29×#333C2212yes—
46C29×#333C2212yes—
47C29×#332C2212yes—
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×C29D412yes—
56C22×C8×C29—22no—
57C29×C4⋊Q8—21no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8—21no—
60C29×C4⋊Q8C2311yescharacteristic
61C29×C4⋊Q8C2312yes—
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—21no—
82C29×#106—22no—
83C29×#106—21no—
84C29×C4⋊C8—22no—
85C29×C4⋊C8—21no—
86C29×C4⋊C8C2312yes—
87C29×C4⋊C8C2311yescharacteristic
88C29×C4⋊C8C2311yescharacteristic
89C29×C4⋊C8C2312yes—
90C29×#103—21no—
91C29×#103—22no—
92C29×#103—22no—
93C29×#103—22no—
94C29×#102—21no—
95C29×#102—22no—
96C29×#102—22no—
97C29×#102—22no—
98C29×#102—21no—
99C29×#102—21no—
100C29×C22⋊C8—21no—
101C29×C22⋊C8—21no—
102C29×C22⋊C8—22no—
103C29×#97—22no—
104C29×#97—21no—
105C29×#97—21no—
106C29×#97D411yescharacteristic
107C29×#97D411yescharacteristic
108C4×C8×C29C2312yes—
109#41×C29—22no—
110#41×C29—41no—
111#41×C29—44no—
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—42no—
135C2×C8×C29—22no—
136C2×C8×C29—22no—
137C2×C8×C29—21no—
138C2×C8×C29—21no—
139C2×C8×C29—44no—
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#19318C2911yesmaximal, characteristic, direct product factor, Sylow
165C23×C29—21no—
166C23×C29—41no—
167C23×C29#12111yescharacteristic
168Q8×C29—21no—
169Q8×C29—21no—
170Q8×C29—42no—
171Q8×C29—82no—
172Q8×C29—82no—
173D4×C29—21no—
174D4×C29—42no—
175D4×C29—41no—
176D4×C29—41no—
177D4×C29—42no—
178D4×C29—81no—
179D4×C29—82no—
180D4×C29#13712yes—
181C2×C4×C29—21no—
182C2×C4×C29—21no—
183C2×C4×C29—22no—
184C2×C4×C29—21no—
185C2×C4×C29—21no—
186C2×C4×C29—21no—
187C2×C4×C29—41no—
188C2×C4×C29—42no—
189C2×C4×C29—42no—
190C2×C4×C29—41no—
191C2×C4×C29—42no—
192C2×C4×C29—81no—
193C2×C4×C29—82no—
194C2×C4×C29—82no—
195C2×C4×C29#12111yescharacteristic
196C2×C4×C29#12111yescharacteristic
197C2×C4×C29#12111yescharacteristic
198C2×C4×C29C22×D411yescharacteristic
199C2×C4×C29C22×D411yescharacteristic
200C2×C4×C29C2×#4111yescharacteristic
201C8×C29—22no—
202C8×C29—22no—
203C8×C29—41no—
204C8×C29—42no—
205C8×C29—42no—
206C8×C29—41no—
207#3141C2×C2911yescharacteristic, complemented
208#3115C2×C2911yescharacteristic
209#3079C2×C2911yescharacteristic, complemented
210#2970C2×C2911yescharacteristic, complemented
211#1704C2×C2912yescomplemented
212#1698C2×C2912yescomplemented
213#1683C2×C2912yescomplemented
214#1677C2×C2912yescomplemented
215#1569C2×C2911yescharacteristic, complemented
216#1558C2×C2911yescharacteristic, complemented
217#1557C2×C2911yescharacteristic, complemented
218C22×C29—21no—
219C22×C29—21no—
220C22×C29—22no—
221C22×C29—21no—
222C22×C29—41no—
223C22×C29—41no—
224C22×C29—81no—
225C22×C29—81no—
226C22×C29—81no—
227C22×C29C2×#12111yescharacteristic
228C4×C29—21no—
229C4×C29—21no—
230C4×C29—21no—
231C4×C29—21no—
232C4×C29—41no—
233C4×C29—41no—
234C4×C29—41no—
235C4×C29—81no—
236C4×C29—82no—
237C4×C29C2×#13711yescharacteristic
238C4×C29#57512yes—
239C4×C29#57511yescharacteristic
240#532C22×C2911yescharacteristic
241C2×C4⋊Q8C22×C2911yescharacteristic
242C4×#41C22×C2911yescharacteristic
243#489—21no—
244#489—21no—
245#487C22×C2912yes—
246#486C22×C2912yes—
247#482—21no—
248#477C22×C2912yes—
249#476C22×C2912yes—
250#475—21no—
251#475C22×C2911yescharacteristic
252#474—21no—
253#474C22×C2911yescharacteristic
254#460C22×C2911yescharacteristic
255#459C22×C2911yescharacteristic
256#449—21no—
257#446C22×C2912yes—
258#442—21no—
259#440—21no—
260#435—22no—
261C8×D4C22×C2912yes—
262#432—21no—
263#432C22×C2911yescharacteristic
264#432C22×C2911yescharacteristic
265#428—21no—
266#423C22×C2911yescharacteristic
267#417—21no—
268#417—22no—
269C4×M16C22×C2911yescharacteristic
270C2×#97—21no—
271#335C22×C2912yes—
272#334C22×C2912yes—
273#333C22×C2912yes—
274#333C22×C2912yes—
275#332C22×C2912yes—
276#331C22×C2912yes—
277C2×C29—41no—
278C2×C29—42no—
279C2×C29—161no—
280C2×C29#304011yescharacteristic
281C2×C29#305611yescharacteristic
282C2×C29#306811yescharacteristic
283C2×#41—21no—
284C2×#41D4×C2911yescharacteristic
285C22×Q8—21no—
286C2×SD16—21no—
287C2×D8—21no—
288C2×M16—21no—
289C2×M16D4×C2912yes—
290C22×C8—22no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8C23×C2912yes—
295C4⋊Q8C23×C2911yescharacteristic
296#127C23×C2911yescharacteristic
297#124—21no—
298#121—21no—
299#121—21no—
300C4×Q8D4×C2911yescharacteristic
301C4×Q8C23×C2911yescharacteristic
302C4×D4—21no—
303C4×D4—21no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4D4×C2911yescharacteristic
307C4×D4C23×C2911yescharacteristic
308#117—21no—
309#117D4×C2911yescharacteristic
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C42—21no—
313C2×C42C23×C2911yescharacteristic
314#107—22no—
315#107—21no—
316#106—22no—
317#106—21no—
318C4⋊C8—22no—
319C4⋊C8—21no—
320C4⋊C8C23×C2912yes—
321C4⋊C8C23×C2912yes—
322C4⋊C8C23×C2911yescharacteristic
323C4⋊C8C23×C2911yescharacteristic
324#103—22no—
325#103—21no—
326#103—22no—
327#103—22no—
328#102—22no—
329#102—21no—
330#102—22no—
331#102—22no—
332#102—21no—
333#102—21no—
334C22⋊C8—21no—
335C22⋊C8—21no—
336C22⋊C8—22no—
337#97—22no—
338#97—21no—
339#97—21no—
340#97D4×C2911yescharacteristic
341#97D4×C2911yescharacteristic
342C4×C8C23×C2912yes—
343C29#1931811yescharacteristic, direct product factor, Sylow
344#41—22no—
345#41—41no—
346#41—44no—
347C2×Q8—21no—
348C2×Q8—22no—
349C2×Q8—41no—
350C2×Q8—82no—
351C2×Q8C2×D4×C2911yescharacteristic
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—41no—
357C2×D4C2×D4×C2911yescharacteristic
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4C2×D4×C2911yescharacteristic
364C22×C4C2×D4×C2911yescharacteristic
365C22×C4#41×C2911yescharacteristic
366SD16—42no—
367D8—42no—
368M16—42no—
369M16—42no—
370C2×C8—22no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—22no—
374C2×C8—44no—
375C2×C8C2×D4×C2912yes—
376C2×C8C2×D4×C2912yes—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4C2×D4×C2911yescharacteristic
386C4⋊C4C2×D4×C2911yescharacteristic
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—21no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C42—21no—
393C42—21no—
394C42—21no—
395C42C2×D4×C2911yescharacteristic
396C42C2×D4×C2911yescharacteristic
397C42#41×C2911yescharacteristic
398C42C24×C2911yescharacteristic
399C23—21no—
400C23—41no—
401C23C29×#12111yescharacteristic
402Q8—21no—
403Q8—21no—
404Q8—42no—
405Q8—82no—
406Q8—82no—
407D4—21no—
408D4—42no—
409D4—41no—
410D4—41no—
411D4—42no—
412D4—81no—
413D4—82no—
414D4C29×#13712yes—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—81no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4C29×#12111yescharacteristic
430C2×C4C29×#12111yescharacteristic
431C2×C4C29×#12111yescharacteristic
432C2×C4C22×D4×C2911yescharacteristic
433C2×C4C22×D4×C2911yescharacteristic
434C2×C4C2×#41×C2911yescharacteristic
435C8—22no—
436C8—22no—
437C8—41no—
438C8—42no—
439C8—42no—
440C8—41no—
441C22—21no—
442C22—21no—
443C22—22no—
444C22—21no—
445C22—41no—
446C22—41no—
447C22—81no—
448C22—81no—
449C22—81no—
450C22C2×C29×#12111yescharacteristic
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—41no—
456C4—41no—
457C4—41no—
458C4—81no—
459C4—82no—
460C4C2×C29×#13711yescharacteristic
461C4C29×#57512yes—
462C4C29×#57511yescharacteristic
463C2—41no—
464C2—42no—
465C2—161no—
466C2C29×#304011yescharacteristic
467C2C29×#305611yescharacteristic
468C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3115C2
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×#3141C2semidirect
3. C29×#3079C2semidirect
4. C29×#2970C2semidirect
5. C29×#1704C2semidirect
6. C29×#1698C2semidirect
7. C29×#1683C2semidirect
8. C29×#1677C2semidirect
9. C29×#1569C2semidirect
10. C29×#1558C2semidirect
11. C29×#1557C2semidirect
164. #19318C29direct (N × H)
207. #3141C2×C29semidirect
209. #3079C2×C29semidirect
210. #2970C2×C29semidirect
211. #1704C2×C29semidirect
212. #1698C2×C29semidirect
213. #1683C2×C29semidirect
214. #1677C2×C29semidirect
215. #1569C2×C29semidirect
216. #1558C2×C29semidirect
217. #1557C2×C29semidirect
343. C29#19318direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31412
C29×#31152
C29×#30792
C29×#29702
C29×#17042
C29×#16982
C29×#16832
C29×#16772
C29×#15692
C29×#15582
C29×#15572
#1931829